LINTILHAC, P and WEI, C.F.

Department of Botany, University of Vermont, Burlington, Vermont, USA
and Department of Physics, Guangxi National University, 530006, China

We propose replacing Preston and Probine's well known and oft-quoted creep/viscoelasticity-based model for cell wall stress-relaxation with a newer and more predictive model based on the Eulerian concept of Loss of Stability as applied to any pressurized water-filled vessel. This model, derived from physical first principles, permits the prediction of working turgor pressures for any growing plant cell for which the geometry, wall thickness, and wall modulus can be determined. Our model eliminates experimental inconsistencies inherent in the viscoelastic/creep model and makes it possible to define a critical pressure (Pcr) for cell wall stress relaxation as turgor pressure rises gradually, implying that turgor pressures in all growing plant cells must necessarily be hovering at or near to their critical pressures. The relationship between increasing pressure, wall instability and cell wall stress relaxation also implies that growth is best understood in terms of a basic control circuit inherent in the biophysics of Loss of Stability, but which is tuned by local biochemistry and wall synthesis. This model provides a ready explanation for cell wall patterning, secondary wall behavior, and possibly for other differential growth phenomena such as nutation.