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.

中文翻译：

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具有产品随机性的生物网络非线性Langevin模型：以SCHNAKENBERG模型为例。

Langevin方程被广泛用于研究分子网络中的随机效应，因为它通常可以很好地近似基础化学主方程。但是，通常不清楚这种近似何时适用，何时分解。本文研究了简单的Schnakenberg模型，该模型由三个可逆反应和两个浓度变化的分子组成。为了减少Langevin方程常规公式的残留误差，作者建议显式地对不同分子种类的宏观浓度之间的有效耦合进行建模。结果表明，该公式可有效地纠正原始的未耦合Langevin方程的残差，并且可以非常精确地近似基础化学主方程。