Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements

2009/03/06 by Murad Banaji, Banaji, Murad, Gheorghe Crăciun +1
Biochemistry, Genetics and Molecular Biology · #05C38 #05C50 #34C99 #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #Protein Structure and Dynamics

paper · pdf · doi:10.48550/arxiv.0903.1190

openalex publication_date 2009/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend previous work on injectivity in chemical reaction networks to general interaction networks. Matrix- and graph-theoretic conditions for injectivity of these systems are presented. A particular signed, directed, labelled, bipartite multigraph, termed the ``DSR graph'', is shown to be a useful representation of an interaction network when discussing questions of injectivity. A graph-theoretic condition, developed previously in the context of chemical reaction networks, is shown to be sufficient to guarantee injectivity for a large class of systems. The graph-theoretic condition is simple to state and often easy to check. Examples are presented to illustrate the wide applicability of the theory developed.

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