Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
J Chem Phys. 2009 Nov 21;131(19):195103. doi: 10.1063/1.3264948.
Recently, stochastic simulations of networks of chemical reactions have shown distributions of steady states that are inconsistent with the steady state solutions of the corresponding deterministic ordinary differential equations. One such class of systems is comprised of networks that have irreversible reactions, and the origin of the anomalous behavior in these cases is understood to be due to the existence of absorbing states. More puzzling is the report of such anomalies in reaction networks without irreversible reactions. One such biologically important example is the futile cycle. Here we show that, in these systems, nonclassical behavior can originate from a stochastic elimination of all the molecules of a key species. This leads to a reduction in the topology of the network and the sampling of steady states corresponding to a truncated network. Surprisingly, we find that, in spite of the purely discrete character of the topology reduction mechanism revealed by "exact" numerical solutions of the master equations, this phenomenon is reproduced by the corresponding Fokker-Planck equations.
最近，化学反应网络的随机模拟显示出的稳态分布与相应的确定性常微分方程的稳态解不一致。这样一类系统由具有不可逆反应的网络组成，这些情况下异常行为的起源被理解为由于吸收态的存在。更令人困惑的是，在没有不可逆反应的反应网络中也有这种异常的报告。一个这样的生物学上重要的例子是无效循环。在这里，我们表明，在这些系统中，非经典行为可能源于关键物种的所有分子的随机消除。这导致网络拓扑的减少和对应于截断网络的稳态的采样。令人惊讶的是，我们发现，尽管通过主方程的“精确”数值解揭示了拓扑减少机制的纯离散性质，但这一现象被相应的福克-普朗克方程所再现。
