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

Abstract Crenation can be thought of as a surface instability caused by intrinsic precurvature of the membrane. Mathematical modeling, on the presupposition that the red blood cell is a thin shell consisting of a connected (coupled) bilayer having uniformly distributed elastic properties shows that crenation can be initiated by negative precurvature, that is, intrinsic curvature having its concavity directed towards the outside of the cell. This is contrary to the currently accepted view which attributes the effect to positive precurvature of an unconnected bilayer. Crenation and the biconcave shape can coexist in the red cell. This suggests that the bilayer must be connected even when the cell is crenated because the biconcave shape could not otherwise be maintained. The progressive development of crenation to more advanced stages, such as the echinocyte type III and the spheroechinocyte can be accounted for if the outer layer of the membrane is stressed beyond the range where strain is proportional to stress. This is consistent with the extremely small radius of curvature at the tips of the crenations. Certain small variations in the uncrenated biconcave shape of the red cell can be interpreted mathematically as due either to negative intrinsic curvature or to shear resistance. Since, however, a small amount of negative precurvature has been shown to be capable of inducing crenation, it is unlikely to be the cause of the variations in the biconcave shape. These must therefore be due to shear resistance. In the light of this new approach, membrane molecular models based on the assumption that crenation is due to positive precurvature need reconsideration.