title: Sharper graph-theoretical conditions for the stabilization of complex reaction networks.
abstract: Across the landscape of all possible chemical reaction networks there is a surprising degree of stable behavior, despite what might be substantial complexity and nonlinearity in the governing differential equations. At the same time there are reaction networks, in particular those that arise in biology, for which richer behavior is exhibited. Thus, it is of interest to understand network-structural features whose presence enforces dull, stable behavior and whose absence permits the dynamical richness that might be necessary for life. We present conditions on a network's Species-Reaction Graph that ensure a high degree of stable behavior, so long as the kinetic rate functions satisfy certain weak and natural constraints. These graph-theoretical conditions are considerably more incisive than those reported earlier.
authors.affiliation: The William G. Lowrie Department of Chemical & Biomolecular Engineering, Koffolt Laboratories, Ohio State University, Columbus, OH 43210, USA. Electronic address: knight.326@osu.edu.
authors.forename: Daniel
authors.initials: D
authors.lastname: Knight
authors.affiliation: Javelin Medical Ltd., 4 Pekeris St., Rehovot 76702, Israel. Electronic address: shinarg@gmail.com.
authors.forename: Guy
authors.initials: G
authors.lastname: Shinar
authors.affiliation: The William G. Lowrie Department of Chemical & Biomolecular Engineering, Koffolt Laboratories, Ohio State University, Columbus, OH 43210, USA; Department of Mathematics, Ohio State University, Columbus, OH 43210, USA. Electronic address: feinberg.14@osu.edu.
authors.forename: Martin
authors.initials: M
authors.lastname: Feinberg
mesh_terms: D001669:Biochemical Phenomena; D003196:Computer Graphics; D007700:Kinetics; D055641:Mathematical Concepts; D053858:Metabolic Networks and Pathways; D008954:Models, Biological; D008956:Models, Chemical
keywords: Bistability; Concordant; Multistability; Reaction network; Species-Reaction Graph; Systems biology