Quantifying the relative contribution of free virus and cell-to-cell transmission routes to the propagation of hepatitis C virus infections in vitro using an agent-based model
Kenneth Blahut, Christian Quirouette, Jordan J. Feld, Shingo Iwami, Catherine A.A. Beauchemin
QQuantifying the relative contribution offree virus and cell-to-cell transmission routesto the propagation of hepatitis C virus infections in vitrousing an agent-based model
Kenneth Blahut , Christian Quirouette , Jordan J. Feld , Shingo Iwami , andCatherine A.A. Beauchemin ∗ Department of Physics, Ryerson University, Toronto, ON, Canada Toronto Centre for Liver Disease, University Health Network, Sandra Rotman Centre forGlobal Health, University of Toronto, Toronto, Canada Department of Biology, Kyushu University, Fukuoka, Japan Institute for the Advanced Study of Human Biology (ASHBi), Kyoto University, Kyoto,Japan NEXT-Ganken Program, Japanese Foundation for Cancer Research (JFCR), Tokyo, Japan Science Groove Inc., Fukuoka, Japan Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN, Wako, JapanFebruary 11, 2021
Abstract
Experiments have shown that hepatitis C virus (HCV) infections in vitro disseminate both distallyvia the release and diffusion of cell-free virus through the medium, and locally via direct, cell-to-celltransmission. To determine the relative contribution of each mode of infection to HCV dissemination,we developed an agent-based model (ABM) that explicitly incorporates both distal and local modes ofinfection. The ABM tracks the concentration of extracellular infectious virus in the supernatant andthe number of intracellular HCV RNA segments within each infected cell over the course of simulatedin vitro HCV infections. Experimental data for in vitro HCV infections conducted in the presence andabsence of free-virus neutralizing antibodies was used to validate the ABM and constrain the value ofits parameters. We found that direct, cell-to-cell infection accounts for 99% (84%–100%, 95% credibleinterval) of infection events, making it the dominant mode of HCV dissemination in vitro. Yet, wheninfection via the free-virus route is blocked, a 57% reduction in the number of infection events at 72 hpi isobserved experimentally; a result consistent with that found by our ABM. Taken together, these findingssuggest that while HCV spread via cell-free virus contributes little to the total number of infection eventsin vitro, it plays a critical role in enhancing cell-to-cell HCV dissemination by providing access to distant,uninfected areas, away from the already established large infection foci. ∗ Corresponding author. Email: [email protected] . a r X i v : . [ q - b i o . CB ] F e b Introduction
Virus infections in vitro can disseminate distally via release and diffusion of cell-free virus through theinfection medium, and/or locally by direct cell-to-cell transmission of virus [22]. Each mode of infectionpresents various evolutionary advantages and disadvantages to the virus in vivo. Cell-free virions releasedinto the extracellular medium can diffuse over large distances to infect cells, but are exposed and vulnerableto the innate and humoral immune responses as well as to antivirals targeting cell-free virus infectivity or thefree virions’ mode of attachment and entry. In contrast, cell-to-cell infection proceeds through close contact,with virions being transmitted directly from an infected cell to an adjacent uninfected cell. This directtransmission can protect virions from extracellular harm, but it also limits the pool of target cells available tothe virions, restricting the spatial extent of infection. Many viruses, including the human immunodeficiencyvirus type 1 [10], the murine leukemia virus [15], the respiratory syncytial virus (RSV) [13], and the hepatitisC virus (HCV) [31], take advantage of both modes of infection.Given the distinct manner by which cell-free and cell-to-cell HCV dissemination can affect and modulatethe efficacy of a therapeutic antiviral intervention or that of the host immune response, it is importantto resolve the relative contribution of either mode to the overall infection course. Unfortunately, this isparticularly challenging to do in vivo, and is nearly as challenging to resolve in vitro for a number of reasons.Direct cell-to-cell HCV dissemination, at least in vitro, is thought to proceed via many of the same cellularreceptors used for cell-free transmission including SR-BI, CLDN1, OCLN and NPC1L1 [1,5,24,31], with somedebate on the necessity of CD81 [36]. However, the route of direct, cell-to-cell transmission (e.g. gap junction,tight junctions, apical surface) and the nature of the matter being transmitted cell-to-cell (e.g. viral RNAsegments, fully-formed encapsidated virion, host-enveloped lipoviral particles) have yet to be identified [7].As such, without knowing the pathways and infectious units specific to each mode of transmission, it is notpossible to develop probes or markers to tag infection events and identify which mode caused each infectionevent. High-density, low-diffusion agar medium or neutralizing antibodies (nAbs), which significantly limitor inhibit cell-free virus dissemination, have been used to perform in vitro HCV infection experimentsand evaluate the role of cell-free infection relative to that of direct cell-to-cell infection [1, 6, 9, 31]. Co-cultures have also been used to control or restrict HCV dissemination to the free-virus or cell-to-cell routeindividually [5, 20, 36, 37]. However, given that blocking cell-free infection modulates (hinders or facilitates)cell-to-cell transmission, and vice-versa, an experimentally-observed reduction in the number of infectionevents when one mode of transmission is blocked cannot simply, directly be ascribed to the contribution ofthat mode to infection.In the case of HIV infections, these experimental limitations were overcome by using a mathematicalmodel to analyze and appropriately interpret the experimental results [14]. Through mathematical analysisof experimental infections, Iwami et al. established that direct, cell-to-cell transmission of HIV was found toaccount for ∼
60% of all infection events in the dissemination of HIV infections in vitro. This was a particu-larly significant finding in light of an earlier experimental observation that the direct, cell-to-cell route of HIVtransmission is resistant to some HIV antiviral therapy [28]. In the case of HCV, the relative contributionof the cell-free versus cell-to-cell modes of transmission has yet to be clearly resolved. Monotherapy withdirect-acting antivirals (DAAs), which have replaced the previous standard-of-care treatment consisting ofinterferon- α and ribavirin therapy, are known to result in the emergence of DAA-resistant HCV mutants invivo [27]. Importantly, these resistant virus appear to predominantly disseminate via the cell-to-cell routein vitro [37]. These recent observations highlight the importance of resolving the relative contribution of thecell-to-cell and cell-free routes of HCV transmission. In this work, we make use of an agent-based model(ABM) to simulate the course of in vitro HCV infections. The ABM is calibrated so as to reproduce thecourse and outcome of experimental HCV infections performed in the presence and absence of nAbs. Thecalibrated ABM is then used to identify the relative contributions of the two routes of HCV transmission invitro. 2 Figure 1:
Hexagonal packing of Huh7 hepatocytes in 2-D cell monolayers in vitro.
The sameimage is repeated 4 × , and in each view two central (shaded) cells are identified in one specific colour, andthe cell’s neighbourhood, i.e. those cells which appear to be in direct contact with that central cell, arecoloured identically and numbered. Most cells appear to be in direct contact with 6 other cells, hence thechoice of a hexagonal grid for the ABM, shown in the right-most panel (screenshot from the ABM renderedgrid). The cell-culture image was captured by confocal microscopy (630 × , bar = 20 µ m) where cell nuclei(blue) were stained by Hoechst dye, and antibodies specific for tight junction protein zona occludens 1(ZO-1, red) appear cleanly localized to intercellular junctions (see Methods for experimental details). Theimage has been adapted, as described in Methods, from the original article “Three-dimensional Huh7 cellculture system for the study of Hepatitis C virus infection” by [Bruno Sainz Jr., Veronica TenCate, SusanL. Uprichard]. Virology Journal 2009, 6:103 (doi: ) [26]. The original article isan open access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproductionin any medium, provided the original work is properly cited. We constructed an ABM which reproduces the spread of HCV infections in vitro by capturing HCV dissemi-nation both locally, via cell-to-cell transmission, and distally, via the release and diffusion of free virus throughthe extracellular medium. The standard experimental in vitro infection system, consisting in a monolayer ofhepatocytes, is represented in the ABM as a hexagonal grid wherein each site, j = 1 , , ..., N cells , correspondsto one hepatocyte. The ABM grid is (100 × ×
2) mm, assuming one hepatocyte is 20 µ m in diameter. The hexagonal grid geometrywas chosen because it best represents the natural arrangement and contact neighbourhood of confluent hep-atocytes in cell cultures in vitro, as shown in Figure 1. Graphically, the ABM grid is first rendered as aregular hexagonal lattice, and then each node is displaced by a random, normally distributed distance withzero mean and a standard deviation equal to 1/3 the hexagons’ regular edge length. The node displacementshave no impact on the resulting infection kinetics because they do not alter which hepatocyte neighbourwhich, but yield a more visually realistic cell layout for display purposes.The ABM tracks the number of intracellular HCV RNA copies contained within each infected hepatocyteover time, R j ( t ) in hepatocyte j at time t , expressed in units of HCV RNA copies. In contrast, the con-centration of extracellular (cell free) infectious HCV is assumed uniform everywhere across the simulationgrid (or cell culture), and is represented in the ABM as a single, global variable, V ( t ), expressed in unitsof focus forming units or FFU/mL. We tested and determined (not shown) that the infection time courseunder this assumption of a spatially uniform virus concentration, V ( t ), does not differ significantly fromthat obtained when tracking local virus concentration at each site, V j ( t ), as we did previously in [3]. This isnot surprising given that the diffusion rate of HCV (10 − m / s, based on Stokes-Einstein for HCV virions60 nm in diameter, assuming a viscosity of 7 × − kg / (m · s) for water at 37 ◦ C) is sufficiently large for thisassumption to hold, as shown in our previous work [12].In this way, the ABM-predicted, cell-free, extracellular, infectious HCV concentration in the medium3FFU/mL), and the average intracellular HCV RNA level per cell (HCV RNA per µ g of cellular RNA)over the course of our in silico HCV infections, can be directly compared against these same experimentalquantities commonly measured in vitro. One important advantage of the in silico infection model, however, isits ability to track, label, and distinguish between hepatocytes infected via the free virus versus the cell-to-cellroutes of transmission, something we exploit later.Both experimentally and in our ABM, the HCV infection is initiated by incubating hepatocytes with aninoculating medium containing extracellular infectious virus (FFU/mL). If the hepatocyte at site j becomesinfected at time t = t j, infected , the number of HCV RNA copies within the newly infected hepatocyte, R j ( t ),grows at rate α , following a Gompertz curve, to ultimately reach a steady state value of ¯ R HCV RNA copies.This is expressed in the ABM as R j ( t ) = (cid:40) ¯ R − exp {− α [ t − ( t j, infected + t RNAoffset )] } if t > t j, infected , (1)where the age of infection of hepatocyte j is given by a j = t − t j, infected . An additional time offset, t RNAoffset ,was introduced to account for the delay between successful HCV infection and the start of significant HCVRNA replication, as observed in Keum et al. [17]. This delay in viral production, referred to as the eclipsephase [4, 11, 12], is implemented in Eqn. (1) such that R j ( t = t j, infected + t RNAoffset ) = R j ( a j = t RNAoffset ) =1 HCV RNA.As the number of HCV RNA within an infected hepatocyte increases towards ¯ R , so do the probabilityof direct cell-to-cell infection of a neighbouring cell and the rate of release of newly produced, infectiousHCV progeny into the extracellular medium. The rate of release of infectious HCV into the medium by allhepatocytes in the ABM is represented as p V ( t ) = ¯ V · c ¯ R · N cells · N cells (cid:88) j =1 (cid:40) R j ( t ) if t > ( t j, infected + t RNAoffset )0 otherwise , where (cid:80) N cells j =1 R j ( t ) for t > ( t j, infected + t RNAoffset ) is the sum of intracellular HCV RNA over all infectedhepatocytes as per Eqn. (1), N cells is the number of hepatocytes considered in the ABM, ¯ V is the steady-state, cell-free infectious HCV concentration in the extracellular medium, and c is the rate at which infectiousHCV loses infectivity. The maximum rate of release of free infectious HCV into the medium, p max V = ¯ V c , isreached when all hepatocytes have been infected for sufficiently long that all have reached their steady stateintracellular HCV RNA concentration of R j = ¯ R for all j . The concentration of cell-free, infectious HCV inthe medium over the course of the infection, as per [3, 12], is given by V ( t + ∆ t ) = V ( t ) e − c ∆ t + p V ( t )∆ t , (2)where ∆ t is the duration of one time step of our ABM simulation, which is adapted at each step, chosen soas to ensure the probability of infection is less than 10% in any one ABM step. The term e − c ∆ t accountsfor the reduction in the concentration of infectious HCV RNA in the medium over the course of one ABMtime step, i.e. from V ( t ) to V ( t + ∆ t ), due to the exponential loss of HCV infectivity at rate c . When therate of infectious HCV release into the medium is maximal, p max V = ¯ V c , it is equal to the rate of loss of virusinfectivity, resulting in a steady state of extracellular infectious HCV concentration in the medium of ¯ V .After hepatocytes infected by the initial inoculum have progressed through the initial phases of virusreplication and release, the following rounds of infection can proceed. In our ABM, the probability that ahepatocyte does not become infected via the free virus route decreases, as the concentration of extracellularinfectious HCV in the medium increases, namely P free-virusnot-infected ( t ) = exp (cid:20) − ∆ tβ V V ( t )¯ V (cid:21) , (3)where the steady state concentration of extracellular infectious HCV, ¯ V , is used to rescale V ( t ) such that β V , a rate representing extracellular HCV infectivity per unit time, is unaffected by and independent of the4ethod used to measure it experimentally (e.g. FFU vs TCID ). Similarly, the probability that a hepatocyte does not become infected via the cell-to-cell route decreases as the fraction of the cell’s six neighbours whichhave been infected for longer than time t RNAoffset increases, namely P cell-to-cellnot-infected ( t ) = exp (cid:34) − ∆ tβ C (cid:80) I nei ( t )6 (cid:35) where I nei ( t ) = (cid:40) t > ( t j, infected + t RNAoffset )0 otherwise , (4)where β C is a rate representing cell-to-cell HCV infectivity per unit time, analogous to β V for cell-freeinfections. As such, the probability that a hepatocyte is infected by either mode of infection (free virus orcell-to-cell) is given by P infected ( t ) = 1 − (cid:2) P free-virusnot-infected ( t ) · P cell-to-cellnot-infected ( t ) (cid:3) , and the probability that a hepatocyte is infected by one specific mode of infection is given for each mode by P free-virusinfected = P infected · (cid:18) − P free-virusnot-infected − P free-virusnot-infected − P cell-to-cellnot-infected (cid:19) P cell-to-cellinfected = P infected · (cid:18) − P cell-to-cellnot-infected − P free-virusnot-infected − P cell-to-cellnot-infected (cid:19) . In all, our ABM has 3 biological parameters related to intracellular HCV replication ( ¯ R , α , t RNAoffset ) fromEqn. (1), and 4 biological parameters ( ¯ V , c , β V , β C ) related to the kinetics of HCV dissemination fromEqns. (2),(3),(4). These parameters will need to be determined by challenging the ABM with experimentalin vitro HCV infection data, which we tackle in the next section. Three distinct experimental data sets were used to constrain the biologically-relevant parameters of theABM, and to ultimately determine the relative contributions of the cell-free virus versus cell-to-cell modesof infection to HCV dissemination in vitro: Keum et al. [17], Sainz et al. [25], and Timpe et al. [31]. Table1 provides an overview of the source and nature of the data, and how they were used herein to parametrizethe ABM.The data from Keum et al. [17] were used to parameterize the single-cell, intracellular HCV replicationkinetics described by Eqn. (1). The data consist of the mean intracellular, positive-strand HCV RNA per cell,measured over the course of three independent in vitro experiments in which Huh7.5.1 cells were infected at ahigh MOI (6 FFU / cell). The high MOI serves to roughly synchronize the time of infection of all hepatocytesin the assay such that the time course of average intracellular HCV within the culture as a whole representsthat within a single HCV-infected cell. We fit the Gompertz curve, Eqn. (1), representing the intracellularHCV RNA replication, to the Keum et al. [17] data, as shown in Figure 2, with details provided in Methods.From this, we obtained an estimate for the intracellular HCV growth rate of α = 0 .
097 h − .The data from Sainz et al. [25] were used to parametrize the kinetics of HCV dissemination throughthe cell culture. To arrest proliferation of hepatocytes during infection, Sainz et al. [25] treated Huh7 cellswith dimethyl sulphoxide (DMSO) for 20 days prior to HCV infection. The DMSO-treated Huh7 cells wereinfected with an inoculum of HCV JFH1 at a low MOI (0 .
01 FFU / cell), resulting in several cycles of infectionwhich enabled us to establish the kinetics of infection spread, unobserved in Keum et al. [17]. The dataconsist in frequent measurements of both the concentration of intracellular HCV RNA quantified via RT-qPCR (HCV RNA / µ g total RNA) shown in Figure 3A, and the concentration of extracellular infectious HCVin the supernatant quantified via titration on Huh7 cells immunostained with anti-HCV E2 Abs reportedas focus forming units (FFU / mL) shown in Figure 3B. While this data set provides information aboutthe kinetic of HCV dissemination over multiple cycles of infection, it does not provide spatial data norinformation about the mode of dissemination.In order to specifically address the relative contribution of the free virus versus cell-to-cell disseminationof HCV in vitro, additional data from Timpe et al. [31] were considered in parametrizing the ABM. Timpe5able 1: Summary of data used in the analysis.Source of data Figure herein Experiment details ApplicationIntracellular positive strand HCV RNA/cellKeum et al. [17] MOI: 6 FFU/cell Kinetics of HCV replication withina single cell. Fitted with Eqn. (1) toestimate and fix parameter α .Fig. 1A (black diamond) Fig. 2 (red circles) Virus: JFH-m4 a Cell line: Huh7.5.1Intracellular HCV RNA/ µ g total cell RNASainz et al. [25] MOI: 0.01 FFU/cell Intracellular HCV kinetics duringmultiple-cycle infection. Used to fix¯ V = 10 and estimate ABMPPLDs via MCMC with Eqn (8).Fig. 3A (open diamond) Fig. 3A (red stars) Virus: JFH1Fig. 4A (line) Fig. 3A (red circles) Cell line: Huh7Extracellular infectious HCV in FFU / mLSainz et al. [25] MOI: 0.01 FFU/cell Extracellular HCV kinetics duringmultiple-cycle infection. Used to fix¯ R = 120 HCVcell and estimate ABMPPLDs via MCMC with Eqn (8).Fig. 3B (open diamond) Fig. 3B (red stars) Virus: JFH1Fig. 4A (bars) Fig. 3B (red circles) Cell line: Huh7Number of cells infected at 72 hpi in the presence of nAbs, expressed relative to controlTimpe et al. [31] MOI: 0.01 b Number of cells infected in presenceof nAbs is (43 ± b Provides estimate for the foci sizedistribution at 72 hpi. Used tovalidate ABM results post PPLDestimation.Fig. 1E,F (black bars) Fig. 4 Virus: JFH1Cell line: Huh7.5 a JFH-m4 is HCV JFH1-derived, but harbours mutations in E2 and p7 proteins (see Discussion for details). b Units of the MOI were not specified by the authors.Figure 2:
Best-fit to estimate the intracellular HCV RNA growth rate.
The data set by Keum etal. [17] (Fig 1A therein) consists in the mean over three independent experiments of the concentration ofpositive-strand intracellular HCV (vRNA/cell) over the course of an infection with HCV JFH-m4 in Huh7.5.1cells in vitro at a MOI of 6 FFU / cell. Fitting Eqn. (1) (line) to the data (circles) enabled us to estimate thegrowth rate of intracellular HCV RNA to be α = 0 .
097 h − (see Methods for details).6t al. [31] infected Huh7.5 cells with JFH1 at a MOI of 0.01 (presumably 0 .
01 FFU / cell, though this is notspecified in [31]) for one hour. The infections were performed in the presence of either a control (anti-denguenAbs) or anti-HCV nAbs which were shown therein to neutralize >
95% of cell-free, extracellular HCV. ThenAbs were added to the extracellular medium at 8 h post-infection (hpi), and replenished every 24 h thereafterto maintain the neutralizing activity. At 72 hpi, the number of HCV-infected hepatocytes resulting frominfection in the presence of anti-HCV nAbs and the control infection were counted. Unfortunately, Timpeet al. [31] do not report any kinetic information (measurements of virus or cell infection over time) from thetime course of these infections. Instead, they provide the number of infected hepatocytes in the presence ofanti-HCV nAbs and in the control infection, at 72 hpi, in the form of a bar graph (Fig. 2D in [31]), with errorbars representing the standard error of the mean (SEM) based on 4 independent experiments. From thisbar graph, we extract (see Methods) a single quantity: at 72 hpi, the number of HCV-infected hepatocytesin the presence of anti-HCV nAbs is (43 ± V = 10 FFU / mL, and intracellular HCV RNA reaches a steady state of 6 × HCV RNA copies per µ g oftotal cellular RNA. Assuming that all hepatocytes are infected at steady state, and one hepatocyte contains20 pg (or 20 × − µ g) of total cellular RNA [32, 35], then each HCV infected Huh7 cell in the Sainz etal. [25] experiment contained on average approximately ¯ R = 120 HCV RNA copies at steady state. Havingfixed α , ¯ V and ¯ R , only 4 biological parameters ( t RNAoffset , c , β V , β C ) remain to be determined. In addition,two parameters are required to describe the experimental conditions: the initial virus inoculum V ( t = 0),and the efficacy with which this inoculum is rinsed at the end of the incubation period, 0 ≤ f rinse ≤ t RNAoffset , c , β V , β C , V (0), f rinse ), the course of HCVinfections is simulated twice: once in the presence of anti-HCV nAbs and again in their absence. To simulatethe infection in the presence of nAbs, the extracellular infectious HCV concentration, V ( t ), and rate of HCVrelease, p V ( t ), are set to 0 at t ≥ V ( t ≥ R ( t ) , V ( t ), respectively) is compared against the kinetic Sainz etal. [25] data sets, and the number of infected cells in the presence divided by that in the absence of nAbs at72 hpi in the ABM-simulated infections, f I (72 h) (a single number), is compared against the expected valueof 43% from Timpe et al. [31]. Since these three sets of measurements ( R ( t ) , V ( t ) , f I (72 h) ) have differentnumber of points, units, and standard deviations, the sum-of-squared residuals (SSR) for each measurementset were normalized by the variance of their respective residuals, before being summed together, as describedin Methods, Eqn. (8). The time course for R and V in the presence of nAbs, which was simulated byour ABM in order to determine f I (72 h) , is not used because these data were unfortunately not measuredexperimentally.Because the ABM-simulated infections are stochastic, one set of parameters, ( t RNAoffset , c , β V , β C , V (0), f rinse ), does not map to a unique SSR value. To address this issue, we introduce one additional nuisanceparameter, the random number seed (RNS), used to seed the pseudo random number generator at the start ofeach ABM run. This renders the now 7-dimensional parameter space defined by ( t RNAoffset , c , β V , β C , V (0), f rinse , RNS) deterministic, and yields a single goodness-of-fit measure, SSR( (cid:126)p ), for any given parameter set (cid:126)p ,as specified in Methods, Eqn. (8). To estimate (cid:126)p , we used a Markov chain Monte Carlo (MCMC) approach,as described previously [4, 23, 29]. Briefly, each candidate parameter set, (cid:126)p , is accepted with a probabilitybased on its Bayesian likelihood, defined in Eqn. (8) in Methods. The collection of all accepted parametersets forms the posterior parameter likelihood distributions (PPLDs) whose modes and 95% credible intervals(CI) are reported in Table 2.Figure 3(A,B) presents the intracellular HCV RNA and extracellular infectious HCV kinetics over thecourse of the parametrized ABM-simulated HCV infections in the absence of nAbs against the Sainz et al. [25]experimental data. The MCMC-parametrized ABM reproduces this HCV infection kinetics well. In Figure3C, however, the PPLD for the number of HCV-infected hepatocytes in the presence of nAbs relative to thatin the absence of nAbs at 72 hpi in our parametrized ABM-simulated infections visually does not appear to7able 2: MCMC-estimated PPLDs for the ABM. Mode [95%CI] a — Fixed or computed directly from data (see footnotes) —Number of hepatocytes, N cell (cell) 10,000 b Intracellular HCV RNA growth rate, α (h − ) 0 . c Equilibrium extracellular infectious HCV concentration, ¯ V (FFU / mL) 10 d Equilibrium intracellular HCV RNA concentration, ¯ R (HCV RNA/cell) 120 d — PPLDs estimated via MCMC —Intracellular HCV RNA replication delay, t RNAoffset (h) 19 [9 . , c (h − ) 0 .
27 [0 . , . β C (h − ) 85 [3 . , V (0) (FFU / mL) 10 . . , . Multiplicity of infection, MOI (FFU/cell) 10 − . − . , − . Effectiveness of the rinse, f rinse .
47 [0 . , . β V (h − ) 10 − . − . , − . Percent infected cells w/wo nAbs at 72 hpi, f I (72 h) (%) 91 [49 , , . . , a Mode and 95% CI determined from the PPLDs. b The spatial extent of the hexagonal ABM is (100 × ∼ (2 ×
2) mm assuming one hepa-tocyte is ∼ µ m in diameter [19]. c Estimated from the Keum et al. [17] data (see Methods and Figure 2). d Steady states of extracellular infectious HCV and intracellular HCV RNA in experimental data from Sainzet al. [25]. 8igure 3:
Comparison of experimental vs ABM-generated course of HCV infection in vitro.
Thetime course of (A) intracellular HCV RNA and (B) extracellular infectious HCV, measured in duplicate(red stars and circles) from Sainz et al. [25] are shown against the median of ABM-simulated time coursesin the absence of nAbs (red line) and its associated 68% and 95% percentiles of the y -value at each x -value(time point) for 500 ABM simulations performed (grey bands). Data points from Sainz et al. [25] on the reddash line in panel (B) are at the limit of detection (see Methods for discussion). (C) The relative percentageof HCV-infected hepatocytes in the presence vs absence of anti-HCV nAbs at 72 hpi of (43 ± D,E,F ) Same as (A,B,C), but results from a different MCMC PPLD estimation wherein theweight (importance) of the Timpe et al. [31] measurement (C,F) was increased by decreasing σ f (in Eqn.(8)) from 0.16 in (A,B,C) to 0.04 in (D,E,F). The drop in ABM-simulated extracellular HCV titer recurringevery 3 days in panel (B,E) simulates the replacement of the extracellular medium which took place over thecourse of the experimental infection. See Methods for details on how the ABM-predictions were performed.9rovide a good agreement with that reported in Timpe et al. [31]. Quantitatively, this disagreement is notstatistically significant, yielding a fold-change of 1.7 (0.73–5.2, 95% CI), i.e. 1 is included within the 95% CIof the fold-change. The disagreement is more apparent in Figure 3C because it shows a single measure orpoint, but worse agreements can be found at other single time point measurements in Figure 3(A,B), e.g.at 4 dpi in Figure 3A. In establishing the parameter likelihood for the MCMC method, namely Eqn. (8) inMethods, each measure is weighted by its standard deviation, i.e. the degree of uncertainty in that measure,such that less emphasis is placed on measures with larger uncertainty, as it should be. This should not beinterpreted to mean that the ABM could not simultaneously fit the kinetic data a little less well so as toprovide a better agreement with the measure shown in Figure 3C if this weighting was adjusted.To demonstrate this, we placed 16 × more weight ( σ f in Eqn. (8) decreased from 0 . to 0 . ) on themeasure from Timpe et al. [31], and repeated the MCMC PPLD estimation. The results are shown in Figure3(D,E,F), and the modes and 95% CI of the corresponding PPLDs are in Table 3. As expected, the variabilityin the infection kinetics curves (Figure 3A,B vs D,E) increases slightly while the relative percentage of HCV-infected cells in the presence vs absence of nAbs (Figure 3C vs F) now provides perfect agreement withthe measure reported by Timpe et al. [31], albeit with an unphysically narrow PPLD standard deviation.Importantly, imposing this unrealistically strict constraint for agreement with the Timpe et al. [31] measurecauses a statistically significant change in said measure only (1 (cid:54)∈ [0 . , . Figure 4 shows that the parametrized ABM’s simulated foci size distributions agree well with those reportedin Timpe et al. [31] in the presence and absence of nAbs (or agar). This provides some degree of validationof the spatial predictions of the parametrized ABM.Next, the parametrized ABM was used to run in silico simulations to robustly quantify and establish thepercentage of hepatocytes infected via each infection route: cell-to-cell and free virus. To do so, we allowedeach simulated infection parametrized from our PPLD to run their full course (up to 10 days post-infection)such that all or almost all hepatocytes have become infected. At the end of each of these simulated infectionsperformed in the absence of nAbs, we recorded the percentage of all infected hepatocytes infected via thecell-to-cell and free virus route, reported in Table 2. The parametrized ABM estimates that only about 1.2%(0.038%–16%, 95% CI) of all infection events over the full course of the infection (10 days) in the absenceof nAbs occur via the free virus route, with the remainder ( ∼ ∼
13% of hepatocytes in our ABM-simulated infections have become infected.Since experimental infections are initiated by a free virus inoculum, the fraction of infections due to freevirus is initially 100% of infection events. But as time progresses, and several rounds of the more rapid cell-to-cell infections take place, the proportion of infections in the presence vs absence of nAbs will progressivelydecrease. In other words, the 43% reported by Timpe et al. [31] should not be considered a definitivequantification of the contribution of each mode, but rather a much less informative “snap-shot” of thatquantity at a somewhat arbitrary time post-inoculation.The other reason is that there is a synergy between infections via the free virus and cell-to-cell routes,such that a small reduction in the number of free virus infection greatly reduces the number of cell-to-cellinfections. This can be seen in Figure 6 which presents a visualization of the spatial spread of an ABM-simulated in silico HCV infection at 72 hpi. Each new focus is initiated by a seed hepatocyte infected distallyvia free virus (blue), claiming a new, fresh, uninfected area. Direct cell-to-cell infection (yellow) then takesover to efficiently disseminate infection from the initial seed to its neighbouring hepatocytes, which go on to10 mall medium large020406080100 P e r ce n t ag e o ff o c i ( % ) without nAbs small medium large020406080100 P e r ce n t ag e o ff o c i ( % ) with nAbs or agar ABMTimpe Figure 4:
Quantitative comparison of ABM-simulated and experimental foci size distributions.
The ABM-simulated percentage of small ( <
10 cells), medium (10–50 cells), and large ( >
50 cells) foci at72 hpi for 1000 simulations, each simulation containing between 1 and 455 foci, are shown both as scatterdots and percentile bars (median, 68% CI, 95% CI = bar, light grey, dark grey). These are compared againstthat observed by Timpe et al. [31] (Fig. 1E,F therein) who counted and categorized 50 foci (single red scatterdot and red bar). Note that Timpe et al. [31] do not specify if their 50 foci were counted within the samewell or experiment, or summed over several independent experiments, nor provide any error bars. Resultsare shown for HCV infections in the absence (left) and presence (right) of free virus dissemination, whichwas blocked in our ABM by adding nAbs, whereas Timpe et al. [31] used agar. The ABM-simulated focisize distributions are in good agreement with those observed by Timpe et al. [31] (agrees within the 68% CIin all but one that agrees within the 95% CI). See Methods for details on how the ABM-predictions wereperformed. 11igure 5:
Fraction of infection by each mode, and the relative impact of nAbs.
ABM-simulatedtime courses for the (A) fraction of cells that are HCV-infected in the presence of nAbs over that in theirabsence; (B) fraction of cells that are HCV-infected in the absence (grey) and presence (blue) of nAbs; and (C) fraction of HCV-infected cells that were infected via free virus (CF) over the fraction of all cells thatare HCV-infected (I). The solid line (red or blue) indicate the median, and the pale and darker bands (greyor cyan) indicate the 68% and 95% percentiles of the y -value at each x -value (time point) for 500 ABMsimulations performed (see Methods). (D,E,F) same as (A,B,C), but results from the different MCMCPPLD estimation wherein the weight of the Timpe et al. [31] data was increased ( σ f : 0 . → .
04 in Eqn.(8)). The vertical dashed line at 3 dpi illustrates the time of the fraction of cells recorded by Timpe etal. [31]. 12igure 6:
Visualizing the spatial spread of an ABM-simulated in silico HCV infection.
Spatialrepresentation of an ABM simulated in silico HCV infection at 72 hpi, using a parameter set pulled atrandom from the PPLD, (left) without nAbs, (centre) with nAbs and (right) difference between the two.Uninfected hepatocytes (white) become infected via free virus (blue) or by spread of infection via cell-to-cell(yellow). In the right panel, cells which were infected in the simulation without nAbs, but are no longerinfected when nAbs were added appear in black for free virus infected cells, and red from cell-to-cell infectedcells. In rare cases, the simulation with nAbs has some cells infected which were not infected without nAbs(purple) because, despite the simulation with and without nAbs having been run with the same randomnumber seed, different lists of random numbers were generated in each run. This visual comparison showsthat the removal of free virus by nAbs not only affects the number of hepatocytes infected by free virusbut also affects the number infected via cell-to-cell transmission as each new focus begins with a hepatocyteinfected by free virus and then grows almost exclusively via direct, local, cell-to-cell infection.directly infect their neighbours, and so on. The in silico labelling of the mode by which each hepatocyte wasinfected highlights that indeed most hepatocytes are infected via direct cell-to-cell contact (yellow) ratherthan via free virus (blue). In particular, it shows that at 72 hpi, the largest and thus oldest foci have 2–3“concentric rings” of infected hepatocytes, which add up to 20–40 hepatocytes, of which only one was infectedvia free virus, and the remainder via cell-to-cell, which corresponds to ∼
3% (1/30) of infections proceedingvia the free virus route.A more quantitative analysis of this principle is presented in Figure 7 where the ABM was used tosimulate infections starting from a single infected seed hepatocyte, progressing exclusively via either freevirus or cell-to-cell dissemination. As the single focus grows from its initial seed via cell-to-cell infection,the decreasing perimeter-to-area ratio of the focus leads to decreasing number of infections caused by anincreasing number of infected hepatocytes. In contrast, when infection proceeds via free virus alone, therate of infection per infected hepatocyte remains constant. Figure 7A shows that once a single focus hasgrown to ∼ ∼
40% probability that a new focus will have beeninitiated via free virus and the cell-to-cell infection rate per cell has decreased to ∼
5% of its value from thestart of the infection. 13igure 7:
HCV kinetics for dissemination via cell-to-cell alone or free-virus alone.
The ABM wasused to simulate the course of 100 infections, using parameter sets pulled at random with replacement fromthe PPLD, initiated with a single infected hepatocyte wherein infection disseminates via either only cell-to-cell (red, p V ( t ) = 0) or only free virus (black, β C = 0). (A) The infection rate per cell as a function of thenumber of infected cells remains constant for dissemination via free virus (black), but decreases for cell-to-celldissemination (red). The solid lines are the geometric means, the error bars for cell-to-cell infections arethe geometric standard deviations, and the pale and darker grey bands for free virus infections are the 68%and 95% CI over the simulations performed. Dash lines show that when a single focus has grown to ∼ (B) The decrease in the cell-to-cell infection rate per cell as a functionof time for cell-to-cell dissemination alone (red, left y -axis) is shown against the % of ABM simulations inwhich a single growing focus disseminating through cell-to-cell infection alone would have caused at leastone infection via the free virus route (black, right y -axis). Dash lines show that at 3 dpi, when the largestfoci have a 2–3 “concentric rings” of infected cells, there is a ∼
40% probability that a new focus will havebeen initiated via free virus and the cell-to-cell infection rate per cell has decreased to ∼
5% of its value fromthe start of the infection. 14
Discussion
The hepatitis C virus (HCV) is one of many virus which take advantage of both the cell-free and cell-to-cell mechanisms of transmission to spread effectively [22]. Herein, we introduce a spatial ABM simulatorfor HCV infection spread in vitro. In the ABM, the in vitro infection system is represented as a two-dimensional hexagonal grid where each grid site corresponds to one hepatocyte. The ABM tracks both theoverall extracellular infectious HCV concentration in the supernatant, and the amount of intracellular HCVRNA within each hepatocyte. It captures both transmission via free virus in the supernatant, and via directcell-to-cell transmission to a hepatocyte’s six immediate neighbours. Published experimental data fromHCV infections performed in vitro in the presence and absence of nAbs were used to determine the unknownkinetic parameters of the ABM. In particular, data from in vitro infections wherein HCV dissemination viafree virus is suppressed by nAbs were considered. Once calibrated, the ABM was used to simulate the fullcourse of an in vitro HCV infection, and to identify and tag the mode of HCV transmission responsible forthe infection of each hepatocyte. Through this process, it was determined that 99% (84%–100%, 95% CI)of all hepatocytes are infected via the cell-to-cell route, with distal, free virus infection accounting for ∼ ±
16% of hepatocytes are infected in the presence of nAbs when the free virustransmission route is blocked, relative to that in the absence of nAbs. Our estimated fraction for this datawas 91% (49%–100%, 95% CI) when each data set was weighted appropriately. We investigated a tighteragreement between our simulations and the data presented by Timpe et al. [31] (using a standard deviationof 4% instead of 16%) and obtained this way an estimated fraction of 44% (37%–53%, 95% CI) but foundno significant difference in our parameter estimates or the final fractions of cells infected. Our finding that ∼
1% of hepatocytes are infected by free virus might appear inconsistent with the observation by Timpe etal. [31] that blocking this mode of transmission reduces the proportion of infection hepatocytes by as muchas 57%, suggesting a larger contribution of free virus transmission to HCV dissemination. However, thesefindings are not inconsistent when the synergy between these two modes of transmission is considered.Herein, we presented visualization of the course of HCV infection wherein the mode by which eachhepatocyte became infected is tagged by the ABM. The visualization shows that each new focus is initiated byinfection via free virus. Once seeded, a focus grows rapidly and efficiently via direct, cell-to-cell transmission.However, as the focus ages and continues to grow via direct transmission from infected hepatocytes to theirimmediate neighbours, most hepatocytes which make up the focus find themselves surrounded by otherinfected hepatocytes: only hepatocytes along the periphery of the focus with yet uninfected neighbours cancontinue contributing to the focus growth. As Beauchemin explained previously [2], this geometric constraintacts to reduce the effective rate of cell-to-cell transmission as a focus ages. We have observed that most cellsin a monolayer have about 6 neighbours on average, and as such we use a hexagonal grid to represent ourcells. The natural hexagonal arrangement of confluent hepatocytes in vitro is such that the perimeter (6 n )to area (3 n ( n + 1) + 1) ratio of a focus as it ages ( n ) results in an effective cell-to-cell transmission withineach focus which is proportional to the inverse of the age of the focus (1/age). Under these circumstances,infection of distal hepatocytes via free virus offers a much needed escape from the smothering effect of thegeometric constraint imposed on cell-to-cell transmission. Both modes of transmission work in a coordinatedmanner: rapid and efficient cell-to-cell transmission is enhanced through a continuously renewed supply ofyet uninfected distant hepatocytes made accessible via free virus transmission. While free virus infectionaccounts for ∼
1% of all infections, it accounts for 100% of new infection foci which are critical to maintaininga high rate of HCV dissemination.Our results indeed indicate that the rate of cell-free infection must be extremely low to explain the data.It is known that most cell-free virions are lost without further infection, simply because most virions are notinfectious. For HIV, SHIV, RSV, influenza A, HCV, it is common to have 1 infectious virion for every 100or even every 10,000 or more virions and as such, most cell-free virions will not cause infection. In HCV,this is especially true: to this day, only JFH HCV in Huh7.5(.1) cells can cause in vitro infection and yet15CV continues to be transmitted and to successfully infect humans, yet it barely propagates in vitro. Thishas also been an issue with the respiratory syncytial virus (RSV) and recently, an experimental in vitrosystem showed that, at least in that system, most RSV infections occurs directly cell-to-cell, and that cell-free virus are more a consequence/symptom of infected cell death than a significant route of disseminationof the infection to other cells [13]. Yet RSV is a highly infectious virus so it is not clear how to reconcile thisparadox. Our findings for HCV herein would be consistent with such a scenario.The experimental data presented herein were all taken from different sources, and as such, the threeinfections use different viruses/cells. The infection done in Keum et al. [17] used a cell culture derived JFHclone, with modified E2 and p7 protein. The modification of the E2 protein makes the virus more viable(higher concentrations of virus) and the p7 promotes an early stage of viral replication [18]. As such, whenconsidering the data from Keum et al. [17], we did not consider extracting the number of HCV RNA copiesper cell or the t RNAoffset from this data since they could be specifically affected by these virus mutations. Thethree different cell lines, Huh7.5.1, Huh7, and Huh7.5 used by Keum et al. [17], Sainz et al. [25], and Timpeet al. [31], respectively were also considered herein. Huh7.5 and Huh7.5.1 each have mutations reducing theIFN response, making them more susceptible to infection [38]. This should have little effect on our resultsusing Timpe et al. [31] data since this mutation should affect both modes of infection.The ABM developed herein is not the first mathematical study of HCV cell-to-cell dissemination. Graw etal. [9] developed and evaluated different hypotheses, formulated as mathematical models, for the mechanismof HCV dissemination in vitro. In agreement with past experimental work [31] and with our own findingsherein, Graw et al. [9] confirm that free virus transmission alone cannot explain the HCV infection focidistributions observed in vitro. Graw et al. [9] show that claudin-1 and Niemann-Pick C1-like 1 receptorsare critical and potentially necessary for cell-to-cell transmission. Graw et al. [9] consider two mathematicalmodels for the rate of cell-to-cell transmission: one proportional to the number of infected hepatocytes ina focus called the birth model, and another proportional to the number of infected hepatocytes along theperimeter of a focus called the boundary model. They find that while both mathematical models couldreproduce the experimentally observed distribution of focus sizes, the boundary model better reproducedthe frequency of smaller foci, while the birth model performed better for larger focus sizes. This could bebecause the birth and boundary models considered by Graw et al. [9] both neglect transmission via free virus.Indeed, Graw et al. [9] observe foci consisting of a single hepatocyte as late as 72 hpi even in the presence ofnAbs. Since new foci can only be formed via free virus colonization, and given that a focus of that size wouldhave to be relatively new and therefore not the result of the initial inoculum, this suggests that perhaps somefree virus transmission persists in their experiments despite nAbs. If their boundary model, most similarto our ABM’s implementation of cell-to-cell transmission, also included very rare but persistent free virustransmission, it is likely that it would better recapitulate their observed foci size distribution at all focussizes. Nevertheless, our model is better than the models developed by Graw et al. [9], as it incorporates bothcell-to-cell transmission and transmission via free virus and is able to not only determine that cell-to-celltransmission plays an important role in HCV dissemination but can quantify the relative contributions ofeach mode of infection.While our work establishes the clear dominance of cell-to-cell transmission in efficient HCV dissemination,it is not clear to what extent this finding in vitro would translate in vivo. Some of the geometry of tissuearrangement within the human liver resembles the two-dimensional geometry of the in vitro cell culture.However, a number of host factors, such as interferons, which are part of the innate immune response, couldmodulate the effectiveness of cell-to-cell transmission in vivo and skew the relative contribution of the twomodes. It has been observed that the innate immune response is active within days of HCV infection [34] andKandathil et al. [16] and Wieland et al. [33] both observed multiple focus formations in chronically infectedpatients, infecting 1% to 50% of the liver. As the innate immune response is thought to target cell-free virus,this implies that the innate immune response does not efficiently block all cell-free virus in vivo, but canhalt infection to some degree and could affect the relative contribution of the modes of infection.If the mode of HCV transmission in vivo resembles that which we establish here in vitro, then the invitro evaluation of antiviral therapies should enable relevant optimization for compounds which appropriatelytarget both modes of dissemination. If the mode of HCV transmission in vivo differs substantially from that16stablished in vitro, it is likely that in vitro optimization of antiviral targets would be sub-optimal in vivo.In such a case, however, mathematical analyses using our ABM could help discern an antiviral’s efficacy withrespect to each mode. It could also be used to optimize therapy for any relative contribution of each modewhich might exist in vivo. In fact, careful analysis of the differences in antiviral efficacy between the in vitroand in vivo systems could even be used to identify the relative contribution of cell-to-cell versus free-virusdissemination of HCV in vivo. 17 cknowledgements
This work was supported in part by Discovery Grant 355837-2013 (CAAB) from the Natural Sciences andEngineering Research Council of Canada ( ), Early Researcher Award ER13-09-040 (CAAB) from the Ministry of Research and Innovation of the Government of Ontario ( ), and by the Interdisciplinary Theoretical and Mathematical Sciencesprogramme (iTHEMS, ithems.riken.jp ) at RIKEN (CAAB). Additional support was provided by AMED( ) through its Japan Program for Infectious Diseases Research and Infrastructure grantnumbers 20wm0325007h0001, 20wm0325004s0201, 20wm0325012s0301, 20wm0325015s0301 (SI), its Re-search Program on Emerging and Re-emerging Infectious Diseases grant numbers 19fk0108156h0001 and20fk0108140s0801 (SI), its Program for Basic and Clinical Research on Hepatitis grant number 19fk0210036h0502(SI), and by the Japanese Science and Technology Agency ( ) Mirai Program (SI). The fundershad no role in study design, data collection and analysis, or decision to publish.
Disclosures
SI is the Chief Scientific Officer of Science Groove Inc.. Science Groove Inc. had no role in the study design,analysis, writing of the manuscript or decision to publish.
Authors contribution
CAAB, JJF were responsible for study conceptualization and project administration. KB, JJF, SI, CAABcontributed to the development of the methodology. KB, CQ, CAAB contributed to data analysis, software,visualization. CAAB and SI were responsible for funding acquisition. JJF, SI and CAAB were responsiblefor supervision. KB, JJF, CAAB contributed to the original manuscript draft. All authors contributed toits review and editing. 18
Methods
The original image is from the second row, right-most panel of Fig. 3 in [26]. It is an image of the 2-Dmonolayer of Huh7 cells seeded in 8-well chamber slides at 80% confluence and fixed 48 h post-seeding. Theoriginal image was captured by confocal microscopy (630 × , Zeiss LSM 510, Germany) and was co-stainedwith antibodies specific for tight junction protein zona occludens 1 (ZO-1)(Zymed) and Hoechst dye toidentify cell nuclei. The digital image file for the figure was obtained directly from the online (web) versionof the paper. It was edited using version 0.92.3 of the free and open-source software Inkscape TM to copy theimage 4 times over, and to colour the outline of the contact neighbourhood of 2 different hepatocytes perimage. Data from Fig. 1A (black diamond) in Keum et al. [17], which consists in the mean over three independentexperiments of the intracellular HCV RNA per cell over the course of a single-cycle HCV infection (MOI of6 FFU / cell), were extracted from the electronic version of the paper using version 5 of the software EngaugeDigitizer [21]. The first 3 data points (3 h, 6 h, 9 h) were discarded because they represent HCV RNA fromthe inoculum rather than de novo HCV RNA progeny. The last 2 data points (96 h, 120 h) were discardedbecause intracellular HCV RNA begins to decrease at these points, presumably due to virion progeny exportbecoming significant. These two phenomena are not captured by Eqn. (1), and thus their impact in the datahad to be minimized. Our fit of Eqn. (1) to the remaining data points (12 h, 18 h, 24 h, 36 h, 48 h, 72 h),determined through nonlinear least-square minimization, yielded best-fit values of α = 0 .
097 h − , ¯ R = 1790,and t RNAoffset = 10 . α , but not ¯ R nor t RNAoffset because the latter two are strongly dependent on the experimental system. For example, while this data byKeum et al. [17] suggests a steady-state HCV RNA/cell of ∼ ∼ t RNAoffset would include a combination of the delay to infect and that to produce progeny, a timingthat is further masked by the preexisting intracellular HCV RNA from the inoculum virus in this data set.
Data from Sainz et al. [25], specifically Fig. 3A (open diamond) and 4A (line) for intracellular HCV RNA, andFig. 3B (open diamond) and 4A (bars) for extracellular infectious HCV, were extracted from the electronicversion of the paper using version 5 of the software Engauge Digitizer [21]. According to the figure captions(the paper has no Methods section), the experimental procedures and conditions in their Fig. 3 and 4 appearto be identical. Specifically, confluent Huh7 cells treated with 1% DMSO, replenished every 3 days starting20 days prior to infection, were infected with HCV JFH1 at a MOI of 0 .
01 FFU / cell. Data in their Fig. 3are collected over 14 days whereas those in Fig. 4 are collected over 62 days. No error bars or replicates areshown in either of their Fig. 3 or 4, but the authors state only in their Fig. 4 caption that multiple wells wereinfected and that the data are representative of three independent experiments. The authors do not statewhether the “independent” experiments in Fig. 4 were different wells on the same plate or whether actualdistinct experiments were repeated independently. Since no error bars are provided, and since the authorsdo not explain what they mean by “representative of”, herein we interpret the data in their Fig. 3 and 4 astwo distinct and independent repeats of the same experiment. In comparing our ABM against these data,we consider only the early kinetic time points (at 1, 2, 3, 4, 6, 8, 10 days post-infection), after which bothintracellular and extracellular HCV reach a steady state value containing no valuable kinetic information.The day 1 and day 2 time points in Fig. 3A (open diamond) were moved from 10 FFU / mL in the originalpublication to 10 FFU / mL herein which we believe is the actual limit of detection (LOD). These pointswere located on the x -axis in the original publication, suggesting they were below the LOD. The authorsdo not provide a methodology or their LOD, but instead refer readers to another of their publication for19heir methodology [38], wherein data points below the LOD are also located on the x -axis which is now at10 FFU / mL. Parametrization data from Fig. 2D (white and grey bars) in Timpe et al. [31] consists in a bar graph reportingthe number of JFH1-infected Huh7.5 cells at 72 hpi in the presence of anti-HCV nAbs C1, expressed as apercentage of that in the untreated culture. Each bar is given with error bars representing the mean andstandard error of the mean (SEM) of 4 replicates which are said to reflect the results of 4 independentexperiments. From the digital image of the figure, using version 5 of the software Engauge Digitizer [21], wedetermined these bars to correspond to (mean ± SEM) of (100 ± ± σ ) of N measurements, divided by √ N , i.e. SEM = σ/ √ N , these measures correspond to a (mean ± σ =mean ± SEM √
4) of (100 ± ± σ f = 43% (cid:34)(cid:18) (cid:19) + (cid:18) (cid:19) (cid:35) = 16% (5)which is how we come to use (43 ± (cid:126)p , this quantity appears in the numerator as 0.43 and in thedenominator as σ f = 0 .
16. We also explore the contribution of this measure to our PPLD estimates bydecreasing σ f from 0.16 to 0.04. The ABM is implemented in python version 2, and primarily makes use of the numpy , random and math modules. The ABM hexagonal simulation grid contains (100 × i , j ), its state (uninfected, infected by free virus,infected cell-to-cell), a list of its 6 immediate neighbours cell objects, and once infected, its amount ofintracellular RNA and the time at which it became infected. In Sainz et al. [25] (specifically, Fig. 3 therein),the authors indicate a supernatant infectivity of 10 FFU / mL at time zero corresponding to their reportedMOI of 0 .
01 FFU / cell, suggesting 10 cells / mL of supernatant or medium. Furthermore, Sainz et al. [25](specifically, Fig. 2 therein) report a confluent Huh7 density of ∼ ,
000 cells / well on 12-well plates with aculture area of 3 .
84 cm / well. As such, assuming one hepatocyte is 20 µ m in diameter [19], the (100 × ×
2) mm or 1/96 of a 12-well platewell, under a total supernatant volume of 10 µ L.For any given parameter set, (cid:126)p = ( t RNAoffset , c , β V , β C , V (0), f rinse , RNS), we first make use of the RNSto initialize the script’s random numbers generator instance with a call to random.seed(RNS) . All cells areinitialized in the uninfected state, and the extracellular infectious HCV concentration is set to V (0), one ofthe ABM parameters to be determined. As explained in [12], the experimental MOI can be related to therate of infection by extracellular infectious HCV, β V , using β V = MOI · c ¯ VV (0) (cid:2) − e − c (1 h) (cid:3) . (6)After 1 h, the inoculum is rinsed in the ABM following V (1 hpi) post-rinse = f rinse [ V (1 hpi) pre-rinse ] = f rinse (cid:104) V (0) e − c (1 h) (cid:105) , (7)20igure 8: Evaluating the impact of perfect (100%) vs imperfect (95%) anti-HCV neutralizingantibodies.
ABM-simulated time courses for the (A) percentage of all HCV-infected cells where we assumedperfect (100%) nAbs efficacy. (B)
Same as (A) but we assumed an imperfect (95%) efficacy. The solid line(blue or red) indicate the median, and the pale and darker bands (blue or red) indicate the 68% and 95%percentiles of the y -value at each x -value (time point) for 100 ABM simulations performed using parametersets pulled at random, with replacement from the PPLD. (C) Histogram of the percentage of infected cellsat 3 dpi of the ABM simulations, where we assumed perfect (100%, blue) or imperfect (95%, red) nAbsefficacy. The effect of imperfect nAbs efficacy is not significant given the inter-simulation variability due tostochasticity.where f rinse ∈ [0 ,
1] is the effectiveness of the rinse (0 = perfect rinse, 1=no rinse), c is the rate at whichcell-free infectious extracellular HCV loses infectivity, and V (1 hpi) pre-rinse and V (1 hpi) post-rinse are theextracellular infectious HCV concentrations at 1 hpi, immediately prior to and after the rinse, respectively.The rinsing procedure in Eqn. (7) (two leftmost terms) is repeated every 3 days to simulate the mediumreplacement as part of replenishing the DMSO treatment described in Sainz et al. [25]. The infection isallowed to progress for 10 days, over which time the intracellular RNA content in each cell summed over allcells, R ( t ), and the extracellular infectious HCV concentration, V ( t ), are recorded to be compared to theirexperimental equivalents shown in Figure 3A,B (or D,E).Once the infection simulation completes, still using the same (cid:126)p , the simulation grid is re-initialized (bysetting all cells in the uninfected state, and setting the extracellular infectious HCV concentration to V (0)),and the process is repeated a second time to simulate the infection in the presence of anti-HCV nAbs.This infection differs from the one conducted in the absence of nAbs only in the fact that the extracellularinfectious HCV concentration, V ( t ), and rate of HCV release, p V ( t ), are set to 0 at t ≥ V ( t ≥ f I (72 h) , is compared against the (0 . ± .
16) reported for that same quantityby Timpe et al. [31] under equivalent experimental conditions, as shown in Figure 3C (or F).The procedure described above assumes perfect nAbs efficacy (100%). Timpe et al. [31] demonstrated thattheir nAbs’ efficacy is no less than 95%. For completeness, we also evaluated whether a maximally imperfectneutralizing efficacy of 95% would significantly affect the contribution of free virus infection obtained usinga perfect efficacy of 100%. To do so, 100 parameter sets were pulled at random, with replacement from thePPLD, and used to simulate 3 d infections in the presence of perfect (100%) or maximally imperfect (95%)nAbs efficacy. Figure 8 shows the resulting time course simulations and shows that the effect of the nAbsefficacy is insignificant in the face of the ABM inter-experimental variability.21 .6 Estimation of posterior parameter likelihood distributions via MCMC
The parameters estimated are ( t RNAoffset , c , β C , V (0), MOI, f rinse , RNS). The likelihood of a particularparameter set is defined, as in our previous work [4], as L ( (cid:126)p ) ∝ exp[ − SSR( (cid:126)p ) / (2 σ )] whereSSR( (cid:126)p ) σ = (cid:88) vi =1 log (cid:16) V model vi ( (cid:126)p ) V data vi (cid:17) σ V + (cid:88) ri =1 log (cid:16) R model ri ( (cid:126)p ) R data ri (cid:17) σ R + (cid:20) f I (72 h) ( (cid:126)p ) − . σ f (cid:21) . (8)The first two terms correspond to the infection kinetic data from Sainz et al. [25], while the last termcorresponds to the (43 ± V model vi ( (cid:126)p )and V data vi correspond to the ABM-simulated and experimentally measured extracellular infectious HCVconcentrations of the vi th time point measurement, R model ri ( (cid:126)p ) and R data ri correspond to the ABM-simulatedand experimentally measured intracellular HCV RNA concentration of the ri th time point measurement,and f I (72 h) is the ratio of ABM-predicted HCV-infected hepatocytes at 72 hpi in the presence of anti-HCVnAbs divided by that in their absence compared to the ratio of 0.43 reported by Timpe et al. [31]. Eachof the three terms is divided by its standard deviation, namely σ V , σ R , and σ f , in order to give it theappropriate weight in the likelihood measure. Since Sainz et al. [25] do not provide error bars for their data,we performed nonlinear least-square minimization to determine a best-fit (cid:126)p , and computed the standarddeviation of the residuals between the best-fit curve and the data, namely log (cid:0) V model vi ( (cid:126)p ) /V data vi (cid:1) andlog (cid:0) R model ri ( (cid:126)p ) /R data ri (cid:1) . Through this procedure, we found σ V = 0 .
43 and σ R = 0 .
47, which correspond toan estimated experimental variability of about half an order of magnitude (3-fold or half a log ). Theseestimates are consistent with the spread of ∼ σ ) between the pair of experiments (stars and circles)performed by Sainz et al. [25], shown in Figure 3(A,B). We set σ f = 0 .
16 as per Eqn. (5).The Markov chain Monte Carlo (MCMC) method implemented in version 2.1.0 of the emcee pythonmodule [8] was used to estimate the parameters’ posterior likelihood distribution (PPLDs) based on thelikelihood Eqn. (8). The emcee
MCMC implementation is such that at each new step for each chain, givena current position (cid:126)p current , a new parameter set (cid:126)p new is accepted and added to the chain with a probabilityproportional to L ( (cid:126)p ), and if rejected (cid:126)p current is added instead to the chain [8]. Our MCMC run consists in168 chains (or walkers), each 3000 steps in length, out of which we discard the first 1000 steps as burn-in,for a total of 336,000 accepted parameter sets. The burn-in is necessary to remove any dependence of thePPLD on the initial positions chosen for the 168 chains. Though irrelevant, the initial position of each chainwas chosen randomly from a normal or log-normal distribution about the best-fit (cid:126)p , determined through apreliminary nonlinear least-square fit, as in [4].For all parameters, we assume positive uniform priors ∈ [0 , ∞ ), with the following additional constraintson parameters. The offset in the replication of intracellular HCV RNA by newly infected hepatocytes, t RNAoffset , was restricted to > c ∈ [0 . , .
3] h − , the widest possiblebiologically reasonable range, where 0 .
01 h − is the typical degradation rate of vRNA (which is much morestable than infectivity), and 0 . − is, to our knowledge, the largest reported infectivity decay rate forHCV in vitro [30]. The cell-to-cell transmission rate was restricted to β C ∈ [0 ,
100 h − ], since β C >
100 h − corresponds to the instantaneous infection of any cell with a cell-to-cell transmission-capable neighbour,with no further change in infection kinetics for larger values. The initial extracellular infectious HCVconcentration, V (0), was restricted to > FFU / mL, i.e. the limit of detection. The MOI was restricted to > − FFU / cell, i.e. 1000-fold below the experimentally-reported MOI of 0 .
01 FFU / cell. The efficacy of theinoculum rinse was restricted to f rinse ∈ (10 − , f rinse < − yields identical results, and f rinse = 1corresponds to the least efficient rinse possible, i.e. no rinsing at all. Based on python ’s random module,RNS must be a long integer ∈ (0 , × ). The intracellular HCV RNA (A and D), extracellular virus (B and E) from Figure 3 and the differentfractions of cells infected in Figure 5 are representative of 500 parameter sets. These sets were pulled at22andom, with replacement from the PPLD, and simulated using the ABM for 10 d. The red line (or blue line)represents the median, and the pale and darker bands (grey or cyan) indicate the 68% and 95% percentilesof the y -value at each x -value (time point) for the ABM simulations performed. Additional data extracted from Fig. 1E,F (black bars) in Timpe et al. [31] using Engauge Digitizer [21], wereused to provide validation of the behaviour predicted by the parametrized ABM. In their Fig. 1E (blackbars), Timpe et al. [31] report counting frequencies of 0.48 small ( <
10 cells), 0.26 medium (10–50 cells), and0.26 large ( >
50 cells) foci out of a total of 50 foci, observed at 72 hpi in the absence of nAbs. In their Fig.1F (black bars) Timpe et al. [31] report counting frequencies of 0.04 small, 0.26 medium, and 0.70 large fociout of a total of 50 foci, observed 72 hpi in the presence of agar. In both experiments, Huh7.5 cells seededat high density were infected with HCV-JFH1 at a MOI of 0.01 and no error bars were provided on the bargraphs, presumably because all 50 foci considered were from a single replicate, though this is not specifiedin their paper. The actual experimental measurements taken by Timpe et al. [31] were not frequencies, butcounts (24 small, 13 medium and 13 large foci out of 50 foci counted in the absence of nAbs and 2 small, 13medium and 35 large in the presence of agar).In reproducing this experiment with the parametrized ABM, 1000 parameter sets were pulled at random,with replacement from the PPLD, and used to simulate a 72 h infection in the absence of nAbs, or presenceof nAbs, producing a spatial grid like that shown in Figure 6. For each grid we counted the number of foci,and the number of cells in each foci. Any grouping of cells in direct contact (i.e. within one another’s 6-cellneighbourhood) were considered part of the same focus, without discriminating between a single large focusor one resulting from two or more smaller merged foci, analogous to the experimental procedure followed byTimpe et al. [31]. In Timpe et al. [31], the foci size distribution is affected by cell division (doubling time ≈
34 h reported therein) and should be appropriately accounted for when counting our fixed number of cells.Hence, we counted each cell in a foci once if it had been infected for less than 34 h, twice if it had beeninfected between 34 h and 68 h, and 4 times if infected longer than 68 h. The corresponding frequency ofsmall, medium and large foci for each grid is represented in Figure 4.
To determine how the Timpe et al. [31] measure of (43 ± × more weight (using a standard deviation of 4% instead of 16%) on this measure.With the exception of this weight factor, the process was identical to that performed with the physicallycorrect standard deviation for this measure (16%). Our distribution of foci size is similar to our previousresults (Figure 9). From our simulated parameters, apart from the fraction of cell-to-cell infection, the onlynoticeable difference is observed of the clearance rate and the initial concentration of virus (Figure 10). Thisis not unexpected since these two parameters can be determined from features of the extracellular virusconcentration. Since the relative weight on the extracellular virus has been reduced, this would allow for abit more freedom with any parameter which is determined by this data. The overall findings for the fractionof cell infected by cell-to-cell yields similar mode values with a wider distribution (98% [70%–100%, 95% CI]compared to 99% [84%–100%, 95% CI]) (Table 3). 23igure 9: Quantitative comparison of ABM-predicted foci size distributions between our twoMCMC simulations.
The ABM-simulated percentage of small ( <
10 cells), medium (10–50 cells), andlarge ( >
50 cells) foci at 72 hpi for 1000 simulations, shown as percentile bars (median, 68% CI, 98% CI =bar and bands) from MCMC simulation with an appropriate weight on the Timpe et al. [31] data (black barand grey bands, σ f = 0 .
16) and from MCMC simulation with a larger weight on the Timpe et al. [31] data(blue bar and bands, σ f = 0 . a σ f = 0 . b σ f = 0 . b fold-change c — PPLDs estimated via MCMC —Intracellular HCV RNA replication delay, t RNAoffset (h) 18 [7 . ,
25] 19 [9 . ,
26] 0 .
79 [0 . , . c (h − ) 0 .
049 [0 . , .
30] 0 .
27 [0 . , .
30] 0 .
30 [0 . , . β C (h − ) 85 [6 . , . , .
99 [0 . , V (0) (FFU / mL) 10 . . , . . . , . .
073 [0 . , . − . − . , − . − . − . , − . .
36 [0 . , . f rinse .
37 [0 . , .
0] 0 .
47 [0 . , .
0] 1 . . , β V (h − ) 10 − . − . , − . − . − . , − . . . , f I (72 h) (%) 44 [37 ,
53] 91 [49 , .
53 [0 . , . , , .
99 [0 . , . . . ,
30] 1 . . ,
16] 2 . . , a Normal weight on Timpe et al. [31] data is indicated by σ f = 0 .
16 and larger weight by σ f = 0 . b Mode and 95% CI determined from the PPLDs. c Power of 10 of the mode and 95% CI determined from the distribution of log (fold-change) between1,680,000 pairwise comparisons, wherein each pair is formed by drawing one value from the PPLD with alarger ( σ f = 0 .
04) and normal ( σ f = 0 .
16) weight placed on the Timpe et al. [31] data, sampled at randomwith replacement. 24 t RNAoffset (h)0 . . . . . . − − − c (h − )0 . . . . . . − − − β C (h − )0 . . . . . . V (0) (FFU/mL)0 . . . . . . − − − − − MOI (FFU/cell)0 . . . . . . − − − − f rinse . . . . . . − − − − − − β V (h − )0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 10:
Comparison of the ABM parameters between our two MCMC simulations.
Simulatedpredictions of parameters from appropriately weighted MCMC (red, 43 ± ± eferences [1] N. Barretto, B. Sainz Jr., S. Hussain, and S. L. Uprichard. Determining the involvement and therapeuticimplications of host cellular factors in hepatitis C virus cell-to-cell spread. J. Virol. , 88(9):5050–5061,May 2014. doi:10.1128/JVI.03241-13 .[2] C. Beauchemin. Probing the effects of the well-mixed assumption on viral infection dynamics.
J. Theor.Biol. , 242(2):464–477, 21 September 2006. arXiv:q-bio.CB/0505043 , doi:10.1016/j.jtbi.2006.03.014 .[3] C. Beauchemin, S. Forrest, and F. T. Koster. Modeling influenza viral dynamics in tissue. In H. Bersiniand J. Carneiro, editors, Proceedings of the th International Conference on Artificial Immune Systems(ICARIS 06) , number 4163 in Lecture Notes in Computer Science, pages 23–36. Springer-Verlag BerlinHeidelberg, 2006. doi:10.1007/11823940_3 .[4] C. A. A. Beauchemin, T. Miura, and S. Iwami. Duration of SHIV production by infected cells is notexponentially distributed: Implications for estimates of infection parameters and antiviral efficacy.
Sci.Rep. , 7:42765, 16 February 2017. doi:10.1038/srep42765 .[5] C. L. Brimacombe, J. Grove, L. W. Meredith, K. Hu, A. J. Syder, M. V. Flores, J. M. Timpe, S. E.Krieger, T. F. Baumert, T. L. Tellinghuisen, F. Wong-Staal, P. Balfe, and J. A. McKeating. Neutralizingantibody-resistant hepatitis C virus cell-to-cell transmission.
J. Virol. , 85(1):596–605, January 2011. doi:10.1128/JVI.01592-10 .[6] M. T. Catanese, J. Loureiro, C. T. Jones, M. Dorner, T. von Hahn, and C. M. Rice. Different require-ments for scavenger receptor class B type I in hepatitis C virus cell-free versus cell-to-cell transmission.
J. Virol. , 87(15):8282–8293, August 2013. doi:10.1128/JVI.01102-13 .[7] M. T. Catanese, K. Uryu, M. Kopp, T. J. Edwards, L. Andrus, W. J. Rice, M. Silvestry, R. J. Kuhn,and C. M. Rice. Ultrastructural analysis of hepatitis C virus particles.
Proc. Natl. Acad. Sci. U.S.A. ,110(23):9505–9510, 4 June 2013. doi:10.1073/pnas.1307527110 .[8] D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman. emcee: The MCMC hammer.
Publ. Astron.Soc. Pac. , 125(925):306–312, March 2013. URL: http://dan.iel.fm/emcee , arXiv:1202.3665v4 , doi:10.1086/670067 .[9] F. Graw, D. N. Martin, A. S. Perelson, S. L. Uprichard, and H. Dahari. Quantification of hepatitis Cvirus cell-to-cell spread using a stochastic modeling approach. J. Virol. , 89(13):6551–6561, July 2015. doi:10.1128/JVI.00016-15 .[10] P. Gupta, R. Balachandran, M. Ho, A. Enrico, and C. Rinaldo. Cell-to-cell transmission of humanimmunodeficiency virus type 1 in the presence of azidothymidine and neutralizing antibody.
J. Virol. ,63(5):2361–2365, May 1989.[11] B. P. Holder and C. A. A. Beauchemin. Exploring the effect of biological delays in kinetic modelsof influenza within a host or cell culture.
BMC Public Health , 11(Suppl 1):S10, 25 February 2011. doi:10.1186/1471-2458-11-S1-S10 .[12] B. P. Holder, L. E. Liao, P. Simon, G. Boivin, and C. A. A. Beauchemin. Design considerations inbuilding in silico equivalents of common experimental influenza virus assays and the benefits of such anapproach.
Autoimmunity , 44(4):282–293, June 2011. doi:10.3109/08916934.2011.523267 .[13] T. N. Huong, L. I. Ravi, B. H. Tan, and R. J. Sugrue. Evidence for a biphasic mode of respiratorysyncytial virus transmission in permissive HEp2 cell monolayers.
Virol. J. , 13:12, 20 January 2016. doi:10.1186/s12985-016-0467-9 . 2614] S. Iwami, J. S. Takeuchi, S. Nakaoka, F. Mammano, F. Clavel, H. Inaba, T. Kobayashi, N. Misawa,K. Aihara, Y. Koyanagi, and K. Sato. Cell-to-cell infection by HIV contributes over half of virusinfection. eLife , 4:e08150, Oct 2015. doi:10.7554/eLife.08150 .[15] J. Jin, N. M. Sherer, G. Heidecker, D. Derse, and W. Mothes. Assembly of the murine leukemia virus isdirected towards sites of cell-cell contact.
PLoS Biol. , 7(7):e1000163, July 2009. doi:10.1371/journal.pbio.1000163 .[16] A. J. Kandathil, F. Graw, J. Quinn, H. S. Hwang, M. Torbenson, A. S. Perelson, S. C. Ray, D. L.Thomas, R. M. Ribeiro, and A. Balagopal. Use of laser capture microdissection to map hepatitis Cvirus-positive hepatocytes in human liver.
Gastroenterology , 145(6):1404–1413, December 2013. doi:10.1053/j.gastro.2013.08.034 .[17] S. J. Keum, S. M. Park, J. H. Park, J. H. Jung, E. J. Shin, and S. K. Jang. The specific infectivityof hepatitis C virus changes through its life cycle.
Virology , 433(2):462–470, 25 November 2012. doi:10.1016/j.virol.2012.08.046 .[18] C. S. Kim, S. J. Keum, and S. K. Jang. Generation of a cell culture-adapted hepatitis C virus withlonger half life at physiological temperature.
PLoS ONE , 6:e22808, 2011. doi:10.1371/journal.pone.0022808 .[19] V. Lohmann, F. K¨orner, J.-O. Koch, U. Herian, L. Theilmann, and R. Bartenschlager. Replication ofsubgenomic hepatitis C virus RNAs in a hepatoma cell line.
Science , 285:110–113, July 1999. doi:10.1126/science.285.5424.110 .[20] L. W. Meredith, H. J. Harris, G. K. Wilson, N. F. Fletcher, P. Balfe, and J. A. McKeating. Early infectionevents highlight the limited transmissibility of hepatitis C virus in vitro.
J. Hepatol. , 58(6):1074–1080,June 2013. doi:10.1016/j.jhep.2013.01.019 .[21] M. Mitchell. Engauge Digitizer. http://markummitchell.github.io/engauge-digitizer/ , 2015–2016.[22] W. Mothes, N. M. Sherer, J. Jin, and P. Zhong. Virus cell-to-cell transmission.
J. Virol. , 84(17):8360–8368, Sept. 2010. doi:10.1128/JVI.00443-10 .[23] E. G. Paradis, L. Pinilla, B. P. Holder, Y. Abed, G. Boivin, and C. A. A. Beauchemin. Impactof the H275Y and I223V mutations in the neuraminidase of the 2009 pandemic influenza virus invitro and evaluating experimental reproducibility.
PLoS ONE , 10(5):e0126115, 20 May 2015. doi:10.1371/journal.pone.0126115 .[24] B. Sainz, Jr., N. Barretto, D. N. Martin, N. Hiraga, M. Imamura, S. Hussain, K. A. Marsh, X. Yu,K. Chayama, W. A. Alrefai1, and S. L. Uprichard. Identification of the Niemann-Pick C1-like 1 choles-terol absorption receptor as a new hepatitis C virus entry factor.
Nat. Med. , 18(2):281–286, February2012. doi:10.1038/nm.2581 .[25] B. Sainz Jr. and F. V. Chisari. Production of infectious hepatitis C virus by well-differentiated, growth-arrested human hepatoma-derived cells.
J. Virol. , 80(20):10253–10257, October 2006. doi:10.1128/JVI.01059-06 .[26] B. Sainz Jr., V. TenCate, and S. L. Uprichard. Three-dimensional huh7 cell culture system for the studyof hepatitis c virus infection.
Virol. J. , 6:103, 15 July 2009. doi:10.1186/1743-422X-6-103 .[27] C. Sarrazin and S. Zeuzem. Resistance to direct antiviral agents in patients with hepatitis C virusinfection.
Gastroenterology , 138(2):447–462, February 2010. doi:10.1053/j.gastro.2009.11.055 .2728] A. Sigal, J. T. Kim, A. B. Balazs, E. Dekel, A. Mayo, R. Milo, and D. Baltimore. Cell-to-cell spreadof HIV permits ongoing replication despite antiretroviral therapy.
Nature , 477:95–98, 2011. doi:10.1038/nature10347 .[29] P. F. Simon, M.-A. de La Vega, E. Paradis, E. Mendoza, K. M. Coombs, D. Kobasa, and C. A. A.Beauchemin. Avian influenza viruses that cause highly virulent infections in humans exhibit distinctreplicative properties in contrast to human H1N1 viruses.
Sci. Rep. , 6:24154, 15 April 2016. doi:10.1038/srep24154 .[30] H. Song, J. Li, S. Shi, L. Yan, H. Zhuang, and K. Li. Thermal stability and inactivation of hepatitis Cvirus grown in cell culture.
Virol. J. , 7(1):40–52, February 2010. doi:10.1186/1743-422X-7-40 .[31] J. M. Timpe, Z. Stamataki, A. Jennings, K. Hu, M. J. Farquhar, H. J. Harris, A. Schwarz, I. Desombere,G. L. Roels, P. Balfe, and J. A. McKeating. Hepatitis C virus cell-cell transmission in hepatoma cellsin the presence of neutralizing antibodies.
Hepatology , 47(1):17–24, January 2008. doi:10.1002/hep.21959 .[32] A. D. Tomassi, M. Pizzuti, R. Graziani, A. Sbardellati, S. Altamura, G. Paonessa, and C. Traboni. Cellclones selected from the huh7 human hepatoma cell line support efficient replication of a subgenomic GBvirus B replicon.
J. Virol. , 76(15):7736–7746, August 2002. doi:10.1128/JVI.76.15.77367746.2002 .[33] S. Wieland, Z. Makowska, B. Campana, D. Calabrese, M. T. Dill, J. Chung, F. V. Chisari, and M. H.Heim. Simultaneous detection of hepatitis C virus and interferon stimulated gene expression in infectedhuman liver.
Hepatology , 59(6):2121–2130, June 2014. doi:10.1002/hep.26770 .[34] S. F. Wieland and F. V. Chisari. Stealth and cunning: Hepatitis B and hepatitis C viruses.
J. Virol. ,79(15):9369–9380, August 2005. doi:10.1128/JVI.79.15.9369-9380.2005 .[35] S. Wilkening, F. Stahl, and A. Bader. Comparison of primary human hepatocytes and hepatoma cellline HEPG2 with regard to their biotransformation properties.
Drug Metab. Dispos. , 31(8):1035–1042,August 2003. doi:10.2165/11534730-000000000-00000 .[36] J. Witteveldt, M. J. Evans, J. Bitzegeio, G. Koutsoudakis, A. M. Owsianka, A. G. N. Angus, Z.-Y. Keck, S. K. H. Foung, T. Pietschmann, C. M. Rice, and A. H. Patel. CD81 is dispensable forhepatitis C virus cell-to-cell transmission in hepatoma cells.
J. Gen. Virol. , 90(1):48–58, January 2009. doi:10.1099/vir.0.006700-0 .[37] F. Xiao, I. Fofana, L. Heydmann, H. Barth, E. Soulier, F. Habersetzer, M. Doffo¨el, J. Bukh, A. H. Patel,M. B. Zeisel, and T. F. Baumert. Hepatitis C virus cell-cell transmission and resistance to direct-actingantiviral agents.
PLoS Pathog. , 10(5):e1004128, May 2014. doi:10.1371/journal.ppat.1004128 .[38] J. Zhong, P. Gastaminza, G. Cheng, S. Kapadia, T. Kato, D. R. Burton, S. F. Wieland, S. L. Uprichard,T. Wakita, and F. V. Chisari. Robust hepatitis C virus infection in vitro.
Proc. Natl. Acad. Sci. U.S.A. ,102(26):9294–9299, June 2005. doi:10.1073/pnas.0503596102doi:10.1073/pnas.0503596102