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A Strategy to Validate the Role of Callose-mediated Plasmodesmal Gating in the Tropic Response
Published on: April 17, 2016
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.
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.
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