Stochastic simulations of pattern formation in excitable media

Area of Science:

• Computational chemistry
• Biophysics
• Chemical kinetics

Background:

• Excitable reaction-diffusion systems exhibit complex spatiotemporal patterns.
• Simulating these systems across all parameter regimes, from low to high particle numbers, is computationally challenging.
• Existing methods may struggle with the mesoscopic scale and dynamic behavior.

Purpose of the Study:

• To introduce a novel mesoscopic, dynamic Monte Carlo simulation method.
• To enable comprehensive simulations of pattern formation in excitable reaction-diffusion systems.
• To provide a versatile tool for exploring diverse excitable system models.

Main Methods:

• Developed a two-level parallelization approach for dynamic Monte Carlo simulations.
• Applied the method to mesoscopic stochastic simulations.
• Covered the full parameter space, including noise-dominated and quasi-deterministic regimes.
• Achieved simulations with up to 10^10 particles.

Main Results:

• Successfully simulated pattern formation in excitable reaction-diffusion systems at the mesoscopic level.
• Demonstrated the method's applicability across a wide range of parameter values.
• Presented case studies on the Gray-Scott model, intracellular Ca2+ oscillations, and the Oregonator model.
• Achieved unprecedented simulation scale (up to 10^10 particles).

Conclusions:

• The presented method offers a powerful and scalable approach for simulating pattern formation in excitable systems.
• The freely available software and model files facilitate reproducibility and further research.
• This work advances the understanding of complex spatiotemporal dynamics in various scientific fields.