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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, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in MITSO for personal use.date: 02 July 2022

Graphs and the Dynamics of Biochemical Networks

Graphs and the Dynamics of Biochemical Networks

(p.125) 7 Graphs and the Dynamics of Biochemical Networks
Control Theory and Systems Biology

David Angeli

Eduardo D. Sontag

The MIT Press

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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