Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems.
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.
Banaji
Murad
M
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK and Department of Biological Sciences, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, UK.
Craciun
Gheorghe
G