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Control Theory and Systems Biology$
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Pablo A. Iglesias and Brian P. Ingalls

Print publication date: 2009

Print ISBN-13: 9780262013345

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262013345.001.0001

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PRINTED FROM MIT PRESS SCHOLARSHIP ONLINE (www.mitpress.universitypressscholarship.com). (c) Copyright The MIT Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in MITSO for personal use.date: 19 September 2021

Graphs and the Dynamics of Biochemical Networks

Graphs and the Dynamics of Biochemical Networks

Chapter:
(p.125) 7 Graphs and the Dynamics of Biochemical Networks
Source:
Control Theory and Systems Biology
Author(s):

David Angeli

Eduardo D. Sontag

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262013345.003.0007

This chapter describes two approaches, one based on bipartite graphs and Petri net concepts, and another based on decompositions into order-preserving subsystems. It addresses the basic formalism used for modeling biochemical networks. It reviews some results that use bipartite graphs, and specifically Petri nets. It postulates a quasi-steady-state reduction principle (QSSRP) and asks the question, for what types of components is the QSSRP a valid mathematical tool? It presents a (partial) answer to this question, after introducing monotone systems. This chapter shows that the QSSRP has been recently validated using tools from synthetic biology.

Keywords:   bipartite graphs, Petri net concepts, decompositions, biochemical networks, quasi-steady-state reduction principle, monotone systems, synthetic biology

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