A diffusion model to estimate the inter-arrival time of charged molecules in stochastic event based modeling of complex biological networks

With biological experiments generating lots of empirical data, the challenge is to develop a modeling paradigm that integrates structural, molecular and genetic data for a quantitative understanding of physiology and behavior of biological processes at multiple scales - starting from cell, to tissues and finally to the whole organism. The complexity of the problem motivates the use of computer or "in silico" stochastic event based modeling approach. We focus on the signal transduction cascade triggered by extra-cellular Mg²⁺ concentration in the two component PhoPQ regulatory system of Salmonella Enterica serovar Thphimurium, and present the mathematical formulation for the estimation of statistical parameters of inter-arrival time of molecules/ions to a cell receptor as external signal.