On the precision of quasi steady state assumptions in stochastic dynamics
On the precision of quasi steady state assumptions in stochastic dynamics
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DOI：
10.1063/1.4731754
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发表时间：
2012-07-28
影响因子：
4.4
通讯作者：
Shouval, Harel Z.
中科院分区：
文献类型：
--
作者：
Agarwal, Animesh;Adams, Rhys;Shouval, Harel Z.
许多生化网络具有复杂的多维动力学，用于此类反应网络降维的方法已有很长的历史。通常使用确定性的群体作用法；然而，在小量情况下，与平均值的显著波动是群体作用法无法捕捉到的。在这种情况下，应使用随机模拟方法。在这篇文章中，我们评估了一种这样的降维方法的适用性，准稳态近似(QSSA)[L.Menten和M.Michaelis，“Die Kinetik der Invertinwirkung，Biochem”。Z 49,333369(1913年)]用于在随机动力学情况下的降维。首先，评价了QSSA方法在酶反应正则系统中的适用性。在确定的条件下，将QSSA应用于此类反应体系，可以得到反应物种的平衡浓度，从而得到米氏约化动力学。然而，在随机模拟的情况下，稳态的特征是围绕平均平衡浓度的波动。我们的分析表明，基于QSSA的降维方法很好地捕获了从全维模拟获得的分布的平均值，但无法准确地捕获该平均值附近的分布。此外，QSSA近似并不是唯一的。然后，我们将分析扩展到一个简单的双稳态生化网络模型，该模型被提出来解释突触效率的稳定性；学习和记忆的底物[J·E·利斯曼，《对分子周转不敏感的记忆存储机制：双稳态自动磷酸化激酶》，Proc。娜塔莉。阿卡德。SCI。美国第82,3055-3057(1985)号文件]。我们的分析表明，基于QSSA的降维方法在预测两种稳定状态下的停留时间时会产生两个数量级的误差。(C)2012年美国物理研究所。[http://dx.doi.org/10.1063/1.4731754]
Many biochemical networks have complex multidimensional dynamics and there is a long history of methods that have been used for dimensionality reduction for such reaction networks. Usually a deterministic mass action approach is used; however, in small volumes, there are significant fluctuations from the mean which the mass action approach cannot capture. In such cases stochastic simulation methods should be used. In this paper, we evaluate the applicability of one such dimensionality reduction method, the quasi-steady state approximation (QSSA) [L. Menten and M. Michaelis, "Die kinetik der invertinwirkung," Biochem. Z 49, 333369 (1913)] for dimensionality reduction in case of stochastic dynamics. First, the applicability of QSSA approach is evaluated for a canonical system of enzyme reactions. Application of QSSA to such a reaction system in a deterministic setting leads to Michaelis-Menten reduced kinetics which can be used to derive the equilibrium concentrations of the reaction species. In the case of stochastic simulations, however, the steady state is characterized by fluctuations around the mean equilibrium concentration. Our analysis shows that a QSSA based approach for dimensionality reduction captures well the mean of the distribution as obtained from a full dimensional simulation but fails to accurately capture the distribution around that mean. Moreover, the QSSA approximation is not unique. We have then extended the analysis to a simple bistable biochemical network model proposed to account for the stability of synaptic efficacies; the substrate of learning and memory [J. E. Lisman, "A mechanism of memory storage insensitive to molecular turnover: A bistable autophosphorylating kinase," Proc. Natl. Acad. Sci. U.S.A. 82, 3055-3057 (1985)]. Our analysis shows that a QSSA based dimensionality reduction method results in errors as big as two orders of magnitude in predicting the residence times in the two stable states. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4731754]