Spectrin properties and the elasticity of the red blood cell membrane skeleton

Two models of spectrin elasticity are developed and compared to experimental measurements of the red blood cell (RBC) membrane shear modulus through the use of an elastic finite element model of the RBC membrane skeleton. The two molecular models of spectrin are: (i) An entropic spring model of spectrin as a flexible chain. This is a model proposed by several previous authors. (ii) An elastic model of a helical coiled-coil which expands by increasing helical pitch. In previous papers, we have computed the relationship between the stiffness of a single spectrin molecule (K) and the shear modulus of a network (μ), and have shown that this behavior is strongly dependent upon network topology. For realistic network models of the RBC membrane skeleton, we equate μ to micropipette measurements of RBCs and predict K for spectrin that is consistent with the coiled-coil molecular model. The value of spectrin stiffness derived from the entropic molecular model would need to be at least 30 times greater to match the experimental results. Thus, the conclusion of this study is that a helical coiled-coil model for spectrin is more realistic than a purely entropic model.     

The membrane skeleton of erythrocytes. A percolation model.

The spectrin network on the cytoplasmic surface of the erythrocyte membrane is modeled as a triangular lattice of spectrin tetramers. This network obstructs lateral diffusion of proteins and provides mechanical reinforcement to the membrane. These effects are treated in a systematic and unified manner in terms of a percolation model. The diffusion coefficient is obtained as a function of the fraction of normal spectrin tetramers for both static and fluctuating barriers. The elasticity of the network is calculated as a function of the fraction of normal spectrin and the ratio of bending to stretching energies. For static barriers, elasticity and lateral diffusion are incompatible: if a network is connected enough to be elastic, it is connected enough to block long-range lateral diffusion. The elasticity and the force required for mechanical breakdown go to zero at the percolation threshold; experimental evidence suggests the existence of a stability threshold at or near the percolation threshold. The model is qualitatively applicable to other cells with membrane skeletons, such as epithelial cells, in which localization of membrane proteins is essential to differentiation.     

Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte

We present a three-dimensional computational study of whole-cell equilibrium shape and deformation of human red blood cell (RBC) using spectrin-level energetics. Random network models consisting of degree-2, 3, ..., 9 junction complexes and spectrin links are used to populate spherical and biconcave surfaces and intermediate shapes, and coarse-grained molecular dynamics simulations are then performed with spectrin connectivities fixed. A sphere is first filled with cytosol and gradually deflated while preserving its total surface area, until cytosol volume consistent with the real RBC is reached. The equilibrium shape is determined through energy minimization by assuming that the spectrin tetramer links satisfy the worm-like chain free-energy model. Subsequently, direct stretching by optical tweezers of the initial equilibrium shape is simulated to extract the variation of axial and transverse diameters with the stretch force. At persistence length p = 7.5 nm for the spectrin tetramer molecule and corresponding in-plane shear modulus mu(0) approximately 8.3 microN/m, our models show reasonable agreement with recent experimental measurements on the large deformation of RBC with optical tweezers. We find that the choice of the reference state used for the in-plane elastic energy is critical for determining the equilibrium shape. If a position-independent material reference state such as a full sphere is used in defining the in-plane energy, then the bending modulus kappa needs to be at least a decade larger than the widely accepted value of 2 x 10(-19) J to stabilize the biconcave shape against the cup shape. We demonstrate through detailed computations that this paradox can be avoided by invoking the physical hypothesis that the spectrin network undergoes constant remodeling to always relax the in-plane shear elastic energy to zero at any macroscopic shape, at some slow characteristic timescale. We have devised and implemented a liquefied network structure evolution algorithm that relaxes shear stress everywhere in the network and generates cytoskeleton structures that mimic experimental observations.     

Cell fusion generates an inhomogeneous distribution of elasticity and rigidity in plasma membranes

The post-electrofusion oscillation cycle of human erythrocytes (doublets) was evaluated for the first four pump events in order to quantify the spectrin-network rearrangement in the fusion zone. Experiments were carried out on control cells and on cells that received a 40 degree C and a 45 degree C 20-min heat treatment. The amplitude of the geometrical changes depended on the heat-treatment procedure, whereas the roundness on entering the pump event was always identical. The rigid influence of the fusion zone prevented the doublets from adopting a spherical shape. The fusion zone was characterized by a linear elongation modulus that could be calculated from geometrical measurements and earlier findings on erythrocyte membrane mechanics, and that ranged between 1.44E6 Nm(-2) for control doublets and 0.99E6 Nm(-2) after 45 degrees C heat treatment. The membrane composition of the fusion zone differs greatly from that of the other membrane parts not involved in fusion processes and evidence is given that this inhomogeneity stems from a rearrangement of the triangulated spectrin network and other membrane skeletal proteins in the fusion zone.     

Elastic thickness compressibilty of the red cell membrane

We have used an ultrasensitive force probe and optical interferometry to examine the thickness compressibility of the red cell membrane in situ. Pushed into the centers of washed-white red cell ghosts lying on a coverglass, the height of the microsphere-probe tip relative to its closest approach on the adjacent glass surface revealed the apparent material thickness, which began at approximately 90 nm per membrane upon detection of contact (force approximately 1-2 pN). With further impingement, the apparent thickness per membrane diminished over a soft compliant regime that spanned approximately 40 nm and stiffened on approach to approximately 50 nm under forces of approximately 100 pN. The same force-thickness response was obtained on recompression after retraction of the probe, which demonstrated elastic recoverability. Scaled by circumferences of the microspheres, the forces yielded energies of compression per area which exhibited an inverse distance dependence resembling that expected for flexible polymers. Attributed to the spectrin component of the membrane cytoskeleton, the energy density only reached one thermal energy unit (k(B)T) per spectrin tetramer near maximum compression. Hence, we hypothesized that the soft compliant regime probed in the experiments represented the compressibility of the outer region of spectrin loops and that the stiff regime < 50 nm was the response of a compact mesh of spectrin backed by a hardcore structure. To evaluate this hypothesis, we used a random flight theory for the entropic elasticity of polymer loops to model the spectrin network. We also examined the possibility that additional steric repulsion and apparent thickening could arise from membrane thermal-bending excitations. Fixing the energy scale to k(B)T/spectrin tetramer, the combined elastic response of a network of ideal polymer loops plus the membrane steric interaction correlated well with the measured dependence of energy density on distance for a statistical segment length of approximately 5 nm for spectrin (i.e., free chain end-to-end length of approximately 29 nm) and a hardcore limit of approximately 30 nm for underlying structure.     

An elastic network model based on the structure of the red blood cell membrane skeleton.

A finite element network model has been developed to predict the macroscopic elastic shear modulus and the area expansion modulus of the red blood cell (RBC) membrane skeleton on the basis of its microstructure. The topological organization of connections between spectrin molecules is represented by the edges of a random Delaunay triangulation, and the elasticity of an individual spectrin molecule is represented by the spring constant, K, for a linear spring element. The model network is subjected to deformations by prescribing nodal displacements on the boundary. The positions of internal nodes are computed by the finite element program. The average response of the network is used to compute the shear modulus (mu) and area expansion modulus (kappa) for the corresponding effective continuum. For networks with a moderate degree of randomness, this model predicts mu/K = 0.45 and kappa/K = 0.90 in small deformations. These results are consistent with previous computational models and experimental estimates of the ratio mu/kappa. This model also predicts that the elastic moduli vary by 20% or more in networks with varying degrees of randomness. In large deformations, mu increases as a cubic function of the extension ratio lambda 1, with mu/K = 0.62 when lambda 1 = 1.5.     

Red Blood Cell Shape and Fluctuations: Cytoskeleton Confinement and ATP Activity

We review recent theoretical work that analyzes experimental measurements of the shape and fluctuations of red blood cells. Particular emphasis is placed on the role of the cytoskeleton and cell elasticity and we contrast the situation of elastic cells with that of fluid-filled vesicles. In red blood cells (RBCs), the cytoskeleton consists of a two-dimensional network of spectrin proteins. Our analysis of the wave vector and frequency dependence of the fluctuation spectrum of RBCs indicates that the spectrin network acts as a confining potential that reduces the fluctuations of the lipid bilayer membrane. However, since the cytoskeleton is only sparsely connected to the bilayer, one cannot regard the composite cytoskeleton membrane as a polymerized object with a shear modulus. The sensitivity of RBC fluctuations and shapes to ATP concentration may reflect the transient defects induced in the cytoskeleton network by ATP.     

Effects of inherited membrane abnormalities on the viscoelastic properties of erythrocyte membrane.

Several workers have identified molecular abnormalities associated with inherited blood disorders. The present work examines how these alterations in molecular structure affect the viscoelastic properties of the red blood cell membrane. Changes in the membrane shear modulus, the membrane viscosity, and the apparent membrane bending stiffness were observed in cells of eight patients having a variety of disorders: Two had reductions in the number of high-affinity ankyrin binding sites, two had abnormalities associated with the protein band 4.1, and six were known to be deficient in spectrin. The data suggest that the membrane shear modulus is proportional to the density of spectrin on the membrane and support the view that spectrin is primarily responsible for membrane shear elasticity. Although membranes having abnormalities associated with the function of ankyrin or band 4.1 exhibited reduced elasticity, the degree of mechanical dysfunction was quantitatively inconsistent with the extent of the molecular abnormality. This indicates that these skeletal components do not play a primary role in determining membrane shear elasticity. The membrane viscosity was reduced in seven of the eight patients studied. The reduction in viscosity was usually greater than the reduction in shear modulus, but the degree of reduction in viscosity was variable and did not correlate well with the degree of molecular abnormality.     

On the measurement of shear elastic moduli and viscosities of erythrocyte plasma membranes by transient deformation in high frequency electric fields.

We present a new method to measure the shear elastic moduli and viscosities of erythrocyte membranes which is based on the fixation and transient deformation of cells in a high-frequency electric field. A frequency domain of constant force (arising by Maxwell Wagner polarization) is selected to minimize dissipative effects. The electric force is thus calculated by electrostatic principles by considering the cell as a conducting body in a dielectric fluid and neglecting membrane polarization effects. The elongation A of the cells perpendicular to their rotational axis exhibits a linear regime (A proportional to Maxwell tension or to square of the electric field E2) at small, and a nonlinear regime (A proportional to square root of Maxwell tension or to the electric field E) at large extensions with a cross-over at A approximately 0.5 micron. The nonlinearity leads to amplitude-dependent response times and to differences of the viscoelastic response and relaxation functions. The cells exhibit pronounced yet completely reversible tip formations at large extensions. Absolute values of the shear elastic modulus, mu, and membrane viscosity, eta, are determined by assuming that field-induced stretching of the biconcave cell may be approximately described in terms of a sphere to ellipsoid deformation. The (nonlinear) elongation-vs.-force relationship calculated by the elastic theory of shells agress well with the experimentally observed curves and the values of mu = 6.1 x 10(-6) N/m and eta = 3.4 x 10(-7) Ns/m are in good agreement with the micropipette results of Evans and co-workers. The effect of physical, biochemical, and disease-induced structural changes on the viscoelastic parameters is studied. The variability of mu and eta of a cell population of a healthy donor is +/- 45%, which is mainly due to differences in the cell age. The average mu value of cells of different healthy donors scatters by +/- 18%. Osmotic deflation of the cells leads to a fivefold increase of mu and 10-fold increase of eta at 500 mosm. The shear modulus mu increases with temperature showing that the cytoskeleton does not behave as a network of entropy elastic springs. Elliptic cells of patients suffering from elliptocytosis of the Leach phenotype exhibit a threefold larger value of mu than normal discocytes of control donors. Cross-linking of the spectrin by the divalent S-H agents diamide (1 mM, 15 min incubation) leads to an eightfold increase of mu whereas eta is essentially constant. The effect of diamide is reversed after treatment with S-S bond splitting agents.     

Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry.

A magnetic bead microrheometer has been designed which allows the generation of forces up to 10(4) pN on 4.5 micron paramagnetic beads. It is applied to measure local viscoelastic properties of the surface of adhering fibroblasts. Creep response and relaxation curves evoked by tangential force pulses of 500-2500 pN (and approximately 1 s duration) on the magnetic beads fixed to the integrin receptors of the cell membrane are recorded by particle tracking. Linear three-phasic creep responses consisting of an elastic deflection, a stress relaxation, and a viscous flow are established. The viscoelastic response curves are analyzed in terms of a series arrangement of a dashpot and a Voigt body, which allows characterization of the viscoelastic behavior of the adhering cell surface in terms of three parameters: an effective elastic constant, a viscosity, and a relaxation time. The displacement field generated by the local tangential forces on the cell surface is visualized by observing the induced motion of assemblies of nonmagnetic colloidal probes fixed to the membrane. It is found that the displacement field decays rapidly with the distance from the magnetic bead. A cutoff radius of Rc approximately 7 micron of the screened elastic field is established. Partial penetration of the shear field into the cytoplasm is established by observing the induced deflection of intracellular compartments. The cell membrane was modeled as a thin elastic plate of shear modulus mu * coupled to a viscoelastic layer, which is fixed to a solid support on the opposite side; the former accounts for the membrane/actin cortex, and the latter for the contribution of the cytoskeleton to the deformation of the cell envelope. It is characterized by the coupling constant chi characterizing the elasticity of the cytoskeleton. The coupling constant chi and the surface shear modulus mu * are obtained from the measured displacements of the magnetic and nonmagnetic beads. By analyzing the experimental data in terms of this model a surface shear modulus of mu * approximately 2 . 10(-3) Pa m to 4 . 10(-3) Pa m is found. By assuming an approximate plate thickness of 0.1 micron one estimates an average bulk shear modulus of mu approximately (2 / 4) . 10(-4) Pa, which is in reasonable agreement with data obtained by atomic force microscopy. The viscosity of the dashpot is related to the apparent viscosity of the cytoplasm, which is obtained by assuming that the top membrane is coupled to the bottom (fixed) membrane by a viscous medium. By application of the theory of diffusion of membrane proteins in supported membranes we find a coefficient of friction of bc approximately 2 . 10(9) Pa s/m corresponding to a cytoplasmic viscosity of 2 . 10(3) Pa s.     

Formation and maintenance of tubular membrane projections: experiments and numerical calculations

To study the mechanical properties of lipid membranes, we manipulated liposomes by using a system comprising polystyrene beads and laser tweezers, and measured the force required to transform their shapes. When two beads pushed the membrane from inside, spherical liposomes transformed into a lemon-shape. Then a discontinuous shape transformation occurred to form a membrane tube from either end of the liposomes, and the force dropped drastically. We analyzed these processes using a mathematical model based on the bending elasticity of the membranes. Numerical calculations showed that when the bead size was taken into account, the model reproduced both the liposomal shape transformation and the force-extension relation. This result suggests that the size of the beads is responsible for the existence of a force barrier for the tube formation.     

Elasticity of synthetic phospholipid vesicles and submitochondrial particles during osmotic swelling

A rapid and accurate method has been developed for measuring the elastic response of vesicle bilayer membranes to an applied osmotic pressure. The technique of dynamic light scattering is used to measure both the elastic constant and the elastic limit of dioleoylphosphatidic acid (DOPA) and DOPA-cholesterol vesicles and of submitochondrial particles derived from the inner membrane of bovine heart mitochondria. The vesicles prepared by the pH-adjustment method are unilamellar and of uniform size between 240 and 460 nm in diameter. The vesicles swell uniformly upon dilution. The observed change in size is not due to any change in the shape of the vesicles. The data also indicate that the vesicles are spherical and not flaccid. The total vesicle swelling in these studies resulted in a 3-4% increase in surface area for vesicles swollen in 0.15 M KCl and a 5-10% increase in surface area for vesicles swollen in 0.25 M sucrose. This maximum represents the elastic limit of the vesicles. Evidence is presented to show that the vesicles release contents after swelling to this maximum, reseal immediately, and reswell according to the osmotic pressure. For DOPA vesicles in a 0.15 M KCl-tris(hydroxymethyl)aminomethane hydrochloride (Tris-HCl) buffer (pH 7.55), the observed membrane modulus is found to be in the range of 10(8) dyn/cm2. The modulus was found to be in the order of 10(7) dyn/cm2 for DOPA vesicles in a 0.25 M sucrose-Tris-HCl buffer (pH 7.55). This is comparable to that of submitochondrial particles in the same sucrose-Tris-HCl buffer. The observed membrane modulus also decreases with vesicle size. Its magnitude and its variation with ionic strength indicate that the major component of bilayer elasticity is neither the inherent elasticity of the bilayer nor the bending modulus. The variation of the membrane modulus with respect to curvature suggests that its principal component may be related to surface tension effects including the negative charges on the vesicle surface. There is considerable variation between vesicles swollen in sucrose and those swollen in KCl in the membrane modulus, in the elastic limit at which the vesicles burst, and in the transbilayer pressure difference at bursting. The latter was found to be 4-6 mosM (10(5) dyn/cm2) in sucrose solution and 20-4 mosM (10(6) dyn/cm2) in KCl solution.     

Regulation of erythrocyte ghost membrane mechanical stability by chlorpromazine

Chlorpromazine (CPZ), a widely used tranquilizer, is known to induce stomatocytic shape changes in human erythrocytes. However, the effect of CPZ on membrane mechanical properties of erythrocyte membranes has not been documented. In the present study we show that CPZ induces a dose-dependent increase in mechanical stability of erythrocyte ghost membrane. Furthermore, we document that spectrin specifically binds to CPZ intercalated into inside-out vesicles depleted of all peripheral proteins. These findings imply that CPZ-induced mechanical stabilization of the erythrocyte ghost membranes may be mediated by direct binding of spectrin to the bilayer. Membrane active drugs that partition into lipid bilayer can thus induce cytoskeletal protein interactions with the membrane and modulate membrane material properties.     

Structure of the erythrocyte membrane skeleton as observed by atomic force microscopy.

The structure of the membrane skeleton on the cytoplasmic surface of the erythrocyte plasma membrane was observed in dried human erythrocyte ghosts by atomic force microscopy (AFM), taking advantage of its high sensitivity to small height variations in surfaces. The majority of the membrane skeleton can be imaged, even on the extracellular surface of the membrane. Various fixation and drying methods were examined for preparation of ghost membrane samples for AFM observation, and it was found that freeze-drying (freezing by rapid immersion in a cryogen) of unfixed specimens was a fast and simple way to obtain consistently good results for observation without removing the membrane or extending the membrane skeleton. Observation of the membrane skeleton at the external surface of the cell was possible mainly because the bilayer portion of the membrane sank into the cell during the drying process. The average mesh size of the spectrin network observed at the extracellular and cytoplasmic surfaces of the plasma membrane was 4800 and 3000 nm2, respectively, which indicates that spectrin forms a three-dimensionally folded meshwork, and that 80% of spectrin can be observed at the extracellular surface of the plasma membrane.     

Loss of resealing ability in erythrocyte membranes. Effect of divalent cations and spectrin release

Washed human erythrocyte membranes can recover impermeability to macromolecules upon warming in solutions of sufficient ionic strength. This ability is rapidly lost from most ghost preparations in dilute salt solution at temperatures of 15°C or higher. Divalent cations both reseal ghosts in the absence of high ionic strength and prevent loss of resealing ability. The effective concentrations are 40 μM for Ca²⁺ and 200 μM for Mg²⁺. The loss of resealing ability is associated with the release of spectrin polypeptides from the inner surface of the membrane. In ghost preparations that have not become irreversibly leaky, or in the presence of Ca²⁺, loss of spectrin does not occur. These results suggest that an intact spectrin network is required for resealing to macromolecules, and divalent cations stabilize this network. In light of this information, the effect of temperature on resealing kinetics is described.     

Composition of the ternary protein complex of the red cell membrane cytoskeleton

The red cell membrane skeletal network is constructed from actin, spectrin and protein 4.1 in a molar ratio of actin subunits/spectrin heterodimer/protein 4.1 of 2:1:1. This represents saturation of the actin filaments, since incubation with extraneous spectrin and protein 4.1 leads to no binding of additional spectrin, either to the inner surface of ghost membranes or to lipid-free membrane cytoskeletons. Partial extraction of spectrin from the membrane is accompanied by release of actin under all conditions. Regardless of the proportion of spectrin extracted, the molar ratio of spectrin dimers/actin subunits is constant at 1:2. This is not the result of release or cooperative breakdown of whole lattice junctions from the network, for the number of actin filaments, judged by capacity to nucleate polymerisation of added G-actin, remains unchanged even when as much as 60% of the total spectrin has been lost. A similar 1:2:1 stoichiometry characterises the complex formed when G-actin is allowed to polymerise in the presence of varying amounts of spectrin and protein 4.1. When this complex is treated with the depolymerising agent, 1 M guanidine hydrochloride, it breaks down into smaller units of the same stoichiometry. After cross-linking these can be recovered from a gel-filtration column. Complexes prepared starting from G-actin appear to be much more stable than those formed when spectrin and protein 4.1 are bound to F-actin.     

Estimation of cell Young's modulus of adherent cells probed by optical and magnetic tweezers: influence of cell thickness and bead immersion

A precise characterization of cell elastic properties is crucial for understanding the mechanisms by which cells sense mechanical stimuli and how these factors alter cellular functions. Optical and magnetic tweezers are micromanipulation techniques which are widely used for quantifying the stiffness of adherent cells from their response to an external force applied on a bead partially embedded within the cell cortex. However, the relationships between imposed external force and resulting bead translation or rotation obtained from these experimental techniques only characterize the apparent cell stiffness. Indeed, the value of the estimated apparent cell stiffness integrates the effect of different geometrical parameters, the most important being the bead embedding angle 2gamma, bead radius R, and cell height h. In this paper, a three-dimensional finite element analysis was used to compute the cell mechanical response to applied force in tweezer experiments and to explicit the correcting functions which have to be used in order to infer the intrinsic cell Young's modulus from the apparent elasticity modulus. Our analysis, performed for an extensive set of values of gamma, h, and R, shows that the most relevant parameters for computing the correcting functions are the embedding half angle gamma and the ratio h(u)/2R, where h(u) is the under bead cell thickness. This paper provides original analytical expressions of these correcting functions as well as the critical values of the cell thickness below which corrections of the apparent modulus are necessary to get an accurate value of cell Young's modulus. Moreover, considering these results and taking benefit of previous results obtained on the estimation of cell Young's modulus of adherent cells probed by magnetic twisting cytometry (MTC) (Ohayon, J., and Tracqui, P., 2005, Ann. Biomed. Eng., 33, pp. 131-141), we were able to clarify and to solve the still unexplained discrepancies reported between estimations of elasticity modulus performed on the same cell type and probed with MTC and optical tweezers (OT). More generally, this study may strengthen the applicability of optical and magnetic tweezers techniques by insuring a more precise estimation of the intrinsic cell Young's modulus (CYM).     

The formation of vesicles retaining sodium-dependent transport systems for amino acids from protein-depleted membranes of pigeon erythrocytes

The process of the formation of vesicles from pigeon erythrocyte membranes was studied. Mildly alkaline solutions of low ionic strength, which reduce human erythrocyte membranes to small vesicles depleted of spectrin and other proteins, have no such effect on pigeon erythrocyte ghosts. A distinct phase of removal of membrane proteins, including spectrin, began to occur only when pigeon erythrocyte membranes were exposed to 0.2 mM EDTA adjusted to pH values above 10.2. Vesicles which demonstrated Na⁺-dependent amino acid transport were generated between the pH values 10.8 and 11.4. The results show that peripheral proteins, notably spectrin, maintain the integrity of the pigeon erythrocyte ghost. The interaction of these proteins with the membrane is rather different from that well studied in the human erythrocyte ghost and the possible significance of this for the pigeon erythrocyte is discussed.     

Spectrin, red cell shape and deformability. II. The antagonistic action of spectrin and sialic acid residues in determining membrane curvature in genetic spectrin deficiency in mice

In a companion paper, the shapes of spectrin deficient mouse erythrocytes were described; in contrast to previous assumptions, spherules with tethered microvesicles rather than true "spherocytes" were found. Thence, spectrin deficient mouse erythrocytes are endowed with an excess of surface area for the given volume but the membrane is assuming a highly positive curvature. Observations during and after the action of enzymes cleaving the red cell surface charge (Neuraminidase, Trypsin, Chymotrypsin) showed that the previously positive membrane curvature, as well as the tendency of the membrane to flow into fingerlike protrusions was completely abolished. The erythrocytes of the spectrin deficient, desialylated mouse erythrocytes assumed a variety of shapes, often discocytic or even stomatocytic, i.e. their membrane presented with negative curvature. However, while these desialylated membranes could be easily deformed (elongated) by shear flow they did not recoil elastically into any definitive configuration after removal of the deforming forces. It is concluded from these observations that spectrin (acting on the inner interface between membrane and cytoplasm) and sialic acid residues (acting on the outer interface between membrane and plasma) exert antagonizing effects on membrane curvature and membrane bending elasticity. Sialic acid residues, strongly charged and situated on the outer side of the cell, produce positive membrane curvature; this observation can most readily be explained by assuming that this mechanical effect is caused by repulsive coulombic forces expanding the outer half of the bilayer. To explain the effect of the spectrin-complex in counteracting positive or in producing negative membrane curvature, a similar expansive coulombic force acting between the highly charged residues has been postulated. Thence, a model for explaining the overall elastic behaviour of the normal mammalian red cell is developed which is based on the assumption of elastic interactions of proteinacous membrane components coupled to the lipid bilayer of the membrane.     

Shear-response of the spectrin dimer-tetramer equilibrium in the red blood cell membrane

The red cell membrane derives its elasticity and resistance to mechanical stresses from the membrane skeleton, a network composed of spectrin tetramers. These are formed by the head-to-head association of pairs of heterodimers attached at their ends to junctional complexes of several proteins. Here we examine the dynamics of the spectrin dimer-dimer association in the intact membrane. We show that univalent fragments of spectrin, containing the dimer self-association site, will bind to spectrin on the membrane and thereby disrupt the continuity of the protein network. This results in impairment of the mechanical stability of the membrane. When, moreover, the cells are subjected to a continuous low level of shear, even at room temperature, the incorporation of the fragments and the consequent destabilization of the membrane are greatly accentuated. It follows that a modest shearing force, well below that experienced by the red cell in the circulation, is sufficient to sever dimer-dimer links in the network. Our results imply 1) that the membrane accommodates the enormous distortions imposed on it during the passage of the cell through the microvasculature by means of local dissociation of spectrin tetramers to dimers, 2) that the network in situ is in a dynamic state and undergoes a "breathing" action of tetramer dissociation and re-formation.