Nonlinear Coupling for Improved Stochastic Network Model: A Study of Schnakenberg Model∗

Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approximation is applicable and when it breaks down. Here we study the simple Schnakenberg model consisting of two molecular species whose concentrations vary and three reversible reactions. To reduce residual errors from the conventional formulation of the Langevin equation, we propose to explicitly model the effective coupling between macroscopic concentrations of different molecular species. Our preliminary results show that this formulation is effective in correcting residual errors from the original uncoupled Langevin equation and can approximate the underlying chemical master equation very accurately.