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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.

A parallel geometric multigrid solver on hierarchically distributed grids is presented. Using a tree-structure for grid distribution onto the processing entities, the multigrid cycle is performed similarly to the serial algorithm, using additional vertical communication during transfer operations. The workload is gathered to fewer processes on coarser levels. Involved parallel structures are described in detail and the multigrid algorithm is formulated, discussing parallelization details. A performance study is presented that shows close to optimal efficiency for weak scaling up to 262k processes in 2 and 3 space dimensions.

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 described in the present study.

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