Bounds on stationary moments in stochastic chemical kinetics
Bounds on stationary moments in stochastic chemical kinetics
复制标题
随机化学动力学中静止矩的界限
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Abhyudai Singh
中科院分区：
文献类型：
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作者：
K. Ghusinga;C. A. Vargas;Andrew G. Lamperski;Abhyudai Singh
在化学动力学的随机公式中，物种种群计数的平稳矩可以用一组线性方程来描述。然而，除了某些特殊情况，如具有线性反应倾向的系统，力矩方程是欠确定的，因为低阶矩可能依赖于高阶矩。在这里，我们提出了一种方法来寻找化学反应系统中分子计数的稳定矩的下界和上界。该方法利用了任意正值随机变量的统计矩必须满足一定的约束这一事实。这种约束可以表示为关于矩的低阶矩的非线性不等式，与定常矩方程共轭求解它们会得到矩的界。通过两个生化系统的例子，我们证明了不仅得到了给定平稳矩的上界和下界，而且随着使用更多的矩方程和利用相应的高阶矩的不等式，这些界也得到了改善。我们的结果为矩近似的发展提供了途径，该矩近似为其动力学否则难以处理的系统提供了矩动力学的显式界。
In the stochastic formulation of chemical kinetics, the stationary moments of the population count of species can be described via a set of linear equations. However, except for some specific cases such as systems with linear reaction propensities, the moment equations are underdetermined as a lower order moment might depend upon a higher order moment. Here, we propose a method to find lower, and upper bounds on stationary moments of molecular counts in a chemical reaction system. The method exploits the fact that statistical moments of any positive-valued random variable must satisfy some constraints. Such constraints can be expressed as nonlinear inequalities on moments in terms of their lower order moments, and solving them in conjugation with the stationary moment equations results in bounds on the moments. Using two examples of biochemical systems, we illustrate that not only one obtains upper and lower bounds on a given stationary moment, but these bounds also improve as one uses more moment equations and utilizes the inequalities for the corresponding higher order moments. Our results provide avenues for development of moment approximations that provide explicit bounds on moment dynamics for systems whose dynamics are otherwise intractable.