Dynamics of freely oscillating and coupled hair cell bundles under mechanical deflection

In vitro, attachment to the overlying membrane was found to affect the resting position of the hair cell bundles of the bullfrog sacculus. To assess the effects of such a deflection on mechanically decoupled hair bundles, comparable offsets were imposed on decoupled spontaneously oscillating bundles. Strong modulation was observed in their dynamic state under deflection, with qualitative changes in the oscillation profile, amplitude, and characteristic frequency of oscillation seen in response to stimulus. Large offsets were found to arrest spontaneous oscillation, with subsequent recovery upon reversal of the stimulus. The dynamic state of the hair bundle displayed hysteresis and a dependence on the direction of the imposed offset. The coupled system of hair bundles, with the overlying membrane left on top of the preparation, also exhibited a dependence on offset position, with an increase in the linear response function observed under deflections in the inhibitory direction.     

Dynamics of Mechanically Coupled Hair-Cell Bundles of the Inner Ear

The high sensitivity and effective frequency discrimination of sound detection performed by the auditory system rely on the dynamics of a system of hair cells. In the inner ear, these acoustic receptors are primarily attached to an overlying structure that provides mechanical coupling between the hair bundles. Although the dynamics of individual hair bundles has been extensively investigated, the influence of mechanical coupling on the motility of the system of bundles remains underdetermined. We developed a technique of mechanically coupling two active hair bundles, enabling us to probe the dynamics of the coupled system experimentally. We demonstrated that the coupling could enhance the coherence of hair bundles’ spontaneous oscillation, as well as their phase-locked response to sinusoidal stimuli, at the calcium concentration in the surrounding fluid near the physiological level. The empirical data were consistent with numerical results from a model of two coupled nonisochronous oscillators, each displaying a supercritical Hopf bifurcation. The model revealed that a weak coupling can poise the system of unstable oscillators closer to the bifurcation by a shift in the critical point. In addition, the dynamics of strongly coupled oscillators far from criticality suggested that individual hair bundles may be regarded as nonisochronous oscillators. An optimal degree of nonisochronicity was required for the observed tuning behavior in the coherence of autonomous motion of the coupled system.     

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.     

Mechanical Amplification Exhibited by Quiescent Saccular Hair Bundles

Spontaneous oscillations exhibited by free-standing hair bundles from the Bullfrog sacculus suggest the existence of an active process that might underlie the exquisite sensitivity of the sacculus to mechanical stimulation. However, this spontaneous activity is suppressed by coupling to an overlying membrane, which applies a large mechanical load on the bundle. How a quiescent hair bundle utilizes its active process is still unknown. We studied the dynamics of motion of individual hair bundles under different offsets in the bundle position, and observed the occurrence of spikes in hair-bundle motion, associated with the generation of active work. These mechanical spikes can be evoked by a sinusoidal stimulus, leading to an amplified movement of the bundle with respect to the passive response. Amplitude gain reached as high as 100-fold at small stimulus amplitudes. Amplification of motion decreased with increasing amplitude of stimulation, ceasing at ∼6–12 pN stimuli. Results from numerical simulations suggest that the adaptation process, mediated by myosin 1c, is not required for the production of mechanical spikes.     

Making an effort to listen: mechanical amplification in the ear

The inner ear's performance is greatly enhanced by an active process defined by four features: amplification, frequency selectivity, compressive nonlinearity, and spontaneous otoacoustic emission. These characteristics emerge naturally if the mechanoelectrical transduction process operates near a dynamical instability, the Hopf bifurcation, whose mathematical properties account for specific aspects of our hearing. The active process of nonmammalian tetrapods depends upon active hair-bundle motility, which emerges from the interaction of negative hair-bundle stiffness and myosin-based adaptation motors. Taken together, these phenomena explain the four characteristics of the ear's active process. In the high-frequency region of the mammalian cochlea, the active process is dominated instead by the phenomenon of electromotility, in which the cell bodies of outer hair cells extend and contract as the protein prestin alters its membrane surface area in response to changes in membrane potential.     

Modeling the active process of the cochlea: phase relations, amplification, and spontaneous oscillation.

The high sensitivity and sharp frequency selectivity of acoustical signal transduction in the cochlea suggest that an active process pumps energy into the basilar membrane's oscillations. This function is generally attributed to outer hair cells, but its exact mechanism remains uncertain. Several classical models of amplification represent the load upon the basilar membrane as a single mass. Such models encounter a fundamental difficulty, however: the phase difference between basilar-membrane movement and the force generated by outer hair cells inhibits, rather than amplifies, the modeled basilar-membrane oscillations. For this reason, modelers must introduce artificially either negative impedance or an appropriate phase shift, neither of which is justified by physical analysis of the system. We consider here a physical model based upon the recent demonstration that the basilar membrane and reticular lamina can move independently, albeit with elastic coupling through outer hair cells. The mechanical model comprises two resonant masses, representing the basilar membrane and the reticular lamina, coupled through an intermediate spring, the outer hair cells. The spring's set point changes in response to displacement of the reticular lamina, which causes deflection of the hair bundles, variation of outer hair cell length and, hence, force production. Depending upon the frequency of the acoustical input, the basilar membrane and reticular lamina can oscillate either in phase or in counterphase. In the latter instance, the force produced by hair cells leads basilar-membrane oscillation, energy is pumped into basilar-membrane movement, and an external input can be strongly amplified. The model is also capable of producing spontaneous oscillation. In agreement with experimental observations, the model describes mechanical relaxation of the basilar membrane after electrical stimulation causes outer hair cells to change their length.     

Synchronization of Spontaneous Active Motility of Hair Cell Bundles

Hair cells of the inner ear exhibit an active process, believed to be crucial for achieving the sensitivity of auditory and vestibular detection. One of the manifestations of the active process is the occurrence of spontaneous hair bundle oscillations in vitro. Hair bundles are coupled by overlying membranes in vivo; hence, explaining the potential role of innate bundle motility in the generation of otoacoustic emissions requires an understanding of the effects of coupling on the active bundle dynamics. We used microbeads to connect small groups of hair cell bundles, using in vitro preparations that maintain their innate oscillations. Our experiments demonstrate robust synchronization of spontaneous oscillations, with either 1:1 or multi-mode phase-locking. The frequency of synchronized oscillation was found to be near the mean of the innate frequencies of individual bundles. Coupling also led to an improved regularity of entrained oscillations, demonstrated by an increase in the quality factor.     

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.     

Ca2+ changes the force sensitivity of the hair-cell transduction channel

The mechanically gated transduction channels of vertebrate hair cells tend to close in approximately 1 ms after their activation by hair bundle deflection. This fast adaptation is correlated with a quick negative movement of the bundle (a "twitch"), which can exert force and may mediate an active mechanical amplification of sound stimuli in hearing organs. We used an optical trap to deflect bullfrog hair bundles and to measure bundle movement while controlling Ca(2+) entry with a voltage clamp. The twitch elicited by repolarization of the cell varied with force applied to the bundle, going to zero where channels were all open or closed. The force dependence is quantitatively consistent with a model in which a Ca(2+)-bound channel requires approximately 3 pN more force to open, and rules out other models for the site of Ca(2+) action. In addition, we characterized a faster, voltage-dependent "flick", which requires intact tip links but not current through transduction channels.     

Mechanical Overstimulation of Hair Bundles: Suppression and Recovery of Active Motility

We explore the effects of high-amplitude mechanical stimuli on hair bundles of the bullfrog sacculus. Under in vitro conditions, these bundles exhibit spontaneous limit cycle oscillations. Prolonged deflection exerted two effects. First, it induced an offset in the position of the bundle. Recovery to the original position displayed two distinct time scales, suggesting the existence of two adaptive mechanisms. Second, the stimulus suppressed spontaneous oscillations, indicating a change in the hair bundle’s dynamic state. After cessation of the stimulus, active bundle motility recovered with time. Both effects were dependent on the duration of the imposed stimulus. External calcium concentration also affected the recovery to the oscillatory state. Our results indicate that both offset in the bundle position and calcium concentration control the dynamic state of the bundle.     

Force Transmission in the Organ of Corti Micromachine

Auditory discrimination is limited by the performance of the cochlea whose acute sensitivity and frequency tuning are underpinned by electromechanical feedback from the outer hair cells. Two processes may underlie this feedback: voltage-driven contractility of the outer hair cell body and active motion of the hair bundle. Either process must exert its mechanical effect via deformation of the organ of Corti, a complex assembly of sensory and supporting cells riding on the basilar membrane. Using finite element analysis, we present a three-dimensional model to illustrate deformation of the organ of Corti by the two active processes. The model used available measurements of the properties of structural components in low-frequency and high-frequency regions of the rodent cochlea. The simulations agreed well with measurements of the cochlear partition stiffness, the longitudinal space constant for point deflection, and the deformation of the organ of Corti for current injection, as well as displaying a 20-fold increase in passive resonant frequency from apex to base. The radial stiffness of the tectorial membrane attachment was found to be a crucial element in the mechanical feedback. Despite a substantial difference in the maximum force generated by hair bundle and somatic motility, the two mechanisms induced comparable amplitudes of motion of the basilar membrane but differed in the polarity of their feedback on hair bundle position. Compared to the hair bundle motor, the somatic motor was more effective in deforming the organ of Corti than in displacing the basilar membrane.     

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.     

Stereocilium injury mediates hair bundle stiffness loss and recovery following intense water-jet stimulation

Inner ear hair cells exhibit many pathologies following exposure to intense sound, and the hair bundle is a major site of damage. This paper measures in vitro hair bundle motion on chick cochlear hair cells after intense in vitro and in vivo stimulation to explore the nature of hair bundle injury. Hair bundle stiffness, as well as relative and asymmetric motion of individual stereocilia, is controlled largely by the extracellular tip links, and a change in hair bundle motion was used to assess tip-link destruction following overstimulation. Intense in vitro stimulation caused a loss in stiffness that fully recovered within 10 min post-exposure. Relative and asymmetric stereocilia motion, however, were unchanged following the exposure, implying that tip links remained intact while the core or rootlet of the stereocilia were damaged and subsequently repaired. Intense and prolonged in vivo sound exposures produced stereocilia movements, measured in vitro, that were indicative of damage to stereocilia and tip links. Finally, the relative susceptibility of hair bundles to overstimulation was addressed by comparing stiffness loss with morphological features in the hair bundles. The loss of stiffness significantly increased as the amount of curvature in the hair bundle contour increased.     

Stiffness changes in chick hair bundles following in vitro overstimulation

1. The in vitro effect of intense stimulation on the micromechanical stiffness of hair cell sensory hair bundles was studied at three locations on the chick basilar papilla. Threshold levels of hair bundle motion, produced by a water jet stimulus, were examined before and after exposure to a 300 Hz water jet stimulus set at 25 dB above the pre-exposure threshold level.
2. Threshold levels of motion were systematically examined in 8 unexposed control cells. The level of water jet stimulus needed to achieve the detection threshold of motion remained constant in these cells when periodically tested over a 36.5-min interval.
3. Post-exposure changes in the motion detection threshold of hair bundles were examined in 82 hair bundles, and a number of effects were identified: 2.4% of the hair bundles showed no threshold change; 31.7% of the hair bundles had threshold shifts which indicated an increase in stiffness; 18.3% exhibited a threshold shift that indicated a decrease in hair bundle stiffness, but with no recovery; and 47.6% had thresholds that indicated a decrease in hair bundle stiffness with recovery to pre-exposure levels within 16–18 min.
4. The results suggest that chick hair bundles exhibit complex and varied responses to overstimulation which are very different from that seen in the mammal.

     

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 Ca²⁺ 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 Ca²⁺ 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 Ca²⁺ binding kinetics. Spontaneous oscillations persisted, becoming very narrow-band, when the hair bundle was loaded with a tectorial membrane mass.     

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.     

Nonlinear mechanical responses of mouse cochlear hair bundles.

The stiffness of sensory hair bundles of both inner (IHC) and outer (OHC) hair cells was measured with calibrated silica fibres in mouse cochlear cultures to test the hypothesis that the mechanical properties of the hair bundle reflect processes underlying mechanotransduction. For OHCs, the displacement of the hair bundle relaxed with time constants of 6 ms for displacements which open transducer channels and 4 ms for displacements which close the channels. The corresponding values of the time constants for IHCs were 10 ms and 8 ms, respectively. A displacement-dependent change in the stiffness of the hair bundle was not observed when the bundle was displaced orthogonally to the direction of excitation. The stiffness of the hair bundle as a function of nanometre displacements from the resting position was remarkably nonlinear. The stiffness declined to a minimum from the resting stiffness by about 12% for OHCs and 20% for IHCs when the hair bundle was displaced by about 20 nm in the excitatory direction, and it increased by a similar amount when the bundle was displaced by 20 nm in the inhibitory direction. The displacement at which the stiffness reached a minimum was within the most sensitive region of the hair-cell transducer function (receptor potential as a function of hair-bundle displacement), and the displacement at which the stiffness reached a maximum was at the point of saturation of the transducer function in the inhibitory direction. The nonlinear displacement-dependent compliance change is reversibly abolished, and the time constant of relaxation of the bundle for excitatory displacements is reversibly reduced, when mechanotransduction is blocked by the addition of either neomycin sulphate or cobalt chloride to the solution bathing the hair cells. The displacement-dependent compliance change was not apparently reduced when the receptor potential was attenuated through the substitution of sodium in the bathing solution with a less permeant cation, tetraethylammonium. These findings suggest that the nonlinear mechanical properties of the hair bundle are associated with aspects of the hair-cell mechanotransducer process. The mechanical properties of the hair bundle are discussed in relation to the 'gating-spring' hypothesis of hair-cell transduction.     

Amiloride causes changes in the mechanical properties of hair cell bundles in the fish lateral line similar to those induced by dihydrostreptomycin

Amiloride is a known blocker of the mechano-electrical transduction current in sensory hair cells. Measurements of cupular motion in the lateral line organ of fish now show that amiloride concurrently changes the micromechanical properties of the hair cell bundles. The effects of amiloride on the mechanics and receptor potentials of the hair cells resemble those previously observed for the aminoglycoside drug dihydrostreptomycin (DHSM) and are similarly antagonized by Ca²⁺. We hypothesize that amiloride and DHSM act on hair cells in two correlated ways which manifest themselves in both the electrical and mechanical properties of the transduction process. One action is the reduction of the transduction current with a concurrent increase of the hair bundle stiffness. The other action is a shift of the hair cell''s operating point on a current–displacement curve, with a concomitant shift along the associated hair bundle stiffness–displacement curve. The latter action has the opposite effect to that of the first and thus may lead, at relatively low blocker concentrations, to both an increase of transduction current and a decrease in hair bundle stiffness.     

Adaptation in auditory hair cells

The narrow stimulus limits of hair cell transduction, equivalent to a total excursion of about 100nm at the tip of the hair bundle, demand tight regulation of the mechanical input to ensure that the mechanoelectrical transducer (MET) channels operate in their linear range. This control is provided by multiple components of Ca(2+)-dependent adaptation. A slow mechanism limits the mechanical stimulus through the action of one or more unconventional myosins. There is also a fast, sub-millisecond, Ca(2+) regulation of the MET channel, which can generate resonance and confer tuning on transduction. Changing the conductance or kinetics of the MET channels can vary their resonant frequency. The tuning information conveyed in transduction may combine with the somatic motility of outer hair cells to produce an active process that supplies amplification and augments frequency selectivity in the mammalian cochlea.