<?xml version="1.0" ?><!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.3 20210610//EN"  "JATS-archivearticle1-mathml3.dtd"><article xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.3" xml:lang="en">
<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">108921</article-id>
<article-id pub-id-type="doi">10.7554/eLife.108921</article-id>
<article-id pub-id-type="doi" specific-use="version">10.7554/eLife.108921.1</article-id>
<article-version-alternatives>
<article-version article-version-type="publication-state">reviewed preprint</article-version>
<article-version article-version-type="preprint-version">1.1</article-version>
</article-version-alternatives>
<article-categories><subj-group subj-group-type="heading">
<subject>Microbiology and Infectious Disease</subject>
</subj-group>
</article-categories><title-group>
<article-title>Apparent cooperativity between human CMV virions introduces errors in conventional methods of calculating multiplicity of infection</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" equal-contrib="yes">
<name>
<surname>Peterson</surname>
<given-names>Christopher</given-names>
</name>
<xref ref-type="aff" rid="a1">1</xref>
<xref ref-type="author-notes" rid="n1">*</xref>
</contrib>
<contrib contrib-type="author" equal-contrib="yes">
<name>
<surname>Miller</surname>
<given-names>Joshua</given-names>
</name>
<xref ref-type="aff" rid="a2">2</xref>
<xref ref-type="author-notes" rid="n1">*</xref>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Ryckman</surname>
<given-names>Brent J</given-names>
</name>
<xref ref-type="aff" rid="a1">1</xref>
<email>brent.ryckman@mso.umt.edu</email>
</contrib>
<contrib contrib-type="author" corresp="yes">
<contrib-id contrib-id-type="orcid">http://orcid.org/0000-0001-6572-1691</contrib-id>
<name>
<surname>Ganusov</surname>
<given-names>Vitaly V</given-names>
</name>
<xref ref-type="aff" rid="a3">3</xref>
<xref ref-type="aff" rid="a4">4</xref>
<email>vitaly.ganusov@gmail.com</email>
</contrib>
<aff id="a1"><label>1</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/0078xmk34</institution-id><institution>Department of Biological Studies, College of Humanities and Sciences, University of Montana</institution></institution-wrap>, <city>Missoula</city>, <country country="US">United States</country></aff>
<aff id="a2"><label>2</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/0524sp257</institution-id><institution>Department of Geographical Sciences, University of Bristol</institution></institution-wrap>, <city>Bristol</city>, <country country="GB">United Kingdom</country></aff>
<aff id="a3"><label>3</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/00wbskb04</institution-id><institution>Host-Pathogen Interactions program, Texas Biomedical Research Institute</institution></institution-wrap>, <city>San Antonio</city>, <country country="US">United States</country></aff>
<aff id="a4"><label>4</label><institution-wrap><institution-id institution-id-type="ror">https://ror.org/020f3ap87</institution-id><institution>Department of Microbiology, University of Tennessee</institution></institution-wrap>, <city>Knoxville</city>, <country country="US">United States</country></aff>
</contrib-group>
<contrib-group content-type="section">
<contrib contrib-type="editor">
<name>
<surname>Graw</surname>
<given-names>Frederik</given-names>
</name>
<role>Reviewing Editor</role>
<aff>
<institution-wrap>
<institution>Friedrich-Alexander-University Erlangen-Nürnberg</institution>
</institution-wrap>
<city>Erlangen</city>
<country country="DE">Germany</country>
</aff>
</contrib>
<contrib contrib-type="senior_editor">
<name>
<surname>Schoggins</surname>
<given-names>John W</given-names>
</name>
<contrib-id authenticated="true" contrib-id-type="orcid">http://orcid.org/0000-0002-7944-6800</contrib-id><role>Senior Editor</role>
<aff>
<institution-wrap>
<institution-id institution-id-type="ror">https://ror.org/05byvp690</institution-id><institution>The University of Texas Southwestern Medical Center</institution>
</institution-wrap>
<city>Dallas</city>
<country country="US">United States</country>
</aff>
</contrib>
</contrib-group>
<author-notes>
<fn id="n1" fn-type="equal"><label>*</label><p>Equal contribution</p></fn>
<fn fn-type="coi-statement"><p>Competing interests: No competing interests declared</p></fn>
</author-notes>
<pub-date date-type="original-publication" iso-8601-date="2025-11-14">
<day>14</day>
<month>11</month>
<year>2025</year>
</pub-date>
<volume>14</volume>
<elocation-id>RP108921</elocation-id>
<history>
<date date-type="sent-for-review" iso-8601-date="2025-09-09">
<day>09</day>
<month>09</month>
<year>2025</year>
</date>
</history>
<pub-history>
<event>
<event-desc>Preprint posted</event-desc>
<date date-type="preprint" iso-8601-date="2025-04-24">
<day>24</day>
<month>04</month>
<year>2025</year>
</date>
<self-uri content-type="preprint" xlink:href="https://doi.org/10.1101/2025.04.23.650360"/>
</event>
</pub-history>
<permissions>
<copyright-statement>© 2025, Peterson et al</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Peterson et al</copyright-holder>
<ali:free_to_read/>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<ali:license_ref>https://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="https://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-preprint-108921-v1.pdf"/>
<abstract>
<p>Whether infection of cells by individual virions occurs randomly or if there is some form(s) of competition or cooperativity between individual virions remains largely unknown for most virus-cell associations. Here we studied cooperativity/competition for three different strains of human cytomegalovirus (<bold>HCMV</bold>) on two different cell types (fibroblasts and epithelial cells). By titrating viral inocula concentrations in small steps over several orders of magnitude, and by using flow cytometry to precisely measure frequency of infected cells, we found that for most virus-cell associations, the frequency of cell infection increases faster than linear with an increasing inoculum concentration, indicating cooperativity between individual infecting virions. Mathematical modeling suggests that this apparent cooperativity cannot be explained by heterogeneity in either the infectivity of the individual virions or the resistance of individual cells to infection, or by simple aggregation/clumping of viral particles. Stochastic simulations of two additional alternative models that allow for i) reduction in cell resistance to infection when exposed to multiple virions, or ii) compensation in infectivity of poorly infectious virions when coinfecting cells with more infectious virions, resulted in apparent viral cooperativity. Analysis of other published datasets suggests presence of apparent viral cooperativity for HIV and vaccinia virus, infecting CRFK or HeLa cells, respectively, but not for tobacco mosaic virus forming plaques on plant leaves. We thus 1) propose a methodology to rigorously evaluate apparent cooperativity of viruses infecting target cells, and 2) demonstrate that knowing the degree of virus cooperativity for any given virus-cell combination is important for an accurate quantification of multiplicity of infection (<bold>MOI</bold>).</p>
</abstract>
<abstract abstract-type="graphical">
<title>Graphical abstract</title>
<fig id="ufig1" position="float" fig-type="figure">
<caption>
<title>Infections per cell (IU/cell) and specific infectivity (Genomes/IU) of human cytomegalovirus depend on the infecting dose.</title>
</caption>
<graphic xlink:href="650360v1_ufig1.tif" mime-subtype="tiff" mimetype="image"/>
</fig>
</abstract>
<kwd-group kwd-group-type="author">
<title>Keywords</title>
<kwd>virus cooperativity</kwd>
<kwd>human cytomegalovirus</kwd>
<kwd>mathematical model</kwd>
<kwd>flow cytometry</kwd>
<kwd>multiplicity of infection</kwd>
<kwd>infectivity</kwd>
</kwd-group>
<funding-group>
<award-group id="funding-1">
<funding-source>
<institution-wrap>
<institution-id institution-id-type="ror">https://ror.org/01cwqze88</institution-id>
<institution>National Institutes of Health</institution>
</institution-wrap>
</funding-source>
<award-id>R01AI158963</award-id>
</award-group>
<award-group id="funding-1a">
<funding-source>
<institution-wrap>
<institution-id institution-id-type="ror">https://ror.org/01cwqze88</institution-id>
<institution>National Institutes of Health</institution>
</institution-wrap>
</funding-source>
<award-id>R01AI097274</award-id>
</award-group>
</funding-group>
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<meta-name>publishing-route</meta-name>
<meta-value>prc</meta-value>
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</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>The infectivity of virus populations (i.e., virus stocks) is often reported as some value of Infectious Units (<bold>IUs</bold>), such as plaque-forming units (<bold>PFUs</bold>), per unit volume [<xref ref-type="bibr" rid="c1">1</xref>]. Such stock infectivity alone offers no insight into the potential of any individual virion to establish an infection, but instead reflects the gross phenotype of the entire virus population. Specific infectivity (<bold>SI</bold>), a ratio of the number of virions to IUs in a sample, better describes infection ability of individual virions even though it still reflects properties of the average virion. Actual SI values vary widely for different virus-cell combinations. For example, SI of Ebola virus was estimated to be around 500 particles to PFU while for varicella-zoster virus, 40,000 particles to PFU has been reported [<xref ref-type="bibr" rid="c2">2</xref>, <xref ref-type="bibr" rid="c3">3</xref>]. Wide variation can also be observed among different strains within the same viral species and are further dependent on the target cell type. For example we reported particles to IU for three strains of human cytomegalovirus (<bold>HCMV</bold>) at 11 for strain TB40e/BAC4 (<bold>TB</bold>), 217 for TR, and between 5,825 and 100,000 for Merlin (<bold>ME</bold>) when IUs were measured on fibroblasts, but 419, 352,330 and 10,529, respectively, when determined on epithelial cells (<bold>ECs</bold>) [<xref ref-type="bibr" rid="c4">4</xref>, <xref ref-type="bibr" rid="c5">5</xref>]. Although it is generally accepted that there are viral and cellular components responsible for varying SI values, the mechanisms responsible are poorly understood. Moreover, whether particle:PFU ratios <italic>&gt;</italic> 1 reflect the number of non-infectious or otherwise defective viral particles in the sample or is instead a requirement for more than one virion to establish a single infection (i.e., virion cooperation) remains largely unknown.</p>
<p>When it is assumed that a single virion can establish infection and the target cells are not limiting, it is expected that dilution of the stock will result in a proportional decrease in the frequency of productive infections [<xref ref-type="bibr" rid="c6">6</xref>–<xref ref-type="bibr" rid="c8">8</xref>]. Such a linear relationship between the number of viral particles per target cell and the frequency of cell infection is expected from a single-hit model [<xref ref-type="bibr" rid="c8">8</xref>–<xref ref-type="bibr" rid="c10">10</xref>] and is used to then perform experiments with a desired degree of cellular infection as multiplicity of infection (<bold>MOI</bold>). Indeed, classical experiments showed a linear relationship between the concentration of viral stock and number of infections (e.g., in a plaque assay) [<xref ref-type="bibr" rid="c6">6</xref>, <xref ref-type="bibr" rid="c7">7</xref>, <xref ref-type="bibr" rid="c11">11</xref>]; however, deviations from the simple, single hit model have also been observed, especially in plant viruses [<xref ref-type="bibr" rid="c7">7</xref>, <xref ref-type="bibr" rid="c10">10</xref>]. Following work on the probability of infection of a host when exposed to variable doses of pathogens, if target cells vary in their susceptibility to infection, it is expected that the frequency of cellular infection will scale sublinearly with higher viral concentrations [<xref ref-type="bibr" rid="c12">12</xref>–<xref ref-type="bibr" rid="c14">14</xref>]. In such a scenario, infection rises faster initially as highly susceptible cells are infected, but saturates at higher viral concentrations due to the difficulty of infecting the more resistant cells. Moreover, at high virus concentrations, target cells become limiting and there may even be interference between viral particles in infecting cells, including with defective interfering particles (<bold>DIPs</bold>) – a so-called Von Magnus phenomenon [<xref ref-type="bibr" rid="c15">15</xref>]. Because the frequency of cellular infection by viruses has typically been studied in plaque assays, which rely on the assumptions of single-hit kinetics, deviations of the infection rate from that predicted by the single hit model has been difficult to assess at lower virion per cell frequencies, and so it is typically assumed that at low MOI, infection rate scales linearly with the number of virions cells are exposed to [<xref ref-type="bibr" rid="c16">16</xref>]. However, if scaling of the cell infection frequency with the number of virions per cell is non-linear, experiments with MOI different from those used to titrate the viral stock may lead fewer infected cells that anticipated and then to misleading results.</p>
<p>In this study we have used HCMV to systematically study how the frequency of infection of target cells relates to the number of virions present in the culture. HCMV is an enveloped, double-stranded DNA virus in the herpesvirus family with a prevalence rate from 40% to 100%, depending on the particular population [<xref ref-type="bibr" rid="c17">17</xref>, <xref ref-type="bibr" rid="c18">18</xref>]. Infection of immunocompromized adults, such as AIDS patients, organ transplant recipients, or newborn infants can result in severe disease [<xref ref-type="bibr" rid="c19">19</xref>, <xref ref-type="bibr" rid="c20">20</xref>] and infection of otherwise healthy immunocompetent adults may contribute to increased risk of aging related conditions such as Alzheimer’s disease [<xref ref-type="bibr" rid="c21">21</xref>, <xref ref-type="bibr" rid="c22">22</xref>]. To track infection rates we used three different HCMV strains TB, TR, and ME each expressing GFP or mCherry in place of the US11 gene [<xref ref-type="bibr" rid="c23">23</xref>] and counted infected cells with flow cytometry, capable of detecting very low frequencies (<italic>∼</italic>10<sup><italic>−</italic>4</sup>) of infected cells. We also used a carefully designed strategy to dilute the viral stock with a low dilution factor (<italic>d</italic><sub><italic>f</italic></sub> = 1.3 <italic>−</italic> 1.5) and used two types of target cells — fibroblasts that are highly susceptible to HCMV infection and are a typical cell type used in experiments with HCMV and epithelial cells that are notably less susceptible to infection [<xref ref-type="bibr" rid="c24">24</xref>]. Interestingly, we found that for most virus strain-host cell combinations, increase in the number of virions per target cell leads to a nonlinear change in the frequency of infected cells, and for most tested combinations, cell infection frequency increased faster than linearly (slope <italic>n &gt;</italic> 1) with increasing numbers of virions per cell at low virion/cell numbers, a phenomenon we defined as “apparent cooperativity”. This manifests in our data as fewer than expected infections as the viral stock is increasingly diluted, presumably because virions cooperate to infect a single cell, rather than each infecting on their own. By simulating the process of cellular infection we show that apparent cooperativity cannot arise with random virus-cell interactions, and in fact, random interactions produce results predicted by the single hit model. Also, the non-linear response is not due to variability of virion infectivity or differences in target cell susceptibility to infection. We developed three alternative hypotheses to explain the observed non-linear response and simulated those interactions. Faster than linear increase in the frequency of cellular infection with increasing numbers of virions/cell could be achieved if infecting virions compensate each other’s infectivity (viral compensation hypothesis), or if a cell loses its ability to resist infection when exposed to multiple virions (accrued damage hypothesis), or, under some parameter values, when virions aggregate into clumps (aggregation hypothesis). Importantly, we show that apparent cooperativity will bias calculated MOI in experiments where infectivity of the viral stock was measured at a different MOI than that later used for experimentation. Our results also suggest that attributing specific infectivity to viral strains as an immutable trait is fundamentally incorrect as it is as much a property of target cells as it is of the virus or strain, and so references listing particle to PFU ratios should be updated to also include target cell-type and the number of virions/cell used in experiments to calculate the listed specific infectivity.</p>
</sec>
<sec id="s2">
<title>Materials and methods</title>
<sec id="s2a">
<title>Experimental data</title>
<p><bold>Cell lines</bold>. Human foreskin fibroblast cells (<bold>HFF</bold> or fibroblasts) and MRC5 cells were cultured in Dulbecco’s modified Eagle’s medium (<bold>DMEM</bold>, Sigma) supplemented with 5% heat-inactivated fetal bovine serum (<bold>FBS</bold>, Rocky Mountain Biologicals, Missoula, MT, USA) and 5% Fetalgro® (Rocky Mountain Biologicals, Missoula, MT, USA). Human retinal pigment epithelial cells (<bold>ECs</bold> or ARPE-19, American Type Culture Collection, Manassas, VA, USA) were cultured in a 1:1 mixture of DMEM and Ham’s F-12 medium (DMEM:F-12, Gibco) and supplemented with 10% FBS.</p>
</sec>
<sec id="s2b">
<title>Virus stocks</title>
<p>All HCMV strains were derived from bacterial artificial chromosome (BAC) clones. BAC clone TB40/e (BAC4, dubbed <bold>TB</bold>) was provided by Christian Sinzger (University of Ulm, Germany) [<xref ref-type="bibr" rid="c25">25</xref>]. BAC clone <bold>TR</bold> was provided by Jay Nelson (Oregon Health and Sciences University, Portland, OR, USA). BAC clone Merlin or <bold>ME</bold> (pAL1393), which contains tetracycline operator sequences within the transcriptional promoter of UL130 and UL131, was provided by Richard Stanton (Cardiff University, Cardiff, United Kingdom) [<xref ref-type="bibr" rid="c26">26</xref>]. All BAC clones were modified to express green fluorescent protein (<bold>GFP</bold>) or the monomeric red fluorescent protein mCherry (<bold>mCherry</bold>) with En passant recombineering by replacing US11 with the eGFP or mCherry gene, respectively. Infectious HCMV was recovered by electroporation of BAC-DNA into MRC5 cells which were then co-cultured with either HFF cells (TB and TR) or HFF-tet cells (ME).</p>
</sec>
<sec id="s2c">
<title>Virus titer assays</title>
<p>Confluent 6-well plates of NHDF cells were inoculated with 1.0 mL/well of GFP or mCherry-expressing recombinant virus stock, in technical duplicates, at 1:10, 1:100, and 1:1000 dilutions. After a four-hour incubation at 37C, the inoculum was aspirated and replaced with 3.0 mL 2% FBS DMEM. At 3 days post-infection, cells were rinsed with PBS, lifted with trypsin, and quenched with 10% FBS DMEM before counting with a hemocytometer. Cells were then pelleted by centrifuging at 500g for 5 minutes and fixed with 4% paraformaldehyde for 20 minutes at room temperature (<bold>RT</bold>) after aspirating media. Cells were then pelleted again at 500g and resuspended in PBS. GFP-positive cells were counted using a Life Technologies Attune NxT Acoustic Focusing Cytometer and analyzed in FlowJo v10.</p>
</sec>
<sec id="s2d">
<title>Virus Stock Dilution and Dose-Response Assay</title>
<p>Typically, serial dilutions are performed in 10-fold steps, allowing for coverage of a wide range of concentrations to increase the chance that at least one of those dilutions will result in an easily countable number of infections. We found it necessary to perform very small-fold dilutions (i.e., <italic>d</italic><sub><italic>f</italic></sub> = 1.3 <italic>−</italic> 1.5) to increase the resolution of our dose-response curves. We limited our total number of dilutions to 23, plus a mock-infection control, so that a single strain-cell type combination could be assayed with three 24-well plates, allowing for technical triplicates of each concentration. The dilution factor was tailored for each strain-cell type pair to ensure that all the aspects of the dose-response curve could be analyzed, including the highest dilutions, where infections were undetectable, through the analytical region, and including saturation. If a too-small dilution factor were used, too many of the data points would reside within the saturation region of the curve, and the lower end of the curve would not be probed. This resulted in the dilution factor in our experiments to be <italic>d</italic><sub><italic>f</italic></sub> = 1.3 <italic>−</italic> 1.5. The dilution factor was necessarily higher for strains with higher cell-free infectivity (e.g., TB) and also when using highly susceptible cells (e.g., fibroblasts). This allows the dose-response curve to quickly pass through the saturation portion and allow for complete coverage. Conversely, a strain with low infectivity or an assay on cells resistant to infection requires a smaller dilution factor, otherwise, the dilution series would quickly pass through the analytical region and not provide enough resolution for quality results.</p>
<p>We developed a methodology to allow for a consistent, low-dilution factor series, without the requirement to adjust pipette volumes during the experiment. We begin with a large volume of undiluted virus stock, typically 2 to 4 mL, and perform the dilutions as part of the inoculation process. We chose two 1000 uL pipettes and set one to 250 uL, the inoculation volume per well, and the other to 750 uL, the total inoculation volume for triplicate wells. We then measured the mass, after wetting the pipette tip, of 20<sup>0</sup>C DMEM (2%FBS) dispensed by each pipette three times to 0.001 grams. These masses were then converted to volume using the standard curve (<xref rid="tblS1" ref-type="table">Supplemental Table S1</xref> and <xref ref-type="fig" rid="figS1">Supplemental Figure S1</xref>). Three 24-well tissue culture plates were seeded at about 2 <italic>×</italic> 10<sup>4</sup> cells per well with HFFs or about 6 <italic>×</italic> 10<sup>4</sup> cells per well with ECs and allowed to grow to confluency. We aspirated media from triplicate wells, rinsed with PBS, and aspirated again just prior to inoculation.</p>
<p>Starting with undiluted virus stock, triplicate wells were inoculated, using the pipette set to 250 uL after wetting the pipette tip. Then, using the pipette set to 750 uL, 20<sup>0</sup>C DMEM (2% FBS) was added to the virus stock to replace the volume just removed and the stock was gently vortexed to mix. This diluted stock was then used to inoculate the next set of triplicate wells and the process was repeated through the 23rd set of wells. The last set of wells were mock inoculated as a control. The plates were then incubated at 37<sup>0</sup>C for 4 hours before aspirating the inoculum and replacing it with 20<sup>0</sup>C DMEM (2% FBS). The plates continued incubation at 37<sup>0</sup>C for three days before the cells were fixed for analysis.</p>
<p>As the working stock is always diluted by the same volume, using the 750 uL pipette, the starting volume dictates the dilution factor. A larger starting volume is diluted, proportionally, less than a smaller starting volume. We developed this dilution method to reduce the potential for pipetting error, first by using only two pipettes, whose volumes are not adjusted during the experiment, secondly by producing a standard curve to calculate the volumes dispensed (<xref rid="tblS1" ref-type="table">Supplemental Table S1</xref>), and thirdly by performing the dilutions in a single conical tube, thereby decreasing the chance of volume inaccuracy caused by pipetting between containers.</p>
<p>While the dose-response assay would yield valid results by reporting the data using relative concentrations, we chose to anchor the x-axis by using the same units as the resulting infection rates, reporting concentrations as virus particles (genomes) per cell. We determined the concentration of the undiluted virus stock by isolating viral DNA from 200 uL of stock and utilizing qPCR (see below), to count and then calculate the number of viral genomes per 1 mL of stock. Using the pipette volumes determined with our standard curve, we could then calculate the viral genomes present in the inoculant in a well at each concentration.</p>
</sec>
<sec id="s2e">
<title>DMEM Volume Standard Curve</title>
<p>DMEM (2% FBS) at 20<sup>0</sup>C was dispensed using a 1.0 ml serological pipette (FisherBrand cat num 13-678-11B, 2% tolerance) in triplicates at 1000, 900, 800, 750, 700, 600, 500, 400, 300, 250, 200, and 100 ul volumes and weighed to 0.0001 grams. This data was used to create a standard curve within GraphPad Prism and the dose-response assay volumes were determined by interpolation using that software.</p>
</sec>
<sec id="s2f">
<title>Flow cytometry</title>
<p>We performed preliminary experiments to determine that measuring the frequency of infected cells after first round of infection is best done at three days after exposure of cells to the virus (<xref rid="figS2" ref-type="fig">Supplemental Figures S2</xref> and <xref ref-type="fig" rid="figS3">S3</xref>). Three days post infection cells were washed with PBS and lifted with trypsin. Trypsin was quenched with DMEM containing 10% FBS and cells were spun at 500xg for 5 min at RT. Cells were fixed with 4% paraformaldehyde (in PBS) for 15 min at RT before spinning as before and aspirating the fixing buffer. Cells were resuspended in 1 mL PBS and analyzed using an Attune NxT flow cytometer. Cells were separated from debris using FSC-A and SSC-A to gate, and single cells were gated using FSC-W and FSC-H. GFP+ and mCherry+ gates were drawn using mock-infected cells as negative controls.</p>
</sec>
<sec id="s2g">
<title>qPCR</title>
<p>To quantify the viral particle/genome concentration in each stock, a real-time quantitative PCR (qPCR) assay was used to quantify viral DNA molecules, performed as previously described (Zhou 2015). A PureLink Viral RNA/DNA mini kit (Thermo Scientific) was used to isolate viral DNA and a sequence within UL83, conserved among ME, TR, and TB, was chosen as the amplicon. Viral genomes were quantified by SYBR green qPCR. Standard curves were performed using serial dilutions of a single PCR DNA product containing the sequence of the viral UL83. Sample Cq values were fitted to the standard curve to determine viral genomes per 1.0 mL of stock and reported as viral genomes per mL. We then used the value of genomes per mL and known concentration of target cell per mL to calculate genomes/cell (<xref rid="fig1" ref-type="fig">Figure 1</xref>).</p>
<fig id="fig1" position="float" fig-type="figure">
<label>Figure 1:</label>
<caption><title>Experimental design and alternative hypotheses for the apparent cooperativity between viruses infecting the same cell.</title>
<p><bold>A</bold>: We diluted stock of different HCMV strains, cloned with reporter genes for GFP or mCherry, up to 23 times and inoculated these dilutions into culture of fibroblasts or epithelial cells. Concentration of virions was determined for each stock using qPCR and the concentration at each dilution was then calculated using the dilution factor in each experiment. We then used flow cytometry to quantify the frequency of target cells expressing GFP or mCherry at 3 days post infection. Kinetics of expression of GFP or mCherry in infected cells over time or at different viral stock dilutions are shown in <xref ref-type="fig" rid="figS2">Supplemental Figures S2</xref> and <xref ref-type="fig" rid="figS3">S3</xref><bold>. B</bold>: Three alternative mathematical models aimed to explain apparent cooperativity of HCMV. i) Viral clumping model in which infection of cells mostly occurs when a cell is exposed to a viral “clump” consisting of several, independently acting viral particles with the clump size following a distribution. In the model, virions in a clump attempt to infect the cell independently. ii) Accrued damage model in which exposure of a given target cell by several virions (chosen from Poisson distribution for a given viral concentration) reduces the ability of the cell to resist viral infection (i.e., reduces cell resistance parameter indicated by the level of cell transparency in the cartoon). iii) Viral compensation model in which exposure of a cell to several virions (chosen from a Poisson distribution) with different infectivities increases infectivity of all virions to its highest value in the group of virions.</p></caption>
<graphic xlink:href="650360v1_fig1.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
</sec>
<sec id="s2h">
<title>Dynamic Light Scattering (DLS)</title>
<p>Virus stock particle size distributions were measured using a Zetasizer Nano ZS Zen3600 (Malvern Instruments Ltd., Malvern, UK) set at 37<sup>0</sup>C. Virus stocks were diluted 1:3 with DMEM/F-12 without Phenol Red (Gibco, Life Technologies Corp., N.Y., USA), pipetted up and down 10 times to mix, and incubated at 37<sup>0</sup>C for 1 hour. Samples were not filtered, to replicate typical inoculation conditions. Three replicate dilutions were prepared for each stock and analyzed with Zetasizer software (v7.10) using the general size model and viscosity preset for DMEM without phenol.</p>
</sec>
<sec id="s3">
<title>Mathematical Models</title>
<sec id="s3a">
<title>Analytical models</title>
<p>To investigate how the probability of cell infection depends on the number of virions/genomes per cell we used a generic “powerlaw” model similar to our previous work [<xref ref-type="bibr" rid="c27">27</xref>, <xref ref-type="bibr" rid="c28">28</xref>]:
<disp-formula id="eqn1">
<graphic xlink:href="650360v1_eqn1.gif" mimetype="image" mime-subtype="gif"/>
</disp-formula>
where <italic>V</italic> is number of genomes per cell in the well, and <inline-formula id="inline-eqn-1"><inline-graphic xlink:href="650360v1_inline1.gif" mimetype="image" mime-subtype="gif"/></inline-formula> and <italic>n</italic> are model parameters. Parameter <italic>n</italic> denotes a type of interactions between different virions infecting individual cells. Specifically, <italic>n &lt;</italic> 1 implies competition and <italic>n &gt;</italic> 1 implies cooperativity between individual virions for infection, while <italic>n</italic> = 1 indicates that infection of cells proceeds independently (“null” or “single-hit” model, [<xref ref-type="bibr" rid="c9">9</xref>, <xref ref-type="bibr" rid="c10">10</xref>, <xref ref-type="bibr" rid="c27">27</xref>, <xref ref-type="bibr" rid="c28">28</xref>]). Infectivity of a single genome is then given as <italic>p</italic>(1) = e<sup><italic>−λ</italic></sup> or <italic>λ</italic> = <italic>−</italic> ln(1 <italic>− p</italic>(1)).</p>
<p>While the basic “powerlaw” model (<bold>eqn. (1)</bold>) allows for a saturation in the frequency of infected cells at high genome/cell concentrations it only allows such saturation at one (i.e., lim<sub><italic>V →∞</italic></sub> <italic>p</italic>(<italic>V</italic>) = 1 in <bold>eqn. (1)</bold>). Furthermore, this model does not describe saturation in the the infection frequency at low genome/cell concentrations. In some of our experiments we observed both: saturation at low genomes/cell (most likely due to few false positive events in the flow cytometer) and saturation below one at high genomes/cell (mechanism is unclear). Therefore, we propose an alternative, 4 parameter model that takes these two limits into account:
<disp-formula id="eqn2">
<graphic xlink:href="650360v1_eqn2.gif" mimetype="image" mime-subtype="gif"/>
</disp-formula>
where <italic>p</italic><sub>min</sub> and <italic>p</italic><sub>max</sub> are the minimal and maximal frequencies of infection observed in a given experiment.</p>
<p>If the relationship between viral inoculum (genomes/cell) and frequency of infection is known (i.e., estimated from the data), the relationship can be used to predict how the infectious titer depends on the inoculum. Infectious titer (in infection units (<bold>IUs</bold>) per mL of culture) is typically found by infecting target cells (given in concentration <italic>C</italic> as cells/mL) with a given concentration of the viral suspension <italic>G</italic> (given, for example, as viral genomes per mL). If the probability of a cell to become infected when exposed to <italic>V</italic> virions (<italic>V</italic> = <italic>G/C</italic> or <italic>G</italic> = <italic>V C</italic>) is given by <bold>eqn. (1)</bold>, infectious titer is then
<disp-formula id="eqn3">
<graphic xlink:href="650360v1_eqn3.gif" mimetype="image" mime-subtype="gif"/>
</disp-formula>
For a given infectious titer <italic>I</italic>, multiplicity of infection (<bold>MOI</bold>) is then calculated as the ratio of the titer to the cell concentration used for infection (<italic>C</italic><sub>2</sub>):
<disp-formula id="eqn4">
<graphic xlink:href="650360v1_eqn4.gif" mimetype="image" mime-subtype="gif"/>
</disp-formula>
Note that MOI is often calculated for a different target cell cell concentration in experiments than that which was used to titrate the virus stock (i.e., <italic>C</italic> ≠ <italic>C</italic><sub>2</sub>) resulting in different numbers of genomes/cell in different experiments.</p>
</sec>
<sec id="s3b">
<title>Agent-based simulations</title>
<p>To simulate how individual virions infect cells we developed two alternative algorithms: cell-centric and virus-centric. In the cell-centric simulations we focus on individual cells and track if they are infected or not, and in virus-centric simulations we focus on individual virions as to whether it infects a cell or not. Most of our simulations are done using cellcentric approach because ultimately we focus on the probability of a cell to be infected, irrespectively by which virion. We create cell and virion populations by creating cell and virion objects in python or Mathematica. In most simulations, we consider 170,000 cells and 16,000-16,000,000 virions (these values did vary between simulations to reflect differences in experiments). Each cell and virion is given a randomly-generated “resistance” and “infectivity” levels, respectively, which are taken from a distribution (typically normal but we also investigated other, long-tailed distributions such as lognormal). Most simulations were constructed with Python (ver. 3.7.2) where we defined Cell and Virion classes as follows:
<disp-formula id="ueqn1">
<graphic xlink:href="650360v1_ueqn1.gif" mimetype="image" mime-subtype="gif"/>
</disp-formula>
In a cell-centric simulation, when a cell is “visited” by a virion, we determine if the cell becomes infected or not using probability function dependent on the difference between values for virion infectivity <italic>I</italic> and cell resistance <italic>R</italic> (Algorithm 1). Given the number of virions (or genomes) per cell in a given well, a given cell can be exposed to (visited by) multiple virions. To account for the number of virions a given cell is exposed to, we generated an extra loop and determined the number of virions that would visit the cell from a Poisson distribution whose mean would be a function <italic>f</italic> of the genomes/well. The functions <italic>f</italic> also involves a “vMax” term, a large positive integer, which divides the GENOMES/WELL quantity to make it smaller, so that simulations can be run on a personal computer (Algorithm 2).</p>
</sec>
<sec id="s3c">
<title>Clumping hypothesis</title>
<p>In the basic model the number of virions a given cell is exposed to follows a Poisson distribution. However, it is well recognized that viruses may form aggregates (or clumps) are they produced by infected cells, and distribution of virions in each of the clumps/aggregates may deviate from, for example, the Poisson distribution [<xref ref-type="bibr" rid="c29">29</xref>]. In the absence of information of what the clump size distribution is, we simulated viral clumps in two alternative approaches. In our pythonbased simulations, we use SciPy’s minimize function to approximate the ratio of the number of clumps of a given size to the total number of clumps to the Poisson probability density function (<bold>PDF</bold>) value of that clump size. The minimizer has the constraint that the number of total virions, i.e. the sum of the number of clumps times clump size, must be equal to the amount of genomes in the well. After obtaining the number of clumps of each size, each virion is assigned a numerical “clump ID”, and if two or more virions share the same clump ID, then they are part of the same clump. The number of clumps of various sizes is determined by Poisson distribution (<italic>P</italic>) with mean <italic>λ</italic>, where <italic>P</italic> (<italic>k</italic>), <italic>k</italic> is a certain clump size, represents the fraction of virions that are found in clumps of that size. A clump size of 1 represents a single virion. However, because Poisson distributions have domain 0, 1, 2, 3, …, we took 0 to represent a clump size of 1, 1 to represent clump size 2, and so on (Algorithm 3).</p>
<statement id="alg1">
<label>Algorithm 1:</label>
<p><bold>Cell-centric simulation sketch</bold>. In this scheme, we determine a probability of a cell to become infected when exposed to one virion. When the two interact, their intrinsic infectivity and resistance values are compared, and if the infectivity is greater than the resistance, the cell is infected. Otherwise, a random number between 0 and 1 is generated and compared to the value <italic>P</italic><sub><italic>i</italic></sub> = e<sup><italic>γ</italic>(<italic>I−R</italic>)</sup> where <italic>I</italic> is the virion infectivity and <italic>R</italic> is cell resistance. If <italic>P</italic><sub><italic>i</italic></sub> is greater than the random number, then the cell becomes infected, otherwise, cell remains uninfected. In simulations, <italic>γ</italic> = 0.45 unless noted otherwise (<xref rid="tbl1" ref-type="table">Table 1</xref>).</p>
<p><fig id="alg1a" position="float" fig-type="figure">
<graphic xlink:href="650360v1_alg1.tif" mimetype="image" mime-subtype="tiff"/>
</fig></p>
</statement>
<statement id="alg2">
<label>Algorithm 2:</label>
<p><bold>Pseudocode to simulate exposure of a cell to multiple viruses</bold>. This code shows a loop implementing the Poisson distribution to determine the number of virions that will attempt to infect a cell. This loop is used inside the cell-centric simulation so that instead of each cell being visited by just one virion, every cell is visited by <monospace>num virions</monospace> virions.</p>
<p><fig id="alg2a" position="float" fig-type="figure">
<graphic xlink:href="650360v1_alg2.tif" mimetype="image" mime-subtype="tiff"/>
</fig></p>
</statement>
<statement id="alg3">
<label>Algorithm 3:</label>
<p><bold>Pseudocode to model viral clumps</bold>. In this model, clump distributions and clump IDs are created according to a Poisson distribution, <italic>P</italic> (<italic>i</italic>). First, the maximum clump size is chosen by locating the integer where the CDF of the Poisson distribution is greater than 0.99. Next, we choose the number of clumps of size 1, 2, …, max such that the ratio of the number of clumps of size <italic>i</italic> divided by the total number of clumps in the sample is as close to <italic>P</italic> (<italic>i</italic>) as possible. To do this, we use minimize the error between <italic>P</italic> (<italic>i</italic>) and <inline-formula id="inline-eqn-2"><inline-graphic xlink:href="650360v1_inline2.gif" mimetype="image" mime-subtype="gif"/></inline-formula> using the negative log likelihood error function <monospace>NegLogLike</monospace> in <monospace>python</monospace>. After the best values of <italic>NUM CLUMPS</italic>[<italic>i</italic>] are obtained, we assign every clump a unique integer ID which applies to every virion inside that clump.</p>
<p><fig id="alg3a" position="float" fig-type="figure">
<graphic xlink:href="650360v1_alg3.tif" mimetype="image" mime-subtype="tiff"/>
</fig></p>
</statement>
<p>In our alternative, Mathematica-based simulations, we used one-inflated geometric distribution to simulate the number of virions in different clumps, we varied the fraction of clumps that would have one genome and allowed other clumps to have larger mean size (e.g., 50 virions/clump). Specifically, we assumed that a fraction <italic>f</italic><sub>1</sub> of clumps have exactly 1 virion and 1 <italic>− f</italic><sub>1</sub> clumps follow geometric distribution <italic>P</italic> (<italic>k</italic>) = <italic>p</italic>(1 <italic>− p</italic>)<sup><italic>k</italic></sup> with <italic>k</italic> = 1, 2, … where <italic>p</italic> determines skewness of the distribution. We then assigned every virions in the library of 10<sup>5</sup> virions to each clump, and in simulations, when <italic>v</italic> virions attempt to infect cells (chosen from Poisson distribution for a given dilution of the stock), all virions belonging to the clump IDs of the infecting virions also attempt to infect the cell.</p>
<p>To complement our theoretical assumption that clump size distribution follows Poisson or geometric distribution, we also used experimentally measured distribution of clumps in a given viral stock dilution (<xref rid="figS8" ref-type="fig">Supplemental Figure S8</xref>). For infection of a cell, we sampled the clump size from experimental distribution (<xref rid="figS9" ref-type="fig">Supplemental Figure S9</xref>) and then calculated the number of virions in the clump using
</p>
<table-wrap id="tbl1" orientation="portrait" position="float">
<label>Table 1:</label>
<caption><title>Parameters used in simulations.</title>
<p>“Default value” indicates the value of the parameter unless otherwise specified in specific simulations.</p></caption>
<graphic xlink:href="650360v1_tbl1.tif" mimetype="image" mime-subtype="tiff"/>
</table-wrap>
<disp-formula id="eqn5">
<graphic xlink:href="650360v1_eqn5.gif" mimetype="image" mime-subtype="gif"/>
</disp-formula>
<p>where <italic>D</italic> is the clump diameter, <italic>d</italic> = 230 nm is the diameter of HCMV virion [<xref ref-type="bibr" rid="c30">30</xref>, <xref ref-type="bibr" rid="c31">31</xref>], and 0.64 is the packing efficiency of randomly distributed spheres [<xref ref-type="bibr" rid="c32">32</xref>, <xref ref-type="bibr" rid="c33">33</xref>]. The number of virions per clump scales nonlinearly with the clump size, i.e., a clump of size <italic>D</italic> = 2<italic>d</italic> = 460 nm would have 5 virions, and clump of size <italic>D</italic> = 3<italic>d</italic> = 690 nm would have 17 virions.</p>
</sec>
<sec id="s3d">
<title>Accrued damage hypothesis</title>
<p>Exposure of a cell to a virion may trigger generation of antiviral response that may reduce the overall resources the cell has. We hypothesize that for each virion that attempts to infect a cell but fails to do so, the level of cell resistance <italic>R</italic> decreases by a value <italic>β</italic>. This effectively increases infection chances of the next virion in the collection of virions attempting to infect a given cell.</p>
</sec>
<sec id="s3e">
<title>Viral compensation hypothesis</title>
<p>In this scheme, a collection of virions will attempt to infect a cell. We increase infectivity of all infecting virions in the collection to a value proportional to the maximal infectivity of virions in the collection max(<italic>I</italic><sub><italic>j</italic></sub>) and the current infectivity of the virion <italic>I</italic><sub><italic>i</italic></sub> as
<disp-formula id="eqn6">
<graphic xlink:href="650360v1_eqn6.gif" mimetype="image" mime-subtype="gif"/>
</disp-formula>
and in most simulations we allowed <italic>κ</italic> = 0 (i.e., infectivity of each virion in the collection of all virions attempting to infect a cell increases to a maximum value in the collection, <xref rid="tbl1" ref-type="table">Table 1</xref>).</p>
</sec>
<sec id="s3f">
<title>Virus-centric simulations</title>
<p>We also simulated virus infection using a virus-centric approach, where each virion in the initial pool determined by genomes/well in the data, gets one chance to infect a cell. These virus-centric simulations gave the same prediction on how the probability of cell infection scales with the number of virions per cell for the null model and thus are not presented here.</p>
</sec>
</sec>
<sec id="s4">
<title>Statistics</title>
<p>To estimate parameters of the models relating the cell infection probability and the number of virions in culture we use a likelihood approach [<xref ref-type="bibr" rid="c27">27</xref>, <xref ref-type="bibr" rid="c28">28</xref>]. Specifically, the negative log-likelihood of the model (e.g., <bold>eqn. (1)</bold>) is
<disp-formula id="eqn7">
<graphic xlink:href="650360v1_eqn7.gif" mimetype="image" mime-subtype="gif"/>
</disp-formula>
where <italic>V</italic><sub><italic>i</italic></sub> and <italic>I</italic><sub><italic>i</italic></sub> are the number of genomes (or virions) per cell and the proportion of infected cells in the culture, respectively, and <italic>i</italic> denotes sample. Because most data did not exhibit a linear relationship between virion concentration and infection probability we fitted the models to subsets of data best matching the linear relationship on a log-log scale. However, we also fitted an extended powerlaw model (<bold>eqn. (2)</bold>) that accounts for saturation in infection probability to the whole dataset. We used the same approach to estimate degree of apparent cooperativity <italic>n</italic> in simulations.</p>
</sec>
</sec>
<sec id="s5">
<title>Results</title>
<sec id="s5a">
<title>Infection of target cells by fluorescently-tagged HCMV strains often deviates from a single hit model</title>
<p>In our previous studies, we showed that the specific infectivity (<bold>SI</bold>) values of several strains of HCMV were dependent both on the choice of target cell type and on the cell type used to produce the virus stock [<xref ref-type="bibr" rid="c4">4</xref>]. We also noted that even when the same producer cell type and target cell type were used, titer and, consequently, SI values could differ between assays performed with different inoculation concentrations. This concentration-dependent effect suggested that virions may be either cooperating or interfering with each other while infecting a target cell. To examine whether these differences were caused by cooperation between virions (i.e., during coinfection of target cells by multiple virions), we performed small-step titration assays to produce high-resolution dose-response curves for HCMV strains TB, ME, and TR, on two target cell types often used in research: ARPE-19 retinal pigment epithelial cells (epithelial cells) and human foreskin fibroblasts (fibroblasts). Our three virus strains express either GFP or mCherry proteins in place of the US11 gene and the rate of infection was determined by counting either GFP+ or mCherry+ cells by flow cytometry at three days post infection (dpi) [<xref ref-type="bibr" rid="c23">23</xref>]. We chose to quantify infection rates at 3 dpi because HCMV progeny virions are typically released around day 3 [<xref ref-type="bibr" rid="c34">34</xref>–<xref ref-type="bibr" rid="c36">36</xref>] and even though expression levels of GFP or mCherry in cells infected by progeny virus would typically be very low at 1 dpi, robustly detecting infected cells very early after infection may not be fully feasible in our experimental system (<xref rid="figS2" ref-type="fig">Supplemental Figures S2</xref> and <xref ref-type="fig" rid="figS3">S3</xref>). Furthermore, we noted that cell infection rate did not strongly depend on the genome/cell concentration at very low genomes/cell (e.g. TB-GFP on fibroblast, <xref rid="fig2" ref-type="fig">Figure 2A</xref>) further suggesting that such low frequency events may contain false positives (<xref rid="figS2" ref-type="fig">Supplemental Figures S2</xref> and <xref ref-type="fig" rid="figS3">S3</xref>). Yet, for many strain-cell combinations, infection rates of <italic>≥</italic> 10<sup><italic>−</italic>4</sup> were robustly detected (<xref rid="fig2" ref-type="fig">Figure 2</xref>).</p>
<fig id="fig2" position="float" fig-type="figure">
<label>Figure 2:</label>
<caption><title>Apparent cooperativity of human CMV strains at infecting different target cells.</title>
<p>We performed experiments by infecting either fibroblasts (HFF) or epithelial cells (ARPE-19) with three different strains of HCMV (ME, TB, TR) expressing two different reporter genes (GFP or mCherry, see <xref ref-type="fig" rid="fig1">Figure 1A</xref>). We then fitted a “powerlaw” model (<bold>eqn. (1)</bold>) to subsets of these data (shown in color) and calculated parameter <italic>n</italic>, indicating a degree of apparent cooperativity of the virions at infecting cells (<italic>n</italic> = 1 – no cooperativity, <italic>n &gt;</italic> 1 – apparent cooperativity, see Materials and Methods for more detail). For each estimate we also show <italic>p</italic> value from the likelihood ratio test when comparing the powerlaw model fit to the single-hit (<italic>n</italic> = 1) model fit. The solid black lines show the predictions of the mathematical model (<bold>eqn. (1)</bold>) in the range of data that was used in model fitting, the data not used in fitting are shown in gray, and NA denotes an experiment that could not be performed due to lack of cell infection (TR.mCherry on ECs). All experiments were performed at least twice. Data are shown as markers and model fits as black lines. Diagonal dashed lines represent the slope of one (i.e., single hit model). In panel A, we show infectivity of a single genome, <italic>p</italic>(1) from <bold>eqn. (1)</bold>. Fits of the extended powerlaw model (<bold>eqn. (2)</bold>) are shown in <xref ref-type="fig" rid="figS4">Supplemental Figure S4</xref>.</p></caption>
<graphic xlink:href="650360v1_fig2.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<p>All strain-cell combinations displayed saturation at high inoculum concentrations, although none achieved a higher than 98% infection rate. This is not unexpected, as we did not synchronize cell cycle before inoculation and some cells may not be fully susceptible to infection. Also, exposure to a large number of virus particles may render some cells highly resistant to infection [<xref ref-type="bibr" rid="c12">12</xref>]. Interestingly, we noted a decline in the infection rate at higher concentrations for ME and TR strains but not for TB (<xref rid="fig2" ref-type="fig">Figure 2</xref>); such a decline in the infection rate is inconsistent with a single hit model.</p>
<p>To more rigorously characterize deviation of the infection rate from a single hit (null) model, we fitted a “powerlaw” model that allows for a nonlinear change in the infection rate with increasing genomes/cell to the data (see Materials and methods for detail). In this analysis, we sub-selected data that fall on a line on a log-log scale and estimated parameter <italic>n</italic> characterizing how cell infection rate scales with the larger virions/cell and parameter <italic>p</italic>(1) representing infectivity of a single genome (<xref rid="fig2" ref-type="fig">Figure 2A</xref>). The range for which the log of infection/cell scaled linearly with log of genomes/cell varied by specific strain-cell type combinations ranging only 1 order of magnitude for ME-GFP on epithelial cells (<xref rid="fig2" ref-type="fig">Figure 2D</xref>) and 3 orders for TB-GFP on epithelial cells (<xref rid="fig2" ref-type="fig">Figure 2E</xref>). Importantly, we found that for most HCMV strains-target cell combinations estimated <italic>n &gt;</italic> 1 (<xref rid="fig2" ref-type="fig">Figure 2</xref> and <xref rid="tblS2" ref-type="table">Supplemental Table S2</xref>) suggesting that for a range of genomes/cell, increasing the virus concentration results in a faster than linear increase in the probability of a cell to be infected. Values <italic>n &gt;</italic> 1 implies cooperation between virions when infecting cells and we call this phenomenon “apparent cooperativity”. Fitting a more complex model that allows for limit of detection of infected cells at low genomes/cell and saturation in the infection rate at lower than one values at high genomes/cell also resulted in <italic>n &gt;</italic> 1 for most strain-cell combinations although there were clear biases in the model fit of some data (<xref rid="figS4" ref-type="fig">Supplemental Figure S4</xref>). We also found <italic>n &gt;</italic> 1 when fitting the powerlaw model (<bold>eqn. (1)</bold>) to subsets of data defined by a sliding window further supporting existence of apparent cooperativity for a wide range of genomes/cell values (<xref rid="figS5" ref-type="fig">Supplemental Figure S5</xref>). Interestingly, we also found evidence of apparent cooperativity after fitting the powerlaw model to data available on infection of target cells by HIV and vaccinia virus, but not on formation of viral plaques on leaves inoculated with tobacco mosaic virus (<xref rid="figS6" ref-type="fig">Supplemental Figures S6</xref> and <xref rid="figS7" ref-type="fig">S7</xref>).</p>
<p>While the degree of apparent cooperativity, <italic>n</italic>, and infectivity of a single genome, <italic>p</italic>(1), was dependent on the specific strain-cell type combinations, some patterns were evident. In particular, all strains had a higher degree of cooperativity and higher genome infectivity on fibroblasts than those on epithelial cells (<xref rid="fig3" ref-type="fig">Figure 3A</xref>&amp;<xref rid="fig3" ref-type="fig">D</xref>). HCMV TB was the strain with a highest genome infectivity <italic>p</italic>(1) (<xref rid="fig3" ref-type="fig">Figure 3F</xref>) and demonstrated highest degree of cooperativity (<xref rid="fig3" ref-type="fig">Figure 3C</xref>); we detected the highest degree of apparent cooperativity for TB-GFP on fibroblasts (<italic>n</italic> = 1.61, <xref rid="fig2" ref-type="fig">Figure 2B</xref>).</p>
<fig id="fig3" position="float" fig-type="figure">
<label>Figure 3:</label>
<caption><title>All HCMV strains show reduced infectivity and reduced apparent cooperativity when infecting epithelial cells.</title>
<p>We plot the relationship between estimated power parameter <italic>n</italic> (<bold>A</bold>-<bold>C</bold>) or virion infectivity (infectivity of a single genome, <italic>p</italic>(1), <bold>D</bold>-<bold>F</bold>), and other viral and cell characteristics such as target cell type (<bold>A&amp;D</bold>), reporter gene (<bold>B&amp;E</bold>), and HCMV strain (<bold>C&amp;F</bold>). Parameter <italic>n</italic> indicates cooperativity in virus infection of cells (estimates are given in individual panels in <xref rid="fig2" ref-type="fig">Figure 2</xref>). Comparisons were done using paired t-test. In panel <bold>G</bold> we show the relationship between estimated virion infectivity <italic>p</italic>(1) and apparent cooperativity <italic>n</italic> estimated for different strain/cell combinations; we also show the linear fit and <italic>p</italic> value from the test of no relationship.</p></caption>
<graphic xlink:href="650360v1_fig3.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<p>Importantly, the type of the reporter gene had no influence on either <italic>n</italic> or <italic>p</italic>(1) suggesting that a nonlinear relationship between virion concentration and cell infection rate was not due to different virus modifications (<xref rid="fig3" ref-type="fig">Figure 3B&amp;E</xref>). Interestingly, when pooling all estimates together there was a strong positive relationship between virion infectivity <italic>p</italic>(1) and degree of apparent cooperativity <italic>n</italic> (<xref rid="fig3" ref-type="fig">Figure 3G</xref>). Taken together, our careful titrating of stocks of three different strains of HCMV revealed a highly nonlinear relationship between virion concentration and the cell infection probability that deviates from predictions of a commonly assumed single hit model.</p>
</sec>
<sec id="s5b">
<title>Random infection model cannot explain apparent cooperativity of HCMV strains</title>
<p>Finding that a probability of cell infection increases faster than linearly with virion concentration was unexpected and to explore potential mechanisms of such apparent viral cooperativity we created a computational model in which we track infection of cells by virions (see <bold>Algorithms 1–2</bold>). We created an array for cells, each with different level of resistance, and an array of virions, each with different degree of infectivity [<xref ref-type="bibr" rid="c37">37</xref>]. In this model we attempted to mimic experiments by using similar (but scaled) numbers of target cells per well and by varying the number of virions present in a well. We then simulated dilution of viral stock resulting in different numbers of virions/well (and thus, virions/cell) and by using Poisson distribution calculated the number of virions each cell in the population would be exposed to (Algorithm 2). Assuming that each virion attempts to infect a cell independently of other virions and considering that infection event is a random process dependent on actual values of cell’s resistance and virion’s infectivity (<xref rid="tbl1" ref-type="table">Table 1</xref>) we found that this random infection/null model predicts linear increase in the cell infection probability with increasing virions/cell (<xref rid="fig4" ref-type="fig">Figure 4A</xref>), as predicted by a single hit model.</p>
<fig id="fig4" position="float" fig-type="figure">
<label>Figure 4:</label>
<caption><title>Heterogeneity in virion infectivity and/or susceptibility to infection of target cells and aggregation of virions does not result in apparent cooperativity in simulations.</title>
<p>We developed simulations in which individual virions vary in their infectivity and individual cells vary in their resistance (or susceptibility) to infection (see Materials and methods for detail). We then sampled individual virions and cells randomly assuming different ratio of virions (genomes) per target cell and calculated how frequency of infected cells changes with increasing number of viral genomes per cell for a null model (<bold>A</bold>), clumping model in which virions aggregate (<bold>B</bold> and <xref ref-type="fig" rid="fig1">Figure 1Bi</xref>), accrued damage model, in which individual virions attaching to a cell reduces its resistance (<bold>C</bold> and <xref ref-type="fig" rid="fig1">Figure 1Bii</xref>), and viral compensation model in which virions attaching to a cell acquire infectivity of the most infectious virion (<bold>D</bold> and <xref ref-type="fig" rid="fig1">Figure 1Biii</xref>, see Materials and methods for more detail). We simulated infection of target cells by virions according to these models and searched for parameter combinations that qualitatively matched experimental data for HCMV-TB-GFP infection of fibroblasts (with <italic>n</italic> = 1.60, <xref ref-type="fig" rid="fig2">Figure 2B</xref>). We fitted the powerlaw model (<bold>eqn. (1)</bold>) to the results of simulations using likelihood approach (<bold>eqn. (7)</bold>) and estimated the degree of apparent viral cooperativity (<italic>n</italic>) for linear parts of the data at low genome/cell values (shown by red lines). Averages are shown by markers and gray areas indicate the range of values in simulations. Parameters used in simulations are given in <xref rid="tbl1" ref-type="table">Table 1</xref>. Note that to model viral clumps we assumed that clump size followed Poisson distribution; other details are given in Material and methods section.</p></caption>
<graphic xlink:href="650360v1_fig4.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<p>We have tried multiple combinations of parameters in our simulations and also developed simulations from “virus-centric” perspective; none of the simulations resulted in apparent cooperativity with <italic>n &gt;</italic> 1. Because it is possible that there we may have missed just the right set of parameters that would give us indication of apparent cooperativity, we turned to analytical derivations. Let us assume that infection of target cells follows a mass action law, <italic>p</italic>(<italic>V</italic>) = 1 <italic>−</italic> e<sup><italic>−λV</italic></sup> (i.e., with <italic>n</italic> = 1 in <bold>eqn. (1)</bold>); here <italic>λ</italic> indicates susceptibility in the target cell to the infection. Let us also assume that target cells vary in their susceptibility to infection according to a distribution <italic>f</italic> (<italic>λ</italic>). The the probability of a cell to be infected when exposed to <italic>V</italic> virions/genomes is
<disp-formula id="eqn8">
<graphic xlink:href="650360v1_eqn8.gif" mimetype="image" mime-subtype="gif"/>
</disp-formula>
where <italic>L</italic><sub><italic>f</italic></sub> (<italic>V</italic>) is the Laplace transform for <italic>f</italic>. Now we can use Taylor’s expansion for <italic>L</italic><sub><italic>f</italic></sub> (<italic>V</italic>)
<disp-formula id="eqn9">
<graphic xlink:href="650360v1_eqn9.gif" mimetype="image" mime-subtype="gif"/>
</disp-formula>
where <inline-formula id="inline-eqn-3"><inline-graphic xlink:href="650360v1_inline3.gif" mimetype="image" mime-subtype="gif"/></inline-formula> is the average of the distribution <italic>f</italic> (<italic>λ</italic>). Then the infection probability from <bold>eqn. (8)</bold> becomes
<disp-formula id="eqn10">
<graphic xlink:href="650360v1_eqn10.gif" mimetype="image" mime-subtype="gif"/>
</disp-formula>
which proves that in a population of target cells with heterogenous susceptibility to infection at low genome/cell concentrations, the probability of infection scales linearly with genome/cell. This result is independent whether viruses vary in their infectivity.</p>
</sec>
<sec id="s5c">
<title>Three alternative hypotheses to explain apparent cooperativity</title>
<p>We investigated what alternative mechanisms may result in deviation of cell infection from that predicted by the single-hit model. One hypothesis was that individual virions may not simply infect a cell independently but form aggregates (or clumps) and such clumping may increase chances to infect a cell (<xref rid="fig1" ref-type="fig">Figure 1A</xref> and [<xref ref-type="bibr" rid="c16">16</xref>]). We therefore extended our basic model to allow virions to clump, and in this first “clumping model” we assumed that clump size distribution follows a Poisson distribution with the mean <italic>λ</italic> that was scaled (with a parameter vMax<sub><italic>c</italic></sub>) to the calculated number of genomes/well (<xref rid="tbl1" ref-type="table">Table 1</xref>). We then used Poisson distribution to sample clumps and allowed virions in the clump to independently attempt to infect a cell. In contrast with the null model, the Poisson clumping model predicted nonlinear change in the frequency of infected cells with a large increase in infection frequency at about 2 genomes/cell (<xref rid="fig4" ref-type="fig">Figure 4B</xref>). However, at lower genomes/cell values, the model predicted linear relationship between infection frequency and virion concentration, similar to the null model. Thus, virions clumping, at least at these tested model parameters, did not result in apparent cooperativity at small genomes/cell values.</p>
<p>We next explored alternative hypotheses that include some type of “memory” of sequence of interactions between a target cell and individual virions. In particular, we found inspiration in the remarkable experiments by Stiefel et al. [<xref ref-type="bibr" rid="c38">38</xref>] in which the authors discovered that sequentially depositing two or more vaccinia virions on individual target cells resulted in the disproportionally higher probability of a cell to become infected; we estimated a high degree of apparent cooperativity (<italic>n</italic> = 2.24) in these experiments (<xref rid="figS6" ref-type="fig">Supplemental Figure S6B</xref>). One explanation of these results became our “accrued damage” hypothesis in which each interaction between a cell and a virion that does not result in infection does lead to increased susceptibility of the cell upon encounter with another virion (<xref rid="fig1" ref-type="fig">Figure 1B</xref>). This may arise due to depletion of resources a cell must use to prevent productive infection upon interaction with a virion. We added this mechanism in our simulations by allowing resistance of the cell <italic>R</italic> to be reduced by <italic>β</italic> at each virion encounter until either the cell becomes infected or no more virions attempt to infect the cell. Even for a relatively small <italic>β</italic>, model simulations did result in apparent cooperativity at low genomes/cell values and increased even faster at intermediate genomes/cell (<xref rid="fig4" ref-type="fig">Figure 4C</xref>). Interestingly, the overall shape of the relationship between the frequency of cellular infection and viral concentration (genomes/cell) visually matched that observed experimentally for TB-GFP strain of HCMV infecting fibroblasts (<xref rid="fig2" ref-type="fig">Figure 2B</xref>).</p>
<p>Our accrued damage model suggests that interactions between virions and cells result in changes in the cell that lead to its increased susceptibility to infection. However, an alternative hypothesis is that when a cell is exposed to several virions, virions may be augmenting their infectivities by complementing different functions required for infection (<xref rid="fig1" ref-type="fig">Figure 1B</xref>). This “viral compensation” hypothesis has been previously suggested following observations of increased infectivity of viral aggregates [<xref ref-type="bibr" rid="c16">16</xref>, <xref ref-type="bibr" rid="c29">29</xref>, <xref ref-type="bibr" rid="c39">39</xref>]. We therefore investigated whether virions may “cooperate” at infecting target cells even if they do not aggregate but when the number of virions attempting to infect an individual cell is described by the Poisson distribution. In our version of viral compensation model we gather information on the collection of virions attempting to infect a given cell and re-assign infectivity to each virion depending on the maximal virion infectivity present in the collection (see <bold>eqn. (6)</bold> and Materials and methods for more detail). In simulations where all virions (generated by a Poisson distribution) attempting to infect a cell increase their infectivity to the maximal value in the collection, the frequency of cellular infection increased faster than linearly with genomes/cell, i.e., results in apparent cooperativity (<xref rid="fig4" ref-type="fig">Figure 4D</xref>). Thus, our results so far suggest that apparent cooperativity may result in the non-Markovian process of cell infection either by individual virions (accrued damage model) or because of compensation of ability to cause productive infection by virions attempting to infect the same cell (viral compensation model).</p>
</sec>
<sec id="s5d">
<title>Direct testing of the viral clumping hypothesis as explanation for apparent cooperativity of HCMV at infecting targets</title>
<p>Intuitively, it makes sense why accrued damage and viral compensation models may result in apparent cooperativity with <italic>n &gt;</italic> 1 at low genomes/cell values: as more virions attempt to infect a cell, the cell loses resistance quicker (accrued damage model) or virions have higher chance of increasing infectivity (viral compensation model) leading to higher probability of cell infection. It was less clear why a viral clumping model did not lead to apparent cooperativity. A number of previous studies documented increased infectivity of viral clumps as compared to individual virions [<xref ref-type="bibr" rid="c16">16</xref>]; yet, we were not able to find studies that rigorously tested if viral clumping results in apparent cooperativity at low genomes/cell values.</p>
<p>Presence of viral aggregates is common in viral stocks [<xref ref-type="bibr" rid="c16">16</xref>]. For example, by using electron microscopy Galasso &amp; Sharp [<xref ref-type="bibr" rid="c29">29</xref>] quantified the number of vaccinia virions present in different clumps; 67% of particles were single virions and the largest particle had 81 virion. The resulting distribution of virions per clump was highly skewed with the average 3.2 virions per clump [<xref ref-type="bibr" rid="c29">29</xref>]. HCMV can also form aggregates but may also exist as single particles [<xref ref-type="bibr" rid="c30">30</xref>]. To study how dilution of our HCMV stock may influence distribution of viral clumps we utilized dynamic light scattering (<bold>DLS</bold>) to measure the distribution of particle sizes in stocks of all three strains [<xref ref-type="bibr" rid="c40">40</xref>–<xref ref-type="bibr" rid="c42">42</xref>]. For the stock of TB-GFP strain of HCMV grown on fibroblasts we found that the distribution of particle diameter <italic>D</italic> depends strongly on the stock dilution; at low dilutions (i.e., dilution #1-4) nearly all particles were larger than 100 nm but at higher dilutions (e.g., dilution #19), particles with the average size of 20 nm became dominant (<xref rid="fig5" ref-type="fig">Figure 5A</xref> and <xref rid="figS8" ref-type="fig">Supplemental Figure S8</xref>). The larger peak likely represents virions and given that an average HCMV virion diameter is <italic>d</italic> = 230 nm [<xref ref-type="bibr" rid="c30">30</xref>], some of the smaller clumps represent viral particles without capsid and the smallest particles likely represent cellular debris, exosomes, and particles already present in the growth media. By fitting a mixture of two normal distribution to log-transformed clump size data we estimated proportion of the larger clumps (<italic>f</italic><sub>1</sub>) and their average scaled diameter<inline-formula id="inline-eqn-4"><inline-graphic xlink:href="650360v1_inline4.gif" mimetype="image" mime-subtype="gif"/></inline-formula>; the model in which the average of the larger distribution remained constant between dilutions but their fraction declined with higher dilution described the data reasonably well (<xref rid="figS8" ref-type="fig">Supplemental Figure S8</xref>).</p>
<fig id="fig5" position="float" fig-type="figure">
<label>Figure 5:</label>
<caption><title>Incorporating experimentally measured distribution of viral aggregates in simulations did not result in apparent cooperativity in the clumping model.</title>
<p><bold>A</bold>: We used dynamic light scattering to measure distribution of sizes of clumps for various dilutions of the initial stock of TB-GFP strain (see also <xref ref-type="fig" rid="figS8">Supplemental Figure S8</xref>). <bold>B</bold>: We used the same dilutions of TB-GFP from the same cultures to infect fibroblasts and estimated the fraction of infected cells at day 3 after infection. We then fitted the powerlaw model (<bold>eqn. (1)</bold>) to the linear part of the data and estimated degree of apparently cooperativity <italic>n</italic>. <bold>C-D</bold>: We used experimentally measured distribution of clump sizes and estimated how many virions are located in a given clump of a diameter <italic>D</italic> assuming random packing of spheres with <italic>d</italic> = 230 nm (see <bold>eqn. (5)</bold> and text in Materials and methods). We then simulated infection of cells by sampling virions in clumps (clumping model, <bold>C</bold>) and calculating probability of cell infection at different genome/cell dilutions. We show the results of 10 simulations with parameters listed in <xref rid="tbl1" ref-type="table">Table 1</xref> except we used 10<sup>3</sup> target cells. In <bold>D</bold>, we fitted the powerlaw model (<bold>eqn. (1)</bold> to the data from simulations and estimated the degree of apparent cooperativity <italic>n</italic>. Makers denote average values and gray areas show the range of simulation results. Listed p-values were calculated to estimate deviation of estimated <italic>n</italic> from <italic>n</italic> = 1 using LRT. The size of HCMV virion of <italic>d</italic> = 230 nm is indicated by a dashed vertical line in panel <bold>A</bold>.</p></caption>
<graphic xlink:href="650360v1_fig5.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<p>We then used the same stock dilutions to infect fibroblasts and estimated the degree of apparent cooperativity; as in previous experiments we found strong deviation of the infection from the null model with a high degree of apparent cooperativity (<italic>n</italic> = 1.39) for genomes per cell changing over an order of magnitude (<xref rid="fig5" ref-type="fig">Figure 5B</xref>); notably estimated <italic>n</italic> in these experiments was lower than that we observed earlier (<xref rid="fig2" ref-type="fig">Figure 2B</xref>). To investigate whether experimentally measured clump size distribution may be able to result in apparent cooperativity in simulations, we used a previous result suggesting that a number of smaller spheres that could fit inside of a larger sphere scales as cube of the ratio of diameters of the two spheres (<bold>eqn. (5)</bold> and <xref rid="figS9" ref-type="fig">Supplemental Figure S9A</xref>). By using fit of the mixture of two normal distributions we estimated how many virions are predicted to be in the well at a given dilution and how the number of virions per clump changes with dilution of the stock (<xref rid="figS9" ref-type="fig">Supplemental Figure S9B-C</xref>). Interestingly, while the total number of virions declines with higher dilution number, the proportion of clumps with more virions increases with higher dilutions. To allow for skewed distribution of the number of virions per clump we used one-inflated geometric distribution (see Materials and methods for detail and <xref rid="fig5" ref-type="fig">Figure 5C</xref>). Interestingly, by assuming dilution-dependent clump size distribution we found that the cell infection rate scales nearly linearly with increasing virion concentration <xref rid="fig5" ref-type="fig">Figure 5D</xref>). However, these simulations also revealed small (but statistically non-significant) evidence of apparent cooperativity at small genomes/cell values (<italic>n</italic> = 1.08) and even faster increase in infection frequency at higher virion concentrations (<xref rid="fig5" ref-type="fig">Figure 5D</xref>).</p>
<p>We performed many additional simulations with the clumping model by varying the distribution of virions per clump, how clumps and virions are sampled at a given stock dilution, and changing levels of virion infectivity. We found that in some simulations, specifically when the frequency of clumps with many virions was sufficiently large at high dilutions, the clumping model could result in apparent cooperativity with <italic>n &gt;</italic> 1 (e.g., <xref rid="figS10" ref-type="fig">Supplemental Figure S10</xref>). These results suggest that understanding how dilution of the stock impacts the distribution of clump sizes may influence of how cell infection frequency scales with virion concentration. In contrast, additional simulations with the accrued damage and viral compensation models (with different parameter values and different simulation frameworks) nearly always resulted in apparent cooperativity, suggesting that these two hypotheses are more robust to modeling details. In fact, we could find parameter combinations that allowed for relatively high values of the cooperativity parameter <italic>n</italic>, e.g., in the accrued damage model assuming larger reduction in cell resistance per virion encounter (e.g., <italic>β</italic> = <italic>−</italic>2) easily led to <italic>n ∼</italic> 2. Taken together, our results suggest that both accrued damage and viral compensation models, and under some parameters, viral clumping model, may allow for the cell infection rate to increase more rapidly with higher virion concentrations than predicted by the linear, single hit model.</p>
</sec>
<sec id="s5e">
<title>Calculations of MOI are imprecise for virus-cell combinations with apparent viral cooperativity</title>
<p>Our experiments and computational models show that for some virus-target cell combinations the frequency of cell infection increases faster than linearly with higher genomes/cell values. Even though we were not able to discriminate between alternative hypotheses for such apparent viral cooperativity, such nonlinear scaling may impact calculation of the infectivity of a viral stock and may influence interpretation of experiments involving comparison of different viral strains.</p>
<p>To calculate titer of a given stock, the stock is diluted so the number of infectious units (<bold>IUs</bold>) can be calculated. In case of a linear, single hit model, the estimated titer (IU/mL) scales linearly with the virion concentration in the sample independently of the concentration of target cells used in the experiment (<xref rid="fig6" ref-type="fig">Figure 6A</xref>). In contrast, in the presence of apparent cooperativity, estimated titer even when measured at the same virion concentration strongly depends on the concentration of target cells (<xref rid="fig6" ref-type="fig">Figure 6B</xref>) making calculation of stock titer imprecise. This is because as virus and/or target cell concentrations vary, the ratio of virions/cell also varies resulting in different predicted levels of infection.</p>
<fig id="fig6" position="float" fig-type="figure">
<label>Figure 6:</label>
<caption><title>Calculations of MOI are imprecise for virus-cell combinations exhibiting apparent cooperativity.</title>
<p><bold>A</bold>: For viruses with <italic>n</italic> = 1, infectious titer scales linearly with changing genomes/cell (ME.GFP.Epithelial). <bold>B</bold>: However, for viruses with <italic>n &gt;</italic> 1 (TB.GFP.Fibroblast), reduction in genome/cell results in a larger reduction in infections/cell, i.e., in much lower than expected infectious titer. <bold>C</bold>: Expected MOI changes nonlinearly for virus-cell combinations with apparent cooperativity (<italic>n &gt;</italic> 1); MOI<sub><italic>R</italic></sub> is the ratio of MOIs when specific infectivity is reduced 10 fold (i.e., stock is diluted 10 fold, from 10<sup>6</sup> to 10<sup>5</sup> genomes/mL); here target cell concentration is 10<sup>6</sup> cell/mL. In panels A and B, dashed line denotes 1:1 relationship between genomes/mL and infectious titer (IU/mL). We used parameters of the powerlaw model fitted to individual datasets (for ME-GFP on ECs and TB-GFP on fibroblats) to make predictions (<xref rid="tblS2" ref-type="table">Supplemental Table S2</xref>).</p></caption>
<graphic xlink:href="650360v1_fig6.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<p>If different viral strains vary in their degree of apparent cooperativity (characterized by the parameter <italic>n</italic>) then some comparisons of viral characteristics, e.g., specific infectivity or replicative capacity, may be difficult to interpret. For example, it is common to study how specifics of viral strain impacts its ability to replicate in culture by inoculating the strains in the culture at the same, typically low, MOI, and follow accumulation of viral genomes over time [<xref ref-type="bibr" rid="c43">43</xref>, <xref ref-type="bibr" rid="c44">44</xref>]. However, if two viral strains differ in the degree of apparent cooperativity, the same dilution of the stock assuming linear reduction in MOI with dilution may in fact results in dramatically lower MOI for viruses with higher <italic>n</italic> – for example, 10 fold dilution of viral stock would result in nearly 40 fold reduction in infections for a strain with cooperativity degree of <italic>n</italic> = 1.6 (<xref rid="fig6" ref-type="fig">Figure 6C</xref>). Such a strain may then show delay in accumulation of viral particles in culture that may be incorrectly interpreted as reduced replication capacity and not reduced primary infection efficacy [<xref ref-type="bibr" rid="c43">43</xref>, <xref ref-type="bibr" rid="c44">44</xref>].</p>
</sec>
</sec>
<sec id="s6">
<title>Discussion</title>
<p>A single hit model, in which one infectious viral particle can give rise to a productive infection, has been commonly assumed to be correct, excluding, of course, multipartite viruses whose segments are packaged in separate particles. In particular, Pradhan et al. [<xref ref-type="bibr" rid="c16">16</xref>] write that in accord with a single hit model, “Most mammalian viruses show a linear relationship between the number of plaques and dilution of virus plated, holding the framework true in titration assays to determine viral titers and the infectious dose.” In this study and in our analysis of data from others’ studies, we show that a linear relationship between the frequency of infected cells and the virion (or genome) concentration in a sample is an exception rather than the rule for at least three different viruses (HCMV, HIV, VV) and different strains of HCMV (TB, TR, ME) showing that frequency of infected cells often increases faster than linear with higher virion concentration (<xref rid="fig2" ref-type="fig">Figure 2</xref> and <xref rid="figS6" ref-type="fig">Supplemental Figure S6</xref>). In our experiments the degree of such apparent viral cooperativity (characterized by a parameter <italic>n</italic>, see <bold>eqn. (1)</bold>) was dependent on specific stock preparation, HCMV strain and, surprisingly, on the type of target cells used (<xref rid="fig3" ref-type="fig">Figure 3</xref>). We developed stochastic simulations to test whether different hypotheses about how viruses infect target cells may result in apparent cooperativity (<xref rid="fig1" ref-type="fig">Figure 1B</xref>); the basic/null model that allows for variability in virion infectivity and cell resistance to infection did not result in apparent cooperativity (<xref rid="fig4" ref-type="fig">Figure 4A</xref>). Two alternative models — accrued damage and virus compensation models – consistently predicted deviation of the infection curve from the single hit model with <italic>n &gt;</italic> 1 (<xref rid="fig4" ref-type="fig">Figure 4C-D</xref>), and a model in which virions form clumps did not always result in apparent cooperativity (e.g., <xref rid="fig4" ref-type="fig">Figures 4</xref> and <xref rid="fig5" ref-type="fig">5</xref> but see <xref rid="figS10" ref-type="fig">Supplemental Figure S10</xref>). By using DLS we showed that the distribution of clumps in our stock of HCMV-TB strain is skewed; we predict that most of these clumps consist of single virions but few clumps have multiple virions (<xref rid="figS9" ref-type="fig">Supplemental Figure S9</xref>); this is similar to a previous observation made for VV [<xref ref-type="bibr" rid="c29">29</xref>]. Presence of apparent cooperativity (<italic>n &gt;</italic> 1) makes traditional calculations of the stock titer, and as a result, the MOI in a given experiment, imprecise, especially if the degree of apparent cooperativity varies between viral strain (<xref rid="fig6" ref-type="fig">Figure 6</xref>).</p>
<p>Our results are in line with a notion that outcome of infection is dependent both on the virus and target cell details and is highly stochastic [5, 24, 45–47]. It is notable, though, that despite the importance of both virus and cell properties for cell infection, reference sources and classical textbooks when characterizing viruses, e.g., by their specific infectivity, often do not include cell details used for virus titration. Several previous studies have documented deviations of cell infection rate from the single hit/null model but in most of such cases the frequency of infected cells (or the number of viral plaques) increased slower than linearly with virion concentration [<xref ref-type="bibr" rid="c9">9</xref>, <xref ref-type="bibr" rid="c10">10</xref>] (and see <xref rid="figS7" ref-type="fig">Supplemental Figure S7</xref>). One notable exception is rapid reduction in the frequency of plaques formed by the multipartite Guaico Culex virus on C6/36 cells with dilution of the viral stock [<xref ref-type="bibr" rid="c48">48</xref>]; fits of the powerlaw model to these (digitized) data suggested a high degree of apparent cooperativity of <italic>n</italic> = 4.5. Apparent cooperativity may help explain large differences in estimated specific infectivity of viruses between different labs [<xref ref-type="bibr" rid="c49">49</xref>] including even determining genome concentrations in a sample [<xref ref-type="bibr" rid="c50">50</xref>]. Recent studies also suggest that some metrics of viral stock infectivity, e.g., tissue-culture infectious dose 50 (TCID<sub>50</sub>), may not be always robust to the way measurements are performed [<xref ref-type="bibr" rid="c51">51</xref>].</p>
<p>Variable degree of apparent cooperativity between different viral strains may impact interpretation of experimental results [<xref ref-type="bibr" rid="c52">52</xref>]. For example, in comparing replication capacity of different strains it is common to infect cells at low MOI to allow for amplification of small differences in viral replication rates. However, if strains differ in degree of apparent cooperativity, the assumed MOI could differ between strains substantially (<xref rid="fig6" ref-type="fig">Figure 6</xref>). Therefore, the difference in viral titers observed late in culture may not be due to differences in viral replication rates alone [<xref ref-type="bibr" rid="c43">43</xref>, <xref ref-type="bibr" rid="c44">44</xref>]. For example, a recent study documented a lower concentration of drug-resistant transmitted/founder (<bold>T/F</bold>) HIV strains over 8 day culture as compared to drug-susceptible HIV strains [<xref ref-type="bibr" rid="c43">43</xref>]. Most of this differences primarily arose during the first 2 days of culture and may have resulted in differences in actual MOIs and not in replication rates of the T/F viruses. Indeed, visual regression analysis suggests similar replication rates for two sets of T/F viruses from day 2 onward (see <xref rid="fig3" ref-type="fig">Figure 3A</xref> in [<xref ref-type="bibr" rid="c43">43</xref>]).</p>
<p>Our study has several limitations. First, we did not block potential secondary infection by progeny virions produced by the cells infected by the primary inoculum. It is possible that cells that had been infected with more virions would start virion production earlier causing faster than linear increase in the fraction of infected cells with increasing genomes/cell values [<xref ref-type="bibr" rid="c52">52</xref>]. However, HCMV has a long replication cycle with viral progeny release beginning about 3 days after infection [<xref ref-type="bibr" rid="c34">34</xref>–<xref ref-type="bibr" rid="c36">36</xref>] that is consistent with our time course data (<xref rid="figS2" ref-type="fig">Supplemental Figure S2</xref>). Therefore, by measuring the frequency of infected cells at 3 days post virion inoculation we should not detect secondary infections. Second, while we have proposed alternative mechanisms that may result in apparent cooperativity, at present we could not discriminate between these alternatives, in part, because the models lacked specifics – e.g., if virions interacting with a cell reduce its resistance to infection, what does it mean exactly [<xref ref-type="bibr" rid="c12">12</xref>]? If virions in a collection augment their infectivity (which may be expected for segmented viruses), how does that viral compensation actually work? Addressing these questions is an area of future research that will require funding. We would note, however, that our observation that the degree of apparent cooperativity <italic>n</italic> depends on the target cell type, i.e., we found lower <italic>n</italic> on epithelial cells as compared to fibroblasts (<xref rid="fig3" ref-type="fig">Figure 3A</xref>) argues against clumping as the primary mechanism of apparent cooperativity. Indeed, in stochastic simulations we found that changing target cell resistance to infection did shift the infection curve but did not impact estimate of <italic>n</italic> (results not shown). Third, we do not yet have an analytical model that would accurately describe the whole relationship between infections/cell and genomes/cell for all data; a simple extension of the powerlaw model allowing for saturation in the infection frequency at low and high genomes/cell values did not always fit the data accurately (<xref rid="figS4" ref-type="fig">Supplemental Figure S4</xref>). We also do not have a clear explanation of why infection frequency declines at high genomes/cell values for some strain-cell combinations (e.g., <xref rid="fig2" ref-type="fig">Figure 2A, C, D, I, J</xref>). Fourth, even though we measured distribution of clumps in our viral stock of HCMVTB-GFP, we did not determine how many virions there are in clumps of different sizes. Sorting such clumps and using qPCR may be a way to directly measure this critical parameter impacting importance of viral clumping in determining degree of apparent cooperativity [<xref ref-type="bibr" rid="c37">37</xref>]. Fifth and finally, while we assume that at higher genomes/cell values several virions likely initiate the infection we had no ability to measure this directly. Our future studies will use either the same strain or different strains expressing GPF or mCherry to directly measure the rate of cell coinfection with two or more virions.</p>
<p>Our work opens avenues for future research. The key point is that in the presence of apparent cooperativity (<italic>n &gt;</italic> 1), MOI calculated from the stock does not scale linearly with virion concentration; therefore, infectious titer needs to be determined for multiple values of genomes/cell and at different target cell concentrations for each virus-target cell combinations in question (<xref rid="fig6" ref-type="fig">Figure 6C</xref>). It will be important to determine if segmented viruses such as influenza A virus (<bold>IAV</bold>) exhibit even higher degrees of cooperativity than HCMV, as one would expect viral compensation to be important for production of infection of cells by IAV. Whether virion aggregation (or clumping) is the key mechanism explaining apparent cooperativity also will have to be tested for different virus-target cell combinations. Further complicating matters is the possibility that virions may cooperate without the requirement to coinfect the same cell. Faba bean necrotic stunt virus (<bold>FBNSV</bold>), a multipartite plant virus, was shown to share gene products between neighboring infected plant cells, cooperating to provide viral proteins that would otherwise be lacking, due to infection by only a portion of the genome segments [<xref ref-type="bibr" rid="c53">53</xref>]. It would be interesting to explore if such cooperation would be detected by our methodology.</p>
<p>Our work has focused on the initial steps of viral life cycle – infection of a cell. How changes in the virion concentration cells are exposed to impacts the number of virions produced per infected cell remains to be determined. Classical and more recent studies highlighted large heterogeneity in virion production by individual virus-infected cells for different viruses including IAV and HSV-1 [<xref ref-type="bibr" rid="c54">54</xref>]. In our preliminary experiments, we found that the number of HCMV-TB virions produced by fibroblasts was approximately independent of the genomes/cell used for infection, but more research is needed. Finally, there is a need to generate specific and testable hypotheses of how individual virions may cooperate to improve their chances to infect a cell. Manipulation with viral genes regulating entry of virions into the cell and/or efficiency of within-cell virus replication and with target cell genes regulating response to block virus replication would be highly instrumental. Development of more detailed mathematical models of within-cell virus replication may also generate novel hypotheses leading to apparent viral cooperativity [<xref ref-type="bibr" rid="c52">52</xref>]. Combining mathematical models and experiments to parameterize the models and test model predictions should help further understand how virions cooperate at infecting cells.</p>
</sec>
</body>
<back>
<sec id="s7" sec-type="data-availability">
<title>Data and code sharing</title>
<p>The data on HCMV infection from our experiments are available as a supplement to this paper and on github: <ext-link ext-link-type="uri" xlink:href="https://github.com/Joshua-Miller-161/HCMV_Dose_Infection.git">https://github.com/Joshua-Miller-161/HCMV_Dose_Infection.git</ext-link>. Data on HIV infection of target cells from individual experiments (shown in <xref rid="figS5" ref-type="fig">Supplemental Figures S5A</xref>) were provided by Tenthorey et al. [<xref ref-type="bibr" rid="c55">55</xref>]. Data on infection of target cells by VV (shown in <xref rid="figS5" ref-type="fig">Supplemental Figures S5B</xref>) were digitized from the original paper [<xref ref-type="bibr" rid="c38">38</xref>]. Data on TMV infection of leaves was taken from the tables in Nourinejhad Zarghani et al. [<xref ref-type="bibr" rid="c10">10</xref>]. Codes (python and Mathematica) used to simulate cell infection are available on github (see link above).</p>
</sec>
<sec id="s10" sec-type="supplementary">
<title>Supplemental information</title>
<table-wrap id="tblS1" orientation="portrait" position="float">
<label>Supplementary Table S1:</label>
<caption><title>Standardized relationship between volume pipette dispenses and the actual weight of the dispensed volume (standard curve).</title>
<p>We performed experiments by dispensing different volumes of the DMEM media (at 20<sup>0</sup>C room temperature) with a 1 ml serological pipette and measured their weights in three independent replicates (shown in different columns). The pipette had a standard error of 2% (denoted as <italic>±</italic> values in the first column). Analysis of the data is shown in <xref rid="figS1" ref-type="fig">Supplemental Figure S1A</xref>.</p></caption>
<graphic xlink:href="650360v1_tblS1.tif" mimetype="image" mime-subtype="tiff"/>
</table-wrap>
<fig id="figS1" position="float" fig-type="figure">
<label>Supplementary Figure S1:</label>
<caption><title>Using a standard curve converting media mass to volume allows for more accurate quantification of the degree of apparent cooperativity.</title>
<p><bold>A</bold>: We performed experiments in which we carefully measured the relationship between volume a pipette dispenses and the weight of this volume for a range of volume values in 3 independent samples (data are from <xref rid="tblS1" ref-type="table">Supplemental Table S1</xref>). Value <italic>m</italic> denotes the slope of the linear regression of log-transformed values and p-value is from the t-test for <italic>m</italic> = 1. <bold>B-E</bold>: We fitted the powerlaw model (<bold>eqn. (1)</bold>) to the data on ME-mCherry (<bold>B-C</bold>) or TB-GFP (<bold>D-E</bold>) strain infection of fibroblasts at different dilutions of viral stocks assuming that the pipette gives the correct assumed volume (<bold>B&amp;D</bold>) or when correcting the dispensed volume using the calibration curve (<bold>C&amp;E</bold>, see also Materials and methods for more detail). Estimated degree of apparent cooperativity <italic>n</italic> is shown on individual panels. Dilution factor used in calculating genomes/cell is 1.43 and 1.44 in panels <bold>B</bold> and <bold>C</bold>, respectively, and 1.43 and 1.48 in panels <bold>D</bold> and <bold>E</bold>, respectively.</p></caption>
<graphic xlink:href="650360v1_figS1.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<fig id="figS2" position="float" fig-type="figure">
<label>Supplementary Figure S2:</label>
<caption><title>Kinetics of GFP and mCherry expression in fibroblasts exposed to different HCMV strains.</title>
<p><bold>A</bold>: We followed expression of GFP (top row) or mCherry (bottom row) in fibroblast over time after exposure to 0.02 genomes/cell of TB-GFP or 0.07 genomes/cell of TB-mCherry strains of HCMV. The frequency of cells detected as GFP+ or mCherry+ is shown on individual panels. <bold>B</bold>: We followed change in percent of fibroblasts infected with GFP-(<bold>i-iii</bold>) or mCherry-expressing viruses (<bold>iv-v</bold>). We show the data from individual three cultures (gray lines) and average (markers with colored lines).</p></caption>
<graphic xlink:href="650360v1_figS2.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<fig id="figS3" position="float" fig-type="figure">
<label>Supplementary Figure S3:</label>
<caption><title>Detecting cells infected with GFP or mCherry-expressing HCMV virions at different dilutions of the stock.</title>
<p>We show flow cytometry plots of TB-GFP-(<bold>A</bold>) or ME-mCherry-(<bold>B</bold>) exposed fibroblasts at different dilutions of the viral stocks detected at day 3 post exposure. Gates show the percent of cells detected as infected; specific dilutions and calculated genomes/cell (<bold>g/c</bold>) are shown on individual panels.</p></caption>
<graphic xlink:href="650360v1_figS3.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<table-wrap id="tblS2" orientation="portrait" position="float">
<label>Supplementary Table S2:</label>
<caption><title>Estimates of parameters determining infectivity of HCMV strains for different target cells.</title>
<p>The model fits are shown in <xref rid="fig2" ref-type="fig">Figure 2</xref> and details of how the model (<bold>eqn. (1)</bold>) was fit to data are given in Materials and methods. We list the HCMV strain (ME, TB, TR), marker expressed by the virus-infected cells (GFP or mCherry), and the type of target cells (Fibroblasts or Epithelial cells) used in experiments. Parameters are the infectivity of a single genome <italic>p</italic>(1) and the degree of apparent cooperativity <italic>n</italic>; numbers in parentheses are 95% confidence intervals generated by bootstrapping the data with replacement in 1000 simulations. Note that in <bold>eqn. (1)</bold>, <italic>p</italic>(1) = e<sup><italic>−λ</italic></sup>.</p></caption>
<graphic xlink:href="650360v1_tblS2.tif" mimetype="image" mime-subtype="tiff"/>
</table-wrap>
<fig id="figS4" position="float" fig-type="figure">
<label>Supplementary Figure S4:</label>
<caption><title>Apparent cooperativity of HCMV strains at infecting targets is still detected when fitting the extended powerlaw model to all data.</title>
<p>We fitted extended powerlaw model (<bold>eqn. (2)</bold>) to the data; this model allows for saturation in infection probability at low or high genome/cell concentrations. Note that due to a large number of measurements at high genome/cell concentrations, the model fits are biased towards these datapoints in panels B and H.</p></caption>
<graphic xlink:href="650360v1_figS4.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<fig id="figS5" position="float" fig-type="figure">
<label>Supplementary Figure S5:</label>
<caption><title>A degree of apparent cooperativity is dependent on the range of genome/cell and virus-cell combination.</title>
<p>For each HCMV strain and cell combinations (see <xref rid="fig2" ref-type="fig">Figure 2</xref>) we determined the degree of apparent cooperativity <italic>n</italic> by taking subset of the data between different dilutions (starting with the highest dilution 23) and including different numbers of dilutions (denoted as <italic>window</italic>). We then fitted the powerlaw model (<bold>eqn. (1)</bold>) to these data and estimated the degree of apparent cooperativity <italic>n</italic>. Note that at high initial genome/cell subsets of data, <italic>n &lt;</italic> 1 indicating competition between virions at infecting cells.</p></caption>
<graphic xlink:href="650360v1_figS5.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<fig id="figS6" position="float" fig-type="figure">
<label>Supplementary Figure S6:</label>
<caption><title>Apparent cooperativity of HIV and Vaccinia virus at infecting target cells.</title>
<p>We analyzed data from two previously published papers [<xref ref-type="bibr" rid="c38">38</xref>, <xref ref-type="bibr" rid="c55">55</xref>] that measured infection probability of cell exposed to different number of virions and estimated degree of apparent cooperativity from their data. <bold>A</bold>: change infection of TRIM5<italic>α</italic>-deficient CRFK cells (control or transdused with TRIM5<italic>α</italic>) exposed to different dilutions of HIV-1-GFP [<xref ref-type="bibr" rid="c55">55</xref>]. <bold>B</bold>: change in the probability of a HeLa cell exposed to a given number of vaccinia virus virions deposited on the cell surface [<xref ref-type="bibr" rid="c38">38</xref>]. For both studies we calculated the slope <italic>n</italic> by fitting the powerlaw model (<bold>eqn. (1)</bold>) to the data using maximum likelihood method (see Materials and methods for details). Shown <italic>p</italic> values are from likelihood ratio test when comparing model fit with <italic>n</italic> ≠ 1 to that with <italic>n</italic> = 1. Data are shown as markers and model fits as lines. Dashed line represents the slope of one. In <bold>A</bold>, data points shown in gray were excluded from the model fit.</p></caption>
<graphic xlink:href="650360v1_figS6.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<fig id="figS7" position="float" fig-type="figure">
<label>Supplementary Figure S7:</label>
<caption><title>Lack of apparent cooperativity of Tobacco mosaic virus (TMV) on <italic>Nicotiuna glutinom</italic> plants.</title>
<p>We analyzed data from studies documenting formation of lesions on plant leaves exposed to different dilutions of TMV stock [<xref ref-type="bibr" rid="c9">9</xref>, <xref ref-type="bibr" rid="c10">10</xref>]. We show data that were numerically provided in Kleczkowski [<xref ref-type="bibr" rid="c9">9</xref>] and fitted the powerlaw model (<bold>eqn. (1)</bold>) to these data to estimate degree of apparent cooperativity <italic>n</italic> (listed p values are from a LRT with a model fit with <italic>n</italic> = 1). Dashed line represents the slope of one. Data points shown in gray were excluded from the model fit.</p></caption>
<graphic xlink:href="650360v1_figS7.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<fig id="figS8" position="float" fig-type="figure">
<label>Supplementary Figure S8:</label>
<caption><title>Distribution of viral clumps in three different experiments is well described by a mixture of two log-normal distributions.</title>
<p>By using dynamic light scattering we measured distribution of viral clumps in three different preparations and for different dilutions of the viral stock of TB-GFP. We show measurements from three different viral stocks (in different columns). For each dilution we fitted a mixture of normal distributions to log-transformed clump size <italic>D</italic> and calculated the fraction of the larger peak <italic>f</italic><sub>1</sub>; the average of the larger peak <inline-formula id="inline-eqn-5"><inline-graphic xlink:href="650360v1_inline5.gif" mimetype="image" mime-subtype="gif"/></inline-formula> is indicated on individual panels. A diameter of a single virion <italic>d</italic> = 230 nm is indicated by a vertical dashed line [<xref ref-type="bibr" rid="c30">30</xref>].</p></caption>
<graphic xlink:href="650360v1_figS8.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<fig id="figS9" position="float" fig-type="figure">
<label>Supplementary Figure S9:</label>
<caption><title>Quantification of virions in clumps does not result in linear scaling in virions/well at different dilutions of the stock.</title>
<p><bold>A</bold>: From the measured distribution of size (diameter) of viral clumps in a given stock preparation we sampled clumps of different sizes (with a diameter <italic>D</italic>). Assuming that these clumps are spheres and that a given clump is composed of spherical virions of a diameter <italic>d</italic>, we calculate the number of virions (genomes) per clump using <bold>eqn. (5)</bold>. Vertical dashed line in the plot denotes threshold for debris vs. virions when diameter of the clump is smaller than the virion size <italic>d</italic>. <bold>B</bold>: We calculated the predicted number of virions present in clumps of different sizes <italic>D</italic> using estimates of the log-normal distribution fitted to the data generated by dynamic light scattering (<xref rid="figS8" ref-type="fig">Supplemental Figure S8</xref>) and that number of virions per clump of size <italic>D</italic> scales as cube (<bold>eqn. (5)</bold>); the relative number of virions per well (or per cell) is proportional to<inline-formula id="inline-eqn-6"><inline-graphic xlink:href="650360v1_inline6.gif" mimetype="image" mime-subtype="gif"/></inline-formula>. Each marker denotes individual stock dilution (columns in <xref rid="figS8" ref-type="fig">Supplemental Figure S8</xref>). Genome per cell were also calculated by PCR for this particular stock and a dilution factor 1.37. <bold>C</bold>: We plot normalized distribution of virions per clump assuming spherical packing and only accounting for clumps with <italic>D &gt; d</italic> using model fits in <xref rid="figS8" ref-type="fig">Supplemental Figure S8</xref> for three samples (A, B, C) and 8 dilutions (24 curves in total).</p></caption>
<graphic xlink:href="650360v1_figS9.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
<fig id="figS10" position="float" fig-type="figure">
<label>Supplementary Figure S10:</label>
<caption><title>Clumping model may lead to apparent cooperativity at some chosen parameter values.</title>
<p>We simulated infection of target cells by virions assuming that virions form clumps with the number of virions per clump following Poisson distribution (see Materials and methods for more detail). In these simulations we select subset of virions that would be titrated for a given well (and given dilution) and when subselecting virions attempting to infect a given cell we include all virions that belong to the clumps of the attempting-to-infect virions. Virions that succeed at infecting a cell are removed from a given well. <bold>A</bold>: We plot change in cell infection probability with increasing genomes/cell produced in simulations. We fitted the powerlaw model (<bold>eqn. (1)</bold>) to the subsets of simulation data and estimated degree of apparent cooperativity <italic>n</italic>. <bold>B</bold>: We show the mean of the clump size distribution <italic>λ</italic> at different genomes/cell values. <bold>C</bold>: We show an example of distribution of virions/clump simulated different stock dilutions. In these simulations we assume <italic>λ</italic> = 2 and we followed infection of 10<sup>3</sup> cells/well; other parameters are also noted in <bold>A</bold>.</p></caption>
<graphic xlink:href="650360v1_figS10.tif" mimetype="image" mime-subtype="tiff"/>
</fig>
</sec>
<ack>
<title>Acknowledgements</title>
<p>This work was supported by the star-up funds from Texas Biomed and in part by NIH/NIAID grants R01AI158963 to VVG and R01AI097274 to BJR.</p>
</ack>
<sec id="additional-info" sec-type="additional-information">
<title>Additional information</title>
<sec id="s8" sec-type="ethics-statement">
<title>Ethics statement</title>
<p>No animal work.</p>
</sec>
<sec id="s9">
<title>Author’s contributions</title>
<p>Original idea of the study came after talk BJR gave at the Microbiology department of the University of Tennessee. CP performed all experiments under supervision of BJR. VVG performed analyses of experimental data. JM performed most computational simulations under supervision of VVG with some contributions of VVG. VVG wrote the first draft of the paper and all authors read, edited, and agreed on the final version.</p>
</sec>
<glossary>
<title>Abbreviations</title>
<def-list>
<def-item>
<term>HCMV</term>
<def><p>human cytomegalovirus,</p></def></def-item>
<def-item>
<term>ECs</term>
<def><p>epithelial cells,</p></def></def-item>
<def-item>
<term>MOI</term>
<def><p>multiplicity of infection,</p></def></def-item>
<def-item>
<term>IUs</term>
<def><p>infectious units,</p></def></def-item>
<def-item>
<term>PFU</term>
<def><p>plaque-forming unit,</p></def></def-item>
<def-item>
<term>VV</term>
<def><p>vaccinia virus,</p></def></def-item>
<def-item>
<term>PDF</term>
<def><p>probability density function,</p></def></def-item>
<def-item>
<term>LRT</term>
<def><p>Likelihood ratio test,</p></def></def-item>
<def-item>
<term>DIPs</term>
<def><p>defective interfering particles,</p></def></def-item>
<def-item>
<term>DLS</term>
<def><p>dynamic light scattering.</p></def></def-item>
</def-list>
</glossary>
</sec>
<ref-list>
<title>References</title>
<ref id="c1"><label>1.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>McCormick</surname>, <given-names>W.</given-names></string-name> &amp; <string-name><surname>Mermel</surname>, <given-names>L. A.</given-names></string-name></person-group> <year>2021</year> <article-title>The basic reproductive number and particle-to-plaque ratio: comparison of these two parameters of viral infectivity</article-title>. <source>Virology journal</source>, <volume>18</volume>, <fpage>92</fpage>. doi: <pub-id pub-id-type="doi">10.1186/s12985-021-01566-4</pub-id>.</mixed-citation></ref>
<ref id="c2"><label>2.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Carpenter</surname>, <given-names>J. E.</given-names></string-name>, <string-name><surname>Henderson</surname>, <given-names>E. P.</given-names></string-name> &amp; <string-name><surname>Grose</surname>, <given-names>C.</given-names></string-name></person-group> <year>2009</year> <article-title>Enumeration of an extremely high particle-to-PFU ratio for Varicella-zoster virus</article-title>. <source>Journal of virology</source>, <volume>83</volume>, <fpage>6917</fpage>–<lpage>6921</lpage>. doi:<pub-id pub-id-type="doi">10.1128/JVI.00081-09</pub-id>.</mixed-citation></ref>
<ref id="c3"><label>3.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Alfson</surname>, <given-names>K. J.</given-names></string-name>, <string-name><surname>Avena</surname>, <given-names>L. E.</given-names></string-name>, <string-name><surname>Beadles</surname>, <given-names>M. W.</given-names></string-name>, <string-name><surname>Staples</surname>, <given-names>H.</given-names></string-name>, <string-name><surname>Nunneley</surname>, <given-names>J. W.</given-names></string-name>, <string-name><surname>Ticer</surname>, <given-names>A.</given-names></string-name>, <string-name><surname>Dick</surname>, <given-names>E. J.</given-names></string-name>, <string-name><surname>Owston</surname>, <given-names>M. A.</given-names></string-name>, <string-name><surname>Reed</surname>, <given-names>C.</given-names></string-name> <etal>et al.</etal></person-group> <year>2015</year> <article-title>Particle-to-PFU ratio of Ebola virus influences disease course and survival in cynomolgus macaques</article-title>. <source>Journal of virology</source>, <volume>89</volume>, <fpage>6773</fpage>–<lpage>6781</lpage>. doi: <pub-id pub-id-type="doi">10.1128/JVI.00649-15</pub-id>.</mixed-citation></ref>
<ref id="c4"><label>4.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Zhou</surname>, <given-names>M.</given-names></string-name><string-name><surname>Lanchy</surname>, <given-names>J.-M.</given-names></string-name> &amp; <string-name><surname>Ryckman</surname>, <given-names>B. J.</given-names></string-name></person-group> <year>2015</year> <article-title>Human cytomegalovirus gH/gL/gO promotes the fusion step of entry into all cell types, whereas gH/gL/UL128-131 broadens virus tropism through a distinct mechanism</article-title>. <source>Journal of virology</source>, <volume>89</volume>, <fpage>8999</fpage>–<lpage>9009</lpage>. doi:<pub-id pub-id-type="doi">10.1128/JVI.01325-15</pub-id>.</mixed-citation></ref>
<ref id="c5"><label>5.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Schultz</surname>, <given-names>E. P.</given-names></string-name>, <string-name><surname>Lanchy</surname>, <given-names>J.-M.</given-names></string-name>, <string-name><surname>Day</surname>, <given-names>L. Z.</given-names></string-name>, <string-name><surname>Yu</surname>, <given-names>Q.</given-names></string-name>, <string-name><surname>Peterson</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Preece</surname>, <given-names>J.</given-names></string-name> &amp; <string-name><surname>Ryckman</surname>, <given-names>B. J.</given-names></string-name></person-group> <year>2020</year> <article-title>Specialization for cell-free or cell-to-cell spread of BAC-cloned human cytomegalovirus strains is determined by factors beyond the UL128-131 and RL13 loci</article-title>. <source>Journal of virology</source>, <volume>94</volume>. doi: <pub-id pub-id-type="doi">10.1128/JVI.00034-20</pub-id>.</mixed-citation></ref>
<ref id="c6"><label>6.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Dulbecco</surname>, <given-names>R.</given-names></string-name> &amp; <string-name><surname>Vogt</surname>, <given-names>M.</given-names></string-name></person-group> <year>1954</year> <article-title>Plaque formation and isolation of pure lines with poliomyelitis virus es</article-title>. <source>The Journal of experimental medicine</source>, <volume>99</volume>, <fpage>167</fpage>–<lpage>182</lpage>. doi:<pub-id pub-id-type="doi">10.1084/jem.99.2.167</pub-id>.</mixed-citation></ref>
<ref id="c7"><label>7.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Isaacs</surname>, <given-names>A.</given-names></string-name></person-group> <year>1957</year> <article-title>Particle counts and infectivity titrations for animal viruses</article-title>. <source>Advances in virus research</source>, <volume>4</volume>, <fpage>111</fpage>–<lpage>158</lpage>. doi:<pub-id pub-id-type="doi">10.1016/s0065-3527(08)60597-7</pub-id>.</mixed-citation></ref>
<ref id="c8"><label>8.</label><mixed-citation publication-type="web"><person-group person-group-type="author"><string-name><surname>Racaniello</surname>, <given-names>V.</given-names></string-name></person-group> <year>2017</year> <source>The purity of plaques</source>. <ext-link ext-link-type="uri" xlink:href="https://virology.ws/2017/03/30/the-purity-of-plaques/">https://virology.ws/2017/03/30/the-purity-of-plaques/</ext-link>.</mixed-citation></ref>
<ref id="c9"><label>9.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Kleczkowski</surname>, <given-names>A.</given-names></string-name></person-group> <year>1950</year> <article-title>Interpreting relationships between the concentrations of plant viruses and numbers of local lesions</article-title>. <source>Journal of general microbiology</source>, <volume>4</volume>, <fpage>53</fpage>–<lpage>69</lpage>. doi:<pub-id pub-id-type="doi">10.1099/00221287-4-1-53</pub-id>.</mixed-citation></ref>
<ref id="c10"><label>10.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Nourinejhad Zarghani</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Monavari</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Nourinejhad Zarghani</surname>, <given-names>A.</given-names></string-name>, <string-name><surname>Nouri</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Ehlers</surname>, <given-names>J.</given-names></string-name>, <string-name><surname>Hamacher</surname>, <given-names>J.</given-names></string-name>, <string-name><surname>Bandte</surname>, <given-names>M.</given-names></string-name> &amp; <string-name><surname>Büttner</surname>, <given-names>C.</given-names></string-name></person-group> <year>2024</year> <article-title>Quantifying plant viruses: Evolution from bioassay to infectivity dilution curves along the model of Tobamoviruses</article-title>. <source>Viruses</source>, <volume>16</volume>. doi: <pub-id pub-id-type="doi">10.3390/v16030440</pub-id>.</mixed-citation></ref>
<ref id="c11"><label>11.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Galasso</surname>, <given-names>G. J.</given-names></string-name> &amp; <string-name><surname>Sharp</surname>, <given-names>D. G.</given-names></string-name></person-group> <year>1964</year> <article-title>Relative plaque-forming, cell-infecting, and interfering qualities of vaccinia virus</article-title>. <source>Journal of bacteriology</source>, <volume>88</volume>, <fpage>433</fpage>–<lpage>439</lpage>. doi:<pub-id pub-id-type="doi">10.1128/jb.88.2.433-439.1964</pub-id>.</mixed-citation></ref>
<ref id="c12"><label>12.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Wagner</surname>, <given-names>R. R.</given-names></string-name></person-group> <year>1960</year> <article-title>Viral interference. some considerations of basic mechanisms and their potential relationship to host resistance</article-title>. <source>Bacteriological reviews</source>, <volume>24</volume>, <fpage>151</fpage>–<lpage>166</lpage>. doi:<pub-id pub-id-type="doi">10.1128/br.24.1.151-166.1960</pub-id>.</mixed-citation></ref>
<ref id="c13"><label>13.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Turner</surname> <suffix>Jr.</suffix>, <given-names>M.E.</given-names></string-name></person-group> <year>1975</year> <article-title>Some classes of hit theory models</article-title>. <source>Math Biosci</source>, <volume>23</volume>, <fpage>219</fpage>–<lpage>235</lpage>.</mixed-citation></ref>
<ref id="c14"><label>14.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Haas</surname>, <given-names>C. N.</given-names></string-name></person-group> <year>1983</year> <article-title>Estimation of risk due to low doses of microorganisms: a comparison of alternative methodologies</article-title>. <source>Am J Epidemiol</source>, <volume>118</volume>(<issue>4</issue>), <fpage>573</fpage>–<lpage>582</lpage>.</mixed-citation></ref>
<ref id="c15"><label>15.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Frensing</surname>, <given-names>T.</given-names></string-name></person-group> <year>2015</year> <article-title>Defective interfering viruses and their impact on vaccines and viral vectors</article-title>. <source>Biotechnology journal</source>, <volume>10</volume>, <fpage>681</fpage>–<lpage>689</lpage>. doi:<pub-id pub-id-type="doi">10.1002/biot.201400429</pub-id>.</mixed-citation></ref>
<ref id="c16"><label>16.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Pradhan</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Varsani</surname>, <given-names>A.</given-names></string-name>, <string-name><surname>Leff</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Swanson</surname>, <given-names>C. J.</given-names></string-name> &amp; <string-name><surname>Hariadi</surname>, <given-names>R. F.</given-names></string-name></person-group> <year>2022</year> <article-title>Viral aggregation: The knowns and unknowns</article-title>. <source>Viruses</source>, <volume>14</volume>. doi:<pub-id pub-id-type="doi">10.3390/v14020438</pub-id>.</mixed-citation></ref>
<ref id="c17"><label>17.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Zuhair</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Smit</surname>, <given-names>G. S. A.</given-names></string-name>, <string-name><surname>Wallis</surname>, <given-names>G.</given-names></string-name>, <string-name><surname>Jabbar</surname>, <given-names>F.</given-names></string-name>, <string-name><surname>Smith</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Devleesschauwer</surname>, <given-names>B.</given-names></string-name> &amp; <string-name><surname>Griffiths</surname>, <given-names>P.</given-names></string-name></person-group> <year>2019</year> <article-title>Estimation of the worldwide seroprevalence of cytomegalovirus: A systematic review and meta-analysis</article-title>. <source>Reviews in medical virology</source>, <volume>29</volume>, <fpage>e2034</fpage>. doi:<pub-id pub-id-type="doi">10.1002/rmv.2034</pub-id>.</mixed-citation></ref>
<ref id="c18"><label>18.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Cannon</surname>, <given-names>M. J.</given-names></string-name>, <string-name><surname>Schmid</surname>, <given-names>D. S.</given-names></string-name> &amp; <string-name><surname>Hyde</surname>, <given-names>T. B.</given-names></string-name></person-group> <year>2010</year> <article-title>Review of cytomegalovirus seroprevalence and demographic characteristics associated with infection</article-title>. <source>Rev Med Virol</source>, <volume>20</volume>(<issue>4</issue>), <fpage>202</fpage>–<lpage>213</lpage>.</mixed-citation></ref>
<ref id="c19"><label>19.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Davis</surname>, <given-names>N. L.</given-names></string-name>, <string-name><surname>King</surname>, <given-names>C. C.</given-names></string-name> &amp; <string-name><surname>Kourtis</surname>, <given-names>A. P.</given-names></string-name></person-group> <year>2017</year> <article-title>Cytomegalovirus infection in pregnancy</article-title>. <source>Birth defects research</source>, <volume>109</volume>, <fpage>336</fpage>–<lpage>346</lpage>. doi:<pub-id pub-id-type="doi">10.1002/bdra.23601</pub-id>.</mixed-citation></ref>
<ref id="c20"><label>20.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Heldman</surname>, <given-names>M. R.</given-names></string-name>, <string-name><surname>Boeckh</surname>, <given-names>M. J.</given-names></string-name> &amp; <string-name><surname>Limaye</surname>, <given-names>A. P.</given-names></string-name></person-group> <year>2024</year> <article-title>Current and future strategies for the prevention and treatment of cytomegalovirus infections in transplantation</article-title>. <source>Clinical infectious diseases : an official publication of the Infectious Diseases Society of America</source>. doi:<pub-id pub-id-type="doi">10.1093/cid/ciae535</pub-id>.</mixed-citation></ref>
<ref id="c21"><label>21.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Harrison</surname>, <given-names>M. A. A.</given-names></string-name>, <string-name><surname>Morris</surname>, <given-names>S. L.</given-names></string-name>, <string-name><surname>Rudman</surname>, <given-names>G. A.</given-names></string-name>, <string-name><surname>Rittenhouse</surname>, <given-names>D. J.</given-names></string-name>, <string-name><surname>Monk</surname>, <given-names>C. H.</given-names></string-name>, <string-name><surname>Sakamuri</surname>, <given-names>S. S. V. P.</given-names></string-name>, <string-name><surname>Mehedi Hasan</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Shamima Khatun</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Wang</surname>, <given-names>H.</given-names></string-name> <etal>et al.</etal></person-group> <year>2024</year> <article-title>Intermittent cytomegalovirus infection alters neurobiological metabolism and induces cognitive deficits in mice</article-title>. <source>Brain, behavior, and immunity</source>, <volume>117</volume>, <fpage>36</fpage>–<lpage>50</lpage>. doi:<pub-id pub-id-type="doi">10.1016/j.bbi.2023.12.033</pub-id>.</mixed-citation></ref>
<ref id="c22"><label>22.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Readhead</surname>, <given-names>B. P.</given-names></string-name>, <string-name><surname>Mastroeni</surname>, <given-names>D. F.</given-names></string-name>, <string-name><surname>Wang</surname>, <given-names>Q.</given-names></string-name>, <string-name><surname>Sierra</surname>, <given-names>M. A.</given-names></string-name>, <string-name><surname>de Ávila</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Jimoh</surname>, <given-names>T. O.</given-names></string-name>, <string-name><surname>Haure-Mirande</surname>, <given-names>J.-V.</given-names></string-name>, <string-name><surname>Atanasoff</surname>, <given-names>K. E.</given-names></string-name>, <string-name><surname>Nolz</surname>, <given-names>J.</given-names></string-name> <etal>et al.</etal></person-group> <year>2025</year> <article-title>Alzheimer’s disease-associated CD83(+) microglia are linked with increased immunoglobulin G4 and human cytomegalovirus in the gut, vagal nerve, and brain</article-title>. <source>Alzheimer’s &amp; dementia</source>, <volume>21</volume>, <fpage>e14401</fpage>. doi:<pub-id pub-id-type="doi">10.1002/alz.14401</pub-id>.</mixed-citation></ref>
<ref id="c23"><label>23.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Chau</surname>, <given-names>N. H.</given-names></string-name>, <string-name><surname>Vanson</surname>, <given-names>C. D.</given-names></string-name> &amp; <string-name><surname>Kerry</surname>, <given-names>J. A.</given-names></string-name></person-group> <year>1999</year> <article-title>Transcriptional regulation of the human cytomegalovirus US11 early gene</article-title>. <source>Journal of virology</source>, <volume>73</volume>, <fpage>863</fpage>–<lpage>870</lpage>. doi:<pub-id pub-id-type="doi">10.1128/JVI.73.2.863-870.1999</pub-id>.</mixed-citation></ref>
<ref id="c24"><label>24.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Ryckman</surname>, <given-names>B. J.</given-names></string-name>, <string-name><surname>Chase</surname>, <given-names>M. C.</given-names></string-name> &amp; <string-name><surname>Johnson</surname>, <given-names>D. C.</given-names></string-name></person-group> <year>2008</year> <article-title>HCMV gH/gL/UL128-131 interferes with virus entry into epithel ial cells: evidence for cell type-specific receptors</article-title>. <source>Proceedings of the National Academy of Sciences of the United States of America</source>, <volume>105</volume>, <fpage>14 118</fpage>–<lpage>14 123</lpage>. doi: <pub-id pub-id-type="doi">10.1073/pnas.0804365105</pub-id>.</mixed-citation></ref>
<ref id="c25"><label>25.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Sinzger</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Hahn</surname>, <given-names>G.</given-names></string-name>, <string-name><surname>Digel</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Katona</surname>, <given-names>R.</given-names></string-name>, <string-name><surname>Sampaio</surname>, <given-names>K. L.</given-names></string-name>, <string-name><surname>Messerle</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Hengel</surname>, <given-names>H.</given-names></string-name>, <string-name><surname>Koszinowski</surname>, <given-names>U.</given-names></string-name>, <string-name><surname>Brune</surname>, <given-names>W.</given-names></string-name> <etal>et al.</etal></person-group> <year>2008</year> <article-title>Cloning and sequencing of a highly productive, endotheliotropic virus strain derived from human cytomegalovirus TB40/E</article-title>. <source>The Journal of general virology</source>, <volume>89</volume>, <fpage>359</fpage>–<lpage>368</lpage>. doi:<pub-id pub-id-type="doi">10.1099/vir.0.83286-0</pub-id>.</mixed-citation></ref>
<ref id="c26"><label>26.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Stanton</surname>, <given-names>R. J.</given-names></string-name>, <string-name><surname>Baluchova</surname>, <given-names>K.</given-names></string-name>, <string-name><surname>Dargan</surname>, <given-names>D. J.</given-names></string-name>, <string-name><surname>Cunningham</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Sheehy</surname>, <given-names>O.</given-names></string-name>, <string-name><surname>Seirafian</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Mc-Sharry</surname>, <given-names>B. P.</given-names></string-name>, <string-name><surname>Neale</surname>, <given-names>M. L.</given-names></string-name>, <string-name><surname>Davies</surname>, <given-names>J. A.</given-names></string-name> <etal>et al.</etal></person-group> <year>2010</year> <article-title>Reconstruction of the complete human cytomegalovirus genome in a BAC reveals RL13 to be a potent inhibitor of replication</article-title>. <source>The Journal of clinical investigation</source>, <volume>120</volume>, <fpage>3191</fpage>–<lpage>3208</lpage>. doi:<pub-id pub-id-type="doi">10.1172/JCI42955</pub-id>.</mixed-citation></ref>
<ref id="c27"><label>27.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Noecker</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Schaefer</surname>, <given-names>K.</given-names></string-name>, <string-name><surname>Zaccheo</surname>, <given-names>K.</given-names></string-name>, <string-name><surname>Yang</surname>, <given-names>Y.</given-names></string-name>, <string-name><surname>Day</surname>, <given-names>J.</given-names></string-name> &amp; <string-name><surname>Ganusov</surname>, <given-names>V. V.</given-names></string-name></person-group> <year>2015</year> <article-title>Simple mathematical models do not accurately predict early SIV dynamics</article-title>. <source>Viruses</source>, <volume>7</volume>, <fpage>1189</fpage>–<lpage>1217</lpage>.</mixed-citation></ref>
<ref id="c28"><label>28.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Aleshnick</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Ganusov</surname>, <given-names>V. V.</given-names></string-name>, <string-name><surname>Nasir</surname>, <given-names>G.</given-names></string-name>, <string-name><surname>Yenokyan</surname>, <given-names>G.</given-names></string-name> &amp; <string-name><surname>Sinnis</surname>, <given-names>P.</given-names></string-name></person-group> <year>2020</year> <article-title>Experimental determination of the force of malaria infection reveals a non-linear relationship to mosquito sporozoite loads</article-title>. <source>PLoS pathogens</source>, <volume>16</volume>, <fpage>e1008181</fpage>. doi:<pub-id pub-id-type="doi">10.1371/journal.ppat.1008181</pub-id>.</mixed-citation></ref>
<ref id="c29"><label>29.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Galasso</surname>, <given-names>G. J.</given-names></string-name> &amp; <string-name><surname>Sharp</surname>, <given-names>D. G.</given-names></string-name></person-group> <year>1965</year> <article-title>Effect of particle aggregation on the survival of irradiated vaccinia virus</article-title>. <source>Journal of bacteriology</source>, <volume>90</volume>, <fpage>1138</fpage>–<lpage>1142</lpage>. doi:<pub-id pub-id-type="doi">10.1128/jb.90.4.1138-1142.1965</pub-id>.</mixed-citation></ref>
<ref id="c30"><label>30.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Irmiere</surname>, <given-names>A.</given-names></string-name> &amp; <string-name><surname>Gibson</surname>, <given-names>W.</given-names></string-name></person-group> <year>1983</year> <article-title>Isolation and characterization of a noninfectious virion-like particle released from cells infected with human strains of cytomegalovirus</article-title>. <source>Virology</source>, <volume>130</volume>, <fpage>118</fpage>–<lpage>133</lpage>. doi: <pub-id pub-id-type="doi">10.1016/0042-6822(83)90122-8</pub-id>.</mixed-citation></ref>
<ref id="c31"><label>31.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Gibson</surname>, <given-names>W.</given-names></string-name></person-group> <year>1996</year> <article-title>Structure and assembly of the virion</article-title>. <source>Intervirology</source>, <volume>39</volume>, <fpage>389</fpage>–<lpage>400</lpage>. doi:<pub-id pub-id-type="doi">10.1159/000150509</pub-id>.</mixed-citation></ref>
<ref id="c32"><label>32.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Scott</surname>, <given-names>G. D.</given-names></string-name> &amp; <string-name><surname>Kilgour</surname>, <given-names>D. M.</given-names></string-name></person-group> <year>1969</year> <article-title>The density of random close packing of spheres</article-title>. <source>Journal of Physics D: Applied Physics</source>, <volume>2</volume>(<issue>6</issue>), <fpage>863</fpage>. doi:<pub-id pub-id-type="doi">10.1088/0022-3727/2/6/311</pub-id>.</mixed-citation></ref>
<ref id="c33"><label>33.</label><mixed-citation publication-type="web"><person-group person-group-type="author"><string-name><surname>D’Aurizio</surname>, <given-names>J.</given-names></string-name></person-group> <year>2019</year> <source>How many spheres can fit inside this larger sphere?</source> <ext-link ext-link-type="uri" xlink:href="https://math.stackexchange.com/questions/3375911/how-many-spheres-can-fit-inside-this-larger-sphere">https://math.stackexchange.com/questions/3375911/how-many-spheres-can-fit-inside-this-larger-sphere</ext-link>.</mixed-citation></ref>
<ref id="c34"><label>34.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Mocarski</surname>, <given-names>E.</given-names></string-name></person-group> <year>1996</year> <article-title>Cytomegaloviruses and their replication</article-title>. <source>Fields virology</source>.</mixed-citation></ref>
<ref id="c35"><label>35.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Mariame</surname>, <given-names>B.</given-names></string-name>, <string-name><surname>Kappler-Gratias</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Kappler</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Balor</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Gallardo</surname>, <given-names>F.</given-names></string-name> &amp; <string-name><surname>Bystricky</surname>, <given-names>K.</given-names></string-name></person-group> <year>2018</year> <article-title>Real-time visualization and quantification of human cytomegalovirus replication in living cells using the ANCHOR DNA labeling technology</article-title>. <source>Journal of virology</source>, <volume>92</volume>. doi:<pub-id pub-id-type="doi">10.1128/JVI.00571-18</pub-id>.</mixed-citation></ref>
<ref id="c36"><label>36.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Monti</surname>, <given-names>C. E.</given-names></string-name>, <string-name><surname>Mokry</surname>, <given-names>R. L.</given-names></string-name>, <string-name><surname>Schumacher</surname>, <given-names>M. L.</given-names></string-name>, <string-name><surname>Dash</surname>, <given-names>R. K.</given-names></string-name> &amp; <string-name><surname>Terhune</surname>, <given-names>S. S.</given-names></string-name></person-group> <year>2022</year> <article-title>Computational modeling of protracted HCMV replication using genome substrates and protein temporal profiles</article-title>. <source>Proceedings of the National Academy of Sciences of the United States of America</source>, <volume>119</volume>, <fpage>e2201787119</fpage>. doi:<pub-id pub-id-type="doi">10.1073/pnas.2201787119</pub-id>.</mixed-citation></ref>
<ref id="c37"><label>37.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Gaudin</surname>, <given-names>R.</given-names></string-name> &amp; <string-name><surname>Barteneva</surname>, <given-names>N. S.</given-names></string-name></person-group> <year>2015</year> <article-title>Sorting of small infectious virus particles by flow virometry reveals distinct infectivity profiles</article-title>. <source>Nature communications</source>, <volume>6</volume>, <fpage>6022</fpage>. doi:<pub-id pub-id-type="doi">10.1038/ncomms7022</pub-id>.</mixed-citation></ref>
<ref id="c38"><label>38.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Stiefel</surname>, <given-names>P.</given-names></string-name>, <string-name><surname>Schmidt</surname>, <given-names>F. I.</given-names></string-name>, <string-name><surname>orig</surname>, <given-names>P.</given-names></string-name>, <string-name><surname>Behr</surname>, <given-names>P.</given-names></string-name>, <string-name><surname>Zambelli</surname>, <given-names>T.</given-names></string-name>, <string-name><surname>Vorholt</surname>, <given-names>J. A.</given-names></string-name> &amp; <string-name><surname>Mercer</surname>, <given-names>J.</given-names></string-name></person-group> <year>2012</year> <article-title>Cooperative vaccinia infection demonstrated at the single-cell level using FluidFM</article-title>. <source>Nano letters</source>, <volume>12</volume>, <fpage>4219</fpage>–<lpage>4227</lpage>. doi:<pub-id pub-id-type="doi">10.1021/nl3018109</pub-id>.</mixed-citation></ref>
<ref id="c39"><label>39.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Hirst</surname>, <given-names>G. K.</given-names></string-name> &amp; <string-name><surname>Pons</surname>, <given-names>M. W.</given-names></string-name></person-group> <year>1973</year> <article-title>Mechanism of influenza recombination. II. Virus aggregation and its effect on plaque formation by so-called noninfective virus</article-title>. <source>Virology</source>, <volume>56</volume>, <fpage>620</fpage>–<lpage>631</lpage>. doi: <pub-id pub-id-type="doi">10.1016/0042-6822(73)90063-9</pub-id>.</mixed-citation></ref>
<ref id="c40"><label>40.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Makra</surname>, <given-names>I.</given-names></string-name>, <string-name><surname>Terejanszky</surname>, <given-names>P.</given-names></string-name> &amp; <string-name><surname>Gyurcsanyi</surname>, <given-names>R. E.</given-names></string-name></person-group> <year>2015</year> <article-title>A method based on light scattering to estimate the concentration of virus particles without the need for virus particle standards</article-title>. <source>MethodsX</source>, <volume>2</volume>, <fpage>91</fpage>–<lpage>99</lpage>. doi:<pub-id pub-id-type="doi">10.1016/j.mex.2015.02.003</pub-id>.</mixed-citation></ref>
<ref id="c41"><label>41.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Stetefeld</surname>, <given-names>J.</given-names></string-name>, <string-name><surname>McKenna</surname>, <given-names>S. A.</given-names></string-name> &amp; <string-name><surname>Patel</surname>, <given-names>T. R.</given-names></string-name></person-group> <year>2016</year> <article-title>Dynamic light scattering: a practical guide and applications in biomedical sciences</article-title>. <source>Biophysical reviews</source>, <volume>8</volume>, <fpage>409</fpage>–<lpage>427</lpage>. doi: <pub-id pub-id-type="doi">10.1007/s12551-016-0218-6</pub-id>.</mixed-citation></ref>
<ref id="c42"><label>42.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Sripada</surname>, <given-names>S. A.</given-names></string-name>, <string-name><surname>Barbieri</surname>, <given-names>E.</given-names></string-name>, <string-name><surname>Shastry</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Wuestenhagen</surname>, <given-names>E.</given-names></string-name>, <string-name><surname>Aldinger</surname>, <given-names>A.</given-names></string-name>, <string-name><surname>Rammo</surname>, <given-names>O.</given-names></string-name>, <string-name><surname>Schulte</surname>, <given-names>M. M.</given-names></string-name>, <string-name><surname>Daniele</surname>, <given-names>M.</given-names></string-name> &amp; <string-name><surname>Menegatti</surname>, <given-names>S.</given-names></string-name></person-group> <year>2024</year> <article-title>Multiangle light scattering as a lentivirus purification process analytical technology</article-title>. <source>Analytical chemistry</source>, <volume>96</volume>, <fpage>9593</fpage>–<lpage>9600</lpage>. doi:<pub-id pub-id-type="doi">10.1021/acs.analchem.4c01209</pub-id>.</mixed-citation></ref>
<ref id="c43"><label>43.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Sonawane</surname>, <given-names>A.</given-names></string-name>, <string-name><surname>Selvam</surname>, <given-names>D.</given-names></string-name>, <string-name><surname>Yue</surname>, <given-names>L.</given-names></string-name>, <string-name><surname>Nesakumar</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Vivekanandan</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Ashokkumar</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Hunter</surname>, <given-names>E.</given-names></string-name> &amp; <string-name><surname>Hanna</surname>, <given-names>L. E.</given-names></string-name></person-group> <year>2024</year> <article-title>Virulence and replicative fitness of HIV-1 transmitted/founder (T/F) viruses harbouring drug resistance-associated mutation</article-title>. <source>Viruses</source>, <volume>16</volume>(<issue>12</issue>), <fpage>1854</fpage>.</mixed-citation></ref>
<ref id="c44"><label>44.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Mostafa</surname>, <given-names>A.</given-names></string-name>, <string-name><surname>Barre</surname>, <given-names>R. S.</given-names></string-name>, <string-name><surname>Allué-Guardia</surname>, <given-names>A.</given-names></string-name>, <string-name><surname>Escobedo</surname>, <given-names>R. A.</given-names></string-name>, <string-name><surname>Shivanna</surname>, <given-names>V.</given-names></string-name>, <string-name><surname>Rothan</surname>, <given-names>H.</given-names></string-name>, <string-name><surname>Castro</surname>, <given-names>E. M.</given-names></string-name>, <string-name><surname>Ma</surname>, <given-names>Y.</given-names></string-name>, <string-name><surname>Cupic</surname>, <given-names>A.</given-names></string-name> <etal>et al.</etal></person-group> <year>2024</year> <article-title>Replication kinetics, pathogenicity and virus-induced cellular responses of cattle-origin influenza A(H5N1) isolates from Texas, United States</article-title>. <source>Emerging microbes &amp; infections</source>, p. <fpage>2447614</fpage>. doi:<pub-id pub-id-type="doi">10.1080/22221751.2024.2447614</pub-id>.</mixed-citation></ref>
<ref id="c45"><label>45.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Glebe</surname>, <given-names>D.</given-names></string-name> &amp; <string-name><surname>Urban</surname>, <given-names>S.</given-names></string-name></person-group> <year>2007</year> <article-title>Viral and cellular determinants involved in hepadnaviral entry</article-title>. <source>World journal of gastroenterology</source>, <volume>13</volume>, <fpage>22</fpage>–<lpage>38</lpage>. doi:<pub-id pub-id-type="doi">10.3748/wjg.v13.i1.22</pub-id>.</mixed-citation></ref>
<ref id="c46"><label>46.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Russell</surname>, <given-names>A. B.</given-names></string-name>, <string-name><surname>Trapnell</surname>, <given-names>C.</given-names></string-name> &amp; <string-name><surname>Bloom</surname>, <given-names>J. D.</given-names></string-name></person-group> <year>2018</year> <article-title>Extreme heterogeneity of influenza virus infection in single cells</article-title>. <source>eLife</source>, <volume>7</volume>. doi:<pub-id pub-id-type="doi">10.7554/eLife.32303</pub-id>.</mixed-citation></ref>
<ref id="c47"><label>47.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Long</surname>, <given-names>J. S.</given-names></string-name>, <string-name><surname>Mistry</surname>, <given-names>B.</given-names></string-name>, <string-name><surname>Haslam</surname>, <given-names>S. M.</given-names></string-name> &amp; <string-name><surname>Barclay</surname>, <given-names>W. S.</given-names></string-name></person-group> <year>2019</year> <article-title>Host and viral determinants of influenza A virus species specificity</article-title>. <source>Nature reviews. Microbiology</source>, <volume>17</volume>, <fpage>67</fpage>–<lpage>81</lpage>. doi:<pub-id pub-id-type="doi">10.1038/s41579-018-0115-z</pub-id>.</mixed-citation></ref>
<ref id="c48"><label>48.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Ladner</surname>, <given-names>J. T.</given-names></string-name>, <string-name><surname>Wiley</surname>, <given-names>M. R.</given-names></string-name>, <string-name><surname>Beitzel</surname>, <given-names>B.</given-names></string-name>, <string-name><surname>Auguste</surname>, <given-names>A. J.</given-names></string-name>, <string-name><surname>Dupuis</surname>, <given-names>A. P.</given-names></string-name>, <string-name><surname>Lindquist</surname>, <given-names>M. E.</given-names></string-name>, <string-name><surname>Sibley</surname>, <given-names>S. D.</given-names></string-name>, <string-name><surname>Kota</surname>, <given-names>K. P.</given-names></string-name>, <string-name><surname>Fetterer</surname>, <given-names>D.</given-names></string-name> <etal>et al.</etal></person-group> <year>2016</year> <article-title>A multicomponent animal virus isolated from mosquitoes</article-title>. <source>Cell host &amp; microbe</source>, <volume>20</volume>, <fpage>357</fpage>–<lpage>367</lpage>. doi:<pub-id pub-id-type="doi">10.1016/j.chom.2016.07.011</pub-id>.</mixed-citation></ref>
<ref id="c49"><label>49.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Magrath</surname>, <given-names>D. I.</given-names></string-name> &amp; <string-name><surname>Seagroatt</surname>, <given-names>V.</given-names></string-name></person-group> <year>1985</year> <article-title>The standardization of infectivity titrations of poliovaccines– a WHO collaborative study</article-title>. <source>Journal of biological standardization</source>, <volume>13</volume>, <fpage>159</fpage>–<lpage>166</lpage>. doi:<pub-id pub-id-type="doi">10.1016/s0092-1157(85)80022-6</pub-id>.</mixed-citation></ref>
<ref id="c50"><label>50.</label><mixed-citation publication-type="preprint"><person-group person-group-type="author"><string-name><surname>Boutolleau</surname>, <given-names>D.</given-names></string-name>, <string-name><surname>L’Honneur</surname>, <given-names>A.-S.</given-names></string-name>, <string-name><surname>Germi</surname>, <given-names>R.</given-names></string-name>, <string-name><surname>Chanzy</surname>, <given-names>B.</given-names></string-name>, <string-name><surname>Archimbaud-Jallat</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Rzadkowolski</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Raimbourg</surname>, <given-names>J.</given-names></string-name>, <string-name><surname>Gauthier</surname>, <given-names>D.</given-names></string-name> &amp; <string-name><surname>Thibault</surname>, <given-names>V.</given-names></string-name></person-group> <year>2024</year> <article-title>What challenges remain in harmonizing cytomegalovirus viral load quantification across laboratories?</article-title> <source>bioRxiv</source>. doi:<pub-id pub-id-type="doi">10.1101/2024.12.09.627549</pub-id>.</mixed-citation></ref>
<ref id="c51"><label>51.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Cresta</surname>, <given-names>D.</given-names></string-name>, <string-name><surname>Warren</surname>, <given-names>D. C.</given-names></string-name>, <string-name><surname>Quirouette</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Smith</surname>, <given-names>A. P.</given-names></string-name>, <string-name><surname>Lane</surname>, <given-names>L. C.</given-names></string-name>, <string-name><surname>Smith</surname>, <given-names>A. M.</given-names></string-name> &amp; <string-name><surname>Beauchemin</surname>, <given-names>C. A. A.</given-names></string-name></person-group> <year>2021</year> <article-title>Time to revisit the endpoint dilution assay and to replace the TCID50 as a measure of a virus sample’s infection concentration</article-title>. <source>PLoS computational biology</source>, <volume>17</volume>, <fpage>e1009480</fpage>. doi:<pub-id pub-id-type="doi">10.1371/journal.pcbi.1009480</pub-id>.</mixed-citation></ref>
<ref id="c52"><label>52.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Andreu-Moreno</surname>, <given-names>I.</given-names></string-name><string-name><surname>Bou</surname>, <given-names>J.-V.</given-names></string-name> &amp; <string-name><surname>Sanjúan</surname>, <given-names>R.</given-names></string-name></person-group> <year>2020</year> <article-title>Cooperative nature of viral replication</article-title>. <source>Science advances</source>, <volume>6</volume>. doi:<pub-id pub-id-type="doi">10.1126/sciadv.abd4942</pub-id>.</mixed-citation></ref>
<ref id="c53"><label>53.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Sicard</surname>, <given-names>A.</given-names></string-name>, <string-name><surname>Pirolles</surname>, <given-names>E.</given-names></string-name>, <string-name><surname>Gallet</surname>, <given-names>R.</given-names></string-name>, <string-name><surname>Vernerey</surname>, <given-names>M.-S.</given-names></string-name>, <string-name><surname>Yvon</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Urbino</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Peterschmitt</surname>, <given-names>M.</given-names></string-name>, <string-name><surname>Gutierrez</surname>, <given-names>S.</given-names></string-name>, <string-name><surname>Michalakis</surname>, <given-names>Y.</given-names></string-name> <etal>et al.</etal></person-group> <year>2019</year> <article-title>A multicellular way of life for a multipartite virus</article-title>. <source>eLife</source>, <volume>8</volume>, <elocation-id>e43599</elocation-id>. doi:<pub-id pub-id-type="doi">10.7554/eLife.43599</pub-id>.</mixed-citation></ref>
<ref id="c54"><label>54.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Adams</surname>, <given-names>S. K.</given-names></string-name>, <string-name><surname>Ducharme</surname>, <given-names>G. E.</given-names></string-name> &amp; <string-name><surname>Loveday</surname>, <given-names>E. K.</given-names></string-name></person-group> <year>2024</year> <article-title>All the single cells: if you like it then you should put some virus on it</article-title>. <source>Journal of virology</source>, <volume>98</volume>, <fpage>e0127323</fpage>. doi:<pub-id pub-id-type="doi">10.1128/jvi.01273-23</pub-id>.</mixed-citation></ref>
<ref id="c55"><label>55.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Tenthorey</surname>, <given-names>J. L.</given-names></string-name>, <string-name><surname>Young</surname>, <given-names>C.</given-names></string-name>, <string-name><surname>Sodeinde</surname>, <given-names>A.</given-names></string-name>, <string-name><surname>Emerman</surname>, <given-names>M.</given-names></string-name> &amp; <string-name><surname>Malik</surname>, <given-names>H. S.</given-names></string-name></person-group> <year>2020</year> <article-title>Mutational resilience of antiviral restriction favors primate TRIM5a in host-virus evolutionary arms races</article-title>. <source>eLife</source>, <volume>9</volume>. doi:<pub-id pub-id-type="doi">10.7554/eLife.59988</pub-id>.</mixed-citation></ref>
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<article-id pub-id-type="doi">10.7554/eLife.108921.1.sa4</article-id>
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<article-title>eLife Assessment</article-title>
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<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Graw</surname>
<given-names>Frederik</given-names>
</name>
<role specific-use="editor">Reviewing Editor</role>
<aff>
<institution-wrap>
<institution>Friedrich-Alexander-University Erlangen-Nürnberg</institution>
</institution-wrap>
<city>Erlangen</city>
<country>Germany</country>
</aff>
</contrib>
</contrib-group>
<kwd-group kwd-group-type="evidence-strength">
<kwd>Solid</kwd>
</kwd-group>
<kwd-group kwd-group-type="claim-importance">
<kwd>Valuable</kwd>
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<p>The authors combine experiments and mathematical modeling to determine how the infectivity of human cytomegalovirus scales with the viral concentration in the inoculum, i.e., considering the multiplicity of infection (MOI). They propose and test different model assumptions to explain a mechanism termed &quot;apparent cooperativity&quot; of virions based on an observed super-linear increase in the number of infected cells with increasing inocula. The authors present a <bold>solid</bold> study showing <bold>valuable</bold> findings for virologists and quantitative scientists working on the analysis and interpretation of viral infection dynamics. Some of the presented aspects would benefit from additional clarification.</p>
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<article-id pub-id-type="doi">10.7554/eLife.108921.1.sa3</article-id>
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<article-title>Reviewer #1 (Public review):</article-title>
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<contrib contrib-type="author">
<anonymous/>
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<p>Summary:</p>
<p>In this paper, the authors conduct both experiments and modeling of human cytomegalovirus (HCMV) infection in vitro to study how the infectivity of the virus (measured by cell infection) scales with the viral concentration in the inoculum. A naïve thought would be that this is linear in the sense that doubling the virus concentration (and thus the total virus) in the inoculum would lead to doubling the fraction of infected cells. However, the authors show convincingly that this is not the case for HCMV, using multiple strains, two different target cells, and repeated experiments. In fact, they find that for some regimens (inoculum concentration), infected cells increase faster than the concentration of the inoculum, which they term &quot;apparent cooperativity&quot;. The authors then provided possible explanations for this phenomenon and constructed mathematical models and simulations to implement these explanations. They show that these ideas do help explain the cooperativity, but they can't be conclusive as to what the correct explanation is. In any case, this advances our knowledge of the system, and it is very important when quantitative experiments involving MOI are performed.</p>
<p>Strengths:</p>
<p>Careful experiments using state-of-the-art methodologies and advancing multiple competing models to explain the data.</p>
<p>Weaknesses:</p>
<p>There are minor weaknesses in explaining the implementation of the model. However, some specific assumptions, which to this reviewer were unclear, could have a substantial impact on the results. For example, whether cell infection is independent or not. This is expanded below.</p>
<p>Suggestions to clarify the study:</p>
<p>(1) Mathematically, it is clear what &quot;increase linearly&quot; or &quot;increase faster than linearly&quot; (e.g., line 94) means. However, it may be confusing for some readers to then look at plots such as in Figure 2, which appear linear (but on the log-log scale) and about which the authors also say (line 326) &quot;data best matching the linear relationship on a log-log scale&quot;.</p>
<p>(2) One of the main issues that is unclear to me is whether the authors assume that cell infection is independent of other cells. This could be a very important issue affecting their results, both when analyzing the experimental data and running the simulations. One possible outcome of infection could be the generation of innate mediators that could protect (alter the resistance) of nearby cells. I can imagine two opposite results of this: i) one possibility is that resistance would lead to lower infection frequencies and this would result in apparent sub-linear infection (contrary to the observations); or ii) inoculums with more virus lead to faster infection, which doesn't allow enough time for the &quot;resistance&quot; (innate effect) to spread (potentially leading to results similar to the observations, supra-linear infection).</p>
<p>(3) Another unclear aspect of cell infection is whether each cell only has one chance to be infected or multiple chances, i.e., do the authors run the simulation once over all the cells or more times?</p>
<p>(4) On the other hand, the authors address the complementary issue of the virus acting independently or not, with their clumping model (which includes nice experimental measurements). However, it was unclear to me what the assumption of the simulation is in this case. In the case of infection by a clump of virus or &quot;viral compensation&quot;, when infection is successful (the cell becomes infected), how many viruses &quot;disappear&quot; and what happens to the rest? For example, one of the viruses of the clump is removed by infection, but the others are free to participate in another clump, or they also disappear. The only thing I found about this is the caption of Figure S10, and it seems to indicate that only the infected virus is removed. However, a typical assumption, I think, is that viruses aggregate to improve infection, but then the whole aggregate participates in infection of a single cell, and those viruses in the clump can't participate in other infections. Viral cooperativity with higher inocula in this case would be, perhaps, the result of larger numbers of clumps for higher inocula. This seems in agreement with Figure S8, but was a little unclear in the interpretation provided.</p>
<p>(5) In algorithm 1, how does P_i, as defined, relate to equation 1?</p>
<p>(6) In line 228, and several other places (e.g., caption of Table S2), the authors refer to the probability of a single genome infecting a cell p(1)=exp(-lambda), but shouldn't it be p(1)=1-exp(-lambda) according to equation 1?</p>
<p>(7) In line 304, the accrued damage hypothesis is defined, but it is stated as a triggering of an antiviral response; one would assume that exposure to a virion should increase the resistance to infection. Otherwise, the authors are saying that evolution has come up with intracellular viral resistance mechanisms that are detrimental to the cell. As I mentioned above, this could also be a mechanism for non-independent cell infection. For example, infected cells signal to neighboring cells to &quot;become resistance&quot; to infection. This would also provide a mechanism for saturation at high levels.</p>
<p>(8) In Figure 3, and likely other places, t-tests are used for comparisons, but with only an n=5 (experiments). Many would prefer a non-parametric test.</p>
</body>
</sub-article>
<sub-article id="sa2" article-type="referee-report">
<front-stub>
<article-id pub-id-type="doi">10.7554/eLife.108921.1.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>In their article, Peterson et al. wanted to show to what extent the classical &quot;single hit&quot; model of virion infection, where one virion is required to infect a cell, does not match empirical observations based on human cytomegalovirus in vitro infection model, and how this would have practical impacts in experimental protocols.</p>
<p>They first used a very simple experimental assay, where they infected cells with serially diluted virions and measured the proportion of infected cells with flow cytometry. From this, they could elegantly show how the proportion of infected cells differed from a &quot;single hit&quot; model, which they simulated using a simple mathematical model (&quot;powerlaw model&quot;), and better fit a model where virions need to cooperate to infect cells. They then explore which mechanism could explain this apparent cooperation:</p>
<p>(1) Stochasticity alone cannot explain the results, although I am unsure how generalizable the results are, because the mathematical model chosen cannot, by design, explain such observations only by stochasticity.</p>
<p>(2) Virion clumping seemed not to be enough either to generally explain such a pattern. For that, they first use a mathematical model showing that the apparent cooperation would be small. However, I am unsure how extreme the scenario of simulated virion clumping is. They then used dynamic light scattering to measure the distribution of the sizes of clumps. From these estimates, they show that virion clumps cannot reproduce the observed virion cooperation in serial dilution assays. However, the authors remain unprecise on how the uncertainty of these clumps' size distribution would impact the results, as most clumps have a size smaller than a single virion, leaving therefore a limited number of clumps truly containing virions.</p>
<p>The two models remain unidentifiable from each other but could explain the apparent virion cooperativity: either due to an increase in susceptibility of the cell each time a virion tries to infect it, or due to viral compensation, where lesser fit viruses are able to infect cells in co-infection with a better fit virion. Unfortunately, the authors here do not attempt to fit their mathematical model to the experimental data but only show that theoretical models and experimental data generate similar patterns regarding virion apparent cooperation.</p>
<p>Finally, the authors show that this virions cooperation could make the relationship between the estimated multiplicity of infection and viruses/cell deviate from the 1:1 relationship. Consequently, the dilution of a virion stock would lead to an even stronger decrease in infectivity, as more diluted virions can cooperate less for infection.</p>
<p>Overall, this work is very valuable as it raises the general question of how the estimate of infectivity can be biased if extrapolated from a single virus titer assay. The observation that HCMV virions often cooperate and that this cooperation varies between contexts seems robust. The putative biological explanations would require further exploration.</p>
<p>This topic is very well known in the case of segmented viruses and the semi-infectious particles, leading to the idea of studying &quot;sociovirology&quot;, but to my knowledge, this is the first time that it was explored for a nonsegmented virus, and in the context of MOI estimation.</p>
</body>
</sub-article>
<sub-article id="sa3" article-type="referee-report">
<front-stub>
<article-id pub-id-type="doi">10.7554/eLife.108921.1.sa1</article-id>
<title-group>
<article-title>Reviewer #3 (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>The authors dilute fluorescent HCMV stocks in small steps (df ≈ 1.3-1.5) across 23 points, quantify infections by flow cytometry at 3 dpi, and fit a power-law model to estimate a cooperativity parameter n (n &gt; 1 indicates apparent cooperativity). They compare fibroblasts vs epithelial cells and multiple strains/reporters, and explore alternative mechanisms (clumping, accrued damage, viral compensation) via analytical modeling and stochastic simulations. They discuss implications for titer/MOI estimation and suggest a method for detecting &quot;apparent cooperativity,&quot; noting that for viruses showing this behavior, MOI estimation may be biased.</p>
<p>Strengths:</p>
<p>(1) High-resolution titration &amp; rigor: The small-step dilution design (23 serial dilutions; tailored df) improves dose-response resolution beyond conventional 10× series.</p>
<p>(2) Clear quantitative signal: Multiple strain-cell pairs show n &gt; 1, with appropriate model fitting and visualization of the linear regime on log-log axes.</p>
<p>(3) Mechanistic exploration: Side-by-side modeling of clumping vs accrued damage vs compensation frames testable hypotheses for cooperativity.</p>
<p>Weaknesses:</p>
<p>(1) Secondary infection control: The authors argue that 3 dpi largely avoids progeny-mediated secondary infection; this claim should be strengthened (e.g., entry inhibitors/control infections) or add sensitivity checks showing results are robust to a small secondary-infection contribution.</p>
<p>(2) Discriminating mechanisms: At present, simulations cannot distinguish between accrued damage and viral compensation. The authors should propose or add a decisive experiment (e.g., dual-color coinfection to quantify true coinfection rates versus &quot;priming&quot; without coinfection; timed sequential inocula) and outline expected signatures for each mechanism.</p>
<p>(3) Decline at high genomes/cell: Several datasets show a downturn at high input. Hypotheses should be provided (cytotoxicity, receptor depletion, and measurement ceiling) and any supportive controls.</p>
<p>(4) Include experimental data: In Figure 6, please include the experimentally measured titers (IU/mL), if available.</p>
<p>(5) MOI guidance: The practical guidance is important; please add a short &quot;best-practice box&quot; (how to determine titer at multiple genomes/cell and cell densities; when single-hit assumptions fail) for end-users.</p>
</body>
</sub-article>
<sub-article id="sa4" article-type="author-comment">
<front-stub>
<article-id pub-id-type="doi">10.7554/eLife.108921.1.sa0</article-id>
<title-group>
<article-title>Author response:</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Peterson</surname>
<given-names>Christopher</given-names>
</name>
<role specific-use="author">Author</role>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Miller</surname>
<given-names>Joshua</given-names>
</name>
<role specific-use="author">Author</role>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Ryckman</surname>
<given-names>Brent J</given-names>
</name>
<role specific-use="author">Author</role>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Ganusov</surname>
<given-names>Vitaly V</given-names>
</name>
<role specific-use="author">Author</role>
<contrib-id contrib-id-type="orcid">http://orcid.org/0000-0001-6572-1691</contrib-id></contrib>
</contrib-group>
</front-stub>
<body>
<disp-quote content-type="editor-comment">
<p><bold>Reviewer #1 (Public review):</bold></p>
<p>Summary:</p>
<p>In this paper, the authors conduct both experiments and modeling of human cytomegalovirus (HCMV) infection in vitro to study how the infectivity of the virus (measured by cell infection) scales with the viral concentration in the inoculum. A naïve thought would be that this is linear in the sense that doubling the virus concentration (and thus the total virus) in the inoculum would lead to doubling the fraction of infected cells. However, the authors show convincingly that this is not the case for HCMV, using multiple strains, two different target cells, and repeated experiments. In fact, they find that for some regimens (inoculum concentration), infected cells increase faster than the concentration of the inoculum, which they term &quot;apparent cooperativity&quot;. The authors then provided possible explanations for this phenomenon and constructed mathematical models and simulations to implement these explanations. They show that these ideas do help explain the cooperativity, but they can't be conclusive as to what the correct explanation is. In any case, this advances our knowledge of the system, and it is very important when quantitative experiments involving MOI are performed.</p>
<p>Strengths:</p>
<p>Careful experiments using state-of-the-art methodologies and advancing multiple competing models to explain the data.</p>
<p>Weaknesses:</p>
<p>There are minor weaknesses in explaining the implementation of the model. However, some specific assumptions, which to this reviewer were unclear, could have a substantial impact on the results. For example, whether cell infection is independent or not. This is expanded below.</p>
<p>Suggestions to clarify the study:</p>
<p>(1) Mathematically, it is clear what &quot;increase linearly&quot; or &quot;increase faster than linearly&quot; (e.g., line 94) means. However, it may be confusing for some readers to then look at plots such as in Figure 2, which appear linear (but on the log-log scale) and about which the authors also say (line 326) &quot;data best matching the linear relationship on a log-log scale&quot;.</p>
</disp-quote>
<p>This is a good point. In our revision, we will include a clarification to indicate that linear on the log-log scale relationship does not imply linear relationship on the linear-linear scale.</p>
<disp-quote content-type="editor-comment">
<p>(2) One of the main issues that is unclear to me is whether the authors assume that cell infection is independent of other cells. This could be a very important issue affecting their results, both when analyzing the experimental data and running the simulations. One possible outcome of infection could be the generation of innate mediators that could protect (alter the resistance) of nearby cells. I can imagine two opposite results of this: i) one possibility is that resistance would lead to lower infection frequencies and this would result in apparent sub-linear infection (contrary to the observations); or ii) inoculums with more virus lead to faster infection, which doesn't allow enough time for the &quot;resistance&quot; (innate effect) to spread (potentially leading to results similar to the observations, supra-linear infection).</p>
</disp-quote>
<p>In our models we assumed cells to be independent of each other (see also responses to other similar points). Because we measure infection in individual cells, assuming cells are independent is a reasonable first approximation. However, the reviewer makes an excellent point that there may be some between-cell signaling happening in the culture that “alerts” or “conditions” cells to change their “resistance”. It is also possible that at higher genome/cell numbers, exposure of cells to virions or virion debris may change the state of cells in the culture, and more cells become “susceptible” to infection. This is a good point that we will list in Limitations subsection of Discussion; it is a good hypothesis to test in our future experiments.</p>
<disp-quote content-type="editor-comment">
<p>(3) Another unclear aspect of cell infection is whether each cell only has one chance to be infected or multiple chances, i.e., do the authors run the simulation once over all the cells or more times?</p>
</disp-quote>
<p>Each cell has only one chance to be infected. Algorithm 1 clearly states that; we will add an extra sentence in “Agent-based simulations” to indicate this point.</p>
<disp-quote content-type="editor-comment">
<p>(4) On the other hand, the authors address the complementary issue of the virus acting independently or not, with their clumping model (which includes nice experimental measurements). However, it was unclear to me what the assumption of the simulation is in this case. In the case of infection by a clump of virus or &quot;viral compensation&quot;, when infection is successful (the cell becomes infected), how many viruses &quot;disappear&quot; and what happens to the rest? For example, one of the viruses of the clump is removed by infection, but the others are free to participate in another clump, or they also disappear. The only thing I found about this is the caption of Figure S10, and it seems to indicate that only the infected virus is removed. However, a typical assumption, I think, is that viruses aggregate to improve infection, but then the whole aggregate participates in infection of a single cell, and those viruses in the clump can't participate in other infections. Viral cooperativity with higher inocula in this case would be, perhaps, the result of larger numbers of clumps for higher inocula. This seems in agreement with Figure S8, but was a little unclear in the interpretation provided.</p>
</disp-quote>
<p>This is a good point. We did not remove the clump if one of the virions in the clump manages to infect a cell, and indeed, this could be the reason why in some simulations we observe apparent cooperativity when modeling viral clumping. This is something we will explore in our revision.</p>
<disp-quote content-type="editor-comment">
<p>(5) In algorithm 1, how does P_i, as defined, relate to equation 1?</p>
</disp-quote>
<p>These are unrelated because eqn.(1) is a phenomenological model that links infection per cell to genomes per cell. P_i in algorithm 1 is “physics-inspired” potential barrier.</p>
<disp-quote content-type="editor-comment">
<p>(6) In line 228, and several other places (e.g., caption of Table S2), the authors refer to the probability of a single genome infecting a cell p(1)=exp(-lambda), but shouldn't it be p(1)=1-exp(-lambda) according to equation 1?</p>
</disp-quote>
<p>Indeed, it was a typo, p(1)=1-exp(-lambda) per eqn 1. Thank you, it will be corrected in the revised paper.</p>
<disp-quote content-type="editor-comment">
<p>(7) In line 304, the accrued damage hypothesis is defined, but it is stated as a triggering of an antiviral response; one would assume that exposure to a virion should increase the resistance to infection. Otherwise, the authors are saying that evolution has come up with intracellular viral resistance mechanisms that are detrimental to the cell. As I mentioned above, this could also be a mechanism for non-independent cell infection. For example, infected cells signal to neighboring cells to &quot;become resistance&quot; to infection. This would also provide a mechanism for saturation at high levels.</p>
</disp-quote>
<p>We do not know how exposure of a cell to one virion would change its “antiviral state”, i.e., to become more or less resistant to the next infection. If a cell becomes more resistant, there is no possibility to observe apparent cooperativity in infection of cells, so this hypothesis cannot explain our observations with n&gt;1. Whether this mechanism plays a role in saturation of cell infection rate at lower than 1 value when genome/cell is large is unclear but is a possibility. We will add this point to Discussion in revision.</p>
<disp-quote content-type="editor-comment">
<p>(8) In Figure 3, and likely other places, t-tests are used for comparisons, but with only an n=5 (experiments). Many would prefer a non-parametric test.</p>
</disp-quote>
<p>We repeated the analyses in Fig 3 with Mann-Whitney test, results were the same, so we would like to keep results from the t-test in the paper.</p>
<disp-quote content-type="editor-comment">
<p><bold>Reviewer #2 (Public review):</bold></p>
<p>In their article, Peterson et al. wanted to show to what extent the classical &quot;single hit&quot; model of virion infection, where one virion is required to infect a cell, does not match empirical observations based on human cytomegalovirus in vitro infection model, and how this would have practical impacts in experimental protocols.</p>
<p>They first used a very simple experimental assay, where they infected cells with serially diluted virions and measured the proportion of infected cells with flow cytometry. From this, they could elegantly show how the proportion of infected cells differed from a &quot;single hit&quot; model, which they simulated using a simple mathematical model (&quot;powerlaw model&quot;), and better fit a model where virions need to cooperate to infect cells. They then explore which mechanism could explain this apparent cooperation:</p>
<p>(1) Stochasticity alone cannot explain the results, although I am unsure how generalizable the results are, because the mathematical model chosen cannot, by design, explain such observations only by stochasticity.</p>
</disp-quote>
<p>Our null model simulations are not just about stochasticity; they also include variability in virion infectivity and cell resistance to infection. We agree that simulations cannot truly prove that such variability cannot result in apparent cooperativity; however, we also provide a mathematical proof that increase in frequency of infected cells should be linear with virion concentration at small genome/cell numbers.</p>
<disp-quote content-type="editor-comment">
<p>(2) Virion clumping seemed not to be enough either to generally explain such a pattern. For that, they first use a mathematical model showing that the apparent cooperation would be small. However, I am unsure how extreme the scenario of simulated virion clumping is. They then used dynamic light scattering to measure the distribution of the sizes of clumps. From these estimates, they show that virion clumps cannot reproduce the observed virion cooperation in serial dilution assays. However, the authors remain unprecise on how the uncertainty of these clumps' size distribution would impact the results, as most clumps have a size smaller than a single virion, leaving therefore a limited number of clumps truly containing virions.</p>
</disp-quote>
<p>As we stated in the paper, clumping may explain apparent cooperativity in simulations depending on how stock dilution impacts distribution of virions/clump. This could be explored further, however, better experimental measurements of virions/clump would be highly informative (but we do not have resources to do these experiments at present). Our point is that the degree of apparent cooperativity is dependent on the target cell used (n is smaller on epithelial cells than on fibroblasts) that is difficult to explain by clumping which is a virion property. Per comment by reviewer 1, we will do some more analyses of the clumping model to investigate importance of clump removal per successful infection on the detected degree of apparent cooperativity.</p>
<disp-quote content-type="editor-comment">
<p>The two models remain unidentifiable from each other but could explain the apparent virion cooperativity: either due to an increase in susceptibility of the cell each time a virion tries to infect it, or due to viral compensation, where lesser fit viruses are able to infect cells in co-infection with a better fit virion. Unfortunately, the authors here do not attempt to fit their mathematical model to the experimental data but only show that theoretical models and experimental data generate similar patterns regarding virion apparent cooperation.</p>
</disp-quote>
<p>In the revision we will provide examples of simulations that “match” experimental data with a relatively high degree of apparent cooperativity; we have done those before but excluded them from the current version since they are a bit messy. Fitting simulations to data may be an overkill.</p>
<disp-quote content-type="editor-comment">
<p>Finally, the authors show that this virions cooperation could make the relationship between the estimated multiplicity of infection and viruses/cell deviate from the 1:1 relationship. Consequently, the dilution of a virion stock would lead to an even stronger decrease in infectivity, as more diluted virions can cooperate less for infection.</p>
<p>Overall, this work is very valuable as it raises the general question of how the estimate of infectivity can be biased if extrapolated from a single virus titer assay. The observation that HCMV virions often cooperate and that this cooperation varies between contexts seems robust. The putative biological explanations would require further exploration.</p>
<p>This topic is very well known in the case of segmented viruses and the semi-infectious particles, leading to the idea of studying &quot;sociovirology&quot;, but to my knowledge, this is the first time that it was explored for a nonsegmented virus, and in the context of MOI estimation.</p>
</disp-quote>
<p>Thank you.</p>
<disp-quote content-type="editor-comment">
<p><bold>Reviewer #3 (Public review):</bold></p>
<p>Summary:</p>
<p>The authors dilute fluorescent HCMV stocks in small steps (df ≈ 1.3-1.5) across 23 points, quantify infections by flow cytometry at 3 dpi, and fit a power-law model to estimate a cooperativity parameter n (n &gt; 1 indicates apparent cooperativity). They compare fibroblasts vs epithelial cells and multiple strains/reporters, and explore alternative mechanisms (clumping, accrued damage, viral compensation) via analytical modeling and stochastic simulations. They discuss implications for titer/MOI estimation and suggest a method for detecting &quot;apparent cooperativity,&quot; noting that for viruses showing this behavior, MOI estimation may be biased.</p>
<p>Strengths:</p>
<p>(1) High-resolution titration &amp; rigor: The small-step dilution design (23 serial dilutions; tailored df) improves dose-response resolution beyond conventional 10× series.</p>
<p>(2) Clear quantitative signal: Multiple strain-cell pairs show n &gt; 1, with appropriate model fitting and visualization of the linear regime on log-log axes.</p>
<p>(3) Mechanistic exploration: Side-by-side modeling of clumping vs accrued damage vs compensation frames testable hypotheses for cooperativity.</p>
</disp-quote>
<p>Thank you.</p>
<disp-quote content-type="editor-comment">
<p>Weaknesses:</p>
<p>(1) Secondary infection control: The authors argue that 3 dpi largely avoids progeny-mediated secondary infection; this claim should be strengthened (e.g., entry inhibitors/control infections) or add sensitivity checks showing results are robust to a small secondary-infection contribution.</p>
</disp-quote>
<p>This is an important point. We do believe that the current knowledge about HCMV virion production time – it takes 3-4 days to make virions per multiple papers (see Fig 7 in Vonka and Benyesh-Melnick JB 1966; Fig 3B in Stanton et al JCI 2010; and Fig 1A in Li et al. PNAS 2015) – is sufficient to justify our experimental design but we do agree that an additional control to block novel infections with would be useful. We had previously performed experiments with a HCMV TB-gL-KO that cannot make infectious virions (but the stock virions can be made from complemented target cells). We will investigate if our titration experiments with this virus strain have sufficient resolution to detect apparent cooperativity. However, at present we do not have the resources to perform novel experiments.</p>
<disp-quote content-type="editor-comment">
<p>(2) Discriminating mechanisms: At present, simulations cannot distinguish between accrued damage and viral compensation. The authors should propose or add a decisive experiment (e.g., dual-color coinfection to quantify true coinfection rates versus &quot;priming&quot; without coinfection; timed sequential inocula) and outline expected signatures for each mechanism.</p>
</disp-quote>
<p>Excellent suggestion. Because infection of a cell is a result of the joint viral infectivity and cell resistance, it may be hard to discriminate between these alternatives unless we specify them as particular molecular mechanisms. But we will try our best and list potential future experiments in the revised version of the paper.</p>
<disp-quote content-type="editor-comment">
<p>(3) Decline at high genomes/cell: Several datasets show a downturn at high input. Hypotheses should be provided (cytotoxicity, receptor depletion, and measurement ceiling) and any supportive controls.</p>
</disp-quote>
<p>Another good point. We do not have a good explanation, but we do not believe this is because of saturation of available target cells.  It seemed to only happen (or was most pronounced) with the ME stocks, which are typically lower in titer and so the higher MOI were nearly undiluted stock. It may be the effect of the conditioned medium.  Or perhaps there are non-infectious particles like dense bodies (enveloped particles that lack a capsid and genome) and non-infectious, enveloped particles (NIEPs) that compete for receptors or otherwise damage cells and these don’t get diluted out at the higher doses.  We plan to include these points in Discussion of the revised version of the paper.</p>
<disp-quote content-type="editor-comment">
<p>(4) Include experimental data: In Figure 6, please include the experimentally measured titers (IU/mL), if available.</p>
</disp-quote>
<p>This is a model-simulated scenario, and as such, there is no measured titers.</p>
<disp-quote content-type="editor-comment">
<p>(5) MOI guidance: The practical guidance is important; please add a short &quot;best-practice box&quot; (how to determine titer at multiple genomes/cell and cell densities; when single-hit assumptions fail) for end-users.</p>
</disp-quote>
<p>Good suggestion. We will include best-practice box using guidelines developed in Ryckman lab over the years in the revised version of the paper.</p>
<p>Overall note to all reviews: We have deposited our codes and the data on github; yet, none of the reviewers commented on it.</p>
</body>
</sub-article>
</article>