Mechanical Modeling of Tip Growth

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 (Fig. 1).

Fig. 1: Fundamental mechanical relations for cell morphogenesis.

We have developed algorithms to solve these equations numerically and performed simulations of morphogenesis for a variety of walled cells with either steady growth or non-steady changes in cell shape (Fig. 2 and Fig. 3). We have also shown that the mechanical anisotropy built into the model is required to account for observed patterns of wall expansion in plant cells (see Dumais et al. 2004, 2006).

Fig. 2: Simulation of a variety of cell shapes from explicit constitutive equations. (A) Initiation of tip growth as in the Fucus egg. (B) Sporangium formation in Phycomyces. (C) Tip flattening as in the first phase of whorl initiation in Acetabularia. (D) Pulsatile growth in a tip-growing cell. Latitudinal lines show the fluctuations in the rate of advance of the tip. (E) Beaded shape in a tip-growing cell resulting from temporal fluctuations in the pattern of wall expansion.

Fig. 3: The initiation of tip growth is associated with an annular region of meridional contraction (fushia). This curious phenomenon was first observed experimentally and later confirmed by computer simulations.