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arXiv · 2203.02031

Scaling Relations for Auxin Waves

Timothy E. Faver·Hermen Jan Hupkes·Roeland M. H. Merks·Jelle van der Voort
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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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Timothy E. Faver, Hermen Jan Hupkes, Roeland M. H. Merks, Jelle van der Voort. 2022-03-03. Scaling Relations for Auxin Waves. https://arxiv.org/abs/2203.02031

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