具有时滞的循环基因调控网络中振荡的存在性
Existence of Oscillations in Cyclic Gene Regulatory Networks with Time Delay
AI总结：
本文采用简化模型，基于庞加莱-本迪克森型定理和图形化条件，分析了具有负反馈和时滞的循环基因调控网络振荡的存在性，并给出了生化参数解析条件。
摘要：
本文关注具有负循环反馈的基因调控网络中振荡存在的条件，其中明确考虑了转录、翻译和易位过程中的时间延迟。本文的主要目标是提出适用于广泛循环基因调控网络的系统分析工具，并提供新颖的生物学见解。为此，我们采用了一个适合捕捉一大类基因调控网络本质的简化模型。首先，基于庞加莱-本迪克森型定理，证明了唯一平衡态的局部不稳定性导致振荡。然后，推导了等价于唯一平衡态局部不稳定性的图形化存在条件。基于该图形化条件，以生化参数的形式解析地给出了存在条件。这使我们能够找到主要影响振荡存在的无量纲参数，并提供生物学见解。通过两个现有的生化网络——Repressilator和Hes7基因调控网络，说明了解析条件和生物学见解。
英文摘要：
This paper is concerned with conditions for the existence of oscillations in gene regulatory networks with negative cyclic feedback, where time delays in transcription, translation and translocation process are explicitly considered. The primary goal of this paper is to propose systematic analysis tools that are useful for a broad class of cyclic gene regulatory networks, and to provide novel biological insights. To this end, we adopt a simplified model that is suitable for capturing the essence of a large class of gene regulatory networks. It is first shown that local instability of the unique equilibrium state results in oscillations based on a Poincare-Bendixson type theorem. Then, a graphical existence condition, which is equivalent to the local instability of a unique equilibrium, is derived. Based on the graphical condition, the existence condition is analytically presented in terms of biochemical parameters. This allows us to find the dimensionless parameters that primarily affect the existence of oscillations, and to provide biological insights. The analytic conditions and biological insights are illustrated with two existing biochemical networks, Repressilator and the Hes7 gene regulatory networks.
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