Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3, Canada.
J Chem Phys. 2012 Dec 21;137(23):234110. doi: 10.1063/1.4771660.
Stochastic modeling is essential for an accurate description of the biochemical network dynamics at the level of a single cell. Biochemically reacting systems often evolve on multiple time-scales, thus their stochastic mathematical models manifest stiffness. Stochastic models which, in addition, are stiff and computationally very challenging, therefore the need for developing effective and accurate numerical methods for approximating their solution. An important stochastic model of well-stirred biochemical systems is the chemical Langevin Equation. The chemical Langevin equation is a system of stochastic differential equation with multidimensional non-commutative noise. This model is valid in the regime of large molecular populations, far from the thermodynamic limit. In this paper, we propose a variable time-stepping strategy for the numerical solution of a general chemical Langevin equation, which applies for any level of randomness in the system. Our variable stepsize method allows arbitrary values of the time-step. Numerical results on several models arising in applications show significant improvement in accuracy and efficiency of the proposed adaptive scheme over the existing methods, the strategies based on halving/doubling of the stepsize and the fixed step-size ones.
随机建模对于在单细胞水平上准确描述生化网络动力学至关重要。生化反应系统通常在多个时间尺度上演变，因此它们的随机数学模型表现出刚性。此外，随机模型是刚性的，计算上非常具有挑战性，因此需要开发有效的、准确的数值方法来逼近它们的解。一个重要的混合生化系统的随机模型是化学朗之万方程。化学朗之万方程是一个具有多维非交换噪声的随机微分方程系统。该模型在远离热力学极限的大分子群体的范围内是有效的。在本文中，我们提出了一种用于一般化学朗之万方程数值解的变时步策略，该策略适用于系统中任意级别的随机性。我们的变步长方法允许时间步长的任意值。在几个应用模型上的数值结果表明，与现有的基于二分法/倍增法和固定步长法的策略相比，所提出的自适应方案在准确性和效率方面有了显著的提高。
