Multiscale Stochastic Reaction-Diffusion Algorithms Combining Markov Chain Models with Stochastic Partial...

Area of Science:

• Computational chemistry
• Biophysics
• Mathematical modeling

Background:

• Reaction-diffusion processes are fundamental in biological and chemical systems.
• Simulating these processes across vastly different scales (e.g., molecular vs. continuum) presents significant computational challenges.
• Existing methods often struggle with systems exhibiting large gradients in molecular concentrations.

Purpose of the Study:

• To analyze and compare two novel multiscale algorithms for stochastic simulations of reaction-diffusion systems.
• To provide efficient computational tools for systems with heterogeneous molecular concentrations.
• To explore extensions for adaptively defined interfaces between modeling approaches.

Main Methods:

• Development and analysis of two distinct multiscale algorithms.
• Algorithm 1: Couples continuous-time Markov chain (compartment-based) models with reaction-diffusion stochastic partial differential equations (SPDEs) using an overlapping region.
• Algorithm 2: Couples compartment models with SPDEs without an overlapping region, employing an interface-based coupling.

Main Results:

• Both algorithms demonstrate applicability to systems with significantly different molecular concentrations.
• The first algorithm utilizes a pseudo-compartment (overlap region) for coupling Markov chain models and SPDEs.
• The second algorithm achieves coupling without an overlap region, offering a potentially simpler approach.
• Extensions include adaptive boundary selection for improved flexibility.

Conclusions:

• The presented multiscale algorithms offer effective strategies for simulating complex reaction-diffusion systems.
• These methods provide computational advantages for systems with spatial heterogeneity in molecular densities.
• The flexibility of adaptive boundaries enhances the applicability of these simulation techniques.