Bending undulations and elasticity of the erythrocyte membrane: effects of cell shape and membrane organization

The undulatory excitations (flickering) of human and camel erythrocytes were evaluated by employing the previously used flicker spectroscopy and by local measurements of the autocorrelation function K (t) of the cell thickness fluctuations using a dynamic image processing technique. By fitting theoretical and experimental flicker spectra relative values of the bending elastic modulus K _c of the membrane and of the cytoplasmic viscosity were obtained. The effects of shape changes were monitored by simultaneous measurement of the average light intensity I ₀ passing the cells and by phase contrast microscopic observation of the cells. Evaluation of the cellular excitations in terms of the quasi-spherical model yielded values of K _c /R _inf0 ^sup3 and · R ₀ (R ₀=equivalent sphere radius) and allowed us to account (1) for volume changes, (2) for effects of surface tension and spontaneous curvature and (3) for the non-exponential decay of K (t). From the long time decay of K (t) we obtained an upper limit of the bending elastic modulus of normal cells of K _c = 2–3 · 10^–19 Nm which is an order of magnitude larger than the value found by reflection interference contrast microscopy (RICT, K _c , = 3.4 · 10^–20 Nm, Zilker et al. 1987) but considerably lower than expected for a bilayer containing 50% cholesterol (K _c = 5 · 10^–19 Nm, Duwe et al. 1989). The major part of the paper deals with long time measurements (order of hours) of variations of the apparent K _c and values of single cells (and their reversibility) caused (1) by osmotic volume changes, (2) by discocytestomatocyte transitions induced by albumin and triflouperazine, (3) by discocyte-echinocyte transitions induced by expansion of the lipid/protein bilayer (by incubation with lipid vesicles) and by ATP-depletion in physiological NaCI solution, (4), by coupling or decoupling of bilayer and cytoskeleton using wheat germ agglutinin or erythrocytes with elliptocytosis and (5) by cross-linking the cytoskeleton using diamide. These experiments showed: (1) K _c and are minimal at physiological osmolarity and temperature and well controlled over a large range of these parameters. (2) Echinocyte formation does not markedly alter the apparent membrane bending stiffness. (3) During swelling the cell may undergo a transient discocyte-stomatocyte transition. (4) Strong increases of the apparent K _c and after cup-formation or strong swelling and deflation are due to the effect of shear elasticity and surface tension. Our major conclusions are: (1) The erythrocyte membrane exhibits a shear free deformation regime which requires ATP for its maintenance. (2) Shape transitions may be caused by relative area changes either of the two monolayers of the lipid/protein bilayer (corresponding to the bilayer coupling hypothesis) or of the bilayer and the cytoskeleton where the latter mechanism appears to be more frequent. (3) The low bending stiffness and the shear free deformation regime are explained in terms of a slight excess area of the lipid bilayer leading to a pre-undulated surface profile. Freeze fracture electron microscopy studies provide direct evidence for a pre-undulated bilayer with an undulation wavelength of approximately 100 nm. Offprint requests to: E. Sackmann