PRODUCT-FORM POISSON-LIKE DISTRIBUTIONS AND COMPLEX BALANCED REACTION SYSTEMS
PRODUCT-FORM POISSON-LIKE DISTRIBUTIONS AND COMPLEX BALANCED REACTION SYSTEMS
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DOI：
10.1137/15m1029916
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发表时间：
2016-01-01
影响因子：
1.9
通讯作者：
Wiuf, Carsten
中科院分区：
文献类型：
--
作者：
Cappelletti, Daniele;Wiuf, Carsten
随机反应网络是生化反应系统的动态模型，在N-n上形成一类特殊的连续马尔可夫链。在这里，我们提供了一个基本的表征，将网络的结构特性与其动态特征联系起来。具体而言，我们根据网络的平稳分布定义了“随机复杂平衡系统”的概念，并提供了随机复杂平衡系统的特征，与20世纪70年代和80年代为确定性反应网络建立的特征相似。此外，我们建立了一个网络是随机复杂平衡的当且仅当一个相关的确定性网络是复杂平衡的（在确定性意义上），从而证明了随机和确定性网络理论之间的紧密联系。进一步，我们证明了“亏零定理”的一个随机版本，并证明了任何（不仅是复杂平衡的）亏零反应网络在所有不可约分量上都具有积型泊松类平稳分布。最后，我们提供了当单个（或所有）组件上的产品形式类泊松分布意味着网络是复杂平衡的充分条件，并且我们探索了用产品形式类泊松平稳分布来表征复杂平衡系统的可能性。
Stochastic reaction networks are dynamical models of biochemical reaction systems and form a particular class of continuous-time Markov chains on N-n. Here we provide a fundamental characterization that connects structural properties of a network to its dynamical features. Specifically, we define the notion of "stochastically complex balanced systems" in terms of the network's stationary distribution and provide a characterization of stochastically complex balanced systems, parallel to that established in the 1970s and 1980s for deterministic reaction networks. Additionally, we establish that a network is stochastically complex balanced if and only if an associated deterministic network is complex balanced (in the deterministic sense), thereby proving a strong link between the theory of stochastic and deterministic networks. Further, we prove a stochastic version of the "deficiency zero theorem" and show that any (not only complex balanced) deficiency zero reaction network has a product-form Poisson-like stationary distribution on all irreducible components. Finally, we provide sufficient conditions for when a product-form Poisson-like distribution on a single (or all) component(s) implies the network is complex balanced, and we explore the possibility to characterize complex balanced systems in terms of product-form Poisson-like stationary distributions.