Multi-Grid Reaction-Diffusion Master Equation: Applications to Morphogen Gradient Modelling

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 resolutions on lattices for biochemical species with different...

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Bibliographic Details
Published in:Bulletin of mathematical biology Vol. 87; no. 1; p. 6
Main Authors: Erban, Radek, Winkelmann, Stefanie
Format: Journal Article
Language:English
Published: United States Springer Nature B.V 01.01.2025
Springer US
Subjects:
Animals
Brownian motion
Chemical reactions
Computer Simulation
Diffusion
Diffusion models
Mathematical Concepts
Modelling
Models, Biological
Morphogenesis - physiology
Multiple objective analysis
Original
Partial differential equations
Species diffusion
Stochastic Processes
Morphogen gradient formation
Reaction-diffusion master equation
Multi-grid methods
Stochastic simulation algorithms
ISSN:0092-8240, 1522-9602, 1522-9602
Online Access:Get full text
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Summary: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 resolutions on lattices for biochemical species with different diffusion constants, the mgRDME approach improves both accuracy and efficiency of compartment-based reaction-diffusion simulations. The mgRDME framework is examined through its application to morphogen gradient formation in stochastic reaction-diffusion scenarios, using both an analytically tractable first-order reaction network and a model with a second-order reaction. The results obtained by the mgRDME modelling are compared with the standard RDME model and with the (more detailed) particle-based Brownian dynamics simulations. The dependence of error and numerical cost on the compartment sizes is defined and investigated through a multi-objective optimization problem.
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ISSN:0092-8240
1522-9602
1522-9602
DOI:10.1007/s11538-024-01377-y