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Reaction-diffusion patterns in plant tip morphogenesis: bifurcations on spherical caps.

Wayne Nagata¹, Hamid R Z Zangeneh, David M Holloway

¹Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z2, nagata@math.ubc.ca.

Bulletin of Mathematical Biology

|September 28, 2013

Summary

This summary is machine-generated.

This study models plant tip development using the Brusselator reaction-diffusion model. It shows how tip shape and chemical concentrations influence cotyledon pattern formation in conifer embryos.

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Area of Science:

Developmental biology
Mathematical modeling
Chemical kinetics

Background:

Plant organogenesis involves complex pattern formation.
Reaction-diffusion systems, like the Brusselator, are key models for biological pattern generation.
Understanding early plant development, particularly cotyledon formation, is crucial.

Purpose of the Study:

To investigate pattern formation in developing plant tips using a chemical reaction-diffusion model.
To explore the influence of geometric factors (tip flatness, radius) and chemical concentrations on pattern development.
To model the specific case of cotyledon formation in conifer embryos.

Main Methods:

Utilized the Brusselator reaction-diffusion model.
Employed a family of spherical cap domains to represent developing plant tips.
Analyzed the system's behavior, focusing on pitchfork bifurcations.

Main Results:

Demonstrated that pattern formation depends significantly on tip flatness, radius, and precursor concentrations.
Showcased how the Brusselator model in spherical cap domains can generate patterns mimicking cotyledon formation.
Identified parameters leading to supercritical pitchfork bifurcations corresponding to observed cotyledon patterns.

Conclusions:

The Brusselator model effectively simulates cotyledon pattern formation in conifer embryos.
Geometric and chemical factors play critical roles in early plant development patterns.
This modeling approach provides insights into the mechanisms of plant morphogenesis.