Stochastic Turing patterns: analysis of compartment-based approaches.

Area of Science:

• Chemical kinetics
• Pattern formation
• Computational modeling

Background:

• Turing patterns arise in reaction-diffusion systems with differing diffusion rates.
• Stochastic models show broader parameter regimes for Turing patterns than deterministic partial differential equation (PDE) models.
• Compartment-based (lattice-based) models are common for simulating stochastic reaction-diffusion systems.

Purpose of the Study:

• Investigate the impact of compartment size on stochastic Turing patterns.
• Propose and analyze a novel compartment-based model where each chemical species has its own set of compartments.
• Compare pattern formation parameter regions between the new model, classical deterministic PDE models, and single-compartment stochastic models.

Main Methods:

• Developed a compartment-based reaction-diffusion model.
• Each chemical species was assigned a distinct set of compartments.
• Simulated the model to identify parameter regimes for spatial pattern formation.
• Compared results with deterministic PDE models and single-compartment stochastic models.

Main Results:

• The parameter regions for spatial pattern formation differ significantly from classical deterministic PDE models.
• Results also diverge from stochastic reaction-diffusion models employing a single set of compartments for all species.
• The proposed multi-compartment model reveals distinct parameter dependencies on compartment size.

Conclusions:

• The choice of compartment size critically affects stochastic Turing pattern formation.
• Using separate compartment sets for different species alters the predicted parameter regimes for pattern formation.
• Previous findings on noise effects in biological Turing patterns may require reinterpretation based on these results.