Morphogene adsorption as a Turing instability regulator: Theoretical analysis and possible applications in...

Area of Science:

• Developmental Biology
• Mathematical Biology
• Biophysics

Background:

• Turing instability in reaction-diffusion systems is key to morphogen gradient self-organization in embryonic development.
• Classical models require significantly different diffusion rates for morphogens, which is unrealistic for molecules of similar size.
• Differences in morphogen adsorption to the extracellular matrix (ECM) offer a plausible explanation for differing diffusion rates.

Purpose of the Study:

• To develop a novel mathematical model explaining Turing instability with similar morphogen diffusion rates.
• To incorporate extracellular matrix (ECM) adsorption into a reaction-diffusion model for biological patterning.
• To investigate how ECM binding sites influence the diversity of self-organizing spatial patterns.

Main Methods:

• Developed a three-component reaction-diffusion model extending the Gierer-Meinhardt model.
• Included immobile binding sites representing ECM adsorption as a third reaction substance.
• Analyzed model behavior to demonstrate Turing-type instability and pattern formation.

Main Results:

• The model successfully demonstrates Turing instability for morphogens with similar diffusion coefficients.
• Incorporating ECM binding sites allows for validation against experimental parameters.
• A gradient of binding sites generates a wider variety of spatial patterns compared to two-component models.

Conclusions:

• Morphogen adsorption to the ECM provides a mechanism for Turing instability with similar diffusion rates.
• The novel model validates the importance of ECM interactions in biological self-organization.
• ECM binding sites significantly increase the potential for diverse self-organizing structures in embryonic development.