The human erythrocyte membrane skeleton may be an ionic gel. III. Micropipette aspiration of unswollen erythrocytes

Energy Dissipation in the Human Red Cell Membrane

The membrane of the human red cell consists of a lipid bilayer and a so-called membrane skeleton attached on the cytoplasmic side of the bilayer. Upon the deformation of red cells, energy is dissipated in their cytoplasm and their membrane. As to the membrane, three contributions can be distinguished: (i) A two-dimensional shear deformation with the membrane viscosity as the frictional parameter; (ii) A motion of the membrane skeleton relative to the bilayer; (iii) A relative motion of the two monolayers of the bilayer. The frictional parameter in contributions (ii) and (iii) is a frictional coefficient specific for the respective contribution. This perspective describes the history up to recent advances in the knowledge of these contributions. It reviews the mechanisms of energy dissipation on a molecular scale and suggests new ones, particularly for the first contribution. It proposes a parametric fitting expected to shed light on the discrepant values found for the membrane viscosity by different experimental approaches. It proposes strategies that could allow the determination of the frictional coefficients pertaining to the second and the third contribution. It highlights the consequences characteristic times have on the state of the red cell membrane in circulation as well as on the adaptation of computer models to the red cell history in an in vitro experiment.

Mechanical properties of the cell nucleus and the effect of emerin deficiency

Nuclear structure and mechanics are gaining recognition as important factors that affect gene expression, development, and differentiation in normal function and disease, yet the physical mechanisms that govern nuclear mechanical stability remain unclear. Here we examined the physical properties of the cell nucleus by imaging fluorescently labeled components of the inner nucleus (chromatin and nucleoli) and the nuclear envelope (lamins and membranes) in nuclei deformed by micropipette aspiration (confocal imaged microdeformation). We investigated nuclei, both isolated and in intact, living cells, and found that nuclear volume significantly decreased by 60-70% during aspiration. While nuclear membranes exhibited blebbing and fluid characteristics during aspiration, the nuclear lamina exhibited behavior of a solid-elastic shell. Under large deformations of GFP-lamin A-labeled nuclei, we observed a decay of fluorescence intensity into the tip of the deformed tongue that we interpreted in terms of nonlinear, two-dimensional elasticity theory. Here we applied this method to study nuclear envelope stability in disease and found that mouse embryo fibroblasts lacking the inner nuclear membrane protein, emerin, had a significantly decreased ratio of the area expansion to shear moduli (K/mu) compared to wild-type cells (2.1 +/- 0.2 versus 5.1 +/- 1.3). These data suggest that altered nuclear envelope elasticity caused by loss of emerin could contribute to increased nuclear fragility in Emery-Dreifuss muscular dystrophy patients with mutations in the emerin gene. Based on our experimental results and theoretical considerations, we present a model describing how the nucleus is stabilized in the pipette. Such a model is essential for interpreting the results of any micropipette study of the nucleus and porous materials in general.

Characterization of the elastic properties of the nuclear envelope

Underlying the nuclear envelope (NE) of most eukaryotic cells is the nuclear lamina, a meshwork consisting largely of coiled-coil nuclear intermediate filament proteins that play a critical role in nuclear organization and gene expression, and are vital for the structural stability of the NE/nucleus. By confocal microscopy and micromanipulation of the NE in living cells and isolated nuclei, we show that the NE undergoes deformations without large-scale rupture and maintains structural stability when exposed to mechanical stress. In conjunction with image analysis, we have developed theory for a two-dimensional elastic material to quantify NE elastic behaviour. We show that the NE is elastic and exhibits characteristics of a continuous two-dimensional solid, including connections between lamins and the embedded nuclear pore complexes. Correlating models of NE lateral organization to the experimental findings indicates a heterogeneous lateral distribution of NE components on a mesoscopic scale.

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.

Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezers study

We have used optical tweezers to study the elasticity of red cell membranes; force was applied to a bead attached to a permeabilized spherical ghost and the force-extension relation was obtained from the response of a second bead bound at a diametrically opposite position. Interruption of the skeletal network by dissociation of spectrin tetramers or extraction of the actin junctions engendered a fourfold reduction in stiffness at low applied force, but only a twofold change at larger extensions. Proteolytic scission of the ankyrin, which links the membrane skeleton to the integral membrane protein, band 3, induced a similar effect. The modified, unlike the native membranes, showed plastic relaxation under a prolonged stretch. Flaccid giant liposomes showed no measurable elasticity. Our observations indicate that the elastic character is at least as much a consequence of the attachment of spectrin as of a continuous membrane-bound network, and they offer a rationale for formation of elliptocytes in genetic conditions associated with membrane-skeletal perturbations. The theory of Parker and Winlove for elastic deformation of axisymmetric shells (accompanying paper) allows us to determine the function BH(2) for the spherical saponin-permeabilized ghost membranes (where B is the bending modulus and H the shear modulus); taking the literature value of 2 x 10(-19) Nm for B, H then emerges as 2 x 10(-6) Nm(-1). This is an order of magnitude higher than the value reported for intact cells from micropipette aspiration. Reasons for the difference are discussed.

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.

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.

Molecular maps of red cell deformation: hidden elasticity and in situ connectivity

Fluorescence-imaged micropipette aspiration was used to map redistribution of the proteins and lipids in highly extended human red blood cell membranes. Whereas the fluid bilayer distributed uniformly (+/- 10 percent), the underlying, solidlike cytoskeleton of spectrin, actin, and protein 4.1 exhibited a steep gradient in density along the aspirated projection, which was reversible on release from deformation. Quantitation of the cytoskeletal protein density gradients showed that skeletal elasticity is well represented by a grafted polymer network with a ratio of surface dilation modulus to shear modulus of approximately 2:1. Fractionally mobile integral proteins, such as band 3, and highly mobile receptors, such as CD59 as well as glycophorin C in protein 4.1-deficient cells, appeared to be squeezed out of areas dense in the underlying network and enriched in areas of network dilation. This complementary segregation demonstrates patterning of cell surface components by cytoskeletal dilation.

Is the surface area of the red cell membrane skeleton locally conserved?

The incompressibility of the lipid bilayer keeps the total surface area of the red cell membrane constant. Local conservation of membrane surface area requires that each surface element of the membrane skeleton keeps its area when its aspect ratio is changed. A change in area would require a flow of lipids past the intrinsic proteins to which the skeleton is anchored. in fast red cell deformations, there is no time for such a flow. Consequently, the bilayer provides for local area conservation. In quasistatic deformations, the extent of local change in surface area is the smaller the larger the isotropic modulus of the skeleton in relation to the shear modulus. Estimates indicate: (a) the velocity of relative flow between lipid and intrinsic proteins is proportional to the gradient in normal tension within the skeleton and inversely proportional to the viscosity of the bilayer; (b) lateral diffusion of lipids is much slower than this flow; (c) membrane tanktreading at frequencies prevailing in vivo as well as the release of a membrane tongue from a micropipette are fast deformations; and (d) the slow phase in micropipette aspiration may be dominated by a local change in skeleton surface.

Effect of magnesium ions on red cell membrane properties

Spectrin forms aggregates in solution when incubated at relatively high concentrations (several millimolar) of divalent cations. According to the evidence of electron microscopy, aggregates of globular appearance and rather uniform size are cooperatively formed from spectrin dimers, no intermediate structures being seen. Inter-dimer chemical cross-linking of spectrin in intact red cell membranes is enhanced if magnesium ions at a concentration of 0.5 mM or more are present. On the other hand, the elimination of magnesium from the interior of intact cells causes no significant change in shear elastic modulus, measured by micropipette assays, nor is there any dependence of membrane filtration rate on intracellular free magnesium concentration in the range 0-1 mM. Magnesium-depleted cells are, however, converted into echinocytes within a short period, in which control cells, exposed to ionophore and external magnesium ions, remain completely discoid. Magnesium-depleted cells also undergo structural changes on heating below the temperature at which vesiculation sets in. These reveal themselves by the transformation of the cells to a unique characteristic shape, by grossly reduced filtrability, and by extensive agglutination of the cells when treated with a bifunctional reagent. Magnesium ions thus regulate the stability, but not to any measurable extent the gross elasticity, of the red cell membrane.

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.

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.