Int. J. Dev. Biol. 50: 209 - 222 (2006)
doi: 10.1387/ijdb.052066jd
© UBC Press

An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth

Jacques Dumais1,*, Sidney L. Shaw2, Charles R. Steele3, Sharon R. Long2 and Peter M. Ray2

1Department of Organismic and Evolutionary Biology, Harvard University, Cambridge MA, USA, 2Department of Biological Sciences and 3Department of Mechanical Engineering, Stanford University, Stanford CA, USA

ABSTRACT Plant cell morphogenesis depends critically on two processes: the deposition of new wall material at the cell surface and the mechanical deformation of this material by the stresses resulting from the cell's turgor pressure. We developed a model of plant cell morphogenesis that is a first attempt at integrating these two processes. The model is based on the theories of thin shells and anisotropic viscoplasticity. It includes three sets of equations that give the connection between wall stresses, wall strains and cell geometry. We present an algorithm to solve these equations numerically. Application of this simulation approach to the morphogenesis of tip-growing cells illustrates how the viscoplastic properties of the cell wall affect the shape of the cell at steady state. The same simulation approach was also used to reproduce morphogenetic transients such as the initiation of tip growth and other non-steady changes in cell shape. Finally, we show that the mechanical anisotropy built into the model is required to account for observed patterns of wall expansion in plant cells.

Keywords:

anisotropy, cell morphogenesis, tip growth, viscoplasticity, wall expansion

*Corresponding author e-mail: jdumais@oeb.harvard.edu