Walczak Aleksandra M, Mugler Andrew, Wiggins Chris H
CNRS-Laboratoire de physique Theorique de l'Ecole Normale Superieure, Paris, France.
Methods Mol Biol. 2012;880:273-322. doi: 10.1007/978-1-61779-833-7_13.
Recent single-cell experiments have revived interest in the unavoidable or intrinsic noise in biochemical and genetic networks arising from the small number of molecules of the participating species. That is, rather than modeling regulatory networks in terms of the deterministic dynamics of concentrations, we model the dynamics of the probability of a given copy number of the reactants in single cells. Most of the modeling activity of the last decade has centered on stochastic simulation, i.e., Monte Carlo methods for generating stochastic time series. Here we review the mathematical description in terms of probability distributions, introducing the relevant derivations and illustrating several cases for which analytic progress can be made either instead of or before turning to numerical computation. Analytic progress can be useful both for suggesting more efficient numerical methods and for obviating the computational expense of, for example, exploring parametric dependence.
近期的单细胞实验重新引发了人们对于生化和遗传网络中不可避免的或内在噪声的兴趣，这种噪声源于参与反应的物种分子数量较少。也就是说，我们不再依据浓度的确定性动力学来对调控网络进行建模，而是对单细胞中反应物特定拷贝数的概率动态进行建模。过去十年里，大部分建模工作都集中在随机模拟上，即用于生成随机时间序列的蒙特卡罗方法。在此，我们回顾基于概率分布的数学描述，给出相关推导，并举例说明在转向数值计算之前或替代数值计算时能够取得解析进展的几种情况。解析进展不仅有助于提出更高效的数值方法，还能避免例如探索参数依赖性时的计算开销。
