Quantification of Ebola virus replication kinetics in vitro
Laura E. Liao, Jonathan Carruthers, Sophie J. Smither, CL4 Virology Team, Simon A. Weller, Diane Williamson, Thomas R. Laws, Isabel Garcia-Dorival, Julian Hiscox, Benjamin P. Holder, Catherine A. A. Beauchemin, Alan S. Perelson, Martin Lopez-Garcia, Grant Lythe, John Barr, Carmen Molina-Paris
QQuantification of Ebola virus replication kinetics in vitro
Laura E. Liao a,1
Jonathan Carruthers b,1
Sophie J. Smither c CL4 Virology Team c,2
Simon A. Weller c Diane Williamson c Thomas R. Laws c Isabel Garc´ıa-Dorival d JulianHiscox d Benjamin P. Holder e Catherine A. A. Beauchemin f,g
Alan S. Perelson a Mart´ınL´opez-Garc´ıa b Grant Lythe b John Barr h Carmen Molina-Par´ıs b,3 a Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos,NM, USA 87545 b Department of Applied Mathematics, School of Mathematics, University of Leeds,Leeds LS2 9JT, UK c Defence Science and Technology Laboratory, Salisbury SP4 0JQ, UK d Institute of Infection and Global Health, University of Liverpool, Liverpool, L69 7BE,UK e Department of Physics, Grand Valley State University, Allendale, MI, USA 49401 f Department of Physics, Ryerson University, Toronto, ON, Canada M5B 2K3 g Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) ResearchProgram at RIKEN, Wako, Saitama, Japan, 351-0198 h School of Molecular and Cellular Biology, University of Leeds, Leeds LS2 9JT, UK1 These authors contributed equally to this work.2 Membership list can be found in the Acknowledgments section.3 [email protected]
Abstract
Mathematical modelling has successfully been used to provide quantitative descriptionsof many viral infections, but for the Ebola virus, which requires biosafety level 4facilities for experimentation, modelling can play a crucial role. Ebola modelling effortshave primarily focused on in vivo virus kinetics, e.g., in animal models, to aid thedevelopment of antivirals and vaccines. But, thus far, these studies have not yielded adetailed specification of the infection cycle, which could provide a foundationaldescription of the virus kinetics and thus a deeper understanding of their clinicalmanifestation. Here, we obtain a diverse experimental data set of the Ebola infection invitro , and then make use of Bayesian inference methods to fully identify parameters in amathematical model of the infection. Our results provide insights into the distributionof time an infected cell spends in the eclipse phase (the period between infection and thestart of virus production), as well as the rate at which infectious virions lose infectivity.We suggest how these results can be used in future models to describe co-infection withdefective interfering particles, which are an emerging alternative therapeutic.
Author summary
The two deadliest Ebola epidemics have both occurred in the past five years, with oneof these epidemics still ongoing. Mathematical modelling has already provided insightsinto the spread of disease at the population level as well as the effect of antiviraltherapy in Ebola-infected animals. However, a quantitative description of thereplication cycle is still missing. Here, we report results from a set of in vitro
October 21, 2020 1/16 a r X i v : . [ q - b i o . CB ] O c t xperiments involving infection with the Ecran strain of Ebola virus. By parameterizinga mathematical model, we are able to determine robust estimates for the duration of thereplication cycle, the infectious burst size, and the viral clearance rate. Introduction
The world’s second largest Ebola outbreak is currently underway in the DemocraticRepublic of Congo. Ebola virus (EBOV) causes severe and fatal disease with deathrates of up to 90% [1]. There is an urgent need to prevent and treat EBOV infections,but no antiviral drugs or monoclonal antibodies have been approved in Africa, the EU,or the US. Recently the first EBOV vaccine has been approved by Europeanregulators [2]. Experimental therapies [3], including antiviral drugs (remdesivir [4] andfavipiravir [5, 6]) and a cocktail of monoclonal antibodies (ZMapp) [7], have beenassessed in the 2013–2016 West Africa Ebola virus disease outbreak. Other promisingmonoclonal antibody therapies, called mAb114 and REGN-EB3, have been deployed inthe current 2018–2019 Kivu Ebola epidemic [8]. A better understanding of the preciseinfection kinetics of EBOV is warranted.Mathematical modelling of viral dynamics has provided a quantitativeunderstanding of within-host viral infections, such as HIV [9], influenza [10], Zika [11],and more recently, EBOV. Mathematical modelling studies have analyzed the plasmaviral load dynamics of EBOV-infected animals (mice [12], non-human primates [13, 14])while under therapy with favipiravir, and have identified estimates of favipiravir efficacyand target drug concentrations. In addition, mechanistic models of innate and adaptiveimmune responses were used to provide an explanation of EBOV infection dynamics innon-human primates [14], and of differences between fatal and non-fatal cases of humaninfection [15]. Moreover, mathematical models have been used to predict the effect oftreatment initiation time on indicators of disease severity [12, 15] and survival rates [14],to predict the clearance of EBOV from seminal fluid of survivors [16], and totheoretically explore treatment of EBOV-infected humans with antivirals that possessdifferent mechanisms of action (i.e., nucleoside analog, siRNA, antibody) [15].Alongside the progress made in understanding within-host infections, acomplementary view of infection can be provided by mathematical modelling ofinfections at the in vitro level. Combined with in vitro time course data, mathematicalmodels (MMs) have provided a detailed quantitative description of the viral replicationcycle of influenza A virus [17, 18], SHIV [19, 20], HIV [21], and other viruses [22–26].Such studies yield estimates of key quantities such as the basic reproductive number(defined as the number of secondary infections caused by one infected cell in apopulation of fully susceptible cells), half-life of infected cells, and viral burst size,which cannot be obtained directly from data [27]. In the context of in vitro infections,parameterized MMs have been used to predict the outcome of competition experimentsbetween virus strains [28–30] (i.e., which strain dominates in a mixed infection), mapdifferences in genotype to changes in phenotype [28, 30] (e.g., associate a single mutationto ten-fold faster viral production), quantify fitness differences between virusstrains [31, 32] (e.g., which strain has a larger infectious burst size), quantify thecontribution of different modes of transmission (cell-to-cell versus cell-free) [21], andidentify the target of antiviral candidates [33] (e.g., whether a drug inhibits viral entryor viral production). One prior study [34] utilized in vitro infection data from theliterature to estimate EBOV infection parameters, but had several parameteridentifiability issues due to insufficient data.Our goal is to obtain robust estimates of viral infection parameters that characterizethe EBOV replication cycle. We follow a mathematical modelling approach that hasbeen successfully applied in the analysis of other viral infections in vitro [17]. To thisOctober 21, 2020 2/16nd, we performed a suite of in vitro infection assays (single-cycle, multiple-cycle, andviral infectivity decay assays) using EBOV and Vero cells, and collected detailedextracellular infectious and total virus time courses. The viral kinetic data weresimulated with a multicompartment ordinary differential equation MM, and posteriordistributions of the MM parameters were estimated using a Markov chain Monte Carlo(MCMC) approach. We estimate that one EBOV-infected cell spends ∼
30 h in aneclipse phase before it releases infectious virions at a rate of 13 / h, over its infectiouslifetime of ∼
83 h. The number of infectious virions produced over an infected cell’slifetime is ∼ ∼ Results
Ebola Virus Kinetics In Vitro
Vero cell monolayers were infected with EBOV at a multiplicity of infection (MOI) of 5,1, 0 . / cell. Infectious and total virus concentrations were determined fromextracellular virus harvested from the supernatant of each well at various timespost-infection (Fig. 1 A–C, E—F). At the start of infection, the virus concentrations donot rise for some time, reflecting the time it takes for viral entry, replication and release.After 24 h, the virus concentrations grow exponentially as infected cells begin producingvirus. When all cells in the well are infected, the virus concentrations peak atapproximately 2 × TCID / mL and 10 copy / mL and the peak is sustained for ∼
72 h. Thereafter, the virus concentrations decline when virus production ceases,presumably due to the death of infected cells. Additionally, the kinetics of viralinfectivity decay and virus degradation were assessed with a mock yield assay (Fig. 1 D,G). In the mock yield assay, an inoculum of virus was incubated in wells under the sameconditions as the growth assays, but in the absence of cells, and sampled over time.
Mathematical Model of Viral Infection and Parameter Estimates
The in vitro
EBOV infection kinetics were captured with a MM that has been usedsuccessfully in past works to capture influenza A virus infection kinetics invitro [28, 30, 31]. The MM is given by the system of ordinary differential equations:d T d t = − βT V inf d E d t = βT V inf − n E τ E E d E i =2 , ,...,n E d t = n E τ E ( E i − − E i )d I d t = n E τ E E n E − n I τ I I (1)d I j =2 , ,...,n I d t = n I τ I ( I j − − I j )d V inf d t = p inf n I X j =1 I j − c inf V inf d V tot d t = p tot n I X j =1 I j − c tot V tot October 21, 2020 3/16 ig 1. Kinetics of EBOV infection in vitro and mock yield assays.
Vero cellmonolayers were infected with EBOV at a multiplicity of infection (MOI) 5, 1, or0 . / cell, as indicated. At various times post-infection, the infectious(TCID /mL; A–C) and total virus (copy/mL; E–G) in the supernatant weredetermined. A mock yield assay was also performed to quantify the decay of infectious(D) and total virus (G). In each assay, the experimental data (circles) were collectedeither in duplicate (MOI 5) or triplicate (all other assays). Note that the total virusconcentration collected in the MOI 5 infection was omitted from the analysis due toinconsistencies in the peak value (S1 Appendix, Fig. A). The lines represent thepointwise median of the time courses simulated from our MM, which are bracketed by68% (light grey) and 95% (dark grey) credible regions (CR). These data were used toextract the posterior probability likelihood distributions of the infection parameters(Fig. 2). Note that parameters of the calibration curve used to convert cycle thresholdvalues (Ct) to total virus (copy/mL) were also estimated (Fig. 3). The variabilityintroduced from this conversion is shown by two error bars on each total virus datapoint, indicating the 68% (same colour) and 95% (black) CR.In this MM, susceptible uninfected target cells T can be infected by infectious virus V inf with infection rate constant β , and subsequently enter the non-productive eclipse phase E i =1 ,...,n E , followed by a transition into the productively infectious phase I j =1 ,...,n I .The eclipse and infectious phases are divided into a number of compartments given by n E and n I , respectively, such that the time spent in each phase follows an Erlangdistribution with an average duration of τ E,I ± τ E,I √ n E,I . While cells are in the infectiousphase, they produce infectious (total) virus V inf ( V tot ) at a rate p inf ( p tot ), which loseinfectivity (viability) at rate c inf ( c tot ). The MM Eq. (1) captures both infectious virus,quantified by TCID measurements of supernatant samples, and total virus, quantifiedby quantitative, real-time, reverse transcriptase PCR (hereafter, RT-qPCR). The latterexperimental quantity was obtained by converting cycle threshold (Ct) values fromRT-qPCR to copy number (Fig. 3) using Eq. (3) (Methods).Predicted virus time courses from the MM are shown in Fig. 1 where the solid linesrepresent the pointwise median and the grey bands show narrow 95% credible regions(CR), indicating that the MM reproduces the viral kinetic data well. Using a Markovchain Monte Carlo (MCMC) approach, we obtained posterior probability likelihooddistributions (PostPLDs) for each of the MM parameters (Fig. 2). Narrow PostPLDswere extracted with mild correlations between parameters (S1 Appendix, Fig. C),indicating good practical identification of all parameters.October 21, 2020 4/16 ig 2. Estimated parameter distributions of EBOV infection in vitro . Posterior probability likelihood distributions (PostPLDs) of parameters in the MM(A–G) were estimated using MCMC and the data in Fig. 1. Secondary parameters werederived from these estimates (H–J). Note that the PostPLDs corresponding to thenumber of eclipse and infectious phase compartments are integer-valued. The remainingPostPLDs of parameters describing the total virus and calibration curve are in S1Appendix, Fig. B.
A Quantitative Description of the EBOV Lifecycle
The MCMC analysis gives us the following quantitative description of the EBOVlifecycle within Vero cells. An EBOV-infected Vero cell spends approximately 30 h witha 95% credible region of [26 h, 37 h] in the eclipse phase before progeny EBOVsuccessfully bud. Subsequently, infectious virus is produced at a rate of 13 [10, 20]virions per cell per hour over a duration of 83 h [64 h, 95 h] before virus productionceases due to cell death. An infectious burst size of 1096 progeny virions [1000, 1259] isreleased from each infected cell over its virus-producing lifetime. Once infectious virusenters the cell culture medium, they lose infectivity at a rate of 0 . / h [0 . / h,0 . / h], which is comparable to other viruses such as influenza A virus [31] orSHIV [19]. Overall, the in vitro spread of infection is rapid, as characterized by aninfecting time of 2 h [1 . . n E of 13 [8, 23] and n I of 14 [3, 85]. This impliesthat the eclipse phase comprises a sequence of many distinct steps of short duration,without any one step lasting significantly longer than the rest. Likewise, the sameinterpretation applies to the infectious phase. The normal-like distribution of the eclipsephase resembles that of influenza A virus [30], but contrasts with the fat-tailed eclipsephase distribution of SHIV [20] which is likely due to a process in the phase that islonger than the rest (e.g., integration). Moreover, neither the eclipse nor infectiousphase are exponentially distributed ( n = 1) as is commonly assumed in analyses withMMs. Such an assumption has been shown to impact estimates of antiviral efficacy thatare based on patterns of viral load decay under simulated therapy in HIV patients [20].October 21, 2020 5/16 iscussion In this work we performed time-course Ebola virus (EBOV) infection experiments atmultiple MOIs in vitro and applied MCMC methods to precisely parameterize amathematical model (MM) of the infection. We extracted fundamental quantitiesconcerning the timing and viral production of EBOV replication. Thistheoretical-experimental approach maximized the output of the costly and difficultexperiments, which must be performed in biosafety level 4 facilities. Previous studies ofthe EBOV lifecycle rely on safer virus-like particles [36]. The only previously knownMM of EBOV infection in vitro [34] is restricted in its use due to problems withparameter identifiability; specifically, the existence of strong correlations betweenparameters, such as the rates of virus degradation and virus production. By obtaining amore complete set of experimental observations, we have provided the first detailedquantitative characterization of EBOV infection kinetics.Some of our estimates of timescales in the EBOV infection kinetics fill gaps in theknowledge of this virus, while others expose some tension with prior mathematicalmodelling work. The eclipse phase, excluded from the previous in vitro
MM [34], hasbeen found to be a significant part of the replication cycle. Lasting approximately 30 h,it is longer than the eclipse phase for influenza A virus and HIV infections in humans(4–24 h) [10, 37]. Although the eclipse phase is included in existing MMs ofEBOV-infected animals, its duration has never been estimated, and the assumed valuesused in these studies were considerably shorter than the value we identify here [12, 14].Moreover, the observation that the length of the eclipse phase follows an Erlangdistribution is contrary to these previous MMs, where it has been represented moresimply as an exponentially distributed time. These MMs also fix the value of the decayrate of infectious virus to ensure that other parameters remain identifiable [12]. Here,the robust estimate of this decay rate demonstrates the benefit of performing a mockyield assay. Existing MMs of in vivo
EBOV infection in humans and non-humanprimates provide considerably shorter estimates of the infection cycle (12.5–15 . τ E + τ I ) obtained here [12, 15]. Such a difference islikely attributed to the inclusion of an implicit immune response in these in vivo models,thereby accounting for the enhanced clearance of infected cells by immune cells, such asCD8 + T cells [38]. This also explains why a faster viral decay rate can be expected invivo , and subsequently why estimates of the basic reproduction number are greater herethan those obtained from in vivo
MMs (5.96-9.01) [12, 15]. It remains to be determinedwhether Vero cells are representative of the cells targeted by EBOV in vivo , but byunderstanding EBOV replication in Vero cells, we have a foundation from which morecomplex cell culture models might be developed.In addition to virus measurements, previous studies have included susceptible andinfected cell measurements to fully parameterize the MM and obtain robust estimates ofthe viral kinetics parameters [19, 39]. We initially set out to obtain a more diverse dataset that also included the kinetics of dead cells and intracellular RNA over the course ofinfection, but encountered unexpected challenges. To quantify cell viability, we treatedinfected monolayers at various times with Trypan blue, which stains cells that have lostthe ability to exclude dye. Unfortunately, we were unable to associate this marker ofcell death to a stage of the viral lifecycle in our MM without making additionalassumptions. Ultimately, when we extended the MM to include these data, the newlyintroduced parameters were dependent on these assumptions, and the extracted valuesof the original parameters were largely unaffected (S1 Appendix). To determineintracellular viral kinetics, the supernatants from infected cell cultures were removedand the remaining monolayers were washed and trypsinized for quantification viaTCID assay and RT-qPCR. These samples showed a high level of EBOV RNA andTCID as early as 4 hours post-infection, which remained at a constant level up to 1October 21, 2020 6/16ay post-infection, but rose thereafter (S1 Appendix). Additionally, the ratio ofRNA-to-TCID resembled the ratio observed in the supernatant. Thus, thesemeasurements likely reflect the large amount of cell-associated virions that remainedafter washing, effectively obscuring the intracellular RNA signal.While a highly-controlled in vitro system was necessary to achieve our precisecharacterization of the EBOV infection kinetics, the applicability of these results to aclinical situation is not immediately obvious, and represents a serious limitation of thestudy. Nevertheless, our findings have some relevance to understanding the EBOVinfection in vivo . EBOV initially replicates within macrophages and dendritic cells insubcutaneous and submucosal compartments, but dissemination in the blood results inthe infection of multiple organs throughout the body [40]. Many different cell types areinfected with varying susceptibility to infection, as well as varying levels of viralreplication. While the infection unfolds, EBOV blocks IFN production early on [6, 41].In this sense, studying the infection of Vero cells—which are IFN-deficient—narrowlymodels the infection of one type of epithelial cell during the early stages of an EBOVinfection in vivo .Vero cells serve as a standard host cell for replication and are widely used for testingantivirals in vitro [42], as well as in the development of viral vaccines [43–45].Mathematical modelling of EBOV infections in vitro using Vero cells has relevance tosuch applications, particularly in the study of emerging therapeutics. While weprovided a quantitative depiction of extracellular infection by EBOV as a valuable firststep, we envisioned that the MM could be extended to include intracellular viral RNAkinetics had the appropriate data been collected. Such multiscale modelling approacheshave been used to provide insight into virus growth and also to the understanding ofdirect-acting antivirals [46–49]. We hope that these experiences might help guide futureefforts to obtain informative cell and intracellular data.As an alternative antiviral strategy, there has been renewed interest in pursuingdefective interfering particles (DIPs) [50] of highly pathogenic viruses. A DIP is a viralparticle that contains defective interfering RNA (DI RNA), which can be a shortenedversion of the parent genome that renders a DIP replication-incompetent on its own(because it may lack the gene for an essential viral component such as viral polymerase),but also elicits virus-interfering properties. Within a cell co-infected by both DIPs andvirus, the DI RNA has a replicative advantage over the full-length RNA andoutcompetes it to produce more DIPs than virus progeny, effectively reducing theinfectious virus yield. EBOV DI RNA has been observed [51] but much remains to beunderstood. Like with any other antiviral, MMs can be used to determine the efficacyand mechanism of action of candidate DI RNAs, and to explore the impact of dose andtiming [15]. In particular, our estimates of EBOV infection kinetics parameters aredirectly applicable to future mathematical modelling of the interactions between EBOVand EBOV DIPs in vitro . Our estimated EBOV infection parameters may also describecertain aspects of EBOV DIP infection. For example, since DIPs have the same viralproteins and capsid as virions, they would infect cells with the same infection rateconstant, β . Since DIPs also piggyback on the virus’ replication cycle, we might expectthe same eclipse and infectious phase lengths ( τ E , τ I ) in a DIP and virus co-infected cell.In summary, the MM described here characterizes the replication cycle of EBOV in aquantitative manner that will be beneficial for those creating in vitro models to aid thedevelopment of antivirals and vaccines. We have made use of a valuable set of in vitro results, carefully considering the structure of the MM in order to maximize theinformation we can extract from them.October 21, 2020 7/16 aterials and Methods Cells and Virus
Vero C1008 cells (ECACC Cat. No.85020206) were obtained from Culture Collection,Public Health England, UK. Vero C1008 cells were maintained in Dulbecco’s minimumessential media supplemented with 10% (v/v) foetal calf serum, 1% (v/v) L-glutamineand 1% (v/v) penicillin/streptomycin (Sigma). For experimental purposes, the foetalcalf serum concentration was reduced to 2% (v/v).Ebola virus
H. sapiens -tc/COD/1976/Yambuku-Ecran, hereafter referred to asEBOV was used in all studies. This virus, previously known as EBOV “E718” [52] wassupplied by Public Health England. Passage 5 material was used to infect Vero C1008cells. Virus was harvested on day 5 post-inoculation and titrated to produce a workingstock at 10 TCID / mL. Quantification of Virus
EBOV was titrated in 96-well plates using the endpoint fifty percent tissue cultureinfectious dose (TCID ) assay [53]. Briefly, virus was ten-fold serially diluted in 96 wellplates of Vero C1008 cells. After one week of incubation at 37 ◦ C/5% CO , all wellswere observed under the microscope and scored for presence or absence of cytopathiceffects. The 50% endpoint was then calculated using the method of Reed &Muench [54]. RNA extractions were performed using the QiAMP Viral RNA Mini Kit(Qiagen, UK). Two 50 µ L elutions were performed for each sample to increase thevolume available for RT-PCR.The genetic material of EBOV was quantified using the RealStar ® Filovirus ScreenRT-PCR Kit (Altona diagnostics, Country) following the instructions of themanufacturer. This assay has been performed many times against a standard curve ofplasmid containing the L gene from EBOV. The number of genomes can be estimatedfrom the Ct values as described in Eq. (3). In this context, the number of genomesmight consist of incomplete negative sense RNA molecules encoding this sequence of theL gene. However, we do not believe that these will be common ( < Infections
Twenty-four-well plates were seeded with Vero C1008 cells at 10 cells / mL. EBOV wasadded at MOIs of either 5, 1, or 0.1. Vero cells were grown to 90% confluence for allinfections. The cell culture medium was not changed during the experiment and allcultures reached confluence within 24 h (S1 Appendix). At pre-determined intervalspost-infection samples were taken by aspiration of supernatant from wells. Sampleswere stored at − ◦ C prior to enumeration by TCID50 assay and RNA extraction forPCR. Note that the RNA from the MOI 5 infection was omitted from further analysisdue to inconsistencies in the peak viral RNA, compared to the MOI 1 and 0.1 infections(S1 Appendix, Fig. A). The viability of Vero cells in the absence of infection is notknown under these conditions, however, we have observed these cells for 168 h at 24 hOctober 21, 2020 8/16 ig 3. Standard RT-qPCR curve.
Cycle threshold values (Ct) were converted tototal virus (copy/mL) using the above calibration curve, where the parameters of thecurve were estimated as a part of the analysis. The lines represent the pointwise medianof the time courses simulated from our MM, which are bracketed by 68% (light grey)and 95% (dark grey) CR.intervals and observed only occasional cells that can be stained with the viability stainTrypan blue.
Mock yield or infectivity decay assay
EBOV was added to twenty-four-well plates at a final estimated density of 5 × TCID . At pre-determined intervals post-infection samples were taken by aspiration ofsupernatant from wells. Samples were stored at − ◦ C prior to enumeration by TCID assay and RNA extraction for PCR. Construction of the standard RT-qPCR curve
The concentration of viral genome copies (copy/mL) in a standard sample i ( V STD ,i )and the number of doubling RT-qPCR cycles ( C t, STD ,i ) required for this concentrationof copies to reach an arbitrarily fixed, chosen threshold concentration ( Q t ), are linkedby the equation Q t = V STD ,i (2 ε ) C t, STD ,i ln( V STD ,i ) = ln( Q t ) | {z } y -intercept − ln(2 ε ) | {z } slope C t, STD ,i (2)where ε is the efficacy of the RT-qPCR doubling, which should ideally be equal to one(i.e., exactly doubles at each cycle) but can vary about this value. In constructing thestandard curve, we took five standard samples ( V STD ,i =1 ... ) with known copyconcentrations (via their mass) and determined their corresponding C t, STD ,i . Thesedata are shown in Fig. 3. Conversion of sample RT-qPCR C t values into V tot In quantifying the concentration of total virus, V tot (copy/mL), in the extracellularvirus samples collected from infection experiments, Eq. (2) was used as followsln( V tot ,i ) = ln( Q t ) − ln(2 ε ) C t, sample ,i ≡ F ( C t, sample ,i ) (3)where V tot ,i is the concentration of copies in sample i , given its RT-qPCR-determined C t, sample ,i value. Here, ln( Q t ) and ln(2 ε ) are two parameters to be estimated as part ofthe MCMC parameter estimation process described later in this section. As differentvalues for these two parameters are sampled in the MCMC process, the total virusconcentration data points vary. The variation in the conversion is denoted by error barson each total virus data point in Fig. 1 E–G.October 21, 2020 9/16 ock-yield assay model Loss of virus infectivity or loss of viral genome integrity over time typically follows anexponential decay [22]. As such, the mock-yield (MY) or infectivity decay assay can becaptured via V ( t ) = V e − c t , such that the experimental MY data are expected to followln( V inf ( t )) = ln( V MYinf , ) − c inf t (4)ln( V tot ( t )) = ln( V MYtot , ) − c tot t (5)where V inf ( t ) and V tot ( t ) are the concentrations of infectious (TCID /mL) and total(copy/mL) virus after an incubation of time t under the same conditions used duringthe infection experiments, given the EBOV rate of loss of infectivity ( c inf ) or integrity( c tot ), and initial concentrations, V MYinf , and V MYtot , . These data are shown in Fig. 1 D, G. Simulated infections and parameter estimation
In estimating the MM parameters, the following experimental data were consideredsimultaneously: the RT-qPCR standardized curve (5 data points), the MY assays (24data points: 4 time points in triplicate for C t and V inf ), and three infection assays atMOI of 5 (24 data points: 6 time points in duplicate for C t and V inf ), MOI of 1 (54 datapoints: 9 time points in triplicate for C t and V inf ), and MOI of 0.1 (53 data points: 9time points in triplicate for C t and V inf , minus one contaminated sample in C t ).Eq. (2) was used to capture the RT-qPCR standard curve, and its agreement withthe 5 experimental data points was computed as the sum-of-squared residuals (SSR)SSR STD = P i =1 [ F ( C t, STD ,i ) − ln( V STD ,i )] σ V tot , where σ V tot is the variance, or squared of the standard error, in experimentallymeasured V tot , which will be discussed in more details below. Eq. (4) and Eq. (5) wereused to capture the MY experiment, performed in triplicate, and sampled at 4 timepoints, for each of C t and V inf , and agreement was computed asSSR MY = P i =1 h ln( V MYinf , ) − c inf t i − ln( V inf ( t i )) i σ V inf + P i =1 (cid:2) ln( V MYtot , ) − c tot t i − F ( C t,i ) (cid:3) σ V tot Finally, MM Eq. (1) was used to reproduce the infection experiments, performed intriplicate, and at 3 different MOIs (5, 1, and 0.1), and quantified via both TCID andRT-qPCR. In reproducing the infections, initial conditions (at t = 0) were such that T (0) = 1, E i =1 ,...,n E (0) = I j =1 ,...,n I (0) = 0, and the initial infectious and total virusconcentrations for the 3 MOIs were computed as: V inf (0) = V INFinf , × MOI V tot (0) = V INFtot , × MOIwhere MOI was either 5, 1 or 0.1, and ( V INFinf , , V INFtot , ) are 2 parameters to be estimated.Agreement between MM Eq. (1) and experimental infection data was computed asSSR INF = X MOI=[5 , , . P i (cid:2) ln( V MMinf ( t i ) − ln( V inf ( t i )) (cid:3) σ V inf + P i (cid:2) ln( V MMtot ( t i ) − F ( C t,i ) (cid:3) σ V tot October 21, 2020 10/16here σ V inf = 0 . σ V tot = 0 . V inf ) and ln( V tot ),respectively, estimated as the variance of the residuals between the 2 to 3 replicates ofln( V inf ) or ln( V tot ) measured at each time point and their corresponding mean, acrossall (STD, MY, and INF) experimental data collected.A total of 15 parameters — 6 parameters associated with experimental conditions(ln( Q t ), ln(2 ε ), ln( V MYinf , ), ln( V MYtot , ), V INFinf , , V INFtot , ) and 9 parameters more closelyassociated with EBOV infection kinetics ( c inf , c tot , p inf , p tot , β , τ E , τ I , n E , n I ) — wereestimated (Table 1) from 160 experimental data points using the python MCMCimplementation phymcmc [55], a wrapping library for emcee [56]. Posterior probabilitylikelihood distributions (PostPLDs) were obtained based on the parameter likelihoodfunction ln( L ( ~p )) = − (cid:2) SSR
STD ( ~p ) + SSR MY ( ~p ) + SSR INF ( ~p ) (cid:3) and the assumption of linearly uniform or ln-uniform priors, where ~p is the15-parameter vector. Table 1. Estimated parameters of EBOV infection in vitro . Parameter Mode [95% CR]Infectiousness, β ( mLTCID · h ) 10 − .
48 [ − . , − . Eclipse phase length, τ E (h) 30 . , n E
13 [8 , τ I (h) 83 . , n I
14 [3 , p inf ( TCID cell · h ) 10 .
12 [1 , . Total virus production rate, p tot ( RNAcell · h ) 10 .
46 [6 . , . Rate of loss of infectious virus, c inf (/h) 0 . . , . c tot (/h) 0 . . , . V INFinf , ( TCID mL ) 10 .
39 [5 . , . Initial total virus inoculum, V INFtot , ( RNAmL ) 10 . , MY initial infectious virus inoculum, ln( V MYinf , ) 13 . , V MYtot , ) 28 . , y -intercept, ln( Q t ) 37 . , ε ) 0 .
613 [0 . , . R .
77 [2 . , Infectious burst size, p inf τ I ( TCID cell ) 10 .
04 [3 , . Infecting time, t inf (h) 10 .
335 [0 . , . Supporting information
S1 Appendix. Kinetics of cell-associated virus and cell viability.
Acknowledgments
Members of the CL4 Virology Team include Lin Eastaugh, Lyn M. O’Brien, James S.Findlay, Mark S. Lever, Amanda Phelps, Sarah Durley-White, Jackie Steward and RuthThom. The authors would like to acknowledge Joseph Gillard for helpful discussionsand the International Centre for Mathematical Sciences (ICMS), where themathematical model was developed during a Research-in-Groups programme.October 21, 2020 11/16 eferences
1. Feldmann H, Geisbert TW. Ebola haemorrhagic fever. Lancet.2011;377(9768):849–862. doi:10.1016/S0140-6736(10)60667-8.2. Callaway E. Make Ebola a thing of the past: First vaccine against deadly virusapproved. Nature. 2019;doi:10.1038/d41586-019-03490-8.3. Rojek A, Horby P, Dunning J. Insights from clinical research completed duringthe west Africa Ebola virus disease epidemic. Lancet Infect Dis.2017;17(9):e280–e292. doi:10.1016/S1473-3099(17)30234-7.4. D¨ornemann J, Burzio C, Ronsse A, Sprecher A, De Clerck H, Van Herp M, et al.First newborn baby to receive experimental therapies survives Ebola virus disease.J Infect Dis. 2017;215(2):171–174. doi:10.1093/infdis/jiw493.5. Sissoko D, Laouenan C, Folkesson E, M’Lebing AB, Beavogui AH, Baize S, et al.Experimental treatment with favipiravir for Ebola virus disease (the JIKI trial):A historically controlled, single-arm proof-of-concept trial in Guinea. PLoS Med.2016;13(3):e1001967. doi:10.1371/journal.pmed.1001967.6. Perez SC, Folkesson E, Anglaret X, Beavogui AH, Berbain E, Camara AM, et al.Challenges in preparing and implementing a clinical trial at field level in anEbola emergency: A cast study in Guinea, West Africa. Plos Negl Trop Dis.2017;11(6):e0005545. doi:10.1371/journal.pntd.0005545.7. Group TPIW. A randomized, controlled trial of ZMapp for Ebola virus infection.N Engl J Med. 2016;375(15):1448–1456. doi:10.1056/NEJMoa1604330.8. Maxmen A. Experimental Ebola drugs face tough test in war zone. Nature.2018;561(7721):14. doi:10.1038/d41586-018-06132-7.9. Perelson AS, Neumann AU, Markowitz M, Leonard JM, Ho DD. HIV-1 dynamicsin vivo: Virion clearance rate, infected cell life-span, and viral generation time.Science. 1996;271(5255):1582–1586. doi:10.1126/science.271.5255.1582.10. Baccam P, Beauchemin CAA, Macken CA, Hayden FG, Perelson AS. Kinetics ofinfluenza A virus infection in humans. J Virol. 2006;80(15):7590–7599.doi:10.1128/JVI.01623-05.11. Best K, Guedj J, Madelain V, de Lamballerie X, Yon Lim S, Osuna CE, et al.Zika plasma viral dynamics in nonhuman primates provides insights into earlyinfection and antiviral strategies. Proc Natl Acad Sci USA.2017;114(33):8847–8852. doi:10.1073/pnas.1704011114.12. Madelain V, Oestereich L, Graw F, Nguyen THT, de Lamballerie X, Mentr´e F,et al. Ebola virus dynamics in mice treated with favipiravir. Antiviral Res.2015;123:70–77. doi:10.1016/j.antiviral.2015.08.015.13. Guedj J, Piorkowski G, Jacquot F, Madelain V, Nguyen T, Rodallec A, et al.Antiviral efficacy of favipiravir against Ebola virus: A translational study incynomolgous macaques. PLoS Med. 2018;15(3):e1002535.doi:10.1371/journal.pmed.1002535.14. Madelain V, Baize S, Jacquot F, Reynard S, Fizet A, Barron S, et al. Ebola viraldynamics in nonhuman primates provides insights into virusimmuno-pathogenesis and antiviral strategies. Nat Commun. 2018;9(1):4013.doi:10.1038/s41467-018-06215-z.October 21, 2020 12/165. Martyushev A, Nakaoka S, Sato K, Noda T, Iwami S. Modelling Ebola virusdynamics: Implications for therapy. Antiviral Res. 2016;135:62–73.doi:10.1016/j.antiviral.2016.10.004.16. Sissoko D, Duraffour S, Kerber R, Kolie JS, Beavogui AH, Camara AM, et al.Persistence and clearance of Ebola virus RNA from seminal fluid of Ebola virusdisease survivors: a longitudinal analysis and modelling study. The Lancet GlobHealth. 2017;5(1):e80–e88. doi:10.1016/S2214-109X(16)30243-1.17. Handel A, Liao LE, Beauchemin CAA. Progress and trends in mathematicalmodelling of influenza A virus infections. Curr Opin Syst Biol. 2018;12:30–36.doi:10.1016/j.coisb.2018.08.009.18. M¨ohler L, Flockerzi D, Sann H, Reichl U. Mathematical model of influenza Avirus production in large-scale microcarrier culture. Biotechnol Bioeng.2005;90(1):46–58. doi:10.1002/bit.20363.19. Iwami S, Holder BP, Beauchemin CAA, Morita S, Tada T, Sato K, et al.Quantification system for the viral dynamics of a highly pathogenicsimian/human immunodeficiency virus based on an in vitro experiment and amathematical model. Retrovirology. 2012;9:18. doi:10.1186/1742-4690-9-18.20. Beauchemin CAA, Miura T, Iwami S. Duration of SHIV production by infectedcells is not exponentially distributed: Implications for estimates of infectionparameters and antiviral efficacy. Sci Rep. 2017;7:42765. doi:10.1038/srep42765.21. Iwami S, Takeuchi JS, Nakaoka S, Mammano F, Clavel F, Inaba H, et al.Cell-to-cell infection by HIV contributes over half of virus infection. Elife. 2015;4.doi:10.7554/eLife.08150.22. Beauchemin CAA, Kim YI, Yu Q, Ciaramella G, DeVincenzo JP. Uncoveringcritical properties of the human respiratory syncytial virus by combining in vitroassays and in silico analyses. PLoS ONE. 2019;14(4):e0214708.doi:10.1371/journal.pone.0214708.23. Gonz`alez-Parra G, De Ridder F, Huntjens D, Roymans D, Ispas G, DobrovolnyHM. A comparison of RSV and influenza in vitro kinetic parameters revealsdifferences in infecting time. PLoS ONE. 2018;13(2):e0192645.doi:10.1371/journal.pone.0192645.24. Fukuhara M, Iwami S, Sato K, Nishimura Y, Shimizu H, Aihara K, et al.Quantification of the dynamics of enterovirus 71 infection byexperimental-mathematical investigation. J Virol. 2013;87(1):701–705.doi:10.1128/JVI.01453-12.25. Gonz`alez-Parra G, Dobrovolny HM, Aranda DF, Chen-Charpentier B, RojasRAG. Quantifying rotavirus kinetics in the REH tumor cell line using in vitrodata. Virus Res. 2018;244:53–63. doi:10.1016/j.virusres.2017.09.023.26. Wethington D, Harder O, Uppulury K, Stewart WCL, Chen P, Kang T, et al..Mathematical modeling identifies the role of adaptive immunity as a keycontroller of respiratory syncytial virus (RSV) titer in cotton rats; 2018.27. Iwami S, Sato K, Boer RJD, Aihara K, Miura T, Koyanagi Y. Identifying viralparameters from in vitro cell cultures. Front Microbiol. 2012;3:319.doi:10.3389/fmicb.2012.00319.October 21, 2020 13/168. Pinilla LT, Holder BP, Abed Y, Boivin G, Beauchemin CAA. The H275Yneuraminidase mutation of the pandemic A/H1N1 virus lengthens the eclipsephase and reduces viral output of infected cells, potentially compromising fitnessin ferrets. J Virol. 2012;86(19):10651–10660. doi:10.1128/JVI.07244-11.29. Song H, Pavlicek JW, Cai F, Bhattacharya T, Li H, Iyer SS, et al. Impact ofimmune escape mutations on HIV-1 fitness in the context of the cognatetransmitted/founder genome. Retrovirology. 2012;9:89.doi:10.1186/1742-4690-9-89.30. Paradis EG, Pinilla L, Holder BP, Abed Y, Boivin G, Beauchemin CAA. Impactof the H275Y and I223V mutations in the neuraminidase of the 2009 pandemicinfluenza virus in vitro and evaluating experimental reproducibility. PLoS ONE.2015;10(5):e0126115. doi:10.1371/journal.pone.0126115.31. Simon PF, de La Vega MA, Paradis E, Mendoza E, Coombs KM, Kobasa D, et al.Avian influenza viruses that cause highly virulent infections in humans exhibitdistinct replicative properties in contrast to human H1N1 viruses. Sci Rep.2016;6:24154. doi:10.1038/srep24154.32. Iwanami S, Kakizoe Y, Morita S, Miura T, Nakaoka S, Iwami S. A highlypathogenic simian/human immunodeficiency virus effectively produces infectiousvirions compared with a less pathogenic virus in cell culture. Theor Biol MedModel. 2017;14(1):9. doi:10.1186/s12976-017-0055-8.33. Ikeda H, Godinho-Santos A, Rato S, Vanwalscappel B, Clavel F, Aihara K, et al.Quantifying the antiviral effect of IFN on HIV-1 replication in cell culture. SciRep. 2015;5:11761. doi:10.1038/srep11761.34. Nguyen VK, Binder SC, Boianelli A, Meyer-Hermann M, Hernandez-Vargas EA.Ebola virus infection modeling and identifiability problems. Front Microbiol.2015;6:257. doi:10.3389/fmicb.2015.00257.35. Holder BP, Beauchemin CAA. Exploring the effect of biological delays in kineticmodels of influenza within a host or cell culture. BMC Public Health. 2011;11Suppl 1:S10. doi:10.1186/1471-2458-11-S1-S10.36. Biedenkopf N, Hoenen T. Modeling the Ebolavirus life cycle with transcriptionand replication-competent viruslike particle assays. In: Ebolaviruses. Springer;2017. p. 119–131.37. Dixit NM, Markowitz M, Ho DD, Perelson AS. Estimates of intracellular delayand average drug efficacy from viral load data of HIV-infected individuals underantiretroviral therapy. Antivir Ther. 2004;9(2):237–246.38. Gupta M, Greer P, Mahanty S, Shieh WJ, Zaki SR, Ahmed R, et al.CD8-mediated protection against Ebola virus infection is perforin dependent.The Journal of Immunology. 2005;174(7):4198–42020.39. Schulze-Horsel J, Schulze M, Agalaridis G, Genzel Y, Reichl U. Infectiondynamics and virus-induced apoptosis in cell culture-based influenza vaccineproduction-Flow cytometry and mathematical modeling. Vaccine.2009;27:2712–2722. doi:10.1016/j.vaccine.2009.02.027.40. Chertow DS, Shekhtman L, Lurie Y, Davey RT, Heller T, Dahari H. Modelingchallenges of Ebola virus–host dynamics during infection and treatment. Viruses.2020;12(1):106.October 21, 2020 14/161. Edwards MR, Liu G, Mire CE, Sureshchandra S, Luthra P, Yen B, et al.Differential regulation of interferon responses by Ebola and Marburg virus VP35proteins. Cell reports. 2016;14(7):1632–1640.42. Postnikova E, Cong Y, DeWald LE, Dyall J, Yu S, Hart BJ, et al. Testingtherapeutics in cell-based assays: Factors that influence the apparent potency ofdrugs. PLoS ONE. 2018;13(3):e0194880. doi:10.1371/journal.pone.0194880.43. Barrett NP, Mundt W, Kistner O, Howard MK. Vero cell platform in vaccineproduction: moving towards cell culture-based viral vaccines. Expert RevVaccines. 2009;8(5):607–618. doi:10.1586/erv.09.19.44. Barrett NP, Terpening SJ, Snow D, Cobb RR, Kistner O. Vero cell technology forrapid development of inactivated whole virus vaccines for emerging viral diseases.Expert Rev Vaccines. 2017;16(9):883–894.45. Paillet C, Forno G, Kratje R, Etcheverrigaray M. Suspension-Vero cell cultures asa platform for viral vaccine production. Vaccine. 2009;27(46):6464–6467.46. Guedj J, Dahari H, Rong L, Sansone ND, Nettles RE, Cotler SJ, et al. Modelingshows that the NS5A inhibitor daclatasvir has two modes of action and yields ashorter estimate of the hepatitis C virus half-life. Proc Natl Acad Sci USA.2013;110(10):3991–3996. doi:10.1073/pnas.1203110110.47. Heldt FS, Frensing T, Pflugmacher A, Gr¨opler R, Peschel B, Reichl U. Multiscalemodeling of influenza A virus infection supports the development of direct-actingantivirals. PLoS Comput Biol. 2013;9:e1003372.doi:10.1371/journal.pcbi.1003372.48. de M Quintela B, Conway JM, Hyman JM, Guedj J, dos Santos RW, Lobosco M,et al. A new age-structured multiscale model of the hepatitis C virus life-cycleduring infection and therapy with direct-acting antiviral agents. Front Microbiol.2018;9:601. doi:10.3389/fmicb.2018.00601.49. Zitzmann C, Kaderali L. Mathematical analysis of viral replication dynamics andantiviral treatment strategies: From basic models to age-based multi-scalemodeling. Front Microbiol. 2018;9:1546. doi:10.3389/fmicb.2018.01546.50. Rezelj VV, Levi LI, Vignuzzi M. The defective component of viral populations.Curr Opin Virol. 2018;33:74–80. doi:10.1016/j.coviro.2018.07.014.51. Calain P, Monroe MC, Nichol ST. Ebola virus defective interfering particles andpersistent infection. Virology. 1999;262(1):114–128. doi:10.1006/viro.1999.9915.52. Kuhn JH, Lofts LL, Kugelman JR, Smither SJ, Lever MS, Groen Gv, et al.Reidentification of Ebola virus E718 and ME as Ebolavirus/H.sapiens-tc/COD/1976/Yambuku-Ecran. Genome Announc. 2014;2(6):pii:e01178–14. doi:10.1128/genomeA.01178-14.53. Smither SJ, Lear-Rooney C, Biggins J, Pettitt J, Lever MS, Jr GGO.Comparison of the plaque assay and 50% tissue culture infectious dose assay asmethods for measuring filovirus infectivity. J Virol Methods. 2013;193(2):565–571.doi:10.1016/j.jviromet.2013.05.015.54. Reed LJ, Muench H. A simple method of estimating fifty per cent endpoints. AmJ Epidemiol. 1938;27(3):493–497. doi:10.1093/oxfordjournals.aje.a118408.October 21, 2020 15/165. Beauchemin CAA. phymcmc: A convenient wrapper for emcee; 2019. https://github.com/cbeauc/phymcmc .56. Foreman-Mackey D, Hogg DW, Lang D, Goodman J. emcee: The MCMChammer. Publ Astron Soc Pac. 2013;125(925):306–312. doi:10.1086/670067.October 21, 2020 16/16 upporting Information S1:
Quantification of Ebola virus replication kinetics in vitro
Laura E. Liao, Jonathan Carruthers, Sophie J. Smither, CL4 Virology Team, Simon A. Weller,Diane Williamson, Thomas R. Laws, Isabel Garc´ıa-Dorival, Julian Hiscox,Benjamin P. Holder, Catherine A. A. Beauchemin, Alan S. Perelson,Mart´ın L´opez-Garc´ıa, Grant Lythe, John Barr, Carmen Molina-Par´ısOctober 21, 2020
Figure A:
Total virus from MOI 5 infection.
The total virus concentration from the MOI 5infection (A) was omitted from the analysis due to an order of magnitude difference in the peakconcentration when compared to the MOI 1.0 and 0.1 infections (B, C). It was unclear whetherthis discrepancy was biologically meaningful or due to systematic experimental error.1 a r X i v : . [ q - b i o . CB ] O c t igure B: Estimated parameter distributions of EBOV infection in vitro.
Posterior prob-ability likelihood distributions describing the total virus, mock yield, and calibration curves.2igure C:
Paired parameter posterior likelihood distributions.
Two-parameter PLDs foreach of the 600,000 MCMC-accepted parameter sets are shown. Although mild correlations wereobserved, they were not important given that narrow PLDs were obtained. The majority of correla-tions were a consequence of performing linear regression to the mock yield and standard qRT-PCRcurve, resulting in correlations between the (slope, y-int) parameter pairs ( c inf , ln( V MYinf , ) and (ln(2 ε ),ln( Q t )), respectively. Since different linear fits to the standard curve impacts the conversion of Ctto RNA, correlations between the total virus parameters are also observed as a result, e.g., (ln(2 ε ), V INFtot , ), (ln( V MYtot , ), p tot ), (ln( V MYtot , ), V INFtot , ). Other correlations are observed such as ( p inf , τ I ), ( n E , τ E ), ( n I , t I ). 3 Kinetics of Cell-associated Virus
Two MOI 5 infection experiments were performed with cells grown to 90% and 70% confluence inExpt 1 and Expt 2, respectively. In Expt 1 (Figure D, panels A, B; green), infectious and totalvirus concentrations were determined from the supernatant of the in vitro assay at times late in theinfection (0 and 72–168 hours post-infection). In Expt 2, earlier and much more frequent sampling(every 2 hours from 0–22 hours post-infection) was performed to determine the infectious andtotal virus concentrations in the supernatant (Figure D, panels A, B; yellow). After supernatantremoval, additional samples were taken where cell monolayers were washed with PBS, trypsinizedand scraped with a pipette tip for total and infectious virus quantification (Figure D, panels C, D).Figure D:
Kinetics of MOI 5 infection.
In two MOI 5 infection experiments, the infectiousand total virus concentrations in the supernatant (A, B) of the in vitro assay were quantified atprimarily late times (Expt 1) or early times (Expt 2). In addition, Expt 2 quantified the virusconcentrations from washed and trypsinized cell monolayers that remained after removal of thesupernatant (C, D). The ratio of RNA-to-TCID in the supernatant is compared to that in thewashed cell monolayers in E. Note that these data have been normalized to the number of cells perwell (10 cells). The lines represent the simulated time course from our MM that corresponds tothe set of parameters with the maximum log-likelihood. The variability from converting Ct valuesto total virus (copy/mL) is shown by two error bars on each total virus data point, denoting the68% (same colour) and 95% (black) CR.We expected that the virus concentrations from the washed cell monolayers would correspond4o intracellular virus concentrations (Figure D, panels C, D). We speculate that the intracellularvirus signal was instead obscured by cell-associated virus for the following reasons. Firstly, a veryhigh level of total virus was detected even as early as 0–2 hours post-infection, before significantviral replication was expected to occur. This was accompanied by a very high level of infectiousvirus which, if we were to believe were due to intracellular virions, is counter to the fact that virionsuncoat and release viral RNA once they enter the cell and would not register as infectious virionsin a TCID assay. Lastly, in Figure D (panel E), we compared the ratio of RNA-to-TCID inthe supernatant (circles) to that from the washed cell monolayers (squares). The ratio at earlytimes from the washed cell monolayers resembled the ratio in the supernatant. If the washed cellmonolayers samples were to reflect the intracellular virus levels, we would expect this ratio tobe much higher (more RNA than TCID within a cell). A likely possibility is that these datareflect the kinetics of cell-associated virions, which are virions that remained attached to the cellmembrane even after washing.Under the interpretation that these data reflect cell-associated virus kinetics, the high levels ofvirus at early times are likely virions that adsorbed to the cell membrane. A small jump in virusconcentration between 0–2 hours post-infection can be observed, perhaps showing that adsorptionis still occurring, until it reaches a steady state by 4 hours post-infection. Once the infected cellcomes out of the eclipse phase, by 48 hours post-infection, the ratio of RNA-to-TCID rises. Thesedata at late times (48, 72 hours post-infection) may no longer be dominated by the cell-associatedvirus signal, and could contain information on the level of intracellular virus. We did not pursuefurther mathematical modelling due to the lack of intracellular virus data, beyond these two datapoints.Our final analysis only included the infectious virus concentration from Expt 1. There wasinsufficient information to justify whether the data from Expt 1 and 2 should be combined. Wecould not verify whether there was consistency in the peak virus concentration, the timing of therise, or the difference between peak and early virus levels since Expt 2 lacked frequent samplinglate enough in the infection to capture such features. As previously mentioned, the total virusconcentration from Expt 1 was also omitted. Ultimately, we found that omission of these data didnot hamper our ability to robustly extract the viral infection kinetics parameters.5 Kinetics of Cell Viability and Infection
Following the removal of the supernatant for virus quantification, three wells (two for the MOI = 5experiment) at each time point were stained with 5% Trypan blue for ≥ / th the area of the image, and computing anaverage (Figure E). Windows in which cell boundaries could not be reliably identified, due toimage artifacts or optical effects, were rejected. The mean and standard deviation of each quantityover the replicates was used for analysis.Figure E: Representative image — one of the two MOI = 5 images at 168 h — of Trypan bluestained cells in infected monolayers (left), and the counting method used to estimate total numberof cells per image (right). Random windows chosen for cell counting were rejected and re-selectedif the cells boundaries were not clearly visible. Trypan–blue-stained cells were counted directly.6 .2 Analysis Figure F: Simultaneous fit of viral kinetics data and cell viability kinetics with extended model(see text). To simulate the infection dynamics of the number of cells in each image, we started theinfection with N image = 1450 target cells in the extended model, and rescaled the viral productionrates (e.g., p inf N well N image ) in order to model the virus concentrations in the entire well. The total cellsper image in the model was given by T + n E P E i + n I P I j + S .7he total cell counts per image revealed a very stable population of intact cells (approximately1450 cells per image for all three MOI experiments), following a brief period of proliferation in thefirst day post-infection (Figure F, Total cells per image). In the MOI = 1 experiment, the percentof cells that were stained — Trypan blue marks cells that have lost the ability to actively excludethe dye — was low ( ∼ S ) represent an earlyphase of cell death prior to their disintegration into uncountable debris ( D ).To simulate these cell viability kinetics in tandem with our infection model (presented in themain text) we assumed that once infected cells cease viral production, they enter a relatively long-lasting phase where their membrane is permeable to Trypan blue and they become stained (S) cells(Figure G). As the stages of cell death progress, stained cells subsequently disintegrate to debris(D) and cannot be counted. Representing the stained phase with a sequence of n S equations toobtain Erlang-distributed timings, i.e., d S d t = n I τ I I n I − n S τ S S d S j =2 , ,...,n S d t = n S τ S ( S j − − S j ) , we found that an average S time of 70 h ( n S = 10) was sufficient to reproduce the observed constanttotal cell count per image over the one week experiment (Figure F, Total cells per image). Finally,to account for the fact that stained cells made up only a modest fraction of the total number ofcells per image, even at late times, we allowed for only 50% of the target cells to be susceptibleto infection. Under these assumptions, we obtained an adequate fit to the stained cell data forall three MOI experiments (Figure F, Stained cells per image) while holding all but one of theinfection parameters (the viral production rate was doubled to account for the halved susceptiblepopulation) at their maximum likelihood values (Table 1, main text), thus maintaining agreementwith the viral kinetics data. 8 .3 Discussion In our final analysis (main text), we chose to exclude cell data from consideration because, at leastin its simplest interpretation, it had no effect on the estimation of the viral kinetics parameters (theonly exception being the viral production rate, which could differ by a factor of two, as discussedabove). Moreover, any additional information that could be determined about the viability kineticsof EBOV-infected cells would be based solely on assumptions about how the timing of Trypan bluestaining fits within the infection timeline. The Trypan blue dye stains cells that can no longeractively exclude it, implying that stained cells are dead. But the onset of this passive permeabilitywith respect to cessation of viral production (the end of the “infectious” phase of infection) is notknown, and therefore acts as a hidden parameter (see below). Future resolution of this problem, orthe use of a staining method that can be registered to the infection timeline, e.g., immuno-staining,could potentially allow for these cell kinetics data to further constrain the viral kinetics parameters.Figure H: Alternative model in which a proliferating “post-infectious” phase ( I ) continuously feedsa quasi–steady-state population of stained cells ( S ). Tuning the relative lifespans of each populationcan yield the observed fractional level of the stained population, without the requirement that sometarget cells are not susceptible to infection.We were able to obtain slightly better agreement to the cell kinetics data (not shown) withadditional model features. Adding logistic proliferation for target and eclipse cells to the above-described model (with a growth rate r = 0 .
105 h − common to all three MOI experiments) allowedfor a very good fit to the first 24 h of cell data, without altering the agreement to the stained cellor viral kinetic data. To avoid the assumption that only half of the target cells are susceptible, analternative model (Figure H) could be used where one assumes: (i) a post-infectious phase ( I ) inwhich infected cells no longer produce virus but continue to actively exclude dye, and (ii) that allliving cells, including those in the post-infectious phase, proliferate. This results in a model withthe following set of equations for the post-infectious phase:d I d t = n I τ I I n I − n I τ I I + r I (cid:18) − T + P E j + P I j + P I j N max (cid:19) d I j =2 , ,...,n I d t = n I τ I ( I j − − I j ) + r I j (cid:18) − T + P E j + P I j + P I j N max (cid:19) ,,