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How nature discovers rare Turing islands: Exploration by common limit cycles
Seyoon Kim1, Antonio Matas-Gil1,2, Robert G Endres1
1Department of Life Sciences & Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ, United Kingdom.
Summary
Biochemical limit cycles can explore Turing space, enabling biological systems to generate transient spatial patterns. This mechanism helps overcome the challenge of finding rare conditions for pattern formation.
Area of Science:
- Developmental Biology
- Systems Biology
- Theoretical Biology
Background:
- Turing patterns are crucial for biological self-organization but require specific, narrow parameter ranges.
- The emergence of these patterns in evolving systems presents a significant challenge due to the rarity of permissive conditions.
Purpose of the Study:
- To investigate how biochemical limit cycles can act as natural explorers of Turing space.
- To demonstrate a mechanism for generating transient spatial patterns in reaction-diffusion systems.
Main Methods:
- Coupling a reaction-diffusion system to an orbit that modulates parameters.
- Utilizing an entropy-based measure in Fourier space to quantify pattern formation.
- Analyzing the effect of positional gradients on pattern reproducibility.
Main Results:
- Biochemical limit cycles dynamically sweep through Turing-permissive regimes, generating transient spatial patterns.
- Oscillatory dynamics enhance the detectability and robustness of Turing patterns.
- Coupling with positional gradients improves the reproducibility of spatial pattern formation.
Conclusions:
- Common biochemical limit cycles provide a mechanism for biological systems to discover and utilize rare Turing space conditions.
- Oscillatory dynamics can serve as a foundation for developing stable developmental programs.
- This work reveals how simple temporal motifs can bootstrap complex spatial structures in nature.
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