On the Relation between Turgor Pressure and Tissue Rigidity. II Theoretical Calculations on Model Systems.

The rigidity (or further Young's modulus) of potato tuber parenchyma and its dependence on turgor pressure is investigated theoretically on the basis of a simple model. In the model the cells of the parenchyma are approximated by more regular geometrical cell-forms (spheres or polyhedra), each cell being bounded by an elastic membrane (cell wall) and filled with an incompressible fluid (cell sap). It is shown that this model yields the correct dependence of cell diameter on turgor pressure and that certain cell-wall constants can be determined using this relation. If a stress is applied to this model of the parenchyma, each cell is elongated in the direction of the stress, its volume remaining constant because of the incompressible cell rigid. In such a deformation the area of the cell surface will increase which is possible by a stretching of the elastic cell walls. According to the model, this is the general mechanism behind the elasticity and rigidity of the tissue. A mathematical theory elaborating this conception yields results for Young's modulus E and its dependence on turgor pressure that are in good agreement with the experimental values, both qualitatively and quantitatively. (Certain apparent deviations of the behaviour of the parenchyma from Hooke's law are briefly discussed. [ABSTRACT FROM AUTHOR]