In-Silico Effects of Mg2+ Diffusion Rates on Stochastic Event Based Simulation of the PhoPQ System

The challenge today is to develop a modeling and simulation paradigm that integrates structural, molecular and genetic data for a quantitative understanding of physiology and behavior of biological processes at multiple scales. This paradigm requires techniques that maintain a reasonable accuracy of the biological process and also reduces the computational overhead. This objective motivates the use of new methods that can transform the problem from energy and affinity based modeling to information theory based modeling. To achieve this, we transform all dynamics within the cell into a random event time, which is specified through an information domain measure like probability distribution. This allows us to use the ``in silico" stochastic event based modeling approach to find the molecular dynamics of the system. In this paper, we present the discrete event simulation concept using the example of the signal transduction cascade triggered by extra-cellular Mg²⁺ concentration in the two component PhoPQ regulatory system of Salmonella Typhimurium. We also present a model to compute the information domain measure of the molecular transport process by estimating the statistical parameters of inter-arrival time between molecules/ions coming to a cell receptor as external signal. This model transforms the diffusion process into the information theory measure of stochastic event completion time to get the distribution of the Mg²⁺ departure events. Using these molecular transport models, we next study the in-silico effects of this external trigger on the PhoPQ system.