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

A possible mechanism determining the stability of spiculated red blood cells

In this work the stability of spiculated red blood cells, called echinocytes, is studied. It is assumed that the stable echinocyte shape corresponds to the minimum of its membrane elastic energy. It is shown that if the membrane skeleton shear elasticity is not taken into account the calculated stable echinocyte shapes always have only one spicule. However, by considering the skeleton shear elastic energy also, the calculated stable echinocyte shapes have many spicula in agreement with experimental observations.

Red cell membrane crenation: a macromodel of the echinocyte I

A physical macromodel of the erythrocyte membrane was constructed to investigate the effect of intrinsic membrane precurvature on a unique non-isotropic, composite material that dissipated shear energy but stored bending energy. The intrinsic precurvature of the material could be modified from strong positive precurvature through neutral to strong negative precurvature. A spherical shell constructed of the negatively precurved variant of this non-isotropic material spontaneously assumed the characteristic shape of the echinocyte I.

The molecular basis of erythrocyte shape

Recent discoveries about the molecular organization and physical properties of the mammalian erythrocyte membrane and its associated structural proteins can now be used to explain, and may eventually be used to predict, the shape of the erythrocyte. Such explanations are possible because the relatively few structural proteins of the erythrocyte are regularly distributed over the entire cytoplasmic surface of the cell membrane and because the well-understood topological associations of these proteins seem to be stable in comparison with the time required for the cell to change shape. These simplifications make the erythrocyte the first nonmuscle cell for which it will be possible to extend our knowledge of molecular interactions to the next hierarchical level of organization that deals with shape and shape transformations.

The human erythrocyte membrane skeleton may be an ionic gel. II. Numerical analyses of cell shapes and shape transformations

In the first paper in this series (Stokke et al. Eur Biophys J 1986, 13:203-218) we developed the general theory of the mechanochemical properties and the elastic free energy of the protein gel--lipid bilayer membrane model. Here we report on an extensive numerical analysis of the human erythrocyte shapes and shape transformations predicted by this new cell membrane model. We have calculated the total elastic free energy of deformation of four different cell shape classes: disc-shaped cells, cup-shaped cells, crenated cells, and cells with membrane invaginations. We find that which of these shape classes is favoured depends strongly on the spectrin gel osmotic tension, IIGu, and the surface tensions, IIEu and IIPu, of the extracellular and protoplasmic halves of the membrane lipid bilayer, respectively. For constant ratio IIEu/IIPu greater than O large negative or positive values of IIGu favour respectively the crenated and invaginated cell shape classes. For small absolute values of IIGu, IIEu, and IIPu, biconcave or cup-shaped cells are the stable ones. Our numerical analysis shows that the higher the membrane skeleton compressibility is, the smaller are the values of IIGu needed to induce cell shape transformation. We find that the stable and metastable shapes of discocytes and stomatocytes generally depend both on the shape of the stressfree membrane skeleton and the membrane skeleton compressibility.

Effects of monovalent cations on red cell shape and size

Human erythrocytes were incubated in isotonic solutions of different monovalent cations. The apparent size of the red cells measured on scanning electron microscopic pictures decreases in the order Li+ greater than Na+ = K+ greater than Rb+. These differences in size are abolished after pretreatment with trypsin, which removes a large part of the charges associated with membrane glycoproteins. Shape alterations are also observed. Normal biconcave shapes are visible after Na+ or K+ incubation, whereas Li+ leads to flabby, flattened cells with a certain tendency to crenation, and Rb+ causes more pronounced biconcavity with a certain tendency to cupping. The overall effects of pretreatment with trypsin are similar to those of Li+. Our results provide evidence that the electrostatic repulsion of glycoproteins and other charged membrane components may play an essential role in maintaining red cell shape.

A continuum model for a red blood cell transformation: sphere to crenated sphere

The evolution of crenations on the spherical red blood cell, which is part of the reversible disc-sphere transformation of these cells, is considered here. A continuum model is developed where the cell is treated as a small viscous droplet encapsulated by a viscoelastic solid membrane. When a small amount of material is deposited into the membrane, the drop responds by increasing its surface area as manifested by the appearance of ripples. A preferred number of crenations form and they are sustained for long time periods. The inception of crenations is due to a dynamic instability in the governing set of nonlinear equations, and depends on the rheological properties of the droplets' interior and membrane.

Echinocyte formation induced by potential changes of human red blood cells

In isotonic 30 mM NaCl-saccharose solution, human red blood cells with intact membrane and normal inside ionic content (C-state) indicate a transmembrane potential between +30 mV (at pH 7.4) and +46 mV (at pH 5.1). After treatment with amphotericin B or nystatin as ionophores, a Donnan equilibrium (D-state) will be reached with the same potential at pH 5.1 but a sharp drop down to -20 mV will occur at pH 7.4. Concerning the erythrocyte shape at these states, a stomatocyte-echinocyte transformation takes place, in correlation with the potential shift. Stomatocytes formed at delta psi greater than +25 mV, echinocytes at delta psi less than +25 mV. At potentials lower than +5 mV, no further effect can be observed. This process is reversible. Neuraminidase treatment as well as outside EDTA do not influence this process significantly. Human serum albumin in concentrations of 2% stabilizes the stomatocytes.

A spin-label study of the correlation between stomatocyte formation and membrane fluidization of erythrocytes

Change in the membrane fluidity of human erythrocytes on transformation to stomatocytes was observed by ESR spectroscopy using 12-doxyl stearic acid or its methyl ester as a probe. When the transformation to stomatocytes was induced by four qualitatively different methods, i.e. (a) addition of cationic amphiphilic agents such as chloropromazine, tetracaine, chloroquine or primaquine, (b) addition of Triton X-100, a non-ionic detergent, (c) lowering the pH, and (d) depleting membrane cholesterol, membrane fluidization was always observed. This indicates the existence of a close correlation between stomatocyte formation and increase in the membrane fluidity. Furthermore, since the stomatocytes fixed by diamide treatment exhibited membrane fluidization only in the presence of the reagent, the enhanced membrane fluidity was a direct consequence of the reagent interacting with, and changing the state of, the lipid bilayer itself, and not through the influence of some structural alteration of spectrin. These results provide experimental support for the theoretical prediction made by Brailsford et al. [J. theoret. Biol. 86, 531 (1980)]. Plausible mechanisms for the discocyte-stomatocyte transformation are discussed.

Lipid monolayer expansion by calcium-chlorotetracycline at the air/water interface and, as inferred from cell shape changes, in the human erythrocyte membrane

Chemically induced shape changes of the human erythrocyte may result from cell membrane bending by surface tension changes at the lipid bilayer (Evans. E.A. (1974( Biophys. J. 14, 923-931) implicating differential expansion of the monolayers coupled to form the red cell membrane (Sheetz, M.P. and Singer, S.J. (1974) Proc. Natl. Acad. Sci. U.S.A. 71, 4457-4461). Interacting with calcium, the antibiotic chlorotetracycline (CTC) transforms crenated cells (echinocytes) into cup-shaped ones (stomatocytes), presumably expanding thereby the red cell membrane inner leaflet relative to the outer one (Behn, C., Lübbemeier, A. and Weskamp, P. (1977) Pflügers Arch. 372, 259-268). Whether the Ca-CTC interaction with lipid monolayers may in fact expand the latter, has now been examined by surface tension measurements at the air/water interface. CTC and lipids appeared to compete for the available sites at the air/water interface, contributing additively to its surface pressure. Ca increased both the adsorption rate of the antibiotic to the interface and the CTC-induced surface pressure increment. The latter was not influenced by the subphase pH and ionic strength, or by the type of phospholipid polar head. Correspondingly, CTC-induced cell shape changes should be determined by the pCa values facing either monolayer of the erythrocyte membrane. Both stomatocytes and echinocytes could indeed by obtained with 0.5 mmol . 1(-1) CTC, the cell shape depending on whether the external medium was adjusted respectively to pCa 9 or to pCa 3. Fluorescence microscopy revealed the Ca-CTC complex to be mostly restricted to the cell in stomatocytes and to the external medium in echinocytes. The possibility of inducing alternative cell shapes by varying the transmembrane Ca-CTC distribution, and the demonstration of a Ca-dependent expansion of even relatively compressed lipid monolayers by CTC, together suggest that the Ca-CTC complex may also differentially expand either leaflet of the red cell membrane.