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Particle dynamics simulations of Turing patterns.

P Dziekan¹, A Lemarchand, B Nowakowski

¹Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.

The Journal of Chemical Physics

|August 28, 2012

Summary

Direct simulation Monte Carlo successfully models microscopic Turing patterns in reaction-diffusion systems using a solvent for varied species diffusion. Fluctuations accelerate pattern formation, supporting robust axial segmentation in biological systems.

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Area of Science:

Chemical kinetics
Computational physics
Theoretical biology

Background:

Reaction-diffusion systems can form spatial patterns like Turing patterns.
Simulating these patterns at the microscopic level is computationally challenging.
Understanding pattern formation is crucial for biological processes like segmentation.

Purpose of the Study:

To reproduce Turing patterns at the microscopic level using the direct simulation Monte Carlo method.
To investigate the role of a solvent in enabling disparate diffusivities for pattern formation.
To analyze the impact of internal fluctuations on Turing pattern development.

Main Methods:

Direct simulation Monte Carlo (DSMC) method.
Modeling reaction-diffusion systems with a solvent to control species diffusivity.

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Simulating one-dimensional structures in systems of varying lengths.

Main Results:

DSMC simulations successfully reproduced Turing patterns, aligning with macroscopic predictions.
Observed temporal transitions between different pattern wavelengths in confined systems.
Internal fluctuations were found to suppress induction periods and accelerate pattern formation.

Conclusions:

The proposed model effectively reproduces microscopic Turing patterns.
Reaction-diffusion models with fluctuations can robustly explain biological axial segmentation.
DSMC is a viable method for simulating complex pattern formation in noisy environments.