Scaling relations for auxin waves

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...

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Bibliographic Details
Published in:Journal of mathematical biology 2022-10, Vol.85 (4), p.41, Article 41
Main Authors: Bakker, Bente Hilde, Faver, Timothy E., Hupkes, Hermen Jan, Merks, Roeland M. H., van der Voort, Jelle
Format: Article
Language:English
Subjects:
Applications of Mathematics
Auxins
Biological Transport
Biology
Hypotheses
Indoleacetic Acids - metabolism
Localization
Mathematical and Computational Biology
Mathematical models
Mathematics
Mathematics and Statistics
Membrane Transport Proteins
Parameter identification
Pin1 protein
Plant Growth Regulators - metabolism
Proteins
Scaling
Traveling waves
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Summary: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.
ISSN:0303-6812
1432-1416
1432-1416
DOI:10.1007/s00285-022-01793-5