Fluctuation analysis for particle-based stochastic reaction-diffusion models

Article Mathematics, Applied

MEAN FIELD LIMITS OF PARTICLE-BASED STOCHASTIC REACTION-DIFFUSION MODELS

Samuel A. Isaacson et al.

Summary: This paper explores the stochastic reaction-diffusion models in biological systems and derives a coarse-grained deterministic model to approximate this type of model. By analyzing a simplified system, the effectiveness of the proposed model is demonstrated, and the convergence in the large-population limit is proven.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2022)

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Article Chemistry, Physical

Detailed balance for particle models of reversible reactions in bounded domains

Ying Zhang et al.

Summary: In particle-based stochastic reaction-diffusion models, the choice of reaction rates and placement kernels is crucial for determining the occurrence probability and location of reactions. This study presents a general partial-integral differential equation model that encompasses common particle models, and derives a detailed balance condition for reversible reactions. It also discusses the requirement for spatially varying unbinding rate functions near the domain boundary in order to maintain detailed balance of spatial reaction fluxes.

JOURNAL OF CHEMICAL PHYSICS (2022)

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Article Mathematics, Applied

HOW REACTION-DIFFUSION PDEs APPROXIMATE THE LARGE-POPULATION LIMIT OF STOCHASTIC PARTICLE MODELS

Samuel A. Isaacson et al.

Summary: This work explores the relationship between reaction-diffusion PDE models and particle-based stochastic reaction-diffusion models, proving their asymptotic approximation in certain cases and establishing the well-posedness of the derived MFM model. Numerical examples illustrate the agreement and disagreement between MFMs, SMs, and underlying particle models.

SIAM JOURNAL ON APPLIED MATHEMATICS (2021)

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Article Mathematics, Applied