Understanding bistability in complex enzyme-driven reaction networks

Abstract

Much attention has been paid recently to bistability and switch-like behavior that might be resident in important biochemical reaction networks. There is, in fact, a great deal of subtlety in the relationship between the structure of a reaction network and its capacity to engender bistability. In common physicochemical settings, large classes of extremely complex networks, taken with mass action kinetics, cannot give rise to bistability no matter what values the rate constants take. On the other hand, bistable behavior can be induced in those same settings by certain very simple and classical mass action mechanisms for enzyme catalysis of a single overall reaction. We present a theorem that distinguishes between those mass action networks that might support bistable behavior and those that cannot. Moreover, we indicate how switch-like behavior results from a well-studied mechanism for the action of human dihydrofolate reductase, an important anti-cancer target.bistability ͉ dihydrofolate reductase

Structural instability in an autophosphorylating kinase switch

“…The reader is referred, for example, for the very impressive and useful work of Feinberg et al (Craciun et al, 2006) or of Sontag and his collaborators Angeli et al, 2006;) (much of it based on the theory of monotone dynamical systems (Smith, 1995) and graph-theoretical methods; see, for example (Angeli et al, 2006)). …”

“…In particular, very surprisingly the model, the derivation of which uses only the rules of enzyme kinetics, turns out not to be structurally stable in the following sense: if protein turnover is incorporated into the equations, bistability can disappear for arbitrarily small values of kinetic constants describing protein turnover. Observe, in this context, that the models of and (Craciun et al, 2006) do not take protein turnover into account.…”

Graph-Theoretic Analysis of Multistability and Monotonicity for Biochemical Reaction Networks

“…The SR graph was first introduced in [10] for the analysis of massaction systems, inspired by the SCL graph of Schlosser and Feinberg [22,23]; see also [12,15]. The case of networks that may contain onestep catalysis is discussed in [10,12,15] for mass-action kinetics, and in [9] for general kinetics.…”

“…The case of networks that may contain onestep catalysis is discussed in [10,12,15] for mass-action kinetics, and in [9] for general kinetics. 8).…”

Modelling of multi-component immunoassay kinetics — A new node-based method for simulation of complex assays

“…Also, the modelling of enzymatic reaction cascades is of interest in drug development mainly to get a better overall view of the biological processes. [29,30,31] In this paper a new method to model multi-component assays with quantitative results is presented. The method uses a network of binding complexes and nodes to calculate and simulate a chemical system.…”