Theoretical Analysis of Discreteness-Induced Transition in Autocatalytic Reaction Dynamics

Abstract

Transitions in the qualitative behavior of chemical reaction dynamics with a decrease in molecule number have attracted much attention. Here, a method based on a Markov process with a tridiagonal transition matrix is applied to the analysis of this transition in reaction dynamics. The transition to bistability due to the small-number effect and the mean switching time between the bistable states are analytically calculated in agreement with numerical simulations. In addition, a novel transition involving the reversal of the chemical reaction flow is found in the model under an external flow, and also in a three-component model. The generality of this transition and its correspondence to biological phenomena are also discussed.

7 pages, 4 figures

References in corpus (4)

• Molecular Discreteness in Reaction-Diffusion Systems Yields Steady States Not Seen in the Continuum Limit
• Noise-induced metastability in biochemical networks
• Transition Phenomena Induced by Internal Noise and Quasi-absorbing State
• Discreteness-induced Transition in Catalytic Reaction Networks

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