First-order patterning transitions on a sphere as a route to cell morphology

Area of Science:

• Biophysics
• Developmental Biology
• Materials Science

Background:

• Biological surfaces exhibit intricate, species-specific patterns.
• Pattern diversity and reproducibility are key features across various organisms.
• Existing models often simplify patterns on flat surfaces.

Purpose of the Study:

• To propose a general theory for biological surface patterning.
• To explain pattern diversity and reproducibility using phase transition concepts.
• To investigate pattern formation on curved biological surfaces.

Main Methods:

• Interpreting pattern development as a first-order phase transition.
• Applying Brazovskii transition theory to finite, spherical geometries.
• Calculating free energy differences, including fluctuations and finite-size effects.

Main Results:

• Phase transitions on spheres yield richer pattern phenomenology than simple stripes or hexagons.
• Topology on spheres necessitates defects, leading to pattern variety.
• The first-order nature of the transition ensures pattern robustness.

Conclusions:

• A unified theory explains diverse biological surface patterns.
• Topological constraints and defects are crucial for pattern complexity on curved surfaces.
• Phase transition dynamics underpin reproducible and robust biological pattern formation.