2008/09/08 by Murad Banaji, Banaji, Murad, Gheorghe Crăciun +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · #05C38 #05C50 #15A15 #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.0809.1308
openalex publication_date 2008/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we discuss the question of how to decide when a general chemical reaction system is incapable of admitting multiple equilibria, regardless of parameter values such as reaction rate constants, and regardless of the type of chemical kinetics, such as mass-action kinetics, Michaelis-Menten kinetics, etc. Our results relate previously described linear algebraic and graph-theoretic conditions for injectivity of chemical reaction systems. After developing a translation between the two formalisms, we show that a graph-theoretic test developed earlier in the context of systems with mass action kinetics, can be applied to reaction systems with arbitrary kinetics. The test, which is easy to implement algorithmically, and can often be decided without the need for any computation, rules out the possibility of multiple equilibria for the systems in question.