A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks
A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks
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DOI：
10.1371/journal.pcbi.1007681
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发表时间：
2020-02-01
影响因子：
4.3
通讯作者：
Sontag, Eduardo D.
中科院分区：
文献类型：
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作者：
Al-Radhawi, M. Ali;Angeli, David;Sontag, Eduardo D.
复杂的分子生物学过程，如转录和翻译、信号转导、翻译后修饰级联和代谢途径，原则上可以通过明确考虑调节细胞生命的复杂化学相互作用网络的生化反应来描述。从一系列反应中推断出这种网络可能的定性行为的能力是系统生物学领域的中心目标和持续挑战。不幸的是，完整数学模型的构建经常受到一个普遍问题的阻碍：尽管关于网络相互作用的定性图形知识丰富，但控制非线性的形式和/或动力学常数的值很难通过实验揭示。动力学也会随着环境的变化而变化。这项工作解决了以下问题：给定一组反应，并且不假设动力学的特定形式，我们可以对网络的渐近行为说些什么？具体地说，它引入了一类“结构（单）吸引”的网络，这意味着它们不能通过反应图表现出多个稳态、振荡或混沌。这些网络的特点是存在一个普遍的类能量函数，称为鲁棒李雅普诺夫函数（RLF）。为了找到这样的函数，引入了一组有限的秩一线性系统，它们构成了一个线性凸锥的极值。然后，这个问题被简化为为这组极值找到一个共同的李雅普诺夫函数。基于这种特征，提供了一个计算包，Lyapunov-Enabled Analysis of Reaction Networks (LEARN)，可以构建这些函数或排除它们的存在。对生化网络的广泛研究表明，LEARN提供了一个新的统一框架。首先研究了基本基序、三体结合和遗传网络。接下来的工作重点是细胞信号网络，包括各种翻译后修饰级联、磷传递和磷中继网络、t细胞动力学校对和ERK信号。研究了核糖体流动模型。
Complex molecular biological processes such as transcription and translation, signal transduction, post-translational modification cascades, and metabolic pathways can be described in principle by biochemical reactions that explicitly take into account the sophisticated network of chemical interactions regulating cell life. The ability to deduce the possible qualitative behaviors of such networks from a set of reactions is a central objective and an ongoing challenge in the field of systems biology. Unfortunately, the construction of complete mathematical models is often hindered by a pervasive problem: despite the wealth of qualitative graphical knowledge about network interactions, the form of the governing nonlinearities and/or the values of kinetic constants are hard to uncover experimentally. The kinetics can also change with environmental variations. This work addresses the following question: given a set of reactions and without assuming a particular form for the kinetics, what can we say about the asymptotic behavior of the network? Specifically, it introduces a class of networks that are "structurally (mono) attractive" meaning that they are incapable of exhibiting multiple steady states, oscillation, or chaos by virtue of their reaction graphs. These networks are characterized by the existence of a universal energy-like function called a Robust Lyapunov function (RLF). To find such functions, a finite set of rank-one linear systems is introduced, which form the extremals of a linear convex cone. The problem is then reduced to that of finding a common Lyapunov function for this set of extremals. Based on this characterization, a computational package, Lyapunov-Enabled Analysis of Reaction Networks (LEARN), is provided that constructs such functions or rules out their existence. An extensive study of biochemical networks demonstrates that LEARN offers a new unified framework. Basic motifs, three-body binding, and genetic networks are studied first. The work then focuses on cellular signalling networks including various post-translational modification cascades, phosphotransfer and phosphorelay networks, T-cell kinetic proofreading, and ERK signalling. The Ribosome Flow Model is also studied.