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Scaling relations for auxin waves.

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.

SUBMITTER: Bakker BH

PROVIDER: S-EPMC9512763 | biostudies-literature | 2022 Sep

REPOSITORIES: biostudies-literature

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Scaling relations for auxin waves.

Bakker Bente Hilde BH Faver Timothy E TE Hupkes Hermen Jan HJ Merks Roeland M H RMH van der Voort Jelle J

Journal of mathematical biology 20220926 4

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 ...[more]

PMID: 36163567

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