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The reaction-diffusion master equation (RDME) is commonly used to model processes where both the spatial and stochastic nature of chemical reactions need to be considered. We show that the RDME in many cases is inconsistent with a…

Quantitative Methods · Quantitative Biology 2009-05-29 Paul Sjoberg , Otto G Berg , Johan Elf

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…

Numerical Analysis · Mathematics 2013-08-05 Samuel A Isaacson

Stochastic modeling of reaction-diffusion kinetics has emerged as a powerful theoretical tool in the study of biochemical reaction networks. Two frequently employed models are the particle-tracking Smoluchowski framework and the on-lattice…

Numerical Analysis · Mathematics 2012-04-27 Stefan Hellander , Andreas Hellander , Linda Petzold

The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system.…

Numerical Analysis · Mathematics 2017-03-08 Stefan Hellander , Linda Petzold

The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit…

Statistical Mechanics · Physics 2022-01-11 Alberto Montefusco , Christof Schütte , Stefanie Winkelmann

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian Dynamics (BD) or…

Numerical Analysis · Mathematics 2017-09-06 Stefan Hellander , Andreas Hellander , Linda Petzold

The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion…

Chemical Physics · Physics 2016-06-22 Stephen Smith , Ramon Grima

The multi-grid reaction-diffusion master equation (mgRDME) provides a generalization of stochastic compartment-based reaction-diffusion modelling described by the standard reaction-diffusion master equation (RDME). By enabling different…

Quantitative Methods · Quantitative Biology 2024-05-06 Radek Erban , Stefanie Winkelmann

The convergent reaction-diffusion master equation (CRDME) was recently developed to provide a lattice particle-based stochastic reaction-diffusion model that is a convergent approximation in the lattice spacing to an underlying…

Numerical Analysis · Mathematics 2018-08-14 Samuel A. Isaacson , Ying Zhang

The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here we introduce the crowded…

Statistical Mechanics · Physics 2016-03-23 Claudia Cianci , Stephen Smith , Ramon Grima

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is…

Numerical Analysis · Mathematics 2016-01-27 Stefan Hellander , Linda Petzold

Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…

Numerical Analysis · Mathematics 2009-03-06 Stefan Engblom , Lars Ferm , Andreas Hellander , Per Lötstedt

Reaction-diffusion PDEs and particle-based stochastic reaction-diffusion (PBSRD) models are commonly-used approaches for modeling the spatial dynamics of chemical and biological systems. Standard reaction-diffusion PDE models ignore the…

Analysis of PDEs · Mathematics 2021-06-02 Samuel A Isaacson , Jingwei Ma , Konstantinos Spiliopoulos

Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…

Analysis of PDEs · Mathematics 2018-02-19 Emilie Blanc , Stefan Engblom , Andreas Hellander , Per Lötstedt

To model bio-chemical reaction systems with diffusion one can either use stochastic, microscopic reaction-diffusion master equations or deterministic, macroscopic reaction-diffusion system. The connection between these two models is not…

Analysis of PDEs · Mathematics 2023-06-21 Malcolm Egan , Bao Quoc Tang

In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…

Chemical Physics · Physics 2019-11-05 Denis S. Grebenkov , Diego Krapf

Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for studying biological systems involving both noise in the reaction process and diffusive transport. In this work we derive coarse-grained deterministic…

Probability · Mathematics 2021-09-02 Samuel A. Isaacson , Jingwei Ma , Konstantinos Spiliopoulos

Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…

Analysis of PDEs · Mathematics 2026-02-23 Marzia Bisi , Davide Cusseddu , Ana Jacinta Soares , Romina Travaglini

We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The…

Numerical Analysis · Mathematics 2025-01-22 Samuel A. Isaacson , Ying Zhang

A mesoscopic multi-particle collision model for fluid dynamics is generalized to incorporate the chemical reactions among species that may diffuse at different rates. This generalization provides a means to simulate reaction-diffusion…

Chemical Physics · Physics 2016-09-08 K. Tucci , R. Kapral
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