Computing weakly reversible linearly conjugate chemical reaction networks with minimal deficiency.

TitleComputing weakly reversible linearly conjugate chemical reaction networks with minimal deficiency.
Publication TypeJournal Article
Year of Publication2013
AuthorsJohnston MD, Siegel D, Szederkényi G
JournalMathematical biosciences
Volume241
Issue1
Pagination88-98
Date Published2013 Jan
Abstract

Mass-action kinetics is frequently used in systems biology to model the behavior of interacting chemical species. Many important dynamical properties are known to hold for such systems if their underlying networks are weakly reversible and have a low deficiency. In particular, the Deficiency Zero and Deficiency One Theorems guarantee strong regularity with regards to the number and stability of positive equilibrium states. It is also known that chemical reaction networks with distinct reaction structure can admit mass-action systems with the same qualitative dynamics. The theory of linear conjugacy encapsulates the cases where this relationship is captured by a linear transformation. In this paper, we propose a mixed-integer linear programming algorithm capable of determining the minimal deficiency weakly reversible reaction network which admits a mass-action system which is linearly conjugate to a given reaction network.

DOI10.1039/c3an36928e
Alternate JournalMath Biosci