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Multigrid analysis of spatially resolved hepatitis C virus protein simulations

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Computing and Visualization in Science

Abstract

Viruses are a major challenge to human health and prosperity. This holds true for various viruses which are either threatening Europe (like Dengue and Yellow fever) or which are currently causing big health problems like the hepatitis C virus (HCV). HCV causes chronic liver diseases like cirrhosis and cancer and is the main reason for liver transplantations. Exploring biophysical properties of virus-encoded components and viral life cycle is an exciting new area of current virological research. In this context, spatial resolution is an aspect that has not yet been received much attention despite strong biological evidence suggesting that intracellular spatial dependence is a crucial factor in the viral replication process. We are developing first spatio-temporal resolved models which mimic the behavior of the important components of virus replication within single liver cells. HCV replication is strongly associated to the intracellular Endoplasmatic Reticulum (ER) network. Here, we present the computational basis for the estimation of the diffusion constant of a central component of HCV genome (viral RNA) replication, namely the NS5a protein, on the surface of realistic reconstructed ER geometries. The basic surface partial differential equation (sPDE) evaluations are performed with UG4 using fast massively parallel multigrid solvers. The numerics of the simulations are studied in detail. Integrated concentrations within special subdomains correspond to experimental FRAP time series. In particular, we analyze the refinement stability in time and space for these integrated concentrations based on diffusion sPDEs upon large unstructured surface grids using heuristic values for the NS5a diffusion constant. This builds up a solid basis for future research not included in this presentation. e.g. the presented refinement stability analysis of the single sPDEs allows for parameter estimations for the NS5a diffusion constant. Our advanced Finite Volume/multigrid techniques also could be applied for studying life cycles of other viruses.

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Notes

  1. For Yellow fever, at least a vaccine exists, which is however dangerous for people with weak immune system.

  2. In the actual version NeuRA2.3 we use Cuda7.5, cudpp2.2 and Qt5.

  3. Since we have only one concentration of evaluation, the node number corresponds to the DoF number.

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Acknowledgments

We thank K. Xylouris (G-CSC) for very fruitful discussions on the evaluation of the simulation results, R. Dutta-Roy (Karolinska Institute, Stockholm, Sweden) and J. McLauchlan (Glasgow University) for profound explanations of FRAP experimental setup and data analysis, and Wouter van Beerendonk (Huygens SVI, Netherlands) for his very friendly support in Huygens usage, backgrounds, and licensing. The HLRS Stuttgart is acknowledged for the supplied computing time on the Hermit and Hornet super computers [28], and M. Lampe for vey friedly technical support on the G-CSC cesari cluster. We thank both anonymous reviewers for very helpful comments and suggestions. This work has been partially financed by Frankfurt University, by Erlangen University, by the Politecnico di Torino and the Fondazione Cassa di Risparmio di Torino in the context of the funding campaign “La Ricerca dei Talenti” (HR – Excellence in Research).

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    Authors and Affiliations

    1. Goethe Center for Scientific Computing (GCSC), Goethe University of Frankfurt, Kettenhofweg 139, 60325, Frankfurt, Germany

      Markus M. Knodel, Arne Nägel, Sebastian Reiter, Martin Rupp, Andreas Vogel & Gabriel Wittum

    2. University Medical Center Erlangen, Institute of Radiology, Palmsanlage 5, 91054, Erlangen, Germany

      Markus M. Knodel

    3. Medivir AB, Huddinge, Sweden

      Paul Targett-Adams

    4. Department of Medicine, Institute for Biostatistics and Mathematic Modeling, Goethe University Frankfurt, Theodor-Stern-Kai 7, 60590, Frankfurt, Germany

      Eva Herrmann

    5. Department of Mathematical Sciences (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129, Turin, Italy

      Markus M. Knodel

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    1. Markus M. Knodel
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    Correspondence to Markus M. Knodel.

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    Eva Herrmann and Gabriel Wittum have contributed equally to this work.

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    Knodel, M.M., Nägel, A., Reiter, S. et al. Multigrid analysis of spatially resolved hepatitis C virus protein simulations. Comput. Visual Sci. 17, 235–253 (2015). https://doi.org/10.1007/s00791-016-0261-7

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