Multicatalyst reactions induce abrupt transition in a dense catalytic reaction network model

Abstract

We generalize the Furusawa--Kaneko model, a simple model of intracellular catalytic reaction networks, to multicatalyst reactions and analyze the generalized model using dynamical mean-field theory. In the thermodynamic and dense-network limit, we derive exact effective equations and analyze their fixed points for arbitrary degree distributions. Under nutrient-poor conditions, network heterogeneity suppresses the metabolic--starvation transition irrespective of the number of catalysts per reaction. In contrast, under nutrient-rich conditions, the bifurcation structure changes with the number of catalysts. With one catalyst per reaction, only continuous transitions occur, whereas two or more catalysts give rise to bistable phases and discontinuous transitions. The bifurcation structure also differs between two and three catalysts per reaction, with three catalysts allowing bistability between metabolic states with different cell growth rates. Our results provide a possible mechanism for bistability and abrupt switching in metabolic dynamics.