A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks
Author(s)
Al-Radhawi, M Ali
Angeli, David
Sontag, Eduardo D
Type
Journal Article
Abstract
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.
Date Issued
2020-02-24
Date Acceptance
2020-01-23
Citation
PLoS Computational Biology, 2020, 16 (2), pp.1-37
ISSN
1553-734X
Publisher
Public Library of Science (PLoS)
Start Page
1
End Page
37
Journal / Book Title
PLoS Computational Biology
Volume
16
Issue
2
Copyright Statement
© 2020 Ali Al-Radhawi et al. This is an open access article distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
License URL
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000526725200009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Life Sciences & Biomedicine
Biochemical Research Methods
Mathematical & Computational Biology
Biochemistry & Molecular Biology
GLOBAL CONVERGENCE RESULT
CHEMICAL-REACTION NETWORKS
STEADY-STATES
MULTISITE PHOSPHORYLATION
SIGNAL-TRANSDUCTION
MESSENGER-RNA
PETRI NETS
STABILITY
SYSTEMS
2-COMPONENT
Publication Status
Published
Article Number
ARTN e1007681
Date Publish Online
2020-02-24