M. A. Al-Radhawi (Northeastern University, Boston, MA), D. Angeli (Imperial College London and University of Florence, Italy), and E.D. Sontag (Northeastern University and Harvard Medical School, Boston, MA): A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks. PLoS Computational Biology, pp 16(2): e1007681, 2020.
This paper deals with the analysis of the dynamics of chemical reaction networks, developing a theoretical framework based only on graphical knowledge and applying regardless of the particular form of kinetics. This paper introduces a class of networks that are "structurally (mono) attractive", by which we mean that they are incapable of exhibiting multiple steady states, oscillation, or chaos by the virtue of their reaction graphs. These networks are characterized by the existence of a universal energy-like function which we call 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. We study basic motifs, three-body binding, and transcriptional networks. We focus on cellular signaling networks including various post-translational modification cascades, phosphotransfer, and phosphorelay networks, T-cell kinetic proofreading, ERK signaling, and the Ribosome Flow Model.
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