Complex Balanced Equilibria of Weakly Reversible Power Law Kinetic Systems

Talabis, Dylan Antonio S. J.; Mendoza, Eduardo R.; Jose, Editha C.

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Complex Balanced Equilibria of Weakly Reversible Power Law Kinetic Systems

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Mendoza, Eduardo R.
Oesterhelt, Dieter / Membrane Biochemistry, Max Planck Institute of Biochemistry, Max Planck Society;

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Talabis, D. A. S. J., Mendoza, E. R., & Jose, E. C. (2019). Complex Balanced Equilibria of Weakly Reversible Power Law Kinetic Systems. Match-Communications in Mathematical and in Computer Chemistry, 82(3), 601-624.

Cite as: https://hdl.handle.net/21.11116/0000-0005-FA35-6

Abstract

In this paper, we use the concept of kinetic reactant deficiency to determine the existence of complex balanced equilibria of power law kinetic systems. We previously introduced a class of power law kinetic systems whose kinetic order vectors (which we call "interactions") are reactant-determined (i.e. reactions with the same reactant complex have identical vectors) and are linear independent per linkage class, denoted by PL-TIK systems. A subset of PL-TIK systems was found to admit a complex balanced equilibrium. In this work, we prove that zero kinetic reactant deficiency systems are precisely the PL-TIK systems. Our main result is the existence of complex balanced equilibria for weakly reversible systems with zero kinetic reactant deficiency (for any rate constant), hence, generalizing the previous study.