Modelling the mechanical properties of yeast cells

An analytical model has been developed to describe the compression of a single yeast cell between parallel flat surfaces. Such cells were considered to be thin walled, liquid filled, spheres. Because yeast cells can be compressed at high deformation rates, time dependent effects such as water loss during compression and visco-elasticity of the cell wall could be and were neglected in the model. As in previously published work, a linear elastic constitutive equation was assumed for the material of the cell walls. However, yeast compression to failure requires large deformations, with high wall strains and associated rotations. New model equations appropriate to such high strains with rotations were therefore developed, based on work-conjugate Kirchhoff stresses and Hencky strains. This is an improvement on the earlier use of infinitesimal strains, and on the alternative of Green strains and 2nd Piola–Kirchhoff stresses. It is shown that the choice of stress and strain definition has a significant influence on model predictions for given wall material properties, and will affect estimates of the wall elastic modulus or other wall material property parameters obtained by fitting experimental data.