Departments of Electrical and Computer Engineering and of Bioengineering, Northeastern University, Boston, Massachusetts, United States of America.
Department of Electrical & Electronic Engineering, Imperial College London, London, United Kingdom.
PLoS Comput Biol. 2020 Feb 24;16(2):e1007681. doi: 10.1371/journal.pcbi.1007681. eCollection 2020 Feb.
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.
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，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。从一组反应中推断这种网络的可能定性行为的能力是系统生物学领域的一个核心目标和持续挑战。不幸的是，完整的数学模型的构建经常受到一个普遍问题的阻碍：尽管有关于网络相互作用的丰富定性图形知识，但控制非线性和/或动力学常数的值很难通过实验揭示。动力学也会随环境变化而变化。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，可以说出网络的渐近行为吗？具体来说，它引入了一类“结构（单）吸引”的网络，这意味着它们由于反应图而无法表现出多个稳定状态、振荡或混沌。这些网络的特点是存在一个通用的能量似的函数，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流体系统，它们构成了一个线性凸锥的极值。问题随后被简化为为这个极值集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，即反应网络的李雅普诺夫启用分析（LEARN），它构建了这样的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。首先研究了基本基元、三体结合和遗传网络。然后，工作重点转向细胞信号网络，包括各种翻译后修饰级联、磷酸转移和磷酸接力网络、T 细胞动力学校对和 ERK 信号转导。核糖体流动模型也进行了研究。
