A virtual hair cell, I: addition of gating spring theory into a 3-D bundle mechanical model

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.

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.

Utricular afferents: morphology of peripheral terminals

The utricle provides critical information about spatiotemporal properties of head movement. It comprises multiple subdivisions whose functional roles are poorly understood. We previously identified four subdivisions in turtle utricle, based on hair bundle structure and mechanics, otoconial membrane structure and hair bundle coupling, and immunoreactivity to calcium-binding proteins. Here we ask whether these macular subdivisions are innervated by distinctive populations of afferents to help us understand the role each subdivision plays in signaling head movements. We quantified the morphology of 173 afferents and identified six afferent classes, which differ in structure and macular locus. Calyceal and dimorphic afferents innervate one striolar band. Bouton afferents innervate a second striolar band; they have elongated terminals and the thickest processes and axons of all bouton units. Bouton afferents in lateral (LES) and medial (MES) extrastriolae have small-diameter axons but differ in collecting area, bouton number, and hair cell contacts (LES >> MES). A fourth, distinctive population of bouton afferents supplies the juxtastriola. These results, combined with our earlier findings on utricular hair cells and the otoconial membrane, suggest the hypotheses that MES and calyceal afferents encode head movement direction with high spatial resolution and that MES afferents are well suited to signal three-dimensional head orientation and striolar afferents to signal head movement onset.

Turtle utricle dynamic behavior using a combined anatomically accurate model and experimentally measured hair bundle stiffness

Anatomically correct turtle utricle geometry was incorporated into two finite element models. The geometrically accurate model included appropriately shaped macular surface and otoconial layer, compact gel and column filament (or shear) layer thicknesses and thickness distributions. The first model included a shear layer where the effects of hair bundle stiffness was included as part of the shear layer modulus. This solid model's undamped natural frequency was matched to an experimentally measured value. This frequency match established a realistic value of the effective shear layer Young's modulus of 16 Pa. We feel this is the most accurate prediction of this shear layer modulus and fits with other estimates (Kondrachuk, 2001b). The second model incorporated only beam elements in the shear layer to represent hair cell bundle stiffness. The beam element stiffness's were further distributed to represent their location on the neuroepithelial surface. Experimentally measured striola hair cell bundles mean stiffness values were used in the striolar region and the mean extrastriola hair cell bundles stiffness values were used in this region. The results from this second model indicated that hair cell bundle stiffness contributes approximately 40% to the overall stiffness of the shear layer-hair cell bundle complex. This analysis shows that high mass saccules, in general, achieve high gain at the sacrifice of frequency bandwidth. We propose the mechanism by which this can be achieved is through increase the otoconial layer mass. The theoretical difference in gain (deflection per acceleration) is shown for saccules with large otoconial layer mass relative to saccules and utricles with small otoconial layer mass. Also discussed is the necessity of these high mass saccules to increase their overall system shear layer stiffness. Undamped natural frequencies and mode shapes for these sensors are shown.

Hearing molecules, mechanism and transportation: modeled in Drosophila melanogaster

Mechanosensory transduction underlies the perception of touch, sound and acceleration. The mechanical signals exist in the environment are resensed by the specialized mechanosensory cells, which convert the external forces into the electrical signals. Hearing is a magnificent example that relies on the mechanotransduction mediated by the auditory cells, for example the inner-ear hair cells in vertebrates and the Johnston's organ (JO) in fly. Previous studies have shown the fundamental physiological processes in the fly and vertebrate auditory organs are similar, suggesting that there might be a set of similar molecules underlying these processes. The molecular studies of the fly JO have been shown to be remarkably successful in discovering the developmental and functional genes that provided further implications in vertebrates. Several evolutionarily conserved molecules and signaling pathways have been shown to govern the development of the auditory organs in both vertebrates and invertebrates. The current review describes the similarities and differences between the vertebrate and fly auditory organs at developmental, structural, molecular, and transportation levels.

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.

A mechanical model of stereocilia that demonstrates a shift in the high-sensitivity region due to the interplay of a negative stiffness and an adaptation mechanism

Stereocilia are the basic sensory units of nature's inertial sensors and are highly sensitive over broad dynamic ranges, which is a major challenge in the design of conventional engineering sensors. The high sensitivity that is maintained by stereocilia was hypothesized to exist due to a combination of adaptation and negative stiffness mechanisms, which shift the region of highest sensitivity toward the active operation range of the stereocilia bundle. To examine the adaptation hypothesis in terms of its potential applicability to future applications regarding the design of inertial sensors, we developed a mechanical mimicry of the interplay between negative stiffness and the adaptation of the stereocilia that produces spontaneous oscillation of the hair bundle. The mechanical model consists of an inverted pendulum and a fixed T-bar that mimic the interaction of two adjacent stereocilia. To focus on the interaction of one gating spring and the corresponding adaptation motor without the effect of coupling from the other gating springs attached to the neighboring stereocilia, we fixed one bar that contains the adaptation motor. To emulate the negative resistance of the tip-link due to the transient stiffness softening by the gating ion channel, a magnet pair was attached to the top of the inverted pendulum and the fixed T-bar. Readjustment of the tip-link tension by the 'slipping down and climbing up' motion of the adaptation molecular motors was demonstrated by the side-to-side movement of the magnet by a step motor. The negative stiffness region was observed near the equilibrium position and shifted with the activation of the adaptation motor. The temporal demonstration of the stiffness shift was measured as a spontaneous oscillation. The results showed that the interplay between the negative stiffness and the adaptation mechanism was mechanically produced by the combination of a repulsive force and its continuous readjustment and is better understood through a parameter study of a biomimetic mechanical system.

Quantifying utricular stimulation during natural behavior

The use of natural stimuli in neurophysiological studies has led to significant insights into the encoding strategies used by sensory neurons. To investigate these encoding strategies in vestibular receptors and neurons, we have developed a method for calculating the stimuli delivered to a vestibular organ, the utricle, during natural (unrestrained) behaviors, using the turtle as our experimental preparation. High-speed digital video sequences are used to calculate the dynamic gravito-inertial (GI) vector acting on the head during behavior. X-ray computed tomography (CT) scans are used to determine the orientation of the otoconial layer (OL) of the utricle within the head, and the calculated GI vectors are then rotated into the plane of the OL. Thus, the method allows us to quantify the spatio-temporal structure of stimuli to the OL during natural behaviors. In the future, these waveforms can be used as stimuli in neurophysiological experiments to understand how natural signals are encoded by vestibular receptors and neurons. We provide one example of the method, which shows that turtle feeding behaviors can stimulate the utricle at frequencies higher than those typically used in vestibular studies. This method can be adapted to other species, to other vestibular end organs, and to other methods of quantifying head movements.

Relative stereociliary motion in a hair bundle opposes amplification at distortion frequencies

Direct gating of mechanoelectrical transduction channels by mechanical force is a basic feature of hair cells that assures fast transduction and underpins the mechanical amplification of acoustic inputs, but the associated non-linearity - the gating compliance - inevitably distorts signals. Because reducing distortion would make the ear a better detector, we sought mechanisms with that effect. Mimicking in vivo stimulation, we used stiff probes to displace individual hair bundles at physiological amplitudes and measured the coherence and phase of the relative stereociliary motions with a dual-beam differential interferometer. Although stereocilia moved coherently and in phase at the stimulus frequencies, large phase lags at the frequencies of the internally generated distortion products indicated dissipative relative motions. Tip links engaged these relative modes and decreased the coherence in both stimulated and free hair bundles. These results show that a hair bundle breaks into a highly dissipative serial arrangement of stereocilia at distortion frequencies, precluding their amplification.

Information analysis of posterior canal afferents in the turtle, Trachemys scripta elegans

We have used sinusoidal and band-limited Gaussian noise stimuli along with information measures to characterize the linear and non-linear responses of morpho-physiologically identified posterior canal (PC) afferents and to examine the relationship between mutual information rate and other physiological parameters. Our major findings are: 1) spike generation in most PC afferents is effectively a stochastic renewal process, and spontaneous discharges are fully characterized by their first order statistics; 2) a regular discharge, as measured by normalized coefficient of variation (cv*), reduces intrinsic noise in afferent discharges at frequencies below the mean firing rate; 3) coherence and mutual information rates, calculated from responses to band-limited Gaussian noise, are jointly determined by gain and intrinsic noise (discharge regularity), the two major determinants of signal to noise ratio in the afferent response; 4) measures of optimal non-linear encoding were only moderately greater than optimal linear encoding, indicating that linear stimulus encoding is limited primarily by internal noise rather than by non-linearities; and 5) a leaky integrate and fire model reproduces these results and supports the suggestion that the combination of high discharge regularity and high discharge rates serves to extend the linear encoding range of afferents to higher frequencies. These results provide a framework for future assessments of afferent encoding of signals generated during natural head movements and for comparison with coding strategies used by other sensory systems. This article is part of a Special Issue entitled: Neural Coding.

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.

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.

A mechanical model of the gating spring mechanism of stereocilia

The stereocilium is the basic sensory unit of nature's mechanotransducers, which include the cochlear and vestibular organs. In noisy environments, stereocilia display high sensitivity to miniscule stimuli, effectively dealing with a situation that is a design challenge in micro systems. The gating spring hypothesis suggests that the mechanical stiffness of stereocilia bundle is softened by tip-link gating in combination with active bundle movement, contributing to the nonlinear amplification of miniscule stimuli. To demonstrate that the amplification is induced mechanically by the gating as hypothesized, we developed a biomimetic model of stereocilia and fabricated the model at the macro scale. The model consists of an inverted pendulum array with bistable buckled springs at its tips, which represent the mechanically gated ion channel. Model simulations showed that at the moment of gating, instantaneous stiffness softening generates an increase in response magnitude, which then sequentially occurs as the number of gating increases. This amplification mechanism appeared to be robust to the change of model parameters. Experimental data from the fabricated macro model also showed a significant increase in the open probability and pendulum deflection at the region having a smaller input magnitude. The results demonstrate that the nonlinear amplification of miniscule stimuli is mechanically produced by stiffness softening from channel gating.

Hair cell bundles: flexoelectric motors of the inner ear

Microvilli (stereocilia) projecting from the apex of hair cells in the inner ear are actively motile structures that feed energy into the vibration of the inner ear and enhance sensitivity to sound. The biophysical mechanism underlying the hair bundle motor is unknown. In this study, we examined a membrane flexoelectric origin for active movements in stereocilia and conclude that it is likely to be an important contributor to mechanical power output by hair bundles. We formulated a realistic biophysical model of stereocilia incorporating stereocilia dimensions, the known flexoelectric coefficient of lipid membranes, mechanical compliance, and fluid drag. Electrical power enters the stereocilia through displacement sensitive ion channels and, due to the small diameter of stereocilia, is converted to useful mechanical power output by flexoelectricity. This motor augments molecular motors associated with the mechanosensitive apparatus itself that have been described previously. The model reveals stereocilia to be highly efficient and fast flexoelectric motors that capture the energy in the extracellular electro-chemical potential of the inner ear to generate mechanical power output. The power analysis provides an explanation for the correlation between stereocilia height and the tonotopic organization of hearing organs. Further, results suggest that flexoelectricity may be essential to the exquisite sensitivity and frequency selectivity of non-mammalian hearing organs at high auditory frequencies, and may contribute to the “cochlear amplifier” in mammals.

The actions of calcium on hair bundle mechanics in mammalian cochlear hair cells

Sound stimuli excite cochlear hair cells by vibration of each hair bundle, which opens mechanotransducer (MT) channels. We have measured hair-bundle mechanics in isolated rat cochleas by stimulation with flexible glass fibers and simultaneous recording of the MT current. Both inner and outer hair-cell bundles exhibited force-displacement relationships with a nonlinearity that reflects a time-dependent reduction in stiffness. The nonlinearity was abolished, and hair-bundle stiffness increased, by maneuvers that diminished calcium influx through the MT channels: lowering extracellular calcium, blocking the MT current with dihydrostreptomycin, or depolarizing to positive potentials. To simulate the effects of Ca(2+), we constructed a finite-element model of the outer hair cell bundle that incorporates the gating-spring hypothesis for MT channel activation. Four calcium ions were assumed to bind to the MT channel, making it harder to open, and, in addition, Ca(2+) was posited to cause either a channel release or a decrease in the gating-spring stiffness. Both mechanisms produced Ca(2+) effects on adaptation and bundle mechanics comparable to those measured experimentally. We suggest that fast adaptation and force generation by the hair bundle may stem from the action of Ca(2+) on the channel complex and do not necessarily require the direct involvement of a myosin motor. The significance of these results for cochlear transduction and amplification are discussed.