Chemical reaction network theory

About: Chemical reaction network theory is a research topic. Over the lifetime, 85 publications have been published within this topic receiving 5025 citations.

General mass action kinetics

Abstract: The familiar idea of mass action kinetics is extended to embrace situations more general than chemically reacting mixtures in closed vessels. Thus, for example, many reaction regions connected by convective or diffusive mass transport, such as the cellular aggregates of biological tissue, are drawn into a common mathematical scheme. The ideas of chemical thermodynamics, such as the algebraic nature of the equilibrium conditions and the decreasing property of the free energy, are also generalized in a natural way, and it is then possible to identify classes of generalized kinetic expressions which ensure consistency with the extended thermodynamic conditions. The principal result of this work shows that there exists a simply identifiable class of kinetic expressions, including the familiar detailed balanced kinetics as a proper subclass, which ensure consistency with the extended thermodynamic conditions. For kinetics of this class, which we call complex balanced kinetics, exotic behavior such as bistability and oscillation is precluded, so the domain of search for kinetic expressions with this type of behavior, which is of considerable biological interest, is greatly narrowed. It is also shown that the ideas of complex balancing and of detailed balancing are closely related to symmetry under time reversal.

Necessary and sufficient conditions for complex balancing in chemical kinetics

Abstract: In a recent publication (Horn & Jackson [1]) it was shown that complex balancing together with mass action type rate laws ensures certain stability properties of a kinetic system, thereby precluding sustained oscillations, bistability and other types of irregular dynamics. In this paper a necessary condition for complex balancing in general kinetics and necessary and sufficient conditions for complex balancing in mass action systems are derived. A theorem is stated which excludes the occurence of equilibria in certain composition regions of general kinetic systems. For mass action systems it is shown that it is sometimes true that the algebraic structure of the reactions suffices to ensure complex balancing, while in other cases complex balancing occurs only if certain relations between the rate constants are satisfied. The number of these relations, called the deficiency of the mass action system is determined by the algebraic structure of the set of reactions underlying that system.

Multiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property

Abstract: The capacity for multiple equilibria in an isothermal homogeneous continuous flow stirred tank reactor is determined by the reaction network. Examples show that there is a very delicate relationship between reaction network structure and the possibility of multiple equilibria. We suggest a new method for discriminating between networks that have the capacity for multiple equilibria and those that do not. Our method can be implemented using standard computer algebra software and gives answers for many reaction networks for which previous methods give no information.

Correction to "Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction"

Abstract: Deals with the theory of structure, stability, robustness, and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks. The results given here extend, but are also heavily based upon, certain previous work by Feinberg (1977, 1979, 1987, 1995) and Horn and Jackson (1972), of which a self-contained and streamlined exposition is included. The theoretical conclusions are illustrated through an application to the kinetic proofreading model proposed by McKeithan (1995) for T-cell receptor signal transduction.