The design principles of discrete turing patterning systems.

Area of Science:

• Developmental Biology
• Mathematical Biology
• Computational Biology

Background:

• Spatial structure formation is key in development, but underlying mechanisms are unclear.
• Turing patterns are a leading hypothesis, yet their sensitivity to parameters in continuous models raises questions about their natural realization.
• Most studies use continuous partial differential equation models.

Purpose of the Study:

• To investigate Turing patterns using discrete cellular automata models.
• To compare the robustness and predictability of Turing patterns in discrete versus continuous models.
• To identify robust network topologies for Turing pattern formation.

Main Methods:

• Conducted a large-scale study of all possible two-species reaction-diffusion networks using cellular automata.
• Compared results from discrete models with established findings from continuous models.
• Evaluated the predictive power of diffusion-driven instabilities and a refined criterion for pattern emergence.

Main Results:

• Identified the same network topologies for Turing pattern formation in discrete models as in continuous models.
• Found Turing pattern topologies to be significantly more robust to parameter variations in discrete models.
• Observed that diffusion-driven instabilities are weaker predictors of Turing patterns in discrete models compared to continuous models.
• Demonstrated a refined criterion as a stronger predictor for pattern emergence in discrete simulations.

Conclusions:

• Turing mechanisms may be more robust in natural systems than suggested by continuous models.
• Discrete modeling provides a more realistic assessment of Turing pattern robustness.
• A deeper, unifying principle likely underlies Turing pattern formation across different modeling frameworks.