Editorial

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Open AccessEditorial

Special Issue “Mathematical Modeling of Viral Infections”

by John M. Murray and Ruy M. Ribeiro

Viruses 2018, 10(6), 303; https://doi.org/10.3390/v10060303 - 04 Jun 2018

Cited by 3 | Viewed by 3386

How an infection will progress in the body is dependent on myriad factors: the rate of spread of the agent, the immune response, what treatment may be applied[...] Full article

(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)

Research

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41 pages, 765 KiB

Open AccessArticle

A New Model for the Dynamics of Hepatitis C Infection: Derivation, Analysis and Implications

by Philip J. Aston

Viruses 2018, 10(4), 195; https://doi.org/10.3390/v10040195 - 13 Apr 2018

Cited by 8 | Viewed by 4728

Abstract

We review various existing models of hepatitis C virus (HCV) infection and show that there are inconsistencies between the models and known behaviour of the infection. A new model for HCV infection is proposed, based on various dynamical processes that occur during the [...] Read more.

We review various existing models of hepatitis C virus (HCV) infection and show that there are inconsistencies between the models and known behaviour of the infection. A new model for HCV infection is proposed, based on various dynamical processes that occur during the infection that are described in the literature. This new model is analysed, and three steady state branches of solutions are found when there is no stem cell generation of hepatocytes. Unusually, the branch of infected solutions that connects the uninfected branch and the pure infection branch can be found analytically and always includes a limit point, subject to a few conditions on the parameters. When the action of stem cells is included, the bifurcation between the pure infection and infected branches unfolds, leaving a single branch of infected solutions. It is shown that this model can generate various viral load profiles that have been described in the literature, which is confirmed by fitting the model to four viral load datasets. Suggestions for possible changes in treatment are made based on the model. Full article

(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)

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10 pages, 462 KiB

Open AccessArticle

Time Intervals in Sequence Sampling, Not Data Modifications, Have a Major Impact on Estimates of HIV Escape Rates

by Vitaly V. Ganusov

Viruses 2018, 10(3), 99; https://doi.org/10.3390/v10030099 - 27 Feb 2018

Cited by 3 | Viewed by 2830

Abstract

The ability of human immunodeficiency virus (HIV) to avoid recognition by humoral and cellular immunity (viral escape) is well-documented, but the strength of the immune response needed to cause such a viral escape remains poorly quantified. Several previous studies observed a more rapid [...] Read more.

The ability of human immunodeficiency virus (HIV) to avoid recognition by humoral and cellular immunity (viral escape) is well-documented, but the strength of the immune response needed to cause such a viral escape remains poorly quantified. Several previous studies observed a more rapid escape of HIV from CD8 T cell responses in the acute phase of infection compared to chronic infection. The rate of HIV escape was estimated with the help of simple mathematical models, and results were interpreted to suggest that CD8 T cell responses causing escape in acute HIV infection may be more efficient at killing virus-infected cells than responses that cause escape in chronic infection, or alternatively, that early escapes occur in epitopes mutations in which there is minimal fitness cost to the virus. However, these conclusions were challenged on several grounds, including linkage and interference of multiple escape mutations due to a low population size and because of potential issues associated with modifying the data to estimate escape rates. Here we use a sampling method which does not require data modification to show that previous results on the decline of the viral escape rate with time since infection remain unchanged. However, using this method we also show that estimates of the escape rate are highly sensitive to the time interval between measurements, with longer intervals biasing estimates of the escape rate downwards. Our results thus suggest that data modifications for early and late escapes were not the primary reason for the observed decline in the escape rate with time since infection. However, longer sampling periods for escapes in chronic infection strongly influence estimates of the escape rate. More frequent sampling of viral sequences in chronic infection may improve our understanding of factors influencing the rate of HIV escape from CD8 T cell responses. Full article

(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)

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26 pages, 7322 KiB

Open AccessArticle

Quantitative Analysis of Hepatitis C NS5A Viral Protein Dynamics on the ER Surface

by Markus M. Knodel, Arne Nägel, Sebastian Reiter, Andreas Vogel, Paul Targett-Adams, John McLauchlan, Eva Herrmann and Gabriel Wittum

Viruses 2018, 10(1), 28; https://doi.org/10.3390/v10010028 - 08 Jan 2018

Cited by 7 | Viewed by 5829

Abstract

Exploring biophysical properties of virus-encoded components and their requirement for virus replication is an exciting new area of interdisciplinary virological research. To date, spatial resolution has only rarely been analyzed in computational/biophysical descriptions of virus replication dynamics. However, it is widely acknowledged that [...] Read more.

Exploring biophysical properties of virus-encoded components and their requirement for virus replication is an exciting new area of interdisciplinary virological research. To date, spatial resolution has only rarely been analyzed in computational/biophysical descriptions of virus replication dynamics. However, it is widely acknowledged that intracellular spatial dependence is a crucial component of virus life cycles. The hepatitis C virus-encoded NS5A protein is an endoplasmatic reticulum (ER)-anchored viral protein and an essential component of the virus replication machinery. Therefore, we simulate NS5A dynamics on realistic reconstructed, curved ER surfaces by means of surface partial differential equations (sPDE) upon unstructured grids. We match the in silico NS5A diffusion constant such that the NS5A sPDE simulation data reproduce experimental NS5A fluorescence recovery after photobleaching (FRAP) time series data. This parameter estimation yields the NS5A diffusion constant. Such parameters are needed for spatial models of HCV dynamics, which we are developing in parallel but remain qualitative at this stage. Thus, our present study likely provides the first quantitative biophysical description of the movement of a viral component. Our spatio-temporal resolved ansatz paves new ways for understanding intricate spatial-defined processes central to specfic aspects of virus life cycles. Full article

(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)

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The Role of Infected Cell Proliferation in the Clearance of Acute HBV Infection in Humans

by Ashish Goyal, Ruy M. Ribeiro and Alan S. Perelson

Viruses 2017, 9(11), 350; https://doi.org/10.3390/v9110350 - 18 Nov 2017

Cited by 25 | Viewed by 6759

Abstract

Around 90–95% of hepatitis B virus (HBV) infected adults do not progress to the chronic phase and, instead, recover naturally. The strengths of the cytolytic and non-cytolytic immune responses are key players that decide the fate of acute HBV infection. In addition, it [...] Read more.

Around 90–95% of hepatitis B virus (HBV) infected adults do not progress to the chronic phase and, instead, recover naturally. The strengths of the cytolytic and non-cytolytic immune responses are key players that decide the fate of acute HBV infection. In addition, it has been hypothesized that proliferation of infected cells resulting in uninfected progeny and/or cytokine-mediated degradation of covalently closed circular DNA (cccDNA) leading to the cure of infected cells are two major mechanisms assisting the adaptive immune response in the clearance of acute HBV infection in humans. We employed fitting of mathematical models to human acute infection data together with physiological constraints to investigate the role of these hypothesized mechanisms in the clearance of infection. Results suggest that cellular proliferation of infected cells resulting in two uninfected cells is required to minimize the destruction of the liver during the clearance of acute HBV infection. In contrast, we find that a cytokine-mediated cure of infected cells alone is insufficient to clear acute HBV infection. In conclusion, our modeling indicates that HBV clearance without lethal loss of liver mass is associated with the production of two uninfected cells upon proliferation of an infected cell. Full article

(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)

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1369 KiB

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RNA Virus Evolution via a Quasispecies-Based Model Reveals a Drug Target with a High Barrier to Resistance

by Richard J. Bingham, Eric C. Dykeman and Reidun Twarock

Viruses 2017, 9(11), 347; https://doi.org/10.3390/v9110347 - 17 Nov 2017

Cited by 19 | Viewed by 6279

Abstract

The rapid occurrence of therapy-resistant mutant strains provides a challenge for anti-viral therapy. An ideal drug target would be a highly conserved molecular feature in the viral life cycle, such as the packaging signals in the genomes of RNA viruses that encode an [...] Read more.

The rapid occurrence of therapy-resistant mutant strains provides a challenge for anti-viral therapy. An ideal drug target would be a highly conserved molecular feature in the viral life cycle, such as the packaging signals in the genomes of RNA viruses that encode an instruction manual for their efficient assembly. The ubiquity of this assembly code in RNA viruses, including major human pathogens, suggests that it confers selective advantages. However, their impact on viral evolution cannot be assessed in current models of viral infection that lack molecular details of virus assembly. We introduce here a quasispecies-based model of a viral infection that incorporates structural and mechanistic knowledge of packaging signal function in assembly to construct a phenotype-fitness map, capturing the impact of this RNA code on assembly yield and efficiency. Details of viral replication and assembly inside an infected host cell are coupled with a population model of a viral infection, allowing the occurrence of therapy resistance to be assessed in response to drugs inhibiting packaging signal recognition. Stochastic simulations of viral quasispecies evolution in chronic HCV infection under drug action and/or immune clearance reveal that drugs targeting all RNA signals in the assembly code collectively have a high barrier to drug resistance, even though each packaging signal in isolation has a lower barrier than conventional drugs. This suggests that drugs targeting the RNA signals in the assembly code could be promising routes for exploitation in anti-viral drug design. Full article

(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)

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5505 KiB

Open AccessArticle

3D Spatially Resolved Models of the Intracellular Dynamics of the Hepatitis C Genome Replication Cycle

by Markus M. Knodel, Sebastian Reiter, Paul Targett-Adams, Alfio Grillo, Eva Herrmann and Gabriel Wittum

Viruses 2017, 9(10), 282; https://doi.org/10.3390/v9100282 - 30 Sep 2017

Cited by 7 | Viewed by 5670

Abstract

Mathematical models of virus dynamics have not previously acknowledged spatial resolution at the intracellular level despite substantial arguments that favor the consideration of intracellular spatial dependence. The replication of the hepatitis C virus (HCV) viral RNA (vRNA) occurs within special replication complexes formed [...] Read more.

Mathematical models of virus dynamics have not previously acknowledged spatial resolution at the intracellular level despite substantial arguments that favor the consideration of intracellular spatial dependence. The replication of the hepatitis C virus (HCV) viral RNA (vRNA) occurs within special replication complexes formed from membranes derived from endoplasmatic reticulum (ER). These regions, termed membranous webs, are generated primarily through specific interactions between nonstructural virus-encoded proteins (NSPs) and host cellular factors. The NSPs are responsible for the replication of the vRNA and their movement is restricted to the ER surface. Therefore, in this study we developed fully spatio-temporal resolved models of the vRNA replication cycle of HCV. Our simulations are performed upon realistic reconstructed cell structures—namely the ER surface and the membranous webs—based on data derived from immunostained cells replicating HCV vRNA. We visualized 3D simulations that reproduced dynamics resulting from interplay of the different components of our models (vRNA, NSPs, and a host factor), and we present an evaluation of the concentrations for the components within different regions of the cell. Thus far, our model is restricted to an internal portion of a hepatocyte and is qualitative more than quantitative. For a quantitative adaption to complete cells, various additional parameters will have to be determined through further in vitro cell biology experiments, which can be stimulated by the results deccribed in the present study. Full article

(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)

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948 KiB

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The Mechanisms for Within-Host Influenza Virus Control Affect Model-Based Assessment and Prediction of Antiviral Treatment

by Pengxing Cao and James M. McCaw

Viruses 2017, 9(8), 197; https://doi.org/10.3390/v9080197 - 26 Jul 2017

Cited by 26 | Viewed by 6867

Abstract

Models of within-host influenza viral dynamics have contributed to an improved understanding of viral dynamics and antiviral effects over the past decade. Existing models can be classified into two broad types based on the mechanism of viral control: models utilising target cell depletion [...] Read more.

Models of within-host influenza viral dynamics have contributed to an improved understanding of viral dynamics and antiviral effects over the past decade. Existing models can be classified into two broad types based on the mechanism of viral control: models utilising target cell depletion to limit the progress of infection and models which rely on timely activation of innate and adaptive immune responses to control the infection. In this paper, we compare how two exemplar models based on these different mechanisms behave and investigate how the mechanistic difference affects the assessment and prediction of antiviral treatment. We find that the assumed mechanism for viral control strongly influences the predicted outcomes of treatment. Furthermore, we observe that for the target cell-limited model the assumed drug efficacy strongly influences the predicted treatment outcomes. The area under the viral load curve is identified as the most reliable predictor of drug efficacy, and is robust to model selection. Moreover, with support from previous clinical studies, we suggest that the target cell-limited model is more suitable for modelling in vitro assays or infection in some immunocompromised/immunosuppressed patients while the immune response model is preferred for predicting the infection/antiviral effect in immunocompetent animals/patients. Full article

(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)

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Understanding the Complex Patterns Observed during Hepatitis B Virus Therapy

by Andrea Carracedo Rodriguez, Matthias Chung and Stanca M. Ciupe

Viruses 2017, 9(5), 117; https://doi.org/10.3390/v9050117 - 19 May 2017

Cited by 8 | Viewed by 4919

Abstract

Data from human clinical trials have shown that the hepatitis B virus (HBV) follows complex profiles, such as bi-phasic, tri-phasic, stepwise decay and rebound. We utilized a deterministic model of HBV kinetics following antiviral therapy to uncover the mechanistic interactions behind HBV dynamics. [...] Read more.

Data from human clinical trials have shown that the hepatitis B virus (HBV) follows complex profiles, such as bi-phasic, tri-phasic, stepwise decay and rebound. We utilized a deterministic model of HBV kinetics following antiviral therapy to uncover the mechanistic interactions behind HBV dynamics. Analytical investigation of the model was used to separate the parameter space describing virus decay and rebound. Monte Carlo sampling of the parameter space was used to determine the virological, pharmacological and immunological factors that separate the bi-phasic and tri-phasic virus profiles. We found that the level of liver infection at the start of therapy best separates the decay patterns. Moreover, drug efficacy, ratio between division of uninfected and infected cells, and the strength of cytotoxic immune response are important in assessing the amount of liver damage experienced over time and in quantifying the duration of therapy leading to virus resolution in each of the observed profiles. Full article

(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)

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Review

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Fighting Cancer with Mathematics and Viruses

by Daniel N. Santiago, Johannes P. W. Heidbuechel, Wendy M. Kandell, Rachel Walker, Julie Djeu, Christine E. Engeland, Daniel Abate-Daga and Heiko Enderling

Viruses 2017, 9(9), 239; https://doi.org/10.3390/v9090239 - 23 Aug 2017

Cited by 26 | Viewed by 9486

Abstract

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, [...] Read more.

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these research fields to increase the value of the preclinical development and the therapeutic efficacy of the resulting treatments. Full article

(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)

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