A model for signal transmission in an ear having hair cells with free-standing stereocilia. III. Micromechanical stage

Distinct roles of Eps8 in the maturation of cochlear and vestibular hair cells

Several genetic mutations affecting the development and function of mammalian hair cells have been shown to cause deafness but not vestibular defects, most likely because vestibular deficits are sometimes centrally compensated. The study of hair cell physiology is thus a powerful direct approach to ascertain the functional status of the vestibular end organs. Deletion of Epidermal growth factor receptor pathway substrate 8 (Eps8), a gene involved in actin remodeling, has been shown to cause deafness in mice. While both inner and outer hair cells from Eps8 knockout (KO) mice showed abnormally short stereocilia, inner hair cells (IHCs) also failed to acquire mature-type ion channels. Despite the fact that Eps8 is also expressed in vestibular hair cells, Eps8 KO mice show no vestibular deficits. In the present study we have investigated the properties of vestibular Type I and Type II hair cells in Eps8-KO mice and compared them to those of cochlear IHCs. In the absence of Eps8, vestibular hair cells show normally long kinocilia, significantly shorter stereocilia and a normal pattern of basolateral voltage-dependent ion channels. We have also found that while vestibular hair cells from Eps8 KO mice show normal voltage responses to injected sinusoidal currents, which were used to mimic the mechanoelectrical transducer current, IHCs lose their ability to synchronize their responses to the stimulus. We conclude that the absence of Eps8 produces a weaker phenotype in vestibular hair cells compared to cochlear IHCs, since it affects the hair bundle morphology but not the basolateral membrane currents. This difference is likely to explain the absence of obvious vestibular dysfunction in Eps8 KO mice.

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.

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.

Coherent reflection without traveling waves: on the origin of long-latency otoacoustic emissions in lizards

Lizard ears produce otoacoustic emissions with characteristics often strikingly reminiscent of those measured in mammals. The similarity of their emissions is surprising, given that lizards and mammals manifest major differences in aspects of inner ear morphology and function believed to be relevant to emission generation. For example, lizards such as the gecko evidently lack traveling waves along their basilar membrane. Despite the absence of traveling waves, the phase-gradient delays of gecko stimulus-frequency otoacoustic emissions (SFOAEs) are comparable to those measured in many mammals. This paper describes a model of emission generation inspired by the gecko inner ear. The model consists of an array of coupled harmonic oscillators whose effective damping manifests a small degree of irregularity. Model delays increase with the assumed sharpness of tuning, reflecting the build-up time associated with mechanical resonance. When tuning bandwidths are chosen to match those of gecko auditory-nerve fibers, the model reproduces the major features of gecko SFOAEs, including their spectral structure and the magnitude and frequency dependence of their phase-gradient delays. The same model with appropriately modified parameters reproduces the features of SFOAEs in alligator lizards. Analysis of the model demonstrates that the basic mechanisms operating in the model are similar to those of the coherent-reflection model developed to describe mammalian emissions. These results support the notion that SFOAE delays provide a noninvasive measure of the sharpness of cochlear tuning.

Two modes of motion of the alligator lizard cochlea: measurements and model predictions

Measurements of motion of an in vitro preparation of the alligator lizard basilar papilla in response to sound demonstrate elliptical trajectories. These trajectories are consistent with the presence of both a translational and rotational mode of motion. The translational mode is independent of frequency, and the rotational mode has a displacement peak near 5 kHz. These measurements can be explained by a simple mechanical system in which the basilar papilla is supported asymmetrically on the basilar membrane. In a quantitative model, the translational admittance is compliant while the rotational admittance is second order. Best-fit model parameters are consistent with estimates based on anatomy and predict that fluid flow across hair bundles is a primary source of viscous damping. The model predicts that the rotational mode contributes to the high-frequency slopes of auditory nerve fiber tuning curves, providing a physical explanation for a low-pass filter required in models of this cochlea. The combination of modes makes the sensitivity of hair bundles more uniform with radial position than that which would result from pure rotation. A mechanical analogy with the organ of Corti suggests that these two modes of motion may also be present in the mammalian cochlea.

The effect of hair bundle shape on hair bundle hydrodynamics of non-mammalian inner ear hair cells for the full frequency range

The effect of the size and the shape of the hair bundle of a hair cell in the inner ear of non-mammals on its motion for the full range of frequencies is determined thereby extending the results of a previous analysis of hair bundle motion for high and low frequencies [Hear Res. 141 (2000) 39-50]. A hemispheroid is used to represent the hair bundle because it can represent a full range of shapes, from thin, pencil-like shapes to wide, flat, disk-like shapes. Boundary element methods are used to approximate the solution for the hydrodynamics. For physiologically relevant parameters, an excellent match is obtained between the model's predictions and measurements of hair bundle motion in the free-standing region of the basilar papilla of the alligator lizard [Aranyosi, Measuring sound-induced motions of the alligator lizard cochlea. Massachusetts Institute of Technology, PhD Thesis, 2002]. Neither in the model's predictions nor in experimental measurements is sharp tuning observed. The model predicted the low frequency region of neural tuning curves for the alligator lizard and bobtail lizard, but could not predict the sharp tuning or the high frequency region. An element that represents an active mechanism is added to the hair bundle model to predict neural tuning curves, which are sharply tuned, and an excellent match is obtained for all the characteristics of neural tuning curves for the alligator lizard, and for the low and high frequency regions for the bobtail lizard. The model does not predict well the sharp tuning of the shorter hair bundles of the bobtail lizard, possibly because it does not represent tectorial sallets.

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.

Evolution of structure and function of the hearing organ of lizards

Following their origin during the early Cretaceous, the lizards radiated early into a number of families. This radiation was accompanied by a diversification in the structure of the inner ear. The morphology of the auditory basilar papilla is family-specific, with large variations in a number of parameters. At the physiologic level, this wide variation does not result in an equivalent range of physiologic parameters. This review considers the possible influence of various morphologic features on function, and correlates these features with physiologic response parameters. Anatomical variety that does not result in significant changes in the inputs to the brain is "neutral" with regard to selection pressures. This independence apparently removed evolutionary constraints and led to some of the great variety of auditory papillae seen. Other anatomical features are more important and do produce significant effects at the level of the auditory nerve.

Frequency glides in click responses of the basilar membrane and auditory nerve: their scaling behavior and origin in traveling-wave dispersion

Frequency modulations (or glides), reported in impulse responses of both the auditory nerve and the basilar membrane, represent a change over time in the instantaneous frequency of oscillation of the response waveform. Although the near invariance of glides with stimulus intensity indicates that they are not the consequence of nonlinear or active processes in the inner ear, their origin has remained otherwise obscure. This paper combines theory with experimental data to explore the basic phenomenology of glides. When expressed in natural dimensionless form, glides are shown to have a universal form nearly independent of cochlear location for characteristic frequencies (CFs) above approximately 1.5 kHz (the "scaling region"). In the apex of the cochlea, by contrast, glides appear to depend strongly on CF. In the scaling region, instantaneous-frequency trajectories are shown to be approximately equal to the "inverse group delays" of basilar-membrane transfer functions measured at the same locations. The inverse group delay, obtained by functionally inverting the transfer-function group-delay-versus-frequency curve, specifies the frequency component of a broadband stimulus expected to be driving the cochlear partition at the measurement point as a function of time. The approximate empirical equality of the two functions indicates that glides are closely related to cochlear traveling-wave dispersion and suggests that they originate primarily through the time dependence of the effective driving pressure force at the measurement location. Calculations in a one-dimensional cochlear model based on solution to the inverse problem in squirrel monkey [Zweig, J. Acoust. Soc. Am. 89, 1229-1254 (1991)] support this conclusion. In contrast to previous models for glides, which locate their origin in the differential build-up and decay of multiple micromechanical resonances local to each radial cross section of the organ of Corti, the model presented here identifies glides as the global consequence of the dispersive character of wave propagation in the cochlea.

The effect of hair bundle shape on hair bundle hydrodynamics of inner ear hair cells at low and high frequencies

The relationship between size and shape of the hair bundle of a hair cell in the inner ear and its sensitivity at asymptotically high and low frequencies was determined, thereby extending the results of an analysis of hair bundle hydrodynamics in two dimensions (Freeman and Weiss, 1990. Hydrodynamic analysis of a two-dimensional model for micromechanical resonance of free-standing hair bundles. Hear. Res. 48, 37-68) to three dimensions. A hemispheroid was used to represent the hair bundle. The hemispheroid had a number of advantages: it could represent shapes that range from thin, pencil-like shapes, to wide, flat, disk-like shapes. Also analytic methods could be used in the high frequency range to obtain an exact solution to the equations of motion. In the low frequency range, where an approximate solution was found using boundary element methods, the sensitivity of the responses of hair cells was mainly proportional to the cube of the heights of their hair bundles, and at high frequencies, the sensitivity of the hair cells was mainly proportional to the inverse of their heights. An excellent match was obtained between measurements of sensitivity curves in the basillar papilla of the alligator and bobtail lizards and the model's predictions. These results also suggest why hair bundles of hair cells in vestibular organs which are sensitive to low frequencies have ranges of heights that are an order of magnitude larger than the range of heights of hair bundles of hair cells found in auditory organs.

Reversed tonotopic map of the basilar papilla in Gekko gecko

A published model of the frequency responses of different locations on the basilar papilla of the Tokay gecko Gekko gecko (Authier and Manley, 1995. Hear. Res. 82, 1-13) had implied that (a) unlike all other amniotes studied so far, the frequency map is reversed, with the low frequencies at the base and the high frequencies at the apex, and (b) the high-frequency area is split into two parallel-lying hair cell areas covering different frequency ranges. To test these hypotheses, the frequency representation along the basilar papilla of Gekko gecko was studied by recording from single auditory afferent nerve fibers and labelling them iontophoretically with horseradish peroxidase. Successfully labelled fibers covered a range of characteristic frequencies from 0.42 to 4.9 kHz, which extended from 78% to 9% of the total papillar length, as measured from the apex. The termination sites of labelled fibers within the basilar papilla correlated with their characteristic frequency, the lowest frequencies being represented basally, and the highest apically. This confirms the first prediction of the model. The map indicates, however, that one of the two high-frequency papillar regions (the postaxial segment) represents the full high-frequency range, from about 1 to 5 kHz. No functionally identified labelling was achieved in the preaxial segment. Thus the assumptions underlying the proposed model need revision. A good mathematical description of the frequency distribution was given by an exponential regression with a mapping constant in the living state of approximately 0.4 mm/octave.

Mechanisms of hair cell tuning

Mechanosensory hair cells of the vertebrate inner ear contribute to acoustic tuning through feedback processes involving voltage-gated channels in the basolateral membrane and mechanotransduction channels in the apical hair bundle. The specific number and kinetics of calcium-activated (BK) potassium channels determine the resonant frequency of electrically tuned hair cells. Kinetic variation among BK channels may arise through alternative splicing of slo gene mRNA and combination with modulatory beta subunits. The number of transduction channels and their rate of adaptation rise with hair cell response frequency along the cochlea's tonotopic axis. Calcium-dependent feedback onto transduction channels may underlie active hair bundle mechanics. The relative contributions of electrical and mechanical feedback to active tuning of hair cells may vary as a function of sound frequency.

A functional map of the pigeon basilar papilla: correlation of the properties of single auditory nerve fibres and their peripheral origin

The purpose of the investigation was to correlate the functional properties of primary auditory fibres with the location of appertaining receptor cells in the avian basilar papilla. The functional properties of 425 single afferent fibres from the auditory nerve of adult pigeons were measured. The peripheral innervation site of 39 fibres was identified by intracellular labelling and correlated with the fibre's functional properties. Mean spontaneous firing rate (SR, 0.1-250/s) was distributed monomodally (mean: 91 +/- 47/s) but not normally. Characteristic frequencies (CFs) were in the range of 0.02-4 kHz. SR, threshold at CF (4-76 dB SPL) and sharpness of tuning (Q10 dB, 0.1-8.8) varied systematically with CF. For a given CF there was a strong correlation of threshold and Q10 dB and of threshold and SR. Labelled fibres innervated different hair cell types over 93% of the length and 97% of the width of the basilar papilla. The majority of fibres innervated hair cells located between 30 and 70% distance from the apex and 0 and 30% distance from the neural edge of the papilla. CFs are mapped tonotopically from high at the base to low at the apex of the papilla, with a mean mapping constant of 0.63 +/- 0.05 mm/octave (in vivo). The highest CF at the base extrapolates to 5.98 +/- 1.17 kHz. The lowest CF mapped at the apex is 0.021 kHz. From the data, together with data from mechanical measurements (Gummer et al., 1987), a frequency-place function of the pigeon papilla was calculated. Transverse gradients of threshold at CF and of Q10 dB were observed across the width of the papilla. Thresholds were lowest and sharpness of tuning was highest above the neural limbus at a distance of 23% from the neural edge of the papilla. Hair cells in this sensitive strip are the tallest and narrowest ones across the width of the papilla. They are packed most densely and receive the largest number of afferent fibres. Fibres innervating (mostly short) hair cells on the free basilar membrane were spontaneously active and responsive to sound. Their Q10 dB was less than average but their sensitivity and SR were comparable to the mean population values. It is concluded that functional properties change gradually not only along the length but also across the width of the pigeon basilar papilla. The results support the idea that sharp frequency tuning of avian primary auditory fibres involves tuning mechanisms supplementary to the tuning of the free part of the basilar membrane.

Quantitative anatomical basis for a model of micromechanical frequency tuning in the Tokay gecko, Gekko gecko

The basilar papilla of the Tokay gecko was studied with standard light- and scanning electron microscopy methods. Several parameters thought to be of particular importance for the mechanical response properties of the system were quantitatively measured, separately for the three different hair-cell areas that are typical for this lizard family. In the basal third, papillar structure was very uniform. The apical two-thirds are subdivided into two hair-cell areas running parallel to each other along the papilla and covered by very different types of tectorial material. Both of those areas showed prominent gradients in hair-cell bundle morphology, i.e., in the height of the stereovillar bundles and the number of stereovilli per bundle, as well as in hair cell density and the size of their respective tectorial covering. Based on the direction of the observed anatomical gradients, a 'reverse' tonotopic organization is suggested, with the highest frequencies represented at the apical end.

A model of frequency tuning in the basilar papilla of the Tokay gecko, Gekko gecko

This paper uses the quantitative details of the anatomy of the auditory papilla in the Tokay gecko Gekko gecko (as described in the companion paper) to make a quantitative model predicting the tonotopic organization of two of the three papillar areas. Assuming that hair-cell bundle stiffness is similar to that of other species, a model of resonance frequencies for the apical areas of the papilla was constructed, taking into account factors such as the number of hair cells per resonant unit, their bundle dimensions, the volume of the tectorial mass, etc. The model predicts that the apical pre- and postaxial areas, although anatomically adjacent, respond to different frequency ranges, a phenomenon not yet reported from any vertebrate. The model predicts that together, these areas respond best to frequencies between 1.1 and 5.3 kHz, close to the range found physiologically [Eatock et al. (1981) J. Comp. Physiol. 142, 203-218] (0.8 to 5 kHz) for the high-frequency range for this species. Only physiological experiments tracing responses to specific papillar nerve fibres can confirm or refute these interesting predictions of the model. The model also indicates that, compared to free-standing hair-cell bundles, the semi-isolated tectorial structures called sallets not only lower the range of characteristic frequencies but also increase the frequency selectivity of the attached hair cells.

The functional morphology of stereociliary bundles on turtle cochlear hair cells

The stereociliary bundles of hair cells from the basilar papilla of the red-eared turtle were examined with transmission and high resolution scanning electron microscopy to provide a description of their morphology, orientation and inter-ciliary connections for comparison with physiological observations. Bundles on hair cells in the basilar membrane region are of a uniform shape and orientation, but bundles on the apical and basal limbus are distinct in having elongated kinocilia more than twice the length of the tallest stereocilia. Bundles in the basilar membrane region show a roughly two-fold increase in height from 5 to 9 microns from base to apex. Electrical recordings from isolated hair cells indicate that the bundle height is inversely proportional to the cell's characteristic frequency. It is argued that the change in dimensions is insufficient to contribute significantly to the cochlea's frequency selectivity. The cytoplasm adjacent to the kinocilium is filled with microtubules and large vesicles, and there are coated pits in the apical membrane which, it is suggested, may be indicative of rapid turnover of the membrane in this region.

Mechanisms that degrade timing information in the cochlea

Action potentials of cochlear nerve fibers are synchronized to the temporal variations of sounds, but this synchronization is attenuated for high-frequency sounds. In cochleas from a number of vertebrates, the frequency dependence of synchronization can be represented as a lowpass filter process whose order is at least three (Weiss and Rose, 1988a); i.e. at least three first-order kinetic processes may be responsible for the loss of synchronization. In this paper we assess the extent to which calcium processes, that are essential for chemical transmission at the hair-cell neuron junction, contribute to this attenuation of synchronization. We analyze a model of calcium processes in hair cells (Lewis, 1985; Hudspeth and Lewis, 1988a) for sinusoidal receptor potentials. We show that: (1) the relation between the receptor potential and the calcium current, which is nonlinear, acts approximately as a first-order lowpass filter whose cut-off frequency decreases with increasing receptor potential magnitude; (2) the relation between calcium current and calcium-concentration is a first-order, lowpass filter with constant cutoff frequency. These two calcium processes plus the lowpass-filter process resulting from the electrical resistance and capacitance of the hair-cell membrane - which limits the rate at which the receptor potential can change (Weiss and Rose, 1988b) - can account for much, although perhaps not for all, of the loss of synchronization of cochlear nerve fibers.

Hydrodynamic forces on hair bundles at low frequencies

We have analyzed a model for the motion of hair bundles of hair cells at low frequencies. In the model, hair-cell organs are represented as a system of rigid mechanical structures surrounded by fluid. A rigid body, that represents a hair bundle, is hinged to a vibrating plate that represents the sensory epithelium. These structures are surmounted by a second vibrating plate that represents a tectorial structure. The analysis shows that both viscous and inertial properties of the fluid are important even at asymptotically low frequencies. The relative importance of these properties depends critically on the presence and mode of motion of the tectorial plate. As a result, the angular displacement of the body at low frequencies can be proportional to basal plate displacement, velocity, acceleration, or to no simple integral of its motion; the functional relation depends upon the disposition of the tectorial plate.

Hydrodynamic analysis of a two-dimensional model for micromechanical resonance of free-standing hair bundles

To investigate the role of inner ear fluids and structures on mechanical stimulation of the hair bundles of hair cells, we analyzed a two-dimensional structure that consists of: a rectangular flap (which represents a hair bundle) attached to a flat basal plate (which represents the surface of the epithelium that contains the hair cells) with a spring-loaded hinge (that represents the compliant attachment of a hair bundle to the hair cell body) and surrounded by a viscous fluid (that represents endolymph). We computed the fluid velocity as well as the forces on and motion of the flap in response to sinusoidal vibration of the plate by numerical integration of the hydrodynamic equations, and--at asymptotically low and high frequencies--by analytic methods. The results suggest that: (1) the surface of the sensory epithelium, from which hair bundles project into fluid, plays an important part in the production of fluid forces on hair bundles; (2) both fluid inertia and viscosity play a key role in hair bundle mechanics; (3) passive mechanical resonances are likely to contribute to both frequency selectivity and frequency-to-place coding in the inner ear.

Superposition of hydrodynamic forces on a hair bundle

Vertebrates sense sound, orientation, and motion by means of bundles of microscopic sensory hairs that protrude from the surfaces of receptor (hair) cells. To determine the effects of the sensory epithelium, tectorial structures, and fluids on the motions of hair bundles, we examine a class of mathematical models in which hair-cell organs are represented as a system of rigid mechanical structures surrounded by fluid. The epithelium and tectorial structures are represented by rigid basal and tectorial plates, respectively; the hair bundle by a rigid body hinged to the basal plate. When the displacements of these structures are small, the equations of motion for the fluid are predominately linear. Therefore, both the fluid velocity and the force of fluid origin on the body can be expressed as a sum of components; each component results from motion of a single structure while all others are stationary. This analysis leads to a network description of the motion of the rigid body in which hydrodynamic forces are segregated from mechanical forces. The separation of hydrodynamics and mechanics not only clarifies the effects of fluids on motion but also minimizes the number of hydrodynamic computations needed to analyze models of hair-bundle motion.

How the ear's works work

The senses of hearing and equilibrium depend on sensory receptors called hair cells which can detect motions of atomic dimensions and respond more than 100,000 times a second. Biophysical studies suggest that mechanical forces control the opening and closing of transduction channels by acting through elastic components in each hair cell's mechanoreceptive hair bundle. Other ion channels, as well as the mechanical and hydrodynamic properties of hair bundles, tune individual hair cells to particular frequencies of stimulation.

Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer

By optically probing with a focused, low-power laser beam, we measured the spontaneous deflection fluctuations of the sensory hair bundles on frog saccular hair cells with a sensitivity of about 1 pm/square root of Hz. The preparation was illuminated by two orthogonally polarized laser beams separated by only about 0.2 microns at their foci in the structure under investigation. Slight movement of the object from one beam toward the other caused a change of the phase difference between the transmitted beams and an intensity modulation at the detector where the beams interfered. Maintenance of the health of the cells and function of the transduction mechanism were occasionally confirmed by measuring the intracellular resting potential and the sensitivity of transduction. The root-mean-square (rms) displacement of approximately 3.5 nm at a hair bundle's tip suggests a stiffness of about 350 microN/m, in agreement with measurements made with a probe attached to a bundle's tip. The spectra resemble those of overdamped harmonic oscillators with roll-off frequencies between 200 and 800 Hz. Because the roll-off frequencies depended strongly on the viscosity of the bathing medium, we conclude that hair-bundle motion is mainly damped by the surrounding fluid.

The role of fluid inertia in mechanical stimulation of hair cells

Hair cells, which are the receptor cells of hearing and equilibrium in vertebrates, produce electrical responses when their hair bundles are displaced by sensory stimuli. This paper summarizes the results of a theoretical study of the fluid mechanics of hair-bundle motion. The principal conclusion is that fluid inertia, which has not been included in previous studies, plays a critical role in the mechanics of hair bundles and, hence, in the processes of sensory reception in hair-cell organs.

Morphology of the basilar papilla of the bobtail lizard Tiliqua rugosa

The morphology of the basilar papilla of the bobtail lizard was investigated with standard light- and scanning-electron-microscopical methods. The papilla can be subdivided into two parts: a small apical segment which is rather uniform in structure and a long basal segment which displays various systematic changes along its length, for example in the density of the hair cells, the height and shape of the hair-cell stereovillar bundles, the number of stereovilli per bundle and the size of the tectorial structure. In addition, the tectorial structures overlying the two segments are very different in size and morphology. Both tectorial structures are probably sensitive to changes in their ionic environment. The possible functional implications of the papillar morphology described here are discussed with respect to a model of frequency tuning in the bobtail lizard.

Auditory peripheral tuning: evidence for a simple resonance phenomenon in the lizard Tiliqua

The origin of the frequency selectivity of neurons in the vertebrate auditory periphery is one of the most important questions in auditory research today. In an attempt to delineate the extent to which structures outside the sensory cells play a role in determining peripheral auditory responses, we measured the mechanical displacement of the basilar membrane and the selectivity of nerve fibres at the same location in the bobtail lizard. These data indicate a contribution to frequency selectivity, the tuning of which resembles a high-pass resonant filter characteristic, arising subsequent to the basilar membrane motion. A comparison of these data with the tuning of auditory-nerve fibres originating from papillar areas in other lizard species without a tectorial membrane, suggests that it is the involvement of the tectorial membrane in a mechanical resonance which increases the frequency selectivity.

Neural tuning in the granite spiny lizard

Scanning electron microscopy was used to examine the basilar papilla of the granite spiny lizard. The papilla contains three distinct hair cell populations: an apical and a basal population with free-standing cilia, and a central population with a tectorial membrane. In the free-standing populations, stereocilium length decreases towards the ends of the papilla. Ciliary tuft morphology differs in the free-standing and the tectorial membrane populations, except that several of the free-standing hair cells with the shortest stereocilia have a tuft morphology like the hair cells in the tectorial membrane population. On the basis of single-fiber physiology, auditory nerve fibers can be divided into a low characteristic frequency (CF) and a high CF population. Mappings of the tonotopic organization of the nerve demonstrated two groups of high CF fibers that correspond to the two free-standing hair cell populations. The low CF fibers are associated with the tectorial membrane hair cell population. Fiber CF correlated with hair cell cilium length, not position on basilar membrane, for hair cells with free-standing cilia. Tonotopic organization of high CF fibers could be predicted reasonably well from the histogram of fiber CFs.

The low-frequency response of inner hair cells in the guinea pig cochlea: implications for fluid coupling and resonance of the stereocilia

AC receptor potentials within the inner hair cells of the basal turn of the guinea pig cochlea have been recorded for stimuli in the frequency range 20 Hz to 3200 Hz. Comparison of these potentials with potentials recorded in scala media suggests that the stereocilia of many inner hair cells are stimulated by the transverse velocity of the cochlear partition for very low frequency, but above a transition frequency in the range 400 Hz to 1000 Hz they become entrained with partition displacement. It is suggested that such a transition is probably a simple consequence of the fluid coupling that drives these cells, and that mechanical resonance of the free-standing stereocilia of the inner hair cells does not occur in the basal turn of the guinea pig. These results do not, however, preclude the possibility of mechanical resonance involving the stereocilia of the outer hair cells. The results also indicate that the bodies of these cells low-pass filter the intracellular receptor potential, with a cutoff frequency of approximately 1000 Hz.

The cellular basis of hearing: the biophysics of hair cells

A crucial event in the hearing process is the transduction of mechanical stimuli into electrical signals by hair cells, the sensory receptors of the internal ear. Stimulation results in the rapid opening of ionic channels in the mechanically sensitive organelles of these cells, their hair bundles. These transduction channels, which are nonselectively permeable, are directly excited by hair-bundle displacement. Hair cells are selectively responsive to particular frequencies of stimulation, both due to the mechanical properties of their hair bundles and because of an ensemble of ionic channels that constitute an electrical resonator.

A model for signal transmission in an ear having hair cells with free-standing stereocilia. II. Macromechanical stage

A model of the signal-processing properties of the macromechanical system of the alligator-lizard middle and inner ear is developed. The model is based on measurements (as a function of tone frequency) of ossicular and basilar-membrane motion and of acoustic input-admittance at the tympanic membrane before and after alterations of middle-ear and inner-ear structures. From the structure of the ear, we formulate an equivalent electric network consisting of six admittance blocks and two transformers. The admittance blocks represent the mechanical properties of particular structures, e.g. the tympanic membrane (TM), the ossicle, the TM-ossicular joint, the vestibule, the basilar membrane and the helicotrema. The transformers represent the conversions from acoustical to mechanical variables performed by the TM-ossicular system and by the columella footplate. The block admittances and transformer ratios are inferred from the measurements, and each admittance is approximated by a network with a few simple elements. The resulting model fits the experimental results satisfactorily, allows correlations between specific structures and response behavior, and predicts the macromechanical transfer function. This transfer function acts as the first stage of a model of the alligator-lizard auditory periphery (Weiss et al., Weiss and Leong, 1985, Hearing Res. 20, 131-138, 157-174, 175-195). In the model the frequency dependence of basilar-membrane motion (1) is determined primarily by the tympanic membrane and extracolumella in the middle frequencies and (2) is affected by the helicotrema at low frequencies and the TM-ossicular joint at high frequencies.

A model for signal transmission in an ear having hair cells with free-standing stereocilia. I. Empirical basis for model structure

No adequate theory for the signal-transmission properties of the peripheral auditory system exists for any vertebrate ear. Because the mammalian ear seems to pose conceptual and technical problems that complicate the development of an adequate theory, it is worthwhile to investigate simpler ears. The ear of the alligator lizard is simpler than mammalian ears in several respects: the motion of the basilar membrane is approximately independent of longitudinal position and is approximately linearly related to the sound pressure at the tympanic membrane; in a large region of the cochlea the hair cells have free-standing stereocilia that are not in contact with a tectorial membrane; the receptor potential of these hair cells is related to the sound pressure at the tympanic membrane in a relatively simple manner; the cochlear-nerve fiber responses from this region do not exhibit two-tone rate suppression. Also, the relative accessibility of this ear has enabled measurement of several response variables: tympanic-membrane volume velocity, extracolumella velocity, basilar-membrane velocity, hair-cell stereociliary displacement, hair-cell receptor potentials, and cochlear-nerve-fiber discharges. A model is developed to represent these results in terms of underlying anatomical structures and physiological mechanisms.(ABSTRACT TRUNCATED AT 250 WORDS)