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dc.contributor.authorKnodel, Markus
dc.contributor.authorTargett-Adams, Paul
dc.contributor.authorGrillo, Alfio
dc.contributor.authorHerrmann, Eva
dc.contributor.authorWittum, Gabriel
dc.identifier.citationKnodel M, Targett-Adams P, Grillo A, Herrmann E, Wittum G (2019) Advanced Hepatitis C Virus Replication PDE Models within a Realistic Intracellular Geometric Environment. International Journal of Environmental Research and Public Health 16: 513. Available:
dc.description.abstractThe hepatitis C virus (HCV) RNA replication cycle is a dynamic intracellular process occurring in three-dimensional space (3D), which is difficult both to capture experimentally and to visualize conceptually. HCV-generated replication factories are housed within virus-induced intracellular structures termed membranous webs (MW), which are derived from the Endoplasmatic Reticulum (ER). Recently, we published 3D spatiotemporal resolved diffusion–reaction models of the HCV RNA replication cycle by means of surface partial differential equation (sPDE) descriptions. We distinguished between the basic components of the HCV RNA replication cycle, namely HCV RNA, non-structural viral proteins (NSPs), and a host factor. In particular, we evaluated the sPDE models upon realistic reconstructed intracellular compartments (ER/MW). In this paper, we propose a significant extension of the model based upon two additional parameters: different aggregate states of HCV RNA and NSPs, and population dynamics inspired diffusion and reaction coefficients instead of multilinear ones. The combination of both aspects enables realistic modeling of viral replication at all scales. Specifically, we describe a replication complex state consisting of HCV RNA together with a defined amount of NSPs. As a result of the combination of spatial resolution and different aggregate states, the new model mimics a cis requirement for HCV RNA replication. We used heuristic parameters for our simulations, which were run only on a subsection of the ER. Nevertheless, this was sufficient to allow the fitting of core aspects of virus reproduction, at least qualitatively. Our findings should help stimulate new model approaches and experimental directions for virology.
dc.description.sponsorshipFunding: AG acknowledges the Dipartimento di Scienze Matematiche (DISMA) “G.L. Lagrange”, Dipartimento di Eccellenza 2018-2022, E11G18000350001. The major part of this study was performed without external funding. Acknowledgments: We thank Andreas Vogel (Bochum University) and Sebastian Reiter (G-CSC) for technical help and helpful discussions and Wouter van Beerendonk (Huygens SVI, Netherlands) for his very friendly support in Huygens usage, backgrounds, and licensing. M.M.K. thanks Dikeos Mario Soumpasis (Professor Emeritus Technical University of Denmark) for very helpful hints, and Serge Kräutle (University Erlangen-Nürnberg) for a stimulating discussion on general proofs of existence and uniqueness of coupled nonlinear PDE systems. The HLRS Stuttgart is acknowledged for the supplied computing time on the Hermit and Hornet super computers [37], and Michael Lampe (GCSC) for very friendly technical support on the G-CSC cesari cluster. The authors acknowledge the Goethe-University Frankfurt for general support and computational resources. In particular, M.M.K. acknowledges the GCSC Frankfurt University for general support during his employment at the GCSC and for the possibility to perform the major part of this study during his employment at the GCSC, and he further acknowledges University Erlangen-Nürnberg, chair of applied mathematics 1 (AM1), for general support since his employment at AM1, namely for the possibility to perform the revision of the paper. The Authors wish to express their sincere thanks to the anonymous Referees which reviewed this paper for their thorough and critical reviews of our work. To this end, we thank the MDPI editing team for carefully editing the final version of this manuscript.
dc.publisherMDPI AG
dc.rightsThis article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (
dc.subjectcomputational virology
dc.subjecthepatitis C virus (HCV)
dc.subjectviral dynamics
dc.subjectwithin-host viral modeling
dc.subjectmathematical models of viral RNA cycle
dc.subjectpopulation dynamics
dc.subject3D spatiotemporal resolved mathematical models
dc.subjectrealistic geometries
dc.subject(surface) partial differential equations
dc.subjectFinite Volumes
dc.subjectmassively parallel multigrid solvers
dc.titleAdvanced Hepatitis C Virus Replication PDE Models within a Realistic Intracellular Geometric Environment
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentExtreme Computing Research Center
dc.identifier.journalInternational Journal of Environmental Research and Public Health
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionDepartment of Mathematics, Chair of Applied Mathematics 1, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
dc.contributor.institutionMedivir AB, Department of Biology, 141 22 Huddinge, Sweden
dc.contributor.institutionDipartimento di Scienze Matematiche (DISMA) “G.L. Lagrange”, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino (TO), Italy
dc.contributor.institutionDepartment of Medicine, Institute for Biostatistics and Mathematic Modeling, Goethe Universität Frankfurt, Theodor-Stern-Kai 7, 60590 Frankfurt am Main, Germany
dc.contributor.institutionGoethe Center for Scientific Computing (G-CSC), Goethe Universität Frankfurt, Kettenhofweg 139, 60325 Frankfurt am Main, Germany
kaust.personWittum, Gabriel

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