Rate Constant in Far-from-Equilibrium States of a Replicating System with Mutually Catalyzing Chemicals

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  • Kamimura Atsushi
    Department of Applied Physics, School of Engineering, The University of Tokyo
  • Yukawa Satoshi
    Department of Applied Physics, School of Engineering, The University of Tokyo
  • Ito Nobuyasu
    Department of Applied Physics, School of Engineering, The University of Tokyo

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As a first step to study reaction dynamics in far-from-equilibrium open systems, we propose a stochastic protocell model in which two mutually catalyzing chemicals are replicating depending on the external flow of energy resources J. This model exhibits an Arrhenius type reaction; furthermore, it produces a non-Arrhenius reaction that exhibits a power-law reaction rate with regard to the activation energy. These dependences are explained using the dynamics of J; the asymmetric random walk of J results in the Arrhenius equation and conservation of J results in a power-law dependence. Further, we find that the discreteness of molecules results in the power change. Effects of cell divisions are also discussed in our model.

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