Adaptive two-regime method: application to front propagation.

Area of Science:

• Computational biology
• Chemical physics
• Mathematical modeling

Background:

• Reaction-diffusion systems are crucial for modeling biological processes.
• Stochastic fluctuations significantly impact phenomena like front propagation.
• Accurate multiscale simulation methods are needed for complex systems.

Purpose of the Study:

• To introduce and validate the Adaptive Two-Regime Method (ATRM) for hybrid stochastic simulations.
• To apply ATRM to study front propagation in a stochastic Fisher equation model.
• To analyze the computational efficiency and accuracy of ATRM for reaction-diffusion problems.

Main Methods:

• Developed the Adaptive Two-Regime Method (ATRM) to couple Brownian dynamics with lattice-based models.
• Applied ATRM to simulate front propagation in a stochastic reaction-diffusion system based on the Fisher equation.
• Performed error analysis of ATRM using a morphogen gradient model.

Main Results:

• ATRM successfully couples detailed Brownian dynamics with coarser models for reaction-diffusion problems.
• Simulations of Fisher wave propagation using ATRM yield results consistent with purely off-lattice models.
• ATRM achieves significant computational savings while maintaining accuracy.

Conclusions:

• The Adaptive Two-Regime Method provides an efficient and accurate approach for multiscale stochastic simulations.
• ATRM is particularly effective for studying phenomena like front propagation sensitive to stochastic effects.
• This method offers a viable alternative to computationally expensive purely off-lattice simulations.