On a theory of stability for nonlinear stochastic chemical reaction networks.
On a theory of stability for nonlinear stochastic chemical reaction networks.
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DOI：
10.1063/1.4919834
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发表时间：
2015-05
期刊：
影响因子：
--
通讯作者：
P. Smadbeck;Y. Kaznessis
中科院分区：
文献类型：
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作者：
P. Smadbeck;Y. Kaznessis
我们提出了小型、随机、非线性化学反应网络的稳定性理论的要素。稳态概率分布是用零信息 (ZI) 闭包计算的，这是一种求解小型任意非线性反应的化学主方程的闭包算法。随机模型可以通过 ZI 闭合在稳态周围线性化，并且可以轻松计算雅可比矩阵的特征值。特征值控制稳定状态下波动自相关函数的松弛。自相关函数揭示了非线性反应网络动力学背后现象的时间尺度。根据涨落耗散定理，这些函数被发现与小扰动的响应函数一致。在确定性和随机建模形式之间的非线性反应系统的稳定性方面观察到显着差异。
We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.