A Convergent Reaction-Diffusion Master Equation
arXiv:1211.6772 · doi:10.1063/1.4816377
Abstract
The reaction-diffusion master equation (RDME) is a lattice stochastic reaction-diffusion model that has been used to study spatially distributed cellular processes. The RDME is often interpreted as an approximation to spatially-continuous models in which molecules move by Brownian motion and react by one of several mechanisms when sufficiently close. In the limit that the lattice spacing approaches zero, in two or more dimensions, the RDME has been shown to lose bimolecular reactions. The RDME is therefore not a convergent approximation to any spatially-continuous model that incorporates bimolecular reactions. In this work we derive a new convergent RDME (CRDME) by finite volume discretization of a spatially-continuous stochastic reaction-diffusion model popularized by Doi. We demonstrate the numerical convergence of reaction time statistics associated with the CRDME. For sufficiently large lattice spacings or slow bimolecular reaction rates, we also show the reaction time statistics of the CRDME may be approximated by those from the RDME. The original RDME may therefore be interpreted as an approximation to the CRDME in several asymptotic limits.
29 pages, 6 figures
References in corpus (2)
Cited by in corpus (32)
- Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
- Stochastic Simulation of Reaction-Diffusion Systems: A Fluctuating-Hydrodynamics Approach
- A Kernel-based Lagrangian Method for Imperfectly-mixed Chemical Reactions
- Reaction rates for mesoscopic reaction-diffusion kinetics
- Hybrid approaches for multiple-species stochastic reaction-diffusion models
- A Comparison of Bimolecular Reaction Models for Stochastic Reaction Diffusion Systems
- Efficient Reactive Brownian Dynamics
- Molecular finite-size effects in stochastic models of equilibrium chemical systems
- A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations
- The breakdown of the reaction-diffusion master equation with non-elementary rates
- An Unstructured Mesh Convergent Reaction-Diffusion Master Equation for Reversible Reactions
- A First-Passage Kinetic Monte Carlo Method for Reaction-Drift-Diffusion Processes
- Chemical diffusion master equation: formulations of reaction--diffusion processes on the molecular level
- Grand canonical diffusion-influenced reactions: a stochastic theory with applications to multiscale reaction-diffusion simulations
- New homogenization approaches for stochastic transport through heterogeneous media
- Reaction-diffusion kinetics on lattice at the microscopic scale
- Reaction rates for a generalized reaction-diffusion master equation
- Reaction rates for reaction-diffusion kinetics on unstructured meshes
- Field theories and quantum methods for stochastic reaction-diffusion systems
- On the Continuum Time Limit of Reaction-Diffusion Systems
- Detailed Balance for Particle Models of Reversible Reactions in Bounded Domains
- Optimisation of Simulations of Stochastic Processes by Removal of Opposing Reactions
- Stochastic reaction networks within interacting compartments
- Drift-Diffusion Dynamics and Phase Separation in Curved Cell Membranes and Dendritic Spines: Hybrid Discrete-Continuum Methods
- Reactions, Diffusion and Volume Exclusion in a Heterogeneous System of Interacting Particles
- Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs
- Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems
- Open reaction-diffusion systems: bridging probabilistic theory and simulations across scales
- Stochastic and Coarse-Grained Two-Dimensional Modeling of Directional Particle Movement
- Unbiased on-lattice domain growth
- Mean field limits of particle-based stochastic reaction-drift-diffusion models
- An Unstructured Mesh Reaction-Drift-Diffusion Master Equation with Reversible Reactions