Mechanical properties of the red cell membrane skeleton: analysis of axisymmetric deformations

The mechanical properties of erythrocyte membrane composed of a membrane bilayer and membrane skeleton are considered. Two membrane models are described: the model of free boundaries (MFB) and the model of immobilized boundaries (MIB). In MFB, the skeleton is assumed to be attached to the bilayer at a finite number of points, whereas MIB allows the interaction of each spectrin filament with the bilayer along its whole length. For MFB an estimate was made of the mechanical strain generated in the membrane by sucking erythrocytes into a micropipette. The existence of the deformation threshold is demonstrated, below which no mechanical strain, except that of bending, appears in the membrane. Thus only deformations exceeding this threshold result in strain. The relationship between the applied tension and the height of erythrocyte "tongue" sucked into a micropipette was determined. The MIB characteristics correspond to the model of Evans: strains in the membrane are generated at any deformation, however small, i.e. the threshold is equal to zero. A basic feature of this model is quite a different distribution of the skeleton deformations in the membrane. A comparison of the theoretical models and experimental data demonstrated the possibility of either MFB or MIB occurring, depending on the characteristic measurement time.     

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.     

Time-dependent elastic extensional RBC deformation by micropipette aspiration: redistribution of the spectrin network?

The time dependence of small elastic extensional RBC deformation by micropipette aspiration has been analyzed. This process shows two-phases which are characterized by time constants of the order of some tenths of seconds and about ten seconds, respectively. The equilibrium tongue length is reached after about 30 s. For the first, fast step we assume that the membrane model of immobilized boundaries holds, i.e., the skeleton is tightly associated with the lipid bilayer and no redistribution of the skeleton with respect to the lipid bilayer is allowed. This lipid-spectrin interaction or anchorage is characterized by some association force density. It has been shown that at a given tongue length the force generated owing to the membrane deformation and acting to redistribute the spectrin, overcomes (in some membrane area) the association force density and results in an additional increase of the sucked membrane length. Equations have been derived to describe this process. From the experimental conditions of an RBC aspiration and the determined tongue length corresponding to the second slow aspiration step, the association force density between the lipid bilayer and the spectrin network may be determined. From literature data and our own results a force density of between 40 and 50 Pa has been estimated. Offprint requests to: D. Lerche     

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.     

Protein 4.1N is required for the formation of the lateral membrane domain in human bronchial epithelial cells

The membrane skeleton forms a scaffold on the cytoplasmic side of the plasma membrane. The erythrocyte membrane represents an archetype of such structural organization. It has been documented that a similar membrane skeleton also exits in the Golgi complex. It has been previously shown that βII spectrin and ankyrin G are localized at the lateral membrane of human bronchial epithelial cells. Here we show that protein 4.1N is also located at the lateral membrane where it associates E-cadherin, β-catenin and βII spectrin. Importantly, depletion of 4.1N by RNAi in human bronchial epithelial cells resulted in decreased height of lateral membrane, which was reversed following re-expression of mouse 4.1N. Furthermore, although the initial phase of lateral membrane biogenesis proceeded normally in 4.1N-depleted cells, the final height of the lateral membrane of 4.1N-depleted cells was shorter compared to that of control cells. Our findings together with previous findings imply that 4.1N, βII spectrin and ankyrin G are structural components of the lateral membrane skeleton and that this skeleton plays an essential role in the assembly of a fully functional lateral membrane.     

Direct measures of large, anisotropic strains in deformation of the erythrocyte cytoskeleton.

The erythrocyte's spectrin-actin membrane skeleton is directly shown to be capable of sustaining large, anisotropic strains. Photobleaching of an approximately 1-micrometer stripe in rhodamine phalloidin-labeled actin appears stable up to at least 37 degrees C, and is used to demonstrate large in-surface stretching during elastic deformation of the skeleton. Principal extension or stretch ratios of at least approximately 200% and contractions down to approximately 40%, both referenced to an essentially undistorted cell, are visually demonstrated in micropipette-imposed deformation. Such anisotropic straining is seen to be consistent at a qualitative level with now classic analyses (Evans. 1973. Biophys. J. 13:941-954) and is generally nonhomogeneous though axisymmetric down to the submicron scale. Local, direct measurements of stretching prove quantitatively consistent (within approximately 10%) with integrated estimates that are based simply on a measured relative density distribution of actin. The measurements are also in close agreement with direct computation of mean spectrin chain extension in full statistical mechanical simulations of a coarse-grained network held in a micropipette. Finally, as a cell thermally fragments near approximately 48 degrees C, the patterned photobleaching demonstrates a destructuring of the surface network in a process that is more readily attributable to transitions in spectrin than in F-actin.     

Constitutive Model of Erythrocyte Membranes with Distributions of Spectrin Orientations and Lengths

We present an analytical hyperelastic constitutive model of the red blood cell (erythrocyte) membrane based on recently improved characterizations of density and microscopic structure of its spectrin network from proteomics and cryo-electron tomography. The model includes distributions of both orientations and natural lengths of spectrin and updated copy numbers of proteins. By applying finite deformation to the spectrin network, we obtain the total free energy and stresses in terms of invariants of shear and area deformation. We generalize an expression of the initial shear modulus, which is independent of the number of molecular orientations within the network and also derive a simplified version of the model. We apply the model and its simplified version to analyze micropipette aspiration computationally and analytically and explore the effect of local cytoskeletal density change. We also explore the discrepancies among shear modulus values measured using different experimental techniques reported in the literature. We find that the model exhibits hardening behavior and can explain many of these discrepancies. Moreover, we find that the distribution of natural lengths plays a crucial role in the hardening behavior when the correct copy numbers of proteins are used. The initial shear modulus values we obtain using our current model (5.9–15.6 pN/μm) are close to the early estimates (6–9 pN/μm). This new, to our knowledge, constitutive model establishes a direct connection between the molecular structure of spectrin networks and constitutive laws and also defines a new picture of a much denser spectrin network than assumed in prior studies.     

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.     

Remodeling the shape of the skeleton in the intact red cell.

The role of the membrane skeleton in determining the shape of the human red cell was probed by weakening it in situ with urea, a membrane-permeable perturbant of spectrin. Urea by itself did not alter the biconcave disk shape of the red cell; however, above threshold conditions (1.5 M, 37 degrees C, 10 min), it caused an 18% reduction in the membrane elastic shear modulus. It also potentiated the spiculation of cells by lysophosphatidylcholine. These findings suggest that the contour of the resting cell is not normally dependent on the elasticity of or tension in the membrane skeleton. Rather, the elasticity of the skeleton stabilizes membranes against deformation. Urea treatment also caused the projections induced both by micropipette aspiration and by lysophosphatidylcholine to become irreversible. Furthermore, urea converted the axisymmetric conical spicules induced by lysophosphatidylcholine into irregular, curved and knobby spicules; i.e., echinocytosis became acanthocytosis. Unlike controls, the ghosts and membrane skeletons obtained from urea-generated acanthocytes were imprinted with spicules. These data suggest that perturbing interprotein associations with urea in situ allowed the skeleton to evolve plastically to accommodate the contours imposed upon it by the overlying membrane.     

Influence of the membrane undercoat on filipin perturbation of the red blood cell membrane

Filipin, a polyene antibiotic, interacts with beta-hydroxy sterols such as cholesterol in most cell membranes, forming bumps and pits that are visible by electron microscopy of freeze-fracture replicas. The markedly reduced perturbability of the red blood cell (RBC) membrane, compared to other cells, has been attributed to the constraining influence of the red cell membrane skeleton, the undercoat composed of spectrin, actin, and protein 4.1. To test the influence of the membrane skeleton on filipin-induced perturbation of the RBC membrane, we studied the interaction of filipin with red cells that were inherently devoid of spectrin and RBC in which spectrin had been crosslinked or denatured. These spectrin-deficient, crosslinked, and denatured cells have a fivefold increase in the number of filipin-induced perturbations as compared to control cells, despite equivalent membrane cholesterol content. These findings confirm that the spectrin-based membrane skeleton strongly influences the organization of the membrane so as to limit perturbation by filipin:cholesterol interaction and that for membranes in which the cholesterol content is known, filipin is a useful probe for testing the avidity of spectrin-based cytoskeletal attachment.     

Gaps in the erythrocyte membrane skeleton: a stretched net model.

The geometry of spectrin-free regions in the erythrocyte membrane skeleton is modeled using Monte Carlo calculations for an incomplete triangular lattice of entropy springs under tension. Intact springs correspond to normal spectrin molecules, and cut springs correspond to spectrin that is missing or unable to associate normally. As springs are cut and the network is allowed to relax to mechanical equilibrium, gaps in the network appear. Geometrical properties of these gaps are obtained as a function of the fraction of springs cut. The most important property modeled is the area of the largest spectrin-free region; this area increases approximately exponentially as the fraction of normal spectrin decreases from 100% to approximately 50%. The effect of these gaps on lateral diffusion and vesiculation is discussed.     

Thermal properties of young red blood cells are indicative of an age-dependent regulation of membrane-skeleton interaction

The effects of red blood cell (RBC) age on membrane thermal properties have been investigated by using a 16-nitroxide stearic acid spin probe. We detected in unfractionated and most dense cells (2% fraction of circulating cells) a thermal transition at 40 degrees C that in young cells (1% fraction) was lowered at 33-35 degrees C. Spectrin seems to be directly involved in the transition detected in both young and unfractionated cells, as showed by the disappearance of the breaks after low salt extraction of spectrin. A further indication for a role of spectrin in this transition comes from its characteristic thermal unfolding above 40 degrees C. However, young cells did not show changes either in the thermal unfolding of spectrin or in the distribution of spectrin dimer, tetramer, and high oligomeric forms. These data rule out that spectrin of young RBC is modified in its thermal properties and indicate that young cells may have a different spectrin-membrane interaction. Treatment of unfractionated ghosts with an antibody specific for a fragment of the 10K domain of protein 4.1, which is fully competent for the spectrin-actin binding, produced an evident lowering of the transition temperature. The same antibody did not affect the thermal transition of young ghosts. Our results suggest that spectrin-membrane interactions may be regulated during RBC lifespan.     

Mechanical and functional aspects of membrane skeletons

Membrane skeletons can be characterized as cytoskeletal structures lying parallel to the bilayer part of cellular and organelle membranes. Typical examples are spectrin network and actin-myosin cortex. We approach the problem of elucidating the function of membrane skeletons by theoretically analyzing mechanical models of the cellular behavior. Membranes of different physical and chemical properties are considered. In erythrocytes and some organelles membrane bilayers are smooth and simply underlaid or overlaid by membrane skeletons. It is argued that there the role of a membrane skeleton is, either, to keep the membrane composition laterally homogeneous as it is in the case of the erythrocyte, or, that it is involved in the processes of the lateral separation of integral membrane proteins as it is happening in the case of some intermediate steps of the vesicular membrane trafficking. In the second type of membranes the bilayer part is ruffled and folded, and there the membrane skeletons play a role in the determination of the cortical tension. Here we explore in more detail the mechanical behavior of a cell with such properties of its boundary. The shape transformations are described which occur under the influence (i) of different external forces, i.e., when an originally spherical cell is aspirated into the micropipette or when such a cell is adsorbed on a flat surface, and (ii) of different internal forces on the cell boundary exerted by the cytoskeletal elements.     

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.     

Interactions between Plasmodium falciparum skeleton-binding protein 1 and the membrane skeleton of malaria-infected red blood cells

During development inside red blood cells (RBCs), Plasmodium falciparum malaria parasites export proteins that associate with the RBC membrane skeleton. These interactions cause profound changes to the biophysical properties of RBCs that underpin the often severe and fatal clinical manifestations of falciparum malaria. P. falciparum erythrocyte membrane protein 1 (PfEMP1) is one such exported parasite protein that plays a major role in malaria pathogenesis since its exposure on the parasitised RBC surface mediates their adhesion to vascular endothelium and placental syncytioblasts. En route to the RBC membrane skeleton, PfEMP1 transiently associates with Maurer's clefts (MCs), parasite-derived membranous structures in the RBC cytoplasm. We have previously shown that a resident MC protein, skeleton-binding protein 1 (SBP1), is essential for the placement of PfEMP1 onto the RBC surface and hypothesised that the function of SBP1 may be to target MCs to the RBC membrane. Since this would require additional protein interactions, we set out to identify binding partners for SBP1. Using a combination of approaches, we have defined the region of SBP1 that binds specifically to defined sub-domains of two major components of the RBC membrane skeleton, protein 4.1R and spectrin. We show that these interactions serve as one mechanism to anchor MCs to the RBC membrane skeleton, however, while they appear to be necessary, they are not sufficient for the translocation of PfEMP1 onto the RBC surface. The N-terminal domain of SBP1 that resides within the lumen of MCs clearly plays an essential, but presently unknown role in this process.     

Ubiquitination of erythrocyte spectrin regulates the dissociation of the spectrin-adducin-f-actin ternary complex in vitro.

We demonstrate that ubiquitinated red blood cell (RBC) spectrin dissociates more rapidly from the spectrin-adducin-actin ternary complex, than non-ubiquitinated spectrin. Homozygous (SS) sickle cell spectrin has substantially diminished ubiquitination of alpha-spectrin resulting in slower dissociation from the spectrin-adducin-actin ternary complex, than normal (AA) cell spectrin. These results supply a partial explanation of the slow dissociation of the irreversible sickle cell (ISC) membrane skeleton, which leads to the inability of the ISC to change shape.     

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.     

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.