ADAPTIVE DISCRETE GALERKIN METHODS APPLIED TO THE CHEMICAL MASTER EQUATION
ADAPTIVE DISCRETE GALERKIN METHODS APPLIED TO THE CHEMICAL MASTER EQUATION
复制标题
DOI：
10.1137/070689759
复制
发表时间：
2008-01-01
影响因子：
3.1
通讯作者：
Wulkow, M.
中科院分区：
文献类型：
--
作者：
Deuflhard, P.;Huisinga, W.;Wulkow, M.
在系统生物学中，生物化学反应动力学的随机描述越来越多地被用来模拟基因调控网络和信号通路。从数学上讲，这样的模型需要基本演化方程的数值解，称为化学主方程（CME）。迄今为止，CME的研究主要采用蒙特卡罗方法，其中最突出的是随机模拟算法[D。T.吉莱斯皮，J.物理、22（1976），pp. 403-434]。本文提出了一种替代方案，其重点是离散偏微分方程（PDE）结构的CME。这使我们能够采用Deuflhard和Wulkow [IMPACT COMPUT. Sci.工程师，1（1989），pp. 269-301]，由Engblom独立开发。从两种不同的选择离散的CME作为一个离散的PDE，Engblom选择的方法线的方法（首先空间，然后时间），而我们强烈主张使用Rothe方法（首先时间，然后空间）明确的理论和算法的原因。在两个相当具有挑战性的问题的数值结果说明了所提出的方法的有前途的功能，并在同一时间，表明线的必要进一步改进的方法在这里工作。
In systems biology, the stochastic description of biochemical reaction kinetics is increasingly being employed to model gene regulatory networks and signaling pathways. Mathematically speaking, such models require the numerical solution of the underlying evolution equation, known as the chemical master equation (CME). Until now, the CME has primarily been treated by Monte Carlo techniques, the most prominent of which is the stochastic simulation algorithm [D. T. Gillespie, J. Comput. Phys., 22 (1976), pp. 403-434]. The paper presents an alternative, which focuses on the discrete partial differential equation (PDE) structure of the CME. This allows us to adopt ideas from adaptive discrete Galerkin methods as first suggested by Deuflhard and Wulkow [IMPACT Comput. Sci. Engrg., 1 (1989), pp. 269-301] for polyreaction kinetics and independently developed by Engblom. From the two different options for discretizing the CME as a discrete PDE, Engblom chose the method of lines approach (first space, then time), whereas we strongly advocate use of the Rothe method (first time, then space) for clear theoretical and algorithmic reasons. Numerical findings at two rather challenging problems illustrate the promising features of the proposed method and, at the same time, indicate lines of necessary further improvement of the method worked out here.