title: NONLINEAR LANGEVIN MODEL WITH PRODUCT STOCHASTICITY FOR BIOLOGICAL NETWORKS: THE CASE OF THE SCHNAKENBERG MODEL.
abstract: 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. This paper studies the simple Schnakenberg model consisting of three reversible reactions and two molecular species whose concentrations vary. To reduce the residual errors from the conventional formulation of the Langevin equation, the authors propose to explicitly model the effective coupling between macroscopic concentrations of different molecular species. The 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.
authors.affiliation: Ministry of Education Key Laboratory of Systems Biomedicine, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China; Department of Bioengineering, University of Illinois at Chicago, USA.
authors.forename: Youfang
authors.initials: Y
authors.lastname: Cao
authors.affiliation: Ministry of Education Key Laboratory of Systems Biomedicine, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China; Department of Bioengineering, University of Illinois at Chicago, USA.
authors.forename: Jie
authors.initials: J
authors.lastname: Liang
keywords: Langevin equation; Schnakenberg model; master equation; noise