动力学不稳定高维生化网络中的伪随机涨落、随机协同性和突发性
Pseudo-Random Fluctuations, Stochastic Cooperativity and Burstiness in Dynamically Unstable High-Dimensional Biochemical Networks
摘要：
本文的目标是概述一个方案，新兴的随机性在高维高度非线性系统，如遗传调控网络（GRN）。我们关注的事实是，在这样的系统中，基因表达所需的所有因子的汇合是一个相对罕见的事件，只有大量的冗余才能使这样的事件足够频繁。这种稀有性的直接后果是mRNA和蛋白质拷贝数的突发性，这是一种众所周知的实验观察到的效应。我们引入了随机协同性的概念，并表明这种现象是一个自然的结果，高维耦合高度非线性的动力系统。在数学术语中，突发性与描述系统动态的随机过程的重尾概率分布相关联。随机协同事件的序列允许从连续的确定性动力学表示的常微分方程（ODE）的朗之万和福克-普朗克方程表示的离散随机动力学的过渡。我们还表明，高维非线性系统，即使在没有明确的机制，抑制固有的不稳定性，仍然可能驻留在一个国家的平稳伪随机波动，为所有实际目的可以被视为随机过程。这种类型的随机行为是这种系统的固有属性，既不需要外部随机力，也不需要高度专业化的双稳态条件。
英文摘要：
The goal of this paper is to outline a scenario of emerging stochasticity in high-dimensional highly nonlinear systems, such as genetic regulatory networks (GRN). We focus attention on the fact that in such systems confluence of all the factors necessary for gene expression is a comparatively rare event, and only massive redundancy makes such events sufficiently frequent. An immediate consequence of this rareness is burstiness in mRNA and protein copy numbers, a well known experimentally observed effect. We introduce the concept of stochastic cooperativity and show that this phenomenon is a natural consequence of high dimensionality coupled with highly nonlinearity of a dynamical system. In mathematical terms, burstiness is associated with heavy-tailed probability distributions of stochastic processes describing the dynamics of the system. The sequence of stochastic cooperativity events allows for transition from continuous deterministic dynamics expressed in terms of ordinary differential equations (ODE) to discrete stochastic dynamics expressed in terms of Langevin and Fokker-Plank equations. We demonstrate also that high-dimensional nonlinear systems, even in the absence of explicit mechanisms for suppressing inherent instability, may nevertheless reside in a state of stationary pseudo-random fluctuations which for all practical purposes may be regarded as stochastic process. This type of stochastic behavior is an inherent property of such systems and requires neither an external random force, nor highly specialized conditions of bistability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
