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The Dynamics of Root Growth: A Geometric Model
Julia Pulwicki1, David Hobill2
1INRIA Virtual Plants Group, Bat. 5, 860 Rue St Priest, 34095, Montpellier, France.
Bulletin of Mathematical Biology
|July 9, 2017
Summary
A novel dynamical Riemannian geometry model explains macroscopic root growth. This model reveals how geometric reaction-diffusion and material expansion drive root elongation and complex growth patterns observed in plants.
Area of Science:
- Mathematical Biology
- Plant Biology
- Theoretical Biology
Background:
- Macroscopic root growth is a complex process.
- Existing models lack a comprehensive explanation for observed growth dynamics.
- High-resolution studies reveal spatio-temporal patterns in root growth rates.
Purpose of the Study:
- To present a new model for macroscopic root growth.
- To explain the observed elongation zones and relative elemental growth rates.
- To provide a biological hypothesis for complex root growth dynamics.
Main Methods:
- Developed a dynamical Riemannian geometry model for 1D tissues.
- Used coupled tensor equations for tissue metric and material transport velocity.
- Performed 1D numerical simulations of the growth equations.
Main Results:
- Simulations show an elongation zone consistent with plant roots.
- The model reproduces spatio-temporal dynamics of relative elemental growth rates.
- These dynamics arise from growth as a geometric reaction-diffusion process and material expansion.
Conclusions:
- The dynamical Riemannian geometry model offers a novel framework for understanding root growth.
- The model successfully explains key aspects of root elongation and growth rate dynamics.
- It provides a mechanistic explanation for complex growth patterns based on geometry and material transport.
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