Red blood cell shape and deformability in the context of the functional evolution of its membrane structure

It is proposed that it is possible to identify some of the problems that had to be solved in the course of evolution for the red blood cell (RBC) to achieve its present day effectiveness, by studying the behavior of systems featuring different, partial characteristics of its membrane. The appropriateness of the RBC volume to membrane area ratio for its circulation in the blood is interpreted on the basis of an analysis of the shape behavior of phospholipid vesicles. The role of the membrane skeleton is associated with preventing an RBC from transforming into a budded shape, which could form in its absence due to curvature-dependent transmembrane protein-membrane interaction. It is shown that, by causing the formation of echinocytes, the skeleton also acts protectively when, in vesicles with a bilayer membrane, the budded shapes would form due to increasing difference between the areas of their outer and inner layers.     

Energy of dissociation of lipid bilayer from the membrane skeleton of red blood cells

The association between the lipid bilayer and the membrane skeleton is important to cell function. In red blood cells, defects in this association can lead to various forms of hemolytic anemia. Although proteins involved in this association have been well characterized biochemically, the physical strength of this association is only beginning to be studied. Formation of a small cylindrical strand of membrane material (tether) from the membrane involves separation of the lipid bilayer from the membrane skeleton. By measuring the force required to form a tether, and knowing the contribution to the force due to the deformation of a lipid bilayer, it is possible to calculate the additional contribution to the work of tether formation due to the separation of membrane skeleton from the lipid bilayer. In the present study, we measured the tethering force during tether formation using a microcantilever (a thin, flexible glass fiber) as a force transducer. Numerical calculations of the red cell contour were performed to examine how the shape of the contour affects the calculation of tether radius, and subsequently separation work per unit area W(sk) and bending stiffness k(c). At high aspiration pressure and small external force, the red cell contour can be accurately modeled as a sphere, but at low aspiration pressure and large external force, the contour deviates from a sphere and may affect the calculation. Based on an energy balance and numerical calculations of the cell contour, values of the membrane bending stiffness k(c) = 2.0 x 10(-19) Nm and the separation work per unit area W(sk) = 0.06 mJ/m2 were obtained.     

Integral protein linkage and the bilayer-skeletal separation energy in red blood cells

Stabilization of the lipid bilayer membrane in red blood cells by its association with an underlying membrane-associated cytoskeleton has long been recognized as critical for proper red blood cell function. One of the principal connections between skeleton and bilayer is via linkages between band 3, the integral membrane protein that transports anions across the cell surface, and membrane skeletal elements including ankyrin, adducin, spectrin, and the junctional complex of the skeleton. Here, we use membrane tether formation coupled with fluorescent labeling of membrane components to examine the importance of band 3 in stabilizing the bilayer-skeletal association. In membranes from a patient deficient in band 3, the energy associated with the bilayer skeleton is approximately zero, whereas when band 3 is immobilized by ligation with the monoclonal antibody R10, the energy of association approximately doubles. Fluorescence images of tethers reveal that ∼40% of the band 3 on the normal cell surface can be pulled into the tether, confirming a lateral segregation of membrane components during tether formation. These results validate a critical role for band 3 in stabilizing the bilayer-skeletal association in red cells.     

Amphiphile induced echinocyte-spheroechinocyte transformation of red blood cell shape

A possible physical explanation of the echinocyte-spheroechinocyte red blood cell (RBC) shape transformation induced by the intercalation of amphiphilic molecules into the outer layer of the RBC plasma membrane bilayer is given. The stable RBC shape is determined by the minimization of the membrane elastic energy, consisting of the bilayer bending energy, the bilayer relative stretching energy and the skeleton shear elastic energy. It is shown that for a given relative cell volume the calculated number of echinocyte spicula increases while their size decreases as the number of the intercalated amphiphilic molecules in the outer layer of the cell membrane bilayer is increased, which is in agreement with experimental observations. Further, it is shown that the equilibrium difference between the outer and the inner membrane leaflet areas of the stable RBC shapes increases if the amount of the intercalated amphiphiles is increased, thereby verifying theoretically the original bilayer couple hypothesis of Sheetz and Singer (1974) and Evans (1974). Received: 22 August 1997 / Revised version: 25 November 1997 / Accepted: 11 February 1998     

Analysis of adhesion of large vesicles to surfaces.

An experimental procedure that can be used to measure the interfacial free energy density for the adhesion of membranes of large vesicles to other surfaces is outlined and analyzed. The approach can be used for both large phospholipid bilayer vesicles and red blood cells when the membrane force resultants are dominated by isotropic tension. The large vesicle or red cell is aspirated by a micropipet with sufficient suction pressure to form a spherical segment outside the pipet. The vesicle is then brought into close proximity of the surface to be tested and, the suction pressure reduced to permit adhesion, and the new equilibrium configuration is established. The mechanical analysis of the equilibrium shape provides the interfacial free energy density for the surface affinity. With this approach, the measurable range of membrane surface affinity is 10(-4)-3 erg/cm2 for large phospholipid bilayer vesicles and 10(-2)-10 erg/cm2 for red blood cells.     

The membrane skeleton--a distinct structure that regulates the function of cells

It has long been known that the red blood cell contains a membrane skeleton that stabilizes the plasma membrane, determines its shape, and regulates the lateral distribution of the membrane glyco-proteins to which it is attached. The way in which these functions are regulated in other cells has not been understood. It has now been shown that platelets also contain a membrane skeleton. In contrast to the membrane skeleton of the red blood cell, the platelet membrane skeleton has actin-binding protein, not spectrin, as a major component. The platelet membrane skeleton regulates the same cellular functions as the red blood cell membrane skeleton. Other cells may contain a membrane skeleton that is critical to their viability and normal functioning.     

Elastic energy of curvature-driven bump formation on red blood cell membrane.

Model calculations were performed to explore quantitative aspects of the discocyte-echinocyte shape transformation in red blood cells. The shape transformation was assumed to be driven by changes in the preferred curvature of the membrane bilayer and opposed by the elastic shear rigidity of the membrane skeleton. The energy required for echinocyte bump formation was calculated for a range of bump shapes for different preferred curvatures. Energy minima corresponding to nonzero bump heights were found when the stress-free area difference between the membrane leaflets or the spontaneous curvature of the membrane became sufficiently large, but the calculations predict that the membrane can tolerate significant differences in the resting areas of the inner and outer leaflets or significant spontaneous curvature without visible changes in shape. Thus, if the cell is near the threshold for bump formation, the calculations predict that small changes in membrane properties would produce large changes in cellular geometry. These results provide a rational framework for interpreting observations of shape transformations in red cells and for understanding the mechanism by which small changes in membrane elastic properties might lead to significant changes in geometry.     

Shape variation of bilayer membrane daughter vesicles induced by anisotropic membrane inclusions

A theoretical model of a two-component bilayer membrane was used in order to describe the influence of anisotropic membrane inclusions on shapes of membrane daughter micro and nano vesicles. It was shown that for weakly anisotropic inclusions the stable vesicle shapes are only slightly out-of-round. In contrast, for strongly anisotropic inclusions the stable vesicle shapes may significantly differ from spheres, i.e. they have a flattened oblate shape at small numbers of inclusions in the membrane, and an elongated cigar-like prolate shape at high numbers of inclusions in the vesicle membrane.     

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

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.     

Spectrin, human erythrocyte shapes, and mechanochemical properties.

Physical studies of human erythrocyte spectrin indicate that isolated spectrin dimers and tetramers in solution are worm-like coils with a persistence length of approximately 20 nm. This finding, the known polyelectrolytic nature of spectrin, and other structural information about spectrin and the membrane skeleton molecular organization have lead us to the hypothesis that the human erythrocyte membrane skeleton constitutes a two-dimensional ionic gel (swollen ionic elastomer). This concept is incorporated in what we refer to as the protein gel-lipid bilayer membrane model. The model accounts quantitatively for red elastic shear modulus and the maximum elastic extension ratio reported for the human erythrocytes membrane. Gel theory further predicts that depending on the environmental conditions, the membrane skeleton modulus of area compression may be small or large relative to the membrane elastic shear modulus. Our analyses show that the ratio between these two parameters affects both the geometry and the stability of the favored cell shapes and that the higher the membrane skeleton compressibility the smaller the values of the gel tension needed to induce cell shape transformations. The main virtue of the protein gel-lipid bilayer membrane model is that it offers a novel theoretical and molecular basis for the various mechanical properties of the membrane skeleton such as the membrane skeleton modulus of area compression and osmotic tension, and the effects of these properties on local membrane skeleton density, cell shape, and shape transformations.     

Stress-free state of the red blood cell membrane and the deformation of its skeleton

The response of a red blood cell (RBC) to deformation depends on its membrane, a composite of a lipid bilayer and a skeleton, which is a closed, twodimensional network of spectrin tetramers as its bonds. The deformation of the skeleton and its lateral redistribution are studied in terms of the RBC resting state for a fixed geometry of the RBC, partially aspirated into a micropipette. The geometry of the RBC skeleton in its initial state is taken to be either two concentric circles, a references biconcave shape or a sphere. It is assumed that in its initial state the skeleton is distributed laterally in a homogeneous manner with its bonds either unstressed, presenting its stress-free state, or prestressed. The lateral distribution was calculated using a variational calculation. It was assumed that the spectrin tetramer bonds exhibit a linear elasticity. The results showed a significant effect of the initial skeleton geometry on its lateral distribution in the deformed state. The proposed model is used to analyze the measurements of skeleton extension ratios by the method of applying two modes of RBC micropipette aspiration.     

Separation of the lipid bilayer from the membrane skeleton during discocyte-echinocyte transformation of human erythrocyte ghosts

The membrane skeleton, a protein lattice at the internal side of the red cell membrane, is principally composed of spectrin, actin and proteins 4.1 and 4.9. We have examined negatively stained red cell ghosts and demonstrated, on an ultrastructural level, a separation of the lipid bilayer from the membrane skeleton during echinocytic transformation. The electron micrographs of discoidal red cell ghosts suspended in hypotonic buffer revealed a filamentous reticulum that uniformly laminated the entire submembrane region. transformation of the discoidal ghosts into echinocytic form, as induced by incubation in isotonic buffer, resulted in a disruption of skeletal continuity underlying the surface contour of the membrane spicule. The submembrane reticulum extended into the base and the neck of the spiny processes of the crenated ghosts but was absent at the tip of these projections. In addition, membrane vesicles without a submembrane reticulum were detected either attached to the tips of the spicules or released into the supernatant from the echinocytic ghosts. Protein analysis revealed that the released vesicles were enriched in bands 3, 4.1 and 7 and contained very little of the membrane skeletal proteins, spectrin and actin. The data indicate that during echinocyte formation, parts of the lipid bilayer physically separate from the membrane skeleton, leading to a formation of skeleton-poor lipid vesicles.     

Elastic properties of the red blood cell membrane that determine echinocyte deformability

The natural biconcave shape of red blood cells (RBC) may be altered by injury or environmental conditions into a spiculated form (echinocyte). An analysis is presented of the effect of such a transformation on the resistance of RBC to entry into capillary sized cylindrical tubes. The analysis accounts for the elasticity of the membrane skeleton in dilation and shear, and the local and nonlocal resistance of the bilayer to bending, the latter corresponding to different area strains in the two leaflets of the bilayer. The shape transformation is assumed to be driven by the equilibrium area difference (A₀, the difference between the equilibrium areas of the bilayer leaflets), which also affects the energy of deformation. The cell shape is approximated by a parametric model. Shape parameters, skeleton shear deformation, and the skeleton density of deformed membrane relative to the skeleton density of undeformed membrane are obtained by minimization of the corresponding thermodynamic potential. Experimentally, A₀ is modified and the corresponding discocyte–echinocyte shape transition obtained by high-pressure aspiration into a narrow pipette, and the deformability of the resulting echinocyte is examined by whole cell aspiration into a larger pipette. We conclude that the deformability of the echinocyte can be accounted for by the mechanical behavior of the normal RBC membrane, where the equilibrium area difference A₀ is modified.     

The human erythrocyte membrane skeleton may be an ionic gel

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.     

Is the surface area of the red cell membrane skeleton locally conserved?

The incompressibility of the lipid bilayer keeps the total surface area of the red cell membrane constant. Local conservation of membrane surface area requires that each surface element of the membrane skeleton keeps its area when its aspect ratio is changed. A change in area would require a flow of lipids past the intrinsic proteins to which the skeleton is anchored. in fast red cell deformations, there is no time for such a flow. Consequently, the bilayer provides for local area conservation. In quasistatic deformations, the extent of local change in surface area is the smaller the larger the isotropic modulus of the skeleton in relation to the shear modulus. Estimates indicate: (a) the velocity of relative flow between lipid and intrinsic proteins is proportional to the gradient in normal tension within the skeleton and inversely proportional to the viscosity of the bilayer; (b) lateral diffusion of lipids is much slower than this flow; (c) membrane tanktreading at frequencies prevailing in vivo as well as the release of a membrane tongue from a micropipette are fast deformations; and (d) the slow phase in micropipette aspiration may be dominated by a local change in skeleton surface.     

A mechanism of formation of protein-free regions in the red cell membrane: the rupture of the membrane skeleton

The process of rupture and redistribution of the red cell membrane skeleton is analyzed theoretically. Following the emergence of the rupture the spectrin-actin network is redistributed on the cytoplasmic surface of the membrane bilayer. Due to the interaction of the membrane skeleton and integral proteins the redistribution of the spectrin-actin network leads to the release of purely lipid regions of the membrane. The scale of the protein redistribution caused by the rupture of the membrane skeleton and the size of the lipid domains produced depend on the shape of the membrane and the value of the electrical interaction of the membrane proteins. The lipid domains occurring as a result of the rupture and relaxation of the spectrinactin network can spontaneously increase or decrease its area. The criteria determining the conditions which result in the system's evolutions leading to the domain growth have been obtained. The character of the evolution is determined by the shape of the membrane region in which the rupture occurs as well as the relation between the effective linear tension of the rupture boundary and the modulus of elasticity of the spectrin-actin network.     

Elastic energy of the discocyte–stomatocyte transformation

The aim of this study is to calculate the membrane elastic energy for the different shapes observed in the discocyte–stomatocyte sequence. This analysis can provide a better quantitative understanding of the hypothesis put forward over the last decades to explain how red blood cells produce and maintain their typical shape. For this purpose, we use geometrical models based on parametric equations. The energy model considered for the elastic properties of RBC membrane includes the local and nonlocal resistance effects of the bilayer to bending. In particular, the results confirm the discocyte as the lowest energy value configuration among the sets of different red blood cell deformations considered in the sequence.     

The structure and function of band 3 (AE1): Recent developments (Review)

This review discusses recent advances in our understanding of the structure, function and molecular genetics of the membrane domain of red cell anion exchanger, band 3 (AE1), and its role in red cell and kidney disease. A new model for the topology of band 3 has been proposed, which suggests the membrane domain has 12 membrane spans, rather than the 14 membrane spans of earlier models. The major difference between the models is in the topology of the region on the C-terminal side of membrane spans 1-7. Two dimensional crystals of the deglycosylated membrane domain of band 3 have yielded two and three dimensional projection maps of the membrane domain dimer at low resolution. The human band 3 gene has been completely sequenced and this has facilitated the study of natural band 3 mutations and their involvement in disease. About 20% of hereditary spherocytosis cases arise from heterozygosity for band 3 mutations, and result in the absence or decrease of the mutant protein in the red cell membrane. Several other natural band 3 mutations are known that appear to be clinically benign, but alter red cell phenotype or are associated with altered red cell blood group antigens. These include the mutant band 3 present in Southeast Asian ovalocytosis, a condition which provides protection against cerebral malaria in children. Familial distal renal tubular acidosis, a condition associated with kidney stones, has been shown to result from a novel group of band 3 mutations. The total absence of band 3 has been described in animals-occurring naturally in cattle and after targeted disruption in mice. Some of these severely anaemic animals survive, so band 3 is not strictly essential for life. Although the band 3-negative red cells were very unstable, they contained a normally-assembled red cell skeleton, suggesting that the bilayer of the normal red cell membrane is stabilized by band 3 interactions with membrane lipids, rather than by interactions with the spectrin skeleton.