Multigrid analysis of spatially resolved hepatitis C virus protein simulations

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.