Mathematical models based on ordinary differential equations (ODE) that describe the population dynamics of viruses and infected cells have been an essential tool to characterize and quantify viral infection dynamics. Although an important aspect of viral infection is the dynamics of viral spread, which includes transmission by cell-free virions and direct cell-to-cell transmission, models used so far ignored cell-to-cell transmission completely, or accounted for this process by simple mass-action kinetics between infected and uninfected cells. In this study, we show that the simple mass-action approach falls short when describing viral spread in a spatially-defined environment. Using simulated data, we present a model extension that allows correct quantification of cell-to-cell transmission dynamics within a monolayer of cells. By considering the decreasing proportion of cells that can contribute to cell-to-cell spread with progressing infection, our extension accounts for the transmission dynamics on a single cell level while still remaining applicable to standard population-based experimental measurements. While the ability to infer the proportion of cells infected by either of the transmission modes depends on the viral diffusion rate, the improved estimates obtained using our novel approach emphasize the need to correctly account for spatial aspects when analyzing viral spread.

Whereas the mode of action of lamivudine (LAM) against hepatitis B virus (HBV) is well established, the inhibition mechanism(s) of interferon-α are less completely defined. To advance our understanding, we mathematically modelled HBV kinetics during 14-day pegylated interferon-α-2a (pegIFN), LAM or pegIFN+LAM treatment of 39 chronically HBV-infected humanized uPA/SCID chimeric mice. Serum HBV DNA and intracellular HBV DNA were measured frequently. We developed a multicompartmental mathematical model and simultaneously fit it to the serum and intracellular HBV DNA data. Unexpectedly, even in the absence of an adaptive-immune response, a biphasic decline in serum HBV DNA and intracellular HBV DNA was observed in response to all treatments. Kinetic analysis and modeling indicate that the 1st phase represents inhibition of intracellular HBV DNA synthesis and secretion which was similar under all treatments with overall mean efficacy of 98%. In contrast, there were distinct differences in HBV decline during the 2nd phase which was accounted for in the model by a time-dependent inhibition of intracellular HBV DNA synthesis with the steepest decline observed during pegIFN + LAM (1.28/d) and the slowest (0.1/d) during pegIFN monotherapy. Reminiscent of observations in patients treated with pegIFN and/or LAM, a biphasic HBV decline was observed in treated humanized mice in the absence of adaptive immune response. Interestingly, combination treatment does not increase the initial inhibition of HBV production, but rather enhanced 2nd phase decline providing insight into the dynamics of HBV treatment response and the mode of action of interferon-α against HBV. Importance Chronic hepatitis B virus (HBV) infection remains a global health care problem as we lack sufficient curative treatment options. Elucidating the dynamics of HBV infection and treatment response at the molecular level could facilitate the development of novel, more effective HBV antivirals. Currently, the only well-established small animal HBV infection model available is the chimeric uPA/SCID mice with humanized livers; however, the HBV inhibition kinetics under pegylated interferon-α (pegIFN) in this model system have not been determined in sufficient detail. In this study, viral kinetics in 39 humanized mice treated with pegIFN and/or lamivudine were monitored and analyzed using a mathematical-modelling approach. We found that the main mode of action of interferon-α is blocking HBV DNA synthesis and that the majority of synthesized HBV DNA is secreted. Our study provides novel insights into HBV DNA dynamics within infected human hepatocytes.

The hepatitis C virus (HCV) is capable of spreading within a host by two different transmission modes: cell-free and cell-to-cell. However, the contribution of each of these transmission mechanisms to HCV spread is unknown. To dissect the contribution of these different transmission modes to HCV spread, we measured HCV lifecycle kinetics and used an in vitro spread assay to monitor HCV spread kinetics after a low multiplicity of infection in the absence and presence of a neutralizing antibody that blocks cell-free spread. By analyzing these data with a spatially explicit mathematical model that describes viral spread on a single-cell level, we quantified the contribution of cell-free, and cell-to-cell spread to the overall infection dynamics and show that both transmission modes act synergistically to enhance the spread of infection. Thus, the simultaneous occurrence of both transmission modes represents an advantage for HCV that may contribute to viral persistence. Notably, the relative contribution of each viral transmission mode appeared to vary dependent on different experimental conditions and suggests that viral spread is optimized according to the environment. Together, our analyses provide insight into the spread dynamics of HCV and reveal how different transmission modes impact each other.

BackgroundWhereas the mode of action of lamivudine (LAM) against hepatitis B virus (HBV) is well established, the inhibition mechanism(s) of interferon-α are less completely defined. To advance our understanding, we mathematically modelled HBV kinetics during pegylated interferon-α-2a (pegIFN), LAM and pegIFN+LAM treatment of chronically HBV-infected humanized uPA/SCID chimeric mice.MethodsThirty-nine uPA/SCID mice with humanized livers whose pre-treatment steady-state serum HBV reached 9.2±0.4 logIU/mL were treated with pegIFN, LAM or pegIFN+LAM for 14 days. Serum HBV DNA and intracellular HBV DNA were measured frequently. We developed a nonlinear mixed effect viral kinetic model and simultaneously fit it to the serum and intracellular HBV DNA data.ResultsUnexpectedly, even in the absence of an adaptive-immune response, a biphasic decline in serum HBV DNA and intracellular HBV DNA was observed in response to all treatments. Modeling predicts that the first phase represents pegIFN inhibiting intracellular HBV DNA synthesis with efficacy of 86%, which was similar under LAM and pegIFN+LAM. In contrast, there were distinct differences in HBV decline during the 2nd phase which was accounted for in the model by a time-dependent inhibition of intracellular HBV DNA synthesis with the steepest decline observed during pegIFN+LAM (0.46/d) and the slowest (0.052/d) during pegIFN mono-treatment.ConclusionsReminiscent of observations in patients treated with pegIFN and/or LAM, a biphasic HBV decline was observed in treated humanized mice in the absence of adaptive immune response. Interestingly, combination treatment does not increase the initial inhibition of HBV production; however, enhancement of second phase decline is observed providing insight into the dynamics of HBV treatment response and the mode of action of interferon-α against HBV.Author SummaryChronic hepatitis B virus (HBV) infection remains a global health care problem as we lack sufficient curative treatment options. Elucidating the dynamic of HBV infection and treatment at the molecular level would potentially facilitate the development of novel, more effective HBV antivirals. Currently, the only well-established small animal HBV infection model available is the chimeric uPA/SCID mice with humanized livers; however, the HBV infection kinetics under interferon-α (IFN) in this model system have not been determined in sufficient detail to support the in-depth studies of HBV treatment response needed to identify/confirm more effective drug targets. In this study 39 chronic HBV-infected uPA/SCID humanized mice treated with IFN and/or lamivudine were analysed using a mathematical modelling approach. We found that IFN main mode of action is blocking HBV DNA synthesis and that 73% of synthesized HBV DNA per are secreted from infected cells. Our data-driven mathematical modeling study provides novel insights into IFN anti-HBV mechanism(s) and viral-host interplay at the molecular level.