Dynamics of complex feedback architectures in metabolic pathways
Dynamics of complex feedback architectures in metabolic pathways
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DOI：
10.1016/j.automatica.2018.10.046
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发表时间：
2019-01-01
期刊：
影响因子：
6.4
通讯作者：
Oyarzun, Diego A.
中科院分区：
文献类型：
--
作者：
Chaves, Madalena;Oyarzun, Diego A.
细胞代谢包含错综复杂的反馈控制回路阵列。这些是细胞适应环境干扰并生存的关键机制。特别是基因调控，通常表现出复杂的结构，结合了代谢物和酶基因之间的正反馈环和负反馈环。然而，由于强非线性和高维性，确定给定反馈架构的闭环动态具有挑战性。在这里，我们提出了一种分析基因调控下代谢途径的新技术。我们的理论融合了时间尺度分离和分段仿射动力系统的思想，应用于陡峭非线性反馈下的各种无分支代谢途径。我们提出了一种系统方法来为给定的监管架构构建状态转换图，从中可以挑选出候选闭环动态进行进一步分析。该方法将高维非线性系统重新转换为在状态空间的多面分区上定义的分段仿射系统。在最一般的设置中，我们的理论可以描述任意长度、任意数量的调节器以及在正反馈环和负反馈环的任意组合下的路径的动态特征。我们在一个显示稳定极限环和双稳态动力学的示例系统上展示了我们的结果。我们还讨论了我们的结果对合成生物学和代谢工程中基因电路设计的影响。 (C) 2018 Elsevier Ltd. 保留所有权利。
Cellular metabolism contains intricate arrays of feedback control loops. These are a key mechanism by which cells adapt and survive environmental disturbances. Gene regulation, in particular, typically displays complex architectures that combine positive and negative feedback loops between metabolites and enzymatic genes. Yet because of strong nonlinearities and high-dimensionality, it is challenging to determine the closed-loop dynamics of a given feedback architecture. Here we present a novel technique for the analysis of metabolic pathways under gene regulation. Our theory blends ideas from timescale separation and piecewise affine dynamical systems, applied to a wide class of unbranched metabolic pathways under steep nonlinear feedback. We propose a systematic method to construct a state transition graph for a given regulatory architecture, from where candidate closed-loop dynamics can be singled out for further analysis. The method recasts a high-dimensional nonlinear system into a piecewise affine system defined on a polytopic partition of the state space. In its most general setup, our theory allows to characterize the dynamics of pathways of arbitrary length, with any number of regulators, and under any combination of positive and negative feedback loops. We illustrate our results on an exemplar system that displays a stable limit cycle and bistable dynamics. We also discuss the implications of our results for the design of gene circuits in synthetic biology and metabolic engineering. (C) 2018 Elsevier Ltd. All rights reserved.