ArticlePhysical review. E, Statistical, nonlinear, and soft matter physics2015
Reaction rates for mesoscopic reaction-diffusion kinetics.
Article in Physical review. E, Statistical, nonlinear, and soft matter physics, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 17 papers.
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17 citing papers in PubMed.
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- A novel stochastic simulation approach enables exploration of mechanisms for regulating polarity site movement.PLoS computational biology · 2021Article
- A multiscale compartment-based model of stochastic gene regulatory networks using hitting-time analysis.The Journal of chemical physics · 2021Article
- Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry.Molecular biology of the cell · 2021Article
- The blending region hybrid framework for the simulation of stochastic reaction-diffusion processes.Journal of the Royal Society, Interface · 2020Article
- Hierarchical algorithm for the reaction-diffusion master equation.The Journal of chemical physics · 2020Article
- Stochastic self-tuning hybrid algorithm for reaction-diffusion systems.The Journal of chemical physics · 2019Article
- Spatial Stochastic Intracellular Kinetics: A Review of Modelling Approaches.Bulletin of mathematical biology · 2019Review
- Learning moment closure in reaction-diffusion systems with spatial dynamic Boltzmann distributions.Physical review. E · 2019Article
- Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning.The Journal of chemical physics · 2017Article
- Multiscale Modeling of Diffusion in a Crowded Environment.Bulletin of mathematical biology · 2017Article
- Reaction rates for reaction-diffusion kinetics on unstructured meshes.The Journal of chemical physics · 2017Article
- Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist.PLoS computational biology · 2016Article
- A framework for discrete stochastic simulation on 3D moving boundary domains.The Journal of chemical physics · 2016Article
- Reaction rates for a generalized reaction-diffusion master equation.Physical review. E · 2016Article
- Hybrid approaches for multiple-species stochastic reaction-diffusion models.Journal of computational physics · 2015Article
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3 authors.
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Abstract
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.
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