The Linear Noise Approximation for Spatially Dependent Biochemical Networks

被引:0
作者
Per Lötstedt
机构
[1] Uppsala University,Division of Scientific Computing, Department of Information Technology
来源
Bulletin of Mathematical Biology | 2019年 / 81卷
关键词
Linear noise approximation; Spatially dependent; Fast algorithm; 60J60; 65C40; 92C45;
D O I
暂无
中图分类号
学科分类号
摘要
An algorithm for computing the linear noise approximation (LNA) of the reaction–diffusion master equation (RDME) is developed and tested. The RDME is often used as a model for biochemical reaction networks. The LNA is derived for a general discretization of the spatial domain of the problem. If M is the number of chemical species in the network and N is the number of nodes in the discretization in space, then the computational work to determine approximations of the mean and the covariances of the probability distributions is proportional to M2N2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M^2N^2$$\end{document} in a straightforward implementation. In our LNA algorithm, the work is proportional to M2N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M^2N$$\end{document}. Since N usually is larger than M, this is a significant reduction. The accuracy of the approximation in the algorithm is estimated analytically and evaluated in numerical experiments.
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页码:2873 / 2901
页数:28
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