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.     

Depletion of membrane skeleton in red blood cell vesicles.

A possible physical interpretation of the partial detachment of the membrane skeleton in the budding region of the cell membrane and consequent depletion of the membrane skeleton in red blood cell vesicles is given. The red blood cell membrane is considered to consist of the bilayer part and the membrane skeleton. The skeleton is, under normal conditions, bound to the bilayer over its whole area. It is shown that, when in such conditions it is in the expanded state, some cell shape changes can induce its partial detachment. The partial detachment of the skeleton from the bilayer is energetically favorable if the consequent decrease of the skeleton expansion energy is larger than the corresponding increase of the bilayer-skeleton binding energy. The effect of shape on the skeleton detachment is analyzed theoretically for a series of the pear class shapes, having decreasing neck diameter and ending with a parent-daughter pair of spheres. The partial detachment of the skeleton is promoted by narrowing of the cell neck, by increasing the lateral tension in the skeleton and its area expansivity modulus, and by diminishing the attraction forces between the skeleton and the bilayer. If the radius of the daughter vesicle is sufficiently small relative to the radius of the parent cell, the daughter vesicle can exist either completely underlaid with the skeleton or completely depleted of the skeleton.     

Axisymmetric optical-trap measurement of red blood cell membrane elasticity

The elastic properties of the cell membrane play a crucial role in determining the equilibrium shape of the cell, as well as its response to the external forces it experiences in its physiological environment. Red blood cells are a favored system for studying membrane properties because of their simple structure: a lipid bilayer coupled to a membrane cytoskeleton and no cytoplasmic cytoskeleton. An optical trap is used to stretch a red blood cell, fixed to a glass surface, along its symmetry axis by pulling on a micron-sized latex bead that is bound at the center of the exposed cell dimple. The system, at equilibrium, shows Hookean behavior with a spring constant of 1.5×10(-6)?N/m over a 1-2 μm range of extension. This choice of simple experimental geometry preserves the axial symmetry of the native cell throughout the stretch, probes membrane deformations in the small-extension regime, and facilitates theoretical analysis. The axisymmetry makes the experiment amenable to simulation using a simple model that makes no a priori assumption on the relative importance of shear and bending in membrane deformations. We use an iterative relaxation algorithm to solve for the geometrical configuration of the membrane at mechanical equilibrium for a range of applied forces. We obtain estimates for the out-of-plane membrane bending modulus B≈1×10(-19)?Nm and an upper limit to the in-plane shear modulus H<2×10(-6)?N/m. The partial agreement of these results with other published values may serve to highlight the dependence of the cell's resistance to deformation on the scale and geometry of the deformation.     

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.     

Hereditary disorders of the red cell membrane skeleton

The hereditary hemolytic anemias include a heterogeneous class of disorders caused by defects in the proteins that constitute the membrane skeleton of the red blood cell. The combination of classical and molecular genetics together with clinical findings is rapidly improving our understanding of the basis of these defects.     

Interactions of Plasmodium falciparum erythrocyte membrane protein 3 with the red blood cell membrane skeleton

Plasmodium falciparum parasites express and traffick numerous proteins into the red blood cell (RBC), where some associate specifically with the membrane skeleton. Importantly, these interactions underlie the major alterations to the modified structural and functional properties of the parasite-infected RBC. P. falciparum Erythrocyte Membrane Protein 3 (PfEMP3) is one such parasite protein that is found in association with the membrane skeleton. Using recombinant PfEMP3 proteins in vitro, we have identified the region of PfEMP3 that binds to the RBC membrane skeleton, specifically to spectrin and actin. Kinetic studies revealed that residues 38-97 of PfEMP3 bound to purified spectrin with moderately high affinity (K(D(kin))=8.5 x 10(-8) M). Subsequent deletion mapping analysis further defined the binding domain to a 14-residue sequence (IFEIRLKRSLAQVL; K(D(kin))=3.8 x 10(-7) M). Interestingly, this same domain also bound to F-actin in a specific and saturable manner. These interactions are of physiological relevance as evidenced by the binding of this region to the membrane skeleton of inside-out RBCs and when introduced into resealed RBCs. Identification of a 14-residue region of PfEMP3 that binds to both spectrin and actin provides insight into the potential function of PfEMP3 in P. falciparum-infected RBCs.     

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.     

Elasticity of the human red blood cell skeleton

We have measured by optical tweezers micromanipulations the area expansion and the shear moduli of spectrin skeletons freshly extracted from human red blood cells, in different controlled salinity conditions. At medium osmolarity (150 mOsm/kg), we measure KC=9.7+/-3.4 microN/m, muC=5.7+/-2.3 microN/m, KC/muC=2.1+/-0.7. When decreasing the osmolarity, both KC and muC decrease, while KC/muC is nearly constant and equal to about 2. This result is consistent with the predictions made when modeling the spectrin skeleton by a two-dimensional triangular lattice of springs. From the measured elastic moduli we estimate the persistence length of a spectrin filament: xi approximately 2.5 nm at 150 mOsm/kg.     

Interaction of the exported malaria protein Pf332 with the red blood cell membrane skeleton

Intra-erythrocytic Plasmodium falciparum malaria parasites synthesize and export numerous proteins into the red blood cell (RBC) cytosol, where some bind to the RBC membrane skeleton. These interactions are responsible for the altered antigenic, morphological and functional properties of parasite-infected red blood cells (IRBCs). Plasmodium falciparum protein 332 (Pf332) is a large parasite protein that associates with the membrane skeleton and who's function has recently been elucidated. Using recombinant fragments of Pf332 in in vitro interaction assays, we have localised the specific domain within Pf332 that binds to the RBC membrane skeleton to an 86 residue sequence proximal to the C-terminus of Pf332. We have shown that this region partakes in a specific and saturable interaction with actin (K_d = 0.60 µM) but has no detectable affinity for spectrin. The only exported malaria protein previously known to bind to actin is PfEMP3 but here we demonstrate that there is no competition for actin-binding between PfEMP3 and Pf332, suggesting that they bind to different target sequences in actin.     

Interactions of Plasmodium falciparum erythrocyte membrane protein 3 with the red blood cell membrane skeleton

Plasmodium falciparum parasites express and traffick numerous proteins into the red blood cell (RBC), where some associate specifically with the membrane skeleton. Importantly, these interactions underlie the major alterations to the modified structural and functional properties of the parasite-infected RBC. P. falciparum Erythrocyte Membrane Protein 3 (PfEMP3) is one such parasite protein that is found in association with the membrane skeleton. Using recombinant PfEMP3 proteins in vitro, we have identified the region of PfEMP3 that binds to the RBC membrane skeleton, specifically to spectrin and actin. Kinetic studies revealed that residues 38-97 of PfEMP3 bound to purified spectrin with moderately high affinity (K_D(kin) = 8.5 × 10^− 8 M). Subsequent deletion mapping analysis further defined the binding domain to a 14-residue sequence (IFEIRLKRSLAQVL; K_D(kin) = 3.8 × 10^− 7 M). Interestingly, this same domain also bound to F-actin in a specific and saturable manner. These interactions are of physiological relevance as evidenced by the binding of this region to the membrane skeleton of inside-out RBCs and when introduced into resealed RBCs. Identification of a 14-residue region of PfEMP3 that binds to both spectrin and actin provides insight into the potential function of PfEMP3 in P. falciparum-infected RBCs.     

Thermoelasticity of red blood cell membrane.

The elastic properties of the human red blood cell membrane have been measured as functions of temperature. The area compressibility modulus and the elastic shear modulus, which together characterize the surface elastic behavior of the membrane, have been measured over the temperature range of 2-50 degrees C with micropipette aspiration of flaccid and osmotically swollen red cells. In addition, the fractional increase in membrane surface area from 2-50 degrees C has been measured to give a value for the thermal area expansivity. The value of the elastic shear modulus at 25 degrees C was measured to be 6.6 X 10(-3) dyne/cm. The change in the elastic shear modulus with temperature was -6 X 10(-5) dyne/cm degrees C. Fractional forces were shown to be only on the order of 10-15%. The area compressibility modulus at 25 degrees C was measured to be 450 dyne/cm. The change in the area compressibility modulus with temperature was -6 dyne/cm degrees C. The thermal area expansivity for red cell membrane was measured to be 1.2 X 10(-3)/degrees C. With this data and thermoelastic relations the heat of expansion is determined to be 110-200 ergs/cm2; the heat of extension is 2 X 10(-2) ergs/cm2 for unit extension of the red cell membrane. The heat of expansion is of the order anticipated for a lipid bilayer idealized as twice the behavior of a monolayer at an oil-water interface. The observation that the heat of extension is positive demonstrates that the entropy of the material increases with extension, and that the dominant mechanism of elastic energy storage is energetic. Assuming that the red cell membrane shear rigidity is associated with "spectrin," unit extension of the membrane increases the configurational entropy of spectrin by 500 cal/mol.     

A physical basis for red cell membrane elasticity

An estimate is made of the effect of lipid-water interactions at the membrane surface on observed membrane elasticity in the red blood cell. It is shown that elastic effects are expected to result from these interactions even in a completely fluid membrane. A simple statistical model is described and used to estimate the magnitude of the resultant elasticity. The estimate thus derived is compared with results of experiments during which a biaxial stress is applied to the membrane. The derived elasticity is sufficient to account for the results of these studies. Other properties of the red cell membrane are discussed in the light of this result.     

Influence of calmodulin on the human red cell membrane skeleton

The calcium receptor calmodulin interacts with components of the human red cell membrane skeleton as well as with the membrane. Under physiological salt conditions, calmodulin has a calcium-dependent affinity for spectrin, one of the major components of the membrane skeleton. It is apparent from our results that calmodulin inhibits the ability of erythrocyte spectrin (when preincubated with filamentous actin) to create nucleation centers and thereby to seed actin polymerization. The gelation of filamentous actin induced by spectrin tetramers is also inhibited by calmodulin. The inhibition is calcium dependent and decreases with increasing pH, similar to the binding of calmodulin to spectrin. Direct binding studies using aqueous two-phase partition indicate that calmodulin interferes with the binding of actin to spectrin. Even in the presence of protein 4.1, which is believed to stabilize the ternary complex, calmodulin has an inhibitory effect. Since calmodulin also inhibits the corresponding activities of brain spectrin (fodrin), it appears likely that calmodulin may modulate the organization of cytoskeletons containing actin and spectrin or spectrin analogues.     

Elasticity of the human red cell membrane skeleton. Effects of temperature and denaturants.

The molecular basis for the elasticity of the human erythrocyte membrane was explored. Skeletons were released from ghosts in Triton X-100 and their dimensions followed by dark-field microscopy and packed volume. The rest size of skeletons was assumed to reflect the balance point between expansion (deformation) driven by electrostatic repulsions among the excess of fixed negative charges on the proteins and contraction (recovery) driven by their elasticity. The size of skeletons decreased with increasing temperature. This finding suggests that entropy drives elasticity. The requisite entropy change could be associated with either the configurational freedom of flexible protein chains or with the solvation of side chains exposed during protein dissociation (hydrophobic effects). To distinguish between these two alternatives, we tested the impact of two weak denaturants, 10% ethanol and 20 nM lithium 3,5-diiodosalicylate. Both agents reversibly promoted the expansion of skeletons, presumably by reducing their elasticity. Since the conformation of random coils and globular proteins should not be significantly altered by these mild treatments, this finding strongly suggests a role for weak interdomain and/or interprotein associations. We conclude that the elasticity of the red cell membrane skeleton may not derive from the configurational entropy of flexible coils. Rather, the elastic energy may arise from reversible dissociations of weak but specific intramolecular and/or intermolecular contacts, presumably within deformed spectrin filaments.     

The stress-free shape of the red blood cell membrane.

The two main proposals found in the literature for the stress-free shape of the red cell membrane are (a) the bioconcave shape and (b) the sphere of the same surface area. These possibilities are evaluated in this paper using theoretical modeling of equilibrium membrane shapes according to Zarda et al. (1977. J. Biomech. 10:211-221) and by comparison to experiments on red cells whose membrane shear modulus has been increased by treatment with diamide. Neither proposal is found to be compatible with all the experimental behaviour of native red cells. Neither proposal is found to be compatible with all the experimental behaviour of native red cells. To account for this discrepancy we propose that either the shear modulus of the native membrane is dependent on the membrane strain or that the bending stiffness is higher than estimated by Evans (1980. Biophys. J. 30:265-286). These studies suggest that the bioconcave disk is the more likely possibility for the stress-free shape.     

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.     

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)