反应网络中噪声诱导的混合与多峰性
Noise-induced Mixing and Multimodality in Reaction Networks
摘要：
本文分析了一类多时间尺度的质量作用动力学化学反应网络，其确定性模型和随机性模型表现出质的差异。这些网络受到基因调控网络的启发，由一个慢子网络和一个快子网络组成，慢子网络描述了不同基因状态之间的转换，快子网络描述了涉及基因产物的生化相互作用。我们表明，这种网络的长期动态可以由一个独特的吸引子在确定性水平（不稳定性），而在随机水平的长期概率分布可能会显示多个最大值（多模态）。动态差异源于一种我们称之为噪声诱导混合的新现象，即基因产物的概率分布是由慢子网络“混合”的快子网络的概率分布的线性组合。这些结果被应用在系统生物学的背景下，噪声诱导的混合被证明发挥了生物化学上的重要作用，产生随机多模态和振荡等现象。
英文摘要：
We analyze a class of chemical reaction networks under mass-action kinetics and involving multiple time-scales, whose deterministic and stochastic models display qualitative differences. The networks are inspired by gene-regulatory networks, and consist of a slow-subnetwork, describing conversions among the different gene states, and fast-subnetworks, describing biochemical interactions involving the gene products. We show that the long-term dynamics of such networks can consist of a unique attractor at the deterministic level (unistability), while the long-term probability distribution at the stochastic level may display multiple maxima (multimodality). The dynamical differences stem from a novel phenomenon we call noise-induced mixing, whereby the probability distribution of the gene products is a linear combination of the probability distributions of the fast-subnetworks which are `mixed' by the slow-subnetworks. The results are applied in the context of systems biology, where noise-induced mixing is shown to play a biochemically important role, producing phenomena such as stochastic multimodality and oscillations.
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