Membrane Shear Elasticity Research Articles

Numerical-experimental estimation of the deformability of human red blood cells from rheometrical data

The deformability of human red blood cells (RBCs), which comprise almost 99% of the cells in whole blood, is largely related not only to pathophysiological blood flow but also to the levels of intracellular compounds. Therefore, statistical estimates of the deformability of individual RBCs are of paramount importance in the clinical diagnosis of blood diseases. Although the microscale hydrodynamic interactions of individual RBCs lead to non-Newtonian blood rheology, there is no established method to estimate individual RBC deformability from the rheological data of RBC suspensions, and the possibility of this estimation has not been proven. To address this issue, we conducted an integrated analysis of a model of the rheology of RBC suspensions, coupled with macrorheological data of human RBCs suspended in plasma. Assuming a nonlinear curve of the relative viscosity of the suspensions as a function of the cell volume fraction, the statistical average of the membrane shear elasticity was estimated for individual intact RBCs or hardened RBCs. Both estimated values reproduced well the experimentally observed shear-thinning non-Newtonian behavior in these suspensions. We hereby conclude that our complementary approach makes it possible to estimate the statistical average of individual RBC deformability from macrorheological data obtained with usual rheometric tests.

Effect of spectrin network elasticity on the shapes of erythrocyte doublets.

Red blood cell (RBC) aggregates play an important role in determining blood rheology. RBCs in plasma or polymer solution interact attractively to form various shapes of RBC doublets, where the attractive interactions can be varied by changing the solution conditions. A systematic numerical study on RBC doublet formation is performed, which takes into account the shear elasticity of the RBC membrane due to the spectrin cytoskeleton, in addition to the membrane bending rigidity. RBC membranes are modeled by two-dimensional triangular networks of linked vertices, which represent three-dimensional cell shapes. The phase space of RBC doublet shapes in a wide range of adhesion strengths, reduced volumes, and shear elasticities is obtained. The shear elasticity of the RBC membrane changes the doublet phases significantly. Experimental images of RBC doublets in different solutions show similar configurations. Furthermore, we show that rouleau formation is affected by the doublet structure.

On the shape memory of red blood cells

Red blood cells (RBCs) undergo remarkably large deformations when subjected to external forces but return to their biconcave discoid resting shape as the forces are withdrawn. In many experiments, such as when RBCs are subjected to a shear flow and undergo the tank-treading motion, the membrane elements are also displaced from their original (resting) locations along the cell surface with respect to the cell axis, in addition to the cell being deformed. A shape memory is said to exist if after the flow is stopped the RBC regains its biconcave shape and the membrane elements also return to their original locations. The shape memory of RBCs was demonstrated by Fischer [“Shape memory of human red blood cells,” Biophys. J. 86, 3304–3313 (2004)] using shear flow go-and-stop experiments. Optical tweezer and micropipette based stretch-relaxation experiments do not reveal the complete shape memory because while the RBC may be deformed, the membrane elements are not significantly displaced from their original locations with respect to the cell axis. Here we present the first three-dimensional computational study predicting the complete shape memory of RBCs using shear flow go-and-stop simulations. The influence of different parameters, namely, membrane shear elasticity and bending rigidity, membrane viscosity, cytoplasmic and suspending fluid viscosity, as well as different stress-free states of the RBC is studied. For all cases, the RBCs always exhibit shape memory. The complete recovery of the RBC in shear flow go-and-stop simulations occurs over a time that is orders of magnitude longer than that for optical tweezer and micropipette based relaxations. The response is also observed to be more complex and composed of widely disparate time scales as opposed to only one time scale that characterizes the optical tweezer and micropipette based relaxations. We observe that the recovery occurs in three phases: a rapid compression of the RBC immediately after the flow is stopped, followed by a slow recovery to the biconcave shape combined with membrane rotation, and a final rotational return of the membrane elements back to their original locations. A fast time scale on the order of a few hundred milliseconds characterizes the initial compression phase while a slow time scale on the order of tens of seconds is associated with the rotational phase. We observe that the response is strongly dependent on the stress-free state of the cells, that is, the relaxation time decreases significantly and the mode of recovery changes from rotation-driven to deformation-driven as the stress-free state becomes more non-spherical. We show that while membrane shear elasticity and non-spherical stress-free shape are necessary and sufficient for the membrane elements to return to their original locations, bending rigidity is needed for the “global” recovery of the biconcave shape. We also perform a novel relaxation simulation in which the cell axis of revolution is not aligned with the shear plane and show that the shape memory is exhibited even when the membrane elements are displaced normal to the imposed flow direction. The results presented here could motivate new experiments to determine the exact stress-free state of the RBC and also to clearly identify different tank-treading modes.

A simple model to understand the effect of membrane shear elasticity and stress-free shape on the motion of red blood cells in shear flow.

An analytical model was proposed by Keller and Skalak in 1982 to understand the motion of red blood cells in shear flow. The cell was described as a fluid ellipsoid of fixed shape. This model was extended in 2007 to introduce shear elasticity of the red blood cell membrane. Here, this model is further extended to take into account that the cell discoid shape physiologically observed is not a stress-free shape. The model shows that spheroid stress-free shapes allow us to fit the experimental data with the values of shear elasticity typical to that found with micropipette and optical tweezer experiments. In the range of moderate shear rates (for which RBCs keep their discoid shape) this model enables us to quantitatively determine (i) an effective cell viscosity, which combines membrane and hemoglobin viscosities and (ii) an effective shear modulus of the membrane that combines the shear modulus and the stress-free shape. This model can also be used to determine RBC mechanical parameters not only in the tanktreading regime when cells are suspended in medium of high viscosity but also in the tumbling regime characteristic of cells suspended in media of low viscosity. In this regime, a transition is predicted between a rigid-like tumbling motion and a fluid-like tumbling motion above a critical shear rate, which is directly related to the mechanical parameters of the cell.

Dynamic motion of red blood cells in simple shear flow

A three-dimensional numerical model is proposed to simulate the dynamic motion of red blood cells (RBCs) in simple shear flow. The RBCs are approximated by ghost cells consisting of Newtonian liquid drops enclosed by Skalak membranes which take into account the membrane shear elasticity and the membrane area incompressibility. The RBCs have an initially biconcave discoid resting shape, and the internal liquid is assumed to have the same physical properties as the matrix fluid. The simulation is based on a hybrid method, in which the immersed boundary concept is introduced into the framework of the lattice Boltzmann method, and a finite element model is incorporated to obtain the forces acting on the nodes of the cell membrane which is discretized into flat triangular elements. The dynamic motion of RBCs is investigated in simple shear flow under a broad range of shear rates. At large shear rates, the cells are found to carry out a swinging motion, in which periodic inclination oscillation and shape deformation superimpose on the membrane tank treading motion. With the shear rate decreasing, the swinging amplitude of the cell increases, and finally triggers a transition to tumbling motion. This is the first direct numerical simulation that predicts both the swinging motion of the RBCs and the shear rate induced transition, which have been observed in a recent experiment. It is also found that as the mode changes from swinging to tumbling, the apparent viscosity of the suspension increases monotonically.

Phase-field approach to three-dimensional vesicle dynamics

We extend our recent phase-field [T. Biben and C. Misbah, Phys. Rev. E 67, 031908 (2003)] approach to 3D vesicle dynamics. Unlike the boundary-integral formulations, based on the use of the Oseen tensor in the small Reynolds number limit, this method offers several important flexibilities. First, there is no need to track the membrane position; rather this is automatically encoded in dynamics of the phase field to which we assign a finite width representing the membrane extent. Secondly, this method allows naturally for any topology change, like vesicle budding, for example. Thirdly, any non-Newtonian constitutive law, that is generically nonlinear, can be naturally accounted for, a fact which is precluded by the boundary integral formulation. The phase-field approach raises, however, a complication due to the local membrane incompressibility, which, unlike usual interfacial problems, imposes a nontrivial constraint on the membrane. This problem is solved by introducing dynamics of a tension field. The first purpose of this paper is to show how to write adequately the advected-field model for 3D vesicles. We shall then perform a singular expansion of the phase field equation to show that they reduce, in the limit of a vanishing membrane extent, to the sharp boundary equations. Then, we present some results obtained by the phase-field model. We consider two examples; (i) kinetics towards equilibrium shapes and (ii) tanktreading and tumbling. We find a very good agreement between the two methods. We also discuss briefly how effects, such as the membrane shear elasticity and stretching elasticity, and the relative sliding of monolayers, can be accounted for in the phase-field approach.

Mechanics of Curved Plasma Membrane Vesicles: Resting Shapes, Membrane Curvature, and In-Plane Shear Elasticity

Highly curved cell membrane structures, such as plasmalemmal vesicles (caveolae) and clathrin-coated pits, facilitate many cell functions, including the clustering of membrane receptors and transport of specific extracellular macromolecules by endothelial cells. These structures are subject to large mechanical deformations when the plasma membrane is stretched and subject to a change of its curvature. To enhance our understanding of plasmalemmal vesicles we need to improve the understanding of the mechanics in regions of high membrane curvatures. We examine here, theoretically, the shapes of plasmalemmal vesicles assuming that they consist of three membrane domains: an inner domain with high curvature, an outer domain with moderate curvature, and an outermost flat domain, all in the unstressed state. We assume the membrane properties are the same in these domains with membrane bending elasticity as well as in-plane shear elasticity. Special emphasis is placed on the effects of membrane curvature and in-plane shear elasticity on the mechanics of vesicle during unfolding by application of membrane tension. The vesicle shapes were computed by minimization of bending and in-plane shear strain energy. Mechanically stable vesicles were identified with characteristic membrane necks. Upon stretch of the membrane, the vesicle necks disappeared relatively abruptly leading to membrane shapes that consist of curved indentations. While the resting shape of vesicles is predominantly affected by the membrane spontaneous curvatures, the membrane shear elasticity (for a range of values recorded in the red cell membrane) makes a significant contribution as the vesicle is subject to stretch and unfolding. The membrane tension required to unfold the vesicle is sensitive with respect to its shape, especially as the vesicle becomes fully unfolded and approaches a relative flat shape.

Motion of red blood cells in a capillary with an endothelial surface layer: effect of flow velocity.

Interior surfaces of capillaries are lined with macromolecules forming an endothelial surface layer (ESL). A theoretical model is used to investigate effects of flow velocity on motion and axisymmetric deformation of red blood cells in a capillary with an ESL. Cell deformation is analyzed, including effects of membrane shear and bending elasticity. Plasma flow around the cell and through the ESL is computed using lubrication theory. The ESL is represented as a porous layer that exerts compressive forces on red blood cells that penetrate it. According to the model, hydrodynamic pressures generated by plasma flow around the cell squeeze moving red blood cells into narrow elongated shapes. If the ESL is 0.7 microm wide, with hydraulic resistivity of 2 x 10(8) dyn x s x cm(-4), and exerts a force of 20 dyn/cm2, predicted variation with flow velocity of the gap width between red blood cell and capillary wall agrees well with observations. Predicted gap at a velocity of 0.1 mm/s is approximately 0.6 microm vs. approximately 0.2 microm with no ESL. Predicted flow resistance increases markedly at low velocities. The model shows that exclusion of red blood cells from the ESL in flowing capillaries can result from hydrodynamic forces generated by plasma flow through the ESL.

Influence of band 3 protein absence and skeletal structures on amphiphile- and Ca 2+-induced shape alterations in erythrocytes: a study with lamprey ( Lampetra fluviatilis), trout ( Onchorhynchus mykiss) and human erythrocytes

Amphiphiles which induce either spiculated (echinocytic) or invaginated (stomatocytic) shapes in human erythrocytes, and ionophore A23187 plus Ca 2+, were studied for their capacity to induce shape alterations, vesiculation and hemolysis in the morphologically and structurally different lamprey and trout erythrocytes. Both qualitative and quantitative differences were found. Amphiphiles induced no gross morphological changes in the non-axisymmetric stomatocyte-like lamprey erythrocyte or in the flat ellipsoidal trout erythrocyte, besides a rounding up at higher amphiphile concentrations. No shapes with large broad spicula were seen. Nevertheless, some of the ‘echinocytogenic’ amphiphiles induced plasma membrane protrusions in lamprey and trout erythrocytes, from where exovesicles were shed. In trout erythrocytes, occurrence of corrugations at the cell rim preceded protrusion formation. Other ‘echinocytogenic’ amphiphiles induced invaginations in lamprey erythrocytes. The ‘stomatocytogenic’ amphiphiles induced invaginations in both lamprey and trout erythrocytes. Surprisingly, in trout erythrocytes, some protrusions also occurred. Some of the amphiphiles hemolyzed lamprey, trout and human erythrocytes at a significantly different concentration/membrane area. Ionophore A23187 plus Ca 2+ induced membrane protrusions and sphering in human and trout erythrocytes; however, the lamprey erythrocyte remained unperturbed. The shape alterations in lamprey erythrocytes, we suggest, are characterized by weak membrane skeleton–lipid bilayer interactions, due to band 3 protein and ankyrin deficiency. In trout erythrocyte, the marginal band of microtubules appears to strongly influence cell shape. Furthermore, the presence of intermediate filaments and nuclei, additionally affecting the cell membrane shear elasticity, apparently influences cell shape changes in lamprey and trout erythrocytes. The different types of shape alterations induced by certain amphiphiles in the cell types indicates that their plasma membrane phospholipid composition differs.

A model for red blood cell motion in glycocalyx-lined capillaries.

The interior surfaces of capillaries are lined with a layer (glycocalyx) of macromolecules bound or absorbed to the endothelium. Here, a theoretical model is used to analyze the effects of the glycocalyx on hematocrit and resistance to blood flow in capillaries. The glycocalyx is represented as a porous layer that resists penetration by red blood cells. Axisymmetric red blood cell shapes are assumed, and effects of cell membrane shear elasticity are included. Lubrication theory is used to compute the flow of plasma around the cell and within the glycocalyx. The effects of the glycocalyx on tube hematocrit (Fahraeus effect) and on flow resistance are predicted as functions of the width and hydraulic resistivity of the layer. A layer of width 1 micron and resistivity 10(8) dyn.s/cm4 leads to a relative apparent viscosity of approximately 10 in a 6-micron capillary at discharge hematocrit 45% and flow velocity of approximately 1 mm/s. This is consistent with experimental observations of increased flow resistance in microvessels in vivo, relative to glass tubes with the same diameters.

Resistance to blood flow in nonuniform capillaries.

Microvessels in living tissues an not uniform cylinders, and red blood cells (RBCs) are continually deformed when traversing them. This may contribute to higher resistance to blood flow observed in microvessels compared with that in corresponding uniform glass tubes. Here, a theoretical model was used to estimate flow resistance in nonuniform capillaries and its dependence on hematocrit, flow rate, and mechanical properties of RBCs. Single-file motion of RBCs through capillaries with sinusoidally varying cross-sections was simulated, assuming axisymmetrical geometry. Effects of cell membrane shear viscosity and elasticity were included. Lubrication theory was used to describe the plasma flow. Predicted resistance to blood flow in capillaries with variable cross-sections was substantially higher than in uniform vessels with the same mean diameters. Resistance depended on vessel geometry, flow rate, and hematocrit. At tube hematocrit 30%, the increase in resistance was 40%-58% when diameter varied between 4.5 and 6 microns with wavelength 20 microns and 58%-77% for variations between 4 and 5 microns with wavelength 10 microns. Larger relative increases in resistance were predicted for RBCs with increased membrane shear viscosity. Effects of transient RBC deformations in irregular capillaries contribute significantly to blood flow resistance in capillaries. However, this effect is not sufficient to account for the flow resistance observed in living tissues.

Motion of red blood cells in capillaries with variable cross-sections.

Red blood cells undergo continual deformation when traversing microvessels in living tissues. This may contribute to higher resistance to blood flow observed in living microvessels, compared with that in corresponding uniform glass tubes. We use a theoretical model to simulate single-file motion of red cells though capillaries with variable cross-sections, assuming axisymmetric geometry. Effects of cell membrane shear viscosity and elasticity are included, but bending resistance is neglected. Lubrication theory is used to describe the flow of surrounding plasma. When a red cell encounters a region of capillary narrowing, additional energy is dissipated, due to membrane viscosity, and due to narrowing of the lubrication layer, increasing the flow resistance. Predicted resistance to cell motion in a vessel with periodic constrictions (diameter varying between 5 microns and 4 microns) is roughly twice that in a uniform vessel with diameter 4.5 microns. Effects of transient red cell deformations may contribute significantly to blood flow resistance in living microvessels.

Analysis of red blood cell motion through cylindrical micropores: effects of cell properties

Filtration through micropores is frequently used to assess red blood cell deformability, but the dependence of pore transit time on cell properties is not well understood. A theoretical model is used to simulate red cell motion through cylindrical micropores with diameters of 3.6, 5, and 6.3 microns, and 11-microns length, at driving pressures of 100-1000 dyn/cm2. Cells are assumed to have axial symmetry and to conserve surface area during deformation. Effects of membrane shear viscosity and elasticity are included, but bending resistance is neglected. A time-dependent lubrication equation describing the motion of the suspending fluid is solved, together with the equations for membrane equilibrium, using a finite difference method. Predicted transit times are consistent with previous experimental observations. Time taken for cells to enter pores represents more than one-half of the transit time. Predicted transit time increases with increasing membrane viscosity and with increasing cell volume. It is relatively insensitive to changes in internal viscosity and to changes in membrane elasticity except in the narrowest pores at low driving pressures. Elevating suspending medium viscosity does not increase sensitivity of transit time to membrane properties. Thus filterability of red cells is sensitively dependent on their resistance to transient deformations, which may be a key determinant of resistance to blood flow in the microcirculation.

Measurement of erythrocyte membrane elasticity by flicker eigenmode decomposition

We have studied the flickering of erythrocytes at wavelengths comparable to the cell dimension. To do this we have analyzed the edge fluctuations of the cell to a resolution of 5 nm by combining phase contrast microscopy with fast image processing. By measuring the edge excitations simultaneously at four orthogonal positions around the cell, the eigenmodes of equal azimuthal mode numbers m = 0,1,2 could be separated. From a continuous time sequence of 100 s of video frames taken at 40 ms time intervals, we determined the time-auto correlation function for the modes m = 0,1,2 and calculated their mean square amplitudes <delta n2m> as well as their decay times tau m. To explain the results we also present the theoretically calculated energy eigenmodes of an erythrocyte, accounting for the constraint that the cell is in contact with the substrate along an annular ring, which agreed well with the experimental findings. We found that the softest mode is a "hindered translational" mode with m = 1 of the adhered cell, which is almost insensitive to the shear elastic modulus. Comparison of the calculated and measured amplitudes yielded an average value for the bending stiffness of kc = 4 x 10(-19) J, which is much larger than the value obtained by flicker analysis at short wavelengths (kc = 2.3 x 10(-20) J). It would, however, agree well with the value expected from the red cell membrane area compressibility modulus of K = 4.5 x 10(-1)N/m, which corresponds to a lipid bilayer containing approximately 50 mol % of cholesterol. In contradiction to our theoretical expectations we found that the flicker eigenmodes seemed not to be influenced by the membrane shear elasticity, which will be discussed in terms of an unusual coupling between the lipid bilayer and the cytoskeleton.

Effects of Two Low-Osmolar Contrast Media, Ioxaglate and Iopamidol, on Erythrocyte Membrane Elasticity

The effect of ioxaglate and iopamidol, two recently developed low-osmolality contrast media, on the shear elasticity of erythrocyte membranes was studied at an iodine concentration of 300 mg/mL and at a 20% volume concentration and compared with that obtained for control solutions matched in osmolality. The authors used a micromanipulation technique, which consists of visualizing deformations of individual erythrocytes when gently aspirated into the tip of a glass micropipette by an accurately controlled pressure. An erythrocyte membrane shear elasticity modulus mu was then deduced. An increase in mu corresponded to an increase in erythrocyte membrane rigidity. In all cases, the erythrocytes remained discocytic. The shear elasticity modulus of the erythrocyte membrane is found to be (1) in the presence of ioxaglate (4.3 +/- 0.9 microN/m) lower (P < .001) than in the presence of hyperosmolar saline (6.2 +/- 1.3 microN/m) and lower (P < .02) than in the presence of iso-osmolar control (4.7 +/- 0.7 microN/m); (2) in the presence of iopamidol (5.4 +/- 0.7 microN/m) lower (P < .001) than in the presence of hyperosmolar sucrose (6.4 +/- 1.2 microN/m) and higher (P < .001) than in the presence of iso-osmolar control (4.7 +/- 0.7 microN/m); and (3) lower (P < .001) in the presence of ioxaglate (4.3 +/- 0.9 microN/m) than in the presence of iopamidol (5.4 +/- 0.7 microN/m). Under the experimental conditions used, both contrast media (ioxaglate and iopamidol) modify the erythrocyte membrane shear elasticity modulus less than do the matched hyperosmolar controls. Moreover, ioxaglate makes the erythrocyte membrane less rigid, and iopamidol makes the erythrocyte membrane more rigid than does the iso-osmolar control.

The axisymmetric deformation of a red blood cell in uniaxial straining Stokes flow

The axisymmetric deformation of a red blood cell placed in a uniaxial straining Stokes flow is considered. The cell is modelled as a fluid capsule that contains a Newtonian fluid, and is bounded by an area-preserving membrane with negligible resistance to bending. First, it is theoretically demonstrated that spheroidal cells with isotropic membrane tension constitute stationary configurations. To compute transient cell deformations, a numerical procedure is developed based on the boundary-integral method for Stokes flow. Calculations show that initially prolate or oblate cells with isotropic membrane tension deform into stationary spheroids. Cells with a highly oblate initial shape may develop a persistent small pocket along their axis during the deformation. The shear elasticity of the membrane prevents folding, but may cause the formation of sharp corners and concave regions along the cell contour. A decrease in the membrane shear elasticity results in substantial increase in the magnitude of the transient and asymptotic membrane tensions. The maximum strain rate below which a red blood cell remains intact is estimated to be ex = 105 s−1.

The influence of red cell mechanical properties on flow through single capillary-sized pores.

The resistive pulse technique was used to study the influence of specific mechanical properties of the red cell on its ability to enter and flow through single capillary-sized pores with diameters of 3.6, 5.0 and 6.3 micron and lengths of 11 micron. A two-fold increase in membrane shear elasticity resulted in a 40 percent increase in the cell's transit time through a 3.6 micron pore but produced no change in transit time through a 6.3 micron pore. A two-fold increase in membrane shear viscosity produced a 40 percent increase in transit time through the 3.6 micron pore and small but significant increases in transit times through the larger pores. Osmotically dehydrated cells showed no increase in transit time through a 6.3 micron pore, but showed increases in transit times of 50 to 70 percent through 5.0 and 3.6 micron pores. Dense red cells showed increased transit times through both 5.0 micron and 6.0 micron pores. These results indicate that for cells with normal geometric properties, the membrane's shear viscosity and elasticity only influence the cell's transit through pores of 5 micron or less in diameter. However, alterations in the cell's geometric properties can extend the influence of membrane shear properties to larger diameter pores.

Reductions of erythrocyte membrane viscoelastic coefficients reflect spectrin deficiencies in hereditary spherocytosis.

Hereditary spherocytosis is a common hemolytic anemia associated with deficiencies in spectrin, the principal structural protein of the erythrocyte membrane-skeleton. We have examined 20 different individuals from 10 spherocytosis kindreds and 2 elliptocytosis kindreds to determine the effects of different levels of spectrin deficiency on the viscoelastic properties of the erythrocyte membrane. Micropipettes were used to perform single-cell micromechanical measurements of approximately 1,000 individual cells to determine the membrane elastic shear modulus, the apparent membrane bending stiffness, and whole cell recovery time constant for the different cell populations. The membrane viscosity was calculated by the product of the shear modulus and the recovery time constant. Results show correlation between the fractional reduction in shear modulus and the fractional reduction in spectrin content (determined by spectrin radioimmunoassay) and spectrin density (determined by the ratios of spectrin to band 3 on electrophoresis gels) suggesting that membrane shear elasticity is directly proportional to the surface density of spectrin on the membrane (P less than 0.001). The apparent membrane bending stiffness is also reduced in proportion to the density of spectrin (P less than 0.001). The membrane viscosity is reduced relative to control (P less than 0.001), but the nature of the relationship between spectrin density and membrane viscosity is less clearly defined. These studies document striking relationships between partial deficiencies of erythrocyte spectrin and specific viscoelastic properties of the mutant membranes.

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.

Selective alteration of erythrocyte deformability by SH-reagents. Evidence for an involvement of spectrin in membrane shear elasticity

In order to elucidate the molecular basis of membrane shear elasticity, the effect of membrane protein modification by SH-reagents on the deformability of human erythrocytes was studied. Deformability was quantified by measuring the elongation of erythrocytes subjected to viscometric flow in a transparent cone-plate viscometer. Impermeable SH-reagents proved to have no mechanical effect. Many, but not all, permeable SH-reagents markedly decreased the elongation. Among these, bifunctional SH-reagents (e.g. diamide, tetrathionate and N, N′- p-phenylenedimaleimide) able to cross-link membrane SH-groups were more effective than monofunctional SH-reagents (e.g. N-ethylmaleimide and ethacrynic acid). The bifunctional SH-reagents produced a 50% decrease of elongation after modification of less than 5% of the membrane SH-groups. In contrast, for a comparable effect, more than 20% of the SH-groups had to be modified by the monofunctional reagents. The effect of SH-oxidizing agents was fully reversible after treatment with disulfide-reducing agents. All bifunctional SH-reagents induced a dimerization of a small fraction of spectrin. Analysis of the distribution of the diamide-induced disulfide bonds among the various membrane protein fractions showed that this agent preferentially acts on the spectrin polypeptides. The results provide direct experimental evidence that the native arrangement of spectrin is essential for the shear resistance of the erythrocyte membrane and that introduction of small numbers of intermolecular cross-links as well as modification within the molecule lead to a rapid loss of this function.