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

Journal article

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.

Authors: Erban, R; Winkelmann, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Bulletin of Mathematical Biology
• Volume: 87
• Issue: 1
• Article number: 6
• Publication date: 2024-11-27
• Acceptance date: 2024-10-21
• DOI: 10.1007/s11538-024-01377-y
• EISSN: 1522-9602
• ISSN: 0092-8240
• Language: English
• Keywords: Stochastic simulation algorithms; Reaction-diffusion master equation; Multi-grid methods; Morphogen gradient formation