Stochastic simulation of fluctuation-induced enzyme kinetics in vicinity of traps, based on probabilistic tunneling and diffusion mechanisms

A stochastic algorithm for simulation of fluctuation-induced enzyme kinetics is developed. The method is generally well applicable when the reactions occur in low-dimensional and disordered media such as biological ones. We suggest a generalization of the Michaelis - Menten scheme of enzyme kinetics that is extended to simulate the quantum tunneling phenomena in the catalytic cycles of enzymatic processes. The stochastic method is suggested as a generalization of the technique developed in our recent studies [12], [13] where this method was developed to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. The stochastic technique is based on the spatially inhomogeneous, nonlinear integro-differential Smoluchowski equations with random source term. We focus in this study on the spatial distribution, and numerically investigate the segregation in the case of a source with a continuous generation in time and randomly distributed in space. The stochastic particle method presented is based on a probabilistic interpretation of the underlying process as a stochastic Markov process of interacting particle system in discrete but randomly progressed time instances. The segregation is analyzed through the correlation analysis of the vector random field of concentrations which appears to be isotropic in space and stationary in time.