Efficient Estimates of Surface Diffusion Parameters for Spatio-Temporally Resolved Virus Replication Dynamics

Advanced methods of treatment are needed to fight the threats of virus-transmitted diseases and pandemics. Often, they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the hepatitis C virus (HCV) proceeds under the influence of nonstructural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5A protein. The diffusion of NSPs has been studied by in vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDEs). Previous work estimated the diffusion coefficient of the NS5A protein by minimizing the discrepancy between an extended set of sufPDE simulations and experimental FRAP time-series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region to its contour length. The quality of this estimate is explored by a comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.