Estimation of the holding Time for Cytoplasmic Reactions in Stochastic Event Based Modeling of Complex Biological Networks

The complexity of biological networks motivates the use of computer or ”in silico” stochastic event based modeling approach to better identify the dynamic interactions of different processes in the cell. This requires the computation of the time taken by different processes in the cell on a per molecule basis. We present a mathematical formulation for the estimation of the reaction time between two molecules within a cell. In particular, we propose two models: 1) The reactant molecules enter the system one at a time to initiate reactions, and 2) The reactant molecules arrive in batches of a certain size. We derive expressions for the average and second moment of the time for reaction that will be used by our stochastic event-based simulation for both models. Unlike rate equations, the proposed model does not require the assumption of concentration stability for multiple molecule reactions.