Wagner Vincent, Castellaz Benjamin, Oesting Marco, Radde Nicole
Institute for Systems Theory and Automatic Control, University of Stuttgart, 70569 Stuttgart, Germany.
Stuttgart Center for Simulation Science, University of Stuttgart, 70569 Stuttgart, Germany.
Bioinformatics. 2022 Sep 15;38(18):4352-4359. doi: 10.1093/bioinformatics/btac501.
The Chemical Master Equation is a stochastic approach to describe the evolution of a (bio)chemical reaction system. Its solution is a time-dependent probability distribution on all possible configurations of the system. As this number is typically large, the Master Equation is often practically unsolvable. The Method of Moments reduces the system to the evolution of a few moments, which are described by ordinary differential equations. Those equations are not closed, since lower order moments generally depend on higher order moments. Various closure schemes have been suggested to solve this problem. Two major problems with these approaches are first that they are open loop systems, which can diverge from the true solution, and second, some of them are computationally expensive.
Here we introduce Quasi-Entropy Closure, a moment-closure scheme for the Method of Moments. It estimates higher order moments by reconstructing the distribution that minimizes the distance to a uniform distribution subject to lower order moment constraints. Quasi-Entropy Closure can be regarded as an advancement of Zero-Information Closure, which similarly maximizes the information entropy. Results show that both approaches outperform truncation schemes. Quasi-Entropy Closure is computationally much faster than Zero-Information Closure, although both methods consider solutions on the space of configurations and hence do not completely overcome the curse of dimensionality. In addition, our scheme includes a plausibility check for the existence of a distribution satisfying a given set of moments on the feasible set of configurations. All results are evaluated on different benchmark problems.
Supplementary data are available at Bioinformatics online.
化学主方程是一种用于描述（生物）化学反应系统演化的随机方法。其解是系统所有可能构型上的时间相关概率分布。由于这个数量通常很大，主方程在实际中往往无法求解。矩量法将系统简化为几个矩的演化，这些矩由常微分方程描述。这些方程是不封闭的，因为低阶矩通常依赖于高阶矩。人们提出了各种封闭方案来解决这个问题。这些方法的两个主要问题，一是它们是开环系统，可能会偏离真实解；二是其中一些计算成本很高。
在此我们引入拟熵封闭，一种用于矩量法的矩封闭方案。它通过重建在低阶矩约束下与均匀分布距离最小的分布来估计高阶矩。拟熵封闭可被视为零信息封闭的一种改进，零信息封闭同样使信息熵最大化。结果表明这两种方法都优于截断方案。拟熵封闭在计算上比零信息封闭快得多，尽管这两种方法都考虑构型空间上的解，因此没有完全克服维数灾难。此外，我们的方案包括对在可行构型集上满足给定矩集的分布存在性的合理性检查。所有结果都在不同的基准问题上进行了评估。
补充数据可在《生物信息学》在线获取。
