Interval analysis of worst-case stationary moments for stochastic chemical reactions with uncertain parameters
Interval analysis of worst-case stationary moments for stochastic chemical reactions with uncertain parameters
复制标题
参数不确定的随机化学反应最坏情况平稳矩的区间分析
DOI：
10.1016/j.automatica.2022.110647
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发表时间：
2022
期刊：
影响因子：
6.4
通讯作者：
Yuta Sakurai and Yutaka Hori
中科院分区：
文献类型：
--
作者：
Tsuzuki Satori;Yanagisawa Daichi;Nishinari Katsuhiro;Yuta Sakurai and Yutaka Hori
细胞化学反应的动力学是可变的，由于随机噪声从内在和外在的来源。内在噪声是由分子的概率相遇引起的分子拷贝数的细胞内波动，并由化学主方程建模。另一方面，外部噪声代表由于影响基因表达的全局因素的变化而引起的动力学参数的细胞间变化。本文的目的是提出一个理论框架来分析的内在和外在的噪声的组合效应的化学主方程建模的不确定参数。更具体地说，我们制定了一个半定的程序来计算的不确定的时刻方程的参数只给出部分的形式，其分布的统计的固定解决方案的间隔。与现有的许多方法相比，半定程序是在不近似控制方程的情况下导出的。因此，我们可以得到保证的最坏的可能值的时刻的所有参数分布满足给定的统计，这是非常难以估计的样本路径模拟，因为从所有可能的不确定分布采样是困难的。我们证明了所提出的优化方法，使用两个随机化学反应的例子，并表明，优化问题的解决方案提供了信息的上限和下限的统计的固定拷贝数分布。
The dynamics of cellular chemical reactions are variable due to stochastic noise from intrinsic and extrinsic sources. The intrinsic noise is the intracellular fluctuations of molecular copy numbers caused by the probabilistic encounter of molecules and is modeled by the chemical master equation. The extrinsic noise, on the other hand, represents the intercellular variation of the kinetic parameters due to the variation of global factors affecting gene expression. The objective of this paper is to propose a theoretical framework to analyze the combined effect of the intrinsic and the extrinsic noise modeled by the chemical master equation with uncertain parameters. More specifically, we formulate a semidefinite program to compute the intervals of the stationary solution of uncertain moment equations whose parameters are given only partially in the form of the statistics of their distributions. The semidefinite program is derived without approximating the governing equation in contrast with many existing approaches. Thus, we can obtain guaranteed intervals of the worst possible values of the moments for all parameter distributions satisfying the given statistics, which are prohibitively hard to estimate from sample-path simulations since sampling from all possible uncertain distributions is difficult. We demonstrate the proposed optimization approach using two examples of stochastic chemical reactions and show that the solution of the optimization problem gives informative upper and lower bounds of the statistics of the stationary copy number distributions.