Theoretical analysis of discreteness-induced transition in autocatalytic reaction dynamics

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Nen Saito, Kunihiko Kaneko

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.

References

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Citations

Dec 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Louise DysonAlan J McKane
Jun 13, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Taichi Haruna
Apr 15, 2016·Physical Review. E·Yoshiya J Matsubara, Kunihiko Kaneko
Sep 10, 2016·The Journal of Chemical Physics·Nen SaitoKunihiko Kaneko
Sep 15, 2016·Physical Review. E·Yohei SaitoTetsuya J Kobayashi
Mar 11, 2017·Scientific Reports·Nen Saito, Kunihiko Kaneko
Jan 27, 2019·The Journal of Physical Chemistry. B·Yuichi Togashi

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