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Enhanced identification and exploitation of time scales for model reduction in stochastic chemical kinetics

机译:增强对时间尺度的识别和利用,以减少随机化学动力学模型

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摘要

Widely different time scales are common in systems of chemical reactions and can be exploited to obtain reduced models applicable to the time scales of interest. These reduced models enable more efficient computation and simplify analysis. A classic example is the irreversible enzymatic reaction, for which separation of time scales in a deterministic mass action kinetics model results in approximate rate laws for the slow dynamics, such as that of Michaelis–Menten. Recently, several methods have been developed for separation of slow and fast time scales in chemical master equation (CME) descriptions of stochastic chemical kinetics, yielding separate reduced CMEs for the slow variables and the fast variables. The paper begins by systematizing the preliminary step of identifying slow and fast variables in a chemical system from a specification of the slow and fast reactions in the system. The authors then present an enhanced time-scale-separation method that can extend the validity and improve the accuracy of existing methods by better accounting for slow reactions when equilibrating the fast subsystem. The resulting method is particularly accurate in systems such as enzymatic and protein interaction networks, where the rates of the slow reactions that modify the slow variables are not a function of the slow variables. The authors apply their methodology to the case of an irreversible enzymatic reaction and show that the resulting improvements in accuracy and validity are analogous to those obtained in the deterministic case by using the total quasi-steady-state approximation rather than the classical Michaelis–Menten. The other main contribution of this paper is to show how mass fluctuation kinetics models, which give approximate evolution equations for the means, variances, and covariances of the concentrations in a chemical system, can feed into time-scale-separation methods at a variety of stages.
机译:在化学反应系统中,普遍存在着截然不同的时标,可以利用它来获得适用于所关注时标的简化模型。这些简化的模型可实现更有效的计算并简化分析。一个经典的例子是不可逆的酶反应,在确定的质量作用动力学模型中时间尺度的分离产生了慢速动力学的近似速率定律,例如米利斯-门腾的速率定律。最近,已经开发了几种方法来分离随机化学动力学的化学主方程(CME)描述中的慢速和快速时间标度,从而分别为慢速变量和快速变量生成减少的CME。本文首先系统化了根据化学反应中慢速和快速反应的规格来识别化学系统中慢速和快速变量的初步步骤。然后,作者提出了一种增强的时标分离方法,该方法可以通过在平衡快速子系统时更好地考虑慢速反应来扩展有效性并提高现有方法的准确性。所得方法在诸如酶促和蛋白质相互作用网络之类的系统中特别准确,其中修改慢变量的慢反应速率不是慢变量的函数。作者将他们的方法学应用于不可逆的酶反应情况,并表明,由此产生的准确性和有效性改善与确定性情况下通过使用总拟稳态近似而不是经典的Michaelis-Menten获得的结果相似。本文的另一主要贡献是展示质量波动动力学模型如何为化学系统中的浓度的均值,方差和协方差给出近似的演化方程,如何将其引入各种时间尺度分离方法中。阶段。

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