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Scaling relations for auxin waves.

Bente Hilde Bakker¹, Timothy E Faver², Hermen Jan Hupkes³

¹Mathematical Institute, Universiteit Leiden, P.O. Box 9512, 2300 RA, Leiden, The Netherlands.

Journal of Mathematical Biology

|September 27, 2022

Summary

This study models plant hormone auxin transport channel formation. Researchers found traveling wave solutions, revealing scaling laws for wave speed and width, crucial for understanding plant development.

Keywords:

Cross-diffusion Lattice differential equations Polar auxin transport Scaling limits Travelling waves Up-the-gradient models

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Area of Science:

Plant biology
Mathematical modeling
Biophysics

Background:

Plant development relies on precise hormone distribution.
Auxin transport is mediated by PIN1 transporter polarization.
Understanding auxin transport dynamics is key to plant morphogenesis.

Purpose of the Study:

To analyze an "up-the-gradient" model for auxin transport channel formation.
To investigate traveling wave solutions in auxin transport.
To establish scaling relations for wave characteristics.

Main Methods:

Mathematical analysis of an "up-the-gradient" model.
Derivation of traveling wave solutions parameterized by auxin pulse height.
Generalization of the Friesecke-Pego scaling principle.
Numerical verification of analytical results.

Main Results:

The model admits a family of traveling wave solutions.
Identified scaling relations for wave speed and width.
Derived explicit expressions for leading-order wave profiles.
Confirmed analytical findings through numerical computations.

Conclusions:

The "up-the-gradient" model provides insights into auxin transport channel formation.
Scaling laws offer a quantitative framework for understanding wave dynamics.
Explicit wave profiles facilitate the identification of biological parameter influences.