Crenation and cupping of the red cell: A new theoretical approach. Part II. Cupping

Typical, axisymmetrical cup shaped cells have been carefully measured and the shapes analyzed mathematically. The results show that the strain energy of a cup shaped cell is always higher than that of a biconcave cell except when the two layers of the membrane involved in resistance to bending are free to slide over one another. This is true whether intrinsic curvature of the membrane is positive, negative or zero. If the two layers can slide over one another, the cup shape becomes the lower energy form. Shear resistance, if appreciable, must cause the cup cell to buckle. Photomicrographs of cup shaped cells show buckled configurations characteristic of those of a partly deflated thin-walled rubber ball, which is a similar object having a low ratio of bending/shear strength.In light of these findings, the cup shape of the red cell can no longer be considered as evidence of intrinsic membrane curvature of opposite sign to that of the crenated cell, but appears to indicate a phase change either in the hydrophobic interior of the bimolecular membrane or in some equivalent interface.