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Phyllotaxis: cooperation and competition between mechanical and biochemical processes.

Alan C Newell1, Patrick D Shipman, Zhiying Sun

  • 1Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA. anewell@math.arizona.edu

Journal of Theoretical Biology
|January 22, 2008
PubMed
Summary

This study reveals that plant growth patterns (phyllotaxis) can be explained by similar mathematical models, whether focusing on auxin transport or mechanical forces. A new combined model shows how these factors can work together or independently.

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Area of Science:

  • Plant Biology
  • Mathematical Modeling
  • Biophysics

Background:

  • Phyllotactic patterns at plant apical meristems are theorized to arise from auxin transport or mechanical buckling.
  • Existing models focus on either biochemical or mechanical processes.

Purpose of the Study:

  • To compare continuum approximations of biochemical and mechanical models of phyllotaxis.
  • To develop and analyze a combined model integrating biochemistry and mechanics.
  • To understand how auxin transport and mechanical forces interact in pattern formation.

Main Methods:

  • Derived a continuum approximation of a discrete biochemical model.
  • Compared this approximation with an existing mechanical model.
  • Developed a combined model by coupling biochemical and mechanical components.

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  • Reduced the combined model to amplitude equations (ordinary differential equations).

    • Main Results:

    • The partial differential equations for both models were found to be similar in form, suggesting universality.
    • A combined model was developed, incorporating coupled auxin concentration and surface deformation.
    • Analysis of amplitude equations identified conditions for cooperation or dominance of biochemical versus mechanical mechanisms.

    Conclusions:

    • The mathematical framework for phyllotaxis exhibits a universality between biochemical and mechanical models.
    • A combined model provides insights into the interplay between auxin and mechanics in plant development.
    • Parameter choices dictate whether biochemical or mechanical factors dominate phyllotactic pattern formation.