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.     

Interaction of calmodulin with the red cell and its membrane skeleton and with spectrin

The binding of calmodulin to red cell membrane cytoskeletons and to purified spectrin from red cells and bovine brain spectrin (fodrin) has been examined. Under physiological solvent conditions binding can be measured by ultracentrifugal pelleting assays. The membrane cytoskeletons contained a single class of binding sites, with a concentration similar to that of spectrin dimers and an association constant of 1.5 X 10(5) M-1. Binding is calcium dependent and is suppressed by the calmodulin inhibitor trifluoperazine. The binding showed a marked dependence on ionic strength, with a maximum at 0.05 M, and a steep dependence on pH, with a maximum at pH 6.5. It was unaffected by 5 mM magnesium. An azidocalmodulin derivative, under the conditions of our experiments, did not label the spectrin-containing complex, although it could be used to demonstrate binding to fodrin. Binding of calmodulin to spectrin tetramers and fodrin in solution could be demonstrated by a pelleting assay after addition of F-actin. Calculations (which are necessarily rough) suggest that at the free calcium concentration prevailing in a normal red cell about 1 in 20 of the calmodulin binding sites in spectrin will be occupied; this proportion will rise rapidly with increasing intracellular calcium. To determine whether inhibition of calmodulin binding to red cell proteins disturbs the control of cell shape, as has been suggested, calcium ions were removed from the cell by addition of an ionophore and of ethylene glycol bis(beta-aminoethyl ether)-N,N,N',N'-tetraacetic acid to the external medium. This did not affect the discoid shape. Trifluoperazine still induced stomatocytosis, exactly as in untreated cells.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Model of red blood cell membrane skeleton: electrical and mechanical properties

A theoretical membrane skeleton model of erythrocyte has been developed and successfully applied to interpret electrical and mechanical properties of the red blood cell spectrin-actin network. The model is based on the structure of the membrane skeleton that is comprised of unit cells each containing an actin protofilament and shooting forth a few spectrin heterodimers. The loose ends of the heterodimers of adjacent cells can form bonds with each other giving rise to an integrated network. The number of bonds depends on the temperature. The bond length being excessive (2.6 times the distance between the centers of adjacent cells), the bonds are flexible, and can thus be regarded as entropy springs. The advanced model has been employed to calculate the shear modulus of the membrane skeleton as well as to establish its temperature dependence. In a wide range of temperatures mu(T) is a decreasing function well fitting the experimental data. The relationship between the membrane bilayer-free size of the skeleton and the ionic strength of the solution has been derived to appear in good agreement with the results obtained previously. Experimental data combined with the advanced theory yield the average number of heterodimers per unit cell, m0, as equal to ca. 5; the spectrin heterodimer charge has been estimated.     

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.     

Conformation and elasticity of the isolated red blood cell membrane skeleton.

We studied the structure and elasticity of membrane skeletons from human red blood cells (RBCs) during and after extraction of RBC ghosts with nonionic detergent. Optical tweezers were used to suspend individual cells inside a flow chamber, away from all surfaces; this procedure allowed complete exchange of medium while the low-contrast protein network of the skeleton was observed by high resolution, video-enhanced differential interference-contrast (DIC) microscopy. Immediately following extraction in a 5 mM salt buffer, skeletons assumed expanded, nearly spherical shapes that were uncorrelated with the shapes of their parent RBCs. Judging by the extent of thermal undulations and by their deformability in small flow fields, the bending rigidity of skeletons was markedly lower than that of either RBCs or ghosts. No further changes were apparent in skeletons maintained in this buffer for up to 40 min at low temperatures (T less than 10 degrees C), but skeletons shrank when the ionic strength of the buffer was increased. When the salt concentration was raised to 1.5 M, shrinkage remained reversible for approximately 1 min but thereafter became irreversible. When maintained in 1.5 M salt buffer for longer periods, skeletons continued to shrink, lost flexibility, and assumed irregular shapes: this rigidification was irreversible. At this stage, skeletons closely resembled those isolated in standard bulk preparations. We propose that the transformation to the rigid, irreversibly shrunken state is a consequence of spectrin dimer-dimer reconnections and that these structural rearrangements are thermally activated. We also measured the salt-dependent size of fresh and bulk extracted skeletons. Our measurements suggest that, in situ, the spectrin tethers are flexible, with a persistence length of approximately 10 nm at 150 mM salt.     

Evidence for a relationship between protein glycation and red blood cell membrane fluidity

This study examines the relationship between protein glycation and membrane fluidity in RBC membranes. Incubation of RBC membranes of healthy subjects with 25mM glucose or galactose at 37 degrees C induced a 38% (p less than 0.02) increase in protein glycation (using furosine determination by HPLC) and higher fluidity (p less than 0.05) in DPH polarization ratio). However, incubation of RBC membranes from diabetic subjects under the same conditions did not modify either membrane fluidity or protein glycation; protein glycation was above normal before incubation because of the high diabetic plasma glucose. There was no difference in the membrane fluidities of 21 healthy subjects and 32 diabetic subjects, despite a significantly elevated protein glycation in diabetics. Furthermore, there was no change with respect to age in either population. We conclude that other in vivo factors, such as membrane lipid changes (increase in CL/PL ratio) or formation of advanced Maillard products and peroxidation in the diabetic subjects, could be responsible for the difference between these in vitro results and the in vivo situation.     

Influence of network topology on the elasticity of the red blood cell membrane skeleton.

A finite-element network model is used to investigate the influence of the topology of the red blood cell membrane skeleton on its macroscopic mechanical properties. Network topology is characterized by the number of spectrin oligomers per actin junction (phi a) and the number of spectrin dimers per self-association junction (phi s). If it is assumed that all associated spectrin is in tetrameric form, with six tetramers per actin junction (i.e., phi a = 6.0 and phi s = 2.0), then the topology of the skeleton may be modeled by a random Delaunay triangular network. Recent images of the RBC membrane skeleton suggest that the values for these topological parameters are in the range of 4.2 < phi a < 5.5 and 2.1 < phi s < 2.3. Model networks that simulate these realistic topologies exhibit values of the shear modulus that vary by more than an order of magnitude relative to triangular networks. This indicates that networks with relatively sparse nontriangular topologies may be needed to model the RBC membrane skeleton accurately. The model is also used to simulate skeletal alterations associated with hereditary spherocytosis and Southeast Asian ovalocytosis.     

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.     

Viscoelastic properties of the human red blood cell membrane. II. Area and volume of individual red cells entering a micropipette.

Previous work demonstrated that human red cells can be drawn into cylindrical glass micropipettes of internal diameter approximately 2.0 mum without lysing. For pipettes of less than approximately 2.9 mum inside diameter, the red cell must become less spherical, that is, reduce its volume-to-area ratio. In this work measurements were made from 16-mm film records that allowed the determination of the cellular area and volume of individual erythrocytes as they were drawn into a 2.0-mum pipette with negative pressures. The results showed that the total surface area of the membrane remains constant and that the cell endures the passage into the pipette by losing volume. The volume loss was interpreted to be due to cell water and solute loss when the membrane is under stress. The loss of cell volume, rather than the stretching of the membrane, adds confirmation that although it is very deformable, the membrane is very resistant to two-dimensional strain.     

Minimum energy analysis of membrane deformation applied to pipet aspiration and surface adhesion of red blood cells.

An experimental procedure is demonstrated which can be used to determine the interfacial free energy density for red cell membrane adhesion and membrane elastic properties. The experiment involves micropipet aspiration of a flaccid red blood cell and manipulation of the cell proximal to a surface where adhesion occurs. A minimum free energy method is developed to model the equilibrium contour of unsupported membrane regions and to evaluate the partial derivatives of the total free energy, which correspond to the micropipet suction force and the interfacial free energy density of adhesion. It is shown that the bending elasticity of the red cell membrane does not contribute significantly to the pressure required to aspirate a flaccid red cell. Based on experimental evidence, the upper bound for the bending or curvature elastic modulus of the red cell membranes is 10-12 ergs (dyn-cm). Analysis of the adhesion experiment shows that interfacial free energy densities for red cell adhesion can be measured from a lower limit of 10-4 ergs/cm2 to an upper limit established by the membrane tension for lysis of 5-10 ergs/cm2.     

The role of human red blood cell membrane skeletal proteins in repetitive membrane strain and rupture

The influence of the membrane skeleton on cell membrane deformability, elasticity, and rupture after repetitive cycles of membrane strain, release and rupture was investigated. Human red blood cells were electrofused to doublets, which showed the post-fusion oscillation-movement. Geometrical developments of heat-treated cells were measured and compared to control cells. Alterations of cluster length and fusion zone diameter during repetitive colloidosmotic swelling period grow with heat treatment, and the number of precedent swell phases has minor influence on these values. Irrespective of the treatment, the geometrical doublet configuration at which a membrane rupture is initiated has an almost constant roundness index of 0.89. Increasing heat treatment temperature was shown to affect both deformability and elasticity of the membrane, such that doublets start each swell phase of the oscillation cycle from decreased roundness values. Evidence is given that there is a difference in the mechanical properties between the membrane at the fusion zone and the membrane of native red blood cells.     

The role of human red blood cell membrane skeletal proteins in repetitive membrane strain and rupture

The influence of the membrane skeleton on cell membrane deformability, elasticity, and rupture after repetitive cycles of membrane strain, release and rupture was investigated. Human red blood cells were electrofused to doublets, which showed the post-fusion oscillation-movement. Geometrical developments of heat-treated cells were measured and compared to control cells. Alterations of cluster length and fusion zone diameter during repetitive colloidosmotic swelling period grow with heat treatment, and the number of precedent swell phases has minor influence on these values. Irrespective of the treatment, the geometrical doublet configuration at which a membrane rupture is initiated has an almost constant roundness index of 0.89. Increasing heat treatment temperature was shown to affect both deformability and elasticity of the membrane, such that doublets start each swell phase of the oscillation cycle from decreased roundness values. Evidence is given that there is a difference in the mechanical properties between the membrane at the fusion zone and the membrane of native red blood cells.     

Deformation-enhanced fluctuations in the red cell skeleton with theoretical relations to elasticity, connectivity, and spectrin unfolding.

To assess local elasticity in the red cell's spectrin-actin network, nano-particles were tethered to actin nodes and their constrained thermal motions were tracked. Cells were both immobilized and controllably deformed by aspiration into a micropipette. Since the network is well-appreciated as soft, thermal fluctuations even in an unstressed portion of network were expected to be many tens of nanometers based on simple equipartition ideas. Real-time particle tracking indeed reveals such root-mean-squared motions for 40-nm fluorescent beads either tethered to actin directly within a cell ghost or connected to actin from outside a cell via glycophorin. Moreover, the elastically constrained displacements are significant on the scale of the network's internodal distance of approximately 60-80 nm. Surprisingly, along the aspirated projection-where the network is axially extended by as much as twofold or more-fluctuations in the axial direction are increased by almost twofold relative to motions in the unstressed network. The molecular basis for such strain softening is discussed broadly in terms of force-driven transitions. Specific considerations are given to 1) protein dissociations that reduce network connectivity, and 2) unfolding kinetics of a localized few of the red cell's approximately 10(7) spectrin repeats.     

Influence of microflow on hepatic sinusoid blood flow and red blood cell deformation

Hepatic sinusoids present complex anatomical structures such as the endothelial sieve pores and the Disse space, which govern the microscopic blood flow in the sinusoids and are associated with structural variations in liver fibrosis and cirrhosis. However, the contributions of the permeability of endothelial and collagen layers and the roughness of hepatocyte microvilli to the features of this microflow remain largely unknown. Here, an immersed boundary method coupled with a lattice Boltzmann method was adopted in an in vitro hepatic sinusoidal model, and flow field and erythrocyte deformation analyses were conducted by introducing three new source terms including permeability of the endothelial layer, resistance of hepatocyte microvilli and collagen layers, and deformation of red blood cells (RBCs). Numerical calculations indicated that alterations in endothelial permeability could significantly affect the flow velocity and flow rate distributions in hepatic sinusoids. Interestingly, a biphasic regulating pattern of shear stress occurred simultaneously on the surface of hepatocytes and the lower side of endothelium, i.e., the shear stress increased with increased thickness of hepatocyte microvilli and collagen layer when the endothelial permeability was high but decreased with the increase of the thickness at low endothelial permeability. Additionally, this specified microflow manipulates typical RBC deformation inside the sinusoid, yielding one-third of the variation of deformable index with varied endothelial permeability. These simulations not only are consistent with experimental measurements using in vitro liver sinusoidal chip but also elaborate the contributions of endothelial and collagen layer permeability and wall roughness. Thus, our results provide a basis for further characterizing this microflow and understanding its effects on cellular migration and deformation in the hepatic sinusoids.     

Effects of intracellular Ca2+ and proteolytic digestion of the membrane skeleton on the mechanical properties of the red blood cell membrane

Intracellular Ca2+ at concentrations ranging from 0 to 10 mumol/l increases the shear modulus of surface elasticity (mu) and the surface viscosity (eta) of human red blood cells by 20% and 70%, respectively. K+ selective channels in the red cell membrane become activated by Ca2+. The activation still occurs to the same extent when the membrane skeleton is degraded by incorporation of trypsin into resealed red cell ghosts, suggesting that the channel activation is not controlled by the proteins of the membrane skeleton and is independent of mu and eta. Incorporation of trypsin at concentrations ranging from 0 to 100 ng/ml into red cell ghosts leads to a graded digestion of spectrin, a cleavage of the band 3 protein and a release of the binding proteins ankyrin and band 4.1. These alterations are accompanied by an increase of the lateral mobility of the band 3 protein which, at 40 ng/ml trypsin, reaches a plateau value where the rate of lateral diffusion is enhanced by about two orders of magnitude above the rate measured in controls without trypsin. Proteolytic digestion by 10-20 ng/ml trypsin leads to a degradation of more than 40% of the spectrin and increases the rate of lateral diffusion to about 20-70% of the value observed at the plateau. Nevertheless, mu and eta remain virtually unaltered. However, the stability of the membrane is decreased to the point where a slight mechanical extension, or the shear produced by centrifugation results in disintegration and vesiculation, precluding measurements of eta and mu in ghosts treated with higher concentrations of trypsin. These findings indicate that alterations of the structural integrity of the membrane skeleton exert drastically different effects on mu and eta on the one hand and on the stability of the membrane on the other.     

Direct measurement of the area expansion and shear moduli of the human red blood cell membrane skeleton.

The area expansion and the shear moduli of the free spectrin skeleton, freshly extracted from the membrane of a human red blood cell (RBC), are measured by using optical tweezers micromanipulation. An RBC is trapped by three silica beads bound to its membrane. After extraction, the skeleton is deformed by applying calibrated forces to the beads. The area expansion modulus K(C) and shear modulus mu(C) of the two-dimensional spectrin network are inferred from the deformations measured as functions of the applied stress. In low hypotonic buffer (25 mOsm/kg), one finds K(C) = 4.8 +/- 2.7 microN/m, mu(C) = 2.4 +/- 0.7 microN/m, and K(C)/mu(C) = 1.9 +/- 1.0. In isotonic buffer, one measures higher values for K(C), mu(C), and K(C)/mu(C), partly because the skeleton collapses in a high-ionic-strength environment. Some data concerning the time evolution of the mechanical properties of the skeleton after extraction and the influence of ATP are also reported. In the Discussion, it is shown that the measured values are consistent with estimates deduced from experiments carried out on the intact membrane and agree with theoretical and numerical predictions concerning two-dimensional networks of entropic springs.     

A modified micropipette aspiration technique and its application to tether formation from human neutrophils

Tether formation, which is mechanically characterized by its threshold force and effective viscosity, is involved in neutrophil emigration from blood circulation. Using the micropipette aspiration technique, which was improved by quantitative contact control and computerized data analysis, we extracted tethers from human neutrophils treated with IL-8, PMA, or cytochalasin D. We found that both IL-8 and PMA elevated the threshold force to about twice as large as the value for passive neutrophils. All these treatments decreased the effective viscosity dramatically (approximately 80%). With a novel method, the residual cortical tension of the cytochalasin-D-treated non-spherical neutrophils was measured to be approximately 8.8 pN/microm.     

The deformation of spherical vesicles with permeable, constant-area membranes: application to the red blood cell

The deformation of an initially spherical vesicle of radius a with a permeable membrane under extensive forces applied at its poles is calculated as a function of the in-plane shear modulus, H, and the out-of-plane bending modulus, B, using an axisymmetric theory that is valid for large deformations. Suitably nondimensionalized, the results depend upon a single nondimensional parameter, C identical with a(2)H/B. For small deformations, the calculated force-polar strain curves are linear and, under these conditions, the slope of the curve determines only C, not the values of H and B separately. Independent determination of H and B from experimental measurements require deformations that are large enough to produce nonlinear behavior. Simple approximations for large and small C are given, which are applied to experimental measurements on red blood cell ghosts that have been made permeable by treatment with saponin.