Scaling relations for auxin waves

Journal of Mathematical Biology, vol. 85, pp. 41

Abstract

We analyze an 'up-the-gradient' model for the formation of transport channels of the phytohormone auxin, through auxin-mediated polarization of the PIN1 auxin transporter. We show that this model admits a family of travelling wave solutions that is parameterized by the height of the auxin-pulse. We uncover scaling relations for the speed and width of these waves and verify these rigorous results with numerical computations. In addition, we provide explicit expressions for the leading-order wave profiles, which allows the influence of the biological parameters in the problem to be readily identified. Our proofs are based on a generalization of the scaling principle developed by Friesecke and Pego to construct pulse solutions to the classic Fermi-Pasta-Ulam-Tsingou model, which describes a one-dimensional chain of coupled nonlinear springs.

Authors 5

1. Bente Hilde Bakker corresponding Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

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

2. Timothy E. Faver corresponding

   Kennesaw State University

   Affiliation as printed

   Department of Mathematics, Kennesaw State University, 850 Polytechnic Lane, MD #9085, Marietta, GA, 30060, USA

3. Hermen Jan Hupkes corresponding Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Universiteit Leiden, P.O. Box 9512, 2300 RA, Leiden, The Netherlands. hhupkes@math.leidenuniv.nl

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

4. Roeland M. H. Merks corresponding Aachen Mathematical Institute Institute of Biology Leiden

   Leiden University

   Affiliation as printed

   Mathematical Institute and Institute of Biology Leiden, Universiteit Leiden, P.O. Box 9512, 2300 RA, Leiden, The Netherlands

5. Jelle van der Voort corresponding Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

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