Scaling relations for auxin waves.

Autor: Bakker BH; Mathematical Institute, Universiteit Leiden, P.O. Box 9512, 2300 RA, Leiden, The Netherlands., Faver TE; Department of Mathematics, Kennesaw State University, 850 Polytechnic Lane, MD #9085, Marietta, GA, 30060, USA., Hupkes HJ; Mathematical Institute, Universiteit Leiden, P.O. Box 9512, 2300 RA, Leiden, The Netherlands. hhupkes@math.leidenuniv.nl., Merks RMH; Mathematical Institute and Institute of Biology Leiden, Universiteit Leiden, P.O. Box 9512, 2300 RA, Leiden, The Netherlands., van der Voort J; Mathematical Institute, Universiteit Leiden, P.O. Box 9512, 2300 RA, Leiden, The Netherlands.
Jazyk: angličtina
Zdroj: Journal of mathematical biology [J Math Biol] 2022 Sep 26; Vol. 85 (4), pp. 41. Date of Electronic Publication: 2022 Sep 26.
DOI: 10.1007/s00285-022-01793-5
Abstrakt: 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.
(© 2022. The Author(s).)
Databáze: MEDLINE
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