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

3D morphology of an outer-hair-cell hair bundle increases its displacement and dynamic range

In mammals, outer-hair-cell hair bundles (OHBs) transduce sound-induced forces into receptor currents and are required for the wide dynamic range and high sensitivity of hearing. OHBs differ conspicuously in morphology from other types of bundles. Here, we show that the 3D morphology of an OHB greatly impacts its mechanics and transduction. An OHB comprises rod-like stereocilia, which pivot on the surface of its sensory outer hair cell. Stereocilium pivot positions are arranged in columns and form a V shape. We measure the pivot positions and determine that OHB columns are far from parallel. To calculate the consequences of an OHB's V shape and far-from-parallel columns, we develop a mathematical model of an OHB that relates its pivot positions, 3D morphology, mechanics, and receptor current. We find that the 3D morphology of the OHB can halve its stiffness, can double its damping coefficient, and causes stereocilium displacements driven by stimulus forces to differ substantially across the OHB. Stereocilium displacements drive the opening and closing of ion channels through which the receptor current flows. Owing to the stereocilium-displacement differences, the currents passing through the ion channels can peak versus the stimulus frequency and vary considerably across the OHB. Consequently, the receptor current peaks versus the stimulus frequency. Ultimately, the OHB's 3D morphology can increase its receptor-current dynamic range more than twofold. Our findings imply that potential pivot-position changes owing to development, mutations, or location within the mammalian auditory organ might greatly alter OHB function.

Anisotropic Material Properties of Wild-Type and Tectb-/- Tectorial Membranes

The tectorial membrane (TM) is an extracellular matrix that is directly coupled with the mechanoelectrical receptors responsible for sensory transduction and amplification. As such, the TM is often hypothesized to play a key role in the remarkable sensory abilities of the mammalian cochlea. Genetic studies targeting TM proteins have shown that changes in TM structure dramatically affect cochlear function in mice. Precise information about the mechanical properties of the TMs of wild-type and mutant mice at audio frequencies is required to elucidate the role of the TM and to understand how these genetic mutations affect cochlear mechanics. In this study, images of isolated TM segments are used to determine both the radial and longitudinal motions of the TM in response to a harmonic radial excitation. The resulting longitudinally propagating radial displacement and highly spatially dependent longitudinal displacement are modeled using finite-element models that take into account the anisotropy and finite dimensions of TMs. An automated, least-square fitting algorithm is used to find the anisotropic material properties of wild-type and Tectb^-/- mice at audio frequencies. Within the auditory frequency range, it is found that the TM is a highly viscoelastic and anisotropic structure with significantly higher stiffness in the direction of the collagen fibers. Although no decrease in the stiffness in the fiber direction is observed, the stiffness of the TM in shear and in the transverse direction is found to be significantly reduced in Tectb^-/- mice. As a result, TMs of the mutant mice tend to be significantly more anisotropic within the frequency range examined in this study. The effects of the Tectb^-/- mutation on the TM's anisotropic material properties may be responsible for the changes in cochlear tuning and sensitivity that have been previously reported for these mice.

A clinically oriented introduction and review on finite element models of the human cochlea

Due to the inaccessibility of the inner ear, direct in vivo information on cochlear mechanics is difficult to obtain. Mathematical modelling is a promising way to provide insight into the physiology and pathology of the cochlea. Finite element method (FEM) is one of the most popular discrete mathematical modelling techniques, mainly used in engineering that has been increasingly used to model the cochlea and its elements. The aim of this overview is to provide a brief introduction to the use of FEM in modelling and predicting the behavior of the cochlea in normal and pathological conditions. It will focus on methodological issues, modelling assumptions, simulation of clinical scenarios, and pathologies.

Basilar membrane and tectorial membrane stiffness in the CBA/CaJ mouse

The mouse has become an important animal model in understanding cochlear function. Structures, such as the tectorial membrane or hair cells, have been changed by gene manipulation, and the resulting effect on cochlear function has been studied. To contrast those findings, physical properties of the basilar membrane (BM) and tectorial membrane (TM) in mice without gene mutation are of great importance. Using the hemicochlea of CBA/CaJ mice, we have demonstrated that tectorial membrane (TM) and basilar membrane (BM) revealed a stiffness gradient along the cochlea. While a simple spring mass resonator predicts the change in the characteristic frequency of the BM, the spring mass model does not predict the frequency change along the TM. Plateau stiffness values of the TM were 0.6 ± 0.5, 0.2 ± 0.1, and 0.09 ± 0.09 N/m for the basal, middle, and upper turns, respectively. The BM plateau stiffness values were 3.7 ± 2.2, 1.2 ± 1.2, and 0.5 ± 0.5 N/m for the basal, middle, and upper turns, respectively. Estimations of the TM Young's modulus (in kPa) revealed 24.3 ± 25.2 for the basal turns, 5.1 ± 4.5 for the middle turns, and 1.9 ± 1.6 for the apical turns. Young's modulus determined at the BM pectinate zone was 76.8 ± 72, 23.9 ± 30.6, and 9.4 ± 6.2 kPa for the basal, middle, and apical turns, respectively. The reported stiffness values of the CBA/CaJ mouse TM and BM provide basic data for the physical properties of its organ of Corti.

Estimation of optimal insertion angle in a mammalian outer hair cell stereocilium

Optimal insertion angle of mammalian stereocilia is estimated from the finite element analysis of the tip motion of outer hair cells (OHCs) stereocilia. The OHC stereocilia motion in the acousticolateral system appears to result in the mechanoelectrical transduction channels. Deflection of the hair bundle towards the tallest row of stereocilia causes increased probability of opening of ion channels. In this work, we focus on one of the physical features of the OHC stereocilium, the initial insertion angle of the tallest row into the tectorial membrane (TM), and its effects on the stereocilia's deflection motion. A three-dimensional model was built for the tallest stereocilium and the TM at the region where the best frequency was 500Hz. The mechanical interactions between the embedded stereocilia and the TM have been implemented into the finite element simulation. We found that, the optimum insertion angle of the tallest stereocilium into the TM was 69.8°, where the stereocilium is maximally deflected. This quantity is consistent with the histological observation obtained from the literature.

Auditory mechanics of the tectorial membrane and the cochlear spiral

PURPOSE OF REVIEW

This review is timely and relevant because new experimental and theoretical findings suggest that cochlear mechanics from the nanoscale to the macroscale are affected by the mechanical properties of the tectorial membrane and the cochlea's spiral shape.

RECENT FINDINGS

Main tectorial membrane themes addressed in this review are composition and morphology, nanoscale mechanical interactions with the outer hair cell bundle, macroscale longitudinal coupling, fluid interaction with inner hair cell bundles, and macroscale dynamics and waves. Main cochlear spiral themes are macroscale, low-frequency energy focusing and microscale organ of Corti shear gain.

SUMMARY

Recent experimental and theoretical findings reveal exquisite sensitivity of cochlear mechanical performance to tectorial membrane structural organization, mechanics, and its positioning with respect to hair bundles. The cochlear spiral geometry is a major determinant of low-frequency hearing. These findings suggest a number of important research directions.

Biophysical mechanisms underlying outer hair cell loss associated with a shortened tectorial membrane

The tectorial membrane (TM) connects to the stereociliary bundles of outer hair cells (OHCs). Humans with an autosomal dominant C1509G mutation in alpha-tectorin, a protein constituent of the TM, are born with a partial hearing loss that worsens over time. The Tecta(C1509/+) transgenic mouse with the same point mutation has partial hearing loss secondary to a shortened TM that only contacts the first row of OHCs. As well, Tecta(C1509G/+) mice have increased expression of the OHC electromotility protein, prestin. We sought to determine whether these changes impact OHC survival. Distortion product otoacoustic emission thresholds in a quiet environment did not change to 6 months of age. However, noise exposure produced acute threshold shifts that fully recovered in Tecta (+/+) mice but only partially recovered in Tecta(C1509G/+) mice. While Tecta(+/+) mice lost OHCs primarily at the base and within all three rows, Tecta(C1509G/+) mice lost most of their OHCs in a more apical region of the cochlea and nearly completely within the first row. In order to estimate the impact of a shorter TM on the forces faced by the stereocilia within the first OHC row, both the wild type and the heterozygous conditions were simulated in a computational model. These analyses predicted that the shear force on the stereocilia is ~50% higher in the heterozygous condition. We then measured electrically induced movements of the reticular lamina in situ and found that while they decreased to the noise floor in prestin null mice, they were increased by 4.58 dB in Tecta(C1509G/+) mice compared to Tecta(+/+) mice. The increased movements were associated with a fourfold increase in OHC death as measured by vital dye staining. Together, these findings indicate that uncoupling the TM from some OHCs leads to partial hearing loss and places the remaining coupled OHCs at higher risk. Both the mechanics of the malformed TM and the increased prestin-related movements of the organ of Corti contribute to this higher risk profile.

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.

The interplay between active hair bundle motility and electromotility in the cochlea

The cochlear amplifier is a nonlinear active process providing the mammalian ear with its extraordinary sensitivity, large dynamic range and sharp frequency tuning. While there is much evidence that amplification results from active force generation by mechanosensory hair cells, there is debate about the cellular processes behind nonlinear amplification. Outer hair cell electromotility has been suggested to underlie the cochlear amplifier. However, it has been shown in frog and turtle that spontaneous movements of hair bundles endow them with a nonlinear response with increased sensitivity that could be the basis of amplification. The present work shows that the properties of the cochlear amplifier could be understood as resulting from the combination of both hair bundle motility and electromotility in an integrated system that couples these processes through the geometric arrangement of hair cells embedded in the cochlear partition. In this scenario, the cochlear partition can become a dynamic oscillator which in the vicinity of a Hopf bifurcation exhibits all the key properties of the cochlear amplifier. The oscillatory behavior and the nonlinearity are provided by active hair bundles. Electromotility is largely linear but produces an additional feedback that allows hair bundle movements to couple to basilar membrane vibrations.

Cochlear outer hair cells undergo an apical circumference remodeling constrained by the hair bundle shape

Epithelial cells acquire diverse shapes relating to their different functions. This is particularly relevant for the cochlear outer hair cells (OHCs), whose apical and basolateral shapes accommodate the functioning of these cells as mechano-electrical and electromechanical transducers, respectively. We uncovered a circumferential shape transition of the apical junctional complex (AJC) of OHCs, which occurs during the early postnatal period in the mouse, prior to hearing onset. Geometric analysis of the OHC apical circumference using immunostaining of the AJC protein ZO1 and Fourier-interpolated contour detection characterizes this transition as a switch from a rounded-hexagon to a non-convex circumference delineating two lateral lobes at the neural side of the cell, with a negative curvature in between. This shape tightly correlates with the 'V'-configuration of the OHC hair bundle, the apical mechanosensitive organelle that converts sound-evoked vibrations into variations in cell membrane potential. The OHC apical circumference remodeling failed or was incomplete in all the mouse mutants affected in hair bundle morphogenesis that we tested. During the normal shape transition, myosin VIIa and myosin II (A and B isoforms) displayed polarized redistributions into and out of the developing lobes, respectively, while Shroom2 and F-actin transiently accumulated in the lobes. Defects in these redistributions were observed in the mutants, paralleling their apical circumference abnormalities. Our results point to a pivotal role for actomyosin cytoskeleton tensions in the reshaping of the OHC apical circumference. We propose that this remodeling contributes to optimize the mechanical coupling between the basal and apical poles of mature OHCs.

Col11a2 deletion reveals the molecular basis for tectorial membrane mechanical anisotropy

The tectorial membrane (TM) has a significantly larger stiffness in the radial direction than other directions, a prominent mechanical anisotropy that is believed to be critical for the proper functioning of the cochlea. To determine the molecular basis of this anisotropy, we measured material properties of TMs from mice with a targeted deletion of Col11a2, which encodes for collagen XI. In light micrographs, the density of TM radial collagen fibers was lower in Col11a2 -/- mice than wild-types. Tone-evoked distortion product otoacoustic emission and auditory brainstem response measurements in Col11a2 -/- mice were reduced by 30-50 dB independent of frequency as compared with wild-types, showing that the sensitivity loss is cochlear in origin. Stress-strain measurements made using osmotic pressure revealed no significant dependence of TM bulk compressibility on the presence of collagen XI. Charge measurements made by placing the TM as an electrical conduit between two baths revealed no change in the density of charge affixed to the TM matrix in Col11a2 -/- mice. Measurements of mechanical shear impedance revealed a 5.5 +/- 0.8 dB decrease in radial shear impedance and a 3.3 +/- 0.3 dB decrease in longitudinal shear impedance resulting from the Col11a2 deletion. The ratio of radial to longitudinal shear impedance fell from 1.8 +/- 0.7 for TMs from wild-type mice to 1.0 +/- 0.1 for those from Col11a2 -/- mice. These results show that the organization of collagen into radial fibrils is responsible for the mechanical anisotropy of the TM. This anisotropy can be attributed to increased mechanical coupling provided by the collagen fibrils. Mechanisms by which changes in TM material properties may contribute to the threshold elevation in Col11a2 -/- mice are discussed.

Collagen-based mechanical anisotropy of the tectorial membrane: implications for inter-row coupling of outer hair cell bundles

Background

The tectorial membrane (TM) in the mammalian cochlea displays anisotropy, where mechanical or structural properties differ along varying directions. The anisotropy arises from the presence of collagen fibrils organized in fibers of ∼1 µm diameter that run radially across the TM. Mechanical coupling between the TM and the sensory epithelia is required for normal hearing. However, the lack of a suitable technique to measure mechanical anisotropy at the microscale level has hindered understanding of the TM's precise role.

Methodology/Principal Findings

Here we report values of the three elastic moduli that characterize the anisotropic mechanical properties of the TM. Our novel technique combined Atomic Force Microscopy (AFM), modeling, and optical tracking of microspheres to determine the elastic moduli. We found that the TM's large mechanical anisotropy results in a marked transmission of deformations along the direction that maximizes sensory cell excitation, whereas in the perpendicular direction the transmission is greatly reduced.

Conclusions/Significance

Computational results, based on our values of elastic moduli, suggest that the TM facilitates the directional cooperativity of sensory cells in the cochlea, and that mechanical properties of the TM are tuned to guarantee that the magnitude of sound-induced tip-link stretching remains similar along the length of the cochlea. Furthermore, we anticipate our assay to be a starting point for other studies of biological tissues that require directional functionality.

The tectorial membrane: one slice of a complex cochlear sandwich

PURPOSE OF REVIEW

The review is both timely and relevant, as recent findings have shown the tectorial membrane plays a more dynamic role in hearing than hitherto suspected, and that many forms of deafness can result from mutations in tectorial membrane proteins.

RECENT FINDINGS

Main themes covered are the molecular composition, the structural organization and properties of the tectorial membrane, the role of the tectorial membrane as a second resonator and a structure within which there is significant longitudinal coupling, and how mutations in tectorial membrane proteins cause deafness in mice and men.

CONCLUSION

Findings from experimental models imply that the tectorial membrane plays multiple, critical roles in hearing. These include coupling elements along the length of the cochlea, supporting a travelling wave and ensuring the gain and timing of cochlear feedback are optimal. The clinical findings suggest stable, moderate-to-severe forms of hereditary hearing loss may be diagnostic of a mutation in TECTA, a gene encoding one of the major, noncollagenous proteins of the tectorial membrane.

Theoretical conditions for high-frequency hair bundle oscillations in auditory hair cells

Substantial evidence exists for spontaneous oscillations of hair cell stereociliary bundles in the lower vertebrate inner ear. Since the oscillations are larger than expected from Brownian motion, they must result from an active process in the stereociliary bundle suggested to underlie amplification of the sensory input as well as spontaneous otoacoustic emissions. However, their low frequency (<100 Hz) makes them unsuitable for amplification in birds and mammals that hear up to 5 kHz or higher. To examine the possibility of high-frequency oscillations, we used a finite-element model of the outer hair cell bundle incorporating previously measured mechanical parameters. Bundle motion was assumed to activate mechanotransducer channels according to the gating spring hypothesis, and the channels were regulated adaptively by Ca(2+) binding. The model generated oscillations of freestanding bundles at 4 kHz whose sharpness of tuning depended on the mechanotransducer channel number and location, and the Ca(2+) concentration. Entrainment of the oscillations by external stimuli was used to demonstrate nonlinear amplification. The oscillation frequency depended on channel parameters and was increased to 23 kHz principally by accelerating Ca(2+) binding kinetics. Spontaneous oscillations persisted, becoming very narrow-band, when the hair bundle was loaded with a tectorial membrane mass.