Dynamical equivalence and linear conjugacy of chemical reaction networks: New results and methods

Matthew D. Johnston, David Siegel, Gábor Szederkényi

Research output: Contribution to journalArticle

19 Citations (Scopus)


In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics. The developed methods are extensions of previously published results on dynamically equivalent reaction networks and are based on mixed-integer linear programming. As related theoretical contributions we show that (i) dense linearly conjugate networks define a unique super-structure for any positive diagonal state transformation if the set of chemical complexes is given, and (ii) the existence of linearly conjugate detailed balanced and complex balanced networks do not depend on the selection of equilibrium points. In the second part of the paper it is shown that determining dynamically equivalent realizations to a network that is structurally fixed but parametrically not can also be written and solved as a mixed-integer linear programming problem. Several examples illustrate the presented computation methods.

Original languageEnglish
Pages (from-to)443-468
Number of pages26
Issue number2
Publication statusPublished - Dec 1 2012

ASJC Scopus subject areas

  • Chemistry(all)
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Dynamical equivalence and linear conjugacy of chemical reaction networks: New results and methods'. Together they form a unique fingerprint.

  • Cite this