Pattern selection in plants: coupling chemical dynamics to surface growth in three dimensions

Area of Science:

• Computational biology
• Plant morphogenesis
• Reaction-diffusion systems

Background:

• Investigates the interplay between growth catalyst patterns and plant surface expansion for shape generation.
• Considers localized morphogenetically active regions and symmetry-breaking processes like branching.
• Highlights the necessity of 3D shape representation for accurate modeling.

Purpose of the Study:

• To computationally model plant morphogenesis using a reaction-diffusion system.
• To simulate pattern formation of growth catalysts on a plant surface.
• To generate organismal shape through surface expansion driven by chemical patterns.

Main Methods:

• Employs the Brusselator reaction-diffusion model on a hemispherical shell to generate chemical concentration patterns.
• Represents the initial hemispherical shape using a finite element mesh of triangles.
• Converts chemical patterns into shape changes by adjusting node positions and refining the mesh.

Main Results:

• Successfully simulates tip growth to ten times the original height and tip flattening.
• Generates dichotomous and higher-order branching, forming whorled structures.
• Achieves partial success in controlling the branching plane during successive dichotomous branchings.

Conclusions:

• Demonstrates a computational model of a growing plant surface using an adaptive mesh.
• Shows that Turing-type reaction-diffusion mechanisms can generate key plant morphogenesis patterns.
• Validates the model's ability to simulate complex developmental processes in plants.