比例反应网络静态分布的渐近分析

Linard Hoessly, Carsten Wiuf, Panqiu Xia
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引用次数: 0

摘要

我们研究随机反应网络中的静态分布。特别是,我们对复杂的平衡反应网络和通过假设一组物种(称为非相互作用物种)快速降解(因此在网络中基本上不存在)来还原此类网络感兴趣,这意味着一些反应速率与其他反应速率相比很大。我们将 $Nto\\infty$ 时的极限静止分布与代数消除非相互作用物种后得到的还原反应网络的静止分布进行比较。一般来说,极限静止分布可能与还原反应网络的静止分布不同。我们确定了这两种分布相同的各种充分条件,包括当反应网络详细平衡时,以及当非相互作用物种集由中间物种组成时。在后一种情况下,极限静态分布基本上保留了复杂平衡分布的形式。鉴于还原反应网络可能是非弱可逆的,并表现出非传统的动力学,这一发现尤其令人惊讶。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotic analysis for stationary distributions of scaled reaction networks
We study stationary distributions in the context of stochastic reaction networks. In particular, we are interested in complex balanced reaction networks and reduction of such networks by assuming a set of species (called non-interacting species) are degraded fast (and therefore essentially absent in the network), implying some reaction rates are large compared to others. Technically, we assume these reaction rates are scaled by a common parameter $N$ and let $N\to\infty$. The limiting stationary distribution as $N\to\infty$ is compared to the stationary distribution of the reduced reaction network obtained by algebraic elimination of the non-interacting species. In general, the limiting stationary distribution might differ from the stationary distribution of the reduced reaction network. We identify various sufficient conditions for when these two distributions are the same, including when the reaction network is detailed balanced and when the set of non-interacting species consists of intermediate species. In the latter case, the limiting stationary distribution essentially retains the form of the complex balanced distribution. This finding is particularly surprising given that the reduced reaction network might be non-weakly reversible and exhibit unconventional kinetics.
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