A compartmentalization model of hepatitis C virus replication: an appropriate distribution of HCV RNA for the effective replication

Kinetic Modeling of Virus Growth in Cells

When a virus infects a host cell, it hijacks the biosynthetic capacity of the cell to produce virus progeny, a process that may take less than an hour or more than a week. The overall time required for a virus to reproduce depends collectively on the rates of multiple steps in the infection process, including initial binding of the virus particle to the surface of the cell, virus internalization and release of the viral genome within the cell, decoding of the genome to make viral proteins, replication of the genome, assembly of progeny virus particles, and release of these particles into the extracellular environment. For a large number of virus types, much has been learned about the molecular mechanisms and rates of the various steps. However, in only relatively few cases during the last 50 years has an attempt been made-using mathematical modeling-to account for how the different steps contribute to the overall timing and productivity of the infection cycle in a cell. Here we review the initial case studies, which include studies of the one-step growth behavior of viruses that infect bacteria (Qβ, T7, and M13), human immunodeficiency virus, influenza A virus, poliovirus, vesicular stomatitis virus, baculovirus, hepatitis B and C viruses, and herpes simplex virus. Further, we consider how such models enable one to explore how cellular resources are utilized and how antiviral strategies might be designed to resist escape. Finally, we highlight challenges and opportunities at the frontiers of cell-level modeling of virus infections.

Elevated Concentration of Defensins in Hepatitis C Virus-Infected Patients

Hepatitis C virus (HCV) is the major etiological agent of human non-A and non-B hepatitis, affecting around 180 million people worldwide. Defensins, small cysteine-rich cationic peptides, are shown to have potent antibacterial, antiviral, and antifungal properties. Defensins can be found in both normal and microbial infected patients, at variable concentrations. Notably, viral infections are often associated with elevated concentrations of defensins. The current study aimed to estimate the concentrations of total, α-, and β-defensins in serum taken from normal and HCV-infected patients. 12 healthy (noninfected) and 34 HCV-infected patients were enrolled. Standardized immunoassay kits were used to obtain serum concentrations of defensins. The obtained results were calibrated against kit standard reagents. Total defensin concentrations in HCV-infected patients were significantly higher (2- to 105-fold) compared to healthy individuals. The concentrations of α-defensins were also significantly elevated in the HCV-infected patients (31–1398 ng/50 μL). However, concentrations of β-defensins ranged from 44.5 ng/50 μL to 1056 ng/50 μL. The results did not reveal differences in serum defensin concentration between male and female HCV-infected patients. A-defensin concentration of ≥250 ng/50 μL was found to contain more β-defensins than total defensins and α-defensins. This study concludes, for the first time, that serum defensin levels are elevated in HCV-infected patients.

Mosaic gene network modelling identified new regulatory mechanisms in HCV infection

Modelling of gene networks is widely used in systems biology to study the functioning of complex biological systems. Most of the existing mathematical modelling techniques are useful for analysis of well-studied biological processes, for which information on rates of reactions is available. However, complex biological processes such as those determining the phenotypic traits of organisms or pathological disease processes, including pathogen-host interactions, involve complicated cross-talk between interacting networks. Furthermore, the intrinsic details of the interactions between these networks are often missing. In this study, we developed an approach, which we call mosaic network modelling, that allows the combination of independent mathematical models of gene regulatory networks and, thereby, description of complex biological systems. The advantage of this approach is that it allows us to generate the integrated model despite the fact that information on molecular interactions between parts of the model (so-called mosaic fragments) might be missing. To generate a mosaic mathematical model, we used control theory and mathematical models, written in the form of a system of ordinary differential equations (ODEs). In the present study, we investigated the efficiency of this method in modelling the dynamics of more than 10,000 simulated mosaic regulatory networks consisting of two pieces. Analysis revealed that this approach was highly efficient, as the mean deviation of the dynamics of mosaic network elements from the behaviour of the initial parts of the model was less than 10%. It turned out that for construction of the control functional, data on perturbation of one or two vertices of the mosaic piece are sufficient. Further, we used the developed method to construct a mosaic gene regulatory network including hepatitis C virus (HCV) as the first piece and the tumour necrosis factor (TNF)-induced apoptosis and NF-κB induction pathways as the second piece. Thus, the mosaic model integrates the model of HCV subgenomic replicon replication with the model of TNF-induced apoptosis and NF-κB induction. Analysis of the mosaic model revealed that the regulation of TNF-induced signaling by the HCV network is crucially dependent on the RIP1, TRADD, TRAF2, FADD, IKK, IκBα, c-FLIP, and BAR genes. Overall, the developed mosaic gene network modelling approach demonstrated good predictive power and allowed the prediction of new regulatory nodes in HCV action on apoptosis and the NF-κB pathway. Those theoretical predictions could be a basis for further experimental verification.

vRNA structured population model for Hepatitis C Virus dynamics

Improvements in the understanding of the Hepatitis C Virus (HCV) life-cycle have led to the identification of targets and the development of drugs affecting the intracellular reproduction of the virus. These advancements have presented new modeling challenges as the classic models have focused on describing the macroscopic viral kinetics only. Our primary objective is to apply the existing theory of Physiologically Structured Population (PSP) modeling to describe dynamics of viral RNA (vRNA) in infected hepatocytes of patients receiving treatment with Direct-acting Antiviral Agents (DAA). Using vRNA as a physiological structure this work expands on previous structured population models allowing exploration of micro- and macroscopic implications of such treatments. The PSP model provides a description of vRNA distribution in the infected cells at steady state and its time evolution following treatment. The long term behavior of the model predicts viral load time courses in plasma and permits to quantify conditions for the virus eradication. Finally, we demonstrate that PSP models can account for additional structures, which are essential for the viral replication process with potentially far reaching implications in our understanding of HCV infections and treatment options.

Mathematical modeling of multi-drugs therapy: a challenge for determining the optimal combinations of antiviral drugs

In the current era of antiviral drug therapy, combining multiple drugs is a primary approach for improving antiviral effects, reducing the doses of individual drugs, relieving the side effects of strong antiviral drugs, and preventing the emergence of drug-resistant viruses. Although a variety of new drugs have been developed for HIV, HCV and influenza virus, the optimal combinations of multiple drugs are incompletely understood. To optimize the benefits of multi-drugs combinations, we must investigate the interactions between the combined drugs and their target viruses. Mathematical models of viral infection dynamics provide an ideal tool for this purpose. Additionally, whether drug combinations computed by these models are synergistic can be assessed by two prominent drug combination theories, Loewe additivity and Bliss independence. By combining the mathematical modeling of virus dynamics with drug combination theories, we could show the principles by which drug combinations yield a synergistic effect. Here, we describe the theoretical aspects of multi-drugs therapy and discuss their application to antiviral research.

A new stochastic model for subgenomic hepatitis C virus replication considers drug resistant mutants

As an RNA virus, hepatitis C virus (HCV) is able to rapidly acquire drug resistance, and for this reason the design of effective anti-HCV drugs is a real challenge. The HCV subgenomic replicon-containing cells are widely used for experimental studies of the HCV genome replication mechanisms, for drug testing in vitro and in studies of HCV drug resistance. The NS3/4A protease is essential for virus replication and, therefore, it is one of the most attractive targets for developing specific antiviral agents against HCV. We have developed a stochastic model of subgenomic HCV replicon replication, in which the emergence and selection of drug resistant mutant viral RNAs in replicon cells is taken into account. Incorporation into the model of key NS3 protease mutations leading to resistance to BILN-2061 (A156T, D168V, R155Q), VX-950 (A156S, A156T, T54A) and SCH 503034 (A156T, A156S, T54A) inhibitors allows us to describe the long term dynamics of the viral RNA suppression for various inhibitor concentrations. We theoretically showed that the observable difference between the viral RNA kinetics for different inhibitor concentrations can be explained by differences in the replication rate and inhibitor sensitivity of the mutant RNAs. The pre-existing mutants of the NS3 protease contribute more significantly to appearance of new resistant mutants during treatment with inhibitors than wild-type replicon. The model can be used to interpret the results of anti-HCV drug testing on replicon systems, as well as to estimate the efficacy of potential drugs and predict optimal schemes of their usage.

Quantification of viral infection dynamics in animal experiments

Analyzing the time-course of several viral infections using mathematical models based on experimental data can provide important quantitative insights regarding infection dynamics. Over the past decade, the importance and significance of mathematical modeling has been gaining recognition among virologists. In the near future, many animal models of human-specific infections and experimental data from high-throughput techniques will become available. This will provide us with the opportunity to develop new quantitative approaches, combining experimental and mathematical analyses. In this paper, we review the various quantitative analyses of viral infections and discuss their possible applications.

Replication vesicles are load- and choke-points in the hepatitis C virus lifecycle

Hepatitis C virus (HCV) infection develops into chronicity in 80% of all patients, characterized by persistent low-level replication. To understand how the virus establishes its tightly controlled intracellular RNA replication cycle, we developed the first detailed mathematical model of the initial dynamic phase of the intracellular HCV RNA replication. We therefore quantitatively measured viral RNA and protein translation upon synchronous delivery of viral genomes to host cells, and thoroughly validated the model using additional, independent experiments. Model analysis was used to predict the efficacy of different classes of inhibitors and identified sensitive substeps of replication that could be targeted by current and future therapeutics. A protective replication compartment proved to be essential for sustained RNA replication, balancing translation versus replication and thus effectively limiting RNA amplification. The model predicts that host factors involved in the formation of this compartment determine cellular permissiveness to HCV replication. In gene expression profiling, we identified several key processes potentially determining cellular HCV replication efficiency.

Hepatitis C is a severe disease and a prime cause for liver transplantation. Up to 3% of the world's population are chronically infected with its causative agent, the Hepatitis C virus (HCV). This capacity to establish long (decades) lasting persistent infection sets HCV apart from other plus-strand RNA viruses typically causing acute, self-limiting infections. A prerequisite for its capacity to persist is HCV's complex and tightly regulated intracellular replication strategy. In this study, we therefore wanted to develop a comprehensive understanding of the molecular processes governing HCV RNA replication in order to pinpoint the most vulnerable substeps in the viral life cycle. For that purpose, we used a combination of biological experiments and mathematical modeling. Using the model to study HCV's replication strategy, we recognized diverse but crucial roles for the membraneous replication compartment of HCV in regulating RNA amplification. We further predict the existence of an essential limiting host factor (or function) required for establishing active RNA replication and thereby determining cellular permissiveness for HCV. Our model also proved valuable to understand and predict the effects of pharmacological inhibitors of HCV and might be a solid basis for the development of similar models for other plus-strand RNA viruses.