An analytical model. to estimate the time taken for cytoplasmic reactions for stochastic simulation of complex biological systems

The complexity of biological systems motivates the use of a computer or "in silico" stochastic event based modeling approach to better identify the dynamic interactions of different processes in the system. This requires the computation of the time taken by different events in the system based on their biological functions and corresponding environment. One such important event is the reactions between the molecules inside the cytoplasm of a cell where the reaction environment is highly chaotic. We present a mathematical formulation for the estimation of the reaction time between two molecules within a cell based on the system state assuming that the reactant molecules enter the system one at a time to initiate reactions. We derive expressions for the average and second moment of the time for reaction to be used by our stochastic event-based simulation. Unlike rate equations, the proposed model does not require the assumption of concentration stability for multiple molecule reactions. The reaction time estimate is considered to be a random variable that suits the stochastic event based simulation method.