Curvature-driven spatial patterns in growing 3D domains: A mechanochemical model for phyllotaxis

Area of Science:

• Theoretical biology
• Plant development
• Biophysics

Background:

• Phyllotaxis, the arrangement of leaves on a plant stem, is crucial for optimizing light capture.
• The phytohormone auxin is known to play a key role in establishing phyllotactic patterns within the shoot apical meristem (SAM).
• Previous models have not fully integrated the dynamic interplay between chemical signaling, mechanical properties, and growth in the SAM.

Purpose of the Study:

• To propose a novel mechanism for phyllotactic pattern formation in growing plant domains.
• To investigate how auxin concentration influences mechanical properties and how mechanical stress orients auxin flux.
• To model the coupled dynamics of chemical concentrations, mechanical stress, and domain growth with variable curvature.

Main Methods:

• A reaction-diffusion system models chemical dynamics, generating 3D concentration patterns.
• A phase-field order parameter models domain growth and boundary changes.
• The model couples chemical concentrations to mechanical stress via a curvature term, creating a feedback loop.

Main Results:

• The model reproduces various observed phyllotactic patterns under specific conditions.
• It demonstrates how changes in domain curvature, size, and mechanical stress influence chemical patterns.
• The study highlights the significant role of mechanical feedback in auxin-mediated pattern formation.

Conclusions:

• The proposed model offers a novel theoretical framework for understanding pattern formation in dynamic biological systems.
• It successfully links chemical signaling, mechanical properties, and growth in the SAM to explain phyllotaxis.
• This approach has broader implications for studying developmental processes influenced by physical factors in organisms.