Frequency-dependent shear impedance of the tectorial membrane

Microscale mechanical probes were designed and bulk-fabricated for applying shearing forces to biological tissues. These probes were used to measure shear impedance of the tectorial membrane (TM) in two dimensions. Forces were applied in the radial and longitudinal directions at frequencies ranging from 0.01-9 kHz and amplitudes from 0.02-4 μN. The force applied was determined by measuring the deflection of the probes’ cantilever arms. TM impedance in the radial direction had a magnitude of 63 ± 28 mN · s/m at 10 Hz and fell with frequency by 16 ± 0.4 dB/decade, with a constant phase of −72 ± 6°. In the longitudinal direction, impedance was 36 ± 9 mN · s/m at 10 Hz and fell by 19 ± 0.4 dB/decade, with a constant phase of −78 ± 4°. Impedance was nearly constant as a function of force except at the highest forces, for which it fell slightly. These results show that the viscoelastic properties of the TM extend over a significant range of audio frequencies, consistent with a poroelastic interpretation of TM mechanics. The shear modulus G′ determined from these measurements was 17-50 kPa, which is larger than in species with a lower auditory frequency range. This value suggests that hair bundles cannot globally shear the TM, but most likely cause bulk TM motion.     

Structural and mechanical analysis of tectorial membrane Tecta mutants

The tectorial membrane (TM) is an extracellular matrix of the cochlea whose prominent role in hearing has been demonstrated through mutation studies. The C1509G mutation of the Tecta gene, which encodes for the α-tectorin protein, leads to hearing loss. The heterozygote TM only attaches to the first row of outer hair cells (OHCs), and the homozygote TM does not attach to any OHCs. Here we measured the morphology and mechanical properties of wild-type, heterozygous, and homozygous Tecta TMs. Morphological analyses conducted with second- and third-harmonic imaging, scanning electron microscopy, and immunolabeling revealed marked changes in the collagen architecture and stereocilin-labeling patterns of the mutant TMs. The mechanical properties of the mutant TM were measured by force spectroscopy. Whereas the axial Young's modulus of the low-frequency (apical) region of Tecta mutant TM samples was similar to that of wild-type TMs, it significantly decreased in the basal region to a value approaching that found at the apex. Modeling simulations suggest that a reduced TM Young's modulus is likely to reduce OHC stereociliary deflection. These findings argue that the heterozygote C1509G mutation results in a lack of attachment of the TM to the OHCs, which in turn reduces both the overall number of OHCs that are involved in mechanotransduction and the degree of mechanotransduction exhibited by the OHCs that remain attached to the TM.     

Ultrastructure of the different zones of the tectorial membrane

The tectorial membrane (t.m.) of mammals, which lies over the organ of Corti, is made up of an agglomerate of protofibrils of varying degrees of hydration. Two types of protofibrils are clearly distinguishable in the mouse t.m. While type-A protofibrils are straight and unbranched (thickness: 110A) demonstrating a periodic structure (period = 70 A), type-B protofibrils are branched and coiled (thickness: 150-200 A). These protofibrils could be systematically ordered according to the different t.m. zones. Type-A protofibrils predominate in the basal layer and in the entire middle zone, where they are interlaced with strongly hydrated type-B protofibrils. Weakly hydrated type-B protofibrils essentially make up the marginal zone (with the marginal net), the covering net, Hensen's stripe and the immediate contact layer with the limbus.     

The tectorial membrane of the lizard ear: types of structure

This study is concerned with the forms of the tectorial membrane in the lizard ear and its manner of attachment to the ciliary tufts of the hair cells. These structures and their variations were observed in 20 species representing eight families of lizards. Three forms of tectorial membrane were found, a continuous form that extends throughout the length of the auditory papilla, an abbreviated form that reaches the papilla only in one region, and a dendritic form that is particularly narrow at first and then branches extensively to supply all the hair cells. Occasionally the lower edge of the tectorial membrane makes direct connections with the hair tufts. More often there are special connecting structures between the membrane and the hair tufts. Seven types of these structures were identified, as follows: (1) simple fibers, (2) open network, (3) heavy network, (4) fiber plate, (5) finger processes, (6) sallets, and (7) remote connections. These types of tectorial connections are described and illustrated.     

Poroelastic bulk properties of the tectorial membrane measured with osmotic stress

The equilibrium stress-strain relation and the pore radius of the isolated tectorial membrane (TM) of the mouse were determined. Polyethylene glycol (PEG), with molecular mass (MM) in the range 20-511 kDa, added to the TM bathing solution was used to exert an osmotic pressure. Strain on the TM induced by isosmotic PEG solutions of different molecular masses was approximately the same for MM > or = 200 kDa. However, for MM < or = 100 kDa, the TM strain was appreciably smaller. We infer that for the smaller molecular mass, PEG entered the TM and exerted a smaller effective osmotic pressure. The pore radius of the TM was estimated as 22 nm. The equilibrium stress-strain relation of the TM was measured using PEG with a molecular mass of 511 kDa. This relation was nonlinear and was fit with a power function. In the radial cochlear direction, the transverse stiffness of the TM was 20% stiffer in the inner than in the outer region. TM segments from the basal region had a larger transverse stiffness on average compared to sections from the apical-middle region. These measurements provide a quantitative basis for a poroelastic model of the TM.     

Sound-evoked deflections of outer hair cell stereocilia arise from tectorial membrane anisotropy

The exceptional performance of mammalian hearing is due to the cochlea's amplification of sound-induced mechanical stimuli. During acoustic stimulation, the vertical motion of the outer hair cells relative to the tectorial membrane (TM) is converted into the lateral motion of their stereocilia. The actual mode of this conversion, which represents a fundamental step in hearing, remains enigmatic, as it is unclear why the stereocilia are deflected when pressed against the TM, rather than penetrating it. In this study we show that deflection of the stereocilia is a direct outcome of the anisotropic material properties of the TM. Using force spectroscopy, we find that the vertical stiffness of the TM is significantly larger than its lateral stiffness. As a result, the TM is more resistant to the vertical motion of stereocilia than to their lateral motion, and so they are deflected laterally when pushed against the TM. Our findings are confirmed by finite element simulations of the mechanical interaction between the TM and stereocilia, which show that the vertical outer hair cells motion is converted into lateral stereocilia motion when the experimentally determined stiffness values are incorporated into the model. Our results thus show that the material properties of the TM play a central and previously unknown role in mammalian hearing.     

Erythrocyte membrane elasticity during in vivo ageing

Changes in the ability of senescent erythrocytes to pass through the micro-circulation may cause them to be trapped in the spleen and removed from the blood. To help understand this process we have measured erythrocyte membrane elasticity, to see whether it changes during in vivo ageing. Human and rabbit red cells were fractionated by isopycnic sedimentation to obtain samples of aged and young cells. These were subjected to micropipette analysis in order to determine their membrane shear elastic modulus. We found that the membrane rigidity did not significantly alter as red cells aged. Previously we have also demonstrated that the changed size and shape of aged cells is unlikely to explain their removal from the circulation (Nash, G.B. and Wyard, S.J. (1981) Biorheology, in the press). Thus we conclude that the lifespan of erythrocytes is not determined by factors related to membrane flexibility or cell shape but may depend on changes in their viscous properties (as suggested by Williams, A.R. and Morris, D.R. (1980), Scand. J. Haematol. 24, 57–62).     

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

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

The 3D structure of the tectorial membrane determined by second-harmonic imaging microscopy

The tectorial membrane (TM) is a highly hydrated non-cellular matrix situated over the sensory cells of the cochlea. It is widely accepted that the mechanical coupling, between the TM and outer hair cells stereocilia bundles, plays an important role in the cochlea energy transduction mechanism. Recently, we provided supporting evidence for the existence of mechanical coupling by demonstrating that the mechanical properties of the TM change along its longitudinal direction. Since the biochemical composition of the TM is similar throughout its entire length, it is likely that structural differences induce the observed material properties changes. Presently, however, the structure of the TM under physiological environments remains unknown. In this work, the 3D structure of native TM samples is shown by using two-photon second-harmonic imaging microscopy. We find that the collagen fibers at the basal region are arranged in a parallel orientation while being tilted in an angle with respect to the plane of the TM surface at the apical region. Moreover, we find an intensified marginal band at the basal OHC zone which forms a shell-like structure which engulfs the stereocilium imprints surface of the TM. In supports of our previous mechanical characterization, the analysis presented here provides a structural basis for the changes in TM's mechanical properties.     

Formation of the tectorial membrane of the cochlear canal during the embryogenesis of birds

By means of electron microscopy formation of the tectorial membrane of the cochlear canal and differentiation of the cells participating in the process (supporting cells of the basilar papilla and anterior homogeneous cells--AHC) have been studied in chick embryos. The AHC, to which the tectorial membrane is fixed, produce fine fibrillar material, included into the composition of the tectorial membrane. The cells mentioned form a number of cytoskeletal structures connected with the mechanical function of the tectorial membrane. Besides the network of the tonofilaments, gradually filling cytoplasm of the AHC, some peculiar attachings in the form of collagenous fibrillar bundles are revealed, they reach the AHC from the sublying connective tissue and have a direct contact with the basal membrane of the cells. The beginning of the tectorial membrane formation precedes the formation of the cytoskeletal structures. The latter appear only when the mass of the tectorial membrane, and hence, the mechanical loading on the AHC is great enough.     

Alamethicin influence on the membrane bending elasticity

We investigate the bending elasticity of lipid membranes with the increase of the alamethicin concentrations in the membrane via analysis of the thermally induced shape fluctuations of quasi-spherical giant vesicles. Our experimental results prove the strong influence of alamethicin molecules on the bending elasticity of diphytanoyl phosphatidylcholine and dilauroyl phosphatidylcholine membranes even in the range of very low peptide concentrations (less than 10⁻³ mol/mol in the membrane). The results presented in this work, testify to the peripheral orientation of alamethicin molecules at low peptide concentrations in the membrane for both types of lipid bilayers. An upper limit of the concentration of the peptide in the membrane is determined below which the system behaves as an ideal two-dimensional solution and the peptide molecules have a planar orientation in the membrane.     

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.     

Bending undulations and elasticity of the erythrocyte membrane: effects of cell shape and membrane organization

The undulatory excitations (flickering) of human and camel erythrocytes were evaluated by employing the previously used flicker spectroscopy and by local measurements of the autocorrelation function K (t) of the cell thickness fluctuations using a dynamic image processing technique. By fitting theoretical and experimental flicker spectra relative values of the bending elastic modulus K _c of the membrane and of the cytoplasmic viscosity were obtained. The effects of shape changes were monitored by simultaneous measurement of the average light intensity I ₀ passing the cells and by phase contrast microscopic observation of the cells. Evaluation of the cellular excitations in terms of the quasi-spherical model yielded values of K _c /R _inf0 ^sup3 and · R ₀ (R ₀=equivalent sphere radius) and allowed us to account (1) for volume changes, (2) for effects of surface tension and spontaneous curvature and (3) for the non-exponential decay of K (t). From the long time decay of K (t) we obtained an upper limit of the bending elastic modulus of normal cells of K _c = 2–3 · 10^–19 Nm which is an order of magnitude larger than the value found by reflection interference contrast microscopy (RICT, K _c , = 3.4 · 10^–20 Nm, Zilker et al. 1987) but considerably lower than expected for a bilayer containing 50% cholesterol (K _c = 5 · 10^–19 Nm, Duwe et al. 1989). The major part of the paper deals with long time measurements (order of hours) of variations of the apparent K _c and values of single cells (and their reversibility) caused (1) by osmotic volume changes, (2) by discocytestomatocyte transitions induced by albumin and triflouperazine, (3) by discocyte-echinocyte transitions induced by expansion of the lipid/protein bilayer (by incubation with lipid vesicles) and by ATP-depletion in physiological NaCI solution, (4), by coupling or decoupling of bilayer and cytoskeleton using wheat germ agglutinin or erythrocytes with elliptocytosis and (5) by cross-linking the cytoskeleton using diamide. These experiments showed: (1) K _c and are minimal at physiological osmolarity and temperature and well controlled over a large range of these parameters. (2) Echinocyte formation does not markedly alter the apparent membrane bending stiffness. (3) During swelling the cell may undergo a transient discocyte-stomatocyte transition. (4) Strong increases of the apparent K _c and after cup-formation or strong swelling and deflation are due to the effect of shear elasticity and surface tension. Our major conclusions are: (1) The erythrocyte membrane exhibits a shear free deformation regime which requires ATP for its maintenance. (2) Shape transitions may be caused by relative area changes either of the two monolayers of the lipid/protein bilayer (corresponding to the bilayer coupling hypothesis) or of the bilayer and the cytoskeleton where the latter mechanism appears to be more frequent. (3) The low bending stiffness and the shear free deformation regime are explained in terms of a slight excess area of the lipid bilayer leading to a pre-undulated surface profile. Freeze fracture electron microscopy studies provide direct evidence for a pre-undulated bilayer with an undulation wavelength of approximately 100 nm. Offprint requests to: E. Sackmann     

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.