A membrane model for elastic deflection of individual plant cell walls

Deformation of plant cells by a fine probe can provide a measure of cell wall stiffness which is responsible for many of the mechanical properties of the plant. An example system of potato tuber parenchyma cells is used, and cell wall deformation approximated as the axisymmetric deformation of a circular membrane made from a nonlinear-elastic material with a Mooney strain energy function. A system of differential equations describing the shape of the membrane is derived and solved. The effects of turgor and initial cell wall strain on the force required to produce a given deflection and on the shape of the deformed cell are examined. Values for the elastic constants of the wall material are proposed, guided by statistical data for cell size and stiffness obtained from micropenetration tests.