Abstract
AbstractWe 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.
Funder
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Modeling and Simulation
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