Analytical Derivation of Moment Equations in Stochastic Chemical Kinetics.
Analytical Derivation of Moment Equations in Stochastic Chemical Kinetics.
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DOI：
10.1016/j.ces.2010.10.024
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发表时间：
2011-02-01
影响因子：
4.7
通讯作者：
Kaznessis YN
中科院分区：
文献类型：
--
作者：
Sotiropoulos V;Kaznessis YN
主概率方程捕捉了各种随机现象的动态行为，这些随机现象可以被建模为马尔可夫过程。主方程的解析解很难得到，因为它们需要枚举所有可能的状态，并确定任何两个状态之间的跃迁概率。这两项任务对于除了最简单的系统之外的所有系统来说都很快变得棘手。我们可以将主概率分布表示为矩的函数，而不是确定概率分布如何随时间变化，然后我们可以写出概率分布矩的瞬态方程。1949年，Moyal定义了主概率分布的导数或跳跃矩。这些是概率分布矩值变化率的度量，即状态之间的任何给定转换对矩值的影响。在本文中，我们提出了一个通用的计划，推导出任何N维马尔可夫过程的函数的跳跃时刻的解析矩方程。重要的是，我们提出了一个计划，推导出任何N维马尔可夫过程的跳跃时刻的解析表达式。为了更好地说明这些概念，我们专注于随机化学动力学模型，我们推导出任意阶跃时刻的解析关系。化学动力学模型被广泛用于捕获生物系统的动态行为。跳跃矩表达式中的元素是化学计量矩阵和反应倾向（即概率反应速率）的函数。我们使用两个玩具的例子，一个线性和非线性的一组反应，以证明该计划的适用性和局限性。最后，我们提供了一个估计的最小数量的时刻，以获得统计上的显着的数据，将唯一地确定潜在的随机化学动力学系统的动态。前两个时刻仅提供有限的信息，特别是当涉及复杂的非线性动力学时。
The master probability equation captures the dynamic behavior of a variety of stochastic phenomena that can be modeled as Markov processes. Analytical solutions to the master equation are hard to come by though because they require the enumeration of all possible states and the determination of the transition probabilities between any two states. These two tasks quickly become intractable for all but the simplest of systems. Instead of determining how the probability distribution changes in time, we can express the master probability distribution as a function of its moments, and, we can then write transient equations for the probability distribution moments. In 1949, Moyal defined the derivative, or jump, moments of the master probability distribution. These are measures of the rate of change in the probability distribution moment values, i.e. what the impact is of any given transition between states on the moment values. In this paper we present a general scheme for deriving analytical moment equations for any N-dimensional Markov process as a function of the jump moments. Importantly, we propose a scheme to derive analytical expressions for the jump moments for any N-dimensional Markov process. To better illustrate the concepts, we focus on stochastic chemical kinetics models for which we derive analytical relations for jump moments of arbitrary order. Chemical kinetics models are widely used to capture the dynamic behavior of biological systems. The elements in the jump moment expressions are a function of the stoichiometric matrix and the reaction propensities, i.e the probabilistic reaction rates. We use two toy examples, a linear and a non-linear set of reactions, to demonstrate the applicability and limitations of the scheme. Finally, we provide an estimate on the minimum number of moments necessary to obtain statistical significant data that would uniquely determine the dynamics of the underlying stochastic chemical kinetic system. The first two moments only provide limited information, especially when complex, non-linear dynamics are involved.
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影响因子：
4.4
作者：
Salis, H;Kaznessis, Y
通讯作者：
Kaznessis, Y
影响因子：
--
作者：
Kaznessis, Yiannis N.
通讯作者：
Kaznessis, Yiannis N.
影响因子：
4.4
作者：
Gillespie, DT
通讯作者：
Gillespie, DT
影响因子：
4.4
作者：
Cao, Y;Gillespie, DT;Petzold, LR
通讯作者：
Petzold, LR
影响因子：
3.9
作者：
Hespanha, JP;Singh, A
通讯作者：
Singh, A