The deformation of spherical vesicles with permeable, constant-area membranes: application to the red blood cell

Abstract

The deformation of an initially spherical vesicle of radius a with a permeable membrane under extensive forces applied at its poles is calculated as a function of the in-plane shear modulus, H, and the out-of-plane bending modulus, B, using an axisymmetric theory that is valid for large deformations. Suitably nondimensionalized, the results depend upon a single nondimensional parameter, C identical with a(2)H/B. For small deformations, the calculated force-polar strain curves are linear and, under these conditions, the slope of the curve determines only C, not the values of H and B separately. Independent determination of H and B from experimental measurements require deformations that are large enough to produce nonlinear behavior. Simple approximations for large and small C are given, which are applied to experimental measurements on red blood cell ghosts that have been made permeable by treatment with saponin.