A Random Walk Modelling Approach for Passive Metabolic Pathways in Gram-Negative Bacteria

Random environment of the cell demands for a stochastic tool to analyze its behavior and bring the aspects of the bio-process that has been shadowed by the kinetic rate law based approach. In this work we present a novel random walk approach to detect the dynamics of passive diffusion of a metabolite in the gram-negative bacteria through phosphoenolpyruvate phospho-transfer system (pts pathway). We adopt a cell abstract model from the literature and build a triphase enzyme limited diffusion process on that. To explain the numerical results, we used the E.coli cell in our analysis to show the model precision. Our approach very finely manipulates the flux and flux responses coefficient with respect to enzyme variations in the cell. Also we have shown that current model would match the experimental in-vivo result better than kinetic rate base equivalent. Furthermore computational complexity of our approach is very light and could run in linear time