# HCV Spread Kinetics Reveal Varying Contributions of Transmission Modes to Infection Dynamics

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Methods

#### 2.1.1. Cells and Virus

_{2}conditions. Stocks of HCV were produced from a plasmid encoding the JFH-1 genome that was provided by Takaji Wakita (National Institute of Infectious Diseases, Tokyo, Japan) [18,19]. Methods for HCV RNA in vitro transcription and electroporation into Huh7 cells have been described previously [20]. Media collected from HCV RNA transfected cells was then used to infect Huh7 cells at a multiplicity of infection (MOI) of 0.01 foci forming units (FFU)/cell. Culture media from those infections were harvested, pooled, aliquoted, frozen, and titered as described previously [20]. To achieve high titer virus stocks for high MOI experiments, the virus was collected in serum-free, phenol red-free media and concentrated via Amicon ultracentrifugation filters (Milipore) prior to aliquoting and freezing.

#### 2.1.2. Reagents

#### 2.1.3. High MOI HCV Life Cycle Kinetics

#### 2.1.4. RNA Isolation and Quantification

#### 2.1.5. HCV Titer Assay

#### 2.1.6. HCV Immunohistochemical Staining

#### 2.1.7. Spread Assay

#### 2.1.8. Quantifying Foci Size

#### 2.2. Mathematical Modeling

#### 2.2.1. Modeling Viral Life Cycle Kinetics

_{C}for individual cells. Intracellular viral RNA was then exported at a constant rate ρ, to become new extracellular viral RNA, V. Furthermore, extracellular viral concentration is assumed to be lost at a rate c. The model could then be described by the following system of ordinary differential equations:

_{r}, that loses its infectivity at rate c, i.e., dV

_{r}/dt = −cV

_{r}. Thus, the measured extracellular viral RNA concentration, $\tilde{V}$, is a combination of V

_{r}and the newly produced viral RNA, V, i.e., $\tilde{V}={V}_{r}+V$. Despite the removal of media, some viral particles adhere to hepatocytes resulting in high initial cell-associated RNA counts and residual viral particles in the media at early time points due to continuous binding and release. Therefore, measurements at 3 and 6 h p.i. were neglected in the fitting procedure. Parameters estimated include the maximal net-replication rate λ, the viral export and loss rates ρ and c, respectively, the maximal carrying capacity R

_{C}, as well as the initial concentrations of intracellular viral RNA R

_{0}and extracellular residual viral RNA V

_{0}(see Table S1). The 95% confidence intervals of estimates were determined using the profile likelihood approach [24].

#### 2.2.2. A Multi-Scale Model to Describe HCV Infection Dynamics

_{i,j}(tn) and V

_{i,j}(tn) denote the concentration of intracellular and extracellular viral RNA for the cell at grid site (i,j) at time step t

_{n}. Exported viral RNA will contribute to the extracellular viral concentration at the respective grid site, V

_{i,j}. Diffusion of viral particles between grid sites follows the approach introduced by Funk et al. [25] with:

_{i0,j0}(t

_{n+}

_{1}) denotes the viral concentration at grid site (i

_{0},j

_{0}) at time step t

_{n+}

_{1}, with m and Ω denoting the fraction of viral particles allowed to diffuse and the set of neighboring grid sites of (i

_{0},j

_{0}), respectively. At the beginning of simulations and following the experimental protocol, infected cells were initialized according to a truncated exponential distribution as described in [17].

_{n}, ${p}_{i,j}^{f}\left({t}_{n}\right)$, depending on the concentration of extracellular virus at the corresponding grid site, V

_{i,j}(t

_{n}), and a scaling factor β

_{f}that corresponds to the cell-free transmission rate as used in deterministic mathematical models to describe viral spread [17,26,27]. Thus, at each time-step, the probability for cell (i,j) to get infected was calculated by:

_{0}. In case V

_{i,j}(t

_{n}) < R

_{0}, additional neighboring grid sites were considered to reduce the local viral concentration by R

_{0}.

_{i,j}(t

_{n}) denotes the concentration of intracellular viral RNA in cell (i,j), and β

_{c}the corresponding scaling factor representing the cell-to-cell transmission rate. If there was at least one uninfected cell in the direct neighborhood, a Bernoulli trial with probability ${p}_{i,j}^{c}\left({t}_{n}\right)$ was performed. In case of a successful infection, the intracellular viral concentration in the infecting cell was reduced by R

_{0}, the estimated initial concentration of viral RNA within an infected cell (Table S1). In addition, to account for possible unsuccessful cell-to-cell transmissions events despite a high intracellular RNA concentration due to non-infectious viral material (i.e., low specific infectivity), a factor τ was introduced that delayed the occurrence of another transmission event originating from the same infected cell. This factor of intracellular HCV-specific infectivity corresponded to the waiting time between two successful cell-to-cell transmission events from one infected cell and was therefore sampled from an exponential distribution with average τ. The delay was also considered for any newly infected cells before they are able to contribute to the cell-to-cell spread.

_{0}denotes the initial concentration of anti-E2 and E2(t

_{n}) the concentration at time point t

_{n}. Through the neutralization of the virus, anti-E2 is depleted/consumed at a rate of ${c}_{E2}$, reducing the concentration according to:

_{0}= 10

^{4}.

#### 2.2.3. Parameter Inference

_{total}= d

_{I}+ d

_{fsd}was then applied in the ABC-SMC algorithm. Due to the surprisingly fast increase of infected cells in anti-E2 treated wells between 83 and 96 h p.i. in Exp. B; in comparison to the slower increase in the untreated culture systems, the last time point was not considered within this analysis.

#### 2.2.4. Parameter Fitting by pyABC

_{1},θ,…,θ

_{ν}) for explaining the data over a sequence of iterations t = 1,…,n

_{t}:

#### 2.3. Evaluating the Synergistic Effect of Simultaneous Occurrence of Cell-Free and Cell-to-Cell Transmission

_{WT}/(I

_{WT}+(I

_{MUT-CF}+ I

_{MUT-CC})). The RSE is related to the expected fold-increase by Fold = (1/RSE − 1)

^{−1}. Thus, an RSE of 0.5 would mean no synergistic effect of the simultaneous occurrence of both transmission modes, while an RSE of 0.8 corresponds to a 4-fold higher number of infected cells in comparison to the separated spread of both mutants.

_{I}= β

_{f}+ β

_{c}, assuming 15 different combinations for the ratio of the transmission factors for cell-to-cell, β

_{c}, vs. cell-free infection, β

_{f}, to cover different proportions of transmission modes. In addition, the impact of viral diffusion on the outcome was tested by varying the effective viral diffusion rate over different orders of magnitude. For each parameter combination, 10 simulations were performed simulating a time period of 10 days. The equilibrium value of the proportion of cells infected by cell-to-cell transmission was determined for each simulation and plotted against the maximal RSE obtained. For better comparison, a third-degree polynomial was then fitted against all 150 simulations for each combination (p

_{I},D) (i.e., 15 ratios β

_{c}/β

_{f}, 10 simulations each) to determine the proportion of cell-to-cell transmission at which the RSE was maximal for the investigated condition. We considered 5 different values for p

_{I}and 4 different viral diffusion rate, D, in total.

#### 2.4. Statistical Analysis

## 3. Results

#### 3.1. Single Round Infection Kinetics Defines the Timing of Viral Life Cycle

#### 3.2. Experimentally Monitoring Viral Spread

#### 3.3. A Multi-Scale Mathematical Model to Analyze HCV Spread Kinetics

^{−1}, the concentration of viral RNA reaching a carrying capacity of R

_{C}= 7.73 (6.30–9.76) × 10

^{4}RNA copies per cell, and a viral export of ρ = 2.10 (1.24–3.47) × 10

^{−3}h

^{−1}(numbers describe the best estimate and 95% confidence intervals of estimates) (see also Table S1). This parameterization of the intracellular replication dynamics within individual cells is then used in the second step, in which we applied the whole multi-scale model to the HCV spread assay data in order to parameterize the kinetics of cell-free and cell-to-cell transmission, the viral diffusion rate, and the loss of anti-E2 neutralization efficacy in the treated cultures. In this second step, we used a distributed, likelihood-free simulation-based method based on approximate Bayesian computation (pyABC [29], see Section 2) to fit the stochastic, computationally demanding models to the experimental measurements. Before analyzing the actual experimental data, we validated the general appropriateness of our approach by simulating data in correspondence to the experimental measurements and testing the ability of our method to retrieve the parameters used for simulation. Our analysis showed a correct recovery of the predefined parameters using focus size distribution of simulated treated and untreated HCV spread assays for model adaptation (Figure S3).

#### 3.4. Mathematical Analysis Allows Determination of Transmission Kinetics and Reveals Varying Contributions of Viral Transmission Modes to HCV Spread

^{−2}, which corresponded to effective viral diffusion coefficients, D, of 10

^{−2}to 10

^{−1}μm

^{2}/s (Figure 4E and Table 1). However, our analysis predicted a higher usage rate of anti-E2 within the later experiment (Exp. B) compared to the first round of experiments (Exp. A), which is consistent with the hypothesis that there was a considerable anti-E2 escape in Exp. B.

_{c}that scales the probability of infection with the amount of intracellular viral RNA for each time-step and corresponds to the cell-to-cell transmission rate (Figures S5 and S6). As such, the parameter combinations to describe the experimental data for both experiments contained estimates for β

_{c}that spanned a broad range between ~10

^{−6}–10

^{−2}min

^{−1}intraRNA

^{−1}. In contrast, parameter estimates for the cell-free transmission factor were in a tighter estimated range and varied between the two experiments with β

_{f}~ 10

^{−4.5}–10

^{−3}min

^{−1}extraRNA

^{−1}in Exp. B compared to β

_{f}~ 10

^{−6.5}–10

^{−5}min

^{−1}extraRNA

^{−1}in Exp. A (Figure 4E and Table 1). Independent of the individual parameter estimates, all obtained parameter combinations provided a robust prediction of the contribution of the individual transmission modes to viral spread. For Exp. A, which had less cell division, the initial phase of viral spread up to 1–1.5 days p.i. was almost exclusively characterized by cell-to-cell transmission even in cultures that were not treated with anti-E2 (Figure 4F). Cell-to-cell transmission remained the dominant mode of spread with on average ~76% (63%–89%) of successful infections mediated by this transmission mode at 96 h p.i. (Numbers in brackets indicate min and max. predictions by selected parameter combinations, see Figure 4F). Cell-free transmission is predicted to also contribute to viral spread in the anti-E2 treated cultures starting around ~2 days p.i. and being responsible for ~9% (0%–25%) of all infections 96 h p.i. Regardless, cell-to-cell transmission was predicted to be the dominant mode of transmission in Exp. A. In contrast, for Exp. B, in which cell division was more significant, the contribution of the individual transmission modes is predicted to change over the time course of the experiment, with most of the infections (~72% (62%–80%) (untreated) and ~72% (64%–81%) (anti-E2 treated)) being mediated by cell-free transmission at later time points (Figure 4G). Thus, the virus shows versatility in the contribution of the individual transmission modes to the progression of infection between the experimental conditions.

#### 3.5. Simultaneous Occurrence of Cell-Free and Cell-to-Cell Transmission Enhances Viral Spread

_{WT}/(I

_{WT}+(I

_{MUT-CF}+ I

_{MUT-CC})). An RSE of 0.5 would mean no synergistic effect of the simultaneous occurrence of both transmission modes, while values close to 1 indicate a large synergistic effect (see also Section 2). We tested various scenarios for the combined probability of both transmission modes, also assuming different rates of viral diffusion (Figure 5A). We find that for comparable viral diffusion rates as in our experiments (Figure 4E), the relative synergistic effects were largest if ~60%–70% of the infections are due to cell-to-cell transmission (Figure 5B and Figure S7), comparable to the cell-to-cell spread contribution predicted for Exp. A (Figure 4F). Thus, under the experimental conditions with low cell division, HCV spread seems to use the optimal combination of both transmission modes for viral spread.

## 4. Discussion

_{c}and β

_{f}, respectively, which were estimated using the observed focus size distributions.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**HCV High MOI Infection Kinetics: Huh7 cells were infected with HCV at an MOI of 6. Cell lysates and culture media was harvested at the indicated time points. (

**A**) Intracellular HCV RNA (black triangles). HCV and cellular GAPDH RNA levels were quantified by RT-qPCR. Cellular GAPDH was used to normalize HCV copies, which are then graphed as average HCV copies/µg RNA in triplicate samples +/− standard deviation (SD). (

**B**) Extracellular HCV RNA (blue triangles) are graphed as average HCV copies/mL. HCV titers (green triangles) are graphed as foci-forming units (FFU)/mL. Pooled culture media samples from the triplicate wells were spiked with equal amounts of mouse liver RNA as an internal control before extracellular RNA was extracted. Extracellular HCV RNA and mouse GAPDH (mGAPDH) RNA levels were quantified by RT-qPCR. HCV copies were normalized to mGAPDH and graphed as average HCV copies/mL in duplicate samples +/− SD. Titers were determined by titrating the pooled media on naïve Huh7 cells. Results are the average of foci counted in three wells +/− SD.

**Figure 2.**HCV Spread Kinetics: (

**A**) Schematic of the experimental protocol: Confluent Huh7 cells were infected with 35 HCV FFU/well. At 17 h p.i. the viral inoculum was removed, and fresh cDMEM was added either in the absence (i.e., untreated) or presence of 10 µg/mL anti-E2. Monolayers were fixed at different times post-infection and then stained for HCV to detect infected cells. Focus size was counted by individual cell counts for small foci or by area using ImageJ to circle each focus and divide the focus area by the average area of single cells for larger foci. The accuracy of ImageJ focus size calculation was determined by comparing three technical replicates ImageJ area counts with three technical replicate manual counts. The graph shows individual cell counts vs. area counts by ImageJ for representative foci, numbered arbitrarily on the X-axis. (

**B**) Representative of early experiments: Duplicate wells fixed at 72, 96, and 120 h p.i. and then stained for HCV with NS5A antibody to detect infected cells. (

**C**) Representative of later experiments: Five to six wells were fixed at 72, 83, and 96 h p.i. and stained for HCV with E2 antibody to detect infected cells. The numbers of foci per well were counted and are indicated below the dot plots as average +/− standard deviation per well. The number of cells/focus was counted and graphed. Red bar: Median focus size. Statistical differences relative to untreated are indicated (*, p < 0.05; **, p < 0.01; ****, p < 0.0001 by Mann–Whitney U-test). Note that foci sizes from individual wells were pooled for the statistical comparison of foci sizes. The results in each panel are representative of two experimental repeats. (

**D**) Total number of infected cells per well over time calculated from the data in (

**B**,

**C**). Individual well counts (open circles/triangles) and mean (closed circles/triangles). (

**E**) Total number of cells per well over time counted in parallel untreated wells for each experiment. Individual (open circles) and mean (closed circles) cell numbers for three wells are shown.

**Figure 3.**A multi-scale agent-based model to describe HCVcc spread assay dynamics: (

**A**) Schematic of the agent-based model showing the multi-level structure considering single-cell and intracellular viral replication dynamics when simulating HCV spread. Individual cells are distributed on a hexagonal grid (left), which represents parts of the in vitro culture system. These uninfected cells are able to proliferate to fill empty grid sites with probability p

_{p}. Starting from a number of initially infected cells, uninfected cells can get infected by cell-free or cell-to-cell transmission by stochastic processes according to the probabilities p

_{f}and p

_{c}, that depend on the extracellular viral concentration, V, or the intracellular viral load, R, of infectious cells, respectively. Intracellular viral replication within these cells considers the changing concentration of intracellular viral RNA, R, and viral production, ρ (right). See Section 2 for a detailed description of the different processes considered. (

**B**) Sketch of the step-wise analytical approach used to infer the contribution of the different transmission modes to the HCV infection dynamics: (1.) Experimental data on viral lifecycle kinetics are combined with a mathematical model to quantify and parameterize intracellular viral replication and viral export. (2.) These results are then incorporated in the multi-scale agent-based model (ABM) that is used to simulate HCV spread dynamics under the various experimental conditions. The ABM was fitted to the time-resolved focus size distribution data with and without the use of anti-E2 using a high-performance computing approach (pyABC). (3.) The parameterization of the individual processes within the ABM to describe the observed dynamics allows us to infer the contribution of the individual transmission modes to viral spread given different scenarios. (4.) In addition, based on the obtained simulation environment, we predict the advantage of combined transmission modes for viral spread. (

**C**) Experimental data (black dots) and model predictions (red line) showing the dynamics of intra- and extracellular viral RNA over time. Red-shaded area indicates the 95% prediction interval of model predictions. For the extracellular RNA (lower panel), the dashed lines indicate the contribution of the initially applied (blue) and newly produced (green) virions to the total viral load.

**Figure 4.**Model fits, parameter estimates, and relative contribution of cell-free and cell-to-cell transmission modes to HCV spread: (

**A**,

**B**) Measured (black/grey) and predicted (red/blue) focus size distributions for Exp. A in the absence (

**A**) and presence (

**B**) of anti-E2 at 48, 72, 96, and 120 h p.i. and calculated across two replicates (=wells) according to the experimental conditions. Predictions are based on an exemplary parameterization of the model as obtained by the fitting procedure. (

**C**,

**D**) Measured (black/grey) and predicted (red/blue) average number of infected cells in untreated (

**C**) and anti-E2 treated (

**D**) wells calculated across two replicates (=wells). (

**E**) Credibility intervals for the individual parameter estimates obtained by the high-performance computing approach (pyABC) for Exp. A (black/grey) and Exp. B (orange/wheat) after 15 generations of optimization. White circles indicate the weighted mean for each parameter. Corresponding estimates are shown in Table 1. (

**F**,

**G**) Predicted proportion of cells infected by cell-free transmission for Exp. A (

**F**) and Exp. B (

**G**) over the course of the experiment. Mean (solid lines) and 95% CI (shaded area) as calculated from all model predictions obtained from the best performing parameter combinations (=particles) with a distance smaller than 4.0, i.e., 10–15 particles, for untreated (red) and anti-E2 treated (blue) simulations. Please note that time courses denote the time point of infection of cells and need to be shifted by 18 h to be related to the empirical data, as a time delay of 18 h was considered to account for the delay between infection and experimental detection of infection (see Section 2).

**Figure 5.**Advantages of combined modes of viral spread: (

**A**) Predicted advantage of combined modes of viral spread indicated by the Relative Synergistic Effect (RSE) of combined viral spread. The RSE is shown dependent on the proportion of infections by cell-to-cell transmission given different viral diffusion coefficients and infection rates. Individual points indicate the maximal RSE obtained for simulating viral spread in the ABM for a 10-day time course with different combinations of the transmission factors for each transmission mode, β

_{c}and β

_{f}, defining the combined infection rate β

_{I}. Curves show the result of a spline function of third-degree fitted to the individual data. (

**B**) Maximal RSE value and proportion of infections due to cell-to-cell transmission at which the fitted curves reached their maximum for different conditions analyzed ((

**A**), Figure S7).

**Table 1.**Estimates of parameters describing HCV spread within the different experiments: The estimate indicates for each experiment the weighted mean out of all parameter combinations obtained after 15 (Exp. A) and 13 (Exp. B) generations of optimizations by pyABC (see Section 2). Numbers in brackets indicate 95% credibility intervals. (* The theoretically derived diffusion coefficient D according to the Stokes-Einstein equation is D = 8.05 μm

^{2}/s (=0.91 on a log10 scale) according to the assumed diameter of a hepatocyte (20 μm), of an HCV virion (30 nm) and the dynamic viscosity of the medium. The estimated diffusion is much slower than the theoretical prediction as it represents the effective diffusion allowing exported virions to reach uninfected cells in the culture.).

Description | Parameter | Unit | Experiment | |
---|---|---|---|---|

Exp. A | Exp. B | |||

Cell-to-Cell transmission rate (i.e., scaling factor) | β_{c} | log10, min^{−1} intraRNA^{−1} | −4.19 (−6.24–−2.15) | −3.74 (−6.13–−2.02) |

Cell-free transmission rate (i.e., scaling factor) | β_{f} | log10, min^{−1} extraRNA^{−1} | −5.75 (−6.48–−5.05) | −3.87 (−4.46–−3.00) |

Rate of anti-E2 usage/depletion due to neutralization of extracellular RNA | c_{E2} | log10, arbitrary unit min^{−1} | −0.98 (−1.95–0.62) | 0.33 (−0.27–0.95) |

Specific infectivity for cell-to-cell transmission | τ | log10 | −3.15 (−3.27–−2.93) | −3.29 (−3.52–−3.07) |

Viral diffusion coefficient * | D | log10, μm^{2}/s | −1.68 (−1.96–−0.91) | −1.67 (−1.91–−1.27) |

**Table 2.**Advantage of combined spread: Mean number of infected cells for experimental (Exp. A) and simulated data with and without anti-E2 treatment 120 h post inoculation. Experimental data allowing for both transmission modes show a 1.66-fold increase in infected cells compared to anti-E2 treated cultures. Similar results for simulated data using the parameterizations obtained for Exp. A with ~22% of infected cells due to cell-free transmission. Simulations show that the additive combination of infected cells by cell-free and cell-to-cell transmission would only lead to a ~10% increase in infected cell numbers compared to anti-E2 treated cultures. (* The results for the ABM show the average over 10 individual simulations).

Treatment | Infected Cells (Mean) | Fraction of Cells Infected by CF | Fold Increase | Expected Fold Increase | |
---|---|---|---|---|---|

Experiment (Exp. A) | anti-E2 | 937.5 | - | 1 | - |

untreated | 1559.5 | - | 1.66 | - | |

Simulation * (ABM) | anti-E2 | 1028 | 0 | 1 | - |

untreated | 1650 | 0.22 | 1.61 | 1.09 |

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**MDPI and ACS Style**

Durso-Cain, K.; Kumberger, P.; Schälte, Y.; Fink, T.; Dahari, H.; Hasenauer, J.; Uprichard, S.L.; Graw, F. HCV Spread Kinetics Reveal Varying Contributions of Transmission Modes to Infection Dynamics. *Viruses* **2021**, *13*, 1308.
https://doi.org/10.3390/v13071308

**AMA Style**

Durso-Cain K, Kumberger P, Schälte Y, Fink T, Dahari H, Hasenauer J, Uprichard SL, Graw F. HCV Spread Kinetics Reveal Varying Contributions of Transmission Modes to Infection Dynamics. *Viruses*. 2021; 13(7):1308.
https://doi.org/10.3390/v13071308

**Chicago/Turabian Style**

Durso-Cain, Karina, Peter Kumberger, Yannik Schälte, Theresa Fink, Harel Dahari, Jan Hasenauer, Susan L. Uprichard, and Frederik Graw. 2021. "HCV Spread Kinetics Reveal Varying Contributions of Transmission Modes to Infection Dynamics" *Viruses* 13, no. 7: 1308.
https://doi.org/10.3390/v13071308