The objective of this talk is to present a physiologically structured population model capable of
describing intracellular dynamics of viral RNA and its integration with observable circulating HCV RNA
(vRNA) levels. The standard model of viral dynamics [1] consists of target cells (T), infected cells (I),
and viral load (V). The circulating virus levels are determined by the production (pI) and elimination rate
(cV). The drug inhibits the viral production rate. To explain the observed shortened half-life of the
circulating vRNA in patients treated with direct-acting antiviral agents, the standard cellular infection (CI)
model was expanded by including the drug effects on intracellular processes of viral RNA production and
virion assembly [2]. The central part of this model is the intracellular level of vRNA. The link between
the intracellular and cellular infection (ICCI) model and CI model has been achieved by replacing the
constant p with a time dependent p(t) = r(t), where r denotes the individual cell vRNA level. To account
for drug effects on the intracellular processes, we propose a new physiologically structured population
(PSP) model with vRNA as the individual cell structure. The production rate for circulating vRNA is
expressed as r(t), where the total intracellular vRNA is a new link between ICCI and CI models. The pstate
equations of the PSP model were integrated resulting in a CI model augmented by a new variable
R(t). The model parameters were obtained from [3]. Simulations were performed to obtain the density
distribution of vRNA among infected hepatocytes i(r,t), as well as short and long-term behavior of V(t).
Analytical solutions were derived for assessment of the impact of key model parameters, including drug
effects, on the time courses of i(r,t) and V(t). The circulating levels of vRNA predicted by the r-structured
population model exhibit tri-exponential behavior with the slopes controlled by drug effects. For strong
acting drugs, the i(r,t) converges to a point distribution and V(t) approaches 0 for large times.
In summary, the vRNA-structured population model describes the drug effect on the intracellular
processes and allows integration with the cell infection model. The viral load time courses predicted by
the PSP model are similar to the time courses generated by the standard CI model.

References:
[1] Neumann AU, Lam NP, Dahari H, Greatch DR, Wiley TE, Mika B, Perelson AS, Hepatitis C viral
dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science (1998) 282:103-107.
[2] Guedj J, Neumann AU, Understanding hepatitis C viral dynamics with direct-acting antiviral agents
due to the interplay between intracellular replication and cellular infection dynamics. J. Theor. Biol.
(2010) 267:330-340.
[3] Guedj J, Dahari H, Rong L, Sansone ND, Nettles RE, Cotler SJ, Layden TJ, Uprichard SL, Perelson
AS, Modeling shows that the NS5A inhibitor daclatasvir has two modes of action and yields a shorter
estimate of the hepatitis C virus half-life. PNAS (2013) 110: 3991-6.