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Patterning via Optical Saturable Transitions - Fabrication and Characterization

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Published on: December 11, 2014

Pattern formation by two-layer Turing system with complementary synthesis.

Hironori Fujita¹, Masayoshi Kawaguchi

¹Division of Symbiotic Systems, National Institute for Basic Biology, National Institute for Natural Sciences, Okazaki 444-8585, Japan. hfujita@nibb.ac.jp

Journal of Theoretical Biology

|January 24, 2013

Summary

This study explores pattern formation in two-layer biological systems using a novel complementary synthesis Turing model. It reveals that layer-specific molecule synthesis and diffusion dynamics are crucial for multicellular development, impacting pattern types and periodicity.

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Area of Science:

Developmental biology
Mathematical biology
Systems biology

Background:

Multicellular organisms exhibit layered structures crucial for development.
Pattern formation is often modeled using Turing systems, typically in single-layered spaces.
Layer-specific molecular expression is vital for developmental processes.

Purpose of the Study:

Investigate a two-layer Turing system with complementary synthesis.
Determine the Turing conditions for this complementary system.
Analyze the effects of lateral and transversal diffusion on pattern formation.

Main Methods:

Linear stability analysis to derive Turing conditions.
Simulations in fixed and expanding two-dimensional spaces.
Application of the model to plant shoot apical meristem pattern formation.

Main Results:

Complementary synthesis requires stronger molecular regulation than ubiquitous synthesis.
Two-layer system affects pattern types similarly to ubiquitous synthesis models.
Lateral diffusion influences pattern periodicity; transversal diffusion affects pattern type, acting as a time delay.

Conclusions:

The two-layer complementary synthesis model provides insights into multicellular pattern formation.
Transversal diffusion's role as a time delay is a key finding.
The model successfully explains pattern formation in the plant shoot apical meristem.