Effects of inherited membrane abnormalities on the viscoelastic properties of erythrocyte membrane.

Several workers have identified molecular abnormalities associated with inherited blood disorders. The present work examines how these alterations in molecular structure affect the viscoelastic properties of the red blood cell membrane. Changes in the membrane shear modulus, the membrane viscosity, and the apparent membrane bending stiffness were observed in cells of eight patients having a variety of disorders: Two had reductions in the number of high-affinity ankyrin binding sites, two had abnormalities associated with the protein band 4.1, and six were known to be deficient in spectrin. The data suggest that the membrane shear modulus is proportional to the density of spectrin on the membrane and support the view that spectrin is primarily responsible for membrane shear elasticity. Although membranes having abnormalities associated with the function of ankyrin or band 4.1 exhibited reduced elasticity, the degree of mechanical dysfunction was quantitatively inconsistent with the extent of the molecular abnormality. This indicates that these skeletal components do not play a primary role in determining membrane shear elasticity. The membrane viscosity was reduced in seven of the eight patients studied. The reduction in viscosity was usually greater than the reduction in shear modulus, but the degree of reduction in viscosity was variable and did not correlate well with the degree of molecular abnormality.     

Modified Protein Expression in the Tectorial Membrane of the Cochlea Reveals Roles for the Striated Sheet Matrix

The tectorial membrane (TM) of the mammalian cochlea is a complex extracellular matrix which, in response to acoustic stimulation, displaces the hair bundles of outer hair cells (OHCs), thereby initiating sensory transduction and amplification. Here, using TM segments from the basal, high-frequency region of the cochleae of genetically modified mice (including models of human hereditary deafness) with missing or modified TM proteins, we demonstrate that frequency-dependent stiffening is associated with the striated sheet matrix (SSM). Frequency-dependent stiffening largely disappeared in all three TM mutations studied where the SSM was absent either entirely or at least from the stiffest part of the TM overlying the OHCs. In all three TM mutations, dissipation of energy is decreased at low (<8 kHz) and increased at high (>8 kHz) stimulus frequencies. The SSM is composed of polypeptides carrying fixed charges, and electrostatic interaction between them may account for frequency-dependent stiffness changes in the material properties of the TM. Through comparison with previous in vivo measurements, it is proposed that implementation of frequency-dependent stiffening of the TM in the OHC attachment region facilitates interaction among tones, backward transmission of energy, and amplification in the cochlea.     

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.     

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.     

Sound-induced motions of individual cochlear hair bundles

We present motions of individual freestanding hair bundles in an isolated cochlea in response to tonal sound stimulation. Motions were measured from images taken by strobing a light source at the tone frequency. The tips and bases of hair bundles moved a comparable amount, but with a phase difference that increased by 180 degrees with frequency, indicating that distributed fluid properties drove hair bundle motion. Hair bundle rotation increased with frequency to a constant value, and underwent >90 degrees of phase change. The frequency at which the phase of rotation relative to deflection of the bundle base was 60 degrees was comparable to the expected best frequency of each hair cell, and varied inversely with the square of bundle height. The sharpness of tuning of individual hair bundles was comparable to that of hair cell receptor potentials at high sound levels. These results indicate that frequency selectivity at high sound levels in this cochlea is purely mechanical, determined by the interaction of hair bundles with the surrounding fluid. The sharper tuning of receptor potentials at lower sound levels is consistent with the presence of a negative damping, but not a negative stiffness, as an active amplifier in hair bundles.     

Three approaches for estimating the elastic modulus of the tympanic membrane

The function of the middle ear is to resolve the acoustic impedance mismatch between the air in the ear canal and the fluid of the inner ear. Without this impedance matching, very little acoustic energy would be absorbed into the cochlea. The first step in this process is the tympanic membrane (TM) converting sound in the ear canal into vibrations of the middle ear bones. Understanding how the TM manages its task so successfully over such a broad frequency range should lead to more satisfactory and less variable TM repairs (myringoplasty). In addition, understanding the mechanics of the TM is necessary to improve the coupling between ossicular prostheses and the TM. Mathematical models have played a central role in helping the research community understand the mechanics of the eardrum. However, all models require parameters as inputs. Unfortunately, most of the parameters needed for modeling the TM are not well known. In this work, several approaches for inferring the material properties of the TM are explored. First, constitutive modeling is used to estimate an elastic modulus based on the elastic modulus of collagen and experimentally observed fiber densities. Second, experimental tension and bending test results from the literature are re-interpreted using composite laminate theory. Lastly, dynamic measurements of the cat TM are used in conjunction with a composite shell model to bound the material parameters. Values from the literature, both measurement and modeling efforts, and from the present analysis are brought together to form a coherent picture of the TM's material properties. In the human, the data bound the elastic modulus between 0.1 and 0.3 GPa. In the cat, the data suggest a range of 0.1-0.4 GPa. These values are significantly higher than previous estimates.     

Effect of hydroperoxides on red blood cell membrane mechanical properties

We investigate the effect of oxidative stress on red blood cell membrane mechanical properties in vitro using detailed analysis of the membrane thermal fluctuation spectrum. Two different oxidants, the cytosol-soluble hydrogen peroxide and the membrane-soluble cumene hydroperoxide, are used, and their effects on the membrane bending elastic modulus, surface tension, strength of confinement due to the membrane skeleton, and 2D shear elastic modulus are measured. We find that both oxidants alter significantly the membrane elastic properties, but their effects differ qualitatively and quantitatively. While hydrogen peroxide mainly affects the elasticity of the membrane protein skeleton (increasing the membrane shear modulus), cumene hydroperoxide has an impact on both membrane skeleton and lipid bilayer mechanical properties, as can be seen from the increased values of the shear and bending elastic moduli. The biologically important implication of these results is that the effects of oxidative stress on the biophysical properties, and hence the physiological functions, of the cell membrane depend on the nature of the oxidative agent. Thermal fluctuation spectroscopy provides a means of characterizing these different effects, potentially in a clinical milieu.     

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.     

Effect of wheat germ agglutinin on the viscoelastic properties of erythrocyte membrane

The elasticity and viscosity of the human erythrocyte membrane were measured as a function of the concentration of wheat germ agglutinin (WGA) in a suspending solution containing 1 mg/ml albumin, approximately 5 X 10(5) cells/ml and between 0.0 and 0.2 microgram/ml WGA. Membrane elasticity was characterized by the elastic shear modulus, which provided a measure of the resistance of the membrane to constant-area elastic deformations that occurred in the membrane plane. The elastic shear modulus was determined by aspirating a portion of the membrane into a micropipette and measuring the extension of the membrane into the pipette as a function of the suction pressure. The results indicated no significant change in shear modulus for concentrations of WGA between 0.0 and 0.2 microgram/ml. Membrane viscosity was characterized by the coefficient of surface viscosity, which, in effect, was a measure of the membrane's resistance to rates of deformation. This coefficient was determined from the time required for an erythrocyte to recover its undeformed shape after it had been elongated by the application of an equal and opposite force applied at diametrically opposite points on the erythrocyte rim. The value for the coefficient of surface viscosity was found to increase by a factor of almost three when the WGA concentration was increased from 0.0 to 0.2 microgram/ml. These results indicated that, in the presence of albumin, WGA can increase membrane dissipation (viscosity) without altering the structural rigidity (elasticity) of the membrane.     

A tethered adhesive particle model of two-dimensional elasticity and its application to the erythrocyte membrane.

A new model of two-dimensional elasticity with application to the erythrocyte membrane is proposed. The system consists of a planar array of self-adhesive particles attached to nearest neighbors with flexible tethers. Stretching from the equilibrium dimension is resisted because force is required to dissociate the particle clusters and to decrease the distribution entropy. Release of the external force is accompanied by a contraction as thermal diffusion randomizes the particles and allows interparticle attachments to form again. Analysis of membrane thermodynamics and mechanics under the two-state particle assumption results in a shear softening stress-strain relation. The shear modulus is found proportional to the square root of the surface density of particles, the interparticle adhesive energy, and is inversely proportional to the tether length. Applied to the erythrocyte membrane under the assumption that band 3 tetramer represents the particle and spectrin the tether, the shear modulus predicted corresponds to the measured value when the interparticle adhesive energy is approximately 4.0-5.9 kT, where kT is the Boltzmann constant multiplied by the temperature. This model suggests a mechanism wherein erythrocyte membrane deformability depends on integral protein homomultimeric interactions and can be modulated from the external surface.     

A new view of mechanotransduction and strain amplification in cells with microvilli and cell processes

In this paper we shall describe new mechanical models for the deformation of the actin filament bundles in kidney microvilli and osteocytic cell processes to see whether these cellular extensions, like the stereocilia on hair cells in the inner ear, can function as mechanotransducers when subject to physiological flow. In the case of kidney microvilli we show that the hydrodynamic drag forces at the microvilli tip are <0.01 pN, but there is a 38-fold force amplification on the actin filaments at the base of the microvilli due to the resisting moment in its terminal web. This leads to forces that are more than sufficient to deform the terminal web complex of the microvillus where ezrin has been shown to couple the actin cytoskeleton to the Na(+)/H(+) exchanger. In the case of bone cell processes we show that the actin filament bundles have an effective Young's modulus that is 200 times > the measured modulus for the actin gel in the cell body. It is, therefore, unlikely that bone cell processes respond in vivo to fluid shear stress, as proposed in [59]. However, we show that the fluid drag forces on the pericellular matrix which tethers the cell processes to the canalicular wall can produce a 20-100 fold amplification of bone tissue strains in the actin filament bundle of the cell process.     

Mechanics of curved plasma membrane vesicles: resting shapes, membrane curvature, and in-plane shear elasticity

Highly curved cell membrane structures, such as plasmalemmal vesicles (caveolae) and clathrin-coated pits, facilitate many cell functions, including the clustering of membrane receptors and transport of specific extracellular macromolecules by endothelial cells. These structures are subject to large mechanical deformations when the plasma membrane is stretched and subject to a change of its curvature. To enhance our understanding of plasmalemmal vesicles we need to improve the understanding of the mechanics in regions of high membrane curvatures. We examine here, theoretically, the shapes of plasmalemmal vesicles assuming that they consist of three membrane domains: an inner domain with high curvature, an outer domain with moderate curvature, and an outermost flat domain, all in the unstressed state. We assume the membrane properties are the same in these domains with membrane bending elasticity as well as in-plane shear elasticity. Special emphasis is placed on the effects of membrane curvature and in-plane shear elasticity on the mechanics of vesicle during unfolding by application of membrane tension. The vesicle shapes were computed by minimization of bending and in-plane shear strain energy. Mechanically stable vesicles were identified with characteristic membrane necks. Upon stretch of the membrane, the vesicle necks disappeared relatively abruptly leading to membrane shapes that consist of curved indentations. While the resting shape of vesicles is predominantly affected by the membrane spontaneous curvatures, the membrane shear elasticity (for a range of values recorded in the red cell membrane) makes a significant contribution as the vesicle is subject to stretch and unfolding. The membrane tension required to unfold the vesicle is sensitive with respect to its shape, especially as the vesicle becomes fully unfolded and approaches a relative flat shape.     

Modeling the mechanics of tethers pulled from the cochlear outer hair cell membrane

Cell membrane tethers are formed naturally (e.g., in leukocyte rolling) and experimentally to probe membrane properties. In cochlear outer hair cells, the plasma membrane is part of the trilayer lateral wall, where the membrane is attached to the cytoskeleton by a system of radial pillars. The mechanics of these cells is important to the sound amplification and frequency selectivity of the ear. We present a modeling study to simulate the membrane deflection, bending, and interaction with the cytoskeleton in the outer hair cell tether pulling experiment. In our analysis, three regions of the membrane are considered: the body of a cylindrical tether, the area where the membrane is attached and interacts with the cytoskeleton, and the transition region between the two. By using a computational method, we found the shape of the membrane in all three regions over a range of tether lengths and forces observed in experiments. We also analyze the effects of biophysical properties of the membrane, including the bending modulus and the forces of the membrane adhesion to the cytoskeleton. The model's results provide a better understanding of the mechanics of tethers pulled from cell membranes.     

Br-rich tips of calcified crab claws are less hard but more fracture resistant: A comparison of mineralized and heavy-element biological materials

We find that the spoon-like tips of the chelipeds (large claws) of the crab Pachygrapsus crassipes differ from the rest of the claw in that they are not calcified, but instead contain about 1% bromine—thus they represent a new example of a class of structural biological materials that contain heavy elements such as Zn, Mn, Fe, Cu, and Br bound in an organic matrix. X-ray absorption spectroscopy data suggest that the bromine is bound to phenyl rings, possibly in tyrosine. We measure a broad array of mechanical properties of a heavy-element biological material for the first time (abrasion resistance, coefficient of kinetic friction, energy of fracture, hardness, modulus of elasticity and dynamic mechanical properties), and we make a direct comparison with a mineralized tissue. Our results suggest that the greatest advantage of bromine-rich cuticle over calcified cuticle is resistance to fracture (the energy of fracture is about an order of magnitude greater than for calcified cuticle). The greatest advantage relative to unenriched cuticle, represented by ant mandible cuticle, is a factor of about 1.5 greater hardness and modulus of elasticity. The spoon-like tips gain additional fracture resistance from the orientation of the constituent laminae and from the viscoelasticity of the material. We suggest that fracture resistance is of greater importance in smaller organisms, and we speculate that one function of heavy elements in structural biological materials is to reduce molecular resonant frequencies and thereby increase absorption of energy from impacts.     

Effectiveness of Hair Bundle Motility as the Cochlear Amplifier

The effectiveness of hair bundle motility in mammalian and avian ears is studied by examining energy balance for a small sinusoidal displacement of the hair bundle. The condition that the energy generated by a hair bundle must be greater than energy loss due to the shear in the subtectorial gap per hair bundle leads to a limiting frequency that can be supported by hair-bundle motility. Limiting frequencies are obtained for two motile mechanisms for fast adaptation, the channel re-closure model and a model that assumes that fast adaptation is an interplay between gating of the channel and the myosin motor. The limiting frequency obtained for each of these models is an increasing function of a factor that is determined by the morphology of hair bundles and the cochlea. Primarily due to the higher density of hair cells in the avian inner ear, this factor is ∼10-fold greater for the avian ear than the mammalian ear, which has much higher auditory frequency limit. This result is consistent with a much greater significance of hair bundle motility in the avian ear than that in the mammalian ear.     

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.     

Membrane bending is critical for the stability of voltage sensor segments in the membrane

The interaction between membrane proteins and the surrounding membrane is becoming increasingly appreciated for its role in regulating protein function, protein localization, and membrane morphology. In particular, recent studies have suggested that membrane deformation is needed to stably accommodate proteins harboring charged amino acids in their transmembrane (TM) region, as it is energetically prohibitive to bury charge in the hydrophobic core of the bilayer. Unfortunately, current computational methods are poorly equipped for describing such deformations, as atomistic simulations are often too short to observe large-scale membrane reorganization and most continuum approaches assume a flat membrane. Previously, we developed a method that overcomes these shortcomings by using elasticity theory to characterize equilibrium membrane distortions in the presence of a TM protein, while using traditional continuum electrostatic and nonpolar energy models to determine the energy of the protein in the membrane. Here, we linked the elastostatics, electrostatics, and nonpolar numeric solvers to permit the calculation of energies for nontrivial membrane deformations. We then coupled this procedure to a robust search algorithm that identifies optimal membrane shapes for a TM protein of arbitrary chemical composition. This advance now permits us to explore a host of biological phenomena that were beyond the scope of our original method. We show that the energy required to embed charged residues in the membrane can be highly nonadditive, and our model provides a simple mechanical explanation for this nonadditivity. Our results also predict that isolated voltage sensor segments do not insert into rigid membranes, but membrane bending dramatically stabilizes these proteins in the bilayer despite their high charge content. Additionally, we use the model to explore hydrophobic mismatch with regard to nonpolar peptides and mechanosensitive channels. Our method is in quantitative agreement with molecular dynamics simulations at a tiny fraction of the computational cost.     

Nanoscale strain-hardening of keratin fibres

Mammalian appendages such as hair, quill and wool have a unique structure composed of a cuticle, a cortex and a medulla. The cortex, responsible for the mechanical properties of the fibers, is an assemblage of spindle-shaped keratinized cells bound together by a lipid/protein sandwich called the cell membrane complex. Each cell is itself an assembly of macrofibrils around 300 nm in diameter that are paracrystalline arrays of keratin intermediate filaments embedded in a sulfur-rich protein matrix. Each macrofibril is also attached to its neighbors by a cell membrane complex. In this study, we combined atomic force microscopy based nano-indentation with peak-force imaging to study the nanomechanical properties of macrofibrils perpendicular to their axis. For indentation depths in the 200 to 500 nm range we observed a decrease of the dynamic elastic modulus at 1 Hz with increasing depth. This yielded an estimate of 1.6GPa for the lateral modulus at 1 Hz of porcupine quill's macrofibrils. Using the same data we also estimated the dynamic elastic modulus at 1 Hz of the cell membrane complex surrounding each macrofibril, i.e., 13GPa. A similar estimate was obtained independently through elastic maps of the macrofibrils surface obtained in peak-force mode at 1 kHz. Furthermore, the macrofibrillar texture of the cortical cells was clearly identified on the elasticity maps, with the boundaries between macrofibrils being 40-50% stiffer than the macrofibrils themselves. Elasticity maps after indentation also revealed a local increase in dynamic elastic modulus over time indicative of a relaxation induced strain hardening that could be explained in term of a α-helix to β-sheet transition within the macrofibrils.     

Spectrin, human erythrocyte shapes, and mechanochemical properties.

Physical studies of human erythrocyte spectrin indicate that isolated spectrin dimers and tetramers in solution are worm-like coils with a persistence length of approximately 20 nm. This finding, the known polyelectrolytic nature of spectrin, and other structural information about spectrin and the membrane skeleton molecular organization have lead us to the hypothesis that the human erythrocyte membrane skeleton constitutes a two-dimensional ionic gel (swollen ionic elastomer). This concept is incorporated in what we refer to as the protein gel-lipid bilayer membrane model. The model accounts quantitatively for red elastic shear modulus and the maximum elastic extension ratio reported for the human erythrocytes membrane. Gel theory further predicts that depending on the environmental conditions, the membrane skeleton modulus of area compression may be small or large relative to the membrane elastic shear modulus. Our analyses show that the ratio between these two parameters affects both the geometry and the stability of the favored cell shapes and that the higher the membrane skeleton compressibility the smaller the values of the gel tension needed to induce cell shape transformations. The main virtue of the protein gel-lipid bilayer membrane model is that it offers a novel theoretical and molecular basis for the various mechanical properties of the membrane skeleton such as the membrane skeleton modulus of area compression and osmotic tension, and the effects of these properties on local membrane skeleton density, cell shape, and shape transformations.     

Kinocilia mediate mechanosensitivity in developing zebrafish hair cells

Mechanosensitive cilia are vital to signaling and development across many species. In sensory hair cells, sound and movement are transduced by apical hair bundles. Each bundle is comprised of a single primary cilium (kinocilium) flanked by multiple rows of actin-filled projections (stereocilia). Extracellular tip links that interconnect stereocilia are thought to gate mechanosensitive channels. In contrast to stereocilia, kinocilia are not critical for hair-cell mechanotransduction. However, by sequentially imaging the structure of hair bundles and mechanosensitivity of individual lateral-line hair cells in?vivo, we uncovered a central role for kinocilia in mechanosensation during development. Our data demonstrate that nascent hair cells require kinocilia and kinocilial links for mechanosensitivity. Although nascent hair bundles have correct planar polarity, the polarity of their responses to mechanical stimuli is initially reversed. Later in development, a switch to correctly polarized mechanosensitivity coincides with the formation of tip links and the onset of tip-link-dependent mechanotransduction.