Journal of Mathematical Biology

, Volume 65, Issue 4, pp 743–785 | Cite as

Multiscale modelling of auxin transport in the plant-root elongation zone

  • L. R. BandEmail author
  • J. R. King
Open Access


In the root elongation zone of a plant, the hormone auxin moves in a polar manner due to active transport facilitated by spatially distributed influx and efflux carriers present on the cell membranes. To understand how the cell-scale active transport and passive diffusion combine to produce the effective tissue-scale flux, we apply asymptotic methods to a cell-based model of auxin transport to derive systematically a continuum description from the spatially discrete one. Using biologically relevant parameter values, we show how the carriers drive the dominant tissue-scale auxin flux and we predict how the overall auxin dynamics are affected by perturbations to these carriers, for example, in knockout mutants. The analysis shows how the dominant behaviour depends on the cells’ lengths, and enables us to assess the relative importance of the diffusive auxin flux through the cell wall. Other distinguished limits are also identified and their potential roles discussed. As well as providing insight into auxin transport, the study illustrates the use of multiscale (cell to tissue) methods in deriving simplified models that retain the essential biology and provide understanding of the underlying dynamics.


Multiscale Asymptotic analysis Plant root Auxin Hormone transport Polar transport 

Mathematics Subject Classification (2000)

34E13 92C80 



This work was carried out at the Centre for Plant Integrative Biology (CPIB), and we are grateful to both the Biotechnology and Biological Sciences Research Council (BBSRC) and the Engineering and Physical Sciences Research Council (EPSRC) for supporting this project financially. In addition, JRK gratefully acknowledges the support of the Royal Society and Wolfson Foundation. We would like to thank our colleagues and collaborators at CPIB, in particular, Prof. Malcolm Bennett, Dr Eric Kramer, Dr Ranjan Swarup and Prof. Tobias Baskin.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2011

Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Centre for Plant Integrative BiologyUniversity of NottinghamNottinghamUK
  2. 2.School of Mathematical SciencesUniversity of NottinghamUniversity Park, NottinghamUK

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