Title
Localised auxin peaks in concentration-based transport models of the shoot apical meristem Localised auxin peaks in concentration-based transport models of the shoot apical meristem
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
London ,
Subject
Computer. Automation
Source (journal)
Journal of the Royal Society interface: physical and life sciences. - London
Volume/pages
(2015) , p. 1-31
ISSN
1742-5689
Carrier
E
Target language
English (eng)
Affiliation
University of Antwerp
Abstract
We study the formation of auxin peaks in a generic class of concentration-based auxin transport models, posed on static plant tissues. Using standard asymptotic analysis we prove that, on bounded domains, auxin peaks are not formed via a Turing instability in the active transport parameter, but via simple corrections to the homogeneous steady state. When the active transport is small, the geometry of the tissue encodes the peaks' amplitude and location: peaks arise where cells have fewer neighbours, that is, at the boundary of the domain. We test our theory and perform numerical bifurcation analysis on two models which are known to generate auxin patterns for biologically plausible parameter values. In the same parameter regimes, we find that realistic tissues are capable of generating a multitude of stationary patterns, with a variable number of auxin peaks, that can be selected by different initial conditions or by quasi-static changes in the active transport parameter. The competition between active transport and production rate determines whether peaks remain localised or cover the entire domain. We relate the occurrence of localised patterns to a snaking bifurcation structure, which is known to arise in a wide variety of nonlinear media but has not yet been reported in plant models.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/a4e140/8eea4625.pdf
Handle