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

Gating-spring stiffness increases outer-hair-cell bundle stiffness, damping, and receptor current

In our ears, outer-hair-cell bundles (OHBs) convert sound-induced forces into receptor currents that drive cochlear amplification, the process responsible for the micropascal-scale threshold and million-fold dynamic range of hearing. OHBs rely on gating springs to open mechanoelectrical-transduction (MET) ion channels, through which the receptor current flows. OHBs have larger gating-spring stiffnesses than other types of hair bundles, but we have a poor understanding of how gating-spring stiffness contributes to OHB mechanics and receptor-current regulation. Using experimentally-constrained mathematical models of the OHB, we show that the increased gating-spring stiffness in an OHB increases its stiffness and damping. The OHB's 3D morphology reduces the contribution of gating-spring stiffness to OHB stiffness, reduces the contribution of MET-channel gating to OHB stiffness and damping, but causes additional OHB damping that rises with gating-spring stiffness. Gating-spring stiffness increases the OHB's receptor current but decreases its displacement-current dynamic range. Strikingly, the OHB's 3D morphology causes its force-current dynamic range to decrease with gating-spring stiffness. Our results suggest a trade-off between threshold and dynamic range regulated by OHB gating-spring stiffness.

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.

Fast adaptation of cooperative channels engenders Hopf bifurcations in auditory hair cells

Since the pioneering work of Thomas Gold, published in 1948, it has been known that we owe our sensitive sense of hearing to a process in the inner ear that can amplify incident sounds on a cycle-by-cycle basis. Called the active process, it uses energy to counteract the viscous dissipation associated with sound-evoked vibrations of the ear's mechanotransduction apparatus. Despite its importance, the mechanism of the active process and the proximate source of energy that powers it have remained elusive, especially at the high frequencies characteristic of amniote hearing. This is partly due to our insufficient understanding of the mechanotransduction process in hair cells, the sensory receptors and amplifiers of the inner ear. It has been proposed previously that cyclical binding of Ca2+ ions to individual mechanotransduction channels could power the active process. That model, however, relied on tailored reaction rates that structurally forced the direction of the cycle. Here we ground our study on our previous model of hair-cell mechanotransduction, which relied on cooperative gating of pairs of channels, and incorporate into it the cyclical binding of Ca2+ ions. With a single binding site per channel and reaction rates drawn from thermodynamic principles, the current model shows that hair cells behave as nonlinear oscillators that exhibit Hopf bifurcations, dynamical instabilities long understood to be signatures of the active process. Using realistic parameter values, we find bifurcations at frequencies in the kilohertz range with physiological Ca2+ concentrations. The current model relies on the electrochemical gradient of Ca2+ as the only energy source for the active process and on the relative motion of cooperative channels within the stereociliary membrane as the sole mechanical driver. Equipped with these two mechanisms, a hair bundle proves capable of operating at frequencies in the kilohertz range, characteristic of amniote hearing.

The speed of the hair cell mechanotransducer channel revealed by fluctuation analysis

Although mechanoelectrical transducer (MET) channels have been extensively studied, uncertainty persists about their molecular architecture and single-channel conductance. We made electrical measurements from mouse cochlear outer hair cells (OHCs) to reexamine the MET channel conductance comparing two different methods. Analysis of fluctuations in the macroscopic currents showed that the channel conductance in apical OHCs determined from nonstationary noise analysis was about half that of single-channel events recorded after tip link destruction. We hypothesized that this difference reflects a bandwidth limitation in the noise analysis, which we tested by simulations of stochastic fluctuations in modeled channels. Modeling indicated that the unitary conductance depended on the relative values of the channel activation time constant and the applied low-pass filter frequency. The modeling enabled the activation time constant of the channel to be estimated for the first time, yielding a value of only a few microseconds. We found that the channel conductance, assayed with both noise and recording of single-channel events, was reduced by a third in a new deafness mutant, Tmc1 p.D528N. Our results indicate that noise analysis is likely to underestimate MET channel amplitude, which is better characterized from recordings of single-channel events.

Multiscale modeling of mechanotransduction in the utricle

We review recent progress in using numerical models to relate utricular hair bundle and otoconial membrane (OM) structure to the functional requirements imposed by natural behavior in turtles. The head movements section reviews the evolution of experimental attempts to understand vestibular system function with emphasis on turtles, including data showing that accelerations occurring during natural head movements achieve higher magnitudes and frequencies than previously assumed. The structure section reviews quantitative anatomical data documenting topographical variation in the structures underlying macromechanical and micromechanical responses of the turtle utricle to head movement: hair bundles, OM, and bundle-OM coupling. The macromechanics section reviews macromechanical models that incorporate realistic anatomical and mechanical parameters and reveal that the system is significantly underdamped, contrary to previous assumptions. The micromechanics: hair bundle motion and met currents section reviews work based on micromechanical models, which demonstrates that topographical variation in the structure of hair bundles and OM, and their mode of coupling, result in regional specializations for signaling of low frequency (or static) head position and high frequency head accelerations. We conclude that computational models based on empirical data are especially promising for investigating mechanotransduction in this challenging sensorimotor system.

Power Dissipation in the Cochlea Can Enhance Frequency Selectivity

The cochlear cavity is filled with viscous fluids, and it is partitioned by a viscoelastic structure called the organ of Corti complex. Acoustic energy propagates toward the apex of the cochlea through vibrations of the organ of Corti complex. The dimensions of the vibrating structures range from a few hundred (e.g., the basilar membrane) to a few micrometers (e.g., the stereocilia bundle). Vibrations of microstructures in viscous fluid are subjected to energy dissipation. Because the viscous dissipation is considered to be detrimental to the function of hearing-sound amplification and frequency tuning-the cochlea uses cellular actuators to overcome the dissipation. Compared to extensive investigations on the cellular actuators, the dissipating mechanisms have not been given appropriate attention, and there is little consensus on damping models. For example, many theoretical studies use an inviscid fluid approximation and lump the viscous effect to viscous damping components. Others neglect viscous dissipation in the organ of Corti but consider fluid viscosity. We have developed a computational model of the cochlea that incorporates viscous fluid dynamics, organ of Corti microstructural mechanics, and electrophysiology of the outer hair cells. The model is validated by comparing with existing measurements, such as the viscoelastic response of the tectorial membrane, and the cochlear input impedance. Using the model, we investigated how dissipation components in the cochlea affect its function. We found that the majority of acoustic energy dissipation of the cochlea occurs within the organ of Corti complex, not in the scalar fluids. Our model suggests that an appropriate dissipation can enhance the tuning quality by reducing the spread of energy provided by the outer hair cells' somatic motility.

Cochlear outer hair cell horizontal top connectors mediate mature stereocilia bundle mechanics

Outer hair cell (OHC) stereocilia bundle deflection opens mechanoelectrical transduction channels at the tips of the stereocilia from the middle and short rows, while bundle cohesion is maintained owing to the presence of horizontal top connectors. Here, we used a quantitative noncontact atomic force microscopy method to investigate stereocilia bundle stiffness and damping, when stimulated at acoustic frequencies and nanometer distances from the bundle. Stereocilia bundle mechanics were determined in stereocilin-deficient mice lacking top connectors and with detached tectorial membrane (Strc -/-/Tecta -/- double knockout) and heterozygous littermate controls (Strc +/-/Tecta -/-). A substantial decrease in bundle stiffness and damping by ~60 and ~74% on postnatal days P13 to P15 was observed when top connectors were absent. Additionally, we followed bundle mechanics during OHC top connectors development between P9 and P15 and quantified the observed increase in OHC bundle stiffness and damping in Strc +/-/Tecta -/- mice while no significant change was detected in Strc -/-/Tecta -/- animals.

An operating principle of the turtle utricle to detect wide dynamic range

The utricle encodes both static information such as head orientation, and dynamic information such as vibrations. It is not well understood how the utricle can encode both static and dynamic information for a wide dynamic range (from <0.05 to >2 times the gravitational acceleration; from DC to > 1000 Hz vibrations). Using computational models of the hair cells in the turtle utricle, this study presents an explanation on how the turtle utricle encodes stimulations over such a wide dynamic range. Two hair bundles were modeled using the finite element method-one representing the striolar hair cell (Cell S), and the other representing the medial extrastriolar hair cell (Cell E). A mechano-transduction (MET) channel model was incorporated to compute MET current (i_MET) due to hair bundle deflection. A macro-mechanical model of the utricle was used to compute otoconial motions from head accelerations (a_Head). According to known anatomical data, Cell E has a long kinocilium that is embedded into the stiff otoconial layer. Unlike Cell E, the hair bundle of Cell S falls short of the otoconial layer. Considering such difference in the mechanical connectivity between the hair cell bundle and the otoconial layer, three cases were simulated: Cell E displacement-clamped, Cell S viscously-coupled, and Cell S displacement-clamped. Head accelerations at different amplitude levels and different frequencies were simulated for the three cases. When a realistic head motion was simulated, Cell E was responsive to head orientation, while the viscously-coupled Cell S was responsive to fast head motion imitating the feeding strike of a turtle.

Two passive mechanical conditions modulate power generation by the outer hair cells

In the mammalian cochlea, small vibrations of the sensory epithelium are amplified due to active electro-mechanical feedback of the outer hair cells. The level of amplification is greater in the base than in the apex of the cochlea. Theoretical studies have used longitudinally varying active feedback properties to reproduce the location-dependent amplification. The active feedback force has been considered to be proportional to the basilar membrane displacement or velocity. An underlying assumption was that organ of Corti mechanics are governed by rigid body kinematics. However, recent progress in vibration measurement techniques reveals that organ of Corti mechanics are too complicated to be fully represented with rigid body kinematics. In this study, two components of the active feedback are considered explicitly-organ of Corti mechanics, and outer hair cell electro-mechanics. Physiological properties for the outer hair cells were incorporated, such as the active force gain, mechano-transduction properties, and membrane RC time constant. Instead of a kinematical model, a fully deformable 3D finite element model was used. We show that the organ of Corti mechanics dictate the longitudinal trend of cochlear amplification. Specifically, our results suggest that two mechanical conditions are responsible for location-dependent cochlear amplification. First, the phase of the outer hair cell's somatic force with respect to its elongation rate varies along the cochlear length. Second, the local stiffness of the organ of Corti complex felt by individual outer hair cells varies along the cochlear length. We describe how these two mechanical conditions result in greater amplification toward the base of the cochlea.

Energy Output from a Single Outer Hair Cell

Electromotility of outer hair cells (OHCs) has been extensively studied with in vitro experiments because of its physiological significance to the cochlear amplifier, which provides the exquisite sensitivity and frequency selectivity of the mammalian ear. However, these studies have been performed largely under load-free conditions or with static load, while these cells function in vivo in a dynamic environment, receiving electrical energy to enhance mechanical oscillation in the inner ear. This gap leaves uncertainties in addressing a key issue, how much mechanical energy an OHC provides. This study is an attempt of bridging the gap by introducing a simple one-dimensional model for electromotility of OHC in a dynamic environment. This model incorporates a feedback loop involving the receptor potential and the mechanical load on OHC, and leads to an analytical expression for the membrane capacitance, which explicitly describes the dependence on the elastic load, viscous drag, and the mass. The derived equation of motion was examined in a mass-less model system with realistic parameter values for OHC. It was found that viscous drag is more effective than elastic load in enhancing the receptor potential that drives the cell. For this reason, it is expected that OHCs are more effective in counteracting viscous drag than providing elastic energy to the system.

Underestimated sensitivity of mammalian cochlear hair cells due to splay between stereociliary columns

Current-displacement (I-X) and the force-displacement (F-X) relationships characterize hair-cell mechano-transduction in the inner ear. A common technique for measuring these relationships is to deliver mechanical stimulations to individual hair bundles with microprobes and measure whole cell transduction currents through patch pipette electrodes at the basolateral membrane. The sensitivity of hair-cell mechano-transduction is determined by two fundamental biophysical properties of the mechano-transduction channel, the stiffness of the putative gating spring and the gating swing, which are derived from the I-X and F-X relationships. Although the hair-cell stereocilia in vivo deflect <100 nm even at high sound pressure levels, often it takes >500 nm of stereocilia displacement to saturate hair-cell mechano-transduction in experiments with individual hair cells in vitro. Despite such discrepancy between in vivo and in vitro data, key biophysical properties of hair-cell mechano-transduction to define the transduction sensitivity have been estimated from in vitro experiments. Using three-dimensional finite-element methods, we modeled an inner hair-cell and an outer hair-cell stereocilia bundle and simulated the effect of probe stimulation. Unlike the natural situation where the tectorial membrane stimulates hair-cell stereocilia evenly, probes deflect stereocilia unevenly. Because of uneven stimulation, 1) the operating range (the 10–90% width of the I-X relationship) increases by a factor of 2–8 depending on probe shapes, 2) the I-X relationship changes from a symmetric to an asymmetric function, and 3) the bundle stiffness is underestimated. Our results indicate that the generally accepted assumption of parallel stimulation leads to an overestimation of the gating swing and underestimation of the gating spring stiffness by an order of magnitude.

Power dissipation in the subtectorial space of the mammalian cochlea is modulated by inner hair cell stereocilia

The stereocilia bundle is the mechano-transduction apparatus of the inner ear. In the mammalian cochlea, the stereocilia bundles are situated in the subtectorial space (STS)--a micrometer-thick space between two flat surfaces vibrating relative to each other. Because microstructures vibrating in fluid are subject to high-viscous friction, previous studies considered the STS as the primary place of energy dissipation in the cochlea. Although there have been extensive studies on how metabolic energy is used to compensate the dissipation, much less attention has been paid to the mechanism of energy dissipation. Using a computational model, we investigated the power dissipation in the STS. The model simulates fluid flow around the inner hair cell (IHC) stereocilia bundle. The power dissipation in the STS because of the presence IHC stereocilia increased as the stimulating frequency decreased. Along the axis of the stimulating frequency, there were two asymptotic values of power dissipation. At high frequencies, the power dissipation was determined by the shear friction between the two flat surfaces of the STS. At low frequencies, the power dissipation was dominated by the viscous friction around the IHC stereocilia bundle--the IHC stereocilia increased the STS power dissipation by 50- to 100-fold. There exists a characteristic frequency for STS power dissipation, CFSTS, defined as the frequency where power dissipation drops to one-half of the low frequency value. The IHC stereocilia stiffness and the gap size between the IHC stereocilia and the tectorial membrane determine the characteristic frequency. In addition to the generally assumed shear flow, nonshear STS flow patterns were simulated. Different flow patterns have little effect on the CFSTS. When the mechano-transduction of the IHC was tuned near the vibrating frequency, the active motility of the IHC stereocilia bundle reduced the power dissipation in the STS.

Consequences of Location-Dependent Organ of Corti Micro-Mechanics

The cochlea performs frequency analysis and amplification of sounds. The graded stiffness of the basilar membrane along the cochlear length underlies the frequency-location relationship of the mammalian cochlea. The somatic motility of outer hair cell is central for cochlear amplification. Despite two to three orders of magnitude change in the basilar membrane stiffness, the force capacity of the outer hair cell’s somatic motility, is nearly invariant over the cochlear length. It is puzzling how actuators with a constant force capacity can operate under such a wide stiffness range. We hypothesize that the organ of Corti sets the mechanical conditions so that the outer hair cell’s somatic motility effectively interacts with the media of traveling waves—the basilar membrane and the tectorial membrane. To test this hypothesis, a computational model of the gerbil cochlea was developed that incorporates organ of Corti structural mechanics, cochlear fluid dynamics, and hair cell electro-physiology. The model simulations showed that the micro-mechanical responses of the organ of Corti are different along the cochlear length. For example, the top surface of the organ of Corti vibrated more than the bottom surface at the basal (high frequency) location, but the amplitude ratio was reversed at the apical (low frequency) location. Unlike the basilar membrane stiffness varying by a factor of 1700 along the cochlear length, the stiffness of the organ of Corti complex felt by the outer hair cell remained between 1.5 and 0.4 times the outer hair cell stiffness. The Y-shaped structure in the organ of Corti formed by outer hair cell, Deiters cell and its phalange was the primary determinant of the elastic reactance imposed on the outer hair cells. The stiffness and geometry of the Deiters cell and its phalange affected cochlear amplification differently depending on the location.

Salient features of otoacoustic emissions are common across tetrapod groups and suggest shared properties of generation mechanisms

Otoacoustic emissions (OAEs) are faint sounds generated by healthy inner ears that provide a window into the study of auditory mechanics. All vertebrate classes exhibit OAEs to varying degrees, yet the biophysical origins are still not well understood. Here, we analyzed both spontaneous (SOAE) and stimulus-frequency (SFOAE) otoacoustic emissions from a bird (barn owl, Tyto alba) and a lizard (green anole, Anolis carolinensis). These species possess highly disparate macromorphologies of the inner ear relative to each other and to mammals, thereby allowing for novel insights into the biomechanical mechanisms underlying OAE generation. All ears exhibited robust OAE activity, and our chief observation was that SFOAE phase accumulation between adjacent SOAE peak frequencies clustered about an integral number of cycles. Being highly similar to published results from human ears, we argue that these data indicate a common underlying generator mechanism of OAEs across all vertebrates, despite the absence of morphological features thought essential to mammalian cochlear mechanics. We suggest that otoacoustic emissions originate from phase coherence in a system of coupled oscillators, which is consistent with the notion of "coherent reflection" but does not explicitly require a mammalian-type traveling wave. Furthermore, comparison between SFOAE delays and auditory nerve fiber responses for the barn owl strengthens the notion that most OAE delay can be attributed to tuning.

Microstructures in the organ of Corti help outer hair cells form traveling waves along the cochlear coil

According to the generally accepted theory of mammalian cochlear mechanics, the fluid in the cochlear scalae interacts with the elastic cochlear partition to generate transversely oscillating displacement waves that propagate along the cochlear coil. Using a computational model of cochlear segments, a different type of propagating wave is reported, an elastic propagating wave that is independent of the fluid-structure interaction. The characteristics of the propagating wave observed in the model, such as the wavelength, speed, and phase lag, are similar to those observed in the living cochlea. Three conditions are required for the existence of the elastic propagating wave in the cochlear partition without fluid-interaction: 1), the stiffness gradient of the cochlear partition; 2), the elastic longitudinal coupling; and 3), the Y-shaped structure in the organ of Corti formed by the outer hair cell, the Deiters cell, and the Deiters cell phalangeal process. The elastic propagating waves in the cochlear partition disappeared without the push-pull action provided by the outer hair cell and Deiters cell phalangeal process. The results suggest that the mechanical feedback of outer hair cells, facilitated by the organ of Corti microstructure, can control the tuning and amplification by modulating the cochlear traveling wave.

Transduction channels' gating can control friction on vibrating hair-cell bundles in the ear

Hearing starts when sound-evoked mechanical vibrations of the hair-cell bundle activate mechanosensitive ion channels, giving birth to an electrical signal. As for any mechanical system, friction impedes movements of the hair bundle and thus constrains the sensitivity and frequency selectivity of auditory transduction. Friction is generally thought to result mainly from viscous drag by the surrounding fluid. We demonstrate here that the opening and closing of the transduction channels produce internal frictional forces that can dominate viscous drag on the micrometer-sized hair bundle. We characterized friction by analyzing hysteresis in the force-displacement relation of single hair-cell bundles in response to periodic triangular stimuli. For bundle velocities high enough to outrun adaptation, we found that frictional forces were maximal within the narrow region of deflections that elicited significant channel gating, plummeted upon application of a channel blocker, and displayed a sublinear growth for increasing bundle velocity. At low velocity, the slope of the relation between the frictional force and velocity was nearly fivefold larger than the hydrodynamic friction coefficient that was measured when the transduction machinery was decoupled from bundle motion by severing tip links. A theoretical analysis reveals that channel friction arises from coupling the dynamics of the conformational change associated with channel gating to tip-link tension. Varying channel properties affects friction, with faster channels producing smaller friction. We propose that this intrinsic source of friction may contribute to the process that sets the hair cell's characteristic frequency of responsiveness.

Auditory Distortions: Origins and Functions

To enhance weak sounds while compressing the dynamic intensity range, auditory sensory cells amplify sound-induced vibrations in a nonlinear, intensity-dependent manner. In the course of this process, instantaneous waveform distortion is produced, with two conspicuous kinds of interwoven consequences, the introduction of new sound frequencies absent from the original stimuli, which are audible and detectable in the ear canal as otoacoustic emissions, and the possibility for an interfering sound to suppress the response to a probe tone, thereby enhancing contrast among frequency components. We review how the diverse manifestations of auditory nonlinearity originate in the gating principle of their mechanoelectrical transduction channels; how they depend on the coordinated opening of these ion channels ensured by connecting elements; and their links to the dynamic behavior of auditory sensory cells. This paper also reviews how the complex properties of waves traveling through the cochlea shape the manifestations of auditory nonlinearity. Examination methods based on the detection of distortions open noninvasive windows on the modes of activity of mechanosensitive structures in auditory sensory cells and on the distribution of sites of nonlinearity along the cochlear tonotopic axis, helpful for deciphering cochlear molecular physiology in hearing-impaired animal models. Otoacoustic emissions enable fast tests of peripheral sound processing in patients. The study of auditory distortions also contributes to the understanding of the perception of complex sounds.

How fast does a signal propagate through proteins?

As the molecular basis of signal propagation in the cell, proteins are regulated by perturbations, such as mechanical forces or ligand binding. The question arises how fast such a signal propagates through the protein molecular scaffold. As a first step, we have investigated numerically the dynamics of force propagation through a single (Ala) protein following a sudden increase in the stretching forces applied to its end termini. The force propagates along the backbone into the center of the chain on the picosecond scale. Both conformational and tension dynamics are found in good agreement with a coarse-grained theory of force propagation through semiflexible polymers. The speed of force propagation of 50Å ps⁻¹ derived from these simulations is likely to determine an upper speed limit of mechanical signal transfer in allosteric proteins or molecular machines.

High-multiple spontaneous otoacoustic emissions confirm theory of local tuned oscillators

Understanding the origin of spontaneous otoacoustic emissions (SOAEs) in mammals has been a challenge for more than three decades. Right from the beginning two mutually exclusive concepts were explored. After 30 years this has now resulted in two well established but incompatible theories, the global standing-wave theory and the local oscillator theory. The outcome of this controversy will be important for our understanding of inner ear functions, because local tuned oscillators in the cochlea would indicate the possibility of frequency analysis via local resonance also in mammals. A previously unexploited opportunity to gain further information on this matter lies in the occasional cases of high-multiple SOAEs in human ears, which present a large number of adjacent small frequency intervals. Here, eight healthy ears of four subjects (12 to 32 SOAEs per ear) are compared with individually simulated ears where frequency spacing was random-generated by two different techniques. Further, a group of 1000 ears was simulated presenting a mean of 21.3 SOAEs per ear. The simulations indicate that the typical frequency spacing of human SOAEs may be due to random distribution of emitters along the cochlea plus a graded probability of mutual close-range suppression between adjacent emitters. It was found that the distribution of frequency intervals of SOAEs shows no above-chance probability of multiples of the preferred minimum distance (PMD) between SOAEs and that the size of PMD is related to SOAE density. The variation in size between adjacent small intervals is not significantly different in random-generated than in measured data. These three results are not in agreement with the global standing-wave theory but are in line with the local oscillator theory. In conclusion, the results are consistent with intrinsic tuning of cochlear outer hair cells.

Optimal electrical properties of outer hair cells ensure cochlear amplification

The organ of Corti (OC) is the auditory epithelium of the mammalian cochlea comprising sensory hair cells and supporting cells riding on the basilar membrane. The outer hair cells (OHCs) are cellular actuators that amplify small sound-induced vibrations for transmission to the inner hair cells. We developed a finite element model of the OC that incorporates the complex OC geometry and force generation by OHCs originating from active hair bundle motion due to gating of the transducer channels and somatic contractility due to the membrane protein prestin. The model also incorporates realistic OHC electrical properties. It explains the complex vibration modes of the OC and reproduces recent measurements of the phase difference between the top and the bottom surface vibrations of the OC. Simulations of an individual OHC show that the OHC somatic motility lags the hair bundle displacement by ∼90 degrees. Prestin-driven contractions of the OHCs cause the top and bottom surfaces of the OC to move in opposite directions. Combined with the OC mechanics, this results in ∼90 degrees phase difference between the OC top and bottom surface vibration. An appropriate electrical time constant for the OHC membrane is necessary to achieve the phase relationship between OC vibrations and OHC actuations. When the OHC electrical frequency characteristics are too high or too low, the OHCs do not exert force with the correct phase to the OC mechanics so that they cannot amplify. We conclude that the components of OHC forward and reverse transduction are crucial for setting the phase relations needed for amplification.

Mechano-electrical vibrations of microtubules--link to subcellular morphology

Spontaneous mechanical oscillations were predicted and experimentally proven on almost every level of cellular structure. Besides morphogenetic potential of oscillatory mechanical force, oscillations may drive vibrations of electrically polar structures or these structures themselves may oscillate on their own natural frequencies. Vibrations of electric charge will generate oscillating electric field, role of which in morphogenesis is discussed in this paper. This idea is demonstrated in silico on the conformation of two growing microtubules.

Biomechanical regulation of contractility: spatial control and dynamics

Cells are active materials; they can change shape using internal energy to build contractile networks of actin filaments and myosin motors. Contractility of the actomyosin cortex is tightly regulated in space and time to orchestrate cell shape changes. Conserved biochemical pathways regulate actomyosin networks in subcellular domains which drive cell shape changes. Actomyosin networks display complex dynamics, such as flows and pulses, which participate in myosin distribution and provide a more realistic description of the spatial distribution and evolution of forces during morphogenesis. Such dynamics are influenced by the mechanical properties of actomyosin networks. Moreover, actomyosin can self-organize and respond to mechanical stimuli through multiple types of biomechanical feedback. In this review we propose a framework encapsulating spatiotemporal regulation of contractility from established pathways with the dynamics and mechanics of actomyosin networks. Through the comparison of cytokinesis, cell migration and epithelial morphogenesis, we delineate emergent properties of contractile activity, including self-organization, adaptability and robustness.

Coupling active hair bundle mechanics, fast adaptation, and somatic motility in a cochlear model

One of the central questions in the biophysics of the mammalian cochlea is determining the contributions of the two active processes, prestin-based somatic motility and hair bundle (HB) motility, to cochlear amplification. HB force generation is linked to fast adaptation of the transduction current via a calcium-dependent process and somatic force generation is driven by the depolarization caused by the transduction current. In this article, we construct a global mechanical-electrical-acoustical mathematical model of the cochlea based on a three-dimensional fluid representation. The global cochlear model is coupled to linearizations of nonlinear somatic motility and HB activity as well as to the micromechanics of the passive structural and electrical elements of the cochlea. We find that the active HB force alone is not sufficient to power high frequency cochlear amplification. However, somatic motility can overcome resistor-capacitor filtering by the basolateral membrane and deliver sufficient mechanical energy for amplification at basal locations. The results suggest a new theory for high frequency active cochlear mechanics, in which fast adaptation controls the transduction channel sensitivity and thereby the magnitude of the energy delivered by somatic motility.

Tectorial membrane morphological variation: effects upon stimulus frequency otoacoustic emissions

The tectorial membrane (TM) is widely believed to play an important role in determining the ear's ability to detect and resolve incoming acoustic information. While it is still unclear precisely what that role is, the TM has been hypothesized to help overcome viscous forces and thereby sharpen mechanical tuning of the sensory cells. Lizards present a unique opportunity to further study the role of the TM given the diverse inner-ear morphological differences across species. Furthermore, stimulus-frequency otoacoustic emissions (SFOAEs), sounds emitted by the ear in response to a tone, noninvasively probe the frequency selectivity of the ear. We report estimates of auditory tuning derived from SFOAEs for 12 different species of lizards with widely varying TM morphology. Despite gross anatomical differences across the species examined herein, low-level SFOAEs were readily measurable in all ears tested, even in non-TM species whose basilar papilla contained as few as 50-60 hair cells. Our measurements generally support theoretical predictions: longer delays/sharper tuning features are found in species with a TM relative to those without. However, SFOAEs from at least one non-TM species (Anolis) with long delays suggest there are likely additional micromechanical factors at play that can directly affect tuning. Additionally, in the one species examined with a continuous TM (Aspidoscelis) where cell-to-cell coupling is presumably relatively stronger, delays were intermediate. This observation appears consistent with recent reports that suggest the TM may play a more complex macromechanical role in the mammalian cochlea via longitudinal energy distribution (and thereby affect tuning). Although significant differences exist between reptilian and mammalian auditory biophysics, understanding lizard OAE generation mechanisms yields significant insight into fundamental principles at work in all vertebrate ears.

The remarkable cochlear amplifier

This composite article is intended to give the experts in the field of cochlear mechanics an opportunity to voice their personal opinion on the one mechanism they believe dominates cochlear amplification in mammals. A collection of these ideas are presented here for the auditory community and others interested in the cochlear amplifier. Each expert has given their own personal view on the topic and at the end of their commentary they have suggested several experiments that would be required for the decisive mechanism underlying the cochlear amplifier. These experiments are presently lacking but if successfully performed would have an enormous impact on our understanding of the cochlear amplifier.

Sliding adhesion confers coherent motion to hair cell stereocilia and parallel gating to transduction channels

When the tip of a hair bundle is deflected by a sensory stimulus, the stereocilia pivot as a unit, producing a shearing displacement between adjacent tips. It is not clear how stereocilia can stick together laterally but still shear. We used dissociated hair cells from the bullfrog saccule and high-speed video imaging to characterize this sliding adhesion. Movement of individual stereocilia was proportional to height, indicating that stereocilia pivot at their basal insertion points. All stereocilia moved by approximately the same angular deflection, and the same motion was observed at 1, 20, and 700 Hz stimulus frequency. Motions were consistent with a geometric model that assumes the stiffness of lateral links holding stereocilia together is >1000 times the pivot stiffness of stereocilia and that these links can slide in the plane of the membrane-in essence, that stereocilia shear without separation. The same motion was observed when bundles were moved perpendicular to the tip links, or when tip links, ankle links, and shaft connectors were cut, ruling out these links as the basis for sliding adhesion. Stereocilia rootlets are angled toward the center of the bundle, tending to push stereocilia tips together for small deflections. However, stereocilia remained cohesive for deflections of up to +/-35 degrees, ruling out rootlet prestressing as the basis for sliding adhesion. These observations suggest that horizontal top connectors mediate a sliding adhesion. They also indicate that all transduction channels of a hair cell are mechanically in parallel, an arrangement that may enhance amplification in the inner ear.

Somatic motility and hair bundle mechanics, are both necessary for cochlear amplification?

Hearing organs have evolved to detect sounds across several orders of magnitude of both intensity and frequency. Detection limits are at the atomic level despite the energy associated with sound being limited thermodynamically. Several mechanisms have evolved to account for the remarkable frequency selectivity, dynamic range, and sensitivity of these various hearing organs, together termed the active process or cochlear amplifier. Similarities between hearing organs of disparate species provides insight into the factors driving the development of the cochlear amplifier. These properties include: a tonotopic map, the emergence of a two hair cell system, the separation of efferent and afferent innervations, the role of the tectorial membrane, and the shift from intrinsic tuning and amplification to a more end organ driven process. Two major contributors to the active process are hair bundle mechanics and outer hair cell electromotility, the former present in all hair cell organs tested, the latter only present in mammalian cochlear outer hair cells. Both of these processes have advantages and disadvantages, and how these processes interact to generate the active process in the mammalian system is highly disputed. A hypothesis is put forth suggesting that hair bundle mechanics provides amplification and filtering in most hair cells, while in mammalian cochlea, outer hair cell motility provides the amplification on a cycle by cycle basis driven by the hair bundle that provides frequency selectivity (in concert with the tectorial membrane) and compressive nonlinearity. Separating components of the active process may provide additional sites for regulation of this process.

Spontaneous oscillations, signal amplification, and synchronization in a model of active hair bundle mechanics

We study spontaneous dynamics and signal transduction in a model of active hair bundle mechanics of sensory hair cells. The hair bundle motion is subjected to internal noise resulted from thermal fluctuations and stochastic dynamics of mechanoelectrical transduction ion channels. Similar to other studies we found that in the presence of noise the coherence of stochastic oscillations is maximal at a point on the bifurcation diagram away from the Andronov-Hopf bifurcation and is close to the point of maximum sensitivity of the system to weak periodic mechanical perturbations. Despite decoherent effect of noise the stochastic hair bundle oscillations can be synchronized by external periodic force of few pN amplitude in a finite range of control parameters. We then study effects of receptor potential oscillations on mechanics of the hair bundle and show that the hair bundle oscillations can be synchronized by oscillating receptor voltage. Moreover, using a linear model for the receptor potential we show that bidirectional coupling of the hair bundle and the receptor potential results in significant enhancement of the coherence of spontaneous oscillations and of the sensitivity to the external mechanical perturbations.

Localization of inner hair cell mechanotransducer channels using high-speed calcium imaging

Hair cells detect vibrations of their stereociliary bundle by activation of mechanically sensitive transducer channels. Although evidence suggests the transducer channels are near the stereociliary tops and are opened by force imparted by tip links connecting contiguous stereocilia, the exact channel site remains controversial. We used fast confocal imaging of fluorescence changes reflecting calcium entry during bundle stimulation to localize the channels. Calcium signals were visible in single stereocilia of rat cochlear inner hair cells and were up to tenfold larger and faster in the second and third stereociliary rows than in the tallest first row. The number of functional stereocilia was proportional to transducer current amplitude, indicating that there were about two channels per stereocilium. Comparable results were obtained in outer hair cells. The observations, supported by theoretical simulations, suggest there are no functional mechanically sensitive transducer channels in first row stereocilia and imply the channels are present only at the bottom of the tip links.