A rigorous mathematical solution of the sphering of a red blood cell is obtained under the assumptions that the red cells is a fluid-filled shell and that it can swell into a perfect sphere in an appropriate hypotonic medium. The solution is valid for finite strain of the cell membrane provided that the membrane is isotropic, elastic and incompressible. The most general nonlinear elastic stress-strain law for the membrane in a state of generalized plane stress is used. A necessary condition for a red cell to be able to sphere is that its extensional stiffness follow a specific distribution over the membrane. This distribution is strongly influenced by the surface tension in the cell membrane. A unique relation exists between the extensional stiffness, pressure differential, surface tension, and the ratio of the radius of the sphere to that of the undeformed red cell. The functional dependence of this stiffness distribution on various physical parameters is presented. A critique of some current literature on red cell mechanics is presented.

In adult polycystic kidney disease (APCKD) the cytoskeleton of renal tubular cells is abnormal. In erythrocytes the cytoskeleton affects the fluidity of membrane lipids. The authors determined fluorescence anisotropy in intact erythrocytes and erythrocyte ghosts in 12 APCKD patients and 12 normal subjects. In APCKD whole erythrocytes had a much lower core-region anisotropy, which indicated higher membrane fluidity than normal (mean 0 center dot 175 vs. 0 center dot 224, P < 0 center dot 01). This abnormality was not detected in erythrocyte ghosts, which suggests that preparation of ghosts altered membrane lipid organization. This could be directly due to ghosting or secondary to the loss of cytoskeletal effects, which may be abnormal in APCKD.

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