Division of Scientific Computing, Department of Information Technology, Uppsala University, SE-75105, Uppsala, Sweden.
Bull Math Biol. 2019 Aug;81(8):2873-2901. doi: 10.1007/s11538-018-0428-0. Epub 2018 Apr 11.
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 [Formula: see text] in a straightforward implementation. In our LNA algorithm, the work is proportional to [Formula: see text]. 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.
开发并测试了一种用于计算反应扩散主方程 (RDME) 的线性噪声逼近 (LNA) 的算法。RDME 通常被用作生化反应网络的模型。LNA 是针对问题的空间域的一般离散化推导出来的。如果网络中的化学物质数量为 M，空间离散化中的节点数量为 N，则在直接实现中，确定概率分布的均值和协方差的近似值的计算工作量与[公式：见文本]成正比。在我们的 LNA 算法中，工作量与[公式：见文本]成正比。由于 N 通常大于 M，这是一个显著的减少。算法中逼近的准确性进行了分析估计，并在数值实验中进行了评估。
