Viral kinetic modeling: state of the art

Ebola Virus Infection: Review of the Pharmacokinetic and Pharmacodynamic Properties of Drugs Considered for Testing in Human Efficacy Trials

The 2014-2015 outbreak of Ebola virus disease is the largest epidemic to date in terms of the number of cases, deaths, and affected areas. In October 2015, no antiviral agents had proven antiviral efficacy in patients. However, in September 2014, the World Health Organization inventoried and has since regularly updated a list of potential drug candidates with demonstrated antiviral efficacy in in vitro or animal models. This includes agents belonging to various therapeutic classes, namely direct antiviral agents (favipiravir and BCX4430), a combination of antibodies (ZMapp), type I interferons, RNA interference-based drugs (TKM-Ebola and AVI-7537), and anticoagulant drugs (rNAPc2). Here, we review the pharmacokinetic and pharmacodynamic information presently available for these drugs, using data obtained in healthy volunteers for pharmacokinetics and data obtained in human clinical trials or animal models for pharmacodynamics. Future studies evaluating these drugs in clinical trials are critical to confirm their efficacy in humans, propose appropriate doses, and evaluate the possibility of treatment combinations.

Oseltamivir PK/PD Modeling and Simulation to Evaluate Treatment Strategies against Influenza-Pneumococcus Coinfection

Influenza pandemics and seasonal outbreaks have shown the potential of Influenza A virus (IAV) to enhance susceptibility to a secondary infection with the bacterial pathogen Streptococcus pneumoniae (Sp). The high morbidity and mortality rate revealed the poor efficacy of antiviral drugs and vaccines to fight IAV infections. Currently, the most effective treatment for IAV is by antiviral neuraminidase inhibitors. Among them, the most frequently stockpiled is Oseltamivir which reduces viral release and transmission. However, effectiveness of Oseltamivir is compromised by the emergence of resistant IAV strains and secondary bacterial infections. To date, little attention has been given to evaluate how Oseltamivir treatment strategies alter Influenza viral infection in presence of Sp coinfection and a resistant IAV strain emergence. In this paper we investigate the efficacy of current approved Oseltamivir treatment regimens using a computational approach. Our numerical results suggest that the curative regimen (75 mg) may yield 47% of antiviral efficacy and 9% of antibacterial efficacy. An increment in dose to 150 mg (pandemic regimen) may increase the antiviral efficacy to 49% and the antibacterial efficacy to 16%. The choice to decrease the intake frequency to once per day is not recommended due to a significant reduction in both antiviral and antibacterial efficacy. We also observe that the treatment duration of 10 days may not provide a clear improvement on the antiviral and antibacterial efficacy compared to 5 days. All together, our in silico study reveals the success and pitfalls of Oseltamivir treatment strategies within IAV-Sp coinfection and calls for testing the validity in clinical trials.

Multiscale modeling of virus replication and spread

Replication and spread of human viruses is based on the simultaneous exploitation of many different host functions, bridging multiple scales in space and time. Mathematical modeling is essential to obtain a systems-level understanding of how human viruses manage to proceed through their life cycles. Here, we review corresponding advances for viral systems of large medical relevance, such as human immunodeficiency virus-1 (HIV-1) and hepatitis C virus (HCV). We will outline how the combination of mathematical models and experimental data has advanced our quantitative knowledge about various processes of these pathogens, and how novel quantitative approaches promise to fill remaining gaps.

Multi-scale model for hepatitis C viral load kinetics under treatment with direct acting antivirals

Hepatitis C virus (HCV) infections are a global health problem, and extensive research over the last decades has been targeted at understanding its molecular biology and developing effective antiviral treatments. Recently, a number of potent direct acting antiviral drugs have been developed targeting specific processes in the viral life cycle. Here, we developed a mathematical multi-scale model of the within-host dynamics of HCV infection by integrating a standard model for viral infection with a detailed model of the viral replication cycle inside infected cells. We use this model to study patient time courses of viral load under treatment with daclatasvir, an inhibitor of the viral non-structural protein NS5A. Model analysis predicts that treatment efficacy can be increased by combining daclatasvir with dedicated viral polymerase inhibitors, corresponding to promising current strategies in drug development. Hence, our model presents a predictive tool for in silico simulations, which can be used to study and optimize direct acting antiviral drug treatment.

Ebola virus dynamics in mice treated with favipiravir

The polymerase inhibitor favipiravir is a candidate for the treatment of Ebola virus disease. Here, we designed a mathematical model to characterize the viral dynamics in 20 mice experimentally infected with Ebola virus, which were either left untreated or treated with favipiravir at 6 or 8days post infection. This approach provided estimates of kinetic parameters of Ebola virus reproduction, such as the half-life of productively infected cells, of about 6h, and the basic reproductive number which indicates that virus produced by a single infected cell productively infects about 9 new cells. Furthermore, the model predicted that favipiravir efficiently blocks viral production, reaching an antiviral effectiveness of 95% and 99.6% at 2 and 6days after initiation of treatment, respectively. The model could be particularly helpful to guide future studies evaluating favipiravir in larger animals.

Modelling hepatitis C therapy--predicting effects of treatment

Mathematically modelling changes in HCV RNA levels measured in patients who receive antiviral therapy has yielded many insights into the pathogenesis and effects of treatment on the virus. By determining how rapidly HCV is cleared when viral replication is interrupted by a therapy, one can deduce how rapidly the virus is produced in patients before treatment. This knowledge, coupled with estimates of the HCV mutation rate, enables one to estimate the frequency with which drug resistant variants arise. Modelling HCV also permits the deduction of the effectiveness of an antiviral agent at blocking HCV replication from the magnitude of the initial viral decline. One can also estimate the lifespan of an HCV-infected cell from the slope of the subsequent viral decline and determine the duration of therapy needed to cure infection. The original understanding of HCV RNA decline under interferon-based therapies obtained by modelling needed to be revised in order to interpret the HCV RNA decline kinetics seen when using direct-acting antiviral agents (DAAs). There also exist unresolved issues involving understanding therapies with combinations of DAAs, such as the presence of detectable HCV RNA at the end of therapy in patients who nonetheless have a sustained virologic response.

Quantification of Hepatitis C Virus Cell-to-Cell Spread Using a Stochastic Modeling Approach

It has been proposed that viral cell-to-cell transmission plays a role in establishing and maintaining chronic infections. Thus, understanding the mechanisms and kinetics of cell-to-cell spread is fundamental to elucidating the dynamics of infection and may provide insight into factors that determine chronicity. Because hepatitis C virus (HCV) spreads from cell to cell and has a chronicity rate of up to 80% in exposed individuals, we examined the dynamics of HCV cell-to-cell spread in vitro and quantified the effect of inhibiting individual host factors. Using a multidisciplinary approach, we performed HCV spread assays and assessed the appropriateness of different stochastic models for describing HCV focus expansion. To evaluate the effect of blocking specific host cell factors on HCV cell-to-cell transmission, assays were performed in the presence of blocking antibodies and/or small-molecule inhibitors targeting different cellular HCV entry factors. In all experiments, HCV-positive cells were identified by immunohistochemical staining and the number of HCV-positive cells per focus was assessed to determine focus size. We found that HCV focus expansion can best be explained by mathematical models assuming focus size-dependent growth. Consistent with previous reports suggesting that some factors impact HCV cell-to-cell spread to different extents, modeling results estimate a hierarchy of efficacies for blocking HCV cell-to-cell spread when targeting different host factors (e.g., CLDN1 > NPC1L1 > TfR1). This approach can be adapted to describe focus expansion dynamics under a variety of experimental conditions as a means to quantify cell-to-cell transmission and assess the impact of cellular factors, viral factors, and antivirals.

IMPORTANCE

The ability of viruses to efficiently spread by direct cell-to-cell transmission is thought to play an important role in the establishment and maintenance of viral persistence. As such, elucidating the dynamics of cell-to-cell spread and quantifying the effect of blocking the factors involved has important implications for the design of potent antiviral strategies and controlling viral escape. Mathematical modeling has been widely used to understand HCV infection dynamics and treatment response; however, these models typically assume only cell-free virus infection mechanisms. Here, we used stochastic models describing focus expansion as a means to understand and quantify the dynamics of HCV cell-to-cell spread in vitro and determined the degree to which cell-to-cell spread is reduced when individual HCV entry factors are blocked. The results demonstrate the ability of this approach to recapitulate and quantify cell-to-cell transmission, as well as the impact of specific factors and potential antivirals.

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.

Inferring viral dynamics in chronically HCV infected patients from the spatial distribution of infected hepatocytes

Chronic liver infection by hepatitis C virus (HCV) is a major public health concern. Despite partly successful treatment options, several aspects of intrahepatic HCV infection dynamics are still poorly understood, including the preferred mode of viral propagation, as well as the proportion of infected hepatocytes. Answers to these questions have important implications for the development of therapeutic interventions. In this study, we present methods to analyze the spatial distribution of infected hepatocytes obtained by single cell laser capture microdissection from liver biopsy samples of patients chronically infected with HCV. By characterizing the internal structure of clusters of infected cells, we are able to evaluate hypotheses about intrahepatic infection dynamics. We found that individual clusters on biopsy samples range in size from infected cells. In addition, the HCV RNA content in a cluster declines from the cell that presumably founded the cluster to cells at the maximal cluster extension. These observations support the idea that HCV infection in the liver is seeded randomly (e.g. from the blood) and then spreads locally. Assuming that the amount of intracellular HCV RNA is a proxy for how long a cell has been infected, we estimate based on models of intracellular HCV RNA replication and accumulation that cells in clusters have been infected on average for less than a week. Further, we do not find a relationship between the cluster size and the estimated cluster expansion time. Our method represents a novel approach to make inferences about infection dynamics in solid tissues from static spatial data.

Around 170 million people worldwide are chronically infected with the hepatitis C virus (HCV). Although partly successful treatment options are available, several aspects of HCV infection dynamics within the liver are still poorly understood. How many hepatocytes are infected during chronic HCV infection? How does the virus propagate, and how do innate immune responses interfere with the spread of the virus? We developed mathematical and computational methods to study liver biopsy samples of patients chronically infected with HCV that were analyzed by single cell laser capture microdissection, to infer the spatial distribution of infected cells. With these methods, we find that infected cells on biopsy sections tend to occur in clusters comprising 4–50 hepatocytes, and, based on their amount of intracellular viral RNA, that these cells have been infected for less than a week. The observed HCV RNA profile within clusters of infected cells suggests that factors such as local immune responses could have shaped cluster expansion and intracellular viral replication. Our methods can be applied to various types of infections in order to infer infection dynamics from spatial data.