<?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"><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">104278</article-id><article-id pub-id-type="doi">10.7554/eLife.104278</article-id><article-id pub-id-type="doi" specific-use="version">10.7554/eLife.104278.3</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>Computational and Systems Biology</subject></subj-group><subj-group subj-group-type="heading"><subject>Immunology and Inflammation</subject></subj-group></article-categories><title-group><article-title>Tissue-resident memory CD4<sup>+</sup> T cells are sustained by site-specific levels of self-renewal and continuous replacement</article-title></title-group><contrib-group><contrib contrib-type="author" equal-contrib="yes"><name><surname>Chandler</surname><given-names>Jodie</given-names></name><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="fn" rid="equal-contrib1">†</xref><xref ref-type="other" rid="fund1"/><xref ref-type="other" rid="fund2"/><xref ref-type="other" rid="fund3"/><xref ref-type="fn" rid="con1"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" equal-contrib="yes"><name><surname>Bullock</surname><given-names>M Elise</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0002-7876-4938</contrib-id><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="fn" rid="equal-contrib1">†</xref><xref ref-type="other" rid="fund1"/><xref ref-type="other" rid="fund2"/><xref ref-type="other" rid="fund3"/><xref ref-type="fn" rid="con2"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author"><name><surname>Swain</surname><given-names>Arpit C</given-names></name><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="other" rid="fund1"/><xref ref-type="other" rid="fund2"/><xref ref-type="other" rid="fund3"/><xref ref-type="fn" rid="con3"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author"><name><surname>Williams</surname><given-names>Cayman</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0002-0518-1379</contrib-id><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="fn" rid="con4"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author"><name><surname>van Dorp</surname><given-names>Christiaan H</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0002-7504-9947</contrib-id><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="other" rid="fund1"/><xref ref-type="other" rid="fund2"/><xref ref-type="other" rid="fund3"/><xref ref-type="fn" rid="con5"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes"><name><surname>Seddon</surname><given-names>Benedict</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0003-4352-3373</contrib-id><email>benedict.seddon@ucl.ac.uk</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="fn" rid="con6"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes"><name><surname>Yates</surname><given-names>Andrew J</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0003-4606-4483</contrib-id><email>andrew.yates@columbia.edu</email><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="other" rid="fund1"/><xref ref-type="other" rid="fund2"/><xref ref-type="other" rid="fund3"/><xref ref-type="fn" rid="con7"/><xref ref-type="fn" rid="conf1"/></contrib><aff id="aff1"><label>1</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/01ge67z96</institution-id><institution>Institute of Immunity and Transplantation, Division of Infection and Immunity, UCL, Royal Free Hospital</institution></institution-wrap><addr-line><named-content content-type="city">London</named-content></addr-line><country>United Kingdom</country></aff><aff id="aff2"><label>2</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/01esghr10</institution-id><institution>Department of Pathology and Cell Biology, Columbia University Irving Medical Center</institution></institution-wrap><addr-line><named-content content-type="city">New York</named-content></addr-line><country>United States</country></aff></contrib-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Belz</surname><given-names>Gabrielle T</given-names></name><role>Reviewing Editor</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/00rqy9422</institution-id><institution>University of Queensland</institution></institution-wrap><country>Australia</country></aff></contrib><contrib contrib-type="senior_editor"><name><surname>Taniguchi</surname><given-names>Tadatsugu</given-names></name><role>Senior Editor</role><aff><institution-wrap><institution-id institution-id-type="ror">https://ror.org/057zh3y96</institution-id><institution>University of Tokyo</institution></institution-wrap><country>Japan</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>25</day><month>06</month><year>2025</year></pub-date><volume>14</volume><elocation-id>RP104278</elocation-id><history><date date-type="sent-for-review" iso-8601-date="2024-11-05"><day>05</day><month>11</month><year>2024</year></date></history><pub-history><event><event-desc>This manuscript was published as a preprint.</event-desc><date date-type="preprint" iso-8601-date="2024-11-07"><day>07</day><month>11</month><year>2024</year></date><self-uri content-type="preprint" xlink:href="https://doi.org/10.1101/2024.09.26.615039"/></event><event><event-desc>This manuscript was published as a reviewed preprint.</event-desc><date date-type="reviewed-preprint" iso-8601-date="2025-03-12"><day>12</day><month>03</month><year>2025</year></date><self-uri content-type="reviewed-preprint" xlink:href="https://doi.org/10.7554/eLife.104278.1"/></event><event><event-desc>The reviewed preprint was revised.</event-desc><date date-type="reviewed-preprint" iso-8601-date="2025-05-12"><day>12</day><month>05</month><year>2025</year></date><self-uri content-type="reviewed-preprint" xlink:href="https://doi.org/10.7554/eLife.104278.2"/></event></pub-history><permissions><copyright-statement>© 2025, Chandler, Bullock et al</copyright-statement><copyright-year>2025</copyright-year><copyright-holder>Chandler, Bullock 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-104278-v1.pdf"/><self-uri content-type="figures-pdf" xlink:href="elife-104278-figures-v1.pdf"/><abstract><p>Tissue-resident memory T cells (T<sub>RM</sub>) protect from repeat infections within organs and barrier sites. The breadth and duration of such protection are defined at minimum by three quantities: the rate at which new T<sub>RM</sub> are generated from precursors, their rate of self-renewal, and their rate of loss through death, egress, or differentiation. Quantifying these processes individually is challenging. Here we combine genetic fate mapping tools and mathematical models to untangle these basic homeostatic properties of CD4<sup>+</sup> T<sub>RM</sub> in the skin and gut lamina propria (LP) of healthy adult mice. We show that CD69<sup>+</sup>CD4<sup>+</sup> T<sub>RM</sub> in skin reside for ∼24 days and self-renew more slowly, such that clones halve in size approximately every 5 weeks, and approximately 2% of cells are replaced daily from precursors. CD69<sup>+</sup>CD4<sup>+</sup> T<sub>RM</sub> in LP have shorter residencies (∼14 days) and are maintained largely by immigration (4–6% per day). We also find evidence that the continuous replacement of CD69<sup>+</sup>CD4<sup>+</sup> T<sub>RM</sub> at both sites derives from circulating effector-memory CD4<sup>+</sup> T cells, in skin possibly via a local CD9<sup>−</sup> intermediate. Our approach maps the ontogeny of CD4<sup>+</sup> T<sub>RM</sub> in skin and LP and exposes their dynamic and distinct behaviours, with continuous seeding and erosion potentially impacting the duration of immunity at these sites.</p></abstract><kwd-group kwd-group-type="author-keywords"><kwd>tissue-resident memory T cells</kwd><kwd>mathematical modelling</kwd><kwd>fate mapping</kwd></kwd-group><kwd-group kwd-group-type="research-organism"><title>Research organism</title><kwd>Mouse</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>R01 AI093870</award-id><principal-award-recipient><name><surname>Chandler</surname><given-names>Jodie</given-names></name><name><surname>Bullock</surname><given-names>M Elise</given-names></name><name><surname>Swain</surname><given-names>Arpit C</given-names></name><name><surname>Williams</surname><given-names>Cayman</given-names></name><name><surname>van Dorp</surname><given-names>Christiaan H</given-names></name><name><surname>Seddon</surname><given-names>Benedict</given-names></name><name><surname>Yates</surname><given-names>Andrew J</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>U01 AI150680</award-id><principal-award-recipient><name><surname>Chandler</surname><given-names>Jodie</given-names></name><name><surname>Bullock</surname><given-names>M Elise</given-names></name><name><surname>Swain</surname><given-names>Arpit C</given-names></name><name><surname>Williams</surname><given-names>Cayman</given-names></name><name><surname>van Dorp</surname><given-names>Christiaan H</given-names></name><name><surname>Seddon</surname><given-names>Benedict</given-names></name><name><surname>Yates</surname><given-names>Andrew J</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/10.13039/501100000265</institution-id><institution>Medical Research Council</institution></institution-wrap></funding-source><award-id>MR/P011225/1</award-id><principal-award-recipient><name><surname>Chandler</surname><given-names>Jodie</given-names></name><name><surname>Bullock</surname><given-names>M Elise</given-names></name><name><surname>Swain</surname><given-names>Arpit C</given-names></name><name><surname>Williams</surname><given-names>Cayman</given-names></name><name><surname>van Dorp</surname><given-names>Christiaan H</given-names></name><name><surname>Seddon</surname><given-names>Benedict</given-names></name><name><surname>Yates</surname><given-names>Andrew J</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>Memory CD4 T cells within tissues are highly dynamic, and their continuous replacement may erode immunity to previous infections.</meta-value></custom-meta><custom-meta specific-use="meta-only"><meta-name>publishing-route</meta-name><meta-value>prc</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="s1" sec-type="intro"><title>Introduction</title><p>Resident memory T cells (T<sub>RM</sub>) provide immune surveillance and protection in tissues throughout the body (<xref ref-type="bibr" rid="bib33">Szabo et al., 2019</xref>), but the mechanisms by which they are maintained are not well understood. Conventional CD4<sup>+</sup> and CD8<sup>+</sup> T<sub>RM</sub> in mice and humans are not intrinsically long-lived, but appear to self-renew slowly as assessed by readouts of cell division such Ki67 expression or BrdU incorporation, at levels that vary across tissues (<xref ref-type="bibr" rid="bib19">Gebhardt et al., 2009</xref>; <xref ref-type="bibr" rid="bib42">Watanabe et al., 2015</xref>; <xref ref-type="bibr" rid="bib29">Park et al., 2018</xref>; <xref ref-type="bibr" rid="bib32">Strobl et al., 2020</xref>; <xref ref-type="bibr" rid="bib15">Divito et al., 2020</xref>; <xref ref-type="bibr" rid="bib10">Christo et al., 2021</xref>). After infection or immune challenge, the numbers of elicited T<sub>RM</sub> may also be sustained by influx from precursor populations, although the extent to which this occurs is unclear and is likely also cell subset- and tissue-dependent. For example, in the lung there is evidence both for (<xref ref-type="bibr" rid="bib48">Zammit et al., 2006</xref>; <xref ref-type="bibr" rid="bib16">Ely et al., 2006</xref>; <xref ref-type="bibr" rid="bib30">Slütter et al., 2017</xref>; <xref ref-type="bibr" rid="bib36">Van Braeckel-Budimir et al., 2018</xref>; <xref ref-type="bibr" rid="bib35">Takamura and Kohlmeier, 2019</xref>) and against (<xref ref-type="bibr" rid="bib34">Takamura et al., 2016</xref>; <xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>, <xref ref-type="bibr" rid="bib38">van Dorp et al., 2025</xref>) ongoing recruitment of new T<sub>RM</sub> following respiratory virus infections. Within skin, T<sub>RM</sub> may be renewed or supplemented slowly from precursors in the setting of graft-versus-host disease (<xref ref-type="bibr" rid="bib15">Divito et al., 2020</xref>), and from circulating central memory T<sub>CM</sub> or effector memory T<sub>EM</sub> following infection or sensitisation (<xref ref-type="bibr" rid="bib17">Gaide et al., 2015</xref>; <xref ref-type="bibr" rid="bib26">Matos et al., 2022</xref>). In the small intestine, however, resident CD4<sup>+</sup> and CD8<sup>+</sup> T<sub>RM</sub> appear to persist for months to years with slow self-renewal without appreciable influx (<xref ref-type="bibr" rid="bib5">Bartolomé-Casado et al., 2019</xref>; <xref ref-type="bibr" rid="bib6">Bartolomé-Casado et al., 2021</xref>).</p><p>The dynamics of production and loss of T<sub>RM</sub> in the steady state are even less well understood, and measuring these processes is important for several reasons. The balance of loss and self-renewal defines the persistence of clonal populations and hence the duration of protective immunity. Further, while self-renewal can at best preserve clonal diversity within a tissue site, any supplementation or replacement by immigrant T<sub>RM</sub> will perturb the local TCR repertoire. In particular, any significant influx into T<sub>RM</sub> niches in the absence of overt infection may be a competitive force, potentially reducing the persistence of T<sub>RM</sub> previously established in response to infection or challenge.</p><p>The kinetics of circulating memory T cells have been quantified extensively in both mice and humans using dye dilution assays (<xref ref-type="bibr" rid="bib9">Choo et al., 2010</xref>), deuterium labelling (<xref ref-type="bibr" rid="bib43">Westera et al., 2013</xref>; <xref ref-type="bibr" rid="bib44">Westera et al., 2015</xref>; <xref ref-type="bibr" rid="bib11">Costa Del Amo et al., 2018</xref>; <xref ref-type="bibr" rid="bib4">Baliu-Piqué et al., 2019</xref>; <xref ref-type="bibr" rid="bib3">Baliu-Piqué et al., 2018</xref>, <xref ref-type="bibr" rid="bib37">van den Berg et al., 2021</xref>), and BrdU labelling, either alone (<xref ref-type="bibr" rid="bib47">Younes et al., 2011</xref>; <xref ref-type="bibr" rid="bib18">Ganusov and De Boer, 2013</xref>) or in combination with fate reporters (<xref ref-type="bibr" rid="bib20">Gossel et al., 2017</xref>; <xref ref-type="bibr" rid="bib22">Hogan et al., 2019</xref>; <xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>) or T cell receptor excision circles (<xref ref-type="bibr" rid="bib14">den Braber et al., 2012</xref>). Using mathematical models to interpret these data, these studies identified rates of production, cellular lifespans, and signatures of heterogeneity in turnover. Modelling has also established evidence for continuous replenishment of circulating memory CD4<sup>+</sup> T cells from precursors throughout life in specific-pathogen-free mice, driven by a combination of environmental, commensal, and self antigens (<xref ref-type="bibr" rid="bib20">Gossel et al., 2017</xref>; <xref ref-type="bibr" rid="bib22">Hogan et al., 2019</xref>; <xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>). Quantification of T<sub>RM</sub> dynamics has to date been restricted largely to measuring the net persistence of CD8<sup>+</sup> T<sub>RM</sub> following infection in mice in a variety of tissues (<xref ref-type="bibr" rid="bib28">Morris et al., 2019</xref>; <xref ref-type="bibr" rid="bib45">Wijeyesinghe et al., 2021</xref>). Far less is known regarding CD4<sup>+</sup> T<sub>RM</sub>, which typically outnumber their CD8<sup>+</sup> counterparts (<xref ref-type="bibr" rid="bib33">Szabo et al., 2019</xref>), and there have been very few attempts to dissect the kinetics of either subset (<xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>, <xref ref-type="bibr" rid="bib38">van Dorp et al., 2025</xref>).</p><p>In general, measuring these basic parameters in isolation is challenging, partly due to their sensitivity to assumptions made in the models (<xref ref-type="bibr" rid="bib12">De Boer and Perelson, 2013</xref>), but also because division-linked labelling alone may not distinguish in situ cell division and the supplementation of a population from labelled precursors. These issues can be addressed by modelling different readouts of cell fate simultaneously (<xref ref-type="bibr" rid="bib2">Bains et al., 2009</xref>; <xref ref-type="bibr" rid="bib14">den Braber et al., 2012</xref>; <xref ref-type="bibr" rid="bib11">Costa Del Amo et al., 2018</xref>; <xref ref-type="bibr" rid="bib13">De Boer and Yates, 2023</xref>; <xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>).</p><p>With these challenges in mind, here we integrated data from two independent inducible fate reporter systems to study CD4<sup>+</sup> T<sub>RM</sub> homeostasis in mice. Each system allows one to track the fates of defined populations of cells and their descendants. One labels all CD4<sup>+</sup> T cell subsets at any given moment, which effectively provides an age ‘timestamp’. The other labels cells that are dividing during a given time window. In combination, these systems allowed us to establish a quantitative model of the basal homeostatic properties of CD4<sup>+</sup> T<sub>RM</sub> within the skin and the lamina propria (LP) of the small intestine in healthy mice. In particular, we could unpick the contributions of self renewal and de novo cell production that underpin their maintenance, and explore their relationships to circulating T cell subsets.</p></sec><sec id="s2" sec-type="results"><title>Results</title><sec id="s2-1"><title>Combining cell fate reporters and models to measure T<sub>RM</sub> replacement, loss, and self-renewal</title><p>To study the homeostatic dynamics of tissue-resident CD4<sup>+</sup> memory T cells in healthy mice, we used in concert two genetic fate mapping tools in which cohorts of peripheral T cells and their offspring can be induced to express permanent fluorescent markers (<xref ref-type="fig" rid="fig1">Figure 1A</xref>). These reporter strains were previously used separately to study the turnover of naive and circulating memory T and B cells (<xref ref-type="bibr" rid="bib40">Verheijen et al., 2020</xref>; <xref ref-type="bibr" rid="bib24">Lukas et al., 2023</xref>; <xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>). In the Ki67<sup>mCherry-CreERT</sup> Rosa26<sup>RcagYFP</sup> system, henceforth Ki67-DIVN, fluorescent reporters are linked to the expression of Ki67, a nuclear protein expressed during cell division and for 3–4 days afterwards (<xref ref-type="bibr" rid="bib20">Gossel et al., 2017</xref>; <xref ref-type="bibr" rid="bib27">Miller et al., 2018</xref>). Specifically, these mice express both a Ki67-mCherry fusion protein and inducible CreERT from the <italic>Mki67</italic> locus, together with a <italic>Rosa26</italic><sup><italic>RcagYFP</italic></sup> Cre reporter construct. Treatment of mice with tamoxifen therefore induces YFP in cells expressing high levels of Ki67, and YFP is then stably expressed by these cells and their offspring. Expression of Ki67-fused mCherry gives a constitutive live readout of Ki67 expression, independent of tamoxifen treatment and YFP expression. In the second fate reporter, CD4<sup>CreERT</sup> Rosa26<sup>RmTom</sup> mice (Cd4-FR), the Cre reporter is constructed such that cells expressing CD4 during tamoxifen treatment permanently and heritably express the fluorescent reporter mTomato (mTom).</p><fig-group><fig id="fig1" position="float"><label>Figure 1.</label><caption><title>Overview of the fate-reporter approach to quantifying the homeostasis of skin- and lamina propria (LP)-resident CD4<sup>+</sup> T cells.</title><p>(<bold>A</bold>) Ki67 and CD4 reporter constructs. (<bold>B</bold>) Schematic of a simple mathematical model of T<sub>RM</sub> homeostasis at steady state. New cells enter a T<sub>RM</sub> subset in skin or LP (the ‘target’ population) from a precursor population at rate <italic>θ</italic> (cells per unit time). YFP and mTom expression among immigrant cells is assumed to be that of the precursor population in bulk. We considered three possibilities for the Ki67 expression levels among new immigrants: a ‘quiescent’ mode (all Ki67<sup>low</sup>), ‘neutral’ recruitment (Ki67<sup>high</sup> frequency identical to that of the precursor), or ‘division-linked’ (all recruited cells Ki67<sup>high</sup>). The target cells are assumed to be a kinetically homogeneous population that self-renews at average rate <inline-formula><alternatives><mml:math id="inf1"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft1">\begin{document}$\rho$\end{document}</tex-math></alternatives></inline-formula>, such that their mean interdivision time is <inline-formula><alternatives><mml:math id="inf2"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>ρ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft2">\begin{document}$1/\rho$\end{document}</tex-math></alternatives></inline-formula>. Cells are also lost through death, differentiation or tissue egress at total rate <inline-formula><alternatives><mml:math id="inf3"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>δ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft3">\begin{document}$\delta$\end{document}</tex-math></alternatives></inline-formula>, implying a mean residence time of <inline-formula><alternatives><mml:math id="inf4"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>δ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft4">\begin{document}$1/\delta$\end{document}</tex-math></alternatives></inline-formula>. The combination of these processes determines the time courses of frequencies of YFP<sup>+</sup> and mTom<sup>+</sup> cells with the target population. (<bold>C</bold>) Experimental design.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-104278-fig1-v1.tif"/></fig><fig id="fig1s1" position="float" specific-use="child-fig"><label>Figure 1—figure supplement 1.</label><caption><title>Flow cytometric analysis of tissue-resident T cell subsets.</title><p>(<bold>A</bold>) Gating strategy for CD4<sup>+</sup> subsets in lymph nodes, LP, and skin. (<bold>B</bold>) Tissue-localised CD4<sup>+</sup> EM subsets defined by protection from short-term in vivo labelling.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-104278-fig1-figsupp1-v1.tif"/></fig></fig-group><p>In a closed population of cells at steady state, self-renewal must be balanced by loss and so, following tamoxifen treatment, the frequencies of cells expressing YFP or mTom within any such population would remain constant. Therefore, any decline in the frequency of either reporter among T<sub>RM</sub> after treatment must derive from the influx of label-negative cells from an upstream (precursor) population. In the Ki67-DIVN mice, these will be descendants of cells that were not dividing at the time of tamoxifen treatment; in the Cd4-FR mice, labelled CD4<sup>+</sup> cells will slowly be replaced by the descendants of those generated in the thymus after treatment. The shape of this decline will be determined by the combination of the net loss rate of T<sub>RM</sub> from the tissue (through death, egress, or differentiation, offset by any self-renewal) and the label content of immigrant T<sub>RM</sub> (<xref ref-type="fig" rid="fig1">Figure 1B</xref>). To refer to the persistence of individual T<sub>RM</sub> cells, we will use the term ‘residence time’ rather than ‘lifespan’ to reflect the multiple potential mechanisms of loss from tissues.</p><p>To quantify these processes, we treated cohorts of both reporter mice, aged between 4 and 15 weeks, with a single 2 mg pulse of tamoxifen (<xref ref-type="fig" rid="fig1">Figure 1C</xref>). Over 9-week (Ki67 reporter) and 57-week (CD4 reporter) chase periods, we measured the frequencies of labelled cells among antigen-experienced CD4<sup>+</sup> T cell subsets isolated from skin and the LP of the small intestine, and within circulating naive and memory T cell subsets derived from lymph nodes (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1A</xref>). By combining these frequencies with measures of Ki67 expression and describing the resulting set of time series with simple mathematical models, we aimed to estimate the basic parameters underlying T<sub>RM</sub> kinetics.</p></sec><sec id="s2-2"><title>CD4<sup>+</sup> T<sub>RM</sub> in skin and lamina propria are continuously replaced from precursors</title><p>We considered two populations within both skin and LP, identified as tissue-localised by virtue of their protection from short-term in vivo labelling (‘Methods’ and <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1B</xref>). One was effector-memory (EM) phenotype (CD4<sup>+</sup>CD44<sup>hi</sup> CD62L<sup>lo</sup>) T cells in bulk, which we studied in order to gain the broadest possible picture of memory T cell dynamics at these sites. We also considered the subset of these cells that expressed CD69, a canonical marker of CD4<sup>+</sup> T cell residency across multiple tissues (<xref ref-type="bibr" rid="bib33">Szabo et al., 2019</xref>). We saw no significant changes with mouse age in the numbers of either population within skin (<xref ref-type="fig" rid="fig2">Figure 2A</xref>, <inline-formula><alternatives><mml:math id="inf5"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0.67</mml:mn></mml:mrow></mml:mstyle></mml:math><tex-math id="inft5">\begin{document}$p \gt 0.67$\end{document}</tex-math></alternatives></inline-formula>) or LP (<xref ref-type="fig" rid="fig2">Figure 2B</xref>, <inline-formula><alternatives><mml:math id="inf6"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0.39</mml:mn></mml:mrow></mml:mstyle></mml:math><tex-math id="inft6">\begin{document}$p \gt 0.39$\end{document}</tex-math></alternatives></inline-formula>). There were also no significant changes in any of these quantities with time since tamoxifen treatment (<inline-formula><alternatives><mml:math id="inf7"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0.24</mml:mn></mml:mrow></mml:mstyle></mml:math><tex-math id="inft7">\begin{document}$p \gt 0.24$\end{document}</tex-math></alternatives></inline-formula>). We therefore assumed that the skin- and LP-localised T cell subsets we considered were at, or close to, homeostatic equilibrium during the chase period. For brevity, we refer to tissue-localised CD4<sup>+</sup>CD44<sup>hi</sup>CD62L<sup>lo</sup> T cells in bulk as EM, and their CD69<sup>+</sup> subset as T<sub>RM</sub>.</p><fig-group><fig id="fig2" position="float"><label>Figure 2.</label><caption><title>Modelling fate reporter dynamics among CD4<sup>+</sup> T cell subsets in skin and lamina propria (LP).</title><p>(<bold>A, B</bold>) Numbers of CD4<sup>+</sup> effector-memory (EM) phenotype and CD4<sup>+</sup>CD69<sup>+</sup> T cells recovered from (<bold>A</bold>) ear skin and (<bold>B</bold>) LP in the small intestine, against mouse age. p-values are derived from Spearman rank correlation on data from the Cd4-FR and Ki67-DIVN strains combined. (<bold>C</bold>) Observed (points), best-fit model trajectories (black lines), and 95% credible intervals (grey envelopes) of the frequencies of mTom<sup>+</sup> and YFP<sup>+</sup> CD4<sup>+</sup> T cell subsets within skin and LP, and the proportions of YFP<sup>+</sup> and YFP<sup>−</sup> cells that expressed Ki67, with time since tamoxifen treatment. Shaded rectangles indicate the 5-day period over which reporter expression was being induced; data from these periods were not used in fitting. (<bold>D</bold>) Frequencies of mTom<sup>+</sup> and YFP<sup>+</sup> cells within lymph node CD4<sup>+</sup> T cell subsets, and within CD4<sup>+</sup>CD44<sup>+</sup>CD69<sup>−</sup> T cells in skin and LP. Overlaid are the empirical descriptions of these trajectories from the best-fitting model in which that population was identified as a precursor (Appendix 1 section ‘Model fitting‘); grey envelopes are 95% credible intervals. (The naive and CM in lymph nodes, and CD69<sup>−</sup> cells in LP, were never identified as favoured precursors.) Number of Cd4-FR mice: 36; number of Ki67-DIVN mice: 31.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-104278-fig2-v1.tif"/></fig><fig id="fig2s1" position="float" specific-use="child-fig"><label>Figure 2—figure supplement 1.</label><caption><title>Prior and posterior distributions of parameters for the best-fitting models.</title><p>Prior distributions of all parameters were truncated lognormal distributions and here are shown as kernel-smoothed samples. Truncation limits: self-renewal rate ρ ∈ (0, 1); loss rate δ ∈ (ρ, 5); rate of loss of Ki67 ∈ (0.2, 0.5); daily influx as fraction of population size ∈ (0.005, 0.1). The Ki67 loss rate was informed by our previous estimates (<xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>; <xref ref-type="bibr" rid="bib20">Gossel et al., 2017</xref>). The constraint ρ &lt; δ ensures that the population is at a steady state. Upper bounds on division and loss rates translate to minimum interdivision and residence times of 24 h and 4.8 h, respectively; the upper bound on the division rate was informed by Ki67 levels observed in tissues (see Appendix 1 section ‘Prior distributions of parameters’).</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-104278-fig2-figsupp1-v1.tif"/></fig><fig id="fig2s2" position="float" specific-use="child-fig"><label>Figure 2—figure supplement 2.</label><caption><title>Fits of top-, second-, and lowest-ranked models for each target population.</title><p>In cases where the best-fit (black) curves are not visible, they are closely overlaid by the blue curves (second-ranked model). Note that because each model was fitted to six timecourses simultaneously, and fractional observations were logittransformed to normalise residuals, apparently small visual differences in fits can nevertheless lead to substantial differences in model support.</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-104278-fig2-figsupp2-v1.tif"/></fig></fig-group><p>During the first few days after tamoxifen treatment, YFP and mTom expression increased continuously within the skin and LP subsets (<xref ref-type="fig" rid="fig2">Figure 2C</xref>), as well as among CD4<sup>+</sup> naive (CD44<sup>lo</sup> CD62L<sup>hi</sup>), central memory (T<sub>CM</sub>, CD44<sup>hi</sup> CD62L<sup>hi</sup>), and effector memory (T<sub>EM</sub>, CD44<sup>hi</sup> CD62L<sup>lo</sup>) T cells recovered from lymph nodes (<xref ref-type="fig" rid="fig2">Figure 2D</xref>). These initial increases were driven in part by the intracellular dynamics of the induction of the fluorescent reporters. We therefore began our analyses at day 5 post-treatment, by which time induction was considered complete and the subsequent trajectories of label frequencies reflected only the dynamic processes of cell production and loss. A key observation was that mTom expression within the skin and LP subsets then declined slowly (roughly seven- to eight-fold over the course of a year, <xref ref-type="fig" rid="fig2">Figure 2C</xref>), indicating immediately that these populations were being continuously replaced from precursors. Early in the chase period YFP<sup>+</sup> T<sub>RM</sub> expressed Ki67 at higher levels than YFP<sup>−</sup> cells, as expected, but Ki67 expression in the two populations converged at later times. We return to the interpretation of these kinetics below.</p><p>We then investigated the extent to which the simple model illustrated in <xref ref-type="fig" rid="fig1">Figure 1B</xref> could explain these trajectories. Given the observation of continued recruitment, any time variation in the label content of T<sub>RM</sub> precursors might leave an imprint on the label kinetics of skin or LP T<sub>RM</sub> themselves and thereby help us identify their developmental pathways. We reasoned that plausible T<sub>RM</sub> precursors were LN-derived CD4<sup>+</sup> naive, T<sub>CM</sub> or T<sub>EM</sub>; we also considered the possibilities that CD69<sup>−</sup> cells within skin and LP are the direct precursors of the local CD69<sup>+</sup> populations. Therefore, we used empirical functions to describe the time courses of the frequencies of YFP<sup>+</sup> and mTom<sup>+</sup> cells within these populations (<xref ref-type="fig" rid="fig2">Figure 2D</xref>) and used these to represent the label composition of cells entering the tissue subsets.</p><p>For each tissue subset (‘target’) and precursor pair, we fitted the model simultaneously to six time courses; the frequencies of (i) YFP expression and (ii) mTom expression among target cells, the proportions of Ki67<sup>high</sup> cells among (iii) YFP<sup>+</sup> and (iv) YFP<sup>−</sup> target cells, and the (v) YFP and (vi) mTom expression kinetics within the precursor (‘Methods’ and Appendix 1). For each precursor/target pair, we considered three modes of influx – one in which new immigrant T<sub>RM</sub> are Ki67<sup>low</sup> (‘quiescent’ recruitment); another in which their Ki67 expression directly reflects that of the precursor (‘neutral’ recruitment); and a third in which immigrants have recently divided (Ki67<sup>high</sup>), perhaps through an antigen-driven process (‘division-linked’ recruitment).</p></sec><sec id="s2-3"><title>Skin and LP CD4<sup>+</sup> T<sub>RM</sub> have similar residence times but exhibit distinct contributions of replacement and self-renewal</title><p>For each combination of target population, potential precursor, and potential mode of recruitment, we were able to estimate rates of influx, mean residence times, and mean interdivision times for the target population (<xref ref-type="fig" rid="fig3">Figure 3</xref> and <xref ref-type="table" rid="app1table1">Appendix 1—table 1</xref>; prior and posterior distributions of the parameters of the best-fitting models are shown in <xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>). The mean residence times of both EM and T<sub>RM</sub> within skin and LP were ∼3 weeks and 2 weeks, respectively. The means of production of new cells differed at the two sites, however. In skin, around 2% of both populations were replaced daily by influx, comparable to the rates of constitutive replacement of circulating memory CD4<sup>+</sup> T cell subsets (<xref ref-type="bibr" rid="bib20">Gossel et al., 2017</xref>; <xref ref-type="bibr" rid="bib22">Hogan et al., 2019</xref>; <xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>), and EM and T<sub>RM</sub> self-renewed every 6 and 7 weeks, respectively. In contrast, within LP these subsets divided less often (every 7–9 weeks) and relied on higher levels of recruitment (4–6% per day) for their maintenance.</p><fig id="fig3" position="float"><label>Figure 3.</label><caption><title>Parameters governing the homeostasis of antigen-experienced CD4<sup>+</sup> T cells localised within skin and lamina propria (LP) in adult mice.</title><p>Violin plots indicate the posterior distributions of parameters. Black points and bars; best (maximum a posteriori) estimates and 95% credible intervals. For each population (target) in skin or LP, potential precursors were from lymph nodes, CD4<sup>+</sup> naive, central memory and effector memory T cells (N, EM, and CM); and for CD4<sup>+</sup> T<sub>RM</sub>, CD69<sup>+</sup> T<sub>RM</sub> within the same tissue. For each precursor/target pair, we considered three potential levels of Ki67 expression on immigrant cells (L-R; orange, red, and blue violin plots). ‘High’, the division-linked model (new cells enter as Ki67<sup>high</sup>); ‘Int’, neutral model (Ki67 expression among new cells mirrors that of the precursor); and ‘Low’, the quiescent model (new cells enter as Ki67<sup>low</sup>). Shaded regions highlight the parameter estimates derived from the favoured model (precursor and Ki67 levels on immigration) for each target (<xref ref-type="fig" rid="fig4">Figure 4A</xref>).</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-104278-fig3-v1.tif"/></fig><p>From these basic quantities, we could derive several other important measures of T<sub>RM</sub> behaviour. First, the balance of the rates of loss (<inline-formula><alternatives><mml:math id="inf8"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>δ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft8">\begin{document}$\delta$\end{document}</tex-math></alternatives></inline-formula>) and self-renewal (<inline-formula><alternatives><mml:math id="inf9"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft9">\begin{document}$\rho$\end{document}</tex-math></alternatives></inline-formula>) defines the persistence of a cohort of T cells, which is distinct from the lifespan of its constituent cells (<xref ref-type="bibr" rid="bib11">Costa Del Amo et al., 2018</xref>; <xref ref-type="bibr" rid="bib13">De Boer and Yates, 2023</xref>). Specifically, the quantity <inline-formula><alternatives><mml:math id="inf10"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>ln</mml:mi><mml:mo>⁡</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>δ</mml:mi><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mstyle></mml:math><tex-math id="inft10">\begin{document}$\ln(2)/(\delta-\rho)$\end{document}</tex-math></alternatives></inline-formula> is the average time taken for a cohort and their descendents to halve in number. While we studied polyclonal populations here, this quantity applies equally well to measuring the persistence of a TCR clonotype, so we refer to it as a clonal half life (<xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>). The substantial rates of self-renewal in skin led to clonal half lives of just over a month. The lower levels of self-renewal and higher levels of replacement in LP resulted in shorter clonal half lives of approximately 2 weeks.</p><p>Importantly, our estimates of these quantities depended to varying degrees on the choice of precursor and mode of recruitment (<xref ref-type="fig" rid="fig3">Figure 3</xref>). For example, intuitively, given the observed level of Ki67 within each target population, the greater the levels of Ki67 within newly recruited cells, the less must derive from self-renewal within the tissue; hence, if one assumes that recruitment is division-linked, estimated division rates are reduced. Similarly, as discussed above, the label content of the precursor influences the net loss rate of label in the target, which was most clearly reflected in the loss of mTom<sup>+</sup> cells over the longer chase period (<xref ref-type="fig" rid="fig2">Figure 2C and D</xref>). For example, mTom was lost most rapidly within naive CD4<sup>+</sup> T cells (<xref ref-type="fig" rid="fig2">Figure 2D</xref>) due to the influx of label-negative cells from the thymus. Models in which naive T cells were the direct precursor of T<sub>RM</sub> therefore predicted greater clonal persistence within tissues.</p><p>We saw very little decline in YFP expression levels during the 2-month chase period (<xref ref-type="fig" rid="fig2">Figure 2C</xref>) due in part to the sustained levels of YFP within the putative precursor populations (<xref ref-type="fig" rid="fig2">Figure 2D</xref>), which ‘topped up’ YFP-expressing T<sub>RM</sub>. As a result, YFP kinetics within the tissues were not strongly informative regarding rates of replacement. However, the rate of convergence of Ki67 within YFP<sup>+</sup> and YFP<sup>−</sup> cells (<xref ref-type="fig" rid="fig2">Figure 2C</xref>) put clear constraints on the duration of Ki67 expression, which at approximately 3 days (<xref ref-type="fig" rid="fig3">Figure 3</xref>) was consistent with previous estimates. This quantity in turn was informative for estimating rates of self-renewal. Further, the observed convergence of Ki67 expresssion within these two subsets is consistent with the assumption of homogeneity in the rates of division and loss within skin and LP.</p></sec><sec id="s2-4"><title>CD4<sup>+</sup> CD69<sup>+</sup> T<sub>RM</sub> within LP likely derive predominantly from circulating T<sub>EM</sub> in lymph nodes, while those in skin may derive from a CD69<sup>−</sup> intermediate</title><p>To more precisely quantify the kinetics of each target population, we assessed the relative support for each combination of precursor and mode of recruitment (<xref ref-type="fig" rid="fig4">Figure 4A</xref>). Each of these weights summarises the magnitude and uncertainty of a model’s out-of-sample prediction error of the label kinetics within the target population (‘Methods’).</p><fig id="fig4" position="float"><label>Figure 4.</label><caption><title>Candidate ontogenic pathways of CD4<sup>+</sup> CD69<sup>+</sup> T<sub>RM</sub> in skin and lamina propria (LP).</title><p>(<bold>A</bold>) For each target population with skin and LP (CD4<sup>+</sup> EM bulk and CD4<sup>+</sup>CD69<sup>+</sup> T cells), we calculated the relative support for alternative pathways and modes of recruitment using LOO-IC weights (‘Methods’). For potential precursors, N, CM, and EM refer to naive, T<sub>CM</sub>, and T<sub>EM</sub> in lymph nodes; for CD69<sup>+</sup> targets we also considered CD69<sup>−</sup> cells within the same tissue as a possible precursor. As described in the text, for each precursor/target pair, there were three potential submodels relating to the possible levels of Ki67 on newly recruited cells. Model weights sum to 1 for each target population, with the width of each arrow reflecting a model’s degree of support. (<bold>B</bold>) Schematics of the most strongly supported pathways of development of CD4<sup>+</sup>CD69<sup>+</sup> T<sub>RM</sub> in skin and LP, with approximate values of key kinetic parameters (<xref ref-type="fig" rid="fig3">Figure 3</xref> and <xref ref-type="table" rid="app1table1">Appendix 1—table 1</xref>).</p></caption><graphic mimetype="image" mime-subtype="tiff" xlink:href="elife-104278-fig4-v1.tif"/></fig><p>We found that the data were quite strongly informative regarding the immediate ancestors of tissue subsets. From the candidate set of models, the weighting strongly favoured lymph-node-derived EM as the closest precursor to CD4<sup>+</sup> EM within both skin and LP. However, within skin, local CD69<sup>−</sup> cells were the favoured precursor to CD69<sup>+</sup> T<sub>RM</sub>. The evidence was generally more equivocal regarding the mode in which cells are recruited into skin and LP, although for skin we saw substantial evidence (66% of model support) for a division-linked transition from CD69<sup>−</sup> to CD69<sup>+</sup> cells. <xref ref-type="fig" rid="fig4">Figure 4B</xref> summarises the developmental trajectories and kinetics of T<sub>RM</sub> in skin and LP that were supported most strongly by our analyses. Parameter estimates and credible intervals for these models are highlighted with vertical shaded regions in <xref ref-type="fig" rid="fig3">Figure 3</xref> and are detailed in <xref ref-type="table" rid="app1table1">Appendix 1—table 1</xref>. Visual differences between models are shown in <xref ref-type="fig" rid="fig2s2">Figure 2—figure supplement 2</xref>, where for each target population we overlay the fits from top-ranked, second-ranked, and lowest-ranked models.</p></sec><sec id="s2-5"><title>Validation of residence times using Ki67 expression directly</title><p>As a consistency check, when a population is at or close to steady state, bounds on the mean residence time of cells can be estimated using only the measured frequency of Ki67 within the target population, and the daily rate of replacement (Appendix 1 section ‘Estimating average cell residence times using Ki67’). In skin, both EM and T<sub>RM</sub> are replaced at the rate of 2% per day and have Ki67 expression frequencies of around 0.15 (<xref ref-type="fig" rid="fig2">Figure 2C</xref>). The approximation then yields residence times in the range 22–28 days, depending on whether immigrant T<sub>RM</sub> are Ki67<sup>low</sup> or Ki67<sup>high</sup>, respectively. In LP, with 5.5% daily replacement and Ki67 frequencies of around 0.07, we estimate residence times of 14–25 days. Both estimates are in good agreement with those from the model fitting. Further validation of these results, and dissection of the kinetics, might be achieved by manipulating cell trafficking, although this would potentially impact multiple processes at once. For example, treating mice with the sphingosine 1-phosphate receptor agonist FTY720 would block tissue ingress and egress. This would leave self-renewal as the only means of T<sub>RM</sub> production and would also remove the component of the loss rate that is due to cells leaving the tissue. In principle, one could then gain estimates of the intrinsic lifespan of T<sub>RM</sub>, rather than their tissue residence time. However, parameter estimation would then require accurate measurements of cell numbers within the tissue.</p></sec></sec><sec id="s3" sec-type="discussion"><title>Discussion</title><p>Our analysis indicates that CD4<sup>+</sup> T<sub>RM</sub> are not intrinsically long-lived, but instead are sustained by both self-renewal and supplementation from circulating precursors. By combining fate reporting methods with mathematical models, we also showed that it is possible to separately quantify the processes that underlie their persistence. We saw quite distinct contributions of recruitment and self-renewal of both subsets within skin and LP. The basis of this difference is unclear, but we speculate that the large antigenic burden within the small intestine drives the higher levels of T<sub>RM</sub> recruitment and clonal erosion within the LP. We showed that estimates of these quantities depend on the identity of the immediate precursor, whose label kinetics propagate downstream into the population of interest, and the extent of any cell division that occurs around the time of differentiation or ingress. However, by using easily interpretable mathematical models we were able to measure the support for different pathways and modes of recruitment into each subset.</p><p>The schematic in <xref ref-type="fig" rid="fig1">Figure 1B</xref> illustrates a hypothetical example in which the frequency of YFP-expressing cells within a precursor declines. This trend is then reflected downstream in the target. However, in our experiments the kinetics of YFP in most of the putative precursors were quite flat (<xref ref-type="fig" rid="fig2">Figure 2D</xref>). As noted above, these kinetics were likely due largely to the continued influx of new cells into circulating memory subsets, in turn likely from naive precursors (<xref ref-type="bibr" rid="bib20">Gossel et al., 2017</xref>; <xref ref-type="bibr" rid="bib22">Hogan et al., 2019</xref>; <xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>). These had increasing levels of YFP (<xref ref-type="fig" rid="fig2">Figure 2D</xref>, left panel) deriving from thymocytes that were dividing rapidly during treatment. YFP levels among naive T cells were also probably sustained to an extent by low-level residual labelling of thymic progenitors (<xref ref-type="bibr" rid="bib24">Lukas et al., 2023</xref>). YFP expression was therefore not cleanly ‘washed out’ in the periphery. The data from the labelling of CD4-expressing cells were more informative for dissecting turnover; mTom<sup>+</sup> cells were clearly diluted out of all peripheral populations by the descendants of mTom<sup>−</sup> thymocytes.</p><p>In these reporter mice, YFP and mTom were induced quickly in all subsets to different degrees; therefore, our inferences regarding precursor–target relationships were not informed by the initial levels of label in each. (For example, imagine a rapidly dividing target fed by a slowly dividing precursor; initially, YFP levels in the target would be higher than those in the precursor.) The hierarchy of levels of label in different subsets <italic>would</italic> be informative if one expects targets to begin with no label at all; for instance, in the busulfan chimeric mouse system (<xref ref-type="bibr" rid="bib21">Hogan et al., 2015</xref>) new, thymically derived ‘labelled’ (donor) cells progressively infiltrate replete ‘unlabelled’ (host) populations. In that case, one can immediately reject certain differentiation pathways by examining the sequence of accrual of donor cells in different subsets. In the systems we use here, information regarding lineage relationships is contained instead in the trends in YFP and mTom frequencies after treatment because precursor kinetics must leave an imprint on the target (<xref ref-type="fig" rid="fig1">Figure 1B</xref>). This information is particularly useful if two populations exhibit opposing trajectories – they are then unlikely to be immediately related.</p><p>On a technical note, in general one can reduce experimental variation by comparing quantities derived from the same individual. We showed previously that in some situations exploiting the within-mouse grouping of observations can reduce uncertainty and refine parameter estimates when modelling cell dynamics (<xref ref-type="bibr" rid="bib46">Yates et al., 2007</xref>). We were not able to take this approach here, however, because the frequency of cells expressing YFP or mTom within a given subset in a particular mouse depends on the accumulated history of label in that subset’s precursor. We were unable to identify these trajectories for each animal, so we were obliged to use population averages (<xref ref-type="fig" rid="fig2">Figure 2D</xref>). To mitigate any biases this averaging might introduce, we fitted these empirical functions simultaneously with the models of label kinetics in the targets. This conservative strategy propagated the uncertainty in the precursor trajectories into our conclusions.</p><p>Our analysis was rooted in the observation that all CD4<sup>+</sup> T cell subsets within these tissues were at steady state. This dynamic equilibrium dictates that immigration of new cells must be accompanied by loss of existing ones. In the SPF mice studied here, these dynamic populations are likely specific for self or commensal antigens that are continuously expressed. It is possible that residence and interdivision times are distinct for T<sub>RM</sub> that might not be replenished long-term from precursors, such as those generated in acute infections. Further, our simple model can explain the stable maintenance of T<sub>RM</sub> numbers in healthy skin and LP without needing to invoke the concept of a homeostatic niche, such as a competitive limit to cell densities. In this model, any increase or decrease in the rate of influx into a tissue will simply lead to a new equilibrium at higher or lower cell densities, respectively. Indeed repeated vaccinia virus challenges can drive progressive increases in the number of virus-specific CD8<sup>+</sup> T<sub>RM</sub> in skin that are detectable for months (<xref ref-type="bibr" rid="bib23">Jiang et al., 2012</xref>), and heterologous challenges appear not to erode pre-existing LCMV-specific CD8<sup>+</sup> T<sub>RM</sub> (<xref ref-type="bibr" rid="bib45">Wijeyesinghe et al., 2021</xref>). However, whether the same flexibility manifests among CD4<sup>+</sup> T<sub>RM</sub> following repeated challenges is unclear.</p><p>Our goal here was to assess the support for external replenishment of effector-memory-like CD4<sup>+</sup> T cells in bulk and the dominant CD69<sup>+</sup> T<sub>RM</sub> subset. We found evidence that CD69<sup>+</sup>CD4<sup>+</sup> T<sub>RM</sub> in skin derive at least in part from a local CD69<sup>−</sup> precursor. With richer phenotyping of tissue-localised cells, we could in principle use labelling trajectories to define more fine-grained differentiation pathways. One issue is that accurate measurement of label frequencies becomes more difficult as one resolves T<sub>RM</sub> into smaller subsets; indeed, we saw that label kinetics within the small CD69<sup>−</sup> populations were relatively noisy. Another issue is that label kinetics operate on the timescales of the net loss rate of cell populations – death and onward differentiation, balanced by self-renewal. More frequent sampling would be required to resolve more transitory intermediates. Nevertheless, our study clearly exposes the highly dynamic nature of CD4<sup>+</sup> T<sub>RM</sub>, sustained throughout life by both self-renewal and continued influx from precursors. This tissue-specific influx, particularly if there are competitive limits to T<sub>RM</sub> occupancy, may contribute to the differential longevity of immunity at different barrier sites.</p></sec><sec id="s4" sec-type="methods"><title>Methods</title><sec id="s4-1"><title>Reporter mouse strains</title><p>Ki67<sup>mCherry-CreERT</sup> Rosa26<sup>RcagYFP</sup> (Ki67-DIVN) and CD4<sup>CreERT</sup> Rosa26<sup>RmTom</sup> (Cd4-FR) mice have been described previously (<xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>). Experimental Ki67-DIVN mice were homozygous for indicated mutations at both the <italic>Ki67</italic> and <italic>Rosa26</italic> loci. Experimental Cd4-FR mice were heterozygous for the indicated mutations at both the <italic>Cd4</italic> and <italic>Rosa26</italic> loci. Tamoxifen (Sigma) was diluted to 20 mg/mL in corn oil (Fisher Scientific) and 100 μl (2 mg) was administered to mice via oral feeding on day 0. Ki67-DIVN mice were injected with 2 µg Thy1.2-BV510 (53-2.1) (BioLegend) 3 min prior to sacrifice to label T cells in the circulation. This protocol typically achieves &gt;99% staining of circulating cells (<xref ref-type="bibr" rid="bib1">Anderson et al., 2014</xref>), and less than 3% of cells recovered from our tissue samples were label positive (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1B</xref>), supporting the assumption of very low rates of false-positive and false-negative events. Mice were subsequently taken down at specified timepoints post tamoxifen treatment for organ collection. All mice were bred in the Comparative Biology Unit of the Royal Free UCL campus and at Charles River laboratories, Manston, UK. Animal experiments were performed according to institutional guidelines and Home Office regulations under project licence PP2330953.</p></sec><sec id="s4-2"><title>Cell preparation</title><p>All peripheral lymph nodes (LNs), the small intestine (SI), and ear skin were taken from mice and processed into single-cell suspensions. LNs were mashed through two pieces of fine gauze in a Petri dish and washed with complete RPMI (Thermo Fisher) supplemented with 5% FCS (Thermo Fisher) (cRPMI). Cells were resuspended in cold PBS and counted using the CASY counter (Cambridge Bioscience). Peyer’s patches were excised from the antimesenteric side of the SI before being opened longitudinally and SI contents scraped out. SI pieces were placed in 20 mL pre-warmed extraction media (cRPMI + 10 mM HEPES [Thermo Fisher] +5 mM EDTA [Sigma]+1 mM DTT [Abcam]) and incubated in 37 °C shaking incubator for 30 min at 200 rpm. Cells were filtered over 70 μm cell strainer (supernatant containing intra-epithelial lymphocytes not used), and SI pieces were placed in cold cRPMI supplemented with 10 mM HEPES and allowed to settle. The supernatant was carefully poured off and SI pieces were finely minced, added to 20 mL pre-warmed digestion media (RPMI + 10% FCS + 1.5 mg/mL collagenase VIII [Sigma]) and incubated in 37 °C shaking incubator for 30 min at 200 rpm. After digestion, cells were passed through 70 μm cell strainer and washed with cRPMI + 10 mM HEPES. The resulting cell suspension contains cells from the LP of the SI. Ear skin was excised and separated into dorsal and ventral sides. Skin was finely minced, added to 4 mL digestion buffer cRPMI + 50 mM HEPES + 37.5 μg/mL Liberase TL [Merck] + 3.125 mg/mL collagenase IV [Thermo Fisher] +1 mg/mL DNAse I [Merck] and incubated in 37 °C shaking incubator for 2 h at 200 rpm. Cells were filtered over 70 μm cell strainer and washed through with cRPMI.</p></sec><sec id="s4-3"><title>Flow cytometry</title><p>All cells isolated from skin and LP, and 5 × 10<sup>6</sup> LN cells were stained for analysis by flow cytometry. Cells were stained in 100 μl PBS with combinations of CD8α-BUV395 (53-6.7), CD25-BUV395 (PC61), CD62L-BUV737 (MEL-14), TCRγδ-BV421 (GL3), CD103-BV786 (M290) (all BD Biosciences); CD25-BV650 (PC61), CD103-BV421 (2E7), CD8α-BV570 (53-6.7), TCRγδ-BV605 (GL3), NK1.1-BV650 (PK136), CD44-BV785 (IM7), CD45.1-BV605 (A20), CD4-BV711 (RM4-5), CD8b.2-APC (53-5.8) (all BioLegend); TCRβ-PerCPCy5.5 (104) (Cambridge Bioscience); CD44-APCef780 (IM7) (eBioscience); and CD3-APCef780 (2C11), CD3-biotin (145-2C11), CD69-PeCy7 (H1.2F3), CD45.2-AF700 (104), nearIR live/dead, blue live/dead, yellow live/dead (all Thermo Fisher). Cells were fixed for 20 min with IC fix (Invitrogen) and washed twice in FACS buffer (PBS + 0.1% BSA). Flow cytometric analysis was performed on either a Cytek Aurora spectral flow cytometer or a conventional BD LSR-Fortessa and analysed using FlowJo software (Treestar).</p></sec><sec id="s4-4"><title>Cell count calculations</title><p>Cell numbers in LN were calculated by dividing the event count in a target population by the event count of live cells, multiplied by the total live cells in LN prep determined by CASY counter. Sizes of LP and skin populations were calculated using AccuCount (Spherotech) counting beads that were spiked into the sample prior to acquisition, as per the manufacturer’s instructions.</p></sec><sec id="s4-5"><title>Mathematical modelling and statistical analysis</title><p>We fitted simultaneously the mathematical model illustrated in <xref ref-type="fig" rid="fig1">Figure 1B</xref> and described in Appendix 1 sections ‘The kinetics of mTom expression derived from Cd4-FR mice’ and ‘Modelling the label trajectories derived from Ki67-DIVN mice’, to the timecourses of frequencies of YFP<sup>+</sup>, Ki67<sup>high</sup> in YFP<sup>+</sup>, Ki67<sup>high</sup> in YFP<sup>−</sup>, and mTom<sup>+</sup> cells in the target populations; and empirical descriptor functions describing the trajectories of the frequencies of YFP<sup>+</sup> and mTom<sup>+</sup> cells within precursor populations (all data shown in <xref ref-type="fig" rid="fig2">Figure 2C</xref>). We used a Bayesian estimation approach using Python and Stan (<xref ref-type="bibr" rid="bib31">Stan Development Team, 2024</xref>) to perform these model fits. Code and data used to perform model fitting, details of the prior distributions for parameters, and figure generation notebooks are available at <ext-link ext-link-type="uri" xlink:href="https://github.com/elisebullock/CD4TRM">https://github.com/elisebullock/CD4TRM</ext-link>; copy archived at <xref ref-type="bibr" rid="bib8">Bullock, 2025</xref>. Models were ranked based on the information criteria estimated using the Leave-One-Out (LOO) cross validation method (<xref ref-type="bibr" rid="bib39">Vehtari et al., 2017</xref>). See Appendix 1 for full details.</p></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-group><fn-group content-type="author-contribution"><title>Author contributions</title><fn fn-type="con" id="con1"><p>Data curation, Formal analysis, Investigation, Methodology</p></fn><fn fn-type="con" id="con2"><p>Data curation, Software, Formal analysis, Investigation, Methodology</p></fn><fn fn-type="con" id="con3"><p>Software, Formal analysis, Investigation</p></fn><fn fn-type="con" id="con4"><p>Investigation, Methodology</p></fn><fn fn-type="con" id="con5"><p>Software, Investigation, Methodology</p></fn><fn fn-type="con" id="con6"><p>Conceptualization, Supervision, Funding acquisition, Investigation, Methodology, Project administration, Writing – review and editing</p></fn><fn fn-type="con" id="con7"><p>Conceptualization, Formal analysis, Supervision, Funding acquisition, Investigation, Methodology, 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>All mice were bred in the Comparative Biology Unit of the Royal Free UCL campus and at Charles River laboratories, Manston, UK. Animal experiments were performed according to institutional guidelines and Home Office regulations under project licence PP2330953.</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-104278-mdarchecklist1-v1.pdf" mimetype="application" mime-subtype="pdf"/></supplementary-material></sec><sec sec-type="data-availability" id="s7"><title>Data availability</title><p>Code and data used to perform model fitting, details of the prior distributions for parameters, and figure generation notebooks are available at <ext-link ext-link-type="uri" xlink:href="https://github.com/elisebullock/CD4TRM">https://github.com/elisebullock/CD4TRM</ext-link>, copy archived at <xref ref-type="bibr" rid="bib8">Bullock, 2025</xref>.</p></sec><ack id="ack"><title>Acknowledgements</title><p>This work was supported by the National Institutes of Health (R01 AI093870 and U01 AI150680) and the Medical Research Council (MR/P011225/1).</p></ack><ref-list><title>References</title><ref id="bib1"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Anderson</surname><given-names>KG</given-names></name><name><surname>Mayer-Barber</surname><given-names>K</given-names></name><name><surname>Sung</surname><given-names>H</given-names></name><name><surname>Beura</surname><given-names>L</given-names></name><name><surname>James</surname><given-names>BR</given-names></name><name><surname>Taylor</surname><given-names>JJ</given-names></name><name><surname>Qunaj</surname><given-names>L</given-names></name><name><surname>Griffith</surname><given-names>TS</given-names></name><name><surname>Vezys</surname><given-names>V</given-names></name><name><surname>Barber</surname><given-names>DL</given-names></name><name><surname>Masopust</surname><given-names>D</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>Intravascular staining for discrimination of vascular and tissue leukocytes</article-title><source>Nature Protocols</source><volume>9</volume><fpage>209</fpage><lpage>222</lpage><pub-id pub-id-type="doi">10.1038/nprot.2014.005</pub-id><pub-id pub-id-type="pmid">24385150</pub-id></element-citation></ref><ref id="bib2"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bains</surname><given-names>I</given-names></name><name><surname>Thiébaut</surname><given-names>R</given-names></name><name><surname>Yates</surname><given-names>AJ</given-names></name><name><surname>Callard</surname><given-names>R</given-names></name></person-group><year iso-8601-date="2009">2009</year><article-title>Quantifying thymic export: combining models of naive T Cell Proliferation and TCR excision circle dynamics gives an explicit measure of thymic output</article-title><source>The Journal of Immunology</source><volume>183</volume><fpage>4329</fpage><lpage>4336</lpage><pub-id pub-id-type="doi">10.4049/jimmunol.0900743</pub-id></element-citation></ref><ref id="bib3"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Baliu-Piqué</surname><given-names>M</given-names></name><name><surname>Verheij</surname><given-names>MW</given-names></name><name><surname>Drylewicz</surname><given-names>J</given-names></name><name><surname>Ravesloot</surname><given-names>L</given-names></name><name><surname>de Boer</surname><given-names>RJ</given-names></name><name><surname>Koets</surname><given-names>A</given-names></name><name><surname>Tesselaar</surname><given-names>K</given-names></name><name><surname>Borghans</surname><given-names>JAM</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Short lifespans of memory T-cells in bone marrow, blood, and lymph nodes suggest that T-cell memory is maintained by continuous self-renewal of recirculating cells</article-title><source>Frontiers in Immunology</source><volume>9</volume><elocation-id>2054</elocation-id><pub-id pub-id-type="doi">10.3389/fimmu.2018.02054</pub-id></element-citation></ref><ref id="bib4"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Baliu-Piqué</surname><given-names>M</given-names></name><name><surname>Otto</surname><given-names>SA</given-names></name><name><surname>Borghans</surname><given-names>JAM</given-names></name><name><surname>Tesselaar</surname><given-names>K</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>In vivo deuterium labelling in mice supports a dynamic model for memory T-cell maintenance in the bone marrow</article-title><source>Immunology Letters</source><volume>210</volume><fpage>29</fpage><lpage>32</lpage><pub-id pub-id-type="doi">10.1016/j.imlet.2019.04.004</pub-id></element-citation></ref><ref id="bib5"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bartolomé-Casado</surname><given-names>R</given-names></name><name><surname>Landsverk</surname><given-names>OJB</given-names></name><name><surname>Chauhan</surname><given-names>SK</given-names></name><name><surname>Richter</surname><given-names>L</given-names></name><name><surname>Phung</surname><given-names>D</given-names></name><name><surname>Greiff</surname><given-names>V</given-names></name><name><surname>Risnes</surname><given-names>LF</given-names></name><name><surname>Yao</surname><given-names>Y</given-names></name><name><surname>Neumann</surname><given-names>RS</given-names></name><name><surname>Yaqub</surname><given-names>S</given-names></name><name><surname>Øyen</surname><given-names>O</given-names></name><name><surname>Horneland</surname><given-names>R</given-names></name><name><surname>Aandahl</surname><given-names>EM</given-names></name><name><surname>Paulsen</surname><given-names>V</given-names></name><name><surname>Sollid</surname><given-names>LM</given-names></name><name><surname>Qiao</surname><given-names>S-W</given-names></name><name><surname>Baekkevold</surname><given-names>ES</given-names></name><name><surname>Jahnsen</surname><given-names>FL</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Resident memory CD8 T cells persist for years in human small intestine</article-title><source>Journal of Experimental Medicine</source><volume>216</volume><fpage>2412</fpage><lpage>2426</lpage><pub-id pub-id-type="doi">10.1084/jem.20190414</pub-id></element-citation></ref><ref id="bib6"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bartolomé-Casado</surname><given-names>R</given-names></name><name><surname>Landsverk</surname><given-names>OJB</given-names></name><name><surname>Chauhan</surname><given-names>SK</given-names></name><name><surname>Sætre</surname><given-names>F</given-names></name><name><surname>Hagen</surname><given-names>KT</given-names></name><name><surname>Yaqub</surname><given-names>S</given-names></name><name><surname>Øyen</surname><given-names>O</given-names></name><name><surname>Horneland</surname><given-names>R</given-names></name><name><surname>Aandahl</surname><given-names>EM</given-names></name><name><surname>Aabakken</surname><given-names>L</given-names></name><name><surname>Bækkevold</surname><given-names>ES</given-names></name><name><surname>Jahnsen</surname><given-names>FL</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>CD4+ T cells persist for years in the human small intestine and display a TH1 cytokine profile</article-title><source>Mucosal Immunology</source><volume>14</volume><fpage>402</fpage><lpage>410</lpage><pub-id pub-id-type="doi">10.1038/s41385-020-0315-5</pub-id></element-citation></ref><ref id="bib7"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bullock</surname><given-names>ME</given-names></name><name><surname>Hogan</surname><given-names>T</given-names></name><name><surname>Williams</surname><given-names>C</given-names></name><name><surname>Morris</surname><given-names>S</given-names></name><name><surname>Nowicka</surname><given-names>M</given-names></name><name><surname>Sharjeel</surname><given-names>M</given-names></name><name><surname>van Dorp</surname><given-names>C</given-names></name><name><surname>Yates</surname><given-names>AJ</given-names></name><name><surname>Seddon</surname><given-names>B</given-names></name></person-group><year iso-8601-date="2024">2024</year><article-title>The dynamics and longevity of circulating CD4+ memory T cells depend on cell age and not the chronological age of the host</article-title><source>PLOS Biology</source><volume>22</volume><elocation-id>e3002380</elocation-id><pub-id pub-id-type="doi">10.1371/journal.pbio.3002380</pub-id><pub-id pub-id-type="pmid">39137219</pub-id></element-citation></ref><ref id="bib8"><element-citation publication-type="software"><person-group person-group-type="author"><name><surname>Bullock</surname><given-names>ME</given-names></name></person-group><year iso-8601-date="2025">2025</year><data-title>CD4TRM</data-title><version designator="swh:1:rev:1b8382b7130843e93bc55f0b58410d46d0f97ddd">swh:1:rev:1b8382b7130843e93bc55f0b58410d46d0f97ddd</version><source>Software Heritage</source><ext-link ext-link-type="uri" xlink:href="https://archive.softwareheritage.org/swh:1:dir:0a1475ac1473130893f0c42e005c7d874d390d3c;origin=https://github.com/elisebullock/CD4TRM;visit=swh:1:snp:32f06e638011af0a16b16f7890a6297b40bed991;anchor=swh:1:rev:1b8382b7130843e93bc55f0b58410d46d0f97ddd">https://archive.softwareheritage.org/swh:1:dir:0a1475ac1473130893f0c42e005c7d874d390d3c;origin=https://github.com/elisebullock/CD4TRM;visit=swh:1:snp:32f06e638011af0a16b16f7890a6297b40bed991;anchor=swh:1:rev:1b8382b7130843e93bc55f0b58410d46d0f97ddd</ext-link></element-citation></ref><ref id="bib9"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Choo</surname><given-names>DK</given-names></name><name><surname>Murali-Krishna</surname><given-names>K</given-names></name><name><surname>Anita</surname><given-names>R</given-names></name><name><surname>Ahmed</surname><given-names>R</given-names></name></person-group><year iso-8601-date="2010">2010</year><article-title>Homeostatic turnover of virus-specific memory CD8 T cells occurs stochastically and is independent of CD4 T cell help</article-title><source>Journal of Immunology</source><volume>185</volume><fpage>3436</fpage><lpage>3444</lpage><pub-id pub-id-type="doi">10.4049/jimmunol.1001421</pub-id><pub-id pub-id-type="pmid">20733203</pub-id></element-citation></ref><ref id="bib10"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Christo</surname><given-names>SN</given-names></name><name><surname>Evrard</surname><given-names>M</given-names></name><name><surname>Park</surname><given-names>SL</given-names></name><name><surname>Gandolfo</surname><given-names>LC</given-names></name><name><surname>Burn</surname><given-names>TN</given-names></name><name><surname>Fonseca</surname><given-names>R</given-names></name><name><surname>Newman</surname><given-names>DM</given-names></name><name><surname>Alexandre</surname><given-names>YO</given-names></name><name><surname>Collins</surname><given-names>N</given-names></name><name><surname>Zamudio</surname><given-names>NM</given-names></name><name><surname>Souza-Fonseca-Guimaraes</surname><given-names>F</given-names></name><name><surname>Pellicci</surname><given-names>DG</given-names></name><name><surname>Chisanga</surname><given-names>D</given-names></name><name><surname>Shi</surname><given-names>W</given-names></name><name><surname>Bartholin</surname><given-names>L</given-names></name><name><surname>Belz</surname><given-names>GT</given-names></name><name><surname>Huntington</surname><given-names>ND</given-names></name><name><surname>Lucas</surname><given-names>A</given-names></name><name><surname>Lucas</surname><given-names>M</given-names></name><name><surname>Mueller</surname><given-names>SN</given-names></name><name><surname>Heath</surname><given-names>WR</given-names></name><name><surname>Ginhoux</surname><given-names>F</given-names></name><name><surname>Speed</surname><given-names>TP</given-names></name><name><surname>Carbone</surname><given-names>FR</given-names></name><name><surname>Kallies</surname><given-names>A</given-names></name><name><surname>Mackay</surname><given-names>LK</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Discrete tissue microenvironments instruct diversity in resident memory T cell function and plasticity</article-title><source>Nature Immunology</source><volume>22</volume><fpage>1140</fpage><lpage>1151</lpage><pub-id pub-id-type="doi">10.1038/s41590-021-01004-1</pub-id></element-citation></ref><ref id="bib11"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Costa Del Amo</surname><given-names>P</given-names></name><name><surname>Lahoz-Beneytez</surname><given-names>J</given-names></name><name><surname>Boelen</surname><given-names>L</given-names></name><name><surname>Ahmed</surname><given-names>R</given-names></name><name><surname>Miners</surname><given-names>KL</given-names></name><name><surname>Zhang</surname><given-names>Y</given-names></name><name><surname>Roger</surname><given-names>L</given-names></name><name><surname>Jones</surname><given-names>RE</given-names></name><name><surname>Marraco</surname><given-names>SAF</given-names></name><name><surname>Speiser</surname><given-names>DE</given-names></name><name><surname>Baird</surname><given-names>DM</given-names></name><name><surname>Price</surname><given-names>DA</given-names></name><name><surname>Ladell</surname><given-names>K</given-names></name><name><surname>Macallan</surname><given-names>D</given-names></name><name><surname>Asquith</surname><given-names>B</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Human TSCM cell dynamics in vivo are compatible with long-lived immunological memory and stemness</article-title><source>PLOS Biology</source><volume>16</volume><elocation-id>e2005523</elocation-id><pub-id pub-id-type="doi">10.1371/journal.pbio.2005523</pub-id><pub-id pub-id-type="pmid">29933397</pub-id></element-citation></ref><ref id="bib12"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>De Boer</surname><given-names>RJ</given-names></name><name><surname>Perelson</surname><given-names>AS</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>Quantifying T lymphocyte turnover</article-title><source>Journal of Theoretical Biology</source><volume>327</volume><fpage>45</fpage><lpage>87</lpage><pub-id pub-id-type="doi">10.1016/j.jtbi.2012.12.025</pub-id><pub-id pub-id-type="pmid">23313150</pub-id></element-citation></ref><ref id="bib13"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>De Boer</surname><given-names>RJ</given-names></name><name><surname>Yates</surname><given-names>AJ</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Modeling T cell fate</article-title><source>Annual Review of Immunology</source><volume>41</volume><fpage>513</fpage><lpage>532</lpage><pub-id pub-id-type="doi">10.1146/annurev-immunol-101721-040924</pub-id><pub-id pub-id-type="pmid">37126420</pub-id></element-citation></ref><ref id="bib14"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>den Braber</surname><given-names>I</given-names></name><name><surname>Mugwagwa</surname><given-names>T</given-names></name><name><surname>Vrisekoop</surname><given-names>N</given-names></name><name><surname>Westera</surname><given-names>L</given-names></name><name><surname>Mögling</surname><given-names>R</given-names></name><name><surname>de Boer</surname><given-names>AB</given-names></name><name><surname>Willems</surname><given-names>N</given-names></name><name><surname>Schrijver</surname><given-names>EHR</given-names></name><name><surname>Spierenburg</surname><given-names>G</given-names></name><name><surname>Gaiser</surname><given-names>K</given-names></name><name><surname>Mul</surname><given-names>E</given-names></name><name><surname>Otto</surname><given-names>SA</given-names></name><name><surname>Ruiter</surname><given-names>AFC</given-names></name><name><surname>Ackermans</surname><given-names>MT</given-names></name><name><surname>Miedema</surname><given-names>F</given-names></name><name><surname>Borghans</surname><given-names>JAM</given-names></name><name><surname>de Boer</surname><given-names>RJ</given-names></name><name><surname>Tesselaar</surname><given-names>K</given-names></name></person-group><year iso-8601-date="2012">2012</year><article-title>Maintenance of peripheral naive T cells is sustained by thymus output in mice but not humans</article-title><source>Immunity</source><volume>36</volume><fpage>288</fpage><lpage>297</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2012.02.006</pub-id><pub-id pub-id-type="pmid">22365666</pub-id></element-citation></ref><ref id="bib15"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Divito</surname><given-names>SJ</given-names></name><name><surname>Aasebø</surname><given-names>AT</given-names></name><name><surname>Matos</surname><given-names>TR</given-names></name><name><surname>Hsieh</surname><given-names>P-C</given-names></name><name><surname>Collin</surname><given-names>M</given-names></name><name><surname>Elco</surname><given-names>CP</given-names></name><name><surname>O’Malley</surname><given-names>JT</given-names></name><name><surname>Bækkevold</surname><given-names>ES</given-names></name><name><surname>Reims</surname><given-names>H</given-names></name><name><surname>Gedde-Dahl</surname><given-names>T</given-names></name><name><surname>Hagerstrom</surname><given-names>M</given-names></name><name><surname>Hilaire</surname><given-names>J</given-names></name><name><surname>Lian</surname><given-names>JW</given-names></name><name><surname>Milford</surname><given-names>EL</given-names></name><name><surname>Pinkus</surname><given-names>GS</given-names></name><name><surname>Ho</surname><given-names>VT</given-names></name><name><surname>Soiffer</surname><given-names>RJ</given-names></name><name><surname>Kim</surname><given-names>HT</given-names></name><name><surname>Mihm</surname><given-names>MC</given-names></name><name><surname>Ritz</surname><given-names>J</given-names></name><name><surname>Guleria</surname><given-names>I</given-names></name><name><surname>Cutler</surname><given-names>CS</given-names></name><name><surname>Clark</surname><given-names>RA</given-names></name><name><surname>Jahnsen</surname><given-names>FL</given-names></name><name><surname>Kupper</surname><given-names>TS</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Peripheral host T cells survive hematopoietic stem cell transplantation and promote graft-versus-host disease</article-title><source>The Journal of Clinical Investigation</source><volume>130</volume><fpage>4624</fpage><lpage>4636</lpage><pub-id pub-id-type="doi">10.1172/JCI129965</pub-id><pub-id pub-id-type="pmid">32516138</pub-id></element-citation></ref><ref id="bib16"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ely</surname><given-names>KH</given-names></name><name><surname>Cookenham</surname><given-names>T</given-names></name><name><surname>Roberts</surname><given-names>AD</given-names></name><name><surname>Woodland</surname><given-names>DL</given-names></name></person-group><year iso-8601-date="2006">2006</year><article-title>Memory T cell populations in the lung airways are maintained by continual recruitment</article-title><source>Journal of Immunology</source><volume>176</volume><fpage>537</fpage><lpage>543</lpage><pub-id pub-id-type="doi">10.4049/jimmunol.176.1.537</pub-id><pub-id pub-id-type="pmid">16365448</pub-id></element-citation></ref><ref id="bib17"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gaide</surname><given-names>O</given-names></name><name><surname>Emerson</surname><given-names>RO</given-names></name><name><surname>Jiang</surname><given-names>X</given-names></name><name><surname>Gulati</surname><given-names>N</given-names></name><name><surname>Nizza</surname><given-names>S</given-names></name><name><surname>Desmarais</surname><given-names>C</given-names></name><name><surname>Robins</surname><given-names>H</given-names></name><name><surname>Krueger</surname><given-names>JG</given-names></name><name><surname>Clark</surname><given-names>RA</given-names></name><name><surname>Kupper</surname><given-names>TS</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Common clonal origin of central and resident memory T cells following skin immunization</article-title><source>Nature Medicine</source><volume>21</volume><fpage>647</fpage><lpage>653</lpage><pub-id pub-id-type="doi">10.1038/nm.3860</pub-id><pub-id pub-id-type="pmid">25962122</pub-id></element-citation></ref><ref id="bib18"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ganusov</surname><given-names>VV</given-names></name><name><surname>De Boer</surname><given-names>RJ</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>A mechanistic model for bromodeoxyuridine dilution naturally explains labelling data of self-renewing T cell populations</article-title><source>Journal of the Royal Society, Interface</source><volume>10</volume><elocation-id>20120617</elocation-id><pub-id pub-id-type="doi">10.1098/rsif.2012.0617</pub-id><pub-id pub-id-type="pmid">23034350</pub-id></element-citation></ref><ref id="bib19"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gebhardt</surname><given-names>T</given-names></name><name><surname>Wakim</surname><given-names>LM</given-names></name><name><surname>Eidsmo</surname><given-names>L</given-names></name><name><surname>Reading</surname><given-names>PC</given-names></name><name><surname>Heath</surname><given-names>WR</given-names></name><name><surname>Carbone</surname><given-names>FR</given-names></name></person-group><year iso-8601-date="2009">2009</year><article-title>Memory T cells in nonlymphoid tissue that provide enhanced local immunity during infection with herpes simplex virus</article-title><source>Nature Immunology</source><volume>10</volume><fpage>524</fpage><lpage>530</lpage><pub-id pub-id-type="doi">10.1038/ni.1718</pub-id></element-citation></ref><ref id="bib20"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gossel</surname><given-names>G</given-names></name><name><surname>Hogan</surname><given-names>T</given-names></name><name><surname>Cownden</surname><given-names>D</given-names></name><name><surname>Seddon</surname><given-names>B</given-names></name><name><surname>Yates</surname><given-names>AJ</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Memory CD4 T cell subsets are kinetically heterogeneous and replenished from naive T cells at high levels</article-title><source>eLife</source><volume>6</volume><elocation-id>e23013</elocation-id><pub-id pub-id-type="doi">10.7554/eLife.23013</pub-id><pub-id pub-id-type="pmid">28282024</pub-id></element-citation></ref><ref id="bib21"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hogan</surname><given-names>T</given-names></name><name><surname>Gossel</surname><given-names>G</given-names></name><name><surname>Yates</surname><given-names>AJ</given-names></name><name><surname>Seddon</surname><given-names>B</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Temporal fate mapping reveals age-linked heterogeneity in naive T lymphocytes in mice</article-title><source>PNAS</source><volume>112</volume><fpage>E6917</fpage><lpage>E6926</lpage><pub-id pub-id-type="doi">10.1073/pnas.1517246112</pub-id><pub-id pub-id-type="pmid">26607449</pub-id></element-citation></ref><ref id="bib22"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hogan</surname><given-names>T</given-names></name><name><surname>Nowicka</surname><given-names>M</given-names></name><name><surname>Cownden</surname><given-names>D</given-names></name><name><surname>Pearson</surname><given-names>CF</given-names></name><name><surname>Yates</surname><given-names>AJ</given-names></name><name><surname>Seddon</surname><given-names>B</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Differential impact of self and environmental antigens on the ontogeny and maintenance of CD4<sup>+</sup> T cell memory</article-title><source>eLife</source><volume>8</volume><elocation-id>e48901</elocation-id><pub-id pub-id-type="doi">10.7554/eLife.48901</pub-id><pub-id pub-id-type="pmid">31742553</pub-id></element-citation></ref><ref id="bib23"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Jiang</surname><given-names>X</given-names></name><name><surname>Clark</surname><given-names>RA</given-names></name><name><surname>Liu</surname><given-names>L</given-names></name><name><surname>Wagers</surname><given-names>AJ</given-names></name><name><surname>Fuhlbrigge</surname><given-names>RC</given-names></name><name><surname>Kupper</surname><given-names>TS</given-names></name></person-group><year iso-8601-date="2012">2012</year><article-title>Skin infection generates non-migratory memory CD8+ T(RM) cells providing global skin immunity</article-title><source>Nature</source><volume>483</volume><fpage>227</fpage><lpage>231</lpage><pub-id pub-id-type="doi">10.1038/nature10851</pub-id><pub-id pub-id-type="pmid">22388819</pub-id></element-citation></ref><ref id="bib24"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lukas</surname><given-names>E</given-names></name><name><surname>Hogan</surname><given-names>T</given-names></name><name><surname>Williams</surname><given-names>C</given-names></name><name><surname>Seddon</surname><given-names>B</given-names></name><name><surname>Yates</surname><given-names>AJ</given-names></name></person-group><year iso-8601-date="2023">2023</year><article-title>Quantifying cellular dynamics in mice using a novel fluorescent division reporter system</article-title><source>Frontiers in Immunology</source><volume>14</volume><elocation-id>1157705</elocation-id><pub-id pub-id-type="doi">10.3389/fimmu.2023.1157705</pub-id><pub-id pub-id-type="pmid">37575229</pub-id></element-citation></ref><ref id="bib25"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>MacDonald</surname><given-names>N</given-names></name></person-group><year iso-8601-date="1978">1978</year><source>Time Lags in Biological Models</source><publisher-loc>Berlin</publisher-loc><publisher-name>Springer</publisher-name><pub-id pub-id-type="doi">10.1007/978-3-642-93107-9</pub-id></element-citation></ref><ref id="bib26"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Matos</surname><given-names>TR</given-names></name><name><surname>Gehad</surname><given-names>A</given-names></name><name><surname>Teague</surname><given-names>JE</given-names></name><name><surname>Dyring-Andersen</surname><given-names>B</given-names></name><name><surname>Benezeder</surname><given-names>T</given-names></name><name><surname>Dowlatshahi</surname><given-names>M</given-names></name><name><surname>Crouch</surname><given-names>J</given-names></name><name><surname>Watanabe</surname><given-names>Y</given-names></name><name><surname>O’Malley</surname><given-names>JT</given-names></name><name><surname>Kupper</surname><given-names>TS</given-names></name><name><surname>Yang</surname><given-names>C</given-names></name><name><surname>Watanabe</surname><given-names>R</given-names></name><name><surname>Clark</surname><given-names>RA</given-names></name></person-group><year iso-8601-date="2022">2022</year><article-title>Central memory T cells are the most effective precursors of resident memory T cells in human skin</article-title><source>Science Immunology</source><volume>7</volume><elocation-id>eabn1889</elocation-id><pub-id pub-id-type="doi">10.1126/sciimmunol.abn1889</pub-id><pub-id pub-id-type="pmid">35452256</pub-id></element-citation></ref><ref id="bib27"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Miller</surname><given-names>I</given-names></name><name><surname>Min</surname><given-names>M</given-names></name><name><surname>Yang</surname><given-names>C</given-names></name><name><surname>Tian</surname><given-names>C</given-names></name><name><surname>Gookin</surname><given-names>S</given-names></name><name><surname>Carter</surname><given-names>D</given-names></name><name><surname>Spencer</surname><given-names>SL</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Ki67 is a graded rather than a binary marker of proliferation versus quiescence</article-title><source>Cell Reports</source><volume>24</volume><fpage>1105</fpage><lpage>1112</lpage><pub-id pub-id-type="doi">10.1016/j.celrep.2018.06.110</pub-id><pub-id pub-id-type="pmid">30067968</pub-id></element-citation></ref><ref id="bib28"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Morris</surname><given-names>SE</given-names></name><name><surname>Farber</surname><given-names>DL</given-names></name><name><surname>Yates</surname><given-names>AJ</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Tissue-resident memory T Cells in mice and humans: towards a quantitative ecology</article-title><source>Journal of Immunology</source><volume>203</volume><fpage>2561</fpage><lpage>2569</lpage><pub-id pub-id-type="doi">10.4049/jimmunol.1900767</pub-id><pub-id pub-id-type="pmid">31685700</pub-id></element-citation></ref><ref id="bib29"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Park</surname><given-names>SL</given-names></name><name><surname>Zaid</surname><given-names>A</given-names></name><name><surname>Hor</surname><given-names>JL</given-names></name><name><surname>Christo</surname><given-names>SN</given-names></name><name><surname>Prier</surname><given-names>JE</given-names></name><name><surname>Davies</surname><given-names>B</given-names></name><name><surname>Alexandre</surname><given-names>YO</given-names></name><name><surname>Gregory</surname><given-names>JL</given-names></name><name><surname>Russell</surname><given-names>TA</given-names></name><name><surname>Gebhardt</surname><given-names>T</given-names></name><name><surname>Carbone</surname><given-names>FR</given-names></name><name><surname>Tscharke</surname><given-names>DC</given-names></name><name><surname>Heath</surname><given-names>WR</given-names></name><name><surname>Mueller</surname><given-names>SN</given-names></name><name><surname>Mackay</surname><given-names>LK</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Local proliferation maintains a stable pool of tissue-resident memory T cells after antiviral recall responses</article-title><source>Nature Immunology</source><volume>19</volume><fpage>183</fpage><lpage>191</lpage><pub-id pub-id-type="doi">10.1038/s41590-017-0027-5</pub-id></element-citation></ref><ref id="bib30"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Slütter</surname><given-names>B</given-names></name><name><surname>Van Braeckel-Budimir</surname><given-names>N</given-names></name><name><surname>Abboud</surname><given-names>G</given-names></name><name><surname>Varga</surname><given-names>SM</given-names></name><name><surname>Salek-Ardakani</surname><given-names>S</given-names></name><name><surname>Harty</surname><given-names>JT</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Dynamics of influenza-induced lung-resident memory T cells underlie waning heterosubtypic immunity</article-title><source>Science Immunology</source><volume>2</volume><elocation-id>eaag2031</elocation-id><pub-id pub-id-type="doi">10.1126/sciimmunol.aag2031</pub-id><pub-id pub-id-type="pmid">28783666</pub-id></element-citation></ref><ref id="bib31"><element-citation publication-type="software"><person-group person-group-type="author"><collab>Stan Development Team</collab></person-group><year iso-8601-date="2024">2024</year><data-title>Stan modeling language users guide and reference manual</data-title><version designator="2.34">2.34</version><source>Github</source><ext-link ext-link-type="uri" xlink:href="https://github.com/stan-dev/docs">https://github.com/stan-dev/docs</ext-link></element-citation></ref><ref id="bib32"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Strobl</surname><given-names>J</given-names></name><name><surname>Pandey</surname><given-names>RV</given-names></name><name><surname>Krausgruber</surname><given-names>T</given-names></name><name><surname>Bayer</surname><given-names>N</given-names></name><name><surname>Kleissl</surname><given-names>L</given-names></name><name><surname>Reininger</surname><given-names>B</given-names></name><name><surname>Vieyra-Garcia</surname><given-names>P</given-names></name><name><surname>Wolf</surname><given-names>P</given-names></name><name><surname>Jentus</surname><given-names>M-M</given-names></name><name><surname>Mitterbauer</surname><given-names>M</given-names></name><name><surname>Wohlfarth</surname><given-names>P</given-names></name><name><surname>Rabitsch</surname><given-names>W</given-names></name><name><surname>Stingl</surname><given-names>G</given-names></name><name><surname>Bock</surname><given-names>C</given-names></name><name><surname>Stary</surname><given-names>G</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Long-term skin-resident memory T cells proliferate in situ and are involved in human graft-versus-host disease</article-title><source>Science Translational Medicine</source><volume>12</volume><elocation-id>eabb7028</elocation-id><pub-id pub-id-type="doi">10.1126/scitranslmed.abb7028</pub-id><pub-id pub-id-type="pmid">33208504</pub-id></element-citation></ref><ref id="bib33"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Szabo</surname><given-names>PA</given-names></name><name><surname>Miron</surname><given-names>M</given-names></name><name><surname>Farber</surname><given-names>DL</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Location, location, location: Tissue resident memory T cells in mice and humans</article-title><source>Science Immunology</source><volume>4</volume><elocation-id>34</elocation-id><pub-id pub-id-type="doi">10.1126/sciimmunol.aas9673</pub-id></element-citation></ref><ref id="bib34"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Takamura</surname><given-names>S</given-names></name><name><surname>Yagi</surname><given-names>H</given-names></name><name><surname>Hakata</surname><given-names>Y</given-names></name><name><surname>Motozono</surname><given-names>C</given-names></name><name><surname>McMaster</surname><given-names>SR</given-names></name><name><surname>Masumoto</surname><given-names>T</given-names></name><name><surname>Fujisawa</surname><given-names>M</given-names></name><name><surname>Chikaishi</surname><given-names>T</given-names></name><name><surname>Komeda</surname><given-names>J</given-names></name><name><surname>Itoh</surname><given-names>J</given-names></name><name><surname>Umemura</surname><given-names>M</given-names></name><name><surname>Kyusai</surname><given-names>A</given-names></name><name><surname>Tomura</surname><given-names>M</given-names></name><name><surname>Nakayama</surname><given-names>T</given-names></name><name><surname>Woodland</surname><given-names>DL</given-names></name><name><surname>Kohlmeier</surname><given-names>JE</given-names></name><name><surname>Miyazawa</surname><given-names>M</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Specific niches for lung-resident memory CD8+ T cells at the site of tissue regeneration enable CD69-independent maintenance</article-title><source>Journal of Experimental Medicine</source><volume>213</volume><fpage>3057</fpage><lpage>3073</lpage><pub-id pub-id-type="doi">10.1084/jem.20160938</pub-id></element-citation></ref><ref id="bib35"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Takamura</surname><given-names>S</given-names></name><name><surname>Kohlmeier</surname><given-names>JE</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Establishment and maintenance of conventional and circulation-driven lung-resident memory CD8+ T cells following respiratory virus infections</article-title><source>Frontiers in Immunology</source><volume>10</volume><elocation-id>733</elocation-id><pub-id pub-id-type="doi">10.3389/fimmu.2019.00733</pub-id></element-citation></ref><ref id="bib36"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Van Braeckel-Budimir</surname><given-names>N</given-names></name><name><surname>Varga</surname><given-names>SM</given-names></name><name><surname>Badovinac</surname><given-names>VP</given-names></name><name><surname>Harty</surname><given-names>JT</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Repeated antigen exposure extends the durability of influenza-specific lung-resident memory CD8<sup>+</sup> T cells and heterosubtypic immunity</article-title><source>Cell Reports</source><volume>24</volume><fpage>3374</fpage><lpage>3382</lpage><pub-id pub-id-type="doi">10.1016/j.celrep.2018.08.073</pub-id><pub-id pub-id-type="pmid">30257199</pub-id></element-citation></ref><ref id="bib37"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>van den Berg</surname><given-names>SPH</given-names></name><name><surname>Derksen</surname><given-names>LY</given-names></name><name><surname>Drylewicz</surname><given-names>J</given-names></name><name><surname>Nanlohy</surname><given-names>NM</given-names></name><name><surname>Beckers</surname><given-names>L</given-names></name><name><surname>Lanfermeijer</surname><given-names>J</given-names></name><name><surname>Gessel</surname><given-names>SN</given-names></name><name><surname>Vos</surname><given-names>M</given-names></name><name><surname>Otto</surname><given-names>SA</given-names></name><name><surname>de Boer</surname><given-names>RJ</given-names></name><name><surname>Tesselaar</surname><given-names>K</given-names></name><name><surname>Borghans</surname><given-names>JAM</given-names></name><name><surname>van Baarle</surname><given-names>D</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Quantification of T-cell dynamics during latent cytomegalovirus infection in humans</article-title><source>PLOS Pathogens</source><volume>17</volume><elocation-id>e1010152</elocation-id><pub-id pub-id-type="doi">10.1371/journal.ppat.1010152</pub-id><pub-id pub-id-type="pmid">34914799</pub-id></element-citation></ref><ref id="bib38"><element-citation publication-type="preprint"><person-group person-group-type="author"><name><surname>van Dorp</surname><given-names>CH</given-names></name><name><surname>Gray</surname><given-names>JI</given-names></name><name><surname>Paik</surname><given-names>DH</given-names></name><name><surname>Farber</surname><given-names>DL</given-names></name><name><surname>Yates</surname><given-names>AJ</given-names></name></person-group><year iso-8601-date="2025">2025</year><article-title>A variational deep-learning approach to modeling memory T cell dynamics</article-title><source>bioRxiv</source><pub-id pub-id-type="doi">10.1101/2024.07.08.602409</pub-id></element-citation></ref><ref id="bib39"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Vehtari</surname><given-names>A</given-names></name><name><surname>Gelman</surname><given-names>A</given-names></name><name><surname>Gabry</surname><given-names>J</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC</article-title><source>Statistics and Computing</source><volume>27</volume><fpage>1413</fpage><lpage>1432</lpage><pub-id pub-id-type="doi">10.1007/s11222-016-9696-4</pub-id></element-citation></ref><ref id="bib40"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Verheijen</surname><given-names>M</given-names></name><name><surname>Rane</surname><given-names>S</given-names></name><name><surname>Pearson</surname><given-names>C</given-names></name><name><surname>Yates</surname><given-names>AJ</given-names></name><name><surname>Seddon</surname><given-names>B</given-names></name></person-group><year iso-8601-date="2020">2020</year><article-title>Fate mapping quantifies the dynamics of b cell development and activation throughout life</article-title><source>Cell Reports</source><volume>33</volume><elocation-id>108376</elocation-id><pub-id pub-id-type="doi">10.1016/j.celrep.2020.108376</pub-id><pub-id pub-id-type="pmid">33207189</pub-id></element-citation></ref><ref id="bib41"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Virtanen</surname><given-names>P</given-names></name><name><surname>Gommers</surname><given-names>R</given-names></name><name><surname>Oliphant</surname><given-names>TE</given-names></name><name><surname>Haberland</surname><given-names>M</given-names></name><name><surname>Reddy</surname><given-names>T</given-names></name><name><surname>Cournapeau</surname><given-names>D</given-names></name><name><surname>Burovski</surname><given-names>E</given-names></name><name><surname>Peterson</surname><given-names>P</given-names></name><name><surname>Weckesser</surname><given-names>W</given-names></name><name><surname>Bright</surname><given-names>J</given-names></name><name><surname>van der Walt</surname><given-names>SJ</given-names></name><name><surname>Brett</surname><given-names>M</given-names></name><name><surname>Wilson</surname><given-names>J</given-names></name><name><surname>Millman</surname><given-names>KJ</given-names></name><name><surname>Mayorov</surname><given-names>N</given-names></name><name><surname>Nelson</surname><given-names>ARJ</given-names></name><name><surname>Jones</surname><given-names>E</given-names></name><name><surname>Kern</surname><given-names>R</given-names></name><name><surname>Larson</surname><given-names>E</given-names></name><name><surname>Carey</surname><given-names>CJ</given-names></name><name><surname>Polat</surname><given-names>İ</given-names></name><name><surname>Feng</surname><given-names>Y</given-names></name><name><surname>Moore</surname><given-names>EW</given-names></name><name><surname>VanderPlas</surname><given-names>J</given-names></name><name><surname>Laxalde</surname><given-names>D</given-names></name><name><surname>Perktold</surname><given-names>J</given-names></name><name><surname>Cimrman</surname><given-names>R</given-names></name><name><surname>Henriksen</surname><given-names>I</given-names></name><name><surname>Quintero</surname><given-names>EA</given-names></name><name><surname>Harris</surname><given-names>CR</given-names></name><name><surname>Archibald</surname><given-names>AM</given-names></name><name><surname>Ribeiro</surname><given-names>AH</given-names></name><name><surname>Pedregosa</surname><given-names>F</given-names></name><name><surname>van Mulbregt</surname><given-names>P</given-names></name><collab>SciPy 1.0 Contributors</collab></person-group><year iso-8601-date="2020">2020</year><article-title>SciPy 1.0: fundamental algorithms for scientific computing in Python</article-title><source>Nature Methods</source><volume>17</volume><fpage>261</fpage><lpage>272</lpage><pub-id pub-id-type="doi">10.1038/s41592-019-0686-2</pub-id><pub-id pub-id-type="pmid">32015543</pub-id></element-citation></ref><ref id="bib42"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Watanabe</surname><given-names>R</given-names></name><name><surname>Gehad</surname><given-names>A</given-names></name><name><surname>Yang</surname><given-names>C</given-names></name><name><surname>Scott</surname><given-names>LL</given-names></name><name><surname>Teague</surname><given-names>JE</given-names></name><name><surname>Schlapbach</surname><given-names>C</given-names></name><name><surname>Elco</surname><given-names>CP</given-names></name><name><surname>Huang</surname><given-names>V</given-names></name><name><surname>Matos</surname><given-names>TR</given-names></name><name><surname>Kupper</surname><given-names>TS</given-names></name><name><surname>Clark</surname><given-names>RA</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Human skin is protected by four functionally and phenotypically discrete populations of resident and recirculating memory T cells</article-title><source>Science Translational Medicine</source><volume>7</volume><elocation-id>279ra39</elocation-id><pub-id pub-id-type="doi">10.1126/scitranslmed.3010302</pub-id><pub-id pub-id-type="pmid">25787765</pub-id></element-citation></ref><ref id="bib43"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Westera</surname><given-names>L</given-names></name><name><surname>Drylewicz</surname><given-names>J</given-names></name><name><surname>den Braber</surname><given-names>I</given-names></name><name><surname>Mugwagwa</surname><given-names>T</given-names></name><name><surname>van der Maas</surname><given-names>I</given-names></name><name><surname>Kwast</surname><given-names>L</given-names></name><name><surname>Volman</surname><given-names>T</given-names></name><name><surname>van de Weg-Schrijver</surname><given-names>EHR</given-names></name><name><surname>Bartha</surname><given-names>I</given-names></name><name><surname>Spierenburg</surname><given-names>G</given-names></name><name><surname>Gaiser</surname><given-names>K</given-names></name><name><surname>Ackermans</surname><given-names>MT</given-names></name><name><surname>Asquith</surname><given-names>B</given-names></name><name><surname>de Boer</surname><given-names>RJ</given-names></name><name><surname>Tesselaar</surname><given-names>K</given-names></name><name><surname>Borghans</surname><given-names>JAM</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>Closing the gap between T-cell life span estimates from stable isotope-labeling studies in mice and humans</article-title><source>Blood</source><volume>122</volume><fpage>2205</fpage><lpage>2212</lpage><pub-id pub-id-type="doi">10.1182/blood-2013-03-488411</pub-id></element-citation></ref><ref id="bib44"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Westera</surname><given-names>L</given-names></name><name><surname>van Hoeven</surname><given-names>V</given-names></name><name><surname>Drylewicz</surname><given-names>J</given-names></name><name><surname>Spierenburg</surname><given-names>G</given-names></name><name><surname>van Velzen</surname><given-names>JF</given-names></name><name><surname>de Boer</surname><given-names>RJ</given-names></name><name><surname>Tesselaar</surname><given-names>K</given-names></name><name><surname>Borghans</surname><given-names>JAM</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Lymphocyte maintenance during healthy aging requires no substantial alterations in cellular turnover</article-title><source>Aging Cell</source><volume>14</volume><fpage>219</fpage><lpage>227</lpage><pub-id pub-id-type="doi">10.1111/acel.12311</pub-id><pub-id pub-id-type="pmid">25627171</pub-id></element-citation></ref><ref id="bib45"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wijeyesinghe</surname><given-names>S</given-names></name><name><surname>Beura</surname><given-names>LK</given-names></name><name><surname>Pierson</surname><given-names>MJ</given-names></name><name><surname>Stolley</surname><given-names>JM</given-names></name><name><surname>Adam</surname><given-names>OA</given-names></name><name><surname>Ruscher</surname><given-names>R</given-names></name><name><surname>Steinert</surname><given-names>EM</given-names></name><name><surname>Rosato</surname><given-names>PC</given-names></name><name><surname>Vezys</surname><given-names>V</given-names></name><name><surname>Masopust</surname><given-names>D</given-names></name></person-group><year iso-8601-date="2021">2021</year><article-title>Expansible residence decentralizes immune homeostasis</article-title><source>Nature</source><volume>592</volume><fpage>457</fpage><lpage>462</lpage><pub-id pub-id-type="doi">10.1038/s41586-021-03351-3</pub-id><pub-id pub-id-type="pmid">33731934</pub-id></element-citation></ref><ref id="bib46"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Yates</surname><given-names>A</given-names></name><name><surname>Graw</surname><given-names>F</given-names></name><name><surname>Barber</surname><given-names>DL</given-names></name><name><surname>Ahmed</surname><given-names>R</given-names></name><name><surname>Regoes</surname><given-names>RR</given-names></name><name><surname>Antia</surname><given-names>R</given-names></name></person-group><year iso-8601-date="2007">2007</year><article-title>Revisiting estimates of CTL killing rates in vivo</article-title><source>PLOS ONE</source><volume>2</volume><elocation-id>e1301</elocation-id><pub-id pub-id-type="doi">10.1371/journal.pone.0001301</pub-id><pub-id pub-id-type="pmid">18074025</pub-id></element-citation></ref><ref id="bib47"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Younes</surname><given-names>S-A</given-names></name><name><surname>Punkosdy</surname><given-names>G</given-names></name><name><surname>Caucheteux</surname><given-names>S</given-names></name><name><surname>Chen</surname><given-names>T</given-names></name><name><surname>Grossman</surname><given-names>Z</given-names></name><name><surname>Paul</surname><given-names>WE</given-names></name></person-group><year iso-8601-date="2011">2011</year><article-title>Memory phenotype CD4 T cells undergoing rapid, nonburst-like, cytokine-driven proliferation can be distinguished from antigen-experienced memory cells</article-title><source>PLOS Biology</source><volume>9</volume><elocation-id>e1001171</elocation-id><pub-id pub-id-type="doi">10.1371/journal.pbio.1001171</pub-id><pub-id pub-id-type="pmid">22022231</pub-id></element-citation></ref><ref id="bib48"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Zammit</surname><given-names>DJ</given-names></name><name><surname>Turner</surname><given-names>DL</given-names></name><name><surname>Klonowski</surname><given-names>KD</given-names></name><name><surname>Lefrançois</surname><given-names>L</given-names></name><name><surname>Cauley</surname><given-names>LS</given-names></name></person-group><year iso-8601-date="2006">2006</year><article-title>Residual antigen presentation after influenza virus infection affects CD8 T cell activation and migration</article-title><source>Immunity</source><volume>24</volume><fpage>439</fpage><lpage>449</lpage><pub-id pub-id-type="doi">10.1016/j.immuni.2006.01.015</pub-id><pub-id pub-id-type="pmid">16618602</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>MAP estimates and 95% credible intervals of parameters from the statistically favoured models.</title><p>LP: lamina propria; LN: lymph node.</p></caption><table frame="hsides" rules="groups"><thead><tr><th rowspan="1" valign="bottom">Parameter</th><th rowspan="1" valign="bottom">Tissue</th><th rowspan="1" valign="bottom">Target</th><th rowspan="1" valign="bottom">Recruitment mode</th><th rowspan="1" valign="bottom">Precursor</th><th rowspan="1" valign="bottom">Estimate</th></tr></thead><tbody><tr><td align="left" valign="bottom" rowspan="4">Mean residence time (days)</td><td align="left" valign="bottom" rowspan="2">LP</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Quiescent (Ki67<sup>low</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">13 (11, 15)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Neutral (Ki67<sup>int</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">14 (13, 16)</td></tr><tr><td align="left" valign="bottom" rowspan="2">Skin</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">22 (20, 24)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">Skin CD69⁻</td><td align="char" char="." valign="bottom">24 (22, 27)</td></tr><tr><td align="left" valign="bottom" rowspan="4">Mean interdivision time (days)</td><td align="left" valign="bottom" rowspan="2">LP</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Quiescent (Ki67<sup>low</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">49 (44, 57)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Neutral (Ki67<sup>int</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">66 (57, 75)</td></tr><tr><td align="left" valign="bottom" rowspan="2">Skin</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">22 (20, 24)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">Skin CD69⁻</td><td align="char" char="." valign="bottom">24 (22, 27)</td></tr><tr><td align="left" valign="bottom" rowspan="4">Clonal half-life (days)</td><td align="left" valign="bottom" rowspan="2">LP</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Quiescent (Ki67<sup>low</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">10 (9, 12)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Neutral (Ki67<sup>int</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">12 (10, 14)</td></tr><tr><td align="left" valign="bottom" rowspan="2">Skin</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">34 (29, 41)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">Skin CD69⁻</td><td align="char" char="." valign="bottom">35 (30, 42)</td></tr><tr><td align="left" valign="bottom" rowspan="4">Percent daily replacement by influx</td><td align="left" valign="bottom" rowspan="2">LP</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Quiescent (Ki67<sup>low</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">5.7 (4.9, 6.9)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Neutral (Ki67<sup>int</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">5.4 (4.5, 6.2)</td></tr><tr><td align="left" valign="bottom" rowspan="2">Skin</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">2.0 (1.7, 2.4)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">Skin CD69⁻</td><td align="char" char="." valign="bottom">2.0 (1.7, 2.3)</td></tr><tr><td align="left" valign="bottom" rowspan="4">Percent production from self-renewal</td><td align="left" valign="bottom" rowspan="2">LP</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Quiescent (Ki67<sup>low</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">26 (22, 30)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Neutral (Ki67<sup>int</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">28 (22, 34)</td></tr><tr><td align="left" valign="bottom" rowspan="2">Skin</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">55 (50, 62)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">Skin CD69⁻</td><td align="char" char="." valign="bottom">52 (46, 59)</td></tr><tr><td align="left" valign="bottom" rowspan="4">Ki67 lifespan (days)</td><td align="left" valign="bottom" rowspan="2">LP</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Quiescent (Ki67<sup>low</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">2.6 (2.3, 2.9)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Neutral (Ki67<sup>int</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">2.0 (1.7, 2.3)</td></tr><tr><td align="left" valign="bottom" rowspan="2">Skin</td><td align="left" valign="bottom">CD4⁺ EM</td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">LN CD4⁺ EM</td><td align="char" char="." valign="bottom">2.8 (2.5, 3.2)</td></tr><tr><td align="left" valign="bottom">CD4⁺CD69⁺ T<sub>RM</sub></td><td align="left" valign="bottom">Division-linked (Ki67<sup>hi</sup>)</td><td align="left" valign="bottom">Skin CD69⁻</td><td align="char" char="." valign="bottom">2.7 (2.4, 3.0)</td></tr></tbody></table></table-wrap><sec sec-type="appendix" id="s8"><title>Kinetics of mTom expression derived from Cd4-FR mice</title><p>We used a simple homogeneous ODE model to describe the kinetics of mTom<sup>+</sup> and mTom<sup>−</sup> cells by tracking their loss (per capita <inline-formula><alternatives><mml:math id="inf11"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>δ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft11">\begin{document}$\delta$\end{document}</tex-math></alternatives></inline-formula>), self-renewal (per capita rate <inline-formula><alternatives><mml:math id="inf12"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft12">\begin{document}$\rho$\end{document}</tex-math></alternatives></inline-formula>), and supplementation from a precursor population at constant total rate <inline-formula><alternatives><mml:math id="inf13"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft13">\begin{document}$\theta$\end{document}</tex-math></alternatives></inline-formula> and with label content <italic>f</italic><sub>mTom</sub>, described empirically (see section ‘Model fitting’ below):<disp-formula id="equ1"><alternatives><mml:math id="m1"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mtable columnalign="left left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mfrac><mml:mi>d</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:msup><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mi>θ</mml:mi><mml:mo>⋅</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>δ</mml:mi><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>⋅</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mspace width="thinmathspace"/><mml:mfrac><mml:mi>d</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:msup><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mi>θ</mml:mi><mml:mo>⋅</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>δ</mml:mi><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>⋅</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mtd></mml:mtr></mml:mtable></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t1">\begin{document}$$\displaystyle \begin{array}{ll}\frac{d}{dt}\mathrm{mTom}^{+}&amp;= \theta \cdot f_{\mathrm{mTom}}(t) - (\delta - \rho) \cdot \mathrm{mTom}^{+}\\\, \frac{d}{dt}\mathrm{mTom}^{-}&amp;= \theta \cdot (1-f_{\mathrm{mTom}}(t))- (\delta - \rho) \cdot \mathrm{mTom}^{-}\end{array}$$\end{document}</tex-math></alternatives></disp-formula></p></sec><sec sec-type="appendix" id="s9"><title>Modelling the label trajectories derived from Ki67-DIVN mice</title><p>The model we used to describe data derived from the Ki67-DIVN mice was is similar to that above, with the same parameters <inline-formula><alternatives><mml:math id="inf14"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft14">\begin{document}$\theta$\end{document}</tex-math></alternatives></inline-formula>, <inline-formula><alternatives><mml:math id="inf15"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>δ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft15">\begin{document}$\delta$\end{document}</tex-math></alternatives></inline-formula>, and <inline-formula><alternatives><mml:math id="inf16"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft16">\begin{document}$\rho$\end{document}</tex-math></alternatives></inline-formula>, but included the kinetics of Ki67 expression (see equations below). Following mitosis, Ki67 protein levels continuously decrease. However, in standard flow cytometry analyses, cells are classified into two categories: Ki67<sup>high</sup> and Ki67<sup>low</sup>. To model the transition between these states, we used the linear chain technique (<xref ref-type="bibr" rid="bib25">MacDonald, 1978</xref>) and introduced intermediate Ki67<sup>high</sup> compartments as in previous studies (<xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>), allowing us to characterise the residence time within the Ki67<sup>high</sup> compartment as gamma-distributed with low variance, with 12 intermediate Ki67 levels (<inline-formula><alternatives><mml:math id="inf17"><mml:mi>ℓ</mml:mi></mml:math><tex-math id="inft17">\begin{document}$\ell$\end{document}</tex-math></alternatives></inline-formula>). The rate at which Ki67<sup>high</sup> cells move between these intermediate stages is given by <inline-formula><alternatives><mml:math id="inf18"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>ℓ</mml:mi><mml:mi>β</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft18">\begin{document}$\ell\beta$\end{document}</tex-math></alternatives></inline-formula>, such that the expected time that a cell spends within the Ki67<sup>high</sup> gate before transitioning to the Ki67<sup>low</sup> gate is <inline-formula><alternatives><mml:math id="inf19"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft19">\begin{document}$1/\beta$\end{document}</tex-math></alternatives></inline-formula>. For each precursor/target pair, we examined three influx modes: one where new immigrant cells are Ki67<sup>low</sup> (quiescent), another where their Ki67 expression mirrors the precursor’s, and a third where they are fully Ki67<sup>high</sup>. To represent these modes we used a parameter (<inline-formula><alternatives><mml:math id="inf20"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math><tex-math id="inft20">\begin{document}$k_{f}$\end{document}</tex-math></alternatives></inline-formula>) which was set to either zero, the mean Ki67<sup>high</sup> fraction within the precursor, or 1, respectively. In the model, the subscripts denote the Ki67 state or expression level (0 is Ki67<sup>low</sup>; 1 <inline-formula><alternatives><mml:math id="inf21"><mml:mrow><mml:mo>…</mml:mo></mml:mrow><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow></mml:math><tex-math id="inft21">\begin{document}$\dots \ell$\end{document}</tex-math></alternatives></inline-formula> are Ki67<sup>high</sup>):<disp-formula id="equ2"><alternatives><mml:math id="m2"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mtable columnalign="left left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mfrac><mml:mi>d</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Y</mml:mi><mml:mi mathvariant="normal">F</mml:mi><mml:mi 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stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">Y</mml:mi><mml:mi mathvariant="normal">F</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mo>⋅</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mi>ℓ</mml:mi><mml:mi>β</mml:mi><mml:mo>⋅</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Y</mml:mi><mml:mi mathvariant="normal">F</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msubsup><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>δ</mml:mi><mml:mo>+</mml:mo><mml:mi>ρ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>⋅</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Y</mml:mi><mml:mi mathvariant="normal">F</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msubsup></mml:mtd></mml:mtr></mml:mtable></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t2">\begin{document}$$\displaystyle \begin{array}{ll}\frac{d}{dt}\mathrm{YFP}_{\ell}^{+}= \theta \cdot f_{\mathrm{YFP}}(t) \cdot k_{f}- (\delta +\ell\beta+\rho) \cdot \mathrm{YFP}_{\ell}^{+}+ 2\rho{\sum_{j=0}^{\ell}\mathrm{YFP}_{j}^{+}}\\ \frac{d}{dt}\mathrm{YFP}_{\ell}^{-}= \theta \cdot (1-f_{\mathrm{YFP}}(t)) \cdot k_{f}- (\delta +\ell\beta+\rho) \cdot \mathrm{YFP}_{\ell}^{+}+ 2\rho{\sum_{j=0}^{\ell} \mathrm{YFP}_{j}^{-}}\\ \frac{d}{dt}\mathrm{YFP}_{j}^{i}= \ell\beta \cdot \mathrm{YFP}_{j+1}^{i}- (\delta +\rho+\ell\beta) \cdot \mathrm{YFP}_{j}^{i}\quad\quad\quad\quad \quad\quad\quad \quad\quad \text{for }i \in \{+, -\} \text{ and }1 \leq j &lt; \ell \\ \frac{d}{dt}\mathrm{YFP}_{0}^{+}= \theta \cdot f_{\mathrm{YFP}}(t) \cdot (1-k_{f})+\ell\beta \cdot \mathrm{YFP}_{1}^{+}- (\delta +\rho) \cdot \mathrm{YFP}_{0}^{+}\\ \frac{d}{dt}\mathrm{YFP}_{0}^{-}= \theta \cdot (1-f_{\mathrm{YFP}}(t)) \cdot (1-k_{f})+\ell\beta \cdot \mathrm{YFP}_{1}^{-}- (\delta +\rho) \cdot \mathrm{YFP}_{0}^{-}\\\end{array}$$\end{document}</tex-math></alternatives></disp-formula></p></sec><sec sec-type="appendix" id="s10"><title>Model fitting</title><sec sec-type="appendix" id="s10-1"><title>Empirical functions describe label dynamics in precursor populations</title><p>We described the trajectories of YFP and mTom expression within the candidate precursors with simple functions based on exponentials. In most populations, the labelled fractions (<inline-formula><alternatives><mml:math id="inf22"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>mTom</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math><tex-math id="inft22">\begin{document}$f_{\text{mTom}}$\end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math id="inf23"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mtext>YFP</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math><tex-math id="inft23">\begin{document}$f_{\text{YFP}}$\end{document}</tex-math></alternatives></inline-formula>), both decreased over time, each described with a curve of the form<disp-formula id="equ3"><label>(1)</label><alternatives><mml:math id="m3"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mi>b</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>.</mml:mo></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t3">\begin{document}$$\displaystyle f(t) = ae^{-bt}.$$\end{document}</tex-math></alternatives></disp-formula></p><p>We used a saturating exponential increase function for the YFP<sup>+</sup> fraction within LN-derived naive CD4 T cells,<disp-formula id="equ4"><label>(2)</label><alternatives><mml:math id="m4"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mi>b</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t4">\begin{document}$$\displaystyle f(t) = a(1-e^{-bt}).$$\end{document}</tex-math></alternatives></disp-formula></p><p>For each precursor, we fitted these functions to its data alone using FME in <italic>R</italic> and in Python using the curvefit() function from the package SciPy (<xref ref-type="bibr" rid="bib41">Virtanen et al., 2020</xref>). These fits are shown in <xref ref-type="fig" rid="fig2">Figure 2D</xref>. The best-fit parameters (see table below) and associated uncertainties were used to inform the priors for fitting precursor and target trajectories simultaneously using our Bayesian approach.</p><table-wrap id="inlinetable1" position="anchor"><table frame="hsides" rules="groups"><thead><tr><th align="left" valign="bottom">Population</th><th align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf24"><mml:msub><mml:mi>a</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math><tex-math id="inft24">\begin{document}$a_{y}$\end{document}</tex-math></alternatives></inline-formula></th><th align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf25"><mml:msub><mml:mi>b</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math><tex-math id="inft25">\begin{document}$b_{y}$\end{document}</tex-math></alternatives></inline-formula></th><th align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf26"><mml:msub><mml:mi>a</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:math><tex-math id="inft26">\begin{document}$a_{t}$\end{document}</tex-math></alternatives></inline-formula></th><th align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf27"><mml:msub><mml:mi>b</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:math><tex-math id="inft27">\begin{document}$b_{t}$\end{document}</tex-math></alternatives></inline-formula></th><th align="left" valign="bottom"><inline-formula><alternatives><mml:math id="inf28"><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:math><tex-math id="inft28">\begin{document}$k_{f}$\end{document}</tex-math></alternatives></inline-formula></th></tr></thead><tbody><tr><td align="left" valign="bottom">LN CD4 CM</td><td align="left" valign="bottom">0.286</td><td align="left" valign="bottom">0.001</td><td align="left" valign="bottom">0.857</td><td align="left" valign="bottom">0.011</td><td align="left" valign="bottom">0.2</td></tr><tr><td align="left" valign="bottom">LN CD4 EM</td><td align="left" valign="bottom">0.289</td><td align="left" valign="bottom">0.002</td><td align="left" valign="bottom">0.833</td><td align="left" valign="bottom">0.007</td><td align="left" valign="bottom">0.12</td></tr><tr><td align="left" valign="bottom">LN CD4 Naive</td><td align="left" valign="bottom">0.372</td><td align="left" valign="bottom">0.081</td><td align="left" valign="bottom">0.919</td><td align="left" valign="bottom">0.030</td><td align="left" valign="bottom">0.16</td></tr><tr><td align="left" valign="bottom">SK CD69⁻</td><td align="left" valign="bottom">0.258</td><td align="left" valign="bottom">0.001</td><td align="left" valign="bottom">0.542</td><td align="left" valign="bottom">0.007</td><td align="left" valign="bottom">0.21</td></tr><tr><td align="left" valign="bottom">LP CD69⁻</td><td align="left" valign="bottom">0.449</td><td align="left" valign="bottom">0.007</td><td align="left" valign="bottom">0.457</td><td align="left" valign="bottom">0.007</td><td align="left" valign="bottom">0.0047</td></tr></tbody></table></table-wrap></sec><sec sec-type="appendix" id="s10-2"><title>Initialising the system before describing post-treatment kinetics of labelled populations</title><p>Motivated by observations (<xref ref-type="fig" rid="fig2">Figure 2A</xref>), we assumed all target populations in skin and LP were at homeostatic equilibrium, and with constant levels of Ki67. To ensure the system was at this equilibrium before tamoxifen treatment, for each set of parameter values we used the steady-state assumption and observed Ki67 fraction (estimated by taking the mean of the observed values in each population) to eliminate two parameters from the model (see below). We then utilised the Runge–Kutta 45 ODE solver within Stan, setting all species to zero, and running for 10<sup>4</sup> days to drive the system to this prescribed steady state. The labeled fractions of cells in the target population at d5 post treatment were free parameters <inline-formula><alternatives><mml:math id="inf29"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>ϵ</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">Y</mml:mi><mml:mi mathvariant="normal">F</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math><tex-math id="inft29">\begin{document}$\epsilon_{\mathrm{YFP}}$\end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math id="inf30"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>ϵ</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math><tex-math id="inft30">\begin{document}$\epsilon_{\mathrm{mTom}}$\end{document}</tex-math></alternatives></inline-formula>, which reflected the cumulative effect of label induction up to that point. Cells were then distributed into labelled and unlabelled populations using these parameters.</p></sec><sec sec-type="appendix" id="s10-3"><title>Modelling noise and mouse-to-mouse variation</title><p>In addition to the empirically described trajectories of label content within each precursor population, from the model we derived the four proportions of interest for the target: the mTom<sup>+</sup> fraction, the YFP<sup>+</sup> fraction, and the Ki67<sup>high</sup> fractions within YFP<sup>+/−</sup> cells. As all of these observations lay within the interval (0, 1), we logit-transformed them to normalise residuals. The normally-distributed noise within each dataset was defined with six separate standard deviations, <inline-formula><alternatives><mml:math id="inf31"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>σ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft31">\begin{document}$\sigma$\end{document}</tex-math></alternatives></inline-formula>, each themselves described with normal priors. Fits were obtained using all six time series simultaneously (summing the log likelihoods). For performing statistical comparisons of different precursor–target relationships using LOO-IC, we used only the log-likelihoods for the four quantities derived from the target cell kinetics; this ensured we were comparing descriptions of the same observations.</p></sec><sec sec-type="appendix" id="s10-4"><title>Prior distributions of parameters</title><p>By assuming that the population was at steady state and that the Ki67 fraction was constant, we could eliminate two of the five parameters (<inline-formula><alternatives><mml:math id="inf32"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft32">\begin{document}$\theta$\end{document}</tex-math></alternatives></inline-formula>, <inline-formula><alternatives><mml:math id="inf33"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft33">\begin{document}$\beta$\end{document}</tex-math></alternatives></inline-formula>, <inline-formula><alternatives><mml:math id="inf34"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft34">\begin{document}$\rho$\end{document}</tex-math></alternatives></inline-formula>, <inline-formula><alternatives><mml:math id="inf35"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>δ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft35">\begin{document}$\delta$\end{document}</tex-math></alternatives></inline-formula>, and <inline-formula><alternatives><mml:math id="inf36"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math><tex-math id="inft36">\begin{document}$k_{F}$\end{document}</tex-math></alternatives></inline-formula>, the fraction of immigrant cells that are assumed to enter as Ki67<sup>high</sup>).</p><p>All parameters were sampled from a range of values such that populations remained positive and finite. The prior on the Ki67 lifetime <inline-formula><alternatives><mml:math id="inf37"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft37">\begin{document}$1/\beta$\end{document}</tex-math></alternatives></inline-formula> peaked at 3.25 days and constrained to remain between 2.5 and 4.5 days, based on previous studies. Based on previous studies (<xref ref-type="bibr" rid="bib20">Gossel et al., 2017</xref>; <xref ref-type="bibr" rid="bib7">Bullock et al., 2024</xref>), the influx rate <inline-formula><alternatives><mml:math id="inf38"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft38">\begin{document}$\theta$\end{document}</tex-math></alternatives></inline-formula> was constrained to be between 0.05% and 10% of the total pool size. We set broad priors on the initialisation induction efficiencies of YFP and mTom (<inline-formula><alternatives><mml:math id="inf39"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>ϵ</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">Y</mml:mi><mml:mi mathvariant="normal">F</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math><tex-math id="inft39">\begin{document}$\epsilon_{\mathrm{YFP}}$\end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math id="inf40"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msub><mml:mi>ϵ</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mstyle></mml:math><tex-math id="inft40">\begin{document}$\epsilon_{\mathrm{mTom}}$\end{document}</tex-math></alternatives></inline-formula>), with upper limits of 1.</p><p>All code and data can be obtained at <ext-link ext-link-type="uri" xlink:href="https://github.com/elisebullock/CD4TRM">https://github.com/elisebullock/CD4TRM</ext-link>.</p></sec></sec><sec sec-type="appendix" id="s11"><title>Estimating average cell residence times using Ki67</title><p>Consider a cell population at steady-state numbers <inline-formula><alternatives><mml:math id="inf41"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft41">\begin{document}$N$\end{document}</tex-math></alternatives></inline-formula> with cells dividing at an average <italic>per capita</italic> rate <inline-formula><alternatives><mml:math id="inf42"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft42">\begin{document}$\rho$\end{document}</tex-math></alternatives></inline-formula>, leaving the population through death, egress, or differentiation at average <italic>per capita</italic> rate <inline-formula><alternatives><mml:math id="inf43"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>δ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft43">\begin{document}$\delta$\end{document}</tex-math></alternatives></inline-formula>, and being replenished from a precursor population at total rate <inline-formula><alternatives><mml:math id="inf44"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft44">\begin{document}$\theta$\end{document}</tex-math></alternatives></inline-formula>:<disp-formula id="equ5"><label>(3)</label><alternatives><mml:math id="m5"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>θ</mml:mi><mml:mo>+</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>ρ</mml:mi><mml:mo>−</mml:mo><mml:mi>δ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mspace width="thickmathspace"/><mml:mo stretchy="false">⟹</mml:mo><mml:mspace width="thickmathspace"/><mml:mi>ρ</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>θ</mml:mi><mml:mo>=</mml:mo><mml:mi>δ</mml:mi><mml:mi>N</mml:mi><mml:mo>.</mml:mo></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t5">\begin{document}$$\displaystyle \frac{dN}{dt}= \theta + (\rho - \delta)N = 0 \implies \rho N + \theta = \delta N.$$\end{document}</tex-math></alternatives></disp-formula></p><p>Assume a fraction <inline-formula><alternatives><mml:math id="inf45"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft45">\begin{document}$f$\end{document}</tex-math></alternatives></inline-formula> of immigrants enter the population as Ki67<sup>high</sup>. We know that Ki67 is expressed for a time <inline-formula><alternatives><mml:math id="inf46"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>T</mml:mi><mml:mo>≃</mml:mo><mml:mn>3</mml:mn><mml:mo>−</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:mstyle></mml:math><tex-math id="inft46">\begin{document}$T\simeq 3-4$\end{document}</tex-math></alternatives></inline-formula> days during and after division. Then the number of cells within the population as a whole that are Ki67<sup>high</sup>, K<sup>+</sup>, is constant and equal to the number that were produced by division or entered as Ki67<sup>high</sup> in the last <inline-formula><alternatives><mml:math id="inf47"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft47">\begin{document}$T$\end{document}</tex-math></alternatives></inline-formula> days, and survived to the present:<disp-formula id="equ6"><label>(4)</label><alternatives><mml:math id="m6"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:msup><mml:mi>K</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∫</mml:mo><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mi>ρ</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>f</mml:mi><mml:mi>θ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mspace width="thinmathspace"/><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>δ</mml:mi><mml:mo>+</mml:mo><mml:mi>ρ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo>−</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mi>d</mml:mi><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi>ρ</mml:mi><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mi>f</mml:mi><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>δ</mml:mi><mml:mo>+</mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:mfrac><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>δ</mml:mi><mml:mo>+</mml:mo><mml:mi>ρ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t6">\begin{document}$$\displaystyle K^{+}= \int_{0}^{T}(2\rho N + f \theta) \, e^{-(\delta + \rho)(T-s)}ds = \frac{2\rho N + f\theta}{\delta + \rho}(1 - e^{-(\delta+\rho) T}),$$\end{document}</tex-math></alternatives></disp-formula></p><p>The Ki67<sup>high</sup> proportion observed within the total population at any time is therefore also constant and equal to <inline-formula><alternatives><mml:math id="inf48"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft48">\begin{document}$k = K^{+}/N$\end{document}</tex-math></alternatives></inline-formula><disp-formula id="equ7"><label>(5)</label><alternatives><mml:math id="m7"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi>ρ</mml:mi><mml:mo>+</mml:mo><mml:mi>f</mml:mi><mml:mspace width="thinmathspace"/><mml:mi>θ</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>δ</mml:mi><mml:mo>+</mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:mfrac><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>δ</mml:mi><mml:mo>+</mml:mo><mml:mi>ρ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t7">\begin{document}$$\displaystyle k = \frac{2\rho + f\,\theta/N}{\delta + \rho}(1 - e^{-(\delta+\rho)T}).$$\end{document}</tex-math></alternatives></disp-formula></p><p>In the general case where influx is substantial, we need an independent estimate of the daily proportional replacement through influx, <inline-formula><alternatives><mml:math id="inf49"><mml:mrow><mml:mi>θ</mml:mi><mml:mi>/</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:math><tex-math id="inft49">\begin{document}$\theta/N$\end{document}</tex-math></alternatives></inline-formula>, which by <xref ref-type="disp-formula" rid="equ5">Equation 3</xref> is equal to the daily net loss rate <inline-formula><alternatives><mml:math id="inf50"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mi>δ</mml:mi><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft50">\begin{document}$\lambda = \delta-\rho$\end{document}</tex-math></alternatives></inline-formula>. Then, eliminating the division rate <inline-formula><alternatives><mml:math id="inf51"><mml:mi>ρ</mml:mi></mml:math><tex-math id="inft51">\begin{document}$\rho$\end{document}</tex-math></alternatives></inline-formula>,<disp-formula id="equ8"><label>(6)</label><alternatives><mml:math id="m8"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mo stretchy="false">(</mml:mo><mml:mi>δ</mml:mi><mml:mo>−</mml:mo><mml:mi>λ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mi>f</mml:mi><mml:mi>λ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>δ</mml:mi><mml:mo>−</mml:mo><mml:mi>λ</mml:mi></mml:mrow></mml:mfrac><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mi>δ</mml:mi><mml:mo>−</mml:mo><mml:mi>λ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t8">\begin{document}$$\displaystyle k = \frac{2 (\delta-\lambda) + f \lambda}{2\delta - \lambda}(1 - e^{-(2\delta-\lambda)T}).$$\end{document}</tex-math></alternatives></disp-formula></p><p>Given an observed value of <inline-formula><alternatives><mml:math id="inf52"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft52">\begin{document}$k$\end{document}</tex-math></alternatives></inline-formula>, the known value of <inline-formula><alternatives><mml:math id="inf53"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft53">\begin{document}$T$\end{document}</tex-math></alternatives></inline-formula>, an estimate of the replacement (influx) rate <inline-formula><alternatives><mml:math id="inf54"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft54">\begin{document}$\lambda$\end{document}</tex-math></alternatives></inline-formula>, and a value for <inline-formula><alternatives><mml:math id="inf55"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft55">\begin{document}$f$\end{document}</tex-math></alternatives></inline-formula> (reflecting the extent to which incoming cells are recently divided), <xref ref-type="disp-formula" rid="equ8">Equation 6</xref> can be solved numerically for the cell lifespan <inline-formula><alternatives><mml:math id="inf56"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>τ</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>δ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft56">\begin{document}$\tau = 1/\delta$\end{document}</tex-math></alternatives></inline-formula>.</p><p>We can consider some simpler limiting cases. If most cell production occurs through self renewal rather than influx, then <inline-formula><alternatives><mml:math id="inf57"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>ρ</mml:mi><mml:mo>≃</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft57">\begin{document}$\rho \simeq \delta$\end{document}</tex-math></alternatives></inline-formula> and <inline-formula><alternatives><mml:math id="inf58"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>≃</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:mstyle></mml:math><tex-math id="inft58">\begin{document}$\lambda \simeq 0$\end{document}</tex-math></alternatives></inline-formula>. <xref ref-type="disp-formula" rid="equ8">Equation 6</xref> then becomes <inline-formula><alternatives><mml:math id="inf59"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>k</mml:mi><mml:mo>≃</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mi>T</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>τ</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mstyle></mml:math><tex-math id="inft59">\begin{document}$k \simeq (1 - e^{-2T/\tau})$\end{document}</tex-math></alternatives></inline-formula>. This yields a simple formula that relates the Ki67 fraction within a closed or nearly closed population to the mean lifespan of its constituent cells:<disp-formula id="equ9"><label>(7)</label><alternatives><mml:math id="m9"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mi>τ</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>ln</mml:mi><mml:mo>⁡</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac><mml:mo>≃</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi>T</mml:mi></mml:mrow><mml:mi>k</mml:mi></mml:mfrac><mml:mo>,</mml:mo></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t9">\begin{document}$$\displaystyle \tau = \frac{-2T}{\ln(1-k)}\simeq \frac{2T}{k}, $$\end{document}</tex-math></alternatives></disp-formula></p><p>where the approximation holds if <inline-formula><alternatives><mml:math id="inf60"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft60">\begin{document}$k$\end{document}</tex-math></alternatives></inline-formula> is small. If influx cannot be disregarded, but we have an indication that cell lifespans are much longer than the duration of Ki67 expression, <inline-formula><alternatives><mml:math id="inf61"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>τ</mml:mi><mml:mo>≫</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft61">\begin{document}$\tau \gg T$\end{document}</tex-math></alternatives></inline-formula> (which will be likely if <inline-formula><alternatives><mml:math id="inf62"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft62">\begin{document}$k$\end{document}</tex-math></alternatives></inline-formula> is small, suggesting slow turnover), then <inline-formula><alternatives><mml:math id="inf63"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mi>δ</mml:mi><mml:mo>−</mml:mo><mml:mi>λ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mo>≃</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mi>δ</mml:mi><mml:mo>−</mml:mo><mml:mi>λ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mstyle></mml:math><tex-math id="inft63">\begin{document}$e^{-(2\delta-\lambda)T}\simeq 1-T(2\delta -\lambda)$\end{document}</tex-math></alternatives></inline-formula> and <xref ref-type="disp-formula" rid="equ8">Equation 6</xref> gives<disp-formula id="equ10"><label>(8)</label><alternatives><mml:math id="m10"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mi>k</mml:mi><mml:mo>≃</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>λ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>f</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>τ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mspace width="thickmathspace"/><mml:mo stretchy="false">⟹</mml:mo><mml:mspace width="thickmathspace"/><mml:mi>τ</mml:mi><mml:mo>≃</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mi>λ</mml:mi><mml:mi>T</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t10">\begin{document}$$\displaystyle k \simeq T(\lambda (f-2) + 2/\tau) \implies \tau \simeq \frac{2T}{k + \lambda T(2-f)}.$$\end{document}</tex-math></alternatives></disp-formula></p><p>Rough bounds on the mean cell lifespan are then<disp-formula id="equ11"><label>(9)</label><alternatives><mml:math id="m11"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi>λ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:mfrac><mml:mo>&lt;</mml:mo><mml:mi>τ</mml:mi><mml:mo>&lt;</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mi>λ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mstyle></mml:mrow></mml:mstyle></mml:math><tex-math id="t11">\begin{document}$$\displaystyle\frac{2T}{k + 2 \lambda T}&lt; \tau &lt;\frac{2T}{k + \lambda T},$$\end{document}</tex-math></alternatives></disp-formula></p><p>spanning the cases <inline-formula><alternatives><mml:math id="inf64"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>f</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:mstyle></mml:math><tex-math id="inft64">\begin{document}$f=0$\end{document}</tex-math></alternatives></inline-formula> (all newly recruited cells are quiescent) and <inline-formula><alternatives><mml:math id="inf65"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>f</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mstyle></mml:math><tex-math id="inft65">\begin{document}$f=1$\end{document}</tex-math></alternatives></inline-formula> (all new immigrants are recently divided; for example, having recently been antigen stimulated). A value of <inline-formula><alternatives><mml:math id="inf66"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft66">\begin{document}$f$\end{document}</tex-math></alternatives></inline-formula> between 0 and 1 might also arise if the mean duration of Ki67 expression on new immigrants is shorter than the 3–4 days expected on very recently-divided cell, reflecting the possibility that they last divided as precursors less than <inline-formula><alternatives><mml:math id="inf67"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:mstyle></mml:math><tex-math id="inft67">\begin{document}$T$\end{document}</tex-math></alternatives></inline-formula> days before entering the population.</p></sec></app></app-group></back><sub-article article-type="editor-report" id="sa0"><front-stub><article-id pub-id-type="doi">10.7554/eLife.104278.3.sa0</article-id><title-group><article-title>eLife Assessment</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Belz</surname><given-names>Gabrielle T</given-names></name><role specific-use="editor">Reviewing Editor</role><aff><institution>University of Queensland</institution><country>Australia</country></aff></contrib></contrib-group><kwd-group kwd-group-type="evidence-strength"><kwd>Compelling</kwd></kwd-group><kwd-group kwd-group-type="claim-importance"><kwd>Fundamental</kwd></kwd-group></front-stub><body><p>This article provides a <bold>compelling</bold> and rigorous quantitative analysis of the turnover and maintenance of CD4<sup>+</sup> tissue-resident memory T cell clones, in the skin and the lamina propria. It provides a <bold>fundamental</bold> advance in our understanding of CD4 T cell regulation. Interestingly, in both tissues, maintenance involves an influx from progenitors on the time scale of months. The evidence that is based on fate mapping and mathematical inference is strong, although open questions on the interpretation of the Ki67-based fate mapping remain.</p></body></sub-article><sub-article article-type="referee-report" id="sa1"><front-stub><article-id pub-id-type="doi">10.7554/eLife.104278.3.sa1</article-id><title-group><article-title>Reviewer #1 (Public review):</article-title></title-group><contrib-group><contrib contrib-type="author"><anonymous/><role specific-use="referee">Reviewer</role></contrib></contrib-group></front-stub><body><p>Summary:</p><p>Compelling and clearly described work that combines two elegant cell fate reporter strains with mathematical modelling to describe the kinetics of CD4+ TRM in mice. The aim is to investigate the cell dynamics underlying maintenance of CD4+TRM.</p><p>The main conclusions are that (1) CD4+ TRM are not intrinsically long-lived (2) even clonal half lives are short: 1 month for TRM in skin, even shorter (12 days) for TRM in lamina propria (3) TRM are maintained by self-renewal and circulating precursors.</p><p>Strengths:</p><p>(1) Very clearly and succinctly written. Though in some places too succinctly! See suggestions below for areas I think could benefit from more detail.</p><p>(2) Powerful combination of mouse strains and modelling to address questions that are hard to answer with other approaches.</p><p>(3) The modelling of different modes of recruitment (quiescent, neutral, division linked) is extremely interesting and often neglected (for simpler neutral recruitment).</p><p>Comments on revised version: This reviewer is satisfied with the author responses and the changes made in the manuscript.</p></body></sub-article><sub-article article-type="referee-report" id="sa2"><front-stub><article-id pub-id-type="doi">10.7554/eLife.104278.3.sa2</article-id><title-group><article-title>Reviewer #2 (Public review):</article-title></title-group><contrib-group><contrib contrib-type="author"><anonymous/><role specific-use="referee">Reviewer</role></contrib></contrib-group></front-stub><body><p>This manuscript addresses a fundamental problem of immunology - the persistence mechanisms of tissue-resident memory T cells (TRMs). It introduces a novel quantitative methodology, combining the in vivo tracing of T cell cohorts with rigorous mathematical modeling and inference. Interestingly, the authors show that immigration plays a key role for maintaining CD4+ TRM populations in both skin and lamina propria (LP), with LP TRMs being more dependent on immigration than skin TRMs. This is an original and potentially impactful manuscript.</p><p>Comments on revised version: This reviewer is satisfied with the author responses and the changes made in the manuscript.</p></body></sub-article><sub-article article-type="author-comment" id="sa3"><front-stub><article-id pub-id-type="doi">10.7554/eLife.104278.3.sa3</article-id><title-group><article-title>Author response</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Chandler</surname><given-names>Jodie</given-names></name><role specific-use="author">Author</role><aff><institution>University College London</institution><addr-line><named-content content-type="city">London</named-content></addr-line><country>United Kingdom</country></aff></contrib><contrib contrib-type="author"><name><surname>Bullock</surname><given-names>M Elise</given-names></name><role specific-use="author">Author</role><aff><institution>Columbia University Medical Center</institution><addr-line><named-content content-type="city">New York</named-content></addr-line><country>United States</country></aff></contrib><contrib contrib-type="author"><name><surname>Swain</surname><given-names>Arpit C</given-names></name><role specific-use="author">Author</role><aff><institution>Columbia University Medical Center</institution><addr-line><named-content content-type="city">New York</named-content></addr-line><country>United States</country></aff></contrib><contrib contrib-type="author"><name><surname>Williams</surname><given-names>Cayman</given-names></name><role specific-use="author">Author</role><aff><institution>University College London</institution><addr-line><named-content content-type="city">London</named-content></addr-line><country>United Kingdom</country></aff></contrib><contrib contrib-type="author"><name><surname>van Dorp</surname><given-names>Christiaan Hendrik</given-names></name><role specific-use="author">Author</role><aff><institution>Columbia University Medical Center</institution><addr-line><named-content content-type="city">New York</named-content></addr-line><country>United States</country></aff></contrib><contrib contrib-type="author"><name><surname>Seddon</surname><given-names>Benedict</given-names></name><role specific-use="author">Author</role><aff><institution>University College London</institution><addr-line><named-content content-type="city">London</named-content></addr-line><country>United Kingdom</country></aff></contrib><contrib contrib-type="author"><name><surname>Yates</surname><given-names>Andrew J</given-names></name><role specific-use="author">Author</role><aff><institution>Department of Pathology and Cell Biology, Columbia University Irving Medical Center</institution><addr-line><named-content content-type="city">New York</named-content></addr-line><country>United States</country></aff></contrib></contrib-group></front-stub><body><p>The following is the authors’ response to the original reviews</p><disp-quote content-type="editor-comment"><p><bold>Reviewer #1 (Public review):</bold></p><p>Summary:</p><p>Compelling and clearly described work that combines two elegant cell fate reporter strains with mathematical modelling to describe the kinetics of CD4+ TRM in mice. The aim is to investigate the cell dynamics underlying the maintenance of CD4+TRM.</p><p>The main conclusions are that:</p><p>(1) CD4+ TRM are not intrinsically long-lived.</p><p>(2) Even clonal half-lives are short: 1 month for TRM in skin, and even shorter (12 days) for TRM in lamina propria.</p><p>(3) TRM are maintained by self-renewal and circulating precursors.</p><p>Strengths:</p><p>(1) Very clearly and succinctly written. Though in some places too succinctly! See suggestions below for areas I think could benefit from more detail.</p><p>(2) Powerful combination of mouse strains and modelling to address questions that are hard to answer with other approaches.</p><p>(3) The modelling of different modes of recruitment (quiescent, neutral, division linked) is extremely interesting and often neglected (for simpler neutral recruitment).</p><p>Weaknesses/scope for improvement:</p><p>(1) The authors use the same data set that they later fit for generating their priors. This double use of the same dataset always makes me a bit squeamish as I worry it could lead to an underestimate of errors on the parameters. Could the authors show plots of their priors and posteriors to check that the priors are not overly-influential? Also, how do differences in priors ultimately influence the degree of support a model gets (if at all)? Could differences in priors lead to one model gaining more support than another?</p></disp-quote><p>We now show the priors and posteriors overlaid in Figure S2. The posteriors lie well within the priors, giving us confidence that the priors are not overly influential.</p><disp-quote content-type="editor-comment"><p>(2) The authors state (line 81) that cells were &quot;identified as tissue-localised by virtue of their protection from short-term in vivo labelling (Methods; Fig. S1B)&quot;. I would like to see more information on this. How short is short term? How long after labelling do cells need to remain unlabelled in order to be designated tissue-localised (presumably label will get to tissue pretty quickly -within hours?). Can the authors provide citations to defend the assumption that all label-negative cells are tissue-localised (no false negatives)?</p><p>And conversely that no label-positive cells can be found in the tissue (no false positives)? I couldn't actually find the relevant section in the methods and Figure S1B didn't contain this information.</p></disp-quote><p>We did describe the in vivo labeling in the first section of Methods (it was for 3 mins before sacrifice). The two aims of Fig S1B were to show the gating strategy (label-positive and negatives from tissue samples were clearly separated) and to address the false-positive issue. Less than 3% of cells in our tissue samples were positive; therefore, at most 3% of truly tissue-resident cells acquired the i.v. label, and likely less. Excluding those (as we did) therefore makes little difference to our analyses in terms of cell numbers. False negative rates are expected to be extremely low; labeling within circulating cells is typically &gt;99% (see refs in Methods).</p><disp-quote content-type="editor-comment"><p>(3) Are the target and precursor populations from the same mice? If so is there any way to reflect the between-individual variation in the precursor population (not captured by the simple empirical fit)? I am thinking particularly of the skin and LP CD4+CD69- populations where the fraction of cells that are mTOM+ (and to a lesser extent YFP+) spans virtually the whole range. Would it be nice to capture this information in downstream predictions if possible?</p></disp-quote><p>This is a great point. We do indeed isolate all populations from each mouse. We are very aware of the advantages of using this grouping of information to reduce within-mouse uncertainty – we employ this as often as we can. The issue here was that the label content within the tissue (target) at any time depends on the entire trajectory of the label frequency in the precursor, in that mouse, up to that point. We can’t identify this curve for each animal individually – so we are obliged to use a population average.</p><p>To mitigate this lack of pairing we do take a very conservative approach and fit this empirical function describing the trajectories of YFP and mTom in precursors at the same time as the label kinetics in the target; that is, we account for uncertainty in label influx in our fits and parameter estimates.</p><p>Another issue is that to be sure that we are performing model selection appropriately, we only use the distribution of the likelihood on the target observations when comparing support for different precursors with LOO-IC. If we had been able to pair the precursor and target data in some way, the two would then be entangled and model comparison across precursors would not be possible.</p><p>We’ve added some of this to the discussion.</p><disp-quote content-type="editor-comment"><p>(4) In Figure 3, estimates of kinetics for cells in LP appear to be more dependent on the input model (quiescent/neutral/division-linked) than the same parameters in the skin. Can the authors explain intuitively why this is the case?</p></disp-quote><p>This is a nice observation and it has a fairly straightforward explanation. As we pointed out in the paper, estimated rates of self renewal become more sensitive to the mode of recruitment the greater the rate of influx. If immigrants are quiescent, all Ki67 in the tissue has to be explained by self renewal. If all new immigrants are Ki67 high, the estimate of the rate of self renewal within the tissue will be lower. Across the board, the estimated rates of influx into gut were consistently higher than those in skin, and so the sensitivity of parameters to the mode of recruitment was much more obvious at that site.</p><p>The importance of this trade-off for the division linked model can also be seen when you look at the neutral and quiescent models; they give similar parameter estimates because the Ki67 levels within all precursor populations were all less than 25% and so those two modes of recruitment are difficult to distinguish.</p><disp-quote content-type="editor-comment"><p>(5) Can the authors include plots of the model fits to data associated with the different strengths of support shown in Figure 4? That is, I would like to know what a difference in the strength of say 0.43 compared with 0.3 looks like in &quot;real terms&quot;. I feel strongly that this is important. Are all the fits fantastic, and some marginally better than others? Are they all dreadful and some are just less dreadful? Or are there meaningful differences?</p></disp-quote><p>This is another good point (and from the author recommendations list, is your most important concern).</p><p>We find that a fairly common issue is that models that are clearly distinguished by information criteria or LRTs can often give visually quite similar fits. Our experience is that this is partly due to the fact that models are usually fit on transformed scales (e.g. log for cell counts, logit for fractions) to normalise residuals, and this uncertainty is compressed when one looks at fits on the observed scale (e.g. linear). Another issue in our case is that for each model (precursor, target, and mode of recruitment) we fit 6 time courses simultaneously. Visual comparisons of fits of different models can then be a little difficult or misleading; apparently small differences in each fitted timecourse can add up to quite significant changes in the combined likelihood. We added this to the Discussion.</p><p>The number of models is combinatorial (Fig. 4) so showing them all seems a bit cumbersome. But now in the supporting information (Fig. S3), for each target we show the best, second best, and the worst model fits overlaid, to give a sense of the dynamic range of the models we considered. As you will now see, visual differences among the most strongly supported models were not huge (but refer to our point just above). Measures of out-of-sample prediction error (LOO-IC) discriminated between these models reasonably well, though (weights shown in Fig. 4).</p><p>It’s also worth mentioning here that we have substantially greater confidence in the identity of the precursors than in the precise modes of recruitment - you can see this clearly in the groupings of weights in Figure 4A. We did comment on this in the text but now emphasise it more.</p><disp-quote content-type="editor-comment"><p>(6) Figure 4 left me unclear about exactly which combinations of precursors and targets were considered. Figure 3 implies there are 5 precursors but in Figure 4A at most 4 are considered. Also, Figure 4B suggests skin CD69- were considered a target. This doesn't seem to be specified anywhere.</p></disp-quote><p>Thanks for pointing this out. When we were considering CD4+ EM in bulk as target, this population includes CD69- cells; in those fits, therefore, we couldn't use CD69- as a precursor. We now clarify this in the caption. Thanks also for the observation about Figure 4B; we didn’t consider CD69- cells as a target, so we’ve also made that clearer.</p><disp-quote content-type="editor-comment"><p><bold>Reviewer #2 (Public review):</bold></p><p>This manuscript addresses a fundamental problem of immunology - the persistence mechanisms of tissue-resident memory T cells (TRMs). It introduces a novel quantitative methodology, combining the in vivo tracing of T-cell cohorts with rigorous mathematical modeling and inference. Interestingly, the authors show that immigration plays a key role in maintaining CD4+ TRM populations in both skin and lamina propria (LP), with LP TRMs being more dependent on immigration than skin TRMs. This is an original and potentially impactful manuscript. However, several aspects were not clear and would benefit from being explained better or worked out in more detail.</p><p>(1) The key observations are as follows:</p><p>a) When heritably labeling cells due to CD4 expression, CD4+ TRM labeling frequency declines with time. This implies that CD4+ TRMs are ultimately replenished from a source not labeled, hence not expressing CD4. Most likely, this would be DN thymocytes.</p></disp-quote><p>That’s correct.</p><disp-quote content-type="editor-comment"><p>b) After labeling by Ki67 expression, labeled CD4+ TRMs also decline - This is what Figure 1B suggests. Hence they would be replaced by a source that was not in the cell cycle at the time of labeling. However, is this really borne out by the experimental data (Figure 2C, middle row)? Please clarify.</p><p>(2) For potential source populations (Figure 2D): Please discuss these data critically. For example, CD4+ CD69- cells in skin and LP start with a much lower initial labeling frequency than the respective TRM populations. Could the former then be precursors of the latter?</p><p>A similar question applies to LN YFP+ cells. Moreover, is the increase in YFP labeling in naïve T cells a result of their production from proliferative thymocytes? How well does the quantitative interpretation of YFP labeling kinetics in a target population work when populations upstream show opposite trends (e.g., naïve T cells increasing in YFP+ frequency but memory cells in effect decreasing, as, at the time of labeling, non-activated = non-proliferative T cells (and hence YFP-) might later become activated and contribute to memory)?</p></disp-quote><p>These are good (and related) points. We've added some text to the discussion, paragraphs 2 and 3; we reproduce it here, slightly expanded.</p><p>Fig 1B was a schematic but did faithfully reflect the impact of any waning of YFP in precursor on its kinetic in the targets. However, in our experiments, as you noted, the kinetics of YFP in most of the precursor populations were quite flat. This was due in part to memory subsets being sustained by the increasing levels of YFP within naïve cells from the cohort of thymocytes labeled during treatment. There is also likely some residual permanent labeling of lymphocyte progenitor populations. We discussed this in Lukas Front Imm 2023. (The latter is not a problem; all that matters for our analysis is that we generate a reasonable empirical description of the label kinetics in naive cells, however it arises). YFP is therefore not cleanly washed out in the periphery; and so for models with circulating memory as the tissue precursor, the flatness of their YFP curves leads to rather flat curves in the tissues.</p><p>The mTom labelling was more informative as it was clearly diluted out of all peripheral populations by mTom-negative descendants of thymically-derived cells, as you point out in (a).</p><p>Regarding (2), re: interpreting the initial levels of labels in precursors and targets. The important point here is that YFP and mTom were induced quickly in all populations we studied; therefore our inferences regarding precursors and targets aren’t informed by the initial levels of levels in each. (Imagine a slow precursor feeding a rapidly dividing target; YFP levels in the former would start lower than those in the latter). The causal issue that we think you’re referring to would matter if one expects the targets to begin with no label at all; for instance, in our busulfan chimeric mouse model (e.g. Hogan PNAS 2015) new, thymically derived ‘labelled’ (donor) cells progressively infiltrate replete ‘unlabelled’ (host) populations. In that case, one can immediately reject certain differentiation pathways by looking the sequence of accrual of donor cells in different subsets.</p><p>The trends in YFP and mTom frequencies after treatment do matter for pathway inference, though, because precursor kinetics must leave an imprint on the target. For the case you mentioned, with opposite trends in label kinetics, such models would unlikely to be supported strongly; indeed, we never saw strong support for naïve cells (strongly increasing YFP) as a direct precursor of TRM (fairly flat).</p><p>We’ve added a condensed version of this to the Discussion.</p><disp-quote content-type="editor-comment"><p>(3) Please add a measure of variation (e.g., suitable credible intervals) to the &quot;best fits&quot; (solid lines in Figure 2).</p></disp-quote><p>Added.</p><disp-quote content-type="editor-comment"><p>(4) Could the authors better explain the motivation for basing their model comparisons on the Leave-OneOut (LOO) cross-validation method? Why not use Bayesian evidence instead?</p></disp-quote><p>Bayes factors are very sensitive to priors and are either computationally unstable if calculated with importance sampling methods, or very expensive to calculate, if ones uses the more stable bridge sampling method. (We also note that fitting just a single model here takes a substantial amount of time). Further, using BF can be unreliable unless one of the models is close to the 'true' data generating model; though they seem to work well, we can be sure that none of our models are! For us, a more tractable and real-world selection criterion is based on the usefulness of a model, for which predictive performance is a reasonable proxy. In this case the mean out-of-sample prediction error (which LOO-IC reflects) is a wellestablished and valid means of ascribing support to different models.</p></body></sub-article></article>