Figures and data
Experimental design and alternative hypotheses for the apparent cooperativity between viruses infecting the same cell.
A: 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 Supplemental Figures S2 and S3. B: 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.
Parameters used in simulations.
“Default value” indicates the value of the parameter unless otherwise specified in specific simulations.
Apparent cooperativity of human CMV strains at infecting different target cells.
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 Figure 1A). We then fitted a “powerlaw” model (eqn. (1)) to subsets of these data (shown in color) and calculated parameter n, indicating a degree of apparent cooperativity of the virions at infecting cells (n = 1 – no cooperativity, n > 1 – apparent cooperativity, see Materials and Methods for more detail). For each estimate we also show p value from the likelihood ratio test when comparing the powerlaw model fit to the single-hit (n = 1) model fit. The solid black lines show the predictions of the mathematical model (eqn. (1)) 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, p(1) from eqn. (1). Fits of the extended powerlaw model (eqn. (2)) are shown in Supplemental Figure S4.
All HCMV strains show reduced infectivity and reduced apparent cooperativity when infecting epithelial cells.
We plot the relationship between estimated power parameter n (A-C) or virion infectivity (infectivity of a single genome, p(1), D-F), and other viral and cell characteristics such as target cell type (A&D), reporter gene (B&E), and HCMV strain (C&F). Parameter n indicates cooperativity in virus infection of cells (estimates are given in individual panels in Figure 2). Comparisons were done using paired t-test. In panel G we show the relationship between estimated virion infectivity p(1) and apparent cooperativity n estimated for different strain/cell combinations; we also show the linear fit and p value from the test of no relationship.
Heterogeneity in virion infectivity and/or susceptibility to infection of target cells and aggregation of virions does not result in apparent cooperativity in simulations.
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 (A), clumping model in which virions aggregate (B and Figure 1Bi), accrued damage model, in which individual virions attaching to a cell reduces its resistance (C and Figure 1Bii), and viral compensation model in which virions attaching to a cell acquire infectivity of the most infectious virion (D and Figure 1Biii, 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 n = 1.60, Figure 2B). We fitted the powerlaw model (eqn. (1)) to the results of simulations using likelihood approach (eqn. (7)) and estimated the degree of apparent viral cooperativity (n) 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 Table 1. Note that to model viral clumps we assumed that clump size followed Poisson distribution; other details are given in Material and methods section.
Incorporating experimentally measured distribution of viral aggregates in simulations did not result in apparent cooperativity in the clumping model.
A: 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 Supplemental Figure S8). B: 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 (eqn. (1)) to the linear part of the data and estimated degree of apparently cooperativity n. C-D: We used experimentally measured distribution of clump sizes and estimated how many virions are located in a given clump of a diameter D assuming random packing of spheres with d = 230 nm (see eqn. (5) and text in Materials and methods). We then simulated infection of cells by sampling virions in clumps (clumping model, C) and calculating probability of cell infection at different genome/cell dilutions. We show the results of 10 simulations with parameters listed in Table 1 except we used 103 target cells. In D, we fitted the powerlaw model (eqn. (1) to the data from simulations and estimated the degree of apparent cooperativity n. Makers denote average values and gray areas show the range of simulation results. Listed p-values were calculated to estimate deviation of estimated n from n = 1 using LRT. The size of HCMV virion of d = 230 nm is indicated by a dashed vertical line in panel A.
Calculations of MOI are imprecise for virus-cell combinations exhibiting apparent cooperativity.
A: For viruses with n = 1, infectious titer scales linearly with changing genomes/cell (ME.GFP.Epithelial). B: However, for viruses with n > 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. C: Expected MOI changes nonlinearly for virus-cell combinations with apparent cooperativity (n > 1); MOIR is the ratio of MOIs when specific infectivity is reduced 10 fold (i.e., stock is diluted 10 fold, from 106 to 105 genomes/mL); here target cell concentration is 106 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 (Supplemental Table S2).
Standardized relationship between volume pipette dispenses and the actual weight of the dispensed volume (standard curve).
We performed experiments by dispensing different volumes of the DMEM media (at 200C 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 ± values in the first column). Analysis of the data is shown in Supplemental Figure S1A.
Using a standard curve converting media mass to volume allows for more accurate quantification of the degree of apparent cooperativity.
A: 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 Supplemental Table S1). Value m denotes the slope of the linear regression of log-transformed values and p-value is from the t-test for m = 1. B-E: We fitted the powerlaw model (eqn. (1)) to the data on ME-mCherry (B-C) or TB-GFP (D-E) strain infection of fibroblasts at different dilutions of viral stocks assuming that the pipette gives the correct assumed volume (B&D) or when correcting the dispensed volume using the calibration curve (C&E, see also Materials and methods for more detail). Estimated degree of apparent cooperativity n is shown on individual panels. Dilution factor used in calculating genomes/cell is 1.43 and 1.44 in panels B and C, respectively, and 1.43 and 1.48 in panels D and E, respectively.
Kinetics of GFP and mCherry expression in fibroblasts exposed to different HCMV strains.
A: 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. B: We followed change in percent of fibroblasts infected with GFP-(i-iii) or mCherry-expressing viruses (iv-v). We show the data from individual three cultures (gray lines) and average (markers with colored lines).
Detecting cells infected with GFP or mCherry-expressing HCMV virions at different dilutions of the stock.
We show flow cytometry plots of TB-GFP-(A) or ME-mCherry-(B) 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 (g/c) are shown on individual panels.
Estimates of parameters determining infectivity of HCMV strains for different target cells.
The model fits are shown in Figure 2 and details of how the model (eqn. (1)) 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 p(1) and the degree of apparent cooperativity n; numbers in parentheses are 95% confidence intervals generated by bootstrapping the data with replacement in 1000 simulations. Note that in eqn. (1), p(1) = e−λ.
Apparent cooperativity of HCMV strains at infecting targets is still detected when fitting the extended powerlaw model to all data.
We fitted extended powerlaw model (eqn. (2)) 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.
A degree of apparent cooperativity is dependent on the range of genome/cell and virus-cell combination.
For each HCMV strain and cell combinations (see Figure 2) we determined the degree of apparent cooperativity n by taking subset of the data between different dilutions (starting with the highest dilution 23) and including different numbers of dilutions (denoted as window). We then fitted the powerlaw model (eqn. (1)) to these data and estimated the degree of apparent cooperativity n. Note that at high initial genome/cell subsets of data, n < 1 indicating competition between virions at infecting cells.
Apparent cooperativity of HIV and Vaccinia virus at infecting target cells.
We analyzed data from two previously published papers [38, 55] that measured infection probability of cell exposed to different number of virions and estimated degree of apparent cooperativity from their data. A: change infection of TRIM5α-deficient CRFK cells (control or transdused with TRIM5α) exposed to different dilutions of HIV-1-GFP [55]. B: change in the probability of a HeLa cell exposed to a given number of vaccinia virus virions deposited on the cell surface [38]. For both studies we calculated the slope n by fitting the powerlaw model (eqn. (1)) to the data using maximum likelihood method (see Materials and methods for details). Shown p values are from likelihood ratio test when comparing model fit with n ≠ 1 to that with n = 1. Data are shown as markers and model fits as lines. Dashed line represents the slope of one. In A, data points shown in gray were excluded from the model fit.
Lack of apparent cooperativity of Tobacco mosaic virus (TMV) on Nicotiuna glutinom plants.
We analyzed data from studies documenting formation of lesions on plant leaves exposed to different dilutions of TMV stock [9, 10]. We show data that were numerically provided in Kleczkowski [9] and fitted the powerlaw model (eqn. (1)) to these data to estimate degree of apparent cooperativity n (listed p values are from a LRT with a model fit with n = 1). Dashed line represents the slope of one. Data points shown in gray were excluded from the model fit.
Distribution of viral clumps in three different experiments is well described by a mixture of two log-normal distributions.
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 D and calculated the fraction of the larger peak f1; the average of the larger peak 
Quantification of virions in clumps does not result in linear scaling in virions/well at different dilutions of the stock.
A: From the measured distribution of size (diameter) of viral clumps in a given stock preparation we sampled clumps of different sizes (with a diameter D). Assuming that these clumps are spheres and that a given clump is composed of spherical virions of a diameter d, we calculate the number of virions (genomes) per clump using eqn. (5). Vertical dashed line in the plot denotes threshold for debris vs. virions when diameter of the clump is smaller than the virion size d. B: We calculated the predicted number of virions present in clumps of different sizes D using estimates of the log-normal distribution fitted to the data generated by dynamic light scattering (Supplemental Figure S8) and that number of virions per clump of size D scales as cube (eqn. (5)); the relative number of virions per well (or per cell) is proportional to
Clumping model may lead to apparent cooperativity at some chosen parameter values.
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. A: We plot change in cell infection probability with increasing genomes/cell produced in simulations. We fitted the powerlaw model (eqn. (1)) to the subsets of simulation data and estimated degree of apparent cooperativity n. B: We show the mean of the clump size distribution λ at different genomes/cell values. C: We show an example of distribution of virions/clump simulated different stock dilutions. In these simulations we assume λ = 2 and we followed infection of 103 cells/well; other parameters are also noted in A.
