Holding time estimation for reactions in stochastic event-based simulation of complex biological systems

The complexity of biological systems motivate the use of an “in silico” stochastic discrete event simulation methodology. This method can incorporate the effects of the recently identified stochastic resonance of a biological system and is computationally capable to process the dynamic interactions of different pathways in the cell. The main requirement for this technique is the event time models for the discrete events of the biological system. Currently such models do not exist for biological functions and this paper proposes one such event model – the biochemical 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 discrete system states. 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. This random time is 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. Also the models incorporate many structural and functional parameters of the biological function, that are lacking in the currently used rate equation model. The parametric nature of the model makes it generic and useful for diverse studies.