A Deficiency-One Algorithm for power-law kinetic systems with reactant-determined interactions

Abstract

© 2018, Springer International Publishing AG, part of Springer Nature. This paper addresses the problem of determining the capacity of a deficiency-one network, endowed with rate laws more general than mass action kinetics, to admit multiple positive steady states—that is, whether there exist rate constants such that the corresponding differential equations admit two distinct stoichiometrically compatible steady states where all concentrations are positive. We extend the Deficiency-One Algorithm of M. Feinberg to deal with PL-RDK systems, which are kinetic systems with power-law rate functions whose kinetic orders are identical for reactions with the same reactant complex. The algorithm is applied to a power-law approximation of the Earth’s pre-industrial carbon cycle model, which gave the original motivation for our study.

Source or Periodical Title

Journal of Mathematical Chemistry

ISSN

2599791

Page

2929-2962

Document Type

Article

Subject

Carbon cycle model, Chemical reaction networks, Deficiency-One Algorithm, Multiple equilibria, Power-law kinetics, Reactant-determined interactions

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