Molecular discreteness in reaction-diffusion systems yields steady states not seen in the continuum limit

2003/10/31 by Yuichi Togashi, Kunihiko Kaneko · 4 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Spectroscopy and Quantum Chemical Studies #nlin.PS #physics.bio-ph #physics.chem-ph #q-bio.SC #stochastic dynamics and bifurcation

paper · pdf · doi:10.1103/physreve.70.020901

published as Phys. Rev. E 70, 020901 (2004) · 5 pages, 3 figures, revtex4

openalex publication_date 2004/08/23 · arxiv created 2004/09/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the effects of the spatial discreteness of molecules in reaction-diffusion systems. It is found that discreteness within the so-called Kuramoto length can lead to a localization of molecules, resulting in novel steady states that do not exist in the continuous case. These states are analyzed theoretically as the fixed points of accelerated localized reactions, an approach that was verified to be in good agreement with stochastic particle simulations. The relevance of this discreteness-induced state to biological intracellular processes is discussed.

Citations

• Stochastic Processes in Physics and Chemistry

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• Particle-based simulation of non-elementary bimolecular kinetics
• Discreteness-Induced Transitions in Autocatalytic Systems
• Switching dynamics in reaction networks induced by molecular discreteness
• Discreteness-induced stochastic steady state in reaction diffusion systems: self-consistent analysis and stochastic simulations

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