Bulletin of Mathematical Biology

, Volume 72, Issue 6, pp 1383–1407 | Cite as

Mathematical Modelling of the Aux/IAA Negative Feedback Loop

  • A. M. MiddletonEmail author
  • J. R. King
  • M. J. Bennett
  • M. R. Owen
Original Article


The hormone auxin is implicated in regulating a diverse range of developmental processes in plants. Auxin acts in part by inducing the Aux/IAA genes. The associated pathway comprises multiple negative feedback loops (whereby Aux/IAA proteins can repress Aux/IAA genes) that are disrupted by auxin mediating the turnover of Aux/IAA protein. In this paper, we develop a mathematical model of a single Aux/IAA negative feedback loop in a population of identical cells. The model has a single steady-state. We explore parameter space to uncover a number of dynamical regimes. In particular, we identify the ratio between the Aux/IAA protein and mRNA turnover rates as a key parameter in the model. When this ratio is sufficiently small, the system can evolve to a stable limit cycle, corresponding to an oscillation in Aux/IAA expression levels. Otherwise, the steady-state is either a stable-node or a stable-spiral. These observations may shed light on recent experimental results.


Auxin Aux/IAA Gene network Oscillations 


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Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  • A. M. Middleton
    • 1
    • 2
    Email author
  • J. R. King
    • 1
  • M. J. Bennett
    • 2
  • M. R. Owen
    • 1
  1. 1.School of Mathematical SciencesUniversity of NottinghamNottinghamUK
  2. 2.CPIB, School of BiosciencesUniversity of NottinghamSutton BoningtonUK

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