<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD with MathML3 v1.3 20210610//EN"  "JATS-archivearticle1-3-mathml3.dtd"><?covid-19-tdm ?><article xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.3"><front><journal-meta><journal-id journal-id-type="nlm-ta">elife</journal-id><journal-id journal-id-type="publisher-id">eLife</journal-id><journal-title-group><journal-title>eLife</journal-title></journal-title-group><issn publication-format="electronic" pub-type="epub">2050-084X</issn><publisher><publisher-name>eLife Sciences Publications, Ltd</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">107042</article-id><article-id pub-id-type="doi">10.7554/eLife.107042</article-id><article-version article-version-type="publication-state">version of record</article-version><article-categories><subj-group subj-group-type="display-channel"><subject>Research Article</subject></subj-group><subj-group subj-group-type="heading"><subject>Microbiology and Infectious Disease</subject></subj-group><subj-group subj-group-type="heading"><subject>Physics of Living Systems</subject></subj-group></article-categories><title-group><article-title>Repeated vaccination with homologous influenza hemagglutinin broadens human antibody responses to unmatched flu viruses</article-title></title-group><contrib-group><contrib contrib-type="author" equal-contrib="yes"><name><surname>Deng</surname><given-names>Yixiang</given-names></name><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="fn" rid="equal-contrib1">†</xref><xref ref-type="other" rid="fund8"/><xref ref-type="fn" rid="con1"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" equal-contrib="yes"><name><surname>Tang</surname><given-names>Melbourne</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0009-0008-4341-7371</contrib-id><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="fn" rid="equal-contrib1">†</xref><xref ref-type="fn" rid="con2"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author"><name><surname>Ross</surname><given-names>Ted M</given-names></name><xref ref-type="aff" rid="aff3">3</xref><xref ref-type="aff" rid="aff4">4</xref><xref ref-type="other" rid="fund9"/><xref ref-type="fn" rid="con3"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author"><name><surname>Schmidt</surname><given-names>Aaron G</given-names></name><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="aff" rid="aff5">5</xref><xref ref-type="other" rid="fund10"/><xref ref-type="other" rid="fund11"/><xref ref-type="other" rid="fund12"/><xref ref-type="fn" rid="con4"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes"><name><surname>Chakraborty</surname><given-names>Arup K</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0003-1268-9602</contrib-id><email>arupc@mit.edu</email><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="aff" rid="aff6">6</xref><xref ref-type="aff" rid="aff7">7</xref><xref ref-type="aff" rid="aff8">8</xref><xref ref-type="other" rid="fund7"/><xref ref-type="fn" rid="con5"/><xref ref-type="fn" rid="conf2"/></contrib><contrib contrib-type="author" corresp="yes"><name><surname>Lingwood</surname><given-names>Daniel</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0001-5631-9238</contrib-id><email>DLINGWOOD@mgh.harvard.edu</email><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="other" rid="fund1"/><xref ref-type="other" rid="fund2"/><xref ref-type="other" rid="fund3"/><xref ref-type="other" rid="fund4"/><xref ref-type="other" rid="fund5"/><xref ref-type="other" rid="fund6"/><xref ref-type="fn" rid="con6"/><xref ref-type="fn" rid="conf3"/></contrib><aff id="aff1"><label>1</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/053r20n13</institution-id><institution>Ragon Institute of Mass General, MIT, and Harvard</institution></institution-wrap><addr-line><named-content content-type="city">Cambridge</named-content></addr-line><country>United States</country></aff><aff id="aff2"><label>2</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/042nb2s44</institution-id><institution>Department of Physics, Massachusetts Institute of Technology</institution></institution-wrap><addr-line><named-content content-type="city">Cambridge</named-content></addr-line><country>United States</country></aff><aff id="aff3"><label>3</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/00te3t702</institution-id><institution>Center for Vaccines and Immunology, University of Georgia</institution></institution-wrap><addr-line><named-content content-type="city">Athens</named-content></addr-line><country>United States</country></aff><aff id="aff4"><label>4</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/00te3t702</institution-id><institution>Department of Infectious Diseases, University of Georgia</institution></institution-wrap><addr-line><named-content content-type="city">Athens</named-content></addr-line><country>United States</country></aff><aff id="aff5"><label>5</label><institution>Department of Microbiology, Harvard Medical School</institution><addr-line><named-content content-type="city">Boston</named-content></addr-line><country>United States</country></aff><aff id="aff6"><label>6</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/042nb2s44</institution-id><institution>Department of Chemical Engineering, Massachusetts Institute of Technology</institution></institution-wrap><addr-line><named-content content-type="city">Cambridge</named-content></addr-line><country>United States</country></aff><aff id="aff7"><label>7</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/042nb2s44</institution-id><institution>Department of Chemistry, Massachusetts Institute of Technology</institution></institution-wrap><addr-line><named-content content-type="city">Cambridge</named-content></addr-line><country>United States</country></aff><aff id="aff8"><label>8</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/042nb2s44</institution-id><institution>Institute for Medical Engineering and Science, Massachusetts Institute of Technology</institution></institution-wrap><addr-line><named-content content-type="city">Cambridge</named-content></addr-line><country>United States</country></aff></contrib-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Kurosaki</surname><given-names>Tomohiro</given-names></name><role>Reviewing Editor</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/035t8zc32</institution-id><institution>The University of Osaka</institution></institution-wrap><addr-line><named-content content-type="city">Osaka</named-content></addr-line><country>Japan</country></aff></contrib><contrib contrib-type="senior_editor"><name><surname>Walczak</surname><given-names>Aleksandra M</given-names></name><role>Senior Editor</role><aff><institution>CNRS</institution><country>France</country></aff></contrib></contrib-group><author-notes><fn fn-type="con" id="equal-contrib1"><label>†</label><p>These authors contributed equally to this work</p></fn></author-notes><pub-date publication-format="electronic" date-type="publication"><day>13</day><month>11</month><year>2025</year></pub-date><volume>14</volume><elocation-id>e107042</elocation-id><history><date date-type="received" iso-8601-date="2025-04-03"><day>03</day><month>04</month><year>2025</year></date><date date-type="accepted" iso-8601-date="2025-09-01"><day>01</day><month>09</month><year>2025</year></date></history><pub-history><event><event-desc>This manuscript was published as a preprint at bioRxiv.</event-desc><date date-type="preprint" iso-8601-date="2024-03-29"><day>29</day><month>03</month><year>2024</year></date><self-uri content-type="preprint" xlink:href="https://doi.org/10.1101/2024.03.27.24303943"/></event></pub-history><permissions><copyright-statement>© 2025, Deng, Tang et al</copyright-statement><copyright-year>2025</copyright-year><copyright-holder>Deng, Tang et al</copyright-holder><ali:free_to_read/><license xlink:href="http://creativecommons.org/licenses/by/4.0/"><ali:license_ref>http://creativecommons.org/licenses/by/4.0/</ali:license_ref><license-p>This article is distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License</ext-link>, which permits unrestricted use and redistribution provided that the original author and source are credited.</license-p></license></permissions><self-uri content-type="pdf" xlink:href="elife-107042-v1.pdf"/><self-uri content-type="figures-pdf" xlink:href="elife-107042-figures-v1.pdf"/><abstract><p>The ongoing diversification of influenza virus necessitates annual vaccine updating. The vaccine antigen, the viral spike protein hemagglutinin (HA), tends to elicit strain-specific neutralizing activity, predicting that sequential immunization with the same HA strain will boost antibodies with narrow coverage. However, repeated vaccination with homologous SARS-CoV-2 vaccine eventually elicits neutralizing activity against highly unmatched variants, questioning this immunological premise. We evaluated a longitudinal influenza vaccine cohort, where each year the subjects received the same, novel H1N1 2009 pandemic vaccine strain. Repeated vaccination gradually enhanced receptor-blocking antibodies (HAI) to highly unmatched H1N1 strains within individuals with no initial memory recall against these historical viruses. An in silico model of affinity maturation in germinal centers (GCs) integrated with a model of differentiation and expansion of memory cells outside GCs during a recall response provides insight into the potential mechanisms underlying these results and shows how repeated exposure to the same immunogen can broaden the antibody response against diversified targets.</p></abstract><abstract abstract-type="plain-language-summary"><title>eLife digest</title><p>Vaccines are the most effective way to prevent many infectious diseases and millions of deaths worldwide every year. They work by training the immune system to react to a protein – the antigen – that is specific to a pathogen. In response, the body produces specific antibodies, large proteins that mark the invaders for destruction. This builds a memory of this particular pathogen, enabling them to fight future infections better.</p><p>Some vaccines contain antigens, while others contain weakened or inactivated viruses or bacteria. Newer vaccines often contain a blueprint for producing antigens, such as DNA or RNA, instead of an antigen.</p><p>Each year, the flu vaccine is updated to match the main flu strains in circulation. This is because the vaccine’s key component – the spike protein hemagglutinin (HA) – works best when it triggers antibodies that recognize and neutralize viruses with the same HA sequence.</p><p>A major obstacle to creating a universal flu vaccine is that influenza viruses constantly mutate, weakening the match between the vaccine and the virus. The problem is made worse because vaccines tend to produce antibodies that target the very parts of HA that change most frequently.</p><p>Repeated vaccination with the same flu shot (called vaccine boosting) was thought to strengthen the original immune response by increasing the number of antibodies targeting the same variable parts of HA. However, recent findings from studies on SARS-CoV-2 (the virus that causes COVID-19) suggest this is not always the case. Instead, repeated vaccination can both boost existing antibodies and generate new ones that target previously unrecognized regions of the antigen. This broader antibody response can help protect against variant viruses that share these newly recognized regions.</p><p>Deng, Tang et al. tested whether this antibody broadening also occurs with repeated influenza vaccination. The researchers evaluated data from a group of people who received the same flu vaccine for four consecutive years between 2013 to 2016, which included the new 2009 pandemic strain that many had never encountered before. The analyses showed that over time, their antibody responses became more diverse and capable of recognizing flu viruses spanning almost a century of evolution.</p><p>To understand how this happens, Deng, Tang et al. built a computational model to trace how a type of immune cell known as the B cells mature and diversify their antibody production after vaccination. The findings suggest that the broad antibody response during vaccination boosting is an inherent feature of the human immune system.</p><p>The next step and challenge will be to harness the natural ability to broaden antibody responses for designing vaccines that can protect against strains that may emerge in the future. This could involve fine-tuning HA or other vaccine proteins to better guide the immune system toward producing a broadly protective set of antibodies. Importantly, this principle of immune broadening could apply to any vaccine antigen – not just influenza.</p></abstract><kwd-group kwd-group-type="author-keywords"><kwd>B cell</kwd><kwd>vaccine</kwd><kwd>breadth</kwd><kwd>influenza virus</kwd><kwd>germinal center</kwd></kwd-group><kwd-group kwd-group-type="research-organism"><title>Research organism</title><kwd>Viruses</kwd></kwd-group><funding-group><award-group id="fund1"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>AI155447</award-id><principal-award-recipient><name><surname>Lingwood</surname><given-names>Daniel</given-names></name></principal-award-recipient></award-group><award-group id="fund2"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>AI137057</award-id><principal-award-recipient><name><surname>Lingwood</surname><given-names>Daniel</given-names></name></principal-award-recipient></award-group><award-group id="fund3"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>AI153098</award-id><principal-award-recipient><name><surname>Lingwood</surname><given-names>Daniel</given-names></name></principal-award-recipient></award-group><award-group id="fund4"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>contract 75N93019C00052</award-id><principal-award-recipient><name><surname>Lingwood</surname><given-names>Daniel</given-names></name></principal-award-recipient></award-group><award-group id="fund5"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100005294</institution-id><institution>Massachusetts General Hospital</institution></institution-wrap></funding-source><award-id>MGH Scholar Award</award-id><principal-award-recipient><name><surname>Lingwood</surname><given-names>Daniel</given-names></name></principal-award-recipient></award-group><award-group id="fund6"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>AI060354</award-id><principal-award-recipient><name><surname>Lingwood</surname><given-names>Daniel</given-names></name></principal-award-recipient></award-group><award-group id="fund7"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>U19AI057229</award-id><principal-award-recipient><name><surname>Chakraborty</surname><given-names>Arup K</given-names></name></principal-award-recipient></award-group><award-group id="fund8"><funding-source><institution-wrap><institution-id institution-id-type="ror">https://ror.org/053r20n13</institution-id><institution>The Ragon Institute of Mass General, MIT and Harvard</institution></institution-wrap></funding-source><award-id>Schwartz AI Initiative</award-id><principal-award-recipient><name><surname>Deng</surname><given-names>Yixiang</given-names></name></principal-award-recipient></award-group><award-group id="fund9"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100008065</institution-id><institution>Georgia Research Alliance</institution></institution-wrap></funding-source><award-id>GRA Eminent Scholar</award-id><principal-award-recipient><name><surname>Ross</surname><given-names>Ted M</given-names></name></principal-award-recipient></award-group><award-group id="fund10"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>AI146779</award-id><principal-award-recipient><name><surname>Schmidt</surname><given-names>Aaron G</given-names></name></principal-award-recipient></award-group><award-group id="fund11"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>AI089618</award-id><principal-award-recipient><name><surname>Schmidt</surname><given-names>Aaron G</given-names></name></principal-award-recipient></award-group><award-group id="fund12"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100000002</institution-id><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>contract 75N93019C00050</award-id><principal-award-recipient><name><surname>Schmidt</surname><given-names>Aaron G</given-names></name></principal-award-recipient></award-group><funding-statement>The funders had no role in study design, data collection, and interpretation, or the decision to submit the work for publication.</funding-statement></funding-group><custom-meta-group><custom-meta specific-use="meta-only"><meta-name>Author impact statement</meta-name><meta-value>Classical antibody boosting effects during vaccination are accompanied by natural broadening mechanisms that help enable human antibodies to engage conserved sites of vulnerability on influenza virus.</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="s1" sec-type="intro"><title>Introduction</title><p>Seasonal influenza vaccines are designed to elicit protective antibody responses against the viral strains predicted to dominate during an upcoming winter season (<xref ref-type="bibr" rid="bib24">Comber et al., 2023</xref>; <xref ref-type="bibr" rid="bib37">Fiore et al., 2009</xref>; <xref ref-type="bibr" rid="bib52">Jordan et al., 2023</xref>; <xref ref-type="bibr" rid="bib87">Sandor et al., 2021</xref>). The vaccine is typically trivalent or quadrivalent and aims to cover human-infecting influenza A viruses (IAV) and influenza B viruses (IBV) (<xref ref-type="bibr" rid="bib30">Demirden et al., 2022</xref>; <xref ref-type="bibr" rid="bib81">Reed et al., 2012</xref>; <xref ref-type="bibr" rid="bib100">Soema et al., 2015</xref>). This has included an H1N1 vaccine strain for group 1 IAV, an H3N2 vaccine strain for group 2 IAV, and Yamagata and/or Victoria lineages for IBV. Elicitation of antibodies engaging the receptor-binding site (RBS) on the influenza spike protein hemagglutinin (HA) to block viral attachment is considered a major source of protection and is routinely measured by the hemagglutination (HA) inhibition (HAI) assay (<xref ref-type="bibr" rid="bib25">Cox, 2013</xref>; <xref ref-type="bibr" rid="bib56">Krammer et al., 2020</xref>; <xref ref-type="bibr" rid="bib76">Pedersen, 2014</xref>; <xref ref-type="bibr" rid="bib101">Spackman and Sitaras, 2020</xref>). Antibody Fc effector functions also provide orthogonal immuno-protective activities (<xref ref-type="bibr" rid="bib15">Boudreau and Alter, 2019</xref>; <xref ref-type="bibr" rid="bib16">Boudreau et al., 2023</xref>; <xref ref-type="bibr" rid="bib34">DiLillo et al., 2016</xref>).</p><p>A concern of seasonal influenza vaccines is the lack of universality, where vaccine coverage can be lowered by antigenic drift of the virus, or even more worrying, antigen shift leading to the emergence of pandemic flu strains (<xref ref-type="bibr" rid="bib12">Bedi et al., 2023</xref>; <xref ref-type="bibr" rid="bib55">Krammer et al., 2018</xref>). These limitations are also underscored by the fact that individual HA molecules tend to elicit strain-specific antibody binding or neutralizing activity (<xref ref-type="bibr" rid="bib4">Altman et al., 2018</xref>; <xref ref-type="bibr" rid="bib8">Angeletti and Yewdell, 2018</xref>; <xref ref-type="bibr" rid="bib12">Bedi et al., 2023</xref>; <xref ref-type="bibr" rid="bib89">Sangesland and Lingwood, 2021</xref>). Here, sequential immunization with homologous influenza HA antigens typically serves to boost strain-limited humoral output (<xref ref-type="bibr" rid="bib49">Henry et al., 2018</xref>; <xref ref-type="bibr" rid="bib55">Krammer et al., 2018</xref>; <xref ref-type="bibr" rid="bib54">Krammer and Palese, 2013</xref>; <xref ref-type="bibr" rid="bib89">Sangesland and Lingwood, 2021</xref>). Addressing these deficits has been a basis for rationally designed immune-focusing concepts tasked with re-orienting humoral immunity upon immune subdominant sites of conservation on influenza HA (<xref ref-type="bibr" rid="bib4">Altman et al., 2018</xref>; <xref ref-type="bibr" rid="bib8">Angeletti and Yewdell, 2018</xref>; <xref ref-type="bibr" rid="bib19">Caradonna and Schmidt, 2021</xref>; <xref ref-type="bibr" rid="bib55">Krammer et al., 2018</xref>; <xref ref-type="bibr" rid="bib89">Sangesland and Lingwood, 2021</xref>; <xref ref-type="bibr" rid="bib115">Wei et al., 2020</xref>). These efforts include structure-based reconfiguration and presentation of conserved HA moieties, and sequential immunization with strain variant antigens to further promote expansion of B cell memory against the invariant sites (<xref ref-type="bibr" rid="bib5">Amitai et al., 2020</xref>; <xref ref-type="bibr" rid="bib9">Angeletti et al., 2019</xref>; <xref ref-type="bibr" rid="bib18">Boyoglu-Barnum et al., 2021</xref>; <xref ref-type="bibr" rid="bib20">Caradonna et al., 2022</xref>; <xref ref-type="bibr" rid="bib71">Nachbagauer and Palese, 2018</xref>; <xref ref-type="bibr" rid="bib79">Ray et al., 2024</xref>; <xref ref-type="bibr" rid="bib88">Sangesland et al., 2019</xref>; <xref ref-type="bibr" rid="bib119">Yassine et al., 2015</xref>). A number of these ‘universal’ vaccine candidates are at various stages of clinical evaluation (<xref ref-type="bibr" rid="bib6">Andrews et al., 2023</xref>; <xref ref-type="bibr" rid="bib72">Nachbagauer et al., 2021</xref>; <xref ref-type="bibr" rid="bib116">Widge et al., 2023</xref>).</p><p>Notably, however, recent human SARS-CoV-2 vaccine data warrants reconsideration of the basic premise that sequential immunization with homologous antigens elicits strong but strain-limited humoral immunity (<xref ref-type="bibr" rid="bib42">Garcia-Beltran et al., 2022</xref>; <xref ref-type="bibr" rid="bib70">Muecksch et al., 2022</xref>; <xref ref-type="bibr" rid="bib94">Schmidt et al., 2022</xref>). Three sequential vaccinations with the homologous Wuhan-strain glycoprotein spike antigen elicit neutralizing antibody responses against highly unmatched Omicron variants. Broad neutralizing activity via engagement of the SARS-CoV-2 RBS was acquired after the third vaccination, consistent with a diversification of the repertoire of the antibodies elicited (<xref ref-type="bibr" rid="bib42">Garcia-Beltran et al., 2022</xref>; <xref ref-type="bibr" rid="bib70">Muecksch et al., 2022</xref>; <xref ref-type="bibr" rid="bib94">Schmidt et al., 2022</xref>). Both antigen presentation dynamics and epitope masking activities within B cell germinal centers (GCs) appear to play key roles in the emergence of this broadened antibody response (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>).</p><p>In the present study, we evaluated whether diversification of antibody binding/neutralization breadth via sequential immunization with homologous antigen is a general principle that characterizes human humoral immune responses. Accordingly, we evaluated an influenza vaccine cohort of individuals sampled longitudinally over 4 years (2013–2016) (<xref ref-type="bibr" rid="bib74">Nuñez et al., 2017</xref>). HAI was measured before and after vaccination in each year, using a virus panel composed of diverse influenza A and B viruses spanning almost 100 years of evolution (<xref ref-type="bibr" rid="bib74">Nuñez et al., 2017</xref>). Importantly, this vaccine cohort closely followed the 2009–2010 H1N1 pandemic and included 4 years of repeat exposure to ‘non-imprinted’/pandemic A/California/7/2009 (pHA) as the sole H1N1 vaccine strain. Annual vaccination boosted HAI to vaccine-matched virus but also to highly divergent H1N1 viruses, despite the strong lack of relatedness. Importantly, this broadening did not occur via initial memory recall but rather intensified gradually over the 4-year vaccination period within individuals that were devoid of initial back-boosting against historical H1N1 viruses. To define a mechanistic framework for this effect, we adapted and extended a previous in silico model that accounts for B cell affinity maturation within GCs and associated memory B cell differentiation and expansion outside GCs (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>). Using this approach, we describe mechanisms that may underlie the broadening of antibody coverage. We find that the broadening of the response is determined by the interplay between enhanced antigen presentation and epitope masking in GCs after booster shots, germline B cell affinities for different HA epitopes, and the level of conservation of these epitopes in the vaccinating strain with those on different historical variants. In these contexts, the capacity to eventually elicit broadly reactive antibody responses using a single influenza vaccine strain is discussed.</p></sec><sec id="s2" sec-type="results"><title>Results</title><sec id="s2-1"><title>The RBS patch of the 2009 H1N1 pandemic virus is strongly divergent from prior influenza strains</title><p>We began by applying a structure-based approach to define amino acid variation within the RBS (the epitope patch responsible for conferring HAI) amongst diverse IAV (H3N2 and H1N1) and IBV, spanning almost 100 years of evolution (<xref ref-type="fig" rid="fig1">Figure 1</xref>, <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref>; <xref ref-type="table" rid="app1table1">Appendix 1—table 1</xref>). We assessed amino acid relatedness of the residues comprising the entire HA ectodomain (<xref ref-type="fig" rid="fig1">Figure 1A, B</xref>, <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref>), and then the RBS patch, as defined by the structures of four human broadly neutralizing RBS-directed antibodies (bnAbs), each in co-complex with HA (<xref ref-type="bibr" rid="bib93">Schmidt et al., 2015</xref>; <xref ref-type="fig" rid="fig1">Figure 1C, D</xref>; <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref>). The paratopes of these bnAbs structurally mimic sialic acid, the primary receptor for influenza virus (<xref ref-type="bibr" rid="bib93">Schmidt et al., 2015</xref>). In each case, the epitope footprint consists of the core viral amino acid residues responsible for binding sialyl oligosaccharide, along with a surrounding ‘ring’ of contact positions that are differentially engaged by the four bnAbs (<xref ref-type="fig" rid="fig1">Figure 1C</xref>, <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref>). We defined the RBS patch as the sialic acid binding residues + the cumulative ‘ring’ of contact positions defined by these antibodies (<xref ref-type="fig" rid="fig1">Figure 1C</xref>, <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref>). Amino acid relatedness values within the HA ectodomain and the RBS patch were then represented as heat maps for the influenza A and B viruses (<xref ref-type="fig" rid="fig1">Figure 1B, D</xref>, <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref>). Within H1N1 viruses, the 2009 pandemic strain (pHA) stands out, along with A/New Jersey/1976, as strongly divergent, particularly within the RBS patch (<xref ref-type="fig" rid="fig1">Figure 1B, D</xref>). This is consistent with previous reports on the structure of the RBS (<xref ref-type="bibr" rid="bib21">Cheung et al., 2020</xref>; <xref ref-type="bibr" rid="bib50">Hong et al., 2013</xref>; <xref ref-type="bibr" rid="bib117">Xu et al., 2010</xref>) and the fact that both 2009 pandemic virus and the 1976 outbreak in Fort Dix, New Jersey, originated from swine lineages of H1N1 (<xref ref-type="bibr" rid="bib43">Garten et al., 2009</xref>; <xref ref-type="bibr" rid="bib44">Gaydos et al., 2006</xref>; <xref ref-type="bibr" rid="bib65">Mena et al., 2016</xref>; <xref ref-type="bibr" rid="bib97">Sencer, 2011</xref>; <xref ref-type="bibr" rid="bib99">Smith et al., 2009</xref>; <xref ref-type="bibr" rid="bib124">Zimmer and Burke, 2009</xref>).</p><fig-group><fig id="fig1" position="float"><label>Figure 1.</label><caption><title>Divergent amino acid relatedness in the ectodomain and receptor-binding site (RBS) patch of the pandemic influenza HA.</title><p>(<bold>A</bold>) The hemagglutinin (HA) ectodomain, where relatedness is calculated using the formula ‘N_matched/N_total’; N_matched is the number of amino acids that match between the compared sequences and N_total is the total number of amino acids in the aligned sequence. (<bold>B</bold>) Heat map of HA ectodomain relatedness values for influenza A (H3N2, H1N1) and B viruses spanning almost 100 years (HA ectodomain sequences analyzed). (<bold>C</bold>) The RBS patch was structurally identified by four human bnAbs whose paratopes engage the RBS by mimicking cell surface sialic acid (CH67, CH67, H2526, 641 I-9) (<xref ref-type="bibr" rid="bib93">Schmidt et al., 2015</xref>). We defined the RBS patch as the viral sialic acid binding residues (black) + the surrounding antibody epitope ‘ring’, collectively identified by the peripheral contacts made by the four bnAbs. Amino relatedness within the RBS patch is then calculated using the same formula except that the residues are now restricted to patch. (<bold>D</bold>) Heat map of HA RBS patch relatedness values for influenza A (H3N2, H1N1) and B viruses spanning almost 100 years (RBS patch sequences from the same 38 HA sequences as in <bold>B</bold>). See also <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref> for extended resolution on the heat map scale.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig1-v1.tif"/></fig><fig id="fig1s1" position="float" specific-use="child-fig"><label>Figure 1—figure supplement 1.</label><caption><title>Relatedness heat maps with extended resolution.</title><p>The scale of the amino acid relatedness heat maps was expanded to visually resolve differences amongst non-pandemic influenza virus strains (compare to <xref ref-type="fig" rid="fig1">Figure 1</xref>). Amino acid relatedness values in the full-length hemagglutinin (HA) ectodomain (<bold>A</bold>) and receptor-binding site (RBS) patch (<bold>B</bold>) for the 38 influenza viral strains covering influenza A (H3N2, H1N1) and B viruses spanning &gt;100 years are directly taken from <xref ref-type="fig" rid="fig1">Figure 1</xref>.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig1-figsupp1-v1.tif"/></fig></fig-group></sec><sec id="s2-2"><title>Sequential vaccination with homologous pHA broadly boosts HAI</title><p>To define how sequential immunization with homologous HA impacts antibody scanning breadth in humans, we evaluated the HAI coverage across the diverse viral strains from our relatedness analysis (<xref ref-type="fig" rid="fig1">Figure 1B, D</xref>), as elicited by repeated (4x) inoculation with influenza vaccine containing the same H1N1 component (pHA) over a 4-year period (2013–2016) (<xref ref-type="bibr" rid="bib74">Nuñez et al., 2017</xref>; <xref ref-type="fig" rid="fig2">Figure 2A</xref>). Individuals were followed longitudinally (<italic>n</italic> = 136 individuals) (<xref ref-type="supplementary-material" rid="fig2sdata1">Figure 2—source data 1</xref>). In each year, a sample was obtained before and then 20 days after vaccination, and we first evaluated the fold change in HAI elicited against the virus panel (IBV, IAV H3N2, IAV H1N1) by each vaccine component within each year (<xref ref-type="fig" rid="fig2">Figure 2B, C</xref>). Notably, this analysis shows that pHA also elicits HAI for the highly unrelated/historical H1N1 strains (i.e. full-length ectodomain relatedness &lt;0.85; RBS patch relatedness &lt;0.7).</p><fig id="fig2" position="float"><label>Figure 2.</label><caption><title>Sequential immunization with homologous pHA also elicits hemagglutination inhibition (HAI) against highly unrelated H1N1 strains.</title><p>(<bold>A</bold>) Four-year influenza vaccine trial (<xref ref-type="bibr" rid="bib74">Nuñez et al., 2017</xref>). We analyzed HAI elicited from subjects that were longitudinally followed and immunized each year with the vaccine strains indicated. Notably, these individuals received the same H1N1 component (A/California/07/2009 = pHA) in each of the 4 years. (<bold>B</bold>) Fold change in HAI titer (pre vs 20 days post-vaccination) elicited each year and graphed as a function of hemagglutinin (HA) ectodomain relatedness between the vaccine strain and the viruses within the HAI panels. Each dot is a single subject at the relatedness value: white dots are fold changes for strains from the virus panel; the colored dots indicate the vaccine-matched viral strain (relatedness = 1.00). (<bold>C</bold>) Same data as in (<bold>B</bold>) only now graphed as a function of receptor-binding site (RBS) patch relatedness between the vaccine strain and the viruses within the panels.</p><p><supplementary-material id="fig2sdata1"><label>Figure 2—source data 1.</label><caption><title>Hemagglutination inhibition (HAI) values for the influenza virus strains, measured across longitudinal vaccine study (2013–2016) for <italic>n</italic> = 136 de-identified subjects &gt;50 years of age and &lt;38 years of age.</title><p>This is the same source data used for <xref ref-type="fig" rid="fig3">Figure 3</xref>, <xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1</xref>.</p></caption><media mimetype="application" mime-subtype="xlsx" xlink:href="elife-107042-fig2-data1-v1.xlsx"/></supplementary-material></p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig2-v1.tif"/></fig></sec><sec id="s2-3"><title>Sequential vaccination with homologous pHA broadens HAI with gradual kinetics in subjects that do not initially back-boost to historical strains</title><p>We next defined the kinetics of relatedness-independent broadening of H1N1 HAI over the 4-year period by graphing the fraction of responders versus non-responders (detectable vs non-detectable boosting of HAI to each H1N1 strain) at each year (<xref ref-type="fig" rid="fig3">Figure 3A–C</xref>). Although pandemic HA will not be historically imprinted, memory recall of pre-existing immunity or ‘back-boosting’ to historical strains would occur in response to the first antigen exposure (<xref ref-type="bibr" rid="bib3">Akkaya et al., 2020</xref>; <xref ref-type="bibr" rid="bib49">Henry et al., 2018</xref>; <xref ref-type="bibr" rid="bib74">Nuñez et al., 2017</xref>; <xref ref-type="bibr" rid="bib75">Palm and Henry, 2019</xref>; <xref ref-type="bibr" rid="bib83">Reusch and Angeletti, 2023</xref>; <xref ref-type="bibr" rid="bib107">Turner et al., 2020</xref>) and cannot be ruled out in the first vaccine year (2013). For this reason, we again focused on the initial non-responders, who boost against pHA (and the other seasonal vaccine components, see <xref ref-type="fig" rid="fig2">Figure 2B, C</xref>) but do not simultaneously broaden/back-boost against historical H1N1 strains post vax in Years 1 or 2, and by definition lacked B cell memory recalled by pHA (<xref ref-type="fig" rid="fig3">Figure 3A–C</xref>). The subsequent reduction of these non-responders upon sequential vaccination with pHA in later years identifies a separate vaccine broadening effect with slower kinetics (<xref ref-type="fig" rid="fig3">Figure 3A–C</xref>). In this effect, the proportion of non-responders to divergent H1N1 gradually decreases during the vaccine regimen, culminating in the near absence of non-responders in Year 4. This effect is seen when the subjects are not age stratified (<xref ref-type="fig" rid="fig3">Figure 3A</xref>) and when the subjects are divided into older and younger ages (&gt;50 vs&lt;38 years) (<xref ref-type="fig" rid="fig3">Figure 3B, C</xref>). The corresponding increases in the proportion of responders are also observed in these groups over the vaccine regimen (<xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1</xref>). Collectively, these data indicate that within individuals that lack initial back-boosting, sequential exposure to pHA can eventually broaden the RBS-directed antibodies against highly unrelated H1N1.</p><fig-group><fig id="fig3" position="float"><label>Figure 3.</label><caption><title>Sequential immunization with homologous pHA gradually broadens the response within individuals with no initial immune memory/recall to historical strains.</title><p>Responders (green) versus non-responders (red) within each year is graphed for each H1N1 strain in the hemagglutination inhibition (HAI) panel. Responders are defined by having non-decreasing fold changes in HAI titers (post-vaccination HAI titer/pre-vaccination HAI titer; i.e. fold change &gt;1). Non-responders are defined by having decreasing fold changes of HAI titers (post-vaccination HAI titer/pre-vaccination HAI titer; fold change &lt;1). Because non-responders (red) do not back-boost against historical strains in the panel, they, by definition, lack imprinted immunity to these viruses that is recalled by pHA. In the regression analyses, each white dot denotes the proportion of non-responders for each viral strain. (<bold>A</bold>) Yearly response for all longitudinally analyzed individuals; at right is a linear regression of the proportion of non-responders over the 4-year vaccine data (p = 6e−04). (<bold>B</bold>) Data for subjects &gt;50 years in age (p = 6e−04, linear regression). (<bold>C</bold>) Data for subjects &lt;38 years in age (p = 0.0164, linear regression). See also <xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1</xref> for linear regression of the proportion of responders in each age group.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig3-v1.tif"/></fig><fig id="fig3s1" position="float" specific-use="child-fig"><label>Figure 3—figure supplement 1.</label><caption><title>H1N1 responders regressed over the vaccine.</title><p>Responders (green) versus non-responders (red) within each year are graphed for each H1N1 strain in the hemagglutination inhibition (HAI) panel, as in <xref ref-type="fig" rid="fig3">Figure 3</xref>. (<bold>A</bold>) Yearly response for all longitudinally analyzed individuals; at right is a linear regression of the proportion of non-responders against over the 4-year vaccine data (p = 6e−04). (<bold>B</bold>) Data for subjects &gt;50 years in age (p = 6e−04, linear regression). (<bold>C</bold>) Data for subjects &lt;38 years in age (p = 0.0164, linear regression).</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig3-figsupp1-v1.tif"/></fig></fig-group></sec><sec id="s2-4"><title>A computational model to study the mechanistic origin of increased coverage following sequential immunization with homologous HA</title><p>To obtain mechanistic insights underlying the observed broadening of the antibody response in the absence of prior immune imprinting and back-boosting, we adapted and extended a computational model of the humoral immune response upon repeated vaccination. The model is principally an extension of our past work modeling humoral immune responses upon repeated vaccination with SARS-CoV-2 vaccine immunogens, but also builds on our other past studies (<xref ref-type="bibr" rid="bib5">Amitai et al., 2020</xref>; <xref ref-type="bibr" rid="bib114">Wang et al., 2015</xref>; <xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>). The purpose of this model is not to quantitatively fit clinical data, but to identify mechanistic principles that support the observations. Below, we outline the structure of the in silico model; mathematical and computational details are provided in the Methods.</p><p>We first coarse-grained the HA RBS into three antibody epitopes (epitopes 1–3) on pHA (strain 1) and on two historical H1N1 strains (strains 2 and 3) (<xref ref-type="fig" rid="fig4">Figure 4A</xref>). In this model, a fraction <italic>p</italic><sub><italic>i</italic></sub> of the germline B cells target epitope <italic>i</italic>, and the immunodominance hierarchy is taken to be epitope 1 &gt; epitope 2 &gt; epitope 3. The immunodominant epitope on pHA (epitope 1) is taken to be very different (heavily mutated) in strain 1 as compared to strains 2 and 3. This is because the pandemic strain is expected to have changed substantially, so it would escape responses that target the immunodominant epitope in historical strains. So, responses to a new immunodominant epitope need to evolve upon immunization with pHA. We further assume that subdominant epitope 2 is relatively conserved between strains 1 and 2, but not conserved between strains 1 and 3; subdominant epitope 3 is relatively conserved between strains 1 and 3, but not strains 1 and 2 (<xref ref-type="fig" rid="fig4">Figure 4A</xref>). In this way, we model three strains that are different from each other but share some similarities, as would be expected for all H1N1 viruses. Modeling only three H1N1 strains instead of dozens and just a few epitopes allows us to gain insights into the mechanism underlying the observed broadening of the response using a simpler computationally tractable system while still considering the complexities of generating immune responses to multiple strains.</p><fig id="fig4" position="float"><label>Figure 4.</label><caption><title>The influenza hemagglutinin (HA) head is coarse-grained into three epitopes that are perceived with different germline-endowed B cell affinities.</title><p>(<bold>A</bold>) Diagram of epitope differences. In the right panel, the level of conservation of the three epitopes is depicted using different shapes (not very conserved) or similar shapes (relatively conserved). Epitope 1 (dominant epitope on pHA) is not conserved between the three variants. Epitope 2 (subdominant epitope) is relatively conserved between strain 1 (vaccine strain) and strain 2, but not between strains 1 and 3. Epitope 3 (another subdominant epitope) is conserved between strains 1 and 3, but not between strains 2 and 3. (<bold>B</bold>) Germline-endowed affinity distribution of naive B cells. Germline B cells targeting more dominant epitopes are more numerous and exhibit a longer high-affinity tail. Epitope 1 is more dominant than epitope 2, and epitope 2 is more dominant than epitope 3. Here, the fractions of naive B cells <inline-formula><alternatives><mml:math id="inf1"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>p</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft1">\begin{document}$p_i$\end{document}</tex-math></alternatives></inline-formula> targeting epitope i are <inline-formula><alternatives><mml:math id="inf2"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi mathvariant="italic">p</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">p</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.15</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">p</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.05</mml:mn></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft2">\begin{document}$\mathit{p}_{1}=0.8,\,\mathit{p}_{2}=0.15,\,\mathit{p}_{3}=0.05$\end{document}</tex-math></alternatives></inline-formula>.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig4-v1.tif"/></fig><p>The immunodominance hierarchy of the three epitopes is reflected in the distribution of germline B cell affinities for antigen, an attribute that is important for B cell recruitment into GCs (<xref ref-type="bibr" rid="bib2">Abbott and Crotty, 2020</xref>; <xref ref-type="bibr" rid="bib1">Abbott et al., 2018</xref>; <xref ref-type="bibr" rid="bib5">Amitai et al., 2020</xref>; <xref ref-type="bibr" rid="bib35">Dosenovic et al., 2018</xref>; <xref ref-type="bibr" rid="bib89">Sangesland and Lingwood, 2021</xref>). Since high germline affinities are rare (<xref ref-type="bibr" rid="bib36">Feldman et al., 2021</xref>; <xref ref-type="bibr" rid="bib58">Kuraoka et al., 2016</xref>; <xref ref-type="bibr" rid="bib61">Lingwood et al., 2012</xref>; <xref ref-type="bibr" rid="bib79">Ray et al., 2024</xref>; <xref ref-type="bibr" rid="bib85">Ronsard et al., 2023</xref>; <xref ref-type="bibr" rid="bib88">Sangesland et al., 2019</xref>; <xref ref-type="bibr" rid="bib90">Sangesland et al., 2022</xref>), we consider the distribution of affinities to be drawn from the tail of a distribution, which decays exponentially. The lowest affinity in the distribution we choose is 10<sup>–6</sup> M, which is an estimate of the threshold for entry into GCs (<xref ref-type="bibr" rid="bib11">Batista and Neuberger, 1998</xref>), which lies within the observed germline affinity range of human BCRs (<xref ref-type="bibr" rid="bib36">Feldman et al., 2021</xref>; <xref ref-type="bibr" rid="bib58">Kuraoka et al., 2016</xref>; <xref ref-type="bibr" rid="bib61">Lingwood et al., 2012</xref>; <xref ref-type="bibr" rid="bib79">Ray et al., 2024</xref>; <xref ref-type="bibr" rid="bib85">Ronsard et al., 2023</xref>; <xref ref-type="bibr" rid="bib88">Sangesland et al., 2019</xref>; <xref ref-type="bibr" rid="bib90">Sangesland et al., 2022</xref>). More immunodominant epitopes constitute a larger fraction <italic>p</italic><sub><italic>i</italic></sub> of germline B cells and exhibit a longer high-affinity tail (<xref ref-type="fig" rid="fig4">Figure 4B</xref>). We varied parameters that reflect the conservation of these epitopes and their relative immunodominance.</p><p>To then study humoral immune reactions to the different epitopes in silico, we modeled key steps that determine the antibody response pathway to protein antigens including: (1) (<xref ref-type="bibr" rid="bib28">Danecek et al., 2011</xref>) antigen deposition on the surface of follicular dendritic cells (FDCs) (<xref ref-type="bibr" rid="bib14">Bhagchandani et al., 2024</xref>; <xref ref-type="bibr" rid="bib32">de Silva and Klein, 2015</xref>; <xref ref-type="bibr" rid="bib113">Victora and Nussenzweig, 2022</xref>); (2) activation and entry of naive B cells into GCs, T helper-cell-driven affinity selection of B cells within GCs (<xref ref-type="bibr" rid="bib32">de Silva and Klein, 2015</xref>; <xref ref-type="bibr" rid="bib113">Victora and Nussenzweig, 2022</xref>; <xref ref-type="bibr" rid="bib120">Young and Brink, 2021</xref>), and differentiation into memory B cells and plasma cells (<xref ref-type="bibr" rid="bib3">Akkaya et al., 2020</xref>; <xref ref-type="bibr" rid="bib26">Crotty, 2015</xref>; <xref ref-type="bibr" rid="bib75">Palm and Henry, 2019</xref>); (3) relatively rapid expansion and differentiation of memory B cells into short-lived plasma cells during the recall responses which occur outside GCs (<xref ref-type="bibr" rid="bib68">Moran et al., 2018</xref>; <xref ref-type="bibr" rid="bib102">Syeda et al., 2024</xref>; <xref ref-type="bibr" rid="bib108">van Beek et al., 2022</xref>); as elaborated in Methods, for brevity, we refer to these compartments outside GCs where memory cells are expanded in an antigen and T helper cell-dependent way as ‘extra germinal centers’ (EGCs).</p><p>A set of differential equations models the dynamics of antigen deposition and presentation on FDCs (see Methods for details). In the first few days after vaccination, soluble antigen rapidly decays in mice and non-human primates (NHP) (<xref ref-type="bibr" rid="bib10">Aung et al., 2023</xref>; <xref ref-type="bibr" rid="bib14">Bhagchandani et al., 2024</xref>; <xref ref-type="bibr" rid="bib63">Martin et al., 2021</xref>). Circulating antibodies can bind to soluble antigen to form immune complexes (ICs) that become coated with complement, resulting in complement-receptor-dependent deposition of antigen on FDCs (<xref ref-type="bibr" rid="bib77">Phan et al., 2007</xref>). ICs deposited on FDCs are longer lived than soluble antigen (<xref ref-type="bibr" rid="bib10">Aung et al., 2023</xref>; <xref ref-type="bibr" rid="bib63">Martin et al., 2021</xref>). For the first immunization, we assume that only weakly binding circulating antibodies are available for binding to the antigen and forming ICs. Therefore, relatively small amounts of ICs are deposited on FDCs before soluble antigen decays. For subsequent immunizations, stronger binding antigen-specific antibodies elicited by the previous immunization are available to bind antigen and form ICs before soluble antigen decays. This results in enhanced antigen deposition on FDCs. In vivo evidence for enhanced antigen deposition on FDCs mediated by antibodies generated at earlier time points has recently been provided by experiments in mice in the context of extended dosing of vaccine antigens (<xref ref-type="bibr" rid="bib14">Bhagchandani et al., 2024</xref>). In our simulations, the differential equations that describe these antigen and antibody dynamics are coupled to an agent-based simulation of the stochastic processes that occur inside GCs and when memory cells are expanded outside GCs during the recall response.</p><p>In the stochastic agent-based simulations of GCs and EGCs, each B cell is an agent and the probabilities of its activation by its B cell receptor’s interactions with an epitope and antigen internalization, T cell-mediated selection, proliferation, mutation, and differentiation are calculated at each time step (0.01 days). Our model accounts for the following immunological principles and factors in the activation and selection of B cells: GC B cells internalize antigen based on their binding affinities to epitopes in the vaccine strain (<xref ref-type="bibr" rid="bib11">Batista and Neuberger, 1998</xref>; <xref ref-type="bibr" rid="bib38">Fleire et al., 2006</xref>); the amount of antigen internalized grows with the antigen binding free energy (or affinity) and saturates above a threshold affinity (<xref ref-type="bibr" rid="bib39">Foote and Eisen, 1995</xref>; <xref ref-type="bibr" rid="bib40">Foote and Eisen, 2000</xref>); and individual B cells that internalize antigen compete for subsequent T cell help to promote B cell survival (<xref ref-type="bibr" rid="bib95">Schwickert et al., 2011</xref>; <xref ref-type="bibr" rid="bib111">Victora et al., 2010</xref>). Among the B cells that are positively selected in the GC, some stochastically exit the GC and differentiate into either plasma or memory B cells (<xref ref-type="bibr" rid="bib3">Akkaya et al., 2020</xref>; <xref ref-type="bibr" rid="bib26">Crotty, 2015</xref>; <xref ref-type="bibr" rid="bib75">Palm and Henry, 2019</xref>). The majority of positively selected B cells are recycled for further mutation-selection cycles, and they proliferate and undergo somatic hypermutation (SHM) (<xref ref-type="bibr" rid="bib23">Collins and Jackson, 2018</xref>; <xref ref-type="bibr" rid="bib32">de Silva and Klein, 2015</xref>; <xref ref-type="bibr" rid="bib45">Glanville et al., 2009</xref>; <xref ref-type="bibr" rid="bib60">Li et al., 2004</xref>; <xref ref-type="bibr" rid="bib66">Mesin et al., 2016</xref>; <xref ref-type="bibr" rid="bib112">Victora and Nussenzweig, 2012</xref>; <xref ref-type="bibr" rid="bib113">Victora and Nussenzweig, 2022</xref>). SHM is responsible for affinity-changing mutations, though it also leads to apoptosis or no affinity change with different probabilities (<xref ref-type="bibr" rid="bib5">Amitai et al., 2020</xref>; <xref ref-type="bibr" rid="bib114">Wang et al., 2015</xref>; <xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>; <xref ref-type="bibr" rid="bib123">Zhang and Shakhnovich, 2010</xref>). Based on data from experiments on affinity changes upon mutations at protein–protein interfaces, the change in affinity due to mutation is drawn from a log-normal distribution with only 5% of mutations being beneficial (<xref ref-type="bibr" rid="bib57">Kumar and Gromiha, 2006</xref>; <xref ref-type="bibr" rid="bib123">Zhang and Shakhnovich, 2010</xref>). Recent data in mice have also shown that ~5% mutations are beneficial (<xref ref-type="bibr" rid="bib33">DeWitt et al., 2025</xref>). The mathematical details of the affinity-driven selection and SHM described above are summarized in the Methods.</p><p>In our model, memory cells are stochastically selected in an affinity-dependent way and expanded in EGCs via the same processes as in GCs, except that there are few to no mutations (none in our model) (<xref ref-type="bibr" rid="bib68">Moran et al., 2018</xref>; <xref ref-type="bibr" rid="bib108">van Beek et al., 2022</xref>; <xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>). B cells exiting EGCs differentiate into antibody-secreting plasma cells with a probability of 0.6, because experimental data shows that 60% of new proliferating memory B cells differentiate into plasma cells (<xref ref-type="bibr" rid="bib68">Moran et al., 2018</xref>). These plasma cells produce antibodies at rates estimated from clinical data on humans immunized with COVID vaccines (<xref ref-type="bibr" rid="bib46">Goel et al., 2021</xref>; <xref ref-type="bibr" rid="bib70">Muecksch et al., 2022</xref>). Our model also incorporates epitope masking in which circulating antibodies specific for a given epitope can enter ongoing GCs and EGCs and compete with B cells specific for the same epitope (<xref ref-type="bibr" rid="bib13">Bergström et al., 2017</xref>; <xref ref-type="bibr" rid="bib64">McNamara et al., 2020</xref>; <xref ref-type="bibr" rid="bib91">Schaefer-Babajew et al., 2023</xref>; <xref ref-type="bibr" rid="bib92">Schiepers et al., 2024</xref>; <xref ref-type="bibr" rid="bib106">Tas et al., 2022</xref>; <xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>; <xref ref-type="bibr" rid="bib121">Zarnitsyna et al., 2015</xref>; <xref ref-type="bibr" rid="bib122">Zarnitsyna et al., 2016</xref>).</p><p>To summarize, the key processes that occur in GCs in our model are mutations during SHM, together with differentiation of positively selected B cells into antibody-producing plasma cells and memory cells. In EGCs, memory cells expand in an affinity-dependent way during the recall response and produce many antibody-secreting plasma cells and more memory B cells.</p><p>While GC and EGC processes are driven by the vaccine antigen (strain 1), we also track the affinities of the resulting memory B cells and antibodies for strains 2 and 3 as well. A B cell’s affinity for each strain depends on its initial affinity and the affinity-changing mutations that occur within the GC. The changes in affinity upon mutation are correlated between different strains. Specifically, the size of affinity changes is drawn from correlated log-normal distributions for the three epitopes, and the level of correlation is described by a parameter, <inline-formula><alternatives><mml:math id="inf3"><mml:mi mathvariant="normal">ρ</mml:mi></mml:math><tex-math id="inft3">\begin{document}${\rho }$\end{document}</tex-math></alternatives></inline-formula>, that determines a covariance matrix. This parameter <inline-formula><alternatives><mml:math id="inf4"><mml:mi mathvariant="normal">ρ</mml:mi></mml:math><tex-math id="inft4">\begin{document}${\rho }$\end{document}</tex-math></alternatives></inline-formula> is related to the level of conservation and amino acid relatedness between the strains for the B cell’s target epitope. For instance, if 70% of the amino acids in an epitope are shared between strains 1 and 2, we can approximate that ~70% of the beneficial mutations for B cells targeting this epitope in strain 1 are beneficial for strain 2 as well. The parameter <inline-formula><alternatives><mml:math id="inf5"><mml:mi mathvariant="normal">ρ</mml:mi></mml:math><tex-math id="inft5">\begin{document}${\rho }$\end{document}</tex-math></alternatives></inline-formula> for the corresponding epitope and strains is chosen to reflect the proportion of mutually beneficial mutations and hence quantifies the level of epitope conservation. We vary the values of <inline-formula><alternatives><mml:math id="inf6"><mml:mi mathvariant="normal">ρ</mml:mi></mml:math><tex-math id="inft6">\begin{document}${\rho }$\end{document}</tex-math></alternatives></inline-formula> to study the effects of different levels of epitope conservations.</p><p>For every immunization, we simulate 200 GCs and 1 EGC. The choice of 200 GCs was based on counts within spleen tissue section from immunized mice (~100 GCs per spleen) (<xref ref-type="bibr" rid="bib51">Jacob et al., 1991</xref>) and would be predicted to be higher in the human secondary lymphoid organs. More details about this choice and the choice of one EGC per simulation are provided in the Methods. Ten different simulations are carried out for any given condition, and the results shown are averages over these simulations. The parameters used in the simulations are provided in <xref ref-type="table" rid="app1table2">Appendix 1—table 2</xref>.</p></sec><sec id="s2-5"><title>Booster shots of homologous pHA provide increasing coverage of historical strains through feedback regulation of the humoral response by modulation of antigen levels in GCs</title><p><xref ref-type="fig" rid="fig5">Figure 5A</xref> shows the results of our simulations for antibody titers elicited against strain 1 (pHA) and the two historical strains (strains 2 and 3) after each of four immunizations with strain 1. The titers are calculated based on the affinity and number of antibodies that target the epitopes in each strain. After the first immunization, significant titers of antibodies are generated only against the dominant epitope of strain 1. However, after the second immunization, the titers are boosted against all strains, including strains 2 and 3. Continued boosting with pHA continues to amplify heterologous coverage, even when the homologous boosting titer has plateaued. Experiments show that injected soluble antigen decays relatively rapidly (<xref ref-type="bibr" rid="bib10">Aung et al., 2023</xref>; <xref ref-type="bibr" rid="bib63">Martin et al., 2021</xref>; <xref ref-type="bibr" rid="bib103">Tam et al., 2016</xref>). The vaccine antigen is the pandemic strain, and the individuals studied do not initially back-boost responses to historical strains. Therefore, upon the first immunization, only generic circulating antibodies, with low affinity for the antigen, are available to form the ICs needed for antigen deposition on FDCs (see computational methods section). Thus, our computational results show that very little antigen is deposited on FDCs after the first immunization with a new antigen (<xref ref-type="fig" rid="fig5">Figure 5B</xref>).</p><fig-group><fig id="fig5" position="float"><label>Figure 5.</label><caption><title>Antibody broadening via feedback regulation of the humoral response.</title><p>(<bold>A</bold>) The antibody titers against both the vaccine strain and historical strains (strains 2 and 3) increase over four immunizations. The antibodies are produced by plasma cells from both the germinal centers (GCs) and the extra germinal centers (EGCs). Antibody coverage increases first for strain 2 (after the second immunization), and strain 3 is engaged after the third immunization. In this simulation, the initial fractions of B cells <inline-formula><alternatives><mml:math id="inf7"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi mathvariant="italic">p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="italic">i</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft7">\begin{document}$\mathit{p}_{\mathit{i}}$\end{document}</tex-math></alternatives></inline-formula> that target epitope i are <inline-formula><alternatives><mml:math id="inf8"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi mathvariant="italic">p</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">p</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.15</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">p</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.05</mml:mn></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft8">\begin{document}$\mathit{p}_{1}=0.8,\,\mathit{p}_{2}=0.15,\,\mathit{p}_{3}=0.05$\end{document}</tex-math></alternatives></inline-formula>. The conservation <inline-formula><alternatives><mml:math id="inf9"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft9">\begin{document}${\rho }_{12}$\end{document}</tex-math></alternatives></inline-formula> of epitope 2 between strains 1 and 2 and the conservation <inline-formula><alternatives><mml:math id="inf10"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft10">\begin{document}${\rho }_{13}$\end{document}</tex-math></alternatives></inline-formula> of epitope 3 between strains 1 and 3 are both equal to 0.95. (<bold>B</bold>) The expansion of pathogen-specific memory B cells from the first immunization and differentiation into plasma cells that produce antibodies significantly increases the antigen concentration on follicular dendritic cells (FDCs) in the second immunization. This allows lower-affinity B cells that target subdominant epitopes to enter GCs and undergo affinity maturation. The antigen concentration on FDCs slightly increases from the second to the third immunization, allowing more B cells that target the subdominant epitopes to enter GCs and undergo affinity maturation. (<bold>C</bold>) The distribution of memory cells produced in the GCs during the first three immunizations. Upon subsequent antigen exposure, these memory cells are selected and expanded in EGCs. Thus, they contribute significantly to circulating antibodies and increased titers during subsequent immunizations. The first immunization primarily produces memory cells that target the dominant epitope (epitope 1), along with some memory cells targeting epitope 2. The second and third vaccinations produce an overall greater number of memory cells bearing generally higher affinity for the subdominant epitopes (epitopes 2 and 3) than the first immunization. (<bold>D</bold>) Strain 3 is engaged less potently when the initial fractions of B cells <inline-formula><alternatives><mml:math id="inf11"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft11">\begin{document}${p}_{{i}}$\end{document}</tex-math></alternatives></inline-formula> that target epitope i are <inline-formula><alternatives><mml:math id="inf12"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thinmathspace"/><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.18</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thinmathspace"/><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.02</mml:mn></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft12">\begin{document}${p}_{1}=0.8, \, {p}_{2}=0.18, \,{p}_{3}=0.02$\end{document}</tex-math></alternatives></inline-formula>. (<bold>E</bold>) The titers against strain 2 are lower than titers against strain 3 when the conservation of epitope 2 is decreased. Here the conservation <inline-formula><alternatives><mml:math id="inf13"><mml:msub><mml:mrow><mml:mi mathvariant="normal">ρ</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:math><tex-math id="inft13">\begin{document}${\rho }_{12}$\end{document}</tex-math></alternatives></inline-formula> of epitope 2 between strains 1 and 2 is 0.7 while the conservation <inline-formula><alternatives><mml:math id="inf14"><mml:msub><mml:mrow><mml:mi mathvariant="normal">ρ</mml:mi></mml:mrow><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:math><tex-math id="inft14">\begin{document}${\rho }_{13}$\end{document}</tex-math></alternatives></inline-formula> of epitope 3 between strains 1 and 3 is kept at 0.95. Other values of <inline-formula><alternatives><mml:math id="inf15"><mml:msub><mml:mrow><mml:mi mathvariant="normal">ρ</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:math><tex-math id="inft15">\begin{document}${\rho }_{12}$\end{document}</tex-math></alternatives></inline-formula> are explored in <xref ref-type="fig" rid="fig5s3">Figure 5—figure supplement 3</xref>. The fractions of B cells <inline-formula><alternatives><mml:math id="inf16"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft16">\begin{document}${p}_{{i}}$\end{document}</tex-math></alternatives></inline-formula> that target epitope i are the same as those in <bold>A</bold>.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig5-v1.tif"/></fig><fig id="fig5s1" position="float" specific-use="child-fig"><label>Figure 5—figure supplement 1.</label><caption><title>Booster shots of homologous pHA increase the number of high-affinity memory cells that target subdominant epitopes.</title><p>The distribution of memory cells produced by the germinal centers (GCs) against each epitope in the first three immunizations of the computational simulations, as in <xref ref-type="fig" rid="fig5">Figure 5C</xref>. Upon subsequent antigen exposure, these memory cells are selected and expanded in extra germinal centers (EGCs). Thus, they contribute significantly to circulating antibodies and increased titers during subsequent immunizations. The effects of epitope masking are not considered here. Among the high-affinity memory cells produced in the first immunization, relatively few target the subdominant epitopes (epitopes 2 and 3) compared to the dominant epitope (epitope 1). After the second and third immunizations, the number of memory cells increases for all epitopes but especially for epitopes 2 and 3.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig5-figsupp1-v1.tif"/></fig><fig id="fig5s2" position="float" specific-use="child-fig"><label>Figure 5—figure supplement 2.</label><caption><title>Germinal centers (GCs) that form upon booster shots persist longer than those that form upon primary immunization.</title><p>Computational results show that the GCs formed after the first immunization last ~110 days, while GCs formed after the second immunization persist for ~165 days, and then subsequent immunizations last ~180 days. The secondary GCs are longer lasting because enhanced antigen presentation on follicular dendritic cells (FDCs) leads to increased and more sustained entry of B cells into the GCs.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig5-figsupp2-v1.tif"/></fig><fig id="fig5s3" position="float" specific-use="child-fig"><label>Figure 5—figure supplement 3.</label><caption><title>Weaker conservation of subdominant epitopes between historical strains and the immunizing strain can outweigh more favorable germline frequencies of B cells that target these epitopes.</title><p>We vary the conservation <inline-formula><alternatives><mml:math id="inf17"><mml:mi mathvariant="normal">ρ</mml:mi></mml:math><tex-math id="inft17">\begin{document}${\rho }$\end{document}</tex-math></alternatives></inline-formula> of epitope 2 between the immunizing strain and strain 2 while fixing the fraction of naive B cells <inline-formula><alternatives><mml:math id="inf18"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft18">\begin{document}${p}_{{i}}$\end{document}</tex-math></alternatives></inline-formula>. Epitope 2 has a more favorable germline distribution than epitope 3 (<xref ref-type="fig" rid="fig4">Figure 4B</xref>). However, if epitope 2 is significantly less conserved between strains 1 and 2 than epitope 3 is between strains 1 and 3, the effects of weaker conservation outweigh the effects of a more favorable germline distribution, resulting in worse titers against strain 2 than against strain 3. The point at which the advantage of the immunodominance hierarchy is overcome by the effects of lower conservation depends on the germline B cell properties. The effects of epitope masking are not considered here. (<bold>A</bold>) Here, we fix the fraction of naive B cells <inline-formula><alternatives><mml:math id="inf19"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft19">\begin{document}${p}_{{i}}$\end{document}</tex-math></alternatives></inline-formula> targeting epitope i to <inline-formula><alternatives><mml:math id="inf20"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thinmathspace"/><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.18</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thinmathspace"/><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.05</mml:mn></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft20">\begin{document}${p}_{1}=0.8,\, {p}_{2}=0.18,\,{p}_{3}=0.05$\end{document}</tex-math></alternatives></inline-formula>. The conservation <inline-formula><alternatives><mml:math id="inf21"><mml:mi mathvariant="normal">ρ</mml:mi></mml:math><tex-math id="inft21">\begin{document}${\rho }$\end{document}</tex-math></alternatives></inline-formula> of epitope 2 between the immunizing strain and strain 2 is varied, and the titers after the second vaccination are shown. When <inline-formula><alternatives><mml:math id="inf22"><mml:mi mathvariant="normal">ρ</mml:mi></mml:math><tex-math id="inft22">\begin{document}${\rho }$\end{document}</tex-math></alternatives></inline-formula> is greater than the crossover point ~0.8, there are higher titers against strain 2 than strain 3. This is the same order as the order of the corresponding epitope in the immunodominance hierarchy; in particular, epitope 2 (which is conserved with strain 2) is more immunodominant than epitope 3 (which is conserved with strain 3). When <inline-formula><alternatives><mml:math id="inf23"><mml:mi mathvariant="normal">ρ</mml:mi></mml:math><tex-math id="inft23">\begin{document}${\rho }$\end{document}</tex-math></alternatives></inline-formula> is less than the crossover point ~0.8, there are higher titers against strain 3 than strain 2, which is not the same order as the immunodominance hierarchy for the corresponding epitopes. (<bold>B</bold>) When we alter the relative dominance of the epitopes by changing the fraction of naive B cells targeting each epitope to <inline-formula><alternatives><mml:math id="inf24"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thinmathspace"/><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.18</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thinmathspace"/><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.02</mml:mn></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft24">\begin{document}${p}_{1}=0.8,\,{p}_{2}=0.18,\,{p}_{3}=0.02$\end{document}</tex-math></alternatives></inline-formula>, the crossover point occurs at a lower conservation value <inline-formula><alternatives><mml:math id="inf25"><mml:mi mathvariant="normal">ρ</mml:mi><mml:mo>≈</mml:mo><mml:mn>0.66</mml:mn></mml:math><tex-math id="inft25">\begin{document}${\rho }\approx 0.66$\end{document}</tex-math></alternatives></inline-formula>.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig5-figsupp3-v1.tif"/></fig><fig id="fig5s4" position="float" specific-use="child-fig"><label>Figure 5—figure supplement 4.</label><caption><title>Increasing selection stringency K (from 0.5 to 0.7) does not change the qualitative results.</title><p>(<bold>A</bold>) The antibody titers increase for both vaccine and non-vaccine strains over four immunizations, although higher stringency results in slightly lower titers against non-vaccine strains after the second vaccination. (<bold>B</bold>) Memory cells produced in the germinal centers (GCs) of the first immunization primarily target the dominant epitope (ep 1). The response to subdominant epitopes (ep 2 and 3) is muted for the higher stringency case. However, sufficient memory cells against the vaccine strain are generated to produce high-affinity antibodies to bind and present antigen on the follicular dendritic cell (FDC) in the second immunization. (<bold>C, D</bold>) The GCs in the second and third immunizations produce high-affinity memory cells that target subdominant epitopes, even after increasing stringency.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig5-figsupp4-v1.tif"/></fig></fig-group><p>The germline B cells targeting the immunodominant epitope on strain 1 are more abundant and generally have higher affinities than the B cells engaging the subdominant epitopes. When antigen available on FDCs is low after the first immunization, the greater abundance and affinities of these germline B cells confer an especially strong advantage to them in entering GCs compared to B cells targeting subdominant epitopes. Furthermore, they are much more likely to dominate GC reactions during affinity maturation. Thus, the high-affinity memory B cells generated after the first immunization predominantly target the immunodominant epitope (<xref ref-type="fig" rid="fig5">Figure 5C</xref>, top panel; <xref ref-type="fig" rid="fig5s1">Figure 5—figure supplement 1</xref>).</p><p>After the second immunization, the EGCs facilitate the production of antibodies that engage strain 1, but not the historical strains. This is because the available memory B cells after the first immunization largely target the immunodominant epitope that is not conserved in the historical strains (<xref ref-type="fig" rid="fig5">Figure 5C</xref>, top panel; <xref ref-type="fig" rid="fig5s1">Figure 5—figure supplement 1</xref>). Thus, for many days after the second immunization, significant titers of antibodies that can target historical strains are not elicited (<xref ref-type="fig" rid="fig5">Figure 5A</xref>). However, secondary GCs also form during this time. Upon the second immunization, higher-affinity, antigen-specific IgG antibodies that were generated during the first immunization are available to bind and deposit the antigen on FDCs before the antigen is degraded for reasons noted earlier (<xref ref-type="bibr" rid="bib14">Bhagchandani et al., 2024</xref>). This results in higher amounts of antigen deposited on FDCs (<xref ref-type="fig" rid="fig5">Figure 5B</xref>) and longer-lasting GCs (<xref ref-type="fig" rid="fig5s2">Figure 5—figure supplement 2</xref>). Higher amounts of deposited antigen allow lower-affinity germline B cells that target subdominant epitopes to enter the GC and be positively selected. As affinity maturation proceeds, these GC B cells acquire higher affinity to the subdominant epitopes that are relatively conserved between strain 1 and the historical strains, generating high affinity, subdominant-targeting memory B cells (<xref ref-type="fig" rid="fig5">Figure 5C</xref>, middle panel; <xref ref-type="fig" rid="fig5s1">Figure 5—figure supplement 1</xref>, middle and bottom panels). The plasma cells produced by the GCs produce antibodies that engage strains 2 and 3 (particularly strain 2 since epitope 2, the second most dominant epitope, is relatively conserved between strains 1 and 2).</p><p>After the third immunization, memory cells from the second immunization that target epitopes 2 and 3 with high affinity are also selected based on their affinities and expanded in the EGC. This results in further amplification of antibodies that target epitopes 2 and 3 (<xref ref-type="fig" rid="fig5">Figure 5A</xref>). Antigen deposition on FDCs is also somewhat elevated after the third immunization (<xref ref-type="fig" rid="fig5">Figure 5B</xref>). As a result, strain 3 is engaged more potently, and the relative number of GC-generated memory B cells targeting epitope 3 compared to epitope 2 increases after the third immunization (<xref ref-type="fig" rid="fig5">Figure 5C</xref>, bottom panel; <xref ref-type="fig" rid="fig5s1">Figure 5—figure supplement 1</xref>). Consequently, the difference between the titers produced against epitopes 2 and 3 is further decreased after the fourth immunization (<xref ref-type="fig" rid="fig5">Figure 5A</xref>). However, the overall improvements to antibody titers are minor because antigen presentation in the GCs and expansion of memory B cells in EGCs is similar to that after the third immunization.</p><p>The relative coverage of strains 2 and 3 upon repeated vaccination depends upon the relative immunodominance of epitopes 2 and 3 in the pool of germline B cells. To test the effects of modifying the immunodominance hierarchy, we increased the fraction of germline B cells that target epitope 2 and decreased the fraction that target epitope 3. This enhances the immunodominance of epitope 2 over epitope 3. Consequently, as shown in <xref ref-type="fig" rid="fig5">Figure 5D</xref>, the responses to epitope 3 and to historical strain 3 in which epitope 3 is conserved are less potent compared to the results shown in <xref ref-type="fig" rid="fig5">Figure 5A</xref>. Variation in the immunodominance patterns could explain variations in the kinetics of broadening against different historical strains as we observe in the clinical results (<xref ref-type="fig" rid="fig3">Figure 3</xref>, <xref ref-type="fig" rid="fig3s1">Figure 3—figure supplement 1</xref>).</p><p>The relative coverage of historical strains also depends on the conservation of subdominant epitopes between the historical and immunizing strains. In <xref ref-type="fig" rid="fig5">Figure 5A</xref>, the conservation of epitope 2 between strains 1 and 2 and of epitope 3 between strains 1 and 3 is the same. The results show that higher titers are elicited against strain 2 than strain 3, which aligns with the immunodominance of epitope 2 over epitope 3. However, it is possible that a more immunodominant epitope is less conserved as viruses mutate to avoid immune detection (<xref ref-type="bibr" rid="bib4">Altman et al., 2018</xref>; <xref ref-type="bibr" rid="bib7">Angeletti et al., 2017</xref>; <xref ref-type="bibr" rid="bib8">Angeletti and Yewdell, 2018</xref>). Thus, we examined the effects of reducing the conservation of epitope 2 while fixing the conservation of epitope 3. If the conservation of epitope 2 between strains 1 and 2 is decreased below a critical value (see <xref ref-type="fig" rid="fig5s3">Figure 5—figure supplement 3</xref>), the advantage of epitope 2 due to a more favorable germline distribution is outweighed by weaker conservation. In <xref ref-type="fig" rid="fig5">Figure 5E</xref>, epitope 2 is more weakly conserved than in <xref ref-type="fig" rid="fig5">Figure 5A</xref> (but the germline immunodominance hierarchy is kept the same), resulting in lower titers against strain 2 than against strain 3. In this way, different levels of conservation of subdominant epitopes could explain why HAI activity against some strains is acquired before others during sequential immunization.</p><p>We also varied a parameter in our simulations that reflects the stringency with which GC B cells are selected in the GC based on their affinities for the antigen. We find that the qualitative results reported in <xref ref-type="fig" rid="fig5">Figure 5</xref> remain the same if this parameter is varied within a reasonable range (<xref ref-type="fig" rid="fig5s4">Figure 5—figure supplement 4</xref>).</p></sec><sec id="s2-6"><title>Feedback regulation of the humoral response by epitope masking enhances the generation of antibodies that can engage historical variants upon boosting with unmatched homologous HA</title><p>Circulating antibodies can enter GCs and bind to their corresponding epitopes on antigen presented on FDCs (<xref ref-type="bibr" rid="bib13">Bergström et al., 2017</xref>; <xref ref-type="bibr" rid="bib27">Cyster and Wilson, 2024</xref>; <xref ref-type="bibr" rid="bib64">McNamara et al., 2020</xref>; <xref ref-type="bibr" rid="bib91">Schaefer-Babajew et al., 2023</xref>; <xref ref-type="bibr" rid="bib92">Schiepers et al., 2024</xref>; <xref ref-type="bibr" rid="bib106">Tas et al., 2022</xref>; <xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>; <xref ref-type="bibr" rid="bib121">Zarnitsyna et al., 2015</xref>; <xref ref-type="bibr" rid="bib122">Zarnitsyna et al., 2016</xref>). This masking of an epitope by soluble antibodies lowers the effective amount of antigen available to GC B cells targeting the same epitope, reducing their competitive fitness within the GC. This property of epitope masking by circulating antibodies can regulate the GC participation of naive B cells according to epitope specificity and modulate the competitive environment for GC B cells (<xref ref-type="bibr" rid="bib13">Bergström et al., 2017</xref>; <xref ref-type="bibr" rid="bib27">Cyster and Wilson, 2024</xref>; <xref ref-type="bibr" rid="bib64">McNamara et al., 2020</xref>; <xref ref-type="bibr" rid="bib91">Schaefer-Babajew et al., 2023</xref>; <xref ref-type="bibr" rid="bib92">Schiepers et al., 2024</xref>; <xref ref-type="bibr" rid="bib106">Tas et al., 2022</xref>; <xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>; <xref ref-type="bibr" rid="bib121">Zarnitsyna et al., 2015</xref>; <xref ref-type="bibr" rid="bib122">Zarnitsyna et al., 2016</xref>). Our computational model shows that after the second immunization, most of the circulating antibodies bind to the dominant epitope. This is because most of the memory B cells produced after the first immunization are directed against the dominant epitope (<xref ref-type="fig" rid="fig5">Figures 5C</xref> and <xref ref-type="fig" rid="fig6">6C</xref>). These memory cells are rapidly expanded in EGCs after the second immunization to generate the corresponding dominant epitope-targeting antibodies. Accordingly, we find that the entry and selection of subdominant-targeting B cells during affinity maturation are enhanced by the masking of the dominant epitope. As a result, more memory cells that target the subdominant epitopes are generated (<xref ref-type="fig" rid="fig6">Figure 6C and D</xref>) and larger antibody titers targeting strains 2 and 3 are elicited (<xref ref-type="fig" rid="fig6">Figure 6A</xref>) if epitope masking is included. Likewise, after the third immunization, the antibodies corresponding to memory cells from the second vaccination begin to mask epitope 2, promoting the generation of memory B cells and antibodies targeting epitope 3 (<xref ref-type="fig" rid="fig6">Figure 6</xref>). This feature of increasing antibody titers against the historical strains is observed when we consider two cases of epitope masking (<xref ref-type="fig" rid="fig6">Figure 6A, B</xref>): (1) (<xref ref-type="bibr" rid="bib28">Danecek et al., 2011</xref>) where the three epitopes under consideration are non-overlapping; and (2) where the epitopes partially overlap with each other. The first case shows the largest effect of epitope masking. In the second case, epitope masking effects remain significant, even if we consider a modest level of epitope overlap (e.g. 30% between epitope 1 (dominant) and epitope 2 (subdominant); and 30% between epitope 1 (dominant) and epitope 3 (subdominant)).</p><fig id="fig6" position="float"><label>Figure 6.</label><caption><title>Regulation of antibody broadening through epitope masking.</title><p>Maximum antibody titers for the historical strains after the second vaccination, with and without epitope masking. Two cases are considered when there is epitope masking: (1) (<xref ref-type="bibr" rid="bib28">Danecek et al., 2011</xref>) the epitopes are absolutely distinct; (2) the epitopes can overlap with each other. In the second case shown here, there is 30% overlap between epitope 1 (dominant) and epitope 2 (subdominant) and between epitope 1 (dominant) and epitope 3 (subdominant). Masking increases the titers against historical strains, even when there is some overlap between the dominant and subdominant epitopes. (<bold>B</bold>) Maximum antibody titers for the historical strains after the third vaccination, with and without masking. After the third vaccination, titers for Variant 2 with epitope masking are higher when there is epitope overlap than when the epitopes are distinct. (<bold>C</bold>) Relative number of memory cells produced with epitope masking. Epitopes are considered to be fully distinct. The epitope that is most targeted by the memory cells is also masked the most after the subsequent immunization. The dominant epitope is targeted most by Vax 1 memory cells and is masked the most in the second immunization. The orange subdominant epitope (epitope 2) and green subdominant epitope (epitope 3) are both relatively well targeted by Vax 2 memory cells. However, the subdominant epitopes are also masked during the third immunization, so the subdominant epitopes lose their advantage compared to the dominant epitope in the affinity maturation process after Vax 3. (<bold>D</bold>) Relative number of memory cells produced with epitope masking and overlap. The epitope that is most targeted by the memory cells is masked the most in the subsequent immunization. The dominant epitope is targeted most by Vax 1 memory cells and is masked the most in the second immunization. The orange subdominant epitope (epitope 2) is targeted most by Vax 2 memory cells, although more memory cells target the dominant epitope than when the epitopes are fully distinct. Due to the masking of epitope 2 in the third immunization, the dominant and green subdominant epitope (epitope 3) are both relatively well targeted by Vax 3 memory cells.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-107042-fig6-v1.tif"/></fig><p>Epitope overlap between dominant and subdominant epitopes generally decreases titers against historical strains compared to fully distinct epitopes. However, after the third vaccination, the antibody response titer against strain 2 is higher when there is epitope overlap (<xref ref-type="fig" rid="fig6">Figure 6B</xref>). This is because the second immunization produces more memory cells targeting the dominant epitope when there is epitope overlap (<xref ref-type="fig" rid="fig6">Figure 6D</xref>). These memory cells are rapidly expanded in EGCs, and so antibodies mask the dominant epitope more strongly during the third immunization when the epitopes overlap. This leads to the production of more high-affinity B cells that target epitope 2 after the third immunization, and subsequently higher titers against strain 2.</p></sec></sec><sec id="s3" sec-type="discussion"><title>Discussion</title><p>Our results reveal broadening of antibody coverage following repeated immunization with homologous pHA. This process occurred gradually within individuals that did not initially ‘back-boost’ against historical H1N1 strains. These findings are consistent with sequential exposure to SARS-CoV-2 mRNA vaccines, where repeated immunization with the homologous Wuhan vaccine strain eventually elicits non-imprinted coverage against highly unmatched Omicron lineages of SARS-CoV-2 (<xref ref-type="bibr" rid="bib42">Garcia-Beltran et al., 2022</xref>; <xref ref-type="bibr" rid="bib70">Muecksch et al., 2022</xref>; <xref ref-type="bibr" rid="bib94">Schmidt et al., 2022</xref>). Our computational results suggest that feedback loops that regulate the recall humoral response (enhanced antigen presentation on FDCs and epitope masking) are a likely origin of eliciting non-imprinted antibody breadth to influenza HA. These mechanisms are consistent with the immune reactions that broaden antibodies after boosting with the homologous SARS-CoV-2 vaccine (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>). More generally, our results point to a general feature of the humoral response that intrinsically broadens antibodies against unmatched/diversified antigen targets upon repeated vaccination with the same novel antigen. The principle of preserving ‘non-homogenized’ antibody output with diverse epitope specificities and binding affinities has emerged as an important theme for GC and memory B cell responses to protein antigens (<xref ref-type="bibr" rid="bib29">de Carvalho et al., 2023</xref>; <xref ref-type="bibr" rid="bib33">DeWitt et al., 2025</xref>; <xref ref-type="bibr" rid="bib48">Hägglöf et al., 2023</xref>; <xref ref-type="bibr" rid="bib58">Kuraoka et al., 2016</xref>; <xref ref-type="bibr" rid="bib66">Mesin et al., 2016</xref>; <xref ref-type="bibr" rid="bib67">Mesin et al., 2020</xref>; <xref ref-type="bibr" rid="bib78">Radmacher et al., 1998</xref>; <xref ref-type="bibr" rid="bib85">Ronsard et al., 2023</xref>; <xref ref-type="bibr" rid="bib86">Sabouri et al., 2014</xref>; <xref ref-type="bibr" rid="bib98">Silver et al., 2018</xref>; <xref ref-type="bibr" rid="bib105">Tas et al., 2016</xref>; <xref ref-type="bibr" rid="bib108">van Beek et al., 2022</xref>; <xref ref-type="bibr" rid="bib125">Zuo et al., 2025</xref>) and our results suggest that intrinsic broadening of the antibodies generated in response to homologous antigen is an extension of this fundamental principle.</p><p>Antibody feedback is now a well-established mechanism that promotes or restricts GC recruitment depending on the concentration, affinity, and epitope specificity of the antibodies in circulation (<xref ref-type="bibr" rid="bib13">Bergström et al., 2017</xref>; <xref ref-type="bibr" rid="bib14">Bhagchandani et al., 2024</xref>; <xref ref-type="bibr" rid="bib27">Cyster and Wilson, 2024</xref>; <xref ref-type="bibr" rid="bib64">McNamara et al., 2020</xref>; <xref ref-type="bibr" rid="bib91">Schaefer-Babajew et al., 2023</xref>; <xref ref-type="bibr" rid="bib92">Schiepers et al., 2024</xref>; <xref ref-type="bibr" rid="bib106">Tas et al., 2022</xref>; <xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>; <xref ref-type="bibr" rid="bib121">Zarnitsyna et al., 2015</xref>; <xref ref-type="bibr" rid="bib122">Zarnitsyna et al., 2016</xref>). Our modeling suggests that such feedback regulation, which includes antigen presentation dynamics and epitope masking effects, can in part enable the polyspecific responses and broad B cell reactivities elicited following immunization with homologous immunogen. During the first exposure to antigen, generic circulating antibodies deposit limited amounts of antigen on FDCs as observed in experiments with NHP (<xref ref-type="bibr" rid="bib63">Martin et al., 2021</xref>). Thus, mostly immunodominant responses result. Antigen-specific memory B cells generated in past exposures to antigen are expanded to generate antigen-specific antibodies that can deposit significantly more antigen on FDCs, consistent with studies on extended dosing vaccination in mice and NHP (<xref ref-type="bibr" rid="bib14">Bhagchandani et al., 2024</xref>; <xref ref-type="bibr" rid="bib22">Cirelli et al., 2019</xref>; <xref ref-type="bibr" rid="bib103">Tam et al., 2016</xref>). Epitope-specific antibodies can also enter secondary GCs that form after re-exposure to antigen to mask their epitopes, thus increasing the relative concentration of other subdominant epitopes (<xref ref-type="bibr" rid="bib13">Bergström et al., 2017</xref>; <xref ref-type="bibr" rid="bib27">Cyster and Wilson, 2024</xref>; <xref ref-type="bibr" rid="bib64">McNamara et al., 2020</xref>; <xref ref-type="bibr" rid="bib91">Schaefer-Babajew et al., 2023</xref>; <xref ref-type="bibr" rid="bib92">Schiepers et al., 2024</xref>; <xref ref-type="bibr" rid="bib106">Tas et al., 2022</xref>; <xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>; <xref ref-type="bibr" rid="bib121">Zarnitsyna et al., 2015</xref>; <xref ref-type="bibr" rid="bib122">Zarnitsyna et al., 2016</xref>). The overall enhancement in the amount of antigen driving GC reactions and epitope masking may promote the evolution of subdominant responses that target epitopes that are shared between the immunizing antigen and historical variants. Epitope masking will also be constrained by the dimensions of the RBS, and our simulations do report attenuation of titers against historical influenza strains when we introduce epitope overlap. Depending upon the degree of overlap between the epitopes and differences in germline characteristics in the B cells targeting dominant and subdominant epitopes, this effect could be compensated during subsequent shots, as seen in our results.</p><p>Operationally, it will be important to integrate this information to define the number of homologous immunizations needed to elicit a given level of vaccine coverage of historical or new strains. Our simulations indicate antibody broadening depends on the interplay of several key factors including: the precursor frequencies of germline B cells targeting these epitopes, the affinities of germline B cells for their target epitopes, and the level of conservation of shared epitopes within the RBS. Precursor frequencies and germline affinities determine the B cell pool’s initial numbers and affinities toward target strains—historical or emergent—while conservation of shared epitopes governs how those affinities change during affinity maturation in response to selection of GC B cells for their affinities to the immunizing strain. Lower frequencies and affinities of germline B cells for conserved epitopes between vaccine and historical strains result in weaker antibody titers (compare strain 3 in <xref ref-type="fig" rid="fig5">Figure 5A, D</xref>) and poorer broadening for a fixed number of immunizations. On the other hand, increased conservation of shared epitopes can strengthen antibody titers (compare strain 2 in <xref ref-type="fig" rid="fig5">Figure 5A, E</xref>) and improve broadening for a given number of immunizations. Thus, the effects of the precursor frequencies and germline affinities can compete with the effects of epitope conservation in determining the coverage of a particular strain (<xref ref-type="fig" rid="fig5s3">Figure 5—figure supplement 3</xref>).</p><p>Our results also suggest that the germline B cell-mediated effects noted above are particularly important in earlier stages of the sequential vaccine regimen. But once higher affinity antibodies circulate (and recall of B cell memory becomes operational), epitope masking effects and enhanced antigen deposition on FDCs further modulate the immunodominance hierarchy to favor responses to subdominant epitopes. While our model does not account for memory B cells seeding secondary GCs, our previous work indicates that if more memory B cells enter secondary GCs, the evolution of broadened antibody responses is diluted (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>).</p><p>In all cases, our simulations recapitulate the clinical vaccine results in a qualitative manner. This owes to our development of a simplified model for the vaccine antigen, its relation to historical strains, and the characteristics of the germline B cells that engage RBS epitopes. While recapitulation of antibody broadening through simplified computational models points to fundamental/core features of adaptive immunity, more comprehensive epitope mapping of the B cell responses to the RBS targets (structure, engagement affinity, immunodominance patterns) will be needed to assemble more complete prediction maps to guide vaccine design.</p><p>In summary, we describe a phenomenon that defies the long-held view that sequential immunization with homologous influenza HA antigens serves to only/principally reinforce the boosting of antibodies with narrow coverage (<xref ref-type="bibr" rid="bib49">Henry et al., 2018</xref>; <xref ref-type="bibr" rid="bib55">Krammer et al., 2018</xref>; <xref ref-type="bibr" rid="bib54">Krammer and Palese, 2013</xref>; <xref ref-type="bibr" rid="bib89">Sangesland and Lingwood, 2021</xref>). Previous B cell epitope prediction algorithms have failed to computationally delineate and accurately predict patterns in the humoral response (<xref ref-type="bibr" rid="bib62">Mahanty et al., 2015</xref>; <xref ref-type="bibr" rid="bib84">Rockberg and Uhlén, 2009</xref>; <xref ref-type="bibr" rid="bib96">Sela-Culang et al., 2013</xref>; <xref ref-type="bibr" rid="bib109">van Regenmortel, 2002</xref>; <xref ref-type="bibr" rid="bib110">van Regenmortel, 2011</xref>), but by modeling the key immunological steps that underscore adaptive immune reactions to protein antigen (<xref ref-type="bibr" rid="bib3">Akkaya et al., 2020</xref>; <xref ref-type="bibr" rid="bib26">Crotty, 2015</xref>; <xref ref-type="bibr" rid="bib32">de Silva and Klein, 2015</xref>; <xref ref-type="bibr" rid="bib75">Palm and Henry, 2019</xref>; <xref ref-type="bibr" rid="bib113">Victora and Nussenzweig, 2022</xref>; <xref ref-type="bibr" rid="bib120">Young and Brink, 2021</xref>), we obtain results in harmony with the clinical findings and describe mechanisms that may underlie them. This broadening effect has thus far only been observed in human antibody responses to vaccination, and we suggest that it may further inform universal vaccine approaches (<xref ref-type="bibr" rid="bib19">Caradonna and Schmidt, 2021</xref>; <xref ref-type="bibr" rid="bib55">Krammer et al., 2018</xref>; <xref ref-type="bibr" rid="bib89">Sangesland and Lingwood, 2021</xref>; <xref ref-type="bibr" rid="bib115">Wei et al., 2020</xref>). Immunologically, we suggest that antibody broadening reflects an in-built feature of continued B cell diversification, a principle that will ensure antibody complementarity to hypervariable antigen targets.</p><sec id="s3-1"><title>Limitations of the study</title><p>Clinically, the vaccination regimen under study lacked an unvaccinated group, meaning that we cannot formally exclude the possibility that additional H1N1 infections also drove antibody broadening the 4-year vaccine period (2013–2016). However, pHA has dominated circulating H1N1 since 2009 (<xref ref-type="bibr" rid="bib47">Guthmiller and Wilson, 2018</xref>; <xref ref-type="bibr" rid="bib80">Raymond et al., 2018</xref>) and would be expected to contribute to broadening through the mechanisms we have described. We also are careful to report this broadening effect as an immunological feature of antigen scanning and do not make conclusions or assertions about its potential contribution to viral protection.</p><p>Computationally, model lays the groundwork to experimentally define factors identified as significant for antibody broadening in vivo, including epitope conservation, epitope masking, and antigen presentation on FDCs. We acknowledge that our computational model is one of many approaches that may be used to describe this effect and that it is not capable of quantitatively predicting outcomes of repeated vaccination because some parameters have not been defined with sufficient accuracy to allow building of general quantitative models of the humoral immune response. We also note that related models that we have employed in the past have been useful in obtaining mechanistic insights that have been experimentally tested in vivo (<xref ref-type="bibr" rid="bib5">Amitai et al., 2020</xref>; <xref ref-type="bibr" rid="bib14">Bhagchandani et al., 2024</xref>; <xref ref-type="bibr" rid="bib114">Wang et al., 2015</xref>; <xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>). We also mention that the number of EGCs (compartments where memory cells are expanded outside GCs) that form is not known. The use of a single EGC in each of our simulations may lead to greater stochastic variations between simulations that are used to calculate average properties. In the Methods, we note why such stochastic effects should not be pronounced in EGCs compared to GCs. The use of one EGC may also have effects on access to T cell help available if one used multiple EGCs, which may further modulate the pathways for broadening of the antibody responses that we describe.</p><p>While our model predicts that epitope conservation impacts titers against historical strains, the data examined in this study do not show a clear trend between amino acid similarity with the vaccine strain and the titer levels or coverage kinetics among H1N1 strains. Exploring alternate experimental metrics for epitope conservation instead of amino acid similarity, along with examination of diverse sets of clinical data, and measuring characteristics of germline B cells targeting different epitopes can improve the model and lead to better congruence between model predictions and data. In addition, experimentally defining the relative contribution of epitope masking and antigen presentation on FDCs will necessitate vaccine/immune challenge models where these parameters can be measured individually and that accurately reflect human humoral response features (<xref ref-type="bibr" rid="bib10">Aung et al., 2023</xref>; <xref ref-type="bibr" rid="bib91">Schaefer-Babajew et al., 2023</xref>; <xref ref-type="bibr" rid="bib106">Tas et al., 2022</xref>; <xref ref-type="bibr" rid="bib122">Zarnitsyna et al., 2016</xref>). In humans, an accurate description of individual imprinted B cell memory to influenza HA will also be needed to predict the broadening activity of homologous influenza vaccine regimen, in lieu of another pandemic influenza virus strain that does not back-boost to historical strains.</p></sec></sec><sec id="s4" sec-type="methods"><title>Methods</title><sec id="s4-1"><title>Lead contact and materials availability</title><sec id="s4-1-1"><title>Lead contact</title><p>Further information and requests for reagents should be directed to and will be fulfilled by Daniel Lingwood (dlingwood@mgh.harvard.edu) and Arup K. Chakraborty (arupc@mit.edu).</p></sec><sec id="s4-1-2"><title>Materials availability</title><p>There are no restrictions on the availability of the materials used in this study.</p></sec></sec><sec id="s4-2"><title>Experimental model and subject details</title><p>We evaluated the HAI titers elicited by a clinical influenza vaccine that was sequentially immunized (4x) over a 4-year period (2013–2016) and contained the same H1 component (A/California/7/2009) in each of the vaccine years (<xref ref-type="bibr" rid="bib74">Nuñez et al., 2017</xref>). An important distinction from the previous analysis is that we focused only on individuals that were longitudinally sampled across the 4-year period (<italic>n</italic> = 136 individuals; subjects are grouped into two age categories: above 50 years old and below 38 years old, see <xref ref-type="supplementary-material" rid="fig2sdata1">Figure 2—source data 1</xref>). In each year, a blood sample was obtained before and then 20 days after vaccination. HAI titers for viruses spanning 100 years of influenza evolution were measured in each of these samples (<xref ref-type="bibr" rid="bib74">Nuñez et al., 2017</xref>; see <xref ref-type="supplementary-material" rid="fig2sdata1">Figure 2—source data 1</xref> and <xref ref-type="table" rid="app1table1">Appendix 1—table 1</xref>). The H1N1 viral panel for HAI comprised: A/South Carolina/1/1918, A/Weiss/JY2/1943, A/Fort Monmouth/1/1947, A/Denver/1/1957, A/New Jersey/6/1976, A/USSR/90/1977, A/Chile/1/1983, A/Singapore/6/1986, A/Texas/36/1991, A/Beijing/262/1995, A/New Caledonia/20/1999, A/Solomon Island/3/2006, A/Brisbane/59/2007, A/California/07/2009. The H3N2 vaccine panel for HAI comprised: A/Hong/Kong/1/1968, A/Hong/Kong/4801/2014, A/Nanchang/933/1995, A/New/York/55/2004, A/Panama/2007/1999, A/Perth/16/2009, A/Port/Chalmers/12/1973, A/Shandong/9/1993, A/Switzerland/9715293/2013A/Sydney/5/1997, A/Texas/1/1977, A/Texas/50/2012, A/Victoria/361/2011, A/Wisconsin/67/2005. The IBV viral panel for HAI included: B/Brisbane/60/2008, B/Florida/4/2006, B/Harbin/7/1994, B/Hong/Kong/330/2001, B/Lee/1940, B/Malaysia/2506/2004, B/Massachusetts/2/2012, B/Phuket/3073/2013, B/Texas/06/2011, B/Wisconsin/1/2010, B/Yamagata/16/1988.</p></sec><sec id="s4-3"><title>Method details</title><sec id="s4-3-1"><title>Amino acid relatedness in HA ectodomains or within the RBS patch</title><p>Amino acid sequences of HA ectodomains from the different strains used in HAI were obtained from Genbank (<ext-link ext-link-type="uri" xlink:href="https://www.ncbi.nlm.nih.gov/genbank/">https://www.ncbi.nlm.nih.gov/genbank/</ext-link>) or GISAID (<ext-link ext-link-type="uri" xlink:href="https://gisaid.org/">https://gisaid.org/</ext-link>; <xref ref-type="table" rid="app1table1">Appendix 1—table 1</xref>). The amino acid positions comprising the HA RBS patch were defined by the structures of four human broadly neutralizing RBS-directed antibodies, each in co-complex with HA (<xref ref-type="bibr" rid="bib93">Schmidt et al., 2015</xref>). We used this information to define amino acid relatedness between the HA glycoproteins of all the influenza viruses used in our HAI panel. Pairwise relatedness was defined for both full-length HA ectodomain and for the RBS patch. In both cases, amino acid sequence relatedness was obtained by first aligning two amino acid sequences and then computing the ratio of matched amino acid counts over the total amino acid counts in the aligned sequences. Heat maps visualizing the pairwise amino acid sequence relatedness values were graphed using ‘pheatmap’ function from R package ‘pheatmap’ (version 1.0.12). Amino acid relatedness is represented as epitope conservation with the parameter <inline-formula><alternatives><mml:math id="inf26"><mml:mi mathvariant="normal">ρ</mml:mi></mml:math><tex-math id="inft26">\begin{document}${\rho }$\end{document}</tex-math></alternatives></inline-formula> in the computational model (see modeling section).</p></sec><sec id="s4-3-2"><title>Analysis of HAI titers in relation to amino acid relatedness</title><p>We constructed dot plots to visualize the relationship between the fold change of HAI titers to the individual viruses in relation to their amino acid relatedness (for both the HA ectodomain and RBS patch) to the vaccine strain used in each year. In the case of the H1 vaccine component, the same H1 vaccine strain (A/California/7/2009) was used in each year. These plots were generated using the ‘geom_point’ function from R package ‘ggplot2’ (version 3.4.2). The fold change of HAI titer for each patient was computed by dividing the post-vaccination HAI titer by the corresponding pre-vaccination HAI titer.</p></sec><sec id="s4-3-3"><title>Longitudinal analysis of antibody broadening</title><p>To evaluate antibody broadening in response to homologous H1 (A/California/7/2009), we divided the HAI titers for H1N1 viruses from each individual subject into responders and non-responders to each viral strain in each year. Responders were defined by having non-decreasing fold changes of HAI titers (post-vaccination HAI titer/pre-vaccination HAI titer), that is fold change of HAI titers greater than 1. The non-responders were defined by having decreasing fold changes of HAI titers (post-vaccination HAI titer/pre-vaccination HAI titer), that is fold change of HAI titers less than 1. We tracked patients in the two age groups: &gt;50 years old, having 4 years of complete HAI titers (2013–2016); and &lt;38 years old, having 3 years of complete HAI titers (2014–2016). Bar plots showing the responder and non-responder ratios were graphed using ‘geom_bar’ function from R package ‘ggplot2’ (version 3.4.2). Linear regression analyses were also performed on the fraction of responders (or non-responders) in each year after standardizing the responder (or non-responder) value to the number of subjects in each age group (&gt;50 years old or &lt;38 years old). The linear regressions were performed using the ‘ggscatter’ function with the fitting equation shown by the ‘stat_regline_equation’ function from R package ‘ggpubr’ (version 0.6.0). Corresponding p and <italic>r</italic><sup>2</sup> values were computed using the ‘lm’ function from R package ‘stats’ (version 4.3.1).</p></sec><sec id="s4-3-4"><title>Immune reactions in silico</title><p>The computational model is adapted from past work on the effects of repeated vaccination with COVID vaccines (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>). Changes to the original model are described in the main text and below, along with key mathematical equations that describe the model. Interested readers can find in-depth rationale for model development, exploration of alternative model structures, and further analysis of parameter sensitivity in the earlier paper on the outcome of multiple immunizations with COVID vaccines (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>). We use the same symbols to denote quantities as in the paper on COVID vaccines (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>).</p><p>Differential equations describe antigen dynamics, and this is combined with stochastic simulations of GC and EGC processes. The time step is 0.01 day. For each situation, 200 GCs are simulated, and from the second immunization on, 1 EGC is simulated along with the GCs. Ten such simulations are carried out for each set of conditions, and the results are averaged over the ten simulations to report results.</p><p>The choice of 200 GCs was based on a paper that dissected sections of spleen in a 6 µm section and found that there were 100 GCs (<xref ref-type="bibr" rid="bib51">Jacob et al., 1991</xref>). That is, there are an order of 10<sup>2</sup> GCs. As the number 100 was for a part of mouse spleen and the number in humans is also likely higher, we used 200 GCs. The number of compartments outside GCs where memory B cells are expanded is unknown. Neither is it known how long they last after exposure to a shot of a vaccine. Using more EGCs, rather than one, would potentially reduce the effect of stochastic variations between simulations when we calculate averages over many simulations. Nevertheless, we expect stochastic effects to be less pronounced in EGCs compared to GCs, especially for the second shot. This is because the memory pool after the first shot is likely to be comprised of a few expanded clones and a representative sample of this pool is sampled for entry into the EGC. In contrast, the naive pool of germline B cells that can enter GCs is much larger, and this pool can be sampled better by modeling many GCs. In addition, stochastic effects within EGCs should also be less than in GCs because there is little to no mutation in the EGCs, while a usually rare mutation of relatively higher affinity could evolve in the GCs. However, in shots after the second one, stochastic fluctuations in EGCs cannot be ruled out. For providing qualitative mechanistic insights, using one EGC and averaging over many simulations should be reasonably adequate for calculating average properties.</p><sec id="s4-3-4-1"><title>Antigen dynamics</title><p>Differential equations describe the reactions that govern the concentration of antigen and antibody, as shown in the table below. We use the following abbreviations and symbols: soluble antigen (Ag), soluble antibody (Ig), soluble immune complex (IC), immune complex on follicular dendritic cell (IC-FDC), plasma cell (PC), rate of decay (<italic>d</italic>), rate of reaction (<italic>k</italic>), dissociation constant of serum antibodies (<inline-formula><alternatives><mml:math id="inf27"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft27">\begin{document}${K}_{{d}}$\end{document}</tex-math></alternatives></inline-formula>), dissociation constant of plasma cell antibodies (<inline-formula><alternatives><mml:math id="inf28"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft28">\begin{document}${K}_{{d}}^{{P}{C}}$\end{document}</tex-math></alternatives></inline-formula>).</p><table-wrap id="inlinetable1" position="anchor"><table frame="hsides" rules="groups"><thead><tr><th align="left" valign="top">Equation</th><th align="left" valign="top">Reaction(s)</th><th align="left" valign="top">Description</th></tr></thead><tbody><tr><td align="left" valign="top"><inline-formula><alternatives><mml:math id="inf29"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft29">\begin{document}$\frac{\left [{A}{g}\right ]\left [{I}{g}\right ]}{\left [{I}{C}\right ]}={K}_{{d}}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="top"><inline-formula><alternatives><mml:math id="inf30"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mo stretchy="false">↔</mml:mo><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft30">\begin{document}${A}{g}+{I}{g}\leftrightarrow {I}{C}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="top">Fast equilibrium for formation of immune complex</td></tr><tr><td align="left" valign="top"><inline-formula><alternatives><mml:math id="inf31"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi mathvariant="normal">∂</mml:mi><mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft31">\begin{document}$\partial _{{t}}\left [{A}{g}\right ]=-{d}_{{A}{g}}\left [{A}{g}\right ]$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="top"><inline-formula><alternatives><mml:math id="inf32"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mi>A</mml:mi><mml:mi>g</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mrow><mml:mi>∅</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft32">\begin{document}$Ag\rightarrow {\varnothing }$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="top">Decay of free soluble antigen</td></tr><tr><td align="left" valign="top"><inline-formula><alternatives><mml:math id="inf33"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi mathvariant="normal">∂</mml:mi><mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>o</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft33">\begin{document}$\partial _{{t}}\left [{I}{C}\right ]=-{k}_{{d}{e}{p}{o}{s}{i}{t}}\left [{I}{C}\right ]$\end{document}</tex-math></alternatives></inline-formula><break/><inline-formula><alternatives><mml:math id="inf34"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mtable columnalign="left left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msub><mml:mi mathvariant="normal">∂</mml:mi><mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mo>−</mml:mo><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>o</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mo>−</mml:mo><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft34">\begin{document}$\begin{array}{ll}\partial_{{t}}\left [{I}{C}-{F}{D}{C}\right ]&amp;={k}_{{d}{e}{p}{o}{s}{i}{t}}\left [{I}{C}\right ]\\&amp;-{d}_{{I}{C}}\left [{I}{C}-{F}{D}{C}\right]\end{array}$\end{document}</tex-math></alternatives></inline-formula><break/></td><td align="left" valign="top"><inline-formula><alternatives><mml:math id="inf35"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mi>I</mml:mi><mml:mi>C</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>I</mml:mi><mml:mi>C</mml:mi><mml:mo>−</mml:mo><mml:mi>F</mml:mi><mml:mi>D</mml:mi><mml:mi>C</mml:mi></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft35">\begin{document}$IC\rightarrow IC-FDC$\end{document}</tex-math></alternatives></inline-formula><break/><break/><inline-formula><alternatives><mml:math id="inf36"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mi>I</mml:mi><mml:mi>C</mml:mi><mml:mo>−</mml:mo><mml:mi>F</mml:mi><mml:mi>D</mml:mi><mml:mi>C</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mrow><mml:mi>∅</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft36">\begin{document}$IC-FDC\rightarrow {\varnothing }$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="top">Immune complex transport to follicular dendritic cells<break/><break/>Deposition and decay of antigen on follicular dendritic cells</td></tr><tr><td align="left" valign="top"><inline-formula><alternatives><mml:math id="inf37"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi mathvariant="normal">∂</mml:mi><mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft37">\begin{document}$\partial _{{t}}\left [{I}{g}\right ]={k}_{{I}{g}}\left [{P}{C}\right ]-{d}_{{I}{g}}\left [{I}{g}\right ]$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="top"><inline-formula><alternatives><mml:math id="inf38"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mo stretchy="false">→</mml:mo><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft38">\begin{document}${P}{C}\rightarrow {P}{C}+{I}{g}$\end{document}</tex-math></alternatives></inline-formula><break/><break/><inline-formula><alternatives><mml:math id="inf39"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mo stretchy="false">→</mml:mo><mml:mrow><mml:mi>∅</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft39">\begin{document}${I}{g}\rightarrow {\varnothing }$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="top">Antibody production by plasma cells<break/>Decay of free soluble antigen</td></tr><tr><td align="left" valign="top"><inline-formula><alternatives><mml:math id="inf40"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi mathvariant="normal">∂</mml:mi><mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow></mml:msubsup><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft40">\begin{document}$\partial _{{t}}{K}_{{a}}=\frac{\left ({K}_{{a}}^{{P}{C}}-{K}_{{a}}\right){k}_{{I}{g}}\left [{P}{C}\right ]}{\left [{I}{g}\right ]+\left [{I}{C}\right ]}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="top">-</td><td align="left" valign="top">Derived from equations above, as detailed in supplement of <xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>.</td></tr></tbody></table></table-wrap><p>For the deposition of antigen on FDCs, it is assumed that the antibodies that bind to and deposit antigen have the same average antigen affinity and numbers as those whose evolution we explicitly simulate. The parameters used in these equations can be found in <xref ref-type="table" rid="app1table2">Appendix 1—table 2</xref> and are identical to our previous publication (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>). Upon the first vaccination, only weakly binding antibodies are available for binding to soluble antigen and depositing ICs onto FDCs. After subsequent vaccinations, antigen-specific antibodies are available.</p></sec><sec id="s4-3-4-2"><title>B cell dynamics in GCs and EGCs</title><p>Each GC is associated with a pool of 2000 naive B cells (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>). This estimate was based on estimating the number of germline B cells that target SARS-CoV-2, and we used the same number. Ideally, we would use values for HA if these measurements were available. A fraction <inline-formula><alternatives><mml:math id="inf41"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft41">\begin{document}${p}_{{i}}$\end{document}</tex-math></alternatives></inline-formula> of these naive B cells targets epitope <inline-formula><alternatives><mml:math id="inf42"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft42">\begin{document}${i}$\end{document}</tex-math></alternatives></inline-formula>. We model 3 epitopes of the influenza spike protein, which is an increase from the 2 epitopes previously used to model the SARS-CoV-2 spike protein (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>). This allows us to better account for the diversity in influenza strains, each with distinct epitopes that may be conserved with the H1N1 CA09 vaccine strain (see main text).</p><p>The germline binding affinities <inline-formula><alternatives><mml:math id="inf43"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft43">\begin{document}${E}=-{\rm log} \left ({K}_{{d}}\right)$\end{document}</tex-math></alternatives></inline-formula> of the naive B cells for the vaccine strain have discrete values between 6 and 8, expressed as <inline-formula><alternatives><mml:math id="inf44"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>6</mml:mn><mml:mo>+</mml:mo><mml:mn>0.287</mml:mn><mml:mspace width="thinmathspace"/><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft44">\begin{document}${E}_{{k}}=6+0.287\,{k}$\end{document}</tex-math></alternatives></inline-formula> for <inline-formula><alternatives><mml:math id="inf45"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thinmathspace"/><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width="thinmathspace"/><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mspace width="thinmathspace"/><mml:mn>10</mml:mn></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft45">\begin{document}${k}=0,\, 1,\,\ldots ,\,10$\end{document}</tex-math></alternatives></inline-formula>. The lower value of 6 was chosen based on data as described in the main text, and germline affinities that are one hundred times greater have also been observed (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>). The frequency of naive B cells targeting epitope <inline-formula><alternatives><mml:math id="inf46"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft46">\begin{document}${i}$\end{document}</tex-math></alternatives></inline-formula> in the affinity bin <inline-formula><alternatives><mml:math id="inf47"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft47">\begin{document}${E}_{{k}}$\end{document}</tex-math></alternatives></inline-formula> is a truncated geometric distribution and is determined as follows:<disp-formula id="equ1"><alternatives><mml:math id="m1"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mfrac><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mrow><mml:munder><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:munder><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mstyle></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t1">\begin{document}$$\displaystyle  {f}_{{i}}\left ({E}_{{k}}\right)={N}_{{n}{a}{i}{v}{e}}{p}_{{i}}\frac{{e}^{-{r}_{{i}}\left ({E}_{{k}}-{E}_{0}\right)}}{\underset{{k}}{\sum }{e}^{-{r}_{{i}}\left ({E}_{{k}}-{E}_{0}\right)}}$$\end{document}</tex-math></alternatives></disp-formula></p><p>where the number of naive B cells <inline-formula><alternatives><mml:math id="inf48"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft48">\begin{document}${N}_{{n}{a}{i}{v}{e}}$\end{document}</tex-math></alternatives></inline-formula> is 2000 and the minimum germline affinity <inline-formula><alternatives><mml:math id="inf49"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft49">\begin{document}${E}_{0}$\end{document}</tex-math></alternatives></inline-formula> is 6 in these simulations. <inline-formula><alternatives><mml:math id="inf50"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft50">\begin{document}${r}_{{i}}$\end{document}</tex-math></alternatives></inline-formula> is determined such that<disp-formula id="equ2"><alternatives><mml:math id="m2"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t2">\begin{document}$$\displaystyle {f}_{{i}}\left ({E}_{{i}}^{{*}}\right)={p}_{{i}}$$\end{document}</tex-math></alternatives></disp-formula></p><p>where <inline-formula><alternatives><mml:math id="inf51"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft51">\begin{document}${E}_{{i}}^{{*}}$\end{document}</tex-math></alternatives></inline-formula> is defined as follows using the parameters <inline-formula><alternatives><mml:math id="inf52"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft52">\begin{document}${E}_{1}^{{h}}$\end{document}</tex-math></alternatives></inline-formula>, <inline-formula><alternatives><mml:math id="inf53"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft53">\begin{document}${d}{E}_{12}$\end{document}</tex-math></alternatives></inline-formula>, and <inline-formula><alternatives><mml:math id="inf54"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft54">\begin{document}${d}{E}_{13}$\end{document}</tex-math></alternatives></inline-formula>:<disp-formula id="equ3"><alternatives><mml:math id="m3"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t3">\begin{document}$$\displaystyle {E}_{1}^{{*}}={E}_{1}^{{h}}$$\end{document}</tex-math></alternatives></disp-formula><disp-formula id="equ4"><alternatives><mml:math id="m4"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:mrow></mml:msubsup><mml:mo>−</mml:mo><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t4">\begin{document}$$\displaystyle {E}_{2}^{{*}}={E}_{1}^{{h}}-{d}{E}_{12}$$\end{document}</tex-math></alternatives></disp-formula><disp-formula id="equ5"><alternatives><mml:math id="m5"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:mrow></mml:msubsup><mml:mo>−</mml:mo><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t5">\begin{document}$$\displaystyle {E}_{3}^{{*}}={E}_{1}^{{h}}-{d}{E}_{13}$$\end{document}</tex-math></alternatives></disp-formula></p><p>The parameters are set such that <inline-formula><alternatives><mml:math id="inf55"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>&gt;</mml:mo><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>&gt;</mml:mo><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mo>∗</mml:mo></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft55">\begin{document}${E}_{1}^*\gt {E}_{2}^*\gt {E}_{3}^*$\end{document}</tex-math></alternatives></inline-formula>, reflecting the generally higher affinities for more dominant epitopes. The immunodominance hierarchy is further modeled by setting, <inline-formula><alternatives><mml:math id="inf56"><mml:mstyle><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>&gt;</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>&gt;</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mstyle></mml:math><tex-math id="inft56">\begin{document}$p_1 \gt p_2 \gt p_3 $\end{document}</tex-math></alternatives></inline-formula> meaning that more dominant epitopes are targeted by a greater number of naive B cells.</p><p>Since individuals initially have a weak response (subdominant) against historical influenza strains, the germline-binding affinity of all naive B cells that target the epitopes that are conserved between the vaccinating strain and historical strains is set to the lowest possible germline affinity in these simulations (<inline-formula><alternatives><mml:math id="inf57"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>6</mml:mn></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft57">\begin{document}${E}=6$\end{document}</tex-math></alternatives></inline-formula>).</p><p>After initializing the pool of naive B cells, the B cells can be stochastically activated. The probability of activation for a naive B cell depends on the quantity of vaccine antigen it captures as it is influenced by the binding affinity of its BCR for antigen, which is determined by both the antigen concentration and binding affinity to the vaccine strain. The amount of antigen captured by B cell <italic>j</italic> is modeled as<disp-formula id="equ6"><alternatives><mml:math id="m6"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mfrac><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo movablelimits="true" form="prefix">min</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width="thinmathspace"/><mml:mn>10</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:mrow></mml:msup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t6">\begin{document}$$\displaystyle {A}_{{j}}=\left (\frac{{C}}{{C}_{0}}10^{\min \left ({E}_{{j}},\, 10\right)-{E}_{0}}\right)^{{K}}$$\end{document}</tex-math></alternatives></disp-formula></p><p>where <inline-formula><alternatives><mml:math id="inf58"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft58">\begin{document}${C}$\end{document}</tex-math></alternatives></inline-formula> is the effective antigen concentration, <inline-formula><alternatives><mml:math id="inf59"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft59">\begin{document}${C}_{0}$\end{document}</tex-math></alternatives></inline-formula> is the reference antigen concentration, <inline-formula><alternatives><mml:math id="inf60"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft60">\begin{document}${E}_{{j}}$\end{document}</tex-math></alternatives></inline-formula> is the B cell’s binding affinity for its epitope, <inline-formula><alternatives><mml:math id="inf61"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft61">\begin{document}${E}_{0}$\end{document}</tex-math></alternatives></inline-formula> is the reference affinity, and <inline-formula><alternatives><mml:math id="inf62"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft62">\begin{document}${K}$\end{document}</tex-math></alternatives></inline-formula> is a measure of the selection stringency. The effective antigen concentration is <inline-formula><alternatives><mml:math id="inf63"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>0.01</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mo>−</mml:mo><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft63">\begin{document}${C}=0.01\left (\left [{A}{g}\right ]+\left [{I}{C}\right ]\right)+\left [{I}{C}-{F}{D}{C}\right ]$\end{document}</tex-math></alternatives></inline-formula>, reflecting that antigens presented on FDCs are more potent at activating B cells (<xref ref-type="bibr" rid="bib53">Kim et al., 2006</xref>). The selection stringency <inline-formula><alternatives><mml:math id="inf64"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft64">\begin{document}${K}$\end{document}</tex-math></alternatives></inline-formula> represents how sensitive the amount of antigen captured is to small differences in antigen concentration or binding affinity. The probability of activation is <inline-formula><alternatives><mml:math id="inf65"><mml:mstyle><mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mspace width="thinmathspace"/><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>l</mml:mi><mml:mi>l</mml:mi><mml:mspace width="thinmathspace"/><mml:mi>j</mml:mi><mml:mspace width="thinmathspace"/><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mspace width="thinmathspace"/><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math><tex-math id="inft65">\begin{document}$P\left(B\, cell\, j\, is\, activated \right) ={\rm min}\left(A_j, 1\right) $\end{document}</tex-math></alternatives></inline-formula>. The approach described above is used to calculate <inline-formula><alternatives><mml:math id="inf66"><mml:mstyle><mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mspace width="thinmathspace"/><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>l</mml:mi><mml:mi>l</mml:mi><mml:mspace width="thinmathspace"/><mml:mi>j</mml:mi><mml:mspace width="thinmathspace"/><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mspace width="thinmathspace"/><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:math><tex-math id="inft66">\begin{document}$P\left(B\, cell\, j\, is\, activated \right) ={\rm min}\left(A_j, 1\right) $\end{document}</tex-math></alternatives></inline-formula> both for GC entry and inside the GC.</p><p>For GC entry, activated B cells can stochastically enter the GC. Entry into the GC depends on antigen captured and competition for limited T cell help (<xref ref-type="bibr" rid="bib59">Lee et al., 2021</xref>; <xref ref-type="bibr" rid="bib95">Schwickert et al., 2011</xref>). The rate of entry for an activated B cell <italic>j</italic> is<disp-formula id="equ7"><alternatives><mml:math id="m7"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msub><mml:mrow><mml:mi>λ</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mfrac><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mfrac><mml:mfrac><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>⟨</mml:mo><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mo>⟩</mml:mo></mml:mrow></mml:mfrac></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mfrac><mml:mfrac><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>⟨</mml:mo><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mo>⟩</mml:mo></mml:mrow></mml:mfrac></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t7">\begin{document}$$\displaystyle {\lambda }_{{j}}=\frac{\frac{{N}_{{m}{a}{x}}}{{N}_{{a}{c}{t}{i}{v}{a}{t}{e}{d}}}\frac{{A}_{{j}}}{\left \langle {A}\right \rangle }}{1+\frac{{N}_{{m}{a}{x}}}{{N}_{{a}{c}{t}{i}{v}{a}{t}{e}{d}}}\frac{{A}_{{j}}}{\left \langle {A}\right \rangle }}$$\end{document}</tex-math></alternatives></disp-formula></p><p>where <inline-formula><alternatives><mml:math id="inf67"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft67">\begin{document}${N}_{{a}{c}{t}{i}{v}{a}{t}{e}{d}}$\end{document}</tex-math></alternatives></inline-formula> is the number of activated B cells, <inline-formula><alternatives><mml:math id="inf68"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft68">\begin{document}${N}_{{m}{a}{x}}$\end{document}</tex-math></alternatives></inline-formula> is the capacity for GC entry based on limited T cell help, and <inline-formula><alternatives><mml:math id="inf69"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mo>⟨</mml:mo><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mo>⟩</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft69">\begin{document}$\left \langle {A}\right \rangle $\end{document}</tex-math></alternatives></inline-formula> is the average amount of antigen captured by all B cells. Thus, <inline-formula><alternatives><mml:math id="inf70"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mfrac></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft70">\begin{document}$\frac{{N}_{{m}{a}{x}}}{{N}_{{a}{c}{t}{i}{v}{a}{t}{e}{d}}}$\end{document}</tex-math></alternatives></inline-formula> represents the competition between B cells for T cell help and <inline-formula><alternatives><mml:math id="inf71"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>⟨</mml:mo><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mo>⟩</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft71">\begin{document}$\frac{{A}_{{j}}}{\left \langle {A}\right \rangle }$\end{document}</tex-math></alternatives></inline-formula> represents the competitive advantage of a particular B cell <italic>j</italic> over other cells. The probability of GC entry is <inline-formula><alternatives><mml:math id="inf72"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mspace width="thinmathspace"/><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mspace width="thinmathspace"/><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mspace width="thinmathspace"/><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mspace width="thinmathspace"/><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>λ</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:msup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft72">\begin{document}${P}\left ({B}\,{c}{e}{l}{l}\,{j}\,{e}{n}{t}{e}{r}{s}\,{G}{C}\right)=1-{e}^{-{\lambda }_{{j}}{d}{t}}$\end{document}</tex-math></alternatives></inline-formula>.</p><p>After internalizing antigen and displaying pMHC molecules on the surface, GC B cells compete for T cell help to become stochastically activated. The rate of positive selection is<disp-formula id="equ8"><alternatives><mml:math id="m8"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msub><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mfrac><mml:mrow><mml:mfrac><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mfrac><mml:mfrac><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>⟨</mml:mo><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mo>⟩</mml:mo></mml:mrow></mml:mfrac></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mfrac><mml:mfrac><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>⟨</mml:mo><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mo>⟩</mml:mo></mml:mrow></mml:mfrac></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t8">\begin{document}$$\displaystyle {\beta }_{{j}}={\beta }_{{m}{a}{x}}\frac{\frac{{N}_{{T}}}{{N}_{{a}{c}{t}{i}{v}{a}{t}{e}{d}}}\frac{{A}_{{j}}}{\left \langle {A}\right \rangle }}{1+\frac{{N}_{{T}}}{{N}_{{a}{c}{t}{i}{v}{a}{t}{e}{d}}}\frac{{A}_{{j}}}{\left \langle {A}\right \rangle }}$$\end{document}</tex-math></alternatives></disp-formula></p><p>where <inline-formula><alternatives><mml:math id="inf73"><mml:msub><mml:mrow><mml:mi mathvariant="normal">β</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">x</mml:mi></mml:mrow></mml:msub></mml:math><tex-math id="inft73">\begin{document}${\beta }_{{m}{a}{x}}$\end{document}</tex-math></alternatives></inline-formula> is the maximum rate of positive selection, <inline-formula><alternatives><mml:math id="inf74"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft74">\begin{document}${N}_{{a}{c}{t}{i}{v}{a}{t}{e}{d}}$\end{document}</tex-math></alternatives></inline-formula> is the number of activated B cells, and <inline-formula><alternatives><mml:math id="inf75"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft75">\begin{document}${N}_{{T}}$\end{document}</tex-math></alternatives></inline-formula> is the number of helper T cells. We model the number of helper T cells <inline-formula><alternatives><mml:math id="inf76"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft76">\begin{document}${N}_{{T}}$\end{document}</tex-math></alternatives></inline-formula> as a simple linear growth until time <inline-formula><alternatives><mml:math id="inf77"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft77">\begin{document}${t}_{0},$\end{document}</tex-math></alternatives></inline-formula> when the number of helper T cells has a peak level of <inline-formula><alternatives><mml:math id="inf78"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft78">\begin{document}${N}_{{T}0}$\end{document}</tex-math></alternatives></inline-formula>, and as first-order decay with decay rate <inline-formula><alternatives><mml:math id="inf79"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft79">\begin{document}${d}_{{T}}$\end{document}</tex-math></alternatives></inline-formula> after <inline-formula><alternatives><mml:math id="inf80"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft80">\begin{document}${t}_{0}$\end{document}</tex-math></alternatives></inline-formula>:<disp-formula id="equ9"><alternatives><mml:math id="m9"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mspace width="thinmathspace"/><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>&lt;</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mspace width="thinmathspace"/><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>&gt;</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"/></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t9">\begin{document}$$\displaystyle {N}_{{T}}=\begin{cases} {N}_{{T}0}\,{t}/{t}_{0},t\lt {t}_{0}\\{N}_{{T}0}\,{e}^{-{d}_{{T}}\left ({t}-{t}_{0}\right)}, t\gt {t}_{0}\end{cases} $$\end{document}</tex-math></alternatives></disp-formula></p><p>If a B cell is positively selected, it exits the GC with probability <inline-formula><alternatives><mml:math id="inf81"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft81">\begin{document}${p}_{{e}{x}{i}{t}}$\end{document}</tex-math></alternatives></inline-formula> or is recycled for mutation-selection cycles in the GC with probability <inline-formula><alternatives><mml:math id="inf82"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft82">\begin{document}$1-{p}_{{e}{x}{i}{t}}$\end{document}</tex-math></alternatives></inline-formula>. If the B cell exits, it becomes a plasma cell with probability <inline-formula><alternatives><mml:math id="inf83"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft83">\begin{document}${p}_{{p}{l}{a}{s}{m}{a}}$\end{document}</tex-math></alternatives></inline-formula> or a memory cell with probability <inline-formula><alternatives><mml:math id="inf84"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft84">\begin{document}$1-{p}_{{p}{l}{a}{s}{m}{a}}$\end{document}</tex-math></alternatives></inline-formula>. If the B cell proliferates, one of the daughter cells mutates. The mutation may change affinity (probability 0.2), result in apoptosis (probability 0.3), or be silent (<xref ref-type="bibr" rid="bib123">Zhang and Shakhnovich, 2010</xref>).</p><p>Each B cell has a string of 0 and 1 s for the residues on the paratope with a total length of <inline-formula><alternatives><mml:math id="inf85"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft85">\begin{document}${n}_{{r}{e}{s}}$\end{document}</tex-math></alternatives></inline-formula>. The string of residues starts as all 0 s in a naive B cell. When there is an affinity-changing mutation, one of the bits (residues) is randomly chosen and flipped. The change in affinity is drawn from a shifted log-normal distribution, independently for each residue (<xref ref-type="bibr" rid="bib57">Kumar and Gromiha, 2006</xref>; <xref ref-type="bibr" rid="bib123">Zhang and Shakhnovich, 2010</xref>). The affinity (binding free energy) of a B cell <italic>j</italic> targeting a particular epitope, which may or may not be conserved in different strains, is determined by both the germline affinity and affinity-changing mutations, as follows (<inline-formula><alternatives><mml:math id="inf86"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft86">\begin{document}${E}_{{j}}^{{s}{t}{r}{a}{i}{n}}$\end{document}</tex-math></alternatives></inline-formula> refers to the affinity of B cell <italic>j</italic> targeting a particular epitope on strain, <italic>j</italic>):<disp-formula id="equ10"><alternatives><mml:math id="m10"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mi>δ</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:msubsup><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mstyle></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t10">\begin{document}$$\displaystyle  {E}_{{j}}^{{s}{t}{r}{a}{i}{n}}={E}_{{j}}^{0,{s}{t}{r}{a}{i}{n}}+\sum \limits_{{k}=0}^{{n}_{{r}{e}{s}}}{\delta }_{{j},{k}}{s}_{{j},{k}}^{{s}{t}{r}{a}{i}{n}}$$\end{document}</tex-math></alternatives></disp-formula></p><p>where <inline-formula><alternatives><mml:math id="inf87"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft87">\begin{document}${E}_{{j}}^{0,{s}{t}{r}{a}{i}{n}}$\end{document}</tex-math></alternatives></inline-formula> is the germline affinity, <inline-formula><alternatives><mml:math id="inf88"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>δ</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>∈</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft88">\begin{document}${\delta }_{{j},{k}}\in \left \{0,1\right \}$\end{document}</tex-math></alternatives></inline-formula> is the mutational state of residue <inline-formula><alternatives><mml:math id="inf89"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft89">\begin{document}${k}$\end{document}</tex-math></alternatives></inline-formula>, and <inline-formula><alternatives><mml:math id="inf90"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft90">\begin{document}${s}_{{j},{k}}^{{s}{t}{r}{a}{i}{n}}$\end{document}</tex-math></alternatives></inline-formula> is the change in affinity due to a mutation at residue <inline-formula><alternatives><mml:math id="inf91"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft91">\begin{document}${k}$\end{document}</tex-math></alternatives></inline-formula>. <inline-formula><alternatives><mml:math id="inf92"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft92">\begin{document}${s}_{{j},{k}}^{{s}{t}{r}{a}{i}{n}}$\end{document}</tex-math></alternatives></inline-formula> is correlated between different strains to different extents depending upon the degree of conservation of the epitope under consideration in these strains (<inline-formula><alternatives><mml:math id="inf93"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft93">\begin{document}${s}_{{j},{k}}^{1}$\end{document}</tex-math></alternatives></inline-formula> is the change in affinity for the epitope in strain 1, <inline-formula><alternatives><mml:math id="inf94"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft94">\begin{document}${s}_{{j},{k}}^{2}$\end{document}</tex-math></alternatives></inline-formula> is the change in affinity for the epitope in strain 2, and so on). The values of <inline-formula><alternatives><mml:math id="inf95"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mi>s</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft95">\begin{document}$s_{j,k}^{strain}$\end{document}</tex-math></alternatives></inline-formula> are drawn from identical log-normal distributions that are correlated as follows:<disp-formula id="equ11"><alternatives><mml:math id="m11"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msubsup><mml:mi>s</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:msubsup><mml:mi>s</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:msubsup><mml:mi>s</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>∼</mml:mo><mml:mo>−</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:msub><mml:mi mathvariant="normal">g</mml:mi><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>μ</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi>σ</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi mathvariant="normal">Σ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mi>ϵ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t11">\begin{document}$$\displaystyle \left [s_{j,k}^{1},{\, }s_{j,k}^{2},{\, }s_{j,k}^{3}\right ]\sim -\left (\rm log_{10}e\right){\, }\left (e^{N\left (\mu ,\sigma ^{2}\Sigma \right)}-\epsilon \right)$$\end{document}</tex-math></alternatives></disp-formula><disp-formula id="equ12"><alternatives><mml:math id="m12"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mtable columnalign="center center center" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mn>1</mml:mn></mml:mtd><mml:mtd><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mn>1</mml:mn></mml:mtd><mml:mtd><mml:mn>0</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mn>0</mml:mn></mml:mtd><mml:mtd><mml:mn>1</mml:mn></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t12">\begin{document}$$\displaystyle \Sigma =\left [\begin{array}{ccc}1 &amp; \rho _{12} &amp; \rho _{13}\\\rho _{12} &amp; 1 &amp; 0\\\rho _{13} &amp; 0 &amp; 1\end{array}\right ]$$\end{document}</tex-math></alternatives></disp-formula></p><p>where <inline-formula><alternatives><mml:math id="inf96"><mml:mstyle><mml:mrow><mml:mi>μ</mml:mi><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:mi>σ</mml:mi><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:mi>ϵ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft96">\begin{document}$\mu ,{\, }\sigma ,{\, }\epsilon $\end{document}</tex-math></alternatives></inline-formula> were chosen such that only ~5% of affinity-changing mutations are beneficial, as shown in experimental studies (<xref ref-type="bibr" rid="bib33">DeWitt et al., 2025</xref>; <xref ref-type="bibr" rid="bib57">Kumar and Gromiha, 2006</xref>; <xref ref-type="bibr" rid="bib123">Zhang and Shakhnovich, 2010</xref>). <inline-formula><alternatives><mml:math id="inf97"><mml:mi>Σ</mml:mi></mml:math><tex-math id="inft97">\begin{document}$\Sigma $\end{document}</tex-math></alternatives></inline-formula> is the correlation matrix and <inline-formula><alternatives><mml:math id="inf98"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:math><tex-math id="inft98">\begin{document}$\rho _{12}$\end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math id="inf99"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:math><tex-math id="inft99">\begin{document}$\rho _{13}$\end{document}</tex-math></alternatives></inline-formula> parameterize the correlation of affinity changes between strains 1 and 2 and strains 1 and 3, respectively. The level of correlation is related to the level of conservation between the strains for B cell <italic>j</italic>’s target epitope, as described in the main text. We only consider correlation between the vaccine strain (strain 1) and historical strains (strains 2 and 3), but not between strains 2 and 3. Since B cells are selected for their affinity to strain 1, the correlation between strains 2 and 3 does not impact the nature of the antibody or memory B cell response.</p><p>In this study, we considered the correlation between three strains compared to two strains in our COVID model (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>) since we examined the effect of sequential immunization on B cell responses against multiple unmatched influenza strains.</p><p>After the first immunization, pre-existing memory cells stochastically expand and differentiate. About 60% of newly proliferating memory cells become short-lived plasma cells that secrete antibodies (<xref ref-type="bibr" rid="bib68">Moran et al., 2018</xref>). Memory cells can be activated whenever they encounter antigen, including at the T-B border, sub-capsular proliferative foci, medullar niches of the lymph node and spleen, and in the bone marrow (<xref ref-type="bibr" rid="bib68">Moran et al., 2018</xref>; <xref ref-type="bibr" rid="bib102">Syeda et al., 2024</xref>). Many types of antigen-presenting cells (APCs) can participate in this process. We coarse-grain these APCs into one cell type and call it ‘FDCs’. Memory B cell expansion is also known to be T helper-cell dependent (<xref ref-type="bibr" rid="bib102">Syeda et al., 2024</xref>). We refer to all locations outside GCs where memory cells are expanded in an antigen and T helper cell-dependent way as the EGC. In the EGC, the memory cells are selected for expansion in the same affinity-dependent way as GC B cells, except memory cells do not undergo mutation in our model. The number of helper T cells is set to its maximum value to reflect the faster kinetics of the EGC in the context of SARS-CoV-2 (<xref ref-type="bibr" rid="bib46">Goel et al., 2021</xref>; <xref ref-type="bibr" rid="bib69">Moran et al., 2019</xref>).</p></sec><sec id="s4-3-4-3"><title>Epitope masking</title><p>When epitope masking is considered, GC B cells specific for a particular epitope cannot capture antigen on FDCs if that epitope is bound to circulating antibodies. These circulating antibodies are produced by plasma cells from previous immunizations and expansion and differentiation of memory cells from previous immunizations. The amount of bound antigen is calculated using fast equilibrium of receptor–ligand binding:<disp-formula id="equ13"><alternatives><mml:math id="m13"><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:msub><mml:mrow><mml:mi>A</mml:mi><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>-</mml:mo><mml:mfenced separators="|"><mml:mrow><mml:mfenced open="[" close="]" separators="|"><mml:mrow><mml:mi>A</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mfenced open="[" close="]" separators="|"><mml:mrow><mml:mi>I</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi mathvariant="normal">*</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="normal">*</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mfenced><mml:mfenced open="[" close="]" separators="|"><mml:mrow><mml:msub><mml:mrow><mml:mi>A</mml:mi><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced open="[" close="]" separators="|"><mml:mrow><mml:mi>A</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:mfenced><mml:msup><mml:mrow><mml:mfenced open="[" close="]" separators="|"><mml:mrow><mml:mi>I</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi mathvariant="normal">*</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math><tex-math id="t13">\begin{document}$$\displaystyle \left [Ag_{masked}\right ]^{2}-\left (\left [Ag\right ]+\left [Ig\right ]^{{*}}+K_{d}^{{*}}\right)\left [Ag_{masked}\right ]+\left [Ag\right ]\left [Ig\right ]^{{*}}=0$$\end{document}</tex-math></alternatives></disp-formula></p><p>where <inline-formula><alternatives><mml:math id="inf100"><mml:mo>[</mml:mo><mml:msub><mml:mrow><mml:mi>A</mml:mi><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:math><tex-math id="inft100">\begin{document}$\left [Ag_{masked}\right ]$\end{document}</tex-math></alternatives></inline-formula> is the concentration of masked (i.e. bound, antigen), <inline-formula><alternatives><mml:math id="inf101"><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mi>I</mml:mi><mml:mi>g</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="normal">*</mml:mi></mml:mrow></mml:msup></mml:math><tex-math id="inft101">\begin{document}$\left [Ig\right ]^{{*}}$\end{document}</tex-math></alternatives></inline-formula> is the total effective antibody concentration before masking, [Ag] is the total antigen concentration before masking, and <inline-formula><alternatives><mml:math id="inf102"><mml:msup><mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="normal">*</mml:mi></mml:mrow></mml:msup></mml:math><tex-math id="inft102">\begin{document}$K_{d}^{{*}}$\end{document}</tex-math></alternatives></inline-formula> is the effective average dissociation constant. The values in the equation above are calculated separately for each epitope. When we do not consider epitope overlap, <inline-formula><alternatives><mml:math id="inf103"><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mi>I</mml:mi><mml:mi>g</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="normal">*</mml:mi></mml:mrow></mml:msup></mml:math><tex-math id="inft103">\begin{document}$\left [Ig\right ]^{{*}}$\end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math id="inf104"><mml:msup><mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="normal">*</mml:mi></mml:mrow></mml:msup></mml:math><tex-math id="inft104">\begin{document}$K_{d}^{{*}}$\end{document}</tex-math></alternatives></inline-formula> are exactly the concentration of antibodies targeting a particular epitope and the average dissociation constant of those antibodies. In the presence of epitope overlap, some antibodies can mask epitopes that spatially overlap with their primary target. In this case<disp-formula id="equ14"><alternatives><mml:math id="m14"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mo>[</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mtable columnalign="center center center" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mn>1</mml:mn></mml:mtd><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mn>1</mml:mn></mml:mtd><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>23</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>23</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mn>1</mml:mn></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t14">\begin{document}$$\displaystyle \left [\begin{array}{c}\left [{I}{g}_{1}\right ]^{{*}}\\\left [{I}{g}_{2}\right ]^{{*}}\\\left [{I}{g}_{3}\right ]^{{*}}\end{array}\right ]=\left [\begin{array}{ccc}1 &amp; {q}_{12} &amp; {q}_{13}\\{q}_{12} &amp; 1 &amp; {q}_{23}\\{q}_{13} &amp; {q}_{23} &amp; 1\end{array}\right ]\left [\begin{array}{c}\left [{I}{g}_{1}\right ]\\\left [{I}{g}_{2}\right ]\\\left [{I}{g}_{3}\right ]\end{array}\right ]$$\end{document}</tex-math></alternatives></disp-formula></p><p>where <inline-formula><alternatives><mml:math id="inf105"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft105">\begin{document}$\left [{I}{g}_{{i}}\right ]^{{*}}$\end{document}</tex-math></alternatives></inline-formula> is the effective concentration of antibodies targeting epitope <inline-formula><alternatives><mml:math id="inf106"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft106">\begin{document}${i}$\end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math id="inf107"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft107">\begin{document}$\left [{I}{g}_{1}\right ]$\end{document}</tex-math></alternatives></inline-formula> is the actual concentration of antibodies targeting epitope <inline-formula><alternatives><mml:math id="inf108"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft108">\begin{document}${i}$\end{document}</tex-math></alternatives></inline-formula>. <inline-formula><alternatives><mml:math id="inf109"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft109">\begin{document}${q}_{{m}{n}}$\end{document}</tex-math></alternatives></inline-formula> describes the overlap between epitope <inline-formula><alternatives><mml:math id="inf110"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft110">\begin{document}${m}$\end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math id="inf111"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft111">\begin{document}${n}$\end{document}</tex-math></alternatives></inline-formula> and is the fraction of antibodies targeting epitope <inline-formula><alternatives><mml:math id="inf112"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft112">\begin{document}${m}$\end{document}</tex-math></alternatives></inline-formula> that can mask epitope <inline-formula><alternatives><mml:math id="inf113"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft113">\begin{document}${n}$\end{document}</tex-math></alternatives></inline-formula> (and vice versa). The effective average dissociation constant <inline-formula><alternatives><mml:math id="inf114"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft114">\begin{document}${K}_{{d},{\, }{i}}^{{*}}$\end{document}</tex-math></alternatives></inline-formula> is calculated similarly:<disp-formula id="equ15"><alternatives><mml:math id="m15"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mo>[</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mtable columnalign="center center center" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mn>1</mml:mn></mml:mtd><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mn>1</mml:mn></mml:mtd><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>23</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>23</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mn>1</mml:mn></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thinmathspace"/></mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo>]</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t15">\begin{document}$$\displaystyle \left [\begin{array}{c}\left [{I}{g}_{1}\right ]^{{*}}/{K}_{{d},{\, }1}^{{*}}\\\left [{I}{g}_{2}\right ]^{{*}}/{K}_{{a},{\, }2}^{{*}}\\\left [{I}{g}_{3}\right ]^{{*}}/{K}_{{a},{\, }3}^{{*}}\end{array}\right ]=\left [\begin{array}{ccc}1 &amp; {q}_{12} &amp;{q}_{13}\\{q}_{12} &amp; 1 &amp; {q}_{23}\\{q}_{13} &amp; {q}_{23} &amp; 1\end{array}\right ]\left [\begin{array}{c}\left [{I}{g}_{1}\right ]/{K}_{{d},{\, }1}\\\left [{I}{g}_{2}\right ]/{K}_{{d},{\, }2}\\\left [{I}{g}_{3}\right ]/{K}_{{d},{\, }3}\end{array}\right ]$$\end{document}</tex-math></alternatives></disp-formula></p><p>The concentration of bound antigen <inline-formula><alternatives><mml:math id="inf115"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft115">\begin{document}$\left [{A}{g}_{{m}{a}{s}{k}{e}{d}}\right ]$\end{document}</tex-math></alternatives></inline-formula> is then calculated and subtracted from the total antigen concentration since bound antigen cannot be seen by B cells. The resulting antigen concentration is then scaled such that the fraction of soluble antigen and fraction of antigen on the FDC match those fractions before epitope masking is not considered.</p></sec><sec id="s4-3-4-4"><title>Modifications to the original model</title><p>As a summary, the revised model includes three epitopes instead of two epitopes and considers three strains instead of two. This manifests in the distribution of naive B cells’ germline affinities, the effective antigen concentration in epitope masking, and the correlated affinity changes in the GC. Using multiple epitopes and strains accounts for the diversity in influenza strains, each with distinct epitopes that may be conserved with the vaccine strain. By examining the relationships between multiple epitopes and strains, we gained general insights into factors that affect the number of immunizations needed to achieve a given level of coverage for historical and emergent strains, as detailed in the main text.</p></sec></sec></sec></sec></body><back><sec sec-type="additional-information" id="s5"><title>Additional information</title><fn-group content-type="competing-interest"><title>Competing interests</title><fn fn-type="COI-statement" id="conf1"><p>No competing interests declared</p></fn><fn fn-type="COI-statement" id="conf2"><p>consultant for Flagship Pioneering, and it's affiliated company Aprioi Bio. He owns equity in these companies, and Metaphore Bio and Dewpoint Therapeutics</p></fn><fn fn-type="COI-statement" id="conf3"><p>reports consulting activities for Metaphore Bio (a Flagship company), Tendel Therapies, Lattice Therapeutics Inc and BioMed X</p></fn></fn-group><fn-group content-type="author-contribution"><title>Author contributions</title><fn fn-type="con" id="con1"><p>Formal analysis, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing</p></fn><fn fn-type="con" id="con2"><p>Formal analysis, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing</p></fn><fn fn-type="con" id="con3"><p>Data curation, Writing – review and editing</p></fn><fn fn-type="con" id="con4"><p>Visualization, Writing – review and editing</p></fn><fn fn-type="con" id="con5"><p>Conceptualization, Resources, Supervision, Funding acquisition, Writing – original draft, Project administration, Writing – review and editing</p></fn><fn fn-type="con" id="con6"><p>Conceptualization, Resources, Supervision, Funding acquisition, Writing – original draft, Project administration, Writing – review and editing</p></fn></fn-group><fn-group content-type="ethics-information"><title>Ethics</title><fn fn-type="other"><p>This study uses de-identified data from a vaccine trial previously published by Nunez et al. (2017). The ethics approval statement for the vaccine trial is stated in that publication was as follows: The study procedures, informed consent, and data collection documents were reviewed and approved by was approved by the Western Institutional Review Board and the Institutional Review Boards of the University of Pittsburgh and the University of Georgia. Informed written consent was obtained from the parents/guardians of the children. The IRB number: WCG1292448. Notably, the study of Nunez et al. (2017) used commercial influenza vaccines and therefore does not fall under the Clinical Trials guidelines.</p></fn></fn-group></sec><sec sec-type="supplementary-material" id="s6"><title>Additional files</title><supplementary-material id="mdar"><label>MDAR checklist</label><media xlink:href="elife-107042-mdarchecklist1-v1.docx" mimetype="application" mime-subtype="docx"/></supplementary-material><supplementary-material id="sdata1"><label>Source data 1.</label><caption><title>Hemagglutination inhibition (HAI) values for the influenza virus strains, measured across longitudinal vaccine study (2013–2016) for n = 136 de-identified subjects &gt;50 years of age and &lt;38 years of age.</title></caption><media xlink:href="elife-107042-data1-v1.xlsx" mimetype="application" mime-subtype="xlsx"/></supplementary-material></sec><sec sec-type="data-availability" id="s7"><title>Data availability</title><p>All longitudinal HAI values used in this study are provided in <xref ref-type="supplementary-material" rid="sdata1">Source data 1</xref>. All original code and data files for the computational results have been deposited at <ext-link ext-link-type="uri" xlink:href="https://github.com/mtang17/flu">https://github.com/mtang17/flu</ext-link>, (copy archived at <xref ref-type="bibr" rid="bib104">Tang, 2025</xref>) and are publicly available.</p></sec><ref-list><title>References</title><ref id="bib1"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Abbott</surname><given-names>RK</given-names></name><name><surname>Lee</surname><given-names>JH</given-names></name><name><surname>Menis</surname><given-names>S</given-names></name><name><surname>Skog</surname><given-names>P</given-names></name><name><surname>Rossi</surname><given-names>M</given-names></name><name><surname>Ota</surname><given-names>T</given-names></name><name><surname>Kulp</surname><given-names>DW</given-names></name><name><surname>Bhullar</surname><given-names>D</given-names></name><name><surname>Kalyuzhniy</surname><given-names>O</given-names></name><name><surname>Havenar-Daughton</surname><given-names>C</given-names></name><name><surname>Schief</surname><given-names>WR</given-names></name><name><surname>Nemazee</surname><given-names>D</given-names></name><name><surname>Crotty</surname><given-names>S</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Precursor frequency and affinity determine B cell competitive fitness in germinal centers, tested with germline-targeting HIV vaccine immunogens</article-title><source>Immunity</source><volume>48</volume><fpage>133</fpage><lpage>146</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2017.11.023</pub-id><pub-id pub-id-type="pmid">29287996</pub-id></element-citation></ref><ref id="bib2"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Abbott</surname><given-names>RK</given-names></name><name><surname>Crotty</surname><given-names>S</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Factors in B cell competition and immunodominance</article-title><source>Immunological Reviews</source><volume>296</volume><fpage>120</fpage><lpage>131</lpage><pub-id pub-id-type="doi">10.1111/imr.12861</pub-id><pub-id pub-id-type="pmid">32483855</pub-id></element-citation></ref><ref id="bib3"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Akkaya</surname><given-names>M</given-names></name><name><surname>Kwak</surname><given-names>K</given-names></name><name><surname>Pierce</surname><given-names>SK</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>B cell memory: building two walls of protection against pathogens</article-title><source>Nature Reviews. Immunology</source><volume>20</volume><fpage>229</fpage><lpage>238</lpage><pub-id pub-id-type="doi">10.1038/s41577-019-0244-2</pub-id><pub-id pub-id-type="pmid">31836872</pub-id></element-citation></ref><ref id="bib4"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Altman</surname><given-names>MO</given-names></name><name><surname>Angeletti</surname><given-names>D</given-names></name><name><surname>Yewdell</surname><given-names>JW</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Antibody immunodominance: the key to understanding influenza virus antigenic drift</article-title><source>Viral Immunology</source><volume>31</volume><fpage>142</fpage><lpage>149</lpage><pub-id pub-id-type="doi">10.1089/vim.2017.0129</pub-id><pub-id pub-id-type="pmid">29356618</pub-id></element-citation></ref><ref id="bib5"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Amitai</surname><given-names>A</given-names></name><name><surname>Sangesland</surname><given-names>M</given-names></name><name><surname>Barnes</surname><given-names>RM</given-names></name><name><surname>Rohrer</surname><given-names>D</given-names></name><name><surname>Lonberg</surname><given-names>N</given-names></name><name><surname>Lingwood</surname><given-names>D</given-names></name><name><surname>Chakraborty</surname><given-names>AK</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Defining and manipulating B cell immunodominance hierarchies to elicit broadly neutralizing antibody responses against influenza virus</article-title><source>Cell Systems</source><volume>11</volume><fpage>573</fpage><lpage>588</lpage><pub-id pub-id-type="doi">10.1016/j.cels.2020.09.005</pub-id><pub-id pub-id-type="pmid">33031741</pub-id></element-citation></ref><ref id="bib6"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Andrews</surname><given-names>SF</given-names></name><name><surname>Cominsky</surname><given-names>LY</given-names></name><name><surname>Shimberg</surname><given-names>GD</given-names></name><name><surname>Gillespie</surname><given-names>RA</given-names></name><name><surname>Gorman</surname><given-names>J</given-names></name><name><surname>Raab</surname><given-names>JE</given-names></name><name><surname>Brand</surname><given-names>J</given-names></name><name><surname>Creanga</surname><given-names>A</given-names></name><name><surname>Gajjala</surname><given-names>SR</given-names></name><name><surname>Narpala</surname><given-names>S</given-names></name><name><surname>Cheung</surname><given-names>CSF</given-names></name><name><surname>Harris</surname><given-names>DR</given-names></name><name><surname>Zhou</surname><given-names>T</given-names></name><name><surname>Gordon</surname><given-names>I</given-names></name><name><surname>Holman</surname><given-names>L</given-names></name><name><surname>Mendoza</surname><given-names>F</given-names></name><name><surname>Houser</surname><given-names>KV</given-names></name><name><surname>Chen</surname><given-names>GL</given-names></name><name><surname>Mascola</surname><given-names>JR</given-names></name><name><surname>Graham</surname><given-names>BS</given-names></name><name><surname>Kwong</surname><given-names>PD</given-names></name><name><surname>Widge</surname><given-names>A</given-names></name><name><surname>Dropulic</surname><given-names>LK</given-names></name><name><surname>Ledgerwood</surname><given-names>JE</given-names></name><name><surname>Kanekiyo</surname><given-names>M</given-names></name><name><surname>McDermott</surname><given-names>AB</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>An influenza H1 hemagglutinin stem-only immunogen elicits a broadly cross-reactive B cell response in humans</article-title><source>Science Translational Medicine</source><volume>15</volume><elocation-id>eade4976</elocation-id><pub-id pub-id-type="doi">10.1126/scitranslmed.ade4976</pub-id><pub-id pub-id-type="pmid">37075126</pub-id></element-citation></ref><ref id="bib7"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Angeletti</surname><given-names>D</given-names></name><name><surname>Gibbs</surname><given-names>JS</given-names></name><name><surname>Angel</surname><given-names>M</given-names></name><name><surname>Kosik</surname><given-names>I</given-names></name><name><surname>Hickman</surname><given-names>HD</given-names></name><name><surname>Frank</surname><given-names>GM</given-names></name><name><surname>Das</surname><given-names>SR</given-names></name><name><surname>Wheatley</surname><given-names>AK</given-names></name><name><surname>Prabhakaran</surname><given-names>M</given-names></name><name><surname>Leggat</surname><given-names>DJ</given-names></name><name><surname>McDermott</surname><given-names>AB</given-names></name><name><surname>Yewdell</surname><given-names>JW</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Defining B cell immunodominance to viruses</article-title><source>Nature Immunology</source><volume>18</volume><fpage>456</fpage><lpage>463</lpage><pub-id pub-id-type="doi">10.1038/ni.3680</pub-id><pub-id pub-id-type="pmid">28192417</pub-id></element-citation></ref><ref id="bib8"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Angeletti</surname><given-names>D</given-names></name><name><surname>Yewdell</surname><given-names>JW</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Understanding and manipulating viral immunity: antibody immunodominance enters center stage</article-title><source>Trends in Immunology</source><volume>39</volume><fpage>549</fpage><lpage>561</lpage><pub-id pub-id-type="doi">10.1016/j.it.2018.04.008</pub-id><pub-id pub-id-type="pmid">29789196</pub-id></element-citation></ref><ref id="bib9"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Angeletti</surname><given-names>D</given-names></name><name><surname>Kosik</surname><given-names>I</given-names></name><name><surname>Santos</surname><given-names>JJS</given-names></name><name><surname>Yewdell</surname><given-names>WT</given-names></name><name><surname>Boudreau</surname><given-names>CM</given-names></name><name><surname>Mallajosyula</surname><given-names>VVA</given-names></name><name><surname>Mankowski</surname><given-names>MC</given-names></name><name><surname>Chambers</surname><given-names>M</given-names></name><name><surname>Prabhakaran</surname><given-names>M</given-names></name><name><surname>Hickman</surname><given-names>HD</given-names></name><name><surname>McDermott</surname><given-names>AB</given-names></name><name><surname>Alter</surname><given-names>G</given-names></name><name><surname>Chaudhuri</surname><given-names>J</given-names></name><name><surname>Yewdell</surname><given-names>JW</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Outflanking immunodominance to target subdominant broadly neutralizing epitopes</article-title><source>PNAS</source><volume>116</volume><fpage>13474</fpage><lpage>13479</lpage><pub-id pub-id-type="doi">10.1073/pnas.1816300116</pub-id><pub-id pub-id-type="pmid">31213541</pub-id></element-citation></ref><ref id="bib10"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Aung</surname><given-names>A</given-names></name><name><surname>Cui</surname><given-names>A</given-names></name><name><surname>Maiorino</surname><given-names>L</given-names></name><name><surname>Amini</surname><given-names>AP</given-names></name><name><surname>Gregory</surname><given-names>JR</given-names></name><name><surname>Bukenya</surname><given-names>M</given-names></name><name><surname>Zhang</surname><given-names>Y</given-names></name><name><surname>Lee</surname><given-names>H</given-names></name><name><surname>Cottrell</surname><given-names>CA</given-names></name><name><surname>Morgan</surname><given-names>DM</given-names></name><name><surname>Silva</surname><given-names>M</given-names></name><name><surname>Suh</surname><given-names>H</given-names></name><name><surname>Kirkpatrick</surname><given-names>JD</given-names></name><name><surname>Amlashi</surname><given-names>P</given-names></name><name><surname>Remba</surname><given-names>T</given-names></name><name><surname>Froehle</surname><given-names>LM</given-names></name><name><surname>Xiao</surname><given-names>S</given-names></name><name><surname>Abraham</surname><given-names>W</given-names></name><name><surname>Adams</surname><given-names>J</given-names></name><name><surname>Love</surname><given-names>JC</given-names></name><name><surname>Huyett</surname><given-names>P</given-names></name><name><surname>Kwon</surname><given-names>DS</given-names></name><name><surname>Hacohen</surname><given-names>N</given-names></name><name><surname>Schief</surname><given-names>WR</given-names></name><name><surname>Bhatia</surname><given-names>SN</given-names></name><name><surname>Irvine</surname><given-names>DJ</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Low protease activity in B cell follicles promotes retention of intact antigens after immunization</article-title><source>Science</source><volume>379</volume><elocation-id>eabn8934</elocation-id><pub-id pub-id-type="doi">10.1126/science.abn8934</pub-id><pub-id pub-id-type="pmid">36701450</pub-id></element-citation></ref><ref id="bib11"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Batista</surname><given-names>FD</given-names></name><name><surname>Neuberger</surname><given-names>MS</given-names></name></person-group><year iso-8601-date="1998">1998</year><article-title>Affinity dependence of the B cell response to antigen: a threshold, a ceiling, and the importance of off-rate</article-title><source>Immunity</source><volume>8</volume><fpage>751</fpage><lpage>759</lpage><pub-id pub-id-type="doi">10.1016/s1074-7613(00)80580-4</pub-id><pub-id pub-id-type="pmid">9655489</pub-id></element-citation></ref><ref id="bib12"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bedi</surname><given-names>R</given-names></name><name><surname>Bayless</surname><given-names>NL</given-names></name><name><surname>Glanville</surname><given-names>J</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Challenges and progress in designing broad-spectrum vaccines against rapidly mutating viruses</article-title><source>Annual Review of Biomedical Data Science</source><volume>6</volume><fpage>419</fpage><lpage>441</lpage><pub-id pub-id-type="doi">10.1146/annurev-biodatasci-020722-041304</pub-id><pub-id pub-id-type="pmid">37196356</pub-id></element-citation></ref><ref id="bib13"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bergström</surname><given-names>JJE</given-names></name><name><surname>Xu</surname><given-names>H</given-names></name><name><surname>Heyman</surname><given-names>B</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Epitope-specific suppression of IgG responses by passively administered specific IgG: evidence of epitope masking</article-title><source>Frontiers in Immunology</source><volume>8</volume><elocation-id>238</elocation-id><pub-id pub-id-type="doi">10.3389/fimmu.2017.00238</pub-id><pub-id pub-id-type="pmid">28321225</pub-id></element-citation></ref><ref id="bib14"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bhagchandani</surname><given-names>SH</given-names></name><name><surname>Yang</surname><given-names>L</given-names></name><name><surname>Lam</surname><given-names>JH</given-names></name><name><surname>Maiorino</surname><given-names>L</given-names></name><name><surname>Ben-Akiva</surname><given-names>E</given-names></name><name><surname>Rodrigues</surname><given-names>KA</given-names></name><name><surname>Romanov</surname><given-names>A</given-names></name><name><surname>Suh</surname><given-names>H</given-names></name><name><surname>Aung</surname><given-names>A</given-names></name><name><surname>Wu</surname><given-names>S</given-names></name><name><surname>Wadhera</surname><given-names>A</given-names></name><name><surname>Chakraborty</surname><given-names>AK</given-names></name><name><surname>Irvine</surname><given-names>DJ</given-names></name></person-group><year iso-8601-date="2024">2024</year><article-title>Two-dose priming immunization amplifies humoral immunity by synchronizing vaccine delivery with the germinal center response</article-title><source>Science Immunology</source><volume>9</volume><elocation-id>eadl3755</elocation-id><pub-id pub-id-type="doi">10.1126/sciimmunol.adl3755</pub-id><pub-id pub-id-type="pmid">39303017</pub-id></element-citation></ref><ref id="bib15"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Boudreau</surname><given-names>CM</given-names></name><name><surname>Alter</surname><given-names>G</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Extra-Neutralizing FcR-mediated antibody functions for a universal influenza vaccine</article-title><source>Frontiers in Immunology</source><volume>10</volume><elocation-id>440</elocation-id><pub-id pub-id-type="doi">10.3389/fimmu.2019.00440</pub-id><pub-id pub-id-type="pmid">30949165</pub-id></element-citation></ref><ref id="bib16"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Boudreau</surname><given-names>CM</given-names></name><name><surname>Roederer</surname><given-names>AL</given-names></name><name><surname>Gorman</surname><given-names>MJ</given-names></name><name><surname>Mundle</surname><given-names>S</given-names></name><name><surname>Lingwood</surname><given-names>D</given-names></name><name><surname>Delagrave</surname><given-names>S</given-names></name><name><surname>Sridhar</surname><given-names>S</given-names></name><name><surname>Ross</surname><given-names>TM</given-names></name><name><surname>Kleanthous</surname><given-names>H</given-names></name><name><surname>Alter</surname><given-names>G</given-names></name><name><surname>Burke</surname><given-names>JS</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Pre-existing Fc profiles shape the evolution of neutralizing antibody breadth following influenza vaccination</article-title><source>Cell Reports. Medicine</source><volume>4</volume><elocation-id>100975</elocation-id><pub-id pub-id-type="doi">10.1016/j.xcrm.2023.100975</pub-id><pub-id pub-id-type="pmid">36921600</pub-id></element-citation></ref><ref id="bib17"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Boyd</surname><given-names>SD</given-names></name><name><surname>Joshi</surname><given-names>SA</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>High-Throughput DNA sequencing analysis of antibody repertoires</article-title><source>Microbiology Spectrum</source><volume>2</volume><elocation-id>00172014</elocation-id><pub-id pub-id-type="doi">10.1128/microbiolspec.AID-0017-2014</pub-id><pub-id pub-id-type="pmid">26104353</pub-id></element-citation></ref><ref id="bib18"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Boyoglu-Barnum</surname><given-names>S</given-names></name><name><surname>Ellis</surname><given-names>D</given-names></name><name><surname>Gillespie</surname><given-names>RA</given-names></name><name><surname>Hutchinson</surname><given-names>GB</given-names></name><name><surname>Park</surname><given-names>Y-J</given-names></name><name><surname>Moin</surname><given-names>SM</given-names></name><name><surname>Acton</surname><given-names>OJ</given-names></name><name><surname>Ravichandran</surname><given-names>R</given-names></name><name><surname>Murphy</surname><given-names>M</given-names></name><name><surname>Pettie</surname><given-names>D</given-names></name><name><surname>Matheson</surname><given-names>N</given-names></name><name><surname>Carter</surname><given-names>L</given-names></name><name><surname>Creanga</surname><given-names>A</given-names></name><name><surname>Watson</surname><given-names>MJ</given-names></name><name><surname>Kephart</surname><given-names>S</given-names></name><name><surname>Ataca</surname><given-names>S</given-names></name><name><surname>Vaile</surname><given-names>JR</given-names></name><name><surname>Ueda</surname><given-names>G</given-names></name><name><surname>Crank</surname><given-names>MC</given-names></name><name><surname>Stewart</surname><given-names>L</given-names></name><name><surname>Lee</surname><given-names>KK</given-names></name><name><surname>Guttman</surname><given-names>M</given-names></name><name><surname>Baker</surname><given-names>D</given-names></name><name><surname>Mascola</surname><given-names>JR</given-names></name><name><surname>Veesler</surname><given-names>D</given-names></name><name><surname>Graham</surname><given-names>BS</given-names></name><name><surname>King</surname><given-names>NP</given-names></name><name><surname>Kanekiyo</surname><given-names>M</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Quadrivalent influenza nanoparticle vaccines induce broad protection</article-title><source>Nature</source><volume>592</volume><fpage>623</fpage><lpage>628</lpage><pub-id pub-id-type="doi">10.1038/s41586-021-03365-x</pub-id><pub-id pub-id-type="pmid">33762730</pub-id></element-citation></ref><ref id="bib19"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Caradonna</surname><given-names>TM</given-names></name><name><surname>Schmidt</surname><given-names>AG</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Protein engineering strategies for rational immunogen design</article-title><source>NPJ Vaccines</source><volume>6</volume><elocation-id>154</elocation-id><pub-id pub-id-type="doi">10.1038/s41541-021-00417-1</pub-id><pub-id pub-id-type="pmid">34921149</pub-id></element-citation></ref><ref id="bib20"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Caradonna</surname><given-names>TM</given-names></name><name><surname>Ronsard</surname><given-names>L</given-names></name><name><surname>Yousif</surname><given-names>AS</given-names></name><name><surname>Windsor</surname><given-names>IW</given-names></name><name><surname>Hecht</surname><given-names>R</given-names></name><name><surname>Bracamonte-Moreno</surname><given-names>T</given-names></name><name><surname>Roffler</surname><given-names>AA</given-names></name><name><surname>Maron</surname><given-names>MJ</given-names></name><name><surname>Maurer</surname><given-names>DP</given-names></name><name><surname>Feldman</surname><given-names>J</given-names></name><name><surname>Marchiori</surname><given-names>E</given-names></name><name><surname>Barnes</surname><given-names>RM</given-names></name><name><surname>Rohrer</surname><given-names>D</given-names></name><name><surname>Lonberg</surname><given-names>N</given-names></name><name><surname>Sempowski</surname><given-names>GD</given-names></name><name><surname>Oguin</surname><given-names>TH</given-names></name><name><surname>Kepler</surname><given-names>TB</given-names></name><name><surname>Kuraoka</surname><given-names>M</given-names></name><name><surname>Lingwood</surname><given-names>D</given-names></name><name><surname>Schmidt</surname><given-names>AG</given-names></name></person-group><year iso-8601-date="2022">2022</year><article-title>An epitope-enriched immunogen expands responses to a conserved viral site</article-title><source>Cell Reports</source><volume>41</volume><elocation-id>111628</elocation-id><pub-id pub-id-type="doi">10.1016/j.celrep.2022.111628</pub-id><pub-id pub-id-type="pmid">36351401</pub-id></element-citation></ref><ref id="bib21"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Cheung</surname><given-names>CSF</given-names></name><name><surname>Fruehwirth</surname><given-names>A</given-names></name><name><surname>Paparoditis</surname><given-names>PCG</given-names></name><name><surname>Shen</surname><given-names>CH</given-names></name><name><surname>Foglierini</surname><given-names>M</given-names></name><name><surname>Joyce</surname><given-names>MG</given-names></name><name><surname>Leung</surname><given-names>K</given-names></name><name><surname>Piccoli</surname><given-names>L</given-names></name><name><surname>Rawi</surname><given-names>R</given-names></name><name><surname>Silacci-Fregni</surname><given-names>C</given-names></name><name><surname>Tsybovsky</surname><given-names>Y</given-names></name><name><surname>Verardi</surname><given-names>R</given-names></name><name><surname>Wang</surname><given-names>L</given-names></name><name><surname>Wang</surname><given-names>S</given-names></name><name><surname>Yang</surname><given-names>ES</given-names></name><name><surname>Zhang</surname><given-names>B</given-names></name><name><surname>Zhang</surname><given-names>Y</given-names></name><name><surname>Chuang</surname><given-names>GY</given-names></name><name><surname>Corti</surname><given-names>D</given-names></name><name><surname>Mascola</surname><given-names>JR</given-names></name><name><surname>Shapiro</surname><given-names>L</given-names></name><name><surname>Kwong</surname><given-names>PD</given-names></name><name><surname>Lanzavecchia</surname><given-names>A</given-names></name><name><surname>Zhou</surname><given-names>T</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Identification and structure of a multidonor class of head-directed influenza-neutralizing antibodies reveal the mechanism for its recurrent elicitation</article-title><source>Cell Reports</source><volume>32</volume><elocation-id>108088</elocation-id><pub-id pub-id-type="doi">10.1016/j.celrep.2020.108088</pub-id><pub-id pub-id-type="pmid">32877670</pub-id></element-citation></ref><ref id="bib22"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Cirelli</surname><given-names>KM</given-names></name><name><surname>Carnathan</surname><given-names>DG</given-names></name><name><surname>Nogal</surname><given-names>B</given-names></name><name><surname>Martin</surname><given-names>JT</given-names></name><name><surname>Rodriguez</surname><given-names>OL</given-names></name><name><surname>Upadhyay</surname><given-names>AA</given-names></name><name><surname>Enemuo</surname><given-names>CA</given-names></name><name><surname>Gebru</surname><given-names>EH</given-names></name><name><surname>Choe</surname><given-names>Y</given-names></name><name><surname>Viviano</surname><given-names>F</given-names></name><name><surname>Nakao</surname><given-names>C</given-names></name><name><surname>Pauthner</surname><given-names>MG</given-names></name><name><surname>Reiss</surname><given-names>S</given-names></name><name><surname>Cottrell</surname><given-names>CA</given-names></name><name><surname>Smith</surname><given-names>ML</given-names></name><name><surname>Bastidas</surname><given-names>R</given-names></name><name><surname>Gibson</surname><given-names>W</given-names></name><name><surname>Wolabaugh</surname><given-names>AN</given-names></name><name><surname>Melo</surname><given-names>MB</given-names></name><name><surname>Cossette</surname><given-names>B</given-names></name><name><surname>Kumar</surname><given-names>V</given-names></name><name><surname>Patel</surname><given-names>NB</given-names></name><name><surname>Tokatlian</surname><given-names>T</given-names></name><name><surname>Menis</surname><given-names>S</given-names></name><name><surname>Kulp</surname><given-names>DW</given-names></name><name><surname>Burton</surname><given-names>DR</given-names></name><name><surname>Murrell</surname><given-names>B</given-names></name><name><surname>Schief</surname><given-names>WR</given-names></name><name><surname>Bosinger</surname><given-names>SE</given-names></name><name><surname>Ward</surname><given-names>AB</given-names></name><name><surname>Watson</surname><given-names>CT</given-names></name><name><surname>Silvestri</surname><given-names>G</given-names></name><name><surname>Irvine</surname><given-names>DJ</given-names></name><name><surname>Crotty</surname><given-names>S</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Slow delivery immunization enhances HIV neutralizing antibody and germinal center responses via modulation of immunodominance</article-title><source>Cell</source><volume>177</volume><fpage>1153</fpage><lpage>1171</lpage><pub-id pub-id-type="doi">10.1016/j.cell.2019.04.012</pub-id><pub-id pub-id-type="pmid">31080066</pub-id></element-citation></ref><ref id="bib23"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Collins</surname><given-names>AM</given-names></name><name><surname>Jackson</surname><given-names>KJL</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>On being the right size: antibody repertoire formation in the mouse and human</article-title><source>Immunogenetics</source><volume>70</volume><fpage>143</fpage><lpage>158</lpage><pub-id pub-id-type="doi">10.1007/s00251-017-1049-8</pub-id><pub-id pub-id-type="pmid">29260260</pub-id></element-citation></ref><ref id="bib24"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Comber</surname><given-names>L</given-names></name><name><surname>Murchu</surname><given-names>EO</given-names></name><name><surname>Jordan</surname><given-names>K</given-names></name><name><surname>Hawkshaw</surname><given-names>S</given-names></name><name><surname>Marshall</surname><given-names>L</given-names></name><name><surname>O’Neill</surname><given-names>M</given-names></name><name><surname>Teljeur</surname><given-names>C</given-names></name><name><surname>Ryan</surname><given-names>M</given-names></name><name><surname>Carnahan</surname><given-names>A</given-names></name><name><surname>Pérez Martín</surname><given-names>JJ</given-names></name><name><surname>Robertson</surname><given-names>AH</given-names></name><name><surname>Johansen</surname><given-names>K</given-names></name><name><surname>de Jonge</surname><given-names>J</given-names></name><name><surname>Krause</surname><given-names>T</given-names></name><name><surname>Nicolay</surname><given-names>N</given-names></name><name><surname>Nohynek</surname><given-names>H</given-names></name><name><surname>Pavlopoulou</surname><given-names>I</given-names></name><name><surname>Pebody</surname><given-names>R</given-names></name><name><surname>Penttinen</surname><given-names>P</given-names></name><name><surname>Soler-Soneira</surname><given-names>M</given-names></name><name><surname>Wichmann</surname><given-names>O</given-names></name><name><surname>Harrington</surname><given-names>P</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Systematic review of the efficacy, effectiveness and safety of high-dose seasonal influenza vaccines for the prevention of laboratory-confirmed influenza in individuals ≥18 years of age</article-title><source>Reviews in Medical Virology</source><volume>33</volume><elocation-id>e2330</elocation-id><pub-id pub-id-type="doi">10.1002/rmv.2330</pub-id><pub-id pub-id-type="pmid">35119149</pub-id></element-citation></ref><ref id="bib25"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Cox</surname><given-names>RJ</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>Correlates of protection to influenza virus, where do we go from here?</article-title><source>Human Vaccines &amp; Immunotherapeutics</source><volume>9</volume><fpage>405</fpage><lpage>408</lpage><pub-id pub-id-type="doi">10.4161/hv.22908</pub-id></element-citation></ref><ref id="bib26"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Crotty</surname><given-names>S</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>A brief history of T cell help to B cells</article-title><source>Nature Reviews. Immunology</source><volume>15</volume><fpage>185</fpage><lpage>189</lpage><pub-id pub-id-type="doi">10.1038/nri3803</pub-id><pub-id pub-id-type="pmid">25677493</pub-id></element-citation></ref><ref id="bib27"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Cyster</surname><given-names>JG</given-names></name><name><surname>Wilson</surname><given-names>PC</given-names></name></person-group><year iso-8601-date="2024">2024</year><article-title>Antibody modulation of B cell responses-Incorporating positive and negative feedback</article-title><source>Immunity</source><volume>57</volume><fpage>1466</fpage><lpage>1481</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2024.06.009</pub-id><pub-id pub-id-type="pmid">38986442</pub-id></element-citation></ref><ref id="bib28"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Danecek</surname><given-names>P</given-names></name><name><surname>Auton</surname><given-names>A</given-names></name><name><surname>Abecasis</surname><given-names>G</given-names></name><name><surname>Albers</surname><given-names>CA</given-names></name><name><surname>Banks</surname><given-names>E</given-names></name><name><surname>DePristo</surname><given-names>MA</given-names></name><name><surname>Handsaker</surname><given-names>RE</given-names></name><name><surname>Lunter</surname><given-names>G</given-names></name><name><surname>Marth</surname><given-names>GT</given-names></name><name><surname>Sherry</surname><given-names>ST</given-names></name><name><surname>McVean</surname><given-names>G</given-names></name><name><surname>Durbin</surname><given-names>R</given-names></name><collab>1000 Genomes Project Analysis Group</collab></person-group><year iso-8601-date="2011">2011</year><article-title>The variant call format and VCFtools</article-title><source>Bioinformatics</source><volume>27</volume><fpage>2156</fpage><lpage>2158</lpage><pub-id pub-id-type="doi">10.1093/bioinformatics/btr330</pub-id><pub-id pub-id-type="pmid">21653522</pub-id></element-citation></ref><ref id="bib29"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>de Carvalho</surname><given-names>RVH</given-names></name><name><surname>Ersching</surname><given-names>J</given-names></name><name><surname>Barbulescu</surname><given-names>A</given-names></name><name><surname>Hobbs</surname><given-names>A</given-names></name><name><surname>Castro</surname><given-names>TBR</given-names></name><name><surname>Mesin</surname><given-names>L</given-names></name><name><surname>Jacobsen</surname><given-names>JT</given-names></name><name><surname>Phillips</surname><given-names>BK</given-names></name><name><surname>Hoffmann</surname><given-names>HH</given-names></name><name><surname>Parsa</surname><given-names>R</given-names></name><name><surname>Canesso</surname><given-names>MCC</given-names></name><name><surname>Nowosad</surname><given-names>CR</given-names></name><name><surname>Feng</surname><given-names>A</given-names></name><name><surname>Leist</surname><given-names>SR</given-names></name><name><surname>Baric</surname><given-names>RS</given-names></name><name><surname>Yang</surname><given-names>E</given-names></name><name><surname>Utz</surname><given-names>PJ</given-names></name><name><surname>Victora</surname><given-names>GD</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Clonal replacement sustains long-lived germinal centers primed by respiratory viruses</article-title><source>Cell</source><volume>186</volume><fpage>131</fpage><lpage>146</lpage><pub-id pub-id-type="doi">10.1016/j.cell.2022.11.031</pub-id><pub-id pub-id-type="pmid">36565697</pub-id></element-citation></ref><ref id="bib30"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Demirden</surname><given-names>SF</given-names></name><name><surname>Alptekin</surname><given-names>K</given-names></name><name><surname>Kimiz-Gebologlu</surname><given-names>I</given-names></name><name><surname>Oncel</surname><given-names>SS</given-names></name></person-group><year iso-8601-date="2022">2022</year><article-title>Influenza vaccine: an engineering vision from virological importance to production</article-title><source>Biotechnology and Bioprocess Engineering</source><volume>27</volume><fpage>714</fpage><lpage>738</lpage><pub-id pub-id-type="doi">10.1007/s12257-022-0115-8</pub-id><pub-id pub-id-type="pmid">36313971</pub-id></element-citation></ref><ref id="bib31"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Demonbreun</surname><given-names>AR</given-names></name><name><surname>Sancilio</surname><given-names>A</given-names></name><name><surname>Velez</surname><given-names>MP</given-names></name><name><surname>Ryan</surname><given-names>DT</given-names></name><name><surname>Saber</surname><given-names>R</given-names></name><name><surname>Vaught</surname><given-names>LA</given-names></name><name><surname>Reiser</surname><given-names>NL</given-names></name><name><surname>Hsieh</surname><given-names>RR</given-names></name><name><surname>D’Aquila</surname><given-names>RT</given-names></name><name><surname>Mustanski</surname><given-names>B</given-names></name><name><surname>McNally</surname><given-names>EM</given-names></name><name><surname>McDade</surname><given-names>TW</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Comparison of IgG and neutralizing antibody responses after one or two doses of COVID-19 mRNA vaccine in previously infected and uninfected individuals</article-title><source>EClinicalMedicine</source><volume>38</volume><elocation-id>101018</elocation-id><pub-id pub-id-type="doi">10.1016/j.eclinm.2021.101018</pub-id><pub-id pub-id-type="pmid">34278286</pub-id></element-citation></ref><ref id="bib32"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>de Silva</surname><given-names>NS</given-names></name><name><surname>Klein</surname><given-names>U</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Dynamics of B cells in germinal centres</article-title><source>Nature Reviews. Immunology</source><volume>15</volume><fpage>137</fpage><lpage>148</lpage><pub-id pub-id-type="doi">10.1038/nri3804</pub-id><pub-id pub-id-type="pmid">25656706</pub-id></element-citation></ref><ref id="bib33"><element-citation publication-type="preprint"><person-group person-group-type="author"><name><surname>DeWitt</surname><given-names>WS</given-names></name><name><surname>Vora</surname><given-names>AA</given-names></name><name><surname>Araki</surname><given-names>T</given-names></name><name><surname>Galloway</surname><given-names>JG</given-names></name><name><surname>Alkutkar</surname><given-names>T</given-names></name><name><surname>Bortolatto</surname><given-names>J</given-names></name><name><surname>Castro</surname><given-names>TBR</given-names></name><name><surname>Dumm</surname><given-names>W</given-names></name><name><surname>Jennings-Shaffer</surname><given-names>C</given-names></name><name><surname>Jia</surname><given-names>T</given-names></name><name><surname>Mesin</surname><given-names>L</given-names></name><name><surname>Ozorowski</surname><given-names>G</given-names></name><name><surname>Pae</surname><given-names>J</given-names></name><name><surname>Ralph</surname><given-names>DK</given-names></name><name><surname>Bloom</surname><given-names>JD</given-names></name><name><surname>Nourmohammad</surname><given-names>A</given-names></name><name><surname>Song</surname><given-names>YS</given-names></name><name><surname>Ward</surname><given-names>AB</given-names></name><name><surname>Starr</surname><given-names>TN</given-names></name><name><surname>Victora</surname><given-names>GD</given-names></name><name><surname>Matsen</surname><given-names>FA</given-names></name></person-group><year iso-8601-date="2025">2025</year><article-title>Replaying Germinal Center Evolution on a Quantified Affinity Landscape</article-title><source>bioRxiv</source><pub-id pub-id-type="doi">10.1101/2025.06.02.656870</pub-id></element-citation></ref><ref id="bib34"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>DiLillo</surname><given-names>DJ</given-names></name><name><surname>Palese</surname><given-names>P</given-names></name><name><surname>Wilson</surname><given-names>PC</given-names></name><name><surname>Ravetch</surname><given-names>JV</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Broadly neutralizing anti-influenza antibodies require Fc receptor engagement for in vivo protection</article-title><source>The Journal of Clinical Investigation</source><volume>126</volume><fpage>605</fpage><lpage>610</lpage><pub-id pub-id-type="doi">10.1172/JCI84428</pub-id><pub-id pub-id-type="pmid">26731473</pub-id></element-citation></ref><ref id="bib35"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Dosenovic</surname><given-names>P</given-names></name><name><surname>Kara</surname><given-names>EE</given-names></name><name><surname>Pettersson</surname><given-names>AK</given-names></name><name><surname>McGuire</surname><given-names>AT</given-names></name><name><surname>Gray</surname><given-names>M</given-names></name><name><surname>Hartweger</surname><given-names>H</given-names></name><name><surname>Thientosapol</surname><given-names>ES</given-names></name><name><surname>Stamatatos</surname><given-names>L</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Anti-HIV-1 B cell responses are dependent on B cell precursor frequency and antigen-binding affinity</article-title><source>PNAS</source><volume>115</volume><fpage>4743</fpage><lpage>4748</lpage><pub-id pub-id-type="doi">10.1073/pnas.1803457115</pub-id><pub-id pub-id-type="pmid">29666227</pub-id></element-citation></ref><ref id="bib36"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Feldman</surname><given-names>J</given-names></name><name><surname>Bals</surname><given-names>J</given-names></name><name><surname>Altomare</surname><given-names>CG</given-names></name><name><surname>St Denis</surname><given-names>K</given-names></name><name><surname>Lam</surname><given-names>EC</given-names></name><name><surname>Hauser</surname><given-names>BM</given-names></name><name><surname>Ronsard</surname><given-names>L</given-names></name><name><surname>Sangesland</surname><given-names>M</given-names></name><name><surname>Moreno</surname><given-names>TB</given-names></name><name><surname>Okonkwo</surname><given-names>V</given-names></name><name><surname>Hartojo</surname><given-names>N</given-names></name><name><surname>Balazs</surname><given-names>AB</given-names></name><name><surname>Bajic</surname><given-names>G</given-names></name><name><surname>Lingwood</surname><given-names>D</given-names></name><name><surname>Schmidt</surname><given-names>AG</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Naive human B cells engage the receptor binding domain of SARS-CoV-2, variants of concern, and related sarbecoviruses</article-title><source>Science Immunology</source><volume>6</volume><elocation-id>eabl5842</elocation-id><pub-id pub-id-type="doi">10.1126/sciimmunol.abl5842</pub-id><pub-id pub-id-type="pmid">34648356</pub-id></element-citation></ref><ref id="bib37"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Fiore</surname><given-names>AE</given-names></name><name><surname>Bridges</surname><given-names>CB</given-names></name><name><surname>Cox</surname><given-names>NJ</given-names></name></person-group><year iso-8601-date="2009">2009</year><article-title>Seasonal influenza vaccines</article-title><source>Current Topics in Microbiology and Immunology</source><volume>333</volume><fpage>43</fpage><lpage>82</lpage><pub-id pub-id-type="doi">10.1007/978-3-540-92165-3_3</pub-id><pub-id pub-id-type="pmid">19768400</pub-id></element-citation></ref><ref id="bib38"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Fleire</surname><given-names>SJ</given-names></name><name><surname>Goldman</surname><given-names>JP</given-names></name><name><surname>Carrasco</surname><given-names>YR</given-names></name><name><surname>Weber</surname><given-names>M</given-names></name><name><surname>Bray</surname><given-names>D</given-names></name><name><surname>Batista</surname><given-names>FD</given-names></name></person-group><year iso-8601-date="2006">2006</year><article-title>B cell ligand discrimination through a spreading and contraction response</article-title><source>Science</source><volume>312</volume><fpage>738</fpage><lpage>741</lpage><pub-id pub-id-type="doi">10.1126/science.1123940</pub-id><pub-id pub-id-type="pmid">16675699</pub-id></element-citation></ref><ref id="bib39"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Foote</surname><given-names>J</given-names></name><name><surname>Eisen</surname><given-names>HN</given-names></name></person-group><year iso-8601-date="1995">1995</year><article-title>Kinetic and affinity limits on antibodies produced during immune responses</article-title><source>PNAS</source><volume>92</volume><fpage>1254</fpage><lpage>1256</lpage><pub-id pub-id-type="doi">10.1073/pnas.92.5.1254</pub-id><pub-id pub-id-type="pmid">7877964</pub-id></element-citation></ref><ref id="bib40"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Foote</surname><given-names>J</given-names></name><name><surname>Eisen</surname><given-names>HN</given-names></name></person-group><year iso-8601-date="2000">2000</year><article-title>Breaking the affinity ceiling for antibodies and T cell receptors</article-title><source>PNAS</source><volume>97</volume><fpage>10679</fpage><lpage>10681</lpage><pub-id pub-id-type="doi">10.1073/pnas.97.20.10679</pub-id><pub-id pub-id-type="pmid">11005851</pub-id></element-citation></ref><ref id="bib41"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gaebler</surname><given-names>C</given-names></name><name><surname>Wang</surname><given-names>Z</given-names></name><name><surname>Lorenzi</surname><given-names>JCC</given-names></name><name><surname>Muecksch</surname><given-names>F</given-names></name><name><surname>Finkin</surname><given-names>S</given-names></name><name><surname>Tokuyama</surname><given-names>M</given-names></name><name><surname>Cho</surname><given-names>A</given-names></name><name><surname>Jankovic</surname><given-names>M</given-names></name><name><surname>Schaefer-Babajew</surname><given-names>D</given-names></name><name><surname>Oliveira</surname><given-names>TY</given-names></name><name><surname>Cipolla</surname><given-names>M</given-names></name><name><surname>Viant</surname><given-names>C</given-names></name><name><surname>Barnes</surname><given-names>CO</given-names></name><name><surname>Bram</surname><given-names>Y</given-names></name><name><surname>Breton</surname><given-names>G</given-names></name><name><surname>Hägglöf</surname><given-names>T</given-names></name><name><surname>Mendoza</surname><given-names>P</given-names></name><name><surname>Hurley</surname><given-names>A</given-names></name><name><surname>Turroja</surname><given-names>M</given-names></name><name><surname>Gordon</surname><given-names>K</given-names></name><name><surname>Millard</surname><given-names>KG</given-names></name><name><surname>Ramos</surname><given-names>V</given-names></name><name><surname>Schmidt</surname><given-names>F</given-names></name><name><surname>Weisblum</surname><given-names>Y</given-names></name><name><surname>Jha</surname><given-names>D</given-names></name><name><surname>Tankelevich</surname><given-names>M</given-names></name><name><surname>Martinez-Delgado</surname><given-names>G</given-names></name><name><surname>Yee</surname><given-names>J</given-names></name><name><surname>Patel</surname><given-names>R</given-names></name><name><surname>Dizon</surname><given-names>J</given-names></name><name><surname>Unson-O’Brien</surname><given-names>C</given-names></name><name><surname>Shimeliovich</surname><given-names>I</given-names></name><name><surname>Robbiani</surname><given-names>DF</given-names></name><name><surname>Zhao</surname><given-names>Z</given-names></name><name><surname>Gazumyan</surname><given-names>A</given-names></name><name><surname>Schwartz</surname><given-names>RE</given-names></name><name><surname>Hatziioannou</surname><given-names>T</given-names></name><name><surname>Bjorkman</surname><given-names>PJ</given-names></name><name><surname>Mehandru</surname><given-names>S</given-names></name><name><surname>Bieniasz</surname><given-names>PD</given-names></name><name><surname>Caskey</surname><given-names>M</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Evolution of antibody immunity to SARS-CoV-2</article-title><source>Nature</source><volume>591</volume><fpage>639</fpage><lpage>644</lpage><pub-id pub-id-type="doi">10.1038/s41586-021-03207-w</pub-id></element-citation></ref><ref id="bib42"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Garcia-Beltran</surname><given-names>WF</given-names></name><name><surname>St Denis</surname><given-names>KJ</given-names></name><name><surname>Hoelzemer</surname><given-names>A</given-names></name><name><surname>Lam</surname><given-names>EC</given-names></name><name><surname>Nitido</surname><given-names>AD</given-names></name><name><surname>Sheehan</surname><given-names>ML</given-names></name><name><surname>Berrios</surname><given-names>C</given-names></name><name><surname>Ofoman</surname><given-names>O</given-names></name><name><surname>Chang</surname><given-names>CC</given-names></name><name><surname>Hauser</surname><given-names>BM</given-names></name><name><surname>Feldman</surname><given-names>J</given-names></name><name><surname>Roederer</surname><given-names>AL</given-names></name><name><surname>Gregory</surname><given-names>DJ</given-names></name><name><surname>Poznansky</surname><given-names>MC</given-names></name><name><surname>Schmidt</surname><given-names>AG</given-names></name><name><surname>Iafrate</surname><given-names>AJ</given-names></name><name><surname>Naranbhai</surname><given-names>V</given-names></name><name><surname>Balazs</surname><given-names>AB</given-names></name></person-group><year iso-8601-date="2022">2022</year><article-title>mRNA-based COVID-19 vaccine boosters induce neutralizing immunity against SARS-CoV-2 Omicron variant</article-title><source>Cell</source><volume>185</volume><fpage>457</fpage><lpage>466</lpage><pub-id pub-id-type="doi">10.1016/j.cell.2021.12.033</pub-id><pub-id pub-id-type="pmid">34995482</pub-id></element-citation></ref><ref id="bib43"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Garten</surname><given-names>RJ</given-names></name><name><surname>Davis</surname><given-names>CT</given-names></name><name><surname>Russell</surname><given-names>CA</given-names></name><name><surname>Shu</surname><given-names>B</given-names></name><name><surname>Lindstrom</surname><given-names>S</given-names></name><name><surname>Balish</surname><given-names>A</given-names></name><name><surname>Sessions</surname><given-names>WM</given-names></name><name><surname>Xu</surname><given-names>X</given-names></name><name><surname>Skepner</surname><given-names>E</given-names></name><name><surname>Deyde</surname><given-names>V</given-names></name><name><surname>Okomo-Adhiambo</surname><given-names>M</given-names></name><name><surname>Gubareva</surname><given-names>L</given-names></name><name><surname>Barnes</surname><given-names>J</given-names></name><name><surname>Smith</surname><given-names>CB</given-names></name><name><surname>Emery</surname><given-names>SL</given-names></name><name><surname>Hillman</surname><given-names>MJ</given-names></name><name><surname>Rivailler</surname><given-names>P</given-names></name><name><surname>Smagala</surname><given-names>J</given-names></name><name><surname>de Graaf</surname><given-names>M</given-names></name><name><surname>Burke</surname><given-names>DF</given-names></name><name><surname>Fouchier</surname><given-names>RAM</given-names></name><name><surname>Pappas</surname><given-names>C</given-names></name><name><surname>Alpuche-Aranda</surname><given-names>CM</given-names></name><name><surname>López-Gatell</surname><given-names>H</given-names></name><name><surname>Olivera</surname><given-names>H</given-names></name><name><surname>López</surname><given-names>I</given-names></name><name><surname>Myers</surname><given-names>CA</given-names></name><name><surname>Faix</surname><given-names>D</given-names></name><name><surname>Blair</surname><given-names>PJ</given-names></name><name><surname>Yu</surname><given-names>C</given-names></name><name><surname>Keene</surname><given-names>KM</given-names></name><name><surname>Dotson</surname><given-names>PD</given-names></name><name><surname>Boxrud</surname><given-names>D</given-names></name><name><surname>Sambol</surname><given-names>AR</given-names></name><name><surname>Abid</surname><given-names>SH</given-names></name><name><surname>George</surname><given-names>K</given-names></name><name><surname>Bannerman</surname><given-names>T</given-names></name><name><surname>Moore</surname><given-names>AL</given-names></name><name><surname>Stringer</surname><given-names>DJ</given-names></name><name><surname>Blevins</surname><given-names>P</given-names></name><name><surname>Demmler-Harrison</surname><given-names>GJ</given-names></name><name><surname>Ginsberg</surname><given-names>M</given-names></name><name><surname>Kriner</surname><given-names>P</given-names></name><name><surname>Waterman</surname><given-names>S</given-names></name><name><surname>Smole</surname><given-names>S</given-names></name><name><surname>Guevara</surname><given-names>HF</given-names></name><name><surname>Belongia</surname><given-names>EA</given-names></name><name><surname>Clark</surname><given-names>PA</given-names></name><name><surname>Beatrice</surname><given-names>ST</given-names></name><name><surname>Donis</surname><given-names>R</given-names></name><name><surname>Katz</surname><given-names>J</given-names></name><name><surname>Finelli</surname><given-names>L</given-names></name><name><surname>Bridges</surname><given-names>CB</given-names></name><name><surname>Shaw</surname><given-names>M</given-names></name><name><surname>Jernigan</surname><given-names>DB</given-names></name><name><surname>Uyeki</surname><given-names>TM</given-names></name><name><surname>Smith</surname><given-names>DJ</given-names></name><name><surname>Klimov</surname><given-names>AI</given-names></name><name><surname>Cox</surname><given-names>NJ</given-names></name></person-group><year iso-8601-date="2009">2009</year><article-title>Antigenic and genetic characteristics of swine-origin 2009 A(H1N1) influenza viruses circulating in humans</article-title><source>Science</source><volume>325</volume><fpage>197</fpage><lpage>201</lpage><pub-id pub-id-type="doi">10.1126/science.1176225</pub-id></element-citation></ref><ref id="bib44"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gaydos</surname><given-names>JC</given-names></name><name><surname>Top</surname><given-names>FH</given-names></name><name><surname>Hodder</surname><given-names>RA</given-names></name><name><surname>Russell</surname><given-names>PK</given-names></name></person-group><year iso-8601-date="2006">2006</year><article-title>Swine influenza a outbreak, Fort Dix</article-title><source>Emerging Infectious Diseases</source><volume>12</volume><fpage>23</fpage><lpage>28</lpage><pub-id pub-id-type="doi">10.3201/eid1201.050965</pub-id></element-citation></ref><ref id="bib45"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Glanville</surname><given-names>J</given-names></name><name><surname>Zhai</surname><given-names>W</given-names></name><name><surname>Berka</surname><given-names>J</given-names></name><name><surname>Telman</surname><given-names>D</given-names></name><name><surname>Huerta</surname><given-names>G</given-names></name><name><surname>Mehta</surname><given-names>GR</given-names></name><name><surname>Ni</surname><given-names>I</given-names></name><name><surname>Mei</surname><given-names>L</given-names></name><name><surname>Sundar</surname><given-names>PD</given-names></name><name><surname>Day</surname><given-names>GMR</given-names></name><name><surname>Cox</surname><given-names>D</given-names></name><name><surname>Rajpal</surname><given-names>A</given-names></name><name><surname>Pons</surname><given-names>J</given-names></name></person-group><year iso-8601-date="2009">2009</year><article-title>Precise determination of the diversity of a combinatorial antibody library gives insight into the human immunoglobulin repertoire</article-title><source>PNAS</source><volume>106</volume><fpage>20216</fpage><lpage>20221</lpage><pub-id pub-id-type="doi">10.1073/pnas.0909775106</pub-id><pub-id pub-id-type="pmid">19875695</pub-id></element-citation></ref><ref id="bib46"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Goel</surname><given-names>RR</given-names></name><name><surname>Painter</surname><given-names>MM</given-names></name><name><surname>Apostolidis</surname><given-names>SA</given-names></name><name><surname>Mathew</surname><given-names>D</given-names></name><name><surname>Meng</surname><given-names>W</given-names></name><name><surname>Rosenfeld</surname><given-names>AM</given-names></name><name><surname>Lundgreen</surname><given-names>KA</given-names></name><name><surname>Reynaldi</surname><given-names>A</given-names></name><name><surname>Khoury</surname><given-names>DS</given-names></name><name><surname>Pattekar</surname><given-names>A</given-names></name><name><surname>Gouma</surname><given-names>S</given-names></name><name><surname>Kuri-Cervantes</surname><given-names>L</given-names></name><name><surname>Hicks</surname><given-names>P</given-names></name><name><surname>Dysinger</surname><given-names>S</given-names></name><name><surname>Hicks</surname><given-names>A</given-names></name><name><surname>Sharma</surname><given-names>H</given-names></name><name><surname>Herring</surname><given-names>S</given-names></name><name><surname>Korte</surname><given-names>S</given-names></name><name><surname>Baxter</surname><given-names>AE</given-names></name><name><surname>Oldridge</surname><given-names>DA</given-names></name><name><surname>Giles</surname><given-names>JR</given-names></name><name><surname>Weirick</surname><given-names>ME</given-names></name><name><surname>McAllister</surname><given-names>CM</given-names></name><name><surname>Awofolaju</surname><given-names>M</given-names></name><name><surname>Tanenbaum</surname><given-names>N</given-names></name><name><surname>Drapeau</surname><given-names>EM</given-names></name><name><surname>Dougherty</surname><given-names>J</given-names></name><name><surname>Long</surname><given-names>S</given-names></name><name><surname>D’Andrea</surname><given-names>K</given-names></name><name><surname>Hamilton</surname><given-names>JT</given-names></name><name><surname>McLaughlin</surname><given-names>M</given-names></name><name><surname>Williams</surname><given-names>JC</given-names></name><name><surname>Adamski</surname><given-names>S</given-names></name><name><surname>Kuthuru</surname><given-names>O</given-names></name><name><surname>Frank</surname><given-names>I</given-names></name><name><surname>Betts</surname><given-names>MR</given-names></name><name><surname>Vella</surname><given-names>LA</given-names></name><name><surname>Grifoni</surname><given-names>A</given-names></name><name><surname>Weiskopf</surname><given-names>D</given-names></name><name><surname>Sette</surname><given-names>A</given-names></name><name><surname>Hensley</surname><given-names>SE</given-names></name><name><surname>Davenport</surname><given-names>MP</given-names></name><name><surname>Bates</surname><given-names>P</given-names></name><name><surname>Luning Prak</surname><given-names>ET</given-names></name><name><surname>Greenplate</surname><given-names>AR</given-names></name><name><surname>Wherry</surname><given-names>EJ</given-names></name><collab>The UPenn COVID Processing Unit‡</collab></person-group><year iso-8601-date="2021">2021</year><article-title>mRNA vaccines induce durable immune memory to SARS-CoV-2 and variants of concern</article-title><source>Science</source><volume>374</volume><elocation-id>abm0829. 10.1126/science.abm0829</elocation-id><pub-id pub-id-type="doi">10.1126/science.abm0829</pub-id></element-citation></ref><ref id="bib47"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Guthmiller</surname><given-names>JJ</given-names></name><name><surname>Wilson</surname><given-names>PC</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Harnessing immune history to combat influenza viruses</article-title><source>Current Opinion in Immunology</source><volume>53</volume><fpage>187</fpage><lpage>195</lpage><pub-id pub-id-type="doi">10.1016/j.coi.2018.05.010</pub-id></element-citation></ref><ref id="bib48"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hägglöf</surname><given-names>T</given-names></name><name><surname>Cipolla</surname><given-names>M</given-names></name><name><surname>Loewe</surname><given-names>M</given-names></name><name><surname>Chen</surname><given-names>ST</given-names></name><name><surname>Mesin</surname><given-names>L</given-names></name><name><surname>Hartweger</surname><given-names>H</given-names></name><name><surname>ElTanbouly</surname><given-names>MA</given-names></name><name><surname>Cho</surname><given-names>A</given-names></name><name><surname>Gazumyan</surname><given-names>A</given-names></name><name><surname>Ramos</surname><given-names>V</given-names></name><name><surname>Stamatatos</surname><given-names>L</given-names></name><name><surname>Oliveira</surname><given-names>TY</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name><name><surname>Viant</surname><given-names>C</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Continuous germinal center invasion contributes to the diversity of the immune response</article-title><source>Cell</source><volume>186</volume><fpage>147</fpage><lpage>161</lpage><pub-id pub-id-type="doi">10.1016/j.cell.2022.11.032</pub-id><pub-id pub-id-type="pmid">36565698</pub-id></element-citation></ref><ref id="bib49"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Henry</surname><given-names>C</given-names></name><name><surname>Palm</surname><given-names>A-KE</given-names></name><name><surname>Krammer</surname><given-names>F</given-names></name><name><surname>Wilson</surname><given-names>PC</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>From original antigenic sin to the universal influenza virus vaccine</article-title><source>Trends in Immunology</source><volume>39</volume><fpage>70</fpage><lpage>79</lpage><pub-id pub-id-type="doi">10.1016/j.it.2017.08.003</pub-id></element-citation></ref><ref id="bib50"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hong</surname><given-names>M</given-names></name><name><surname>Lee</surname><given-names>PS</given-names></name><name><surname>Hoffman</surname><given-names>RMB</given-names></name><name><surname>Zhu</surname><given-names>X</given-names></name><name><surname>Krause</surname><given-names>JC</given-names></name><name><surname>Laursen</surname><given-names>NS</given-names></name><name><surname>Yoon</surname><given-names>S</given-names></name><name><surname>Song</surname><given-names>L</given-names></name><name><surname>Tussey</surname><given-names>L</given-names></name><name><surname>Crowe</surname><given-names>JE</given-names></name><name><surname>Ward</surname><given-names>AB</given-names></name><name><surname>Wilson</surname><given-names>IA</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>Antibody recognition of the pandemic H1N1 influenza virus hemagglutinin receptor binding site</article-title><source>Journal of Virology</source><volume>87</volume><fpage>12471</fpage><lpage>12480</lpage><pub-id pub-id-type="doi">10.1128/JVI.01388-13</pub-id></element-citation></ref><ref id="bib51"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Jacob</surname><given-names>J</given-names></name><name><surname>Kassir</surname><given-names>R</given-names></name><name><surname>Kelsoe</surname><given-names>G</given-names></name></person-group><year iso-8601-date="1991">1991</year><article-title>In situ studies of the primary immune response to (4-hydroxy-3-nitrophenyl)acetyl. I. The architecture and dynamics of responding cell populations</article-title><source>The Journal of Experimental Medicine</source><volume>173</volume><fpage>1165</fpage><lpage>1175</lpage><pub-id pub-id-type="doi">10.1084/jem.173.5.1165</pub-id></element-citation></ref><ref id="bib52"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Jordan</surname><given-names>K</given-names></name><name><surname>Murchu</surname><given-names>EO</given-names></name><name><surname>Comber</surname><given-names>L</given-names></name><name><surname>Hawkshaw</surname><given-names>S</given-names></name><name><surname>Marshall</surname><given-names>L</given-names></name><name><surname>O’Neill</surname><given-names>M</given-names></name><name><surname>Teljeur</surname><given-names>C</given-names></name><name><surname>Harrington</surname><given-names>P</given-names></name><name><surname>Carnahan</surname><given-names>A</given-names></name><name><surname>Pérez-Martín</surname><given-names>JJ</given-names></name><name><surname>Robertson</surname><given-names>AH</given-names></name><name><surname>Johansen</surname><given-names>K</given-names></name><name><surname>de Jonge</surname><given-names>J</given-names></name><name><surname>Krause</surname><given-names>T</given-names></name><name><surname>Nicolay</surname><given-names>N</given-names></name><name><surname>Nohynek</surname><given-names>H</given-names></name><name><surname>Pavlopoulou</surname><given-names>I</given-names></name><name><surname>Pebody</surname><given-names>R</given-names></name><name><surname>Penttinen</surname><given-names>P</given-names></name><name><surname>Soler-Soneira</surname><given-names>M</given-names></name><name><surname>Wichmann</surname><given-names>O</given-names></name><name><surname>Ryan</surname><given-names>M</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Systematic review of the efficacy, effectiveness and safety of cell-based seasonal influenza vaccines for the prevention of laboratory-confirmed influenza in individuals ≥18 years of age</article-title><source>Reviews in Medical Virology</source><volume>33</volume><elocation-id>e2332</elocation-id><pub-id pub-id-type="doi">10.1002/rmv.2332</pub-id><pub-id pub-id-type="pmid">35137512</pub-id></element-citation></ref><ref id="bib53"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kim</surname><given-names>YM</given-names></name><name><surname>Pan</surname><given-names>JYJ</given-names></name><name><surname>Korbel</surname><given-names>GA</given-names></name><name><surname>Peperzak</surname><given-names>V</given-names></name><name><surname>Boes</surname><given-names>M</given-names></name><name><surname>Ploegh</surname><given-names>HL</given-names></name></person-group><year iso-8601-date="2006">2006</year><article-title>Monovalent ligation of the B cell receptor induces receptor activation but fails to promote antigen presentation</article-title><source>PNAS</source><volume>103</volume><fpage>3327</fpage><lpage>3332</lpage><pub-id pub-id-type="doi">10.1073/pnas.0511315103</pub-id></element-citation></ref><ref id="bib54"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Krammer</surname><given-names>F</given-names></name><name><surname>Palese</surname><given-names>P</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>Influenza virus hemagglutinin stalk-based antibodies and vaccines</article-title><source>Current Opinion in Virology</source><volume>3</volume><fpage>521</fpage><lpage>530</lpage><pub-id pub-id-type="doi">10.1016/j.coviro.2013.07.007</pub-id><pub-id pub-id-type="pmid">23978327</pub-id></element-citation></ref><ref id="bib55"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Krammer</surname><given-names>F</given-names></name><name><surname>García-Sastre</surname><given-names>A</given-names></name><name><surname>Palese</surname><given-names>P</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Is it possible to develop a “universal” influenza virus vaccine? potential target antigens and critical aspects for a universal influenza vaccine</article-title><source>Cold Spring Harbor Perspectives in Biology</source><volume>10</volume><elocation-id>a028845</elocation-id><pub-id pub-id-type="doi">10.1101/cshperspect.a028845</pub-id><pub-id pub-id-type="pmid">28663209</pub-id></element-citation></ref><ref id="bib56"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Krammer</surname><given-names>F</given-names></name><name><surname>Weir</surname><given-names>JP</given-names></name><name><surname>Engelhardt</surname><given-names>O</given-names></name><name><surname>Katz</surname><given-names>JM</given-names></name><name><surname>Cox</surname><given-names>RJ</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Meeting report and review: Immunological assays and correlates of protection for next-generation influenza vaccines</article-title><source>Influenza and Other Respiratory Viruses</source><volume>14</volume><fpage>237</fpage><lpage>243</lpage><pub-id pub-id-type="doi">10.1111/irv.12706</pub-id><pub-id pub-id-type="pmid">31837101</pub-id></element-citation></ref><ref id="bib57"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kumar</surname><given-names>MDS</given-names></name><name><surname>Gromiha</surname><given-names>MM</given-names></name></person-group><year iso-8601-date="2006">2006</year><article-title>PINT: protein-protein interactions thermodynamic database</article-title><source>Nucleic Acids Research</source><volume>34</volume><fpage>D195</fpage><lpage>D198</lpage><pub-id pub-id-type="doi">10.1093/nar/gkj017</pub-id><pub-id pub-id-type="pmid">16381844</pub-id></element-citation></ref><ref id="bib58"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kuraoka</surname><given-names>M</given-names></name><name><surname>Schmidt</surname><given-names>AG</given-names></name><name><surname>Nojima</surname><given-names>T</given-names></name><name><surname>Feng</surname><given-names>F</given-names></name><name><surname>Watanabe</surname><given-names>A</given-names></name><name><surname>Kitamura</surname><given-names>D</given-names></name><name><surname>Harrison</surname><given-names>SC</given-names></name><name><surname>Kepler</surname><given-names>TB</given-names></name><name><surname>Kelsoe</surname><given-names>G</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Complex antigens drive permissive clonal selection in germinal centers</article-title><source>Immunity</source><volume>44</volume><fpage>542</fpage><lpage>552</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2016.02.010</pub-id><pub-id pub-id-type="pmid">26948373</pub-id></element-citation></ref><ref id="bib59"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lee</surname><given-names>JH</given-names></name><name><surname>Hu</surname><given-names>JK</given-names></name><name><surname>Georgeson</surname><given-names>E</given-names></name><name><surname>Nakao</surname><given-names>C</given-names></name><name><surname>Groschel</surname><given-names>B</given-names></name><name><surname>Dileepan</surname><given-names>T</given-names></name><name><surname>Jenkins</surname><given-names>MK</given-names></name><name><surname>Seumois</surname><given-names>G</given-names></name><name><surname>Vijayanand</surname><given-names>P</given-names></name><name><surname>Schief</surname><given-names>WR</given-names></name><name><surname>Crotty</surname><given-names>S</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Modulating the quantity of HIV Env-specific CD4 T cell help promotes rare B cell responses in germinal centers</article-title><source>The Journal of Experimental Medicine</source><volume>218</volume><elocation-id>e20201254</elocation-id><pub-id pub-id-type="doi">10.1084/jem.20201254</pub-id><pub-id pub-id-type="pmid">33355623</pub-id></element-citation></ref><ref id="bib60"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Li</surname><given-names>Z</given-names></name><name><surname>Woo</surname><given-names>CJ</given-names></name><name><surname>Iglesias-Ussel</surname><given-names>MD</given-names></name><name><surname>Ronai</surname><given-names>D</given-names></name><name><surname>Scharff</surname><given-names>MD</given-names></name></person-group><year iso-8601-date="2004">2004</year><article-title>The generation of antibody diversity through somatic hypermutation and class switch recombination</article-title><source>Genes &amp; Development</source><volume>18</volume><fpage>1</fpage><lpage>11</lpage><pub-id pub-id-type="doi">10.1101/gad.1161904</pub-id><pub-id pub-id-type="pmid">14724175</pub-id></element-citation></ref><ref id="bib61"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lingwood</surname><given-names>D</given-names></name><name><surname>McTamney</surname><given-names>PM</given-names></name><name><surname>Yassine</surname><given-names>HM</given-names></name><name><surname>Whittle</surname><given-names>JRR</given-names></name><name><surname>Guo</surname><given-names>X</given-names></name><name><surname>Boyington</surname><given-names>JC</given-names></name><name><surname>Wei</surname><given-names>CJ</given-names></name><name><surname>Nabel</surname><given-names>GJ</given-names></name></person-group><year iso-8601-date="2012">2012</year><article-title>Structural and genetic basis for development of broadly neutralizing influenza antibodies</article-title><source>Nature</source><volume>489</volume><fpage>566</fpage><lpage>570</lpage><pub-id pub-id-type="doi">10.1038/nature11371</pub-id><pub-id pub-id-type="pmid">22932267</pub-id></element-citation></ref><ref id="bib62"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Mahanty</surname><given-names>S</given-names></name><name><surname>Prigent</surname><given-names>A</given-names></name><name><surname>Garraud</surname><given-names>O</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Immunogenicity of infectious pathogens and vaccine antigens</article-title><source>BMC Immunology</source><volume>16</volume><elocation-id>95</elocation-id><pub-id pub-id-type="doi">10.1186/s12865-015-0095-y</pub-id><pub-id pub-id-type="pmid">26021448</pub-id></element-citation></ref><ref id="bib63"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Martin</surname><given-names>JT</given-names></name><name><surname>Hartwell</surname><given-names>BL</given-names></name><name><surname>Kumarapperuma</surname><given-names>SC</given-names></name><name><surname>Melo</surname><given-names>MB</given-names></name><name><surname>Carnathan</surname><given-names>DG</given-names></name><name><surname>Cossette</surname><given-names>BJ</given-names></name><name><surname>Adams</surname><given-names>J</given-names></name><name><surname>Gong</surname><given-names>S</given-names></name><name><surname>Zhang</surname><given-names>W</given-names></name><name><surname>Tokatlian</surname><given-names>T</given-names></name><name><surname>Menis</surname><given-names>S</given-names></name><name><surname>Schiffner</surname><given-names>T</given-names></name><name><surname>Franklin</surname><given-names>CG</given-names></name><name><surname>Goins</surname><given-names>B</given-names></name><name><surname>Fox</surname><given-names>PT</given-names></name><name><surname>Silvestri</surname><given-names>G</given-names></name><name><surname>Schief</surname><given-names>WR</given-names></name><name><surname>Ruprecht</surname><given-names>RM</given-names></name><name><surname>Irvine</surname><given-names>DJ</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Combined PET and whole-tissue imaging of lymphatic-targeting vaccines in non-human primates</article-title><source>Biomaterials</source><volume>275</volume><elocation-id>120868</elocation-id><pub-id pub-id-type="doi">10.1016/j.biomaterials.2021.120868</pub-id><pub-id pub-id-type="pmid">34091299</pub-id></element-citation></ref><ref id="bib64"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>McNamara</surname><given-names>HA</given-names></name><name><surname>Idris</surname><given-names>AH</given-names></name><name><surname>Sutton</surname><given-names>HJ</given-names></name><name><surname>Vistein</surname><given-names>R</given-names></name><name><surname>Flynn</surname><given-names>BJ</given-names></name><name><surname>Cai</surname><given-names>Y</given-names></name><name><surname>Wiehe</surname><given-names>K</given-names></name><name><surname>Lyke</surname><given-names>KE</given-names></name><name><surname>Chatterjee</surname><given-names>D</given-names></name><name><surname>Kc</surname><given-names>N</given-names></name><name><surname>Chakravarty</surname><given-names>S</given-names></name><name><surname>Lee Sim</surname><given-names>BK</given-names></name><name><surname>Hoffman</surname><given-names>SL</given-names></name><name><surname>Bonsignori</surname><given-names>M</given-names></name><name><surname>Seder</surname><given-names>RA</given-names></name><name><surname>Cockburn</surname><given-names>IA</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Antibody feedback limits the expansion of B cell responses to malaria vaccination but drives diversification of the humoral response</article-title><source>Cell Host &amp; Microbe</source><volume>28</volume><fpage>572</fpage><lpage>585</lpage><pub-id pub-id-type="doi">10.1016/j.chom.2020.07.001</pub-id></element-citation></ref><ref id="bib65"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Mena</surname><given-names>I</given-names></name><name><surname>Nelson</surname><given-names>MI</given-names></name><name><surname>Quezada-Monroy</surname><given-names>F</given-names></name><name><surname>Dutta</surname><given-names>J</given-names></name><name><surname>Cortes-Fernández</surname><given-names>R</given-names></name><name><surname>Lara-Puente</surname><given-names>JH</given-names></name><name><surname>Castro-Peralta</surname><given-names>F</given-names></name><name><surname>Cunha</surname><given-names>LF</given-names></name><name><surname>Trovão</surname><given-names>NS</given-names></name><name><surname>Lozano-Dubernard</surname><given-names>B</given-names></name><name><surname>Rambaut</surname><given-names>A</given-names></name><name><surname>van Bakel</surname><given-names>H</given-names></name><name><surname>García-Sastre</surname><given-names>A</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Origins of the 2009 H1N1 influenza pandemic in swine in Mexico</article-title><source>eLife</source><volume>5</volume><elocation-id>16777</elocation-id><pub-id pub-id-type="doi">10.7554/eLife.16777</pub-id></element-citation></ref><ref id="bib66"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Mesin</surname><given-names>L</given-names></name><name><surname>Ersching</surname><given-names>J</given-names></name><name><surname>Victora</surname><given-names>GD</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Germinal center B cell dynamics</article-title><source>Immunity</source><volume>45</volume><fpage>471</fpage><lpage>482</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2016.09.001</pub-id></element-citation></ref><ref id="bib67"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Mesin</surname><given-names>L</given-names></name><name><surname>Schiepers</surname><given-names>A</given-names></name><name><surname>Ersching</surname><given-names>J</given-names></name><name><surname>Barbulescu</surname><given-names>A</given-names></name><name><surname>Cavazzoni</surname><given-names>CB</given-names></name><name><surname>Angelini</surname><given-names>A</given-names></name><name><surname>Okada</surname><given-names>T</given-names></name><name><surname>Kurosaki</surname><given-names>T</given-names></name><name><surname>Victora</surname><given-names>GD</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Restricted clonality and limited germinal center reentry characterize memory B cell reactivation by boosting</article-title><source>Cell</source><volume>180</volume><fpage>92</fpage><lpage>106</lpage><pub-id pub-id-type="doi">10.1016/j.cell.2019.11.032</pub-id><pub-id pub-id-type="pmid">31866068</pub-id></element-citation></ref><ref id="bib68"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Moran</surname><given-names>I</given-names></name><name><surname>Nguyen</surname><given-names>A</given-names></name><name><surname>Khoo</surname><given-names>WH</given-names></name><name><surname>Butt</surname><given-names>D</given-names></name><name><surname>Bourne</surname><given-names>K</given-names></name><name><surname>Young</surname><given-names>C</given-names></name><name><surname>Hermes</surname><given-names>JR</given-names></name><name><surname>Biro</surname><given-names>M</given-names></name><name><surname>Gracie</surname><given-names>G</given-names></name><name><surname>Ma</surname><given-names>CS</given-names></name><name><surname>Munier</surname><given-names>CML</given-names></name><name><surname>Luciani</surname><given-names>F</given-names></name><name><surname>Zaunders</surname><given-names>J</given-names></name><name><surname>Parker</surname><given-names>A</given-names></name><name><surname>Kelleher</surname><given-names>AD</given-names></name><name><surname>Tangye</surname><given-names>SG</given-names></name><name><surname>Croucher</surname><given-names>PI</given-names></name><name><surname>Brink</surname><given-names>R</given-names></name><name><surname>Read</surname><given-names>MN</given-names></name><name><surname>Phan</surname><given-names>TG</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Memory B cells are reactivated in subcapsular proliferative foci of lymph nodes</article-title><source>Nature Communications</source><volume>9</volume><elocation-id>3372</elocation-id><pub-id pub-id-type="doi">10.1038/s41467-018-05772-7</pub-id><pub-id pub-id-type="pmid">30135429</pub-id></element-citation></ref><ref id="bib69"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Moran</surname><given-names>I</given-names></name><name><surname>Grootveld</surname><given-names>AK</given-names></name><name><surname>Nguyen</surname><given-names>A</given-names></name><name><surname>Phan</surname><given-names>TG</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Subcapsular sinus macrophages: the seat of innate and adaptive memory in murine lymph nodes</article-title><source>Trends in Immunology</source><volume>40</volume><fpage>35</fpage><lpage>48</lpage><pub-id pub-id-type="doi">10.1016/j.it.2018.11.004</pub-id><pub-id pub-id-type="pmid">30502023</pub-id></element-citation></ref><ref id="bib70"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Muecksch</surname><given-names>F</given-names></name><name><surname>Wang</surname><given-names>Z</given-names></name><name><surname>Cho</surname><given-names>A</given-names></name><name><surname>Gaebler</surname><given-names>C</given-names></name><name><surname>Ben Tanfous</surname><given-names>T</given-names></name><name><surname>DaSilva</surname><given-names>J</given-names></name><name><surname>Bednarski</surname><given-names>E</given-names></name><name><surname>Ramos</surname><given-names>V</given-names></name><name><surname>Zong</surname><given-names>S</given-names></name><name><surname>Johnson</surname><given-names>B</given-names></name><name><surname>Raspe</surname><given-names>R</given-names></name><name><surname>Schaefer-Babajew</surname><given-names>D</given-names></name><name><surname>Shimeliovich</surname><given-names>I</given-names></name><name><surname>Daga</surname><given-names>M</given-names></name><name><surname>Yao</surname><given-names>K-H</given-names></name><name><surname>Schmidt</surname><given-names>F</given-names></name><name><surname>Millard</surname><given-names>KG</given-names></name><name><surname>Turroja</surname><given-names>M</given-names></name><name><surname>Jankovic</surname><given-names>M</given-names></name><name><surname>Oliveira</surname><given-names>TY</given-names></name><name><surname>Gazumyan</surname><given-names>A</given-names></name><name><surname>Caskey</surname><given-names>M</given-names></name><name><surname>Hatziioannou</surname><given-names>T</given-names></name><name><surname>Bieniasz</surname><given-names>PD</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name></person-group><year iso-8601-date="2022">2022</year><article-title>Increased memory B cell potency and breadth after a SARS-CoV-2 mRNA boost</article-title><source>Nature</source><volume>607</volume><fpage>128</fpage><lpage>134</lpage><pub-id pub-id-type="doi">10.1038/s41586-022-04778-y</pub-id><pub-id pub-id-type="pmid">35447027</pub-id></element-citation></ref><ref id="bib71"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nachbagauer</surname><given-names>R</given-names></name><name><surname>Palese</surname><given-names>P</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Development of next generation hemagglutinin-based broadly protective influenza virus vaccines</article-title><source>Current Opinion in Immunology</source><volume>53</volume><fpage>51</fpage><lpage>57</lpage><pub-id pub-id-type="doi">10.1016/j.coi.2018.04.001</pub-id><pub-id pub-id-type="pmid">29680576</pub-id></element-citation></ref><ref id="bib72"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nachbagauer</surname><given-names>R</given-names></name><name><surname>Feser</surname><given-names>J</given-names></name><name><surname>Naficy</surname><given-names>A</given-names></name><name><surname>Bernstein</surname><given-names>DI</given-names></name><name><surname>Guptill</surname><given-names>J</given-names></name><name><surname>Walter</surname><given-names>EB</given-names></name><name><surname>Berlanda-Scorza</surname><given-names>F</given-names></name><name><surname>Stadlbauer</surname><given-names>D</given-names></name><name><surname>Wilson</surname><given-names>PC</given-names></name><name><surname>Aydillo</surname><given-names>T</given-names></name><name><surname>Behzadi</surname><given-names>MA</given-names></name><name><surname>Bhavsar</surname><given-names>D</given-names></name><name><surname>Bliss</surname><given-names>C</given-names></name><name><surname>Capuano</surname><given-names>C</given-names></name><name><surname>Carreño</surname><given-names>JM</given-names></name><name><surname>Chromikova</surname><given-names>V</given-names></name><name><surname>Claeys</surname><given-names>C</given-names></name><name><surname>Coughlan</surname><given-names>L</given-names></name><name><surname>Freyn</surname><given-names>AW</given-names></name><name><surname>Gast</surname><given-names>C</given-names></name><name><surname>Javier</surname><given-names>A</given-names></name><name><surname>Jiang</surname><given-names>K</given-names></name><name><surname>Mariottini</surname><given-names>C</given-names></name><name><surname>McMahon</surname><given-names>M</given-names></name><name><surname>McNeal</surname><given-names>M</given-names></name><name><surname>Solórzano</surname><given-names>A</given-names></name><name><surname>Strohmeier</surname><given-names>S</given-names></name><name><surname>Sun</surname><given-names>W</given-names></name><name><surname>van der Wielen</surname><given-names>M</given-names></name><name><surname>Innis</surname><given-names>BL</given-names></name><name><surname>García-Sastre</surname><given-names>A</given-names></name><name><surname>Palese</surname><given-names>P</given-names></name><name><surname>Krammer</surname><given-names>F</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>A chimeric hemagglutinin-based universal influenza virus vaccine approach induces broad and long-lasting immunity in a randomized, placebo-controlled phase I trial</article-title><source>Nature Medicine</source><volume>27</volume><fpage>106</fpage><lpage>114</lpage><pub-id pub-id-type="doi">10.1038/s41591-020-1118-7</pub-id><pub-id pub-id-type="pmid">33288923</pub-id></element-citation></ref><ref id="bib73"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nowak</surname><given-names>J</given-names></name><name><surname>Baker</surname><given-names>T</given-names></name><name><surname>Georges</surname><given-names>G</given-names></name><name><surname>Kelm</surname><given-names>S</given-names></name><name><surname>Klostermann</surname><given-names>S</given-names></name><name><surname>Shi</surname><given-names>J</given-names></name><name><surname>Sridharan</surname><given-names>S</given-names></name><name><surname>Deane</surname><given-names>CM</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Length-independent structural similarities enrich the antibody CDR canonical class model</article-title><source>mAbs</source><volume>8</volume><fpage>751</fpage><lpage>760</lpage><pub-id pub-id-type="doi">10.1080/19420862.2016.1158370</pub-id><pub-id pub-id-type="pmid">26963563</pub-id></element-citation></ref><ref id="bib74"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nuñez</surname><given-names>IA</given-names></name><name><surname>Carlock</surname><given-names>MA</given-names></name><name><surname>Allen</surname><given-names>JD</given-names></name><name><surname>Owino</surname><given-names>SO</given-names></name><name><surname>Moehling</surname><given-names>KK</given-names></name><name><surname>Nowalk</surname><given-names>P</given-names></name><name><surname>Susick</surname><given-names>M</given-names></name><name><surname>Diagle</surname><given-names>K</given-names></name><name><surname>Sweeney</surname><given-names>K</given-names></name><name><surname>Mundle</surname><given-names>S</given-names></name><name><surname>Vogel</surname><given-names>TU</given-names></name><name><surname>Delagrave</surname><given-names>S</given-names></name><name><surname>Ramgopal</surname><given-names>M</given-names></name><name><surname>Zimmerman</surname><given-names>RK</given-names></name><name><surname>Kleanthous</surname><given-names>H</given-names></name><name><surname>Ross</surname><given-names>TM</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Impact of age and pre-existing influenza immune responses in humans receiving split inactivated influenza vaccine on the induction of the breadth of antibodies to influenza A strains</article-title><source>PLOS ONE</source><volume>12</volume><elocation-id>e0185666</elocation-id><pub-id pub-id-type="doi">10.1371/journal.pone.0185666</pub-id><pub-id pub-id-type="pmid">29091724</pub-id></element-citation></ref><ref id="bib75"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Palm</surname><given-names>AKE</given-names></name><name><surname>Henry</surname><given-names>C</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Remembrance of things past: long-term B cell memory after infection and vaccination</article-title><source>Frontiers in Immunology</source><volume>10</volume><elocation-id>1787</elocation-id><pub-id pub-id-type="doi">10.3389/fimmu.2019.01787</pub-id><pub-id pub-id-type="pmid">31417562</pub-id></element-citation></ref><ref id="bib76"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pedersen</surname><given-names>JC</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>Hemagglutination-inhibition assay for influenza virus subtype identification and the detection and quantitation of serum antibodies to influenza virus</article-title><source>Methods in Molecular Biology</source><volume>1161</volume><fpage>11</fpage><lpage>25</lpage><pub-id pub-id-type="doi">10.1007/978-1-4939-0758-8_2</pub-id><pub-id pub-id-type="pmid">24899416</pub-id></element-citation></ref><ref id="bib77"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Phan</surname><given-names>TG</given-names></name><name><surname>Grigorova</surname><given-names>I</given-names></name><name><surname>Okada</surname><given-names>T</given-names></name><name><surname>Cyster</surname><given-names>JG</given-names></name></person-group><year iso-8601-date="2007">2007</year><article-title>Subcapsular encounter and complement-dependent transport of immune complexes by lymph node B cells</article-title><source>Nature Immunology</source><volume>8</volume><fpage>992</fpage><lpage>1000</lpage><pub-id pub-id-type="doi">10.1038/ni1494</pub-id></element-citation></ref><ref id="bib78"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Radmacher</surname><given-names>MD</given-names></name><name><surname>Kelsoe</surname><given-names>G</given-names></name><name><surname>Kepler</surname><given-names>TB</given-names></name></person-group><year iso-8601-date="1998">1998</year><article-title>Predicted and inferred waiting times for key mutations in the germinal centre reaction: Evidence for stochasticity in selection</article-title><source>Immunology &amp; Cell Biology</source><volume>76</volume><fpage>373</fpage><lpage>381</lpage><pub-id pub-id-type="doi">10.1046/j.1440-1711.1998.00753.x</pub-id></element-citation></ref><ref id="bib79"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ray</surname><given-names>R</given-names></name><name><surname>Nait Mohamed</surname><given-names>FA</given-names></name><name><surname>Maurer</surname><given-names>DP</given-names></name><name><surname>Huang</surname><given-names>J</given-names></name><name><surname>Alpay</surname><given-names>BA</given-names></name><name><surname>Ronsard</surname><given-names>L</given-names></name><name><surname>Xie</surname><given-names>Z</given-names></name><name><surname>Han</surname><given-names>J</given-names></name><name><surname>Fernandez-Quintero</surname><given-names>M</given-names></name><name><surname>Phan</surname><given-names>QA</given-names></name><name><surname>Ursin</surname><given-names>RL</given-names></name><name><surname>Vu</surname><given-names>M</given-names></name><name><surname>Kirsch</surname><given-names>KH</given-names></name><name><surname>Prum</surname><given-names>T</given-names></name><name><surname>Rosado</surname><given-names>VC</given-names></name><name><surname>Bracamonte-Moreno</surname><given-names>T</given-names></name><name><surname>Okonkwo</surname><given-names>V</given-names></name><name><surname>Bals</surname><given-names>J</given-names></name><name><surname>McCarthy</surname><given-names>C</given-names></name><name><surname>Nair</surname><given-names>U</given-names></name><name><surname>Kanekiyo</surname><given-names>M</given-names></name><name><surname>Ward</surname><given-names>AB</given-names></name><name><surname>Schmidt</surname><given-names>AG</given-names></name><name><surname>Batista</surname><given-names>FD</given-names></name><name><surname>Lingwood</surname><given-names>D</given-names></name></person-group><year iso-8601-date="2024">2024</year><article-title>Eliciting a single amino acid change by vaccination generates antibody protection against group 1 and group 2 influenza A viruses</article-title><source>Immunity</source><volume>57</volume><fpage>1141</fpage><lpage>1159</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2024.03.022</pub-id><pub-id pub-id-type="pmid">38670113</pub-id></element-citation></ref><ref id="bib80"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Raymond</surname><given-names>DD</given-names></name><name><surname>Bajic</surname><given-names>G</given-names></name><name><surname>Ferdman</surname><given-names>J</given-names></name><name><surname>Suphaphiphat</surname><given-names>P</given-names></name><name><surname>Settembre</surname><given-names>EC</given-names></name><name><surname>Moody</surname><given-names>MA</given-names></name><name><surname>Schmidt</surname><given-names>AG</given-names></name><name><surname>Harrison</surname><given-names>SC</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Conserved epitope on influenza-virus hemagglutinin head defined by a vaccine-induced antibody</article-title><source>PNAS</source><volume>115</volume><fpage>168</fpage><lpage>173</lpage><pub-id pub-id-type="doi">10.1073/pnas.1715471115</pub-id></element-citation></ref><ref id="bib81"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Reed</surname><given-names>C</given-names></name><name><surname>Meltzer</surname><given-names>MI</given-names></name><name><surname>Finelli</surname><given-names>L</given-names></name><name><surname>Fiore</surname><given-names>A</given-names></name></person-group><year iso-8601-date="2012">2012</year><article-title>Public health impact of including two lineages of influenza B in a quadrivalent seasonal influenza vaccine</article-title><source>Vaccine</source><volume>30</volume><fpage>1993</fpage><lpage>1998</lpage><pub-id pub-id-type="doi">10.1016/j.vaccine.2011.12.098</pub-id><pub-id pub-id-type="pmid">22226861</pub-id></element-citation></ref><ref id="bib82"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Rees</surname><given-names>AR</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Understanding the human antibody repertoire</article-title><source>mAbs</source><volume>12</volume><elocation-id>1729683</elocation-id><pub-id pub-id-type="doi">10.1080/19420862.2020.1729683</pub-id><pub-id pub-id-type="pmid">32097086</pub-id></element-citation></ref><ref id="bib83"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Reusch</surname><given-names>L</given-names></name><name><surname>Angeletti</surname><given-names>D</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Memory B-cell diversity: From early generation to tissue residency and reactivation</article-title><source>European Journal of Immunology</source><volume>53</volume><elocation-id>e2250085</elocation-id><pub-id pub-id-type="doi">10.1002/eji.202250085</pub-id><pub-id pub-id-type="pmid">36811174</pub-id></element-citation></ref><ref id="bib84"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Rockberg</surname><given-names>J</given-names></name><name><surname>Uhlén</surname><given-names>M</given-names></name></person-group><year iso-8601-date="2009">2009</year><article-title>Prediction of antibody response using recombinant human protein fragments as antigen</article-title><source>Protein Science</source><volume>18</volume><fpage>2346</fpage><lpage>2355</lpage><pub-id pub-id-type="doi">10.1002/pro.245</pub-id><pub-id pub-id-type="pmid">19760667</pub-id></element-citation></ref><ref id="bib85"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ronsard</surname><given-names>L</given-names></name><name><surname>Yousif</surname><given-names>AS</given-names></name><name><surname>Nait Mohamed</surname><given-names>FA</given-names></name><name><surname>Feldman</surname><given-names>J</given-names></name><name><surname>Okonkwo</surname><given-names>V</given-names></name><name><surname>McCarthy</surname><given-names>C</given-names></name><name><surname>Schnabel</surname><given-names>J</given-names></name><name><surname>Caradonna</surname><given-names>T</given-names></name><name><surname>Barnes</surname><given-names>RM</given-names></name><name><surname>Rohrer</surname><given-names>D</given-names></name><name><surname>Lonberg</surname><given-names>N</given-names></name><name><surname>Schmidt</surname><given-names>A</given-names></name><name><surname>Lingwood</surname><given-names>D</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Engaging an HIV vaccine target through the acquisition of low B cell affinity</article-title><source>Nature Communications</source><volume>14</volume><elocation-id>409182</elocation-id><pub-id pub-id-type="doi">10.1038/s41467-023-40918-2</pub-id></element-citation></ref><ref id="bib86"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sabouri</surname><given-names>Z</given-names></name><name><surname>Schofield</surname><given-names>P</given-names></name><name><surname>Horikawa</surname><given-names>K</given-names></name><name><surname>Spierings</surname><given-names>E</given-names></name><name><surname>Kipling</surname><given-names>D</given-names></name><name><surname>Randall</surname><given-names>KL</given-names></name><name><surname>Langley</surname><given-names>D</given-names></name><name><surname>Roome</surname><given-names>B</given-names></name><name><surname>Vazquez-Lombardi</surname><given-names>R</given-names></name><name><surname>Rouet</surname><given-names>R</given-names></name><name><surname>Hermes</surname><given-names>J</given-names></name><name><surname>Chan</surname><given-names>TD</given-names></name><name><surname>Brink</surname><given-names>R</given-names></name><name><surname>Dunn-Walters</surname><given-names>DK</given-names></name><name><surname>Christ</surname><given-names>D</given-names></name><name><surname>Goodnow</surname><given-names>CC</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>Redemption of autoantibodies on anergic B cells by variable-region glycosylation and mutation away from self-reactivity</article-title><source>PNAS</source><volume>111</volume><fpage>E2567</fpage><lpage>E2575</lpage><pub-id pub-id-type="doi">10.1073/pnas.1406974111</pub-id></element-citation></ref><ref id="bib87"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sandor</surname><given-names>AM</given-names></name><name><surname>Sturdivant</surname><given-names>MS</given-names></name><name><surname>Ting</surname><given-names>JPY</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Influenza virus and SARS-CoV-2 vaccines</article-title><source>The Journal of Immunology</source><volume>206</volume><fpage>2509</fpage><lpage>2520</lpage><pub-id pub-id-type="doi">10.4049/jimmunol.2001287</pub-id></element-citation></ref><ref id="bib88"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sangesland</surname><given-names>M</given-names></name><name><surname>Ronsard</surname><given-names>L</given-names></name><name><surname>Kazer</surname><given-names>SW</given-names></name><name><surname>Bals</surname><given-names>J</given-names></name><name><surname>Boyoglu-Barnum</surname><given-names>S</given-names></name><name><surname>Yousif</surname><given-names>AS</given-names></name><name><surname>Barnes</surname><given-names>R</given-names></name><name><surname>Feldman</surname><given-names>J</given-names></name><name><surname>Quirindongo-Crespo</surname><given-names>M</given-names></name><name><surname>McTamney</surname><given-names>PM</given-names></name><name><surname>Rohrer</surname><given-names>D</given-names></name><name><surname>Lonberg</surname><given-names>N</given-names></name><name><surname>Chackerian</surname><given-names>B</given-names></name><name><surname>Graham</surname><given-names>BS</given-names></name><name><surname>Kanekiyo</surname><given-names>M</given-names></name><name><surname>Shalek</surname><given-names>AK</given-names></name><name><surname>Lingwood</surname><given-names>D</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Germline-encoded affinity for cognate antigen enables vaccine amplification of a human broadly neutralizing response against influenza virus</article-title><source>Immunity</source><volume>51</volume><fpage>735</fpage><lpage>749</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2019.09.001</pub-id><pub-id pub-id-type="pmid">31563464</pub-id></element-citation></ref><ref id="bib89"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sangesland</surname><given-names>M</given-names></name><name><surname>Lingwood</surname><given-names>D</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Antibody focusing to conserved sites of vulnerability: the immunological pathways for “universal” influenza vaccines</article-title><source>Vaccines</source><volume>9</volume><elocation-id>125</elocation-id><pub-id pub-id-type="doi">10.3390/vaccines9020125</pub-id><pub-id pub-id-type="pmid">33562627</pub-id></element-citation></ref><ref id="bib90"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sangesland</surname><given-names>M</given-names></name><name><surname>Torrents de la Peña</surname><given-names>A</given-names></name><name><surname>Boyoglu-Barnum</surname><given-names>S</given-names></name><name><surname>Ronsard</surname><given-names>L</given-names></name><name><surname>Mohamed</surname><given-names>FAN</given-names></name><name><surname>Moreno</surname><given-names>TB</given-names></name><name><surname>Barnes</surname><given-names>RM</given-names></name><name><surname>Rohrer</surname><given-names>D</given-names></name><name><surname>Lonberg</surname><given-names>N</given-names></name><name><surname>Ghebremichael</surname><given-names>M</given-names></name><name><surname>Kanekiyo</surname><given-names>M</given-names></name><name><surname>Ward</surname><given-names>A</given-names></name><name><surname>Lingwood</surname><given-names>D</given-names></name></person-group><year iso-8601-date="2022">2022</year><article-title>Allelic polymorphism controls autoreactivity and vaccine elicitation of human broadly neutralizing antibodies against influenza virus</article-title><source>Immunity</source><volume>55</volume><fpage>1693</fpage><lpage>1709</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2022.07.006</pub-id><pub-id pub-id-type="pmid">35952670</pub-id></element-citation></ref><ref id="bib91"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Schaefer-Babajew</surname><given-names>D</given-names></name><name><surname>Wang</surname><given-names>Z</given-names></name><name><surname>Muecksch</surname><given-names>F</given-names></name><name><surname>Cho</surname><given-names>A</given-names></name><name><surname>Loewe</surname><given-names>M</given-names></name><name><surname>Cipolla</surname><given-names>M</given-names></name><name><surname>Raspe</surname><given-names>R</given-names></name><name><surname>Johnson</surname><given-names>B</given-names></name><name><surname>Canis</surname><given-names>M</given-names></name><name><surname>DaSilva</surname><given-names>J</given-names></name><name><surname>Ramos</surname><given-names>V</given-names></name><name><surname>Turroja</surname><given-names>M</given-names></name><name><surname>Millard</surname><given-names>KG</given-names></name><name><surname>Schmidt</surname><given-names>F</given-names></name><name><surname>Witte</surname><given-names>L</given-names></name><name><surname>Dizon</surname><given-names>J</given-names></name><name><surname>Shimeliovich</surname><given-names>I</given-names></name><name><surname>Yao</surname><given-names>K-H</given-names></name><name><surname>Oliveira</surname><given-names>TY</given-names></name><name><surname>Gazumyan</surname><given-names>A</given-names></name><name><surname>Gaebler</surname><given-names>C</given-names></name><name><surname>Bieniasz</surname><given-names>PD</given-names></name><name><surname>Hatziioannou</surname><given-names>T</given-names></name><name><surname>Caskey</surname><given-names>M</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Antibody feedback regulates immune memory after SARS-CoV-2 mRNA vaccination</article-title><source>Nature</source><volume>613</volume><fpage>735</fpage><lpage>742</lpage><pub-id pub-id-type="doi">10.1038/s41586-022-05609-w</pub-id></element-citation></ref><ref id="bib92"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Schiepers</surname><given-names>A</given-names></name><name><surname>Van’t Wout</surname><given-names>MFL</given-names></name><name><surname>Hobbs</surname><given-names>A</given-names></name><name><surname>Mesin</surname><given-names>L</given-names></name><name><surname>Victora</surname><given-names>GD</given-names></name></person-group><year iso-8601-date="2024">2024</year><article-title>Opposing effects of pre-existing antibody and memory T cell help on the dynamics of recall germinal centers</article-title><source>Immunity</source><volume>57</volume><fpage>1618</fpage><lpage>1628</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2024.05.009</pub-id><pub-id pub-id-type="pmid">38838672</pub-id></element-citation></ref><ref id="bib93"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Schmidt</surname><given-names>AG</given-names></name><name><surname>Therkelsen</surname><given-names>MD</given-names></name><name><surname>Stewart</surname><given-names>S</given-names></name><name><surname>Kepler</surname><given-names>TB</given-names></name><name><surname>Liao</surname><given-names>HX</given-names></name><name><surname>Moody</surname><given-names>MA</given-names></name><name><surname>Haynes</surname><given-names>BF</given-names></name><name><surname>Harrison</surname><given-names>SC</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Viral receptor-binding site antibodies with diverse germline origins</article-title><source>Cell</source><volume>161</volume><fpage>1026</fpage><lpage>1034</lpage><pub-id pub-id-type="doi">10.1016/j.cell.2015.04.028</pub-id></element-citation></ref><ref id="bib94"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Schmidt</surname><given-names>F</given-names></name><name><surname>Muecksch</surname><given-names>F</given-names></name><name><surname>Weisblum</surname><given-names>Y</given-names></name><name><surname>Da Silva</surname><given-names>J</given-names></name><name><surname>Bednarski</surname><given-names>E</given-names></name><name><surname>Cho</surname><given-names>A</given-names></name><name><surname>Wang</surname><given-names>Z</given-names></name><name><surname>Gaebler</surname><given-names>C</given-names></name><name><surname>Caskey</surname><given-names>M</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name><name><surname>Hatziioannou</surname><given-names>T</given-names></name><name><surname>Bieniasz</surname><given-names>PD</given-names></name></person-group><year iso-8601-date="2022">2022</year><article-title>Plasma neutralization of the SARS-CoV-2 omicron variant</article-title><source>New England Journal of Medicine</source><volume>386</volume><fpage>599</fpage><lpage>601</lpage><pub-id pub-id-type="doi">10.1056/NEJMc2119641</pub-id></element-citation></ref><ref id="bib95"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Schwickert</surname><given-names>TA</given-names></name><name><surname>Victora</surname><given-names>GD</given-names></name><name><surname>Fooksman</surname><given-names>DR</given-names></name><name><surname>Kamphorst</surname><given-names>AO</given-names></name><name><surname>Mugnier</surname><given-names>MR</given-names></name><name><surname>Gitlin</surname><given-names>AD</given-names></name><name><surname>Dustin</surname><given-names>ML</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name></person-group><year iso-8601-date="2011">2011</year><article-title>A dynamic T cell-limited checkpoint regulates affinity-dependent B cell entry into the germinal center</article-title><source>The Journal of Experimental Medicine</source><volume>208</volume><fpage>1243</fpage><lpage>1252</lpage><pub-id pub-id-type="doi">10.1084/jem.20102477</pub-id><pub-id pub-id-type="pmid">21576382</pub-id></element-citation></ref><ref id="bib96"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sela-Culang</surname><given-names>I</given-names></name><name><surname>Kunik</surname><given-names>V</given-names></name><name><surname>Ofran</surname><given-names>Y</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>The structural basis of antibody-antigen recognition</article-title><source>Frontiers in Immunology</source><volume>4</volume><elocation-id>302</elocation-id><pub-id pub-id-type="doi">10.3389/fimmu.2013.00302</pub-id><pub-id pub-id-type="pmid">24115948</pub-id></element-citation></ref><ref id="bib97"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sencer</surname><given-names>DJ</given-names></name></person-group><year iso-8601-date="2011">2011</year><article-title>Perspective: swine-origin influenza: 1976 and 2009</article-title><source>Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America</source><volume>52</volume><fpage>S4</fpage><lpage>S7</lpage><pub-id pub-id-type="doi">10.1093/cid/ciq006</pub-id></element-citation></ref><ref id="bib98"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Silver</surname><given-names>J</given-names></name><name><surname>Zuo</surname><given-names>T</given-names></name><name><surname>Chaudhary</surname><given-names>N</given-names></name><name><surname>Kumari</surname><given-names>R</given-names></name><name><surname>Tong</surname><given-names>P</given-names></name><name><surname>Giguere</surname><given-names>S</given-names></name><name><surname>Granato</surname><given-names>A</given-names></name><name><surname>Donthula</surname><given-names>R</given-names></name><name><surname>Devereaux</surname><given-names>C</given-names></name><name><surname>Wesemann</surname><given-names>DR</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Stochasticity enables BCR-independent germinal center initiation and antibody affinity maturation</article-title><source>The Journal of Experimental Medicine</source><volume>215</volume><fpage>77</fpage><lpage>90</lpage><pub-id pub-id-type="doi">10.1084/jem.20171022</pub-id><pub-id pub-id-type="pmid">29247044</pub-id></element-citation></ref><ref id="bib99"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Smith</surname><given-names>GJD</given-names></name><name><surname>Vijaykrishna</surname><given-names>D</given-names></name><name><surname>Bahl</surname><given-names>J</given-names></name><name><surname>Lycett</surname><given-names>SJ</given-names></name><name><surname>Worobey</surname><given-names>M</given-names></name><name><surname>Pybus</surname><given-names>OG</given-names></name><name><surname>Ma</surname><given-names>SK</given-names></name><name><surname>Cheung</surname><given-names>CL</given-names></name><name><surname>Raghwani</surname><given-names>J</given-names></name><name><surname>Bhatt</surname><given-names>S</given-names></name><name><surname>Peiris</surname><given-names>JSM</given-names></name><name><surname>Guan</surname><given-names>Y</given-names></name><name><surname>Rambaut</surname><given-names>A</given-names></name></person-group><year iso-8601-date="2009">2009</year><article-title>Origins and evolutionary genomics of the 2009 swine-origin H1N1 influenza A epidemic</article-title><source>Nature</source><volume>459</volume><fpage>1122</fpage><lpage>1125</lpage><pub-id pub-id-type="doi">10.1038/nature08182</pub-id><pub-id pub-id-type="pmid">19516283</pub-id></element-citation></ref><ref id="bib100"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Soema</surname><given-names>PC</given-names></name><name><surname>Kompier</surname><given-names>R</given-names></name><name><surname>Amorij</surname><given-names>J-P</given-names></name><name><surname>Kersten</surname><given-names>GFA</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Current and next generation influenza vaccines: Formulation and production strategies</article-title><source>European Journal of Pharmaceutics and Biopharmaceutics</source><volume>94</volume><fpage>251</fpage><lpage>263</lpage><pub-id pub-id-type="doi">10.1016/j.ejpb.2015.05.023</pub-id></element-citation></ref><ref id="bib101"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Spackman</surname><given-names>E</given-names></name><name><surname>Sitaras</surname><given-names>I</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Hemagglutination Inhibition Assay</article-title><source>Methods in Molecular Biology</source><volume>2123</volume><fpage>11</fpage><lpage>28</lpage><pub-id pub-id-type="doi">10.1007/978-1-0716-0346-8_2</pub-id><pub-id pub-id-type="pmid">32170677</pub-id></element-citation></ref><ref id="bib102"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Syeda</surname><given-names>MZ</given-names></name><name><surname>Hong</surname><given-names>T</given-names></name><name><surname>Huang</surname><given-names>C</given-names></name><name><surname>Huang</surname><given-names>W</given-names></name><name><surname>Mu</surname><given-names>Q</given-names></name></person-group><year iso-8601-date="2024">2024</year><article-title>B cell memory: from generation to reactivation: a multipronged defense wall against pathogens</article-title><source>Cell Death Discovery</source><volume>10</volume><elocation-id>18895</elocation-id><pub-id pub-id-type="doi">10.1038/s41420-024-01889-5</pub-id><pub-id pub-id-type="pmid">38453885</pub-id></element-citation></ref><ref id="bib103"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tam</surname><given-names>HH</given-names></name><name><surname>Melo</surname><given-names>MB</given-names></name><name><surname>Kang</surname><given-names>M</given-names></name><name><surname>Pelet</surname><given-names>JM</given-names></name><name><surname>Ruda</surname><given-names>VM</given-names></name><name><surname>Foley</surname><given-names>MH</given-names></name><name><surname>Hu</surname><given-names>JK</given-names></name><name><surname>Kumari</surname><given-names>S</given-names></name><name><surname>Crampton</surname><given-names>J</given-names></name><name><surname>Baldeon</surname><given-names>AD</given-names></name><name><surname>Sanders</surname><given-names>RW</given-names></name><name><surname>Moore</surname><given-names>JP</given-names></name><name><surname>Crotty</surname><given-names>S</given-names></name><name><surname>Langer</surname><given-names>R</given-names></name><name><surname>Anderson</surname><given-names>DG</given-names></name><name><surname>Chakraborty</surname><given-names>AK</given-names></name><name><surname>Irvine</surname><given-names>DJ</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Sustained antigen availability during germinal center initiation enhances antibody responses to vaccination</article-title><source>PNAS</source><volume>113</volume><fpage>E6639</fpage><lpage>E6648</lpage><pub-id pub-id-type="doi">10.1073/pnas.1606050113</pub-id></element-citation></ref><ref id="bib104"><element-citation publication-type="software"><person-group person-group-type="author"><name><surname>Tang</surname><given-names>M</given-names></name></person-group><year iso-8601-date="2025">2025</year><data-title>Flu</data-title><version designator="swh:1:rev:4993b09664070c5b6774ecf9b075043f5c6031bf">swh:1:rev:4993b09664070c5b6774ecf9b075043f5c6031bf</version><source>Software Heritage</source><ext-link ext-link-type="uri" xlink:href="https://archive.softwareheritage.org/swh:1:dir:bf31bb3366a7b3943ae9535bf35127de6ab8031b;origin=https://github.com/mtang17/flu;visit=swh:1:snp:bb4c6d304b91ecdbec85264c0ef28ab904a37577;anchor=swh:1:rev:4993b09664070c5b6774ecf9b075043f5c6031bf">https://archive.softwareheritage.org/swh:1:dir:bf31bb3366a7b3943ae9535bf35127de6ab8031b;origin=https://github.com/mtang17/flu;visit=swh:1:snp:bb4c6d304b91ecdbec85264c0ef28ab904a37577;anchor=swh:1:rev:4993b09664070c5b6774ecf9b075043f5c6031bf</ext-link></element-citation></ref><ref id="bib105"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tas</surname><given-names>JMJ</given-names></name><name><surname>Mesin</surname><given-names>L</given-names></name><name><surname>Pasqual</surname><given-names>G</given-names></name><name><surname>Targ</surname><given-names>S</given-names></name><name><surname>Jacobsen</surname><given-names>JT</given-names></name><name><surname>Mano</surname><given-names>YM</given-names></name><name><surname>Chen</surname><given-names>CS</given-names></name><name><surname>Weill</surname><given-names>JC</given-names></name><name><surname>Reynaud</surname><given-names>CA</given-names></name><name><surname>Browne</surname><given-names>EP</given-names></name><name><surname>Meyer-Hermann</surname><given-names>M</given-names></name><name><surname>Victora</surname><given-names>GD</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Visualizing antibody affinity maturation in germinal centers</article-title><source>Science</source><volume>351</volume><fpage>1048</fpage><lpage>1054</lpage><pub-id pub-id-type="doi">10.1126/science.aad3439</pub-id></element-citation></ref><ref id="bib106"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tas</surname><given-names>JMJ</given-names></name><name><surname>Koo</surname><given-names>JH</given-names></name><name><surname>Lin</surname><given-names>YC</given-names></name><name><surname>Xie</surname><given-names>Z</given-names></name><name><surname>Steichen</surname><given-names>JM</given-names></name><name><surname>Jackson</surname><given-names>AM</given-names></name><name><surname>Hauser</surname><given-names>BM</given-names></name><name><surname>Wang</surname><given-names>X</given-names></name><name><surname>Cottrell</surname><given-names>CA</given-names></name><name><surname>Torres</surname><given-names>JL</given-names></name><name><surname>Warner</surname><given-names>JE</given-names></name><name><surname>Kirsch</surname><given-names>KH</given-names></name><name><surname>Weldon</surname><given-names>SR</given-names></name><name><surname>Groschel</surname><given-names>B</given-names></name><name><surname>Nogal</surname><given-names>B</given-names></name><name><surname>Ozorowski</surname><given-names>G</given-names></name><name><surname>Bangaru</surname><given-names>S</given-names></name><name><surname>Phelps</surname><given-names>N</given-names></name><name><surname>Adachi</surname><given-names>Y</given-names></name><name><surname>Eskandarzadeh</surname><given-names>S</given-names></name><name><surname>Kubitz</surname><given-names>M</given-names></name><name><surname>Burton</surname><given-names>DR</given-names></name><name><surname>Lingwood</surname><given-names>D</given-names></name><name><surname>Schmidt</surname><given-names>AG</given-names></name><name><surname>Nair</surname><given-names>U</given-names></name><name><surname>Ward</surname><given-names>AB</given-names></name><name><surname>Schief</surname><given-names>WR</given-names></name><name><surname>Batista</surname><given-names>FD</given-names></name></person-group><year iso-8601-date="2022">2022</year><article-title>Antibodies from primary humoral responses modulate the recruitment of naive B cells during secondary responses</article-title><source>Immunity</source><volume>55</volume><fpage>1856</fpage><lpage>1871</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2022.07.020</pub-id><pub-id pub-id-type="pmid">35987201</pub-id></element-citation></ref><ref id="bib107"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Turner</surname><given-names>JS</given-names></name><name><surname>Zhou</surname><given-names>JQ</given-names></name><name><surname>Han</surname><given-names>J</given-names></name><name><surname>Schmitz</surname><given-names>AJ</given-names></name><name><surname>Rizk</surname><given-names>AA</given-names></name><name><surname>Alsoussi</surname><given-names>WB</given-names></name><name><surname>Lei</surname><given-names>T</given-names></name><name><surname>Amor</surname><given-names>M</given-names></name><name><surname>McIntire</surname><given-names>KM</given-names></name><name><surname>Meade</surname><given-names>P</given-names></name><name><surname>Strohmeier</surname><given-names>S</given-names></name><name><surname>Brent</surname><given-names>RI</given-names></name><name><surname>Richey</surname><given-names>ST</given-names></name><name><surname>Haile</surname><given-names>A</given-names></name><name><surname>Yang</surname><given-names>YR</given-names></name><name><surname>Klebert</surname><given-names>MK</given-names></name><name><surname>Suessen</surname><given-names>T</given-names></name><name><surname>Teefey</surname><given-names>S</given-names></name><name><surname>Presti</surname><given-names>RM</given-names></name><name><surname>Krammer</surname><given-names>F</given-names></name><name><surname>Kleinstein</surname><given-names>SH</given-names></name><name><surname>Ward</surname><given-names>AB</given-names></name><name><surname>Ellebedy</surname><given-names>AH</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Human germinal centres engage memory and naive B cells after influenza vaccination</article-title><source>Nature</source><volume>586</volume><fpage>127</fpage><lpage>132</lpage><pub-id pub-id-type="doi">10.1038/s41586-020-2711-0</pub-id></element-citation></ref><ref id="bib108"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>van Beek</surname><given-names>M</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name><name><surname>Chakraborty</surname><given-names>AK</given-names></name></person-group><year iso-8601-date="2022">2022</year><article-title>Two complementary features of humoral immune memory confer protection against the same or variant antigens</article-title><source>PNAS</source><volume>119</volume><elocation-id>e2205598119</elocation-id><pub-id pub-id-type="doi">10.1073/pnas.2205598119</pub-id></element-citation></ref><ref id="bib109"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>van Regenmortel</surname><given-names>MHV</given-names></name></person-group><year iso-8601-date="2002">2002</year><article-title>Reductionism and the search for structure–function relationships in antibody molecules</article-title><source>Journal of Molecular Recognition</source><volume>15</volume><fpage>240</fpage><lpage>247</lpage><pub-id pub-id-type="doi">10.1002/jmr.584</pub-id></element-citation></ref><ref id="bib110"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>van Regenmortel</surname><given-names>MHV</given-names></name></person-group><year iso-8601-date="2011">2011</year><article-title>Limitations to the structure‐based design of HIV‐1 vaccine immunogens</article-title><source>Journal of Molecular Recognition</source><volume>24</volume><fpage>741</fpage><lpage>753</lpage><pub-id pub-id-type="doi">10.1002/jmr.1116</pub-id></element-citation></ref><ref id="bib111"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Victora</surname><given-names>GD</given-names></name><name><surname>Schwickert</surname><given-names>TA</given-names></name><name><surname>Fooksman</surname><given-names>DR</given-names></name><name><surname>Kamphorst</surname><given-names>AO</given-names></name><name><surname>Meyer-Hermann</surname><given-names>M</given-names></name><name><surname>Dustin</surname><given-names>ML</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name></person-group><year iso-8601-date="2010">2010</year><article-title>Germinal center dynamics revealed by multiphoton microscopy with a photoactivatable fluorescent reporter</article-title><source>Cell</source><volume>143</volume><fpage>592</fpage><lpage>605</lpage><pub-id pub-id-type="doi">10.1016/j.cell.2010.10.032</pub-id><pub-id pub-id-type="pmid">21074050</pub-id></element-citation></ref><ref id="bib112"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Victora</surname><given-names>GD</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name></person-group><year iso-8601-date="2012">2012</year><article-title>Germinal centers</article-title><source>Annual Review of Immunology</source><volume>30</volume><fpage>429</fpage><lpage>457</lpage><pub-id pub-id-type="doi">10.1146/annurev-immunol-020711-075032</pub-id><pub-id pub-id-type="pmid">22224772</pub-id></element-citation></ref><ref id="bib113"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Victora</surname><given-names>GD</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name></person-group><year iso-8601-date="2022">2022</year><article-title>Germinal Centers</article-title><source>Annual Review of Immunology</source><volume>40</volume><fpage>413</fpage><lpage>442</lpage><pub-id pub-id-type="doi">10.1146/annurev-immunol-120419-022408</pub-id><pub-id pub-id-type="pmid">35113731</pub-id></element-citation></ref><ref id="bib114"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wang</surname><given-names>S</given-names></name><name><surname>Mata-Fink</surname><given-names>J</given-names></name><name><surname>Kriegsman</surname><given-names>B</given-names></name><name><surname>Hanson</surname><given-names>M</given-names></name><name><surname>Irvine</surname><given-names>DJ</given-names></name><name><surname>Eisen</surname><given-names>HN</given-names></name><name><surname>Burton</surname><given-names>DR</given-names></name><name><surname>Wittrup</surname><given-names>KD</given-names></name><name><surname>Kardar</surname><given-names>M</given-names></name><name><surname>Chakraborty</surname><given-names>AK</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Manipulating the selection forces during affinity maturation to generate cross-reactive HIV antibodies</article-title><source>Cell</source><volume>160</volume><fpage>785</fpage><lpage>797</lpage><pub-id pub-id-type="doi">10.1016/j.cell.2015.01.027</pub-id><pub-id pub-id-type="pmid">25662010</pub-id></element-citation></ref><ref id="bib115"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wei</surname><given-names>CJ</given-names></name><name><surname>Crank</surname><given-names>MC</given-names></name><name><surname>Shiver</surname><given-names>J</given-names></name><name><surname>Graham</surname><given-names>BS</given-names></name><name><surname>Mascola</surname><given-names>JR</given-names></name><name><surname>Nabel</surname><given-names>GJ</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Next-generation influenza vaccines: opportunities and challenges</article-title><source>Nature Reviews. Drug Discovery</source><volume>19</volume><fpage>239</fpage><lpage>252</lpage><pub-id pub-id-type="doi">10.1038/s41573-019-0056-x</pub-id><pub-id pub-id-type="pmid">32060419</pub-id></element-citation></ref><ref id="bib116"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Widge</surname><given-names>AT</given-names></name><name><surname>Hofstetter</surname><given-names>AR</given-names></name><name><surname>Houser</surname><given-names>KV</given-names></name><name><surname>Awan</surname><given-names>SF</given-names></name><name><surname>Chen</surname><given-names>GL</given-names></name><name><surname>Burgos Florez</surname><given-names>MC</given-names></name><name><surname>Berkowitz</surname><given-names>NM</given-names></name><name><surname>Mendoza</surname><given-names>F</given-names></name><name><surname>Hendel</surname><given-names>CS</given-names></name><name><surname>Holman</surname><given-names>LA</given-names></name><name><surname>Gordon</surname><given-names>IJ</given-names></name><name><surname>Apte</surname><given-names>P</given-names></name><name><surname>Liang</surname><given-names>CJ</given-names></name><name><surname>Gaudinski</surname><given-names>MR</given-names></name><name><surname>Coates</surname><given-names>EE</given-names></name><name><surname>Strom</surname><given-names>L</given-names></name><name><surname>Wycuff</surname><given-names>D</given-names></name><name><surname>Vazquez</surname><given-names>S</given-names></name><name><surname>Stein</surname><given-names>JA</given-names></name><name><surname>Gall</surname><given-names>JG</given-names></name><name><surname>Adams</surname><given-names>WC</given-names></name><name><surname>Carlton</surname><given-names>K</given-names></name><name><surname>Gillespie</surname><given-names>RA</given-names></name><name><surname>Creanga</surname><given-names>A</given-names></name><name><surname>Crank</surname><given-names>MC</given-names></name><name><surname>Andrews</surname><given-names>SF</given-names></name><name><surname>Castro</surname><given-names>M</given-names></name><name><surname>Serebryannyy</surname><given-names>LA</given-names></name><name><surname>Narpala</surname><given-names>SR</given-names></name><name><surname>Hatcher</surname><given-names>C</given-names></name><name><surname>Lin</surname><given-names>BC</given-names></name><name><surname>O’Connell</surname><given-names>S</given-names></name><name><surname>Freyn</surname><given-names>AW</given-names></name><name><surname>Rosado</surname><given-names>VC</given-names></name><name><surname>Nachbagauer</surname><given-names>R</given-names></name><name><surname>Palese</surname><given-names>P</given-names></name><name><surname>Kanekiyo</surname><given-names>M</given-names></name><name><surname>McDermott</surname><given-names>AB</given-names></name><name><surname>Koup</surname><given-names>RA</given-names></name><name><surname>Dropulic</surname><given-names>LK</given-names></name><name><surname>Graham</surname><given-names>BS</given-names></name><name><surname>Mascola</surname><given-names>JR</given-names></name><name><surname>Ledgerwood</surname><given-names>JE</given-names></name><collab>VRC 321 study team</collab></person-group><year iso-8601-date="2023">2023</year><article-title>An influenza hemagglutinin stem nanoparticle vaccine induces cross-group 1 neutralizing antibodies in healthy adults</article-title><source>Science Translational Medicine</source><volume>15</volume><elocation-id>eade4790</elocation-id><pub-id pub-id-type="doi">10.1126/scitranslmed.ade4790</pub-id><pub-id pub-id-type="pmid">37075129</pub-id></element-citation></ref><ref id="bib117"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Xu</surname><given-names>R</given-names></name><name><surname>Ekiert</surname><given-names>DC</given-names></name><name><surname>Krause</surname><given-names>JC</given-names></name><name><surname>Hai</surname><given-names>R</given-names></name><name><surname>Crowe</surname><given-names>JE</given-names></name><name><surname>Wilson</surname><given-names>IA</given-names></name></person-group><year iso-8601-date="2010">2010</year><article-title>Structural basis of preexisting immunity to the 2009 H1N1 pandemic influenza virus</article-title><source>Science</source><volume>328</volume><fpage>357</fpage><lpage>360</lpage><pub-id pub-id-type="doi">10.1126/science.1186430</pub-id><pub-id pub-id-type="pmid">20339031</pub-id></element-citation></ref><ref id="bib118"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Yang</surname><given-names>L</given-names></name><name><surname>Van Beek</surname><given-names>M</given-names></name><name><surname>Wang</surname><given-names>Z</given-names></name><name><surname>Muecksch</surname><given-names>F</given-names></name><name><surname>Canis</surname><given-names>M</given-names></name><name><surname>Hatziioannou</surname><given-names>T</given-names></name><name><surname>Bieniasz</surname><given-names>PD</given-names></name><name><surname>Nussenzweig</surname><given-names>MC</given-names></name><name><surname>Chakraborty</surname><given-names>AK</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Antigen presentation dynamics shape the antibody response to variants like SARS-CoV-2 Omicron after multiple vaccinations with the original strain</article-title><source>Cell Reports</source><volume>42</volume><elocation-id>112256</elocation-id><pub-id pub-id-type="doi">10.1016/j.celrep.2023.112256</pub-id></element-citation></ref><ref id="bib119"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Yassine</surname><given-names>HM</given-names></name><name><surname>Boyington</surname><given-names>JC</given-names></name><name><surname>McTamney</surname><given-names>PM</given-names></name><name><surname>Wei</surname><given-names>C-J</given-names></name><name><surname>Kanekiyo</surname><given-names>M</given-names></name><name><surname>Kong</surname><given-names>W-P</given-names></name><name><surname>Gallagher</surname><given-names>JR</given-names></name><name><surname>Wang</surname><given-names>L</given-names></name><name><surname>Zhang</surname><given-names>Y</given-names></name><name><surname>Joyce</surname><given-names>MG</given-names></name><name><surname>Lingwood</surname><given-names>D</given-names></name><name><surname>Moin</surname><given-names>SM</given-names></name><name><surname>Andersen</surname><given-names>H</given-names></name><name><surname>Okuno</surname><given-names>Y</given-names></name><name><surname>Rao</surname><given-names>SS</given-names></name><name><surname>Harris</surname><given-names>AK</given-names></name><name><surname>Kwong</surname><given-names>PD</given-names></name><name><surname>Mascola</surname><given-names>JR</given-names></name><name><surname>Nabel</surname><given-names>GJ</given-names></name><name><surname>Graham</surname><given-names>BS</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Hemagglutinin-stem nanoparticles generate heterosubtypic influenza protection</article-title><source>Nature Medicine</source><volume>21</volume><fpage>1065</fpage><lpage>1070</lpage><pub-id pub-id-type="doi">10.1038/nm.3927</pub-id><pub-id pub-id-type="pmid">26301691</pub-id></element-citation></ref><ref id="bib120"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Young</surname><given-names>C</given-names></name><name><surname>Brink</surname><given-names>R</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>The unique biology of germinal center B cells</article-title><source>Immunity</source><volume>54</volume><fpage>1652</fpage><lpage>1664</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2021.07.015</pub-id></element-citation></ref><ref id="bib121"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Zarnitsyna</surname><given-names>VI</given-names></name><name><surname>Ellebedy</surname><given-names>AH</given-names></name><name><surname>Davis</surname><given-names>C</given-names></name><name><surname>Jacob</surname><given-names>J</given-names></name><name><surname>Ahmed</surname><given-names>R</given-names></name><name><surname>Antia</surname><given-names>R</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Masking of antigenic epitopes by antibodies shapes the humoral immune response to influenza</article-title><source>Philosophical Transactions of the Royal Society B</source><volume>370</volume><elocation-id>20140248</elocation-id><pub-id pub-id-type="doi">10.1098/rstb.2014.0248</pub-id><pub-id pub-id-type="pmid">26194761</pub-id></element-citation></ref><ref id="bib122"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Zarnitsyna</surname><given-names>VI</given-names></name><name><surname>Lavine</surname><given-names>J</given-names></name><name><surname>Ellebedy</surname><given-names>A</given-names></name><name><surname>Ahmed</surname><given-names>R</given-names></name><name><surname>Antia</surname><given-names>R</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Multi-epitope models explain how pre-existing antibodies affect the generation of broadly protective responses to influenza</article-title><source>PLOS Pathogens</source><volume>12</volume><elocation-id>e1005692</elocation-id><pub-id pub-id-type="doi">10.1371/journal.ppat.1005692</pub-id><pub-id pub-id-type="pmid">27336297</pub-id></element-citation></ref><ref id="bib123"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Zhang</surname><given-names>J</given-names></name><name><surname>Shakhnovich</surname><given-names>EI</given-names></name></person-group><year iso-8601-date="2010">2010</year><article-title>Optimality of mutation and selection in germinal centers</article-title><source>PLOS Computational Biology</source><volume>6</volume><elocation-id>e1000800</elocation-id><pub-id pub-id-type="doi">10.1371/journal.pcbi.1000800</pub-id></element-citation></ref><ref id="bib124"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Zimmer</surname><given-names>SM</given-names></name><name><surname>Burke</surname><given-names>DS</given-names></name></person-group><year iso-8601-date="2009">2009</year><article-title>Historical perspective — emergence of influenza a (h1n1) viruses</article-title><source>New England Journal of Medicine</source><volume>361</volume><fpage>279</fpage><lpage>285</lpage><pub-id pub-id-type="doi">10.1056/NEJMra0904322</pub-id></element-citation></ref><ref id="bib125"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Zuo</surname><given-names>T</given-names></name><name><surname>Gautam</surname><given-names>A</given-names></name><name><surname>Saghaei</surname><given-names>S</given-names></name><name><surname>Khobragade</surname><given-names>SN</given-names></name><name><surname>Ahmed</surname><given-names>R</given-names></name><name><surname>Mahdavinia</surname><given-names>A</given-names></name><name><surname>Zarghami</surname><given-names>M</given-names></name><name><surname>Pacheco</surname><given-names>GA</given-names></name><name><surname>Green</surname><given-names>K</given-names></name><name><surname>Travers</surname><given-names>M</given-names></name><name><surname>Garcia</surname><given-names>N</given-names></name><name><surname>Allahyari</surname><given-names>Z</given-names></name><name><surname>Rao</surname><given-names>V</given-names></name><name><surname>Kumar</surname><given-names>S</given-names></name><name><surname>Novak</surname><given-names>R</given-names></name><name><surname>Hwang</surname><given-names>JK</given-names></name><name><surname>Wesemann</surname><given-names>DR</given-names></name></person-group><year iso-8601-date="2025">2025</year><article-title>Somatic hypermutation generates antibody specificities beyond the primary repertoire</article-title><source>Immunity</source><volume>58</volume><fpage>1396</fpage><lpage>1410</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2025.04.014</pub-id><pub-id pub-id-type="pmid">40339575</pub-id></element-citation></ref></ref-list><app-group><app id="appendix-1"><title>Appendix 1</title><table-wrap id="app1table1" position="float"><label>Appendix 1—table 1.</label><caption><title>HA sequence information for the influenza stains in this study.</title></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" valign="bottom">Strain</th><th align="left" valign="bottom">Genbank</th><th align="left" valign="bottom">Type</th><th align="left" valign="bottom">Year</th><th align="left" valign="bottom">Location</th><th align="left" valign="bottom">GISAID</th></tr></thead><tbody><tr><td align="left" valign="bottom">H1N1 A_Beijing_262_1995</td><td align="left" valign="bottom">AB304819.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1995</td><td align="left" valign="bottom">Beijing</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_Brazil_11_1978</td><td align="left" valign="bottom">HQ008267.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1978</td><td align="left" valign="bottom">Brazil</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_Brisbane_59_2007</td><td align="left" valign="bottom">JN899402.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">2007</td><td align="left" valign="bottom">Brisbane</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Brisbane_10_2007</td><td align="left" valign="bottom">KM978061.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">2007</td><td align="left" valign="bottom">Brisbane</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Brisbane_60_2008</td><td align="left" valign="bottom">FJ766842.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">2008</td><td align="left" valign="bottom">Brisbane</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_California_07_2009</td><td align="left" valign="bottom">NC_026433.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">2009</td><td align="left" valign="bottom">California</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_California_10_1978</td><td align="left" valign="bottom">CY021717.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1978</td><td align="left" valign="bottom">California</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_Chile_1_1983</td><td align="left" valign="bottom">CY121261.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1983</td><td align="left" valign="bottom">Chile</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Colorado_06_2017</td><td align="left" valign="bottom">CY236607.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">2017</td><td align="left" valign="bottom">Colorado</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_Denver_1957</td><td align="left" valign="bottom">CY146793.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1957</td><td align="left" valign="bottom">Denver</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Florida_4_2006</td><td align="left" valign="bottom">EU515992.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">2006</td><td align="left" valign="bottom">Florida</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_Fort_Monmouth_1_1947</td><td align="left" valign="bottom">AF494250.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1947</td><td align="left" valign="bottom">Fort_Monmouth</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Fujian_411_2002</td><td align="left" valign="bottom">EU501153.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">2002</td><td align="left" valign="bottom">Fujian</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Harbin_7_1994</td><td align="left" valign="bottom">CY040441.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">1994</td><td align="left" valign="bottom">Harbin</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Hong_Kong_330_2001</td><td align="left" valign="bottom">AF532549.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">2001</td><td align="left" valign="bottom">Hong_Kong</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Hong_Kong_1_1968</td><td align="left" valign="bottom">AF348177.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">1968</td><td align="left" valign="bottom">Hong_Kong</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Hong_Kong_4801_2014</td><td align="left" valign="bottom"/><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">2014</td><td align="left" valign="bottom">Hong_Kong</td><td align="left" valign="bottom">EPI1026711</td></tr><tr><td align="left" valign="bottom">H3N2 A_Kentucky_UR07-0028_2008</td><td align="left" valign="bottom">CY037791.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">2008</td><td align="left" valign="bottom">Kentucky_UR07-0028</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Lee_1940</td><td align="left" valign="bottom">K00423.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">1940</td><td align="left" valign="bottom">Lee</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Malaysia_2506_2004</td><td align="left" valign="bottom">EU124275.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">2004</td><td align="left" valign="bottom">Malaysia</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Massachusetts_2_2012</td><td align="left" valign="bottom">MT056027.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">2012</td><td align="left" valign="bottom">Massachusetts</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_Michigan_45_2015</td><td align="left" valign="bottom">KY117023.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">2015</td><td align="left" valign="bottom">Michigan</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Mississippi_1_1985</td><td align="left" valign="bottom">L19003.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">1985</td><td align="left" valign="bottom">Mississippi</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Nanchang_933_1995</td><td align="left" valign="bottom">CY108293.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">1995</td><td align="left" valign="bottom">Nanchang</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_New_Caledonia_29_1999</td><td align="left" valign="bottom">DQ508857.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1999</td><td align="left" valign="bottom">New_Caledonia</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_New_Jersey_1976</td><td align="left" valign="bottom">CY147422.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1976</td><td align="left" valign="bottom">New_Jersey</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_New_York_55_2004</td><td align="left" valign="bottom">KM821338.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">2004</td><td align="left" valign="bottom">New_York</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Panama_2007_1999</td><td align="left" valign="bottom">EF626612.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">1999</td><td align="left" valign="bottom">Panama</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Perth_16_2009</td><td align="left" valign="bottom">GQ293081.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">2009</td><td align="left" valign="bottom">Perth</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Phuket_3073_2013</td><td align="left" valign="bottom"/><td align="left" valign="bottom">B</td><td align="left" valign="bottom">2013</td><td align="left" valign="bottom">Phuket</td><td align="left" valign="bottom">EPI2195537</td></tr><tr><td align="left" valign="bottom">H3N2 A_Port_Chalmers_12_1973</td><td align="left" valign="bottom">CY113109.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">1973</td><td align="left" valign="bottom">Port_Chalmers</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_Puerto_Rico_8_1934</td><td align="left" valign="bottom">EF467821.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1934</td><td align="left" valign="bottom">Puerto_Rico</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Shangdong_9_1993</td><td align="left" valign="bottom">Z46417.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">1993</td><td align="left" valign="bottom">Shangdong</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Sichuan_379_1999</td><td align="left" valign="bottom">EF566113.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">1999</td><td align="left" valign="bottom">Sichuan</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Sichuan_30_1989</td><td align="left" valign="bottom">CY108211.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">1989</td><td align="left" valign="bottom">Sichuan</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_Singapore_6_1986</td><td align="left" valign="bottom">D00406.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1986</td><td align="left" valign="bottom">Singapore</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_Solomon_Islands_03_2006</td><td align="left" valign="bottom">EU100724.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">2006</td><td align="left" valign="bottom">Solomon_Islands</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_South_Carolina_1_1918</td><td align="left" valign="bottom">AF117241.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1918</td><td align="left" valign="bottom">South_Carolina</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Switzerland_9715293_2013</td><td align="left" valign="bottom"/><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">2013</td><td align="left" valign="bottom">Switzerland</td><td align="left" valign="bottom">EPI814528</td></tr><tr><td align="left" valign="bottom">H3N2 A_Sydney_5_1997</td><td align="left" valign="bottom">KM821316.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">1997</td><td align="left" valign="bottom">Sydney</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_Texas_36_1991</td><td align="left" valign="bottom">DQ508889.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1991</td><td align="left" valign="bottom">Texas</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Texas_1_1977</td><td align="left" valign="bottom">EF626623.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">1977</td><td align="left" valign="bottom">Texas</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Texas_50_2012</td><td align="left" valign="bottom">KC892952.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">2012</td><td align="left" valign="bottom">Texas</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Texas_06_2011</td><td align="left" valign="bottom">KC813979.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">2011</td><td align="left" valign="bottom">Texas</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_USSR_90_1977</td><td align="left" valign="bottom">HQ008265.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1977</td><td align="left" valign="bottom">USSR</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Victoria_361_2011</td><td align="left" valign="bottom">KM821347.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">2011</td><td align="left" valign="bottom">Victoria</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H1N1 A_Weiss_1943</td><td align="left" valign="bottom">CY147366.1</td><td align="left" valign="bottom">H1N1</td><td align="left" valign="bottom">1943</td><td align="left" valign="bottom">Weiss</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">H3N2 A_Wisconsin_67_2005</td><td align="left" valign="bottom">CY163704.1</td><td align="left" valign="bottom">H3N2</td><td align="left" valign="bottom">2005</td><td align="left" valign="bottom">Wisconsin</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Wisconsin_1_2010</td><td align="left" valign="bottom">CY115183.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">2010</td><td align="left" valign="bottom">Wisconsin</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom">B_Yamagata_16_1988</td><td align="left" valign="bottom">M36105.1</td><td align="left" valign="bottom">B</td><td align="left" valign="bottom">1988</td><td align="left" valign="bottom">Yamagata</td><td align="left" valign="bottom"/></tr></tbody></table></table-wrap><table-wrap id="app1table2" position="float"><label>Appendix 1—table 2.</label><caption><title>Simulation parameters.</title><p>Highlighted parameters were modified from the original model.</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" valign="bottom">­Parameter</th><th align="left" valign="bottom">Value</th><th align="left" valign="bottom">Description</th><th align="left" valign="bottom">Note</th></tr></thead><tbody><tr><td align="left" valign="bottom" colspan="3">Antigen and antibody dynamics</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf116"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>I</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft116">\begin{document}$k_{Ig}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf117"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mn>0.8</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft117">\begin{document}$0.8\times 10^{-2}$\end{document}</tex-math></alternatives></inline-formula> nM day<sup>–1</sup> PC<sup>–1</sup></td><td align="left" valign="bottom">Rate of antibody production per plasma cell per day</td><td align="left" valign="bottom">Picked to match antibody titers at peak response to second SARS-CoV-2 vaccination (<xref ref-type="bibr" rid="bib46">Goel et al., 2021</xref>; <xref ref-type="bibr" rid="bib70">Muecksch et al., 2022</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf118"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>I</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft118">\begin{document}$d_{Ig}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">0.025 day<sup>–1</sup></td><td align="left" valign="bottom">Antibody decay rate</td><td align="left" valign="bottom">Picked to give antibody a half-life of ~28 days (<xref ref-type="bibr" rid="bib46">Goel et al., 2021</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf119"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>A</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft119">\begin{document}$d_{Ag}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">3 day<sup>–1</sup></td><td align="left" valign="bottom">Antigen decay rate</td><td align="left" valign="bottom">Picked such that antigen decays rapidly in the first few days after vaccination (<xref ref-type="bibr" rid="bib10">Aung et al., 2023</xref>; <xref ref-type="bibr" rid="bib14">Bhagchandani et al., 2024</xref>; <xref ref-type="bibr" rid="bib63">Martin et al., 2021</xref>; <xref ref-type="bibr" rid="bib103">Tam et al., 2016</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf120"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft120">\begin{document}$k_{deposit}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">1 hour<sup>–1</sup></td><td align="left" valign="bottom">Rate of immune complex transport to FDC</td><td align="left" valign="bottom">Picked such that antigen is rapidly transported to the FDC within ~48 hours after vaccination (<xref ref-type="bibr" rid="bib10">Aung et al., 2023</xref>; <xref ref-type="bibr" rid="bib14">Bhagchandani et al., 2024</xref>; <xref ref-type="bibr" rid="bib63">Martin et al., 2021</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf121"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>I</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft121">\begin{document}$d_{Ic}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">0.15 day<sup>–1</sup></td><td align="left" valign="bottom">Rate of decay of immune complex on FDC</td><td align="left" valign="bottom">Picked such that the secondary GCs last at least 3 months after SARS-CoV-2 vaccination as observed (<xref ref-type="bibr" rid="bib41">Gaebler et al., 2021</xref>; <xref ref-type="bibr" rid="bib70">Muecksch et al., 2022</xref>)</td></tr><tr><td align="left" valign="top"><inline-formula><alternatives><mml:math id="inf122"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mo stretchy="false">[</mml:mo><mml:mi>A</mml:mi><mml:mi>g</mml:mi><mml:msub><mml:mo stretchy="false">]</mml:mo><mml:mn>0</mml:mn></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft122">\begin{document}$[Ag]_0$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="top">10 nM</td><td align="left" valign="bottom" rowspan="3">Initial conditions</td><td align="left" valign="top">Picked within reasonable physiological ranges (<xref ref-type="bibr" rid="bib63">Martin et al., 2021</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf123"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mo stretchy="false">[</mml:mo><mml:mi>I</mml:mi><mml:mi>g</mml:mi><mml:msub><mml:mo stretchy="false">]</mml:mo><mml:mn>0</mml:mn></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft123">\begin{document}$[Ig]_0$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">10<sup>–2</sup> nM</td><td align="left" valign="bottom">Picked within reasonable physiological ranges (<xref ref-type="bibr" rid="bib31">Demonbreun et al., 2021</xref>)</td></tr><tr><td align="left" valign="bottom"/><td align="left" valign="bottom">0 nM</td><td align="left" valign="bottom">No initial IC exists</td></tr><tr><td align="left" valign="bottom" colspan="3">B cell affinities</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf124"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft124">\begin{document}$N_{native}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">2000 cells/GC</td><td align="left" valign="bottom">Number of naïve B cells per GC</td><td align="left" valign="bottom">Based on the total number of naïve B cells (<xref ref-type="bibr" rid="bib17">Boyd and Joshi, 2014</xref>; <xref ref-type="bibr" rid="bib82">Rees, 2020</xref>) and frequency of naïve B cells that target the SARS-CoV-2 RBD (<xref ref-type="bibr" rid="bib36">Feldman et al., 2021</xref>), divided across 200 GCs</td></tr><tr><td style="background-color: #90CAF9;"><inline-formula><alternatives><mml:math id="inf125"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft125">\begin{document}$p_{1}$\end{document}</tex-math></alternatives></inline-formula></td><td style="background-color: #90CAF9;">0.8</td><td style="background-color: #90CAF9;">Fraction of naïve B cells that target epitope 1</td><td style="background-color: #90CAF9;">Tested for robustness in previous simulations (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>).</td></tr><tr><td style="background-color: #90CAF9;"><inline-formula><alternatives><mml:math id="inf126"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft126">\begin{document}$p_{2}$\end{document}</tex-math></alternatives></inline-formula></td><td style="background-color: #90CAF9;">varied: 0.15, 0.18</td><td style="background-color: #90CAF9;">Fraction of naïve B cells that target epitope 2</td><td style="background-color: #90CAF9;">Varied in simulations</td></tr><tr><td style="background-color: #90CAF9;"><inline-formula><alternatives><mml:math id="inf127"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft127">\begin{document}$p_{3}$\end{document}</tex-math></alternatives></inline-formula></td><td style="background-color: #90CAF9;">varied: 0.05, 0.02</td><td style="background-color: #90CAF9;">Fraction of naïve B cells that target epitope 3</td><td style="background-color: #90CAF9;">Varied in simulations</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf128"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msubsup><mml:mi>E</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:msubsup></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft128">\begin{document}$E_{1}^{h}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">7</td><td align="left" valign="bottom">Parameter for the germline affinity distribution of epitope 1. Affinity at which there is on average one naïve B cell targeting epitope 1 available for each GC</td><td align="left" valign="bottom">Tested for robustness in previous simulations (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf129"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mi>d</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft129">\begin{document}$dE_{12}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">0.4</td><td align="left" valign="bottom">Parameter for the germline affinity distribution of epitope 2. is the affinity at which there is on average one naïve B cell targeting epitope 2 available for each GC</td><td align="left" valign="bottom">Tested for robustness in previous simulations (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>)</td></tr><tr><td style="background-color: #90CAF9;"><inline-formula><alternatives><mml:math id="inf130"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mi>d</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft130">\begin{document}$dE_{13}$\end{document}</tex-math></alternatives></inline-formula></td><td style="background-color: #90CAF9;">0.8</td><td style="background-color: #90CAF9;">Parameter for the germline affinity distribution of epitope 3. is the affinity at which there is on average one naïve B cell targeting epitope 2 available for each GC</td><td style="background-color: #90CAF9;">Picked such that the germline affinity distribution for epitope 3 has a shorter high-affinity tail than epitope 2, i.e. epitope 3 is less immunodominant than epitope 2</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf131"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft131">\begin{document}$n_{res}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">80</td><td align="left" valign="bottom">Length of string representation of B cell residues</td><td align="left" valign="bottom">Upper range of sum of CDR lengths in light and heavy chain (<xref ref-type="bibr" rid="bib73">Nowak et al., 2016</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf132"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mi>μ</mml:mi><mml:mo>,</mml:mo><mml:mi>σ</mml:mi><mml:mo>,</mml:mo><mml:mi>ϵ</mml:mi></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft132">\begin{document}$\mu,\sigma ,\epsilon $\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">3.1, 1.2, 3.08</td><td align="left" valign="bottom">Parameters for shifted log-normal distribution that models the effect of affinity-changing mutations</td><td align="left" valign="bottom">Based on empirical distribution of affinity changes due to point-mutations in proteins (<xref ref-type="bibr" rid="bib123">Zhang and Shakhnovich, 2010</xref>)</td></tr><tr><td style="background-color: #90CAF9;"><inline-formula><alternatives><mml:math id="inf133"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft133">\begin{document}$\rho _{12}$\end{document}</tex-math></alternatives></inline-formula></td><td style="background-color: #90CAF9;">epitope 1: 0.4 epitope 2: typically 0.95, varied: 0.6–0.95 epitope 3: 0.4</td><td style="background-color: #90CAF9;">Level of conservation between strain 1 and 2</td><td style="background-color: #90CAF9;">Picked such that a large portion of affinity-increasing mutations (~30 to 72%) in the conserved epitope (epitope 2) are beneficial for both strain 1 and 2;~19% for the other epitopes</td></tr><tr><td style="background-color: #90CAF9;"><inline-formula><alternatives><mml:math id="inf134"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft134">\begin{document}$\rho _{13}$\end{document}</tex-math></alternatives></inline-formula></td><td style="background-color: #90CAF9;">epitope 1: 0.4 epitope 2: 0.4 epitope 3: 0.95</td><td style="background-color: #90CAF9;">Level of conservation between strain 1 and 3</td><td style="background-color: #90CAF9;">Picked such that ~72% of affinity-increasing mutations in the conserved epitope (epitope 3) are beneficial for both strain 1 and 3;~19% for the other epitopes</td></tr><tr><td style="background-color: #90CAF9;"><inline-formula><alternatives><mml:math id="inf135"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft135">\begin{document}$q_{12}$\end{document}</tex-math></alternatives></inline-formula></td><td style="background-color: #90CAF9;">0 without overlap 0.3 with overlap</td><td style="background-color: #90CAF9;">Fraction of antibodies that target epitope 1 that can mask epitope 2 and vice versa (i.e. the amount of spatial overlap between epitope 1 and 2)</td><td style="background-color: #90CAF9;">Varied in simulations; effects are also studied in previous simulations (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>)</td></tr><tr><td style="background-color: #90CAF9;"><inline-formula><alternatives><mml:math id="inf136"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mn>13</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft136">\begin{document}$q_{13}$\end{document}</tex-math></alternatives></inline-formula></td><td style="background-color: #90CAF9;">0 without overlap 0.3 with overlap</td><td style="background-color: #90CAF9;">Fraction of antibodies that target epitope 1 that can mask epitope 3 and vice versa (i.e. the amount of spatial overlap between epitope 1 and 3)</td><td style="background-color: #90CAF9;">Varied in simulations; effects are also studied in previous simulations (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>)</td></tr><tr><td style="background-color: #90CAF9;"><inline-formula><alternatives><mml:math id="inf137"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mn>23</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft137">\begin{document}$q_{23}$\end{document}</tex-math></alternatives></inline-formula></td><td style="background-color: #90CAF9;">0</td><td style="background-color: #90CAF9;">Fraction of antibodies that target epitope 2 that can mask epitope 3 and vice versa (i.e. the amount of spatial overlap between epitope 2 and 3)</td><td style="background-color: #90CAF9;">Picked such that the subdominant epitopes (epitopes 2 and 3) are distinct</td></tr><tr><td align="left" valign="bottom" colspan="3">GC and EGC dynamics</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf138"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft138">\begin{document}$C_0$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">nM</td><td align="left" valign="bottom">Reference antigen concentration</td><td align="left" valign="bottom">Tested for robustness in previous simulations (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf139"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>E</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft139">\begin{document}$E_0$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">6</td><td align="left" valign="bottom">Reference binding affinity</td><td align="left" valign="bottom">Typical threshold for naïve B cell activation is (<xref ref-type="bibr" rid="bib11">Batista and Neuberger, 1998</xref>)</td></tr><tr><td align="left" valign="bottom"/><td align="left" valign="bottom">typically 0.5 varied: 0.5, 0.7</td><td align="left" valign="bottom">Stringency of selection of naïve and GC B cells by helper T cells based on amount of captured antigen</td><td align="left" valign="bottom">Varied in simulations; effects are also studied in previous simulations (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf140"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft140">\begin{document}$N_{max}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">10 day<sup>–1</sup></td><td align="left" valign="bottom">Approximately the maximum number of naïve B cells that can enter the GC per day</td><td align="left" valign="bottom">Based on experimental observation in mice for the number of GC B cells after 7 days (<xref ref-type="bibr" rid="bib105">Tas et al., 2016</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf141"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>β</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft141">\begin{document}$\beta _{max}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">2.5 day<sup>–1</sup></td><td align="left" valign="bottom">Maximum rate of positive selection for GC and EGC B cells</td><td align="left" valign="bottom">Maximum proliferation is about ~4 times / day (<xref ref-type="bibr" rid="bib105">Tas et al., 2016</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf142"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:mi>α</mml:mi></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft142">\begin{document}$\alpha $\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">0.5 day<sup>–1</sup></td><td align="left" valign="bottom">Death rate of GC B cells</td><td align="left" valign="bottom">Picked to allow B cells to survive for ~2 days before death if they are not selected</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf143"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft143">\begin{document}$N_{T0}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">1200</td><td align="left" valign="bottom">Maximum number of helper T cells involved in positive selection in GC and EGC</td><td align="left" valign="bottom">Picked such that GCs have a peak size of ~1,000 B cells for computational tractibility</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf144"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>t</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft144">\begin{document}$t_0$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">14 days</td><td align="left" valign="bottom">Time at which number of helper T cells is maximal</td><td align="left" valign="bottom">Matches dynamics of T cell response to SARS-CoV-2 vaccination (<xref ref-type="bibr" rid="bib46">Goel et al., 2021</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf145"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft145">\begin{document}$d_{T}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">0.01 day<sup>–1</sup></td><td align="left" valign="bottom">Death rate of helper T cells after time</td><td align="left" valign="bottom">Matches dynamics of T cell response to SARS-CoV-2 vaccination (<xref ref-type="bibr" rid="bib46">Goel et al., 2021</xref>)</td></tr><tr><td align="left" valign="bottom" colspan="3">Plasma and memory cell dynamics</td><td align="left" valign="bottom"/></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf146"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft146">\begin{document}$p_{exit}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">0.05</td><td align="left" valign="bottom">Probability that a positively selected GC B cell exits and differentiates</td><td align="left" valign="bottom">Tested for robustness in previous simulations (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf147"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>l</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft147">\begin{document}$p_{plasma}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">0.1</td><td align="left" valign="bottom">Probability that a differentiating GC B cell becomes a plasma cell</td><td align="left" valign="bottom">Tested for robustness in previous simulations (<xref ref-type="bibr" rid="bib118">Yang et al., 2023</xref>)</td></tr><tr><td align="left" valign="bottom"/><td align="left" valign="bottom">0.6</td><td align="left" valign="bottom">Probability that a proliferating memory cell in EGC differentiates into a plasma cell</td><td align="left" valign="bottom">Based on observation in mice that ~60% of reactivated B memory cells differentiate into short-lived plasma cells (<xref ref-type="bibr" rid="bib111">Victora et al., 2010</xref>)</td></tr><tr><td align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf148"><mml:mstyle><mml:mrow><mml:mstyle displaystyle="false"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="inft148">\begin{document}$d_{PC}$\end{document}</tex-math></alternatives></inline-formula></td><td align="left" valign="bottom">0.17 day<sup>–1</sup></td><td align="left" valign="bottom">Death rate of plasma cells</td><td align="left" valign="bottom">Short-lived plasma cells have a half-life of ~4 days (<xref ref-type="bibr" rid="bib68">Moran et al., 2018</xref>)</td></tr></tbody></table></table-wrap></app></app-group></back><sub-article article-type="editor-report" id="sa0"><front-stub><article-id pub-id-type="doi">10.7554/eLife.107042.sa0</article-id><title-group><article-title>Editor's evaluation</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Kurosaki</surname><given-names>Tomohiro</given-names></name><role specific-use="editor">Reviewing Editor</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/035t8zc32</institution-id><institution>The University of Osaka</institution></institution-wrap><addr-line><named-content content-type="city">Osaka</named-content></addr-line><country>Japan</country></aff></contrib></contrib-group><related-object id="sa0ro1" object-id-type="id" object-id="10.1101/2024.03.27.24303943" link-type="continued-by" xlink:href="https://sciety.org/articles/activity/10.1101/2024.03.27.24303943"/></front-stub><body><p>How to develop the vaccination method to induce broadly reactive neutralizing antibodies against variant viruses such as influenza is now a central issue in this field. In this regard, this valuable study provides outlines the mechanism by which repeated vaccination broadens the breadth of antibody responses against epitope unmatched virus strains. The authors' mathematical model is solid and incorporates varipous parameteres that regulate B cell activation and antibody response.</p></body></sub-article><sub-article article-type="decision-letter" id="sa1"><front-stub><article-id pub-id-type="doi">10.7554/eLife.107042.sa1</article-id><title-group><article-title>Decision letter</article-title></title-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Kurosaki</surname><given-names>Tomohiro</given-names></name><role>Reviewing Editor</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/035t8zc32</institution-id><institution>The University of Osaka</institution></institution-wrap><addr-line><named-content content-type="city">Osaka</named-content></addr-line><country>Japan</country></aff></contrib></contrib-group><contrib-group><contrib contrib-type="reviewer"><name><surname>Miyauchi</surname><given-names>Kosuke</given-names></name><role>Reviewer</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/04mb6s476</institution-id><institution>RIKEN Center for Integrative Medical Sciences</institution></institution-wrap><country>Japan</country></aff></contrib></contrib-group></front-stub><body><boxed-text id="sa2-box1"><p>Our editorial process produces two outputs: (i) <ext-link ext-link-type="uri" xlink:href="https://sciety.org/articles/activity/10.1101/2024.03.27.24303943">public reviews</ext-link> designed to be posted alongside <ext-link ext-link-type="uri" xlink:href="https://www.medrxiv.org/content/10.1101/2024.03.27.24303943v1">the preprint</ext-link> for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.</p></boxed-text><p><bold>Decision letter after peer review:</bold></p><p>Thank you for submitting your article &quot;Repeated vaccination with homologous influenza hemagglutinin broadens human antibody responses to unmatched flu viruses&quot; for consideration by <italic>eLife</italic>. Your article has been reviewed by 2 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Aleksandra Walczak as the Senior Editor.</p><p>The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.</p><p>Essential Revisions:</p><p>Given the importance of GC reaction, incorporating the parameters for GC presitency would enhance the model to reflect the actual humoral responses.</p><p><italic>Reviewer #1 (Recommendations for the authors):</italic></p><p>Persistency of germinal center (GC) reaction in the secondary lymphoid organs plays a critical role in antibody diversification and affinity maturation, as exemplified in the case of SARS-CoV-2 mRNA vaccines, which induce robust and long-lasting GC responses in humans. Incorporating such parameters would enhance the model's ability to more accurately reflect the actual humoral immune responses observed in vaccinated and infected individuals.</p></body></sub-article><sub-article article-type="reply" id="sa2"><front-stub><article-id pub-id-type="doi">10.7554/eLife.107042.sa2</article-id><title-group><article-title>Author response</article-title></title-group></front-stub><body><disp-quote content-type="editor-comment"><p>Essential Revisions:</p><p>Given the importance of GC reaction, incorporating the parameters for GC presitency would enhance the model to reflect the actual humoral responses.</p></disp-quote><p>We agree with the reviewer. Our simulations did account for this important phenomenon, but we did not explicitly note this. After booster shots, antigen-specific antibodies generated due to humoral processes from previous immunizations deposit more antigen on FDCs in GCs (Figure 5B). Recently we showed experimentally in a different context that enhanced antigen on FDCs at later time points is a consequence of past antibody responses [Bhagachandani et al., Science Immunology 2024]. This is an important reason that secondary GCs persist for onger times than GCs that form after primary immunization and our simulation results reflect this phenomenon. In our simulations, the GCs that form after primary immunization last for ~ 110 days, after the second immunization they persist for ~165 days, and then after subsequent immunizations last for ~ 180 days. We now provide an additional graph (Figure 5 —figure supplement 2; also reproduced below) in the revised manuscript, to explicitly note these results.</p><disp-quote content-type="editor-comment"><p>Reviewer #1 (Recommendations for the authors):</p><p>Persistency of germinal center (GC) reaction in the secondary lymphoid organs plays a critical role in antibody diversification and affinity maturation, as exemplified in the case of SARS-CoV-2 mRNA vaccines, which induce robust and long-lasting GC responses in humans. Incorporating such parameters would enhance the model's ability to more accurately reflect the actual humoral immune responses observed in vaccinated and infected individuals.</p></disp-quote><p>We agree with the reviewer. Our simulations did account for this important phenomenon, but we did not explicitly note this. After booster shots, antigen-specific antibodies generated due to humoral processes from previous immunizations deposit more antigen on FDCs in GCs (Figure 5B). Recently we showed experimentally in a different context that enhanced antigen on FDCs at later time points is a consequence of past antibody responses [Bhagachandani et al., Science Immunology 2024]. This is an important reason that secondary GCs persist for onger times than GCs that form after primary immunization and our simulation results reflect this phenomenon. In our simulations, the GCs that form after primary immunization last for ~ 110 days, after the second immunization they persist for ~165 days, and then after subsequent immunizations last for ~ 180 days. We now provide an additional graph (Figure 5 —figure supplement 2; also reproduced below) in the revised manuscript, to explicitly note these results.</p></body></sub-article></article>