Two adaptation processes in auditory hair cells together can provide an active amplifier

Neural control and innate self-tuning of the hair cell's active process

We propose a model for the feedback control processes that underlie the robustness and high sensitivity of mechanosensory hair cells. Our model encompasses self-tuning active processes intrinsic to these cells, which drive the amplification of mechanical stimuli by consuming metabolic energy, and a neural input process that protects these cells from damage caused by powerful stimuli. We explore the effects of these two feedback mechanisms on mechanical self-oscillations of the sense cells and their response to external forcing.

Time scales of adaptation to context in horizontal sound localization

Psychophysical experiments explored how the repeated presentation of a context, consisting of an adaptor and a target, induces plasticity in the localization of an identical target presented alone on interleaved trials. The plasticity, and its time course, was examined both in a classroom and in an anechoic chamber. Adaptors and targets were 2 ms noise clicks and listeners were tasked with localizing the targets while ignoring the adaptors (when present). The context was either simple, consisting of a single-click adaptor and a target, or complex, containing either a single-click or an eight-click adaptor that varied from trial to trial. The adaptor was presented either from a frontal or a lateral location, fixed within a run. The presence of context caused responses to the isolated targets to be displaced up to 14° away from the adaptor location. This effect was stronger and slower if the context was complex, growing over the 5 min duration of the runs. Additionally, the simple context buildup had a slower onset in the classroom. Overall, the results illustrate that sound localization is subject to slow adaptive processes that depend on the spatial and temporal structure of the context and on the level of reverberation in the environment.

Modeling Active Non-Markovian Oscillations

Modeling noisy oscillations of active systems is one of the current challenges in physics and biology. Because the physical mechanisms of such processes are often difficult to identify, we propose a linear stochastic model driven by a non-Markovian bistable noise that is capable of generating self-sustained periodic oscillation. We derive analytical predictions for most relevant dynamical and thermodynamic properties of the model. This minimal model turns out to describe accurately bistablelike oscillatory motion of hair bundles in bullfrog sacculus, extracted from experimental data. Based on and in agreement with these data, we estimate the power required to sustain such active oscillations to be of the order of 100  k_{B}T per oscillation cycle.

Myosin-VIIa is expressed in multiple isoforms and essential for tensioning the hair cell mechanotransduction complex

Mutations in myosin-VIIa (MYO7A) cause Usher syndrome type 1, characterized by combined deafness and blindness. MYO7A is proposed to function as a motor that tensions the hair cell mechanotransduction (MET) complex, but conclusive evidence is lacking. Here we report that multiple MYO7A isoforms are expressed in the mouse cochlea. In mice with a specific deletion of the canonical isoform (Myo7a-ΔC mouse), MYO7A is severely diminished in inner hair cells (IHCs), while expression in outer hair cells is affected tonotopically. IHCs of Myo7a-ΔC mice undergo normal development, but exhibit reduced resting open probability and slowed onset of MET currents, consistent with MYO7A's proposed role in tensioning the tip link. Mature IHCs of Myo7a-ΔC mice degenerate over time, giving rise to progressive hearing loss. Taken together, our study reveals an unexpected isoform diversity of MYO7A expression in the cochlea and highlights MYO7A's essential role in tensioning the hair cell MET complex.

Transition between multimode oscillations in a loaded hair bundle

In this paper, we study the dynamics of an autonomous system for a hair bundle subject to mechanical load. We demonstrated the spontaneous oscillations that arise owing to interactions between the linear stiffness and the adapting stiffness. It is found that by varying the linear stiffness, the system can induce a weakly chaotic attractor in a certain region where the stable periodic orbit is infinitely close to a parabolic curve composed of unstable equilibrium points. By altering the adapting stiffness associated with the calcium concentration, the system is able to trigger the transition from the bistable resting state, through a pair of symmetric Hopf bifurcation, into the bistable limit cycle, even to the chaotic attractor. At a negative adapting stiffness, the system exhibits a double-scroll chaotic attractor. According to the method of qualitative theory of fast-slow decomposition, the trajectory of a double-scroll chaotic attractor in the whole system depends upon the symmetric fold/fold bifurcation in a fast system. Furthermore, the control of the adapting stiffness in the improved system with two slow variables can trigger a new transition from the bistable resting state into the chaotic attractor, even to the hyperchaotic attractor by observing the Lyapunov exponent.

Stiffness and tension gradients of the hair cell's tip-link complex in the mammalian cochlea

Sound analysis by the cochlea relies on frequency tuning of mechanosensory hair cells along a tonotopic axis. To clarify the underlying biophysical mechanism, we have investigated the micromechanical properties of the hair cell's mechanoreceptive hair bundle within the apical half of the rat cochlea. We studied both inner and outer hair cells, which send nervous signals to the brain and amplify cochlear vibrations, respectively. We find that tonotopy is associated with gradients of stiffness and resting mechanical tension, with steeper gradients for outer hair cells, emphasizing the division of labor between the two hair-cell types. We demonstrate that tension in the tip links that convey force to the mechano-electrical transduction channels increases at reduced Ca2+. Finally, we reveal gradients in stiffness and tension at the level of a single tip link. We conclude that mechanical gradients of the tip-link complex may help specify the characteristic frequency of the hair cell.

Homeostatic enhancement of sensory transduction

Our sense of hearing boasts exquisite sensitivity, precise frequency discrimination, and a broad dynamic range. Experiments and modeling imply, however, that the auditory system achieves this performance for only a narrow range of parameter values. Small changes in these values could compromise hair cells' ability to detect stimuli. We propose that, rather than exerting tight control over parameters, the auditory system uses a homeostatic mechanism that increases the robustness of its operation to variation in parameter values. To slowly adjust the response to sinusoidal stimulation, the homeostatic mechanism feeds back a rectified version of the hair bundle's displacement to its adaptation process. When homeostasis is enforced, the range of parameter values for which the sensitivity, tuning sharpness, and dynamic range exceed specified thresholds can increase by more than an order of magnitude. Signatures in the hair cell's behavior provide a means to determine through experiment whether such a mechanism operates in the auditory system. Robustness of function through homeostasis may be ensured in any system through mechanisms similar to those that we describe here.

Frequency locking in auditory hair cells: Distinguishing between additive and parametric forcing

- The auditory system displays remarkable sensitivity and frequency discrimination, attributes shown to rely on an amplification process that involves a mechanical as well as a biochemical response. Models that display proximity to an oscillatory onset (also known as Hopf bifurcation) exhibit a resonant response to distinct frequencies of incoming sound, and can explain many features of the amplification phenomenology. To understand the dynamics of this resonance, frequency locking is examined in a system near the Hopf bifurcation and subject to two types of driving forces: additive and parametric. Derivation of a universal amplitude equation that contains both forcing terms enables a study of their relative impact on the hair cell response. In the parametric case, although the resonant solutions are 1 : 1 frequency locked, they show the coexistence of solutions obeying a phase shift of π, a feature typical of the 2 : 1 resonance. Different characteristics are predicted for the transition from unlocked to locked solutions, leading to smooth or abrupt dynamics in response to different types of forcing. The theoretical framework provides a more realistic model of the auditory system, which incorporates a direct modulation of the internal control parameter by an applied drive. The results presented here can be generalized to many other media, including Faraday waves, chemical reactions, and elastically driven cardiomyocytes, which are known to exhibit resonant behavior.

Voltage-Mediated Control of Spontaneous Bundle Oscillations in Saccular Hair Cells

Hair cells of the vertebrate vestibular and auditory systems convert mechanical inputs into electrical signals that are relayed to the brain. This transduction involves mechanically gated ion channels that open following the deflection of mechanoreceptive hair bundles that reside on top of these cells. The mechano-electrical transduction includes one or more active feedback mechanisms to keep the mechanically gated ion channels in their most sensitive operating range. Coupling between the gating of the mechanosensitive ion channels and this adaptation mechanism leads to the occurrence of spontaneous limit-cycle oscillations, which indeed have been observed in vitro in hair cells from the frog sacculus and the turtle basilar papilla. We obtained simultaneous optical and electrophysiological recordings from bullfrog saccular hair cells with such spontaneously oscillating hair bundles. The spontaneous bundle oscillations allowed us to characterize several properties of mechano-electrical transduction without artificial loading the hair bundle with a mechanical stimulus probe. We show that the membrane potential of the hair cell can modulate or fully suppress innate oscillations, thus controlling the dynamic state of the bundle. We further demonstrate that this control is exerted by affecting the internal calcium concentration, which sets the resting open probability of the mechanosensitive channels. The auditory and vestibular systems could use the membrane potential of hair cells, possibly controlled via efferent innervation, to tune the dynamic states of the cells.

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.

Phase-locked spiking of inner ear hair cells and the driven noisy Adler equation

The inner ear constitutes a remarkably sensitive mechanical detector. This detection occurs in a noisy and highly viscous environment, as the sensory cells-the hair cells-are immersed in a fluid-filled compartment and operate at room or higher temperatures. We model the active motility of hair cell bundles of the vestibular system with the Adler equation, which describes the phase degree of freedom of bundle motion. We explore both analytically and numerically the response of the system to external signals, in the presence of white noise. The theoretical model predicts that hair bundles poised in the quiescent regime can exhibit sporadic spikes-sudden excursions in the position of the bundle. In this spiking regime, the system exhibits stochastic resonance, with the spiking rate peaking at an optimal level of noise. Upon the application of a very weak signal, the spikes occur at a preferential phase of the stimulus cycle. We compare the theoretical predictions of our model to experimental measurements obtained in vitro from individual hair cells. Finally, we show that an array of uncoupled hair cells could provide a sensitive detector that encodes the frequency of the applied signal.

Effect of bidirectional mechanoelectrical coupling on spontaneous oscillations and sensitivity in a model of hair cells

Sensory hair cells of amphibians exhibit spontaneous activity in their hair bundles and membrane potentials, reflecting two distinct active amplification mechanisms employed in these peripheral mechanosensors. We use a two-compartment model of the bullfrog's saccular hair cell to study how the interaction between its mechanical and electrical compartments affects the emergence of distinct dynamical regimes, and the role of this interaction in shaping the response of the hair cell to weak mechanical stimuli. The model employs a Hodgkin-Huxley-type system for the basolateral electrical compartment and a nonlinear hair bundle oscillator for the mechanical compartment, which are coupled bidirectionally. In the model, forward coupling is provided by the mechanoelectrical transduction current, flowing from the hair bundle to the cell soma. Backward coupling is due to reverse electromechanical transduction, whereby variations of the membrane potential affect adaptation processes in the hair bundle. We isolate oscillation regions in the parameter space of the model and show that bidirectional coupling affects significantly the dynamics of the cell. In particular, self-sustained oscillations of the hair bundles and membrane potential can result from bidirectional coupling, and the coherence of spontaneous oscillations can be maximized by tuning the coupling strength. Consistent with previous experimental work, the model demonstrates that dynamical regimes of the hair bundle change in response to variations in the conductances of basolateral ion channels. We show that sensitivity of the hair cell to weak mechanical stimuli can be maximized by varying coupling strength, and that stochasticity of the hair bundle compartment is a limiting factor of the sensitivity.

Olfactory coding in the insect brain: data and conjectures

Much progress has been made recently in understanding how olfactory coding works in insect brains. Here, I propose a wiring diagram for the major steps from the first processing network (the antennal lobe) to behavioral readout. I argue that the sequence of lateral inhibition in the antennal lobe, non-linear synapses, threshold-regulating gated spring network, selective lateral inhibitory networks across glomeruli, and feedforward inhibition to the lateral protocerebrum cover most of the experimental results from different research groups and model species. I propose that the main difference between mushroom bodies and the lateral protocerebrum is not about learned vs. innate behavior. Rather, mushroom bodies perform odor identification, whereas the lateral protocerebrum performs odor evaluation (both learned and innate). I discuss the concepts of labeled line and combinatorial coding and postulate that, under restrictive experimental conditions, these networks lead to an apparent existence of 'labeled line' coding for special odors. Modulatory networks are proposed as switches between different evaluating systems in the lateral protocerebrum. A review of experimental data and theoretical conjectures both contribute to this synthesis, creating new hypotheses for future research.

Low frequency entrainment of oscillatory bursts in hair cells

Sensitivity of mechanical detection by the inner ear is dependent upon a highly nonlinear response to the applied stimulus. Here we show that a system of differential equations that support a subcritical Hopf bifurcation, with a feedback mechanism that tunes an internal control parameter, captures a wide range of experimental results. The proposed model reproduces the regime in which spontaneous hair bundle oscillations are bistable, with sporadic transitions between the oscillatory and the quiescent state. Furthermore, it is shown, both experimentally and theoretically, that the application of a high-amplitude stimulus to the bistable system can temporarily render it quiescent before recovery of the limit cycle oscillations. Finally, we demonstrate that the application of low-amplitude stimuli can entrain bundle motility either by mode-locking to the spontaneous oscillation or by mode-locking the transition between the quiescent and oscillatory states.

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.

Subdiffusion in hair bundle dynamics: the role of protein conformational fluctuations

The detection of sound signals in vertebrates involves a complex network of different mechano-sensory elements in the inner ear. An especially important element in this network is the hair bundle, an antenna-like array of stereocilia containing gated ion channels that operate under the control of one or more adaptation motors. Deflections of the hair bundle by sound vibrations or thermal fluctuations transiently open the ion channels, allowing the flow of ions through them, and producing an electrical signal in the process, eventually causing the sensation of hearing. Recent high frequency (0.1-10 kHz) measurements by Kozlov et al. [Proc. Natl. Acad. Sci. U.S.A. 109, 2896 (2012)] of the power spectrum and the mean square displacement of the thermal fluctuations of the hair bundle suggest that in this regime the dynamics of the hair bundle are subdiffusive. This finding has been explained in terms of the simple Brownian motion of a filament connecting neighboring stereocilia (the tip link), which is modeled as a viscoelastic spring. In the present paper, the diffusive anomalies of the hair bundle are ascribed to tip link fluctuations that evolve by fractional Brownian motion, which originates in fractional Gaussian noise and is characterized by a power law memory. The predictions of this model for the power spectrum of the hair bundle and its mean square displacement are consistent with the experimental data and the known properties of the tip link.

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.

Mode-locking dynamics of hair cells of the inner ear

We explore mode locking of spontaneous oscillations of saccular hair cell bundles to periodic mechanical deflections. A simple dynamic systems framework is presented that captures the main features of the experimentally observed behavior in the form of an Arnold tongue. We propose that the phase-locking transition can proceed via different bifurcations. At low stimulus amplitudes F, the transition to mode locking as a function of the stimulus frequency ω has the character of a saddle-node bifurcation on an invariant circle. At higher stimulus amplitudes, the mode-locking transition has the character of a supercritical Andronov-Hopf bifurcation.

A mean-field approach to elastically coupled hair bundles

We study the dynamics of oscillatory hair bundles which are coupled elastically in their deflection variable and are subject to noise. We present a stochastic description capturing the dynamics of the hair bundles' mean field. In particular, the presented derivation elucidates the origin of the previously described noise reduction by coupling. By comparison of simulations of the approximate dynamics and the full system, we verify our results. Furthermore, we demonstrate that the specific type of coupling considered implies coupling-induced changes in the dynamics beyond mere noise reduction.

The diverse effects of mechanical loading on active hair bundles

Hair cells in the auditory, vestibular, and lateral-line systems of vertebrates receive inputs through a remarkable variety of accessory structures that impose complex mechanical loads on the mechanoreceptive hair bundles. Although the physiological and morphological properties of the hair bundles in each organ are specialized for detecting the relevant inputs, we propose that the mechanical load on the bundles also adjusts their responsiveness to external signals. We use a parsimonious description of active hair-bundle motility to show how the mechanical environment can regulate a bundle's innate behavior and response to input. We find that an unloaded hair bundle can behave very differently from one subjected to a mechanical load. Depending on how it is loaded, a hair bundle can function as a switch, active oscillator, quiescent resonator, or low-pass filter. Moreover, a bundle displays a sharply tuned, nonlinear, and sensitive response for some loading conditions and an untuned or weakly tuned, linear, and insensitive response under other circumstances. Our simple characterization of active hair-bundle motility explains qualitatively most of the observed features of bundle motion from different organs and organisms. The predictions stemming from this description provide insight into the operation of hair bundles in a variety of contexts.

Auditory and vestibular hair cell stereocilia: relationship between functionality and inner ear disease

The stereocilia of the inner ear are unique cellular structures which correlate anatomically with distinct cochlear functions, including mechanoelectrical transduction, cochlear amplification, adaptation, frequency selectivity and tuning. Their function is impaired by inner ear stressors, by various types of hereditary deafness, syndromic hearing loss and inner ear disease (e.g. Ménière's disease). The anatomical and physiological characteristics of stereocilia are discussed in relation to inner ear malfunctions.

Dual contribution to amplification in the mammalian inner ear

The inner ear achieves a wide dynamic range of responsiveness by mechanically amplifying weak sounds. The enormous mechanical gain reported for the mammalian cochlea, which exceeds a factor of 4000, poses a challenge for theory. Here we show how such a large gain can result from an interaction between amplification by low-gain hair bundles and a pressure wave: hair bundles can amplify both their displacement per locally applied pressure and the pressure wave itself. A recently proposed ratchet mechanism, in which hair-bundle forces do not feed back on the pressure wave, delineates the two effects. Our analytical calculations with a WKB approximation agree with numerical solutions.

The role of Hopf bifurcation dynamics in sensory processes

We emphasize here the role of the Hopf bifurcation in detection of stimuli in sensory processes--we discuss in particular chemosensors. It is shown that the essential nonlinearities inherent in the signal transduction mechanism can take advantage of the noise from the environment the system is subject to, to display a highly amplified response to stimuli in a frequency-selective manner. It is shown that in the absence of any externally applied stimulus, the feedback mechanisms playing a regulatory role in the transduction mechanism can give rise, in the presence of noise, to peaks in the spectral power density, suggesting enhanced spontaneous activity in sensory cells. The power law in this spectrum is determined.

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.

An adaptive model simulating the somatic motility and the active hair bundle motion of the OHC

The outer hair cells (OHC) of the mammalian inner ear change the sensitivity and frequency selectivity of the filtering system of the cochlea using two kinds of mechanical activity: the somatic motility and the active hair bundle motion. We designed a non-linear adaptive model of the OHC employing both mechanisms of the mechanical activity. The modeling results show that the high sensitivity and frequency selectivity of the filtering system of the cochlea depend on the somatic motility of the OHC. However, both mechanisms of mechanical activity are involved in the adaptation to sound intensity and efferent-synaptic influence. The fast (alternating) component (AC) of the mechanical-electrical transduction signal controls the motor protein prestin and fast changes in axial length of the cell. The slow (direct) component (DC) appearing at high signal intensity affects the axial stiffness, the cell length and the position of the hair bundle. The efferent influence is realized by the same mechanism.

Distribution of frequencies of spontaneous oscillations in hair cells of the bullfrog sacculus

Under in vitro conditions, free-standing hair bundles of the bullfrog (Rana catesbeiana) sacculus have exhibited spontaneous oscillations. We used a high-speed complementary metal oxide semiconductor camera to track the active movements of multiple hair cells in a single field of view. Our techniques enabled us to probe for correlations between pairs of cells, and to acquire records on over 100 actively oscillating bundles per epithelium. We measured the statistical distribution of oscillation periods of cells from different areas within the sacculus, and on different epithelia. Spontaneous oscillations exhibited a peak period of 33 ms (+29 ms, -14 ms) and uniform spatial distribution across the sacculus.

Scale-free topology-induced double resonance in networked two-state systems

We study numerically the effect of a scale-free topology on the signal-to-noise ratio of networked two-state systems and find a double resonance phenomenon, i.e., a resonance on coupling strength and a stochastic resonance on noise strength. This finding suggests an alternative approach of self-tuning, i.e., tuning from the scale-free topology, instead of the self-tuning of potential. A heuristic theory through a starlike network is presented to explain the double resonance.

Linear and nonlinear processing in hair cells

Mechanosensory hair cells in the ear are exquisitely responsive to minute sensory inputs, nearly to the point of instability. Active mechanisms bias the transduction apparatus and subsequent electrical amplification away from saturation in either the negative or positive direction, to an operating point where the response to small signals is approximately linear. An active force generator coupled directly to the transducer enhances sensitivity and frequency selectivity, and counteracts energy loss to viscous drag. Active electrical amplification further enhances gain and frequency selectivity. In both cases, nonlinear properties may maintain the system close to instability, as evidenced by small spontaneous oscillations, while providing a compressive nonlinearity that increases the cell's operating range. Transmitter release also appears to be frequency selective and biased to operate most effectively near the resting potential. This brief overview will consider the resting stability of hair cells, and their responses to small perturbations that correspond to soft sounds or small accelerations.

Voltage-dependent outer hair cell stereocilia stiffness at acoustic frequencies

The aim of this report is to show the effects of voltage changes on stereocilia stiffness in mammalian outer hair cells (OHCs). With the OHC cuticular plate anchored at a microchamber tip, step voltage commands drove an OHC inside the microchamber to move freely while stereocilia were oscillated at 510 Hz by a constant fluid-jet force. With basolateral OHC depolarized and shortened, the amplitude of stereocilia motion was increased, suggesting a decrease in stereocilia stiffness. Such a decrease in stiffness may serve as an important adjusting factor inside the cochlear amplifying loop.

Frequency clustering in spontaneous otoacoustic emissions from a lizard's ear

Spontaneous otoacoustic emissions (SOAEs) are indicators of an active process in the inner ear that enhances the sensitivity and frequency selectivity of hearing. They are particularly regular and robust in certain lizards, so these animals are good model organisms for studying how SOAEs are generated. We show that the published properties of SOAEs in the bobtail lizard are wholly consistent with a mathematical model in which active oscillators, with exponentially varying characteristic frequencies, are coupled together in a chain by visco-elastic elements. Physically, each oscillator corresponds to a small group of hair cells, covered by a tectorial sallet, so our theoretical analysis directly links SOAEs to the micromechanics of active hair bundles.

Physiologically inspired signal preprocessing for auditory prostheses: Insights from the electro-motility of the OHC

We designed a non-linear functional model of the outer hair cell (OHC) functioning in the filtering system of the cochlea and then isolated from it two second-order structures, one employing the mechanism of the somatic motility and the other the hair bundle motion of the OHC. The investigation of these circuits showed that the main mechanism increasing the sensitivity and frequency selectivity of the filtering system is the somatic motility. The mechanism of the active hair bundle motion appeared less suitable for realization of the band-pass filtering structures due to the dependence of the sensitivity, natural frequency and selectivity on the signal intensity. We combined three second-order filtering structures employing the mechanism of the somatic motility and the lateral inhibition to form a parallel-type filtering channel of the sixth order with the frequency characteristics of the Butterworth-type and Gaussian-type. The investigation of these channels showed that the Gaussian-type channel has the advantage over the Butterworth-type channel. It is more suitable for realization of a filter bank with common lateral circuits and has less distorted frequency characteristic in the nonlinear mode.

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.

Amplification in the auditory periphery: the effect of coupling tuning mechanisms

A mathematical model describing the coupling between two independent amplification mechanisms in auditory hair cells is proposed and analyzed. Hair cells are cells in the inner ear responsible for translating sound-induced mechanical stimuli into an electrical signal that can then be recorded by the auditory nerve. In nonmammals, two separate mechanisms have been postulated to contribute to the amplification and tuning properties of the hair cells. Models of each of these mechanisms have been shown to be poised near a Hopf bifurcation. Through a weakly nonlinear analysis that assumes weak periodic forcing, weak damping, and weak coupling, the physiologically based models of the two mechanisms are reduced to a system of two coupled amplitude equations describing the resonant response. The predictions that follow from an analysis of the reduced equations, as well as performance benefits due to the coupling of the two mechanisms, are discussed and compared with published experimental auditory nerve data.

A virtual hair cell, II: evaluation of mechanoelectric transduction parameters

The virtual hair cell we have proposed utilizes a set of parameters related to its mechanoelectric transduction. In this work, we observed the effect of such channel gating parameters as the gating threshold, critical tension, resting tension, and Ca(2+) concentration. The gating threshold is the difference between the resting and channel opening tension exerted by the tip link assembly on the channel. The critical tension is the tension in the tip link assembly over which the channel cannot close despite Ca(2+) binding. Our results show that 1), the gating threshold dominated the initial sensitivity of the hair cell; 2), the critical tension minimally affects the peak response, (I), but considerably affects the time course of response, I(t), and the force-displacement, F-X, relationship; and 3), higher intracellular [Ca(2+)] resulted in a smaller fast adaptation time constant. Based on the simulation results we suggest a role of the resting tension: to help overcome the viscous drag of the hair bundle during the oscillatory movement of the bundle. Also we observed the three-dimensional bundle effect on the hair cell response by varying the number of cilia forced. These varying forcing conditions affected the hair cell response.

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

We have developed a virtual hair cell that simulates hair cell mechanoelectrical transduction in the turtle utricle. This study combines a full three-dimensional hair bundle mechanical model with a gating spring theory. Previous mathematical models represent the hair bundle with a single degree of freedom system which, we have argued, cannot fully explain hair bundle mechanics. In our computer model, the tip link tension and fast adaptation modulator kinetics determine the opening and closing of each channel independently. We observed the response of individual transduction channels with our presented model. The simulated results showed three features of hair cells in vitro. First, a transient rebound of the bundle tip appeared when fast adaptation dominated the dynamics. Second, the dynamic stiffness of the bundle was minimized when the response-displacement (I-X) curve was steepest. Third, the hair cell showed "polarity", i.e., activation decreased from a peak to zero as the forcing direction rotated from the excitatory to the inhibitory direction.

Oscillations in molecular motor assemblies

Autonomous oscillations in biological systems may have a biochemical origin or result from an interplay between force-generating and visco-elastic elements. In molecular motor assemblies the force-generating elements are molecular engines and the visco-elastic elements are stiff cytoskeletal polymers. The physical mechanism leading to oscillations depends on the particular architecture of the assembly. Existing models can be grouped into two distinct categories: systems with a delayed force activation and anomalous force-velocity relations. We discuss these systems within phase plane analysis known from the theory of dynamic systems and by adopting methods from control theory, the Nyquist stability criterion.

Ion channel regulation of the dynamical instability of the resting membrane potential in saccular hair cells of the green frog (Rana esculenta)

AIMS

We investigated the ion channel regulation of the resting membrane potential of hair cells with the aim to determine if the resting membrane potential is poised close to instability and thereby a potential cause of the spontaneous afferent spike activity.

METHODS

The ionic mechanism and the dynamic properties of the resting membrane potential were examined with the whole-cell patch clamp technique in dissociated saccular hair cells and in a mathematical model including all identified ion channels.

RESULTS

In hair cells showing I/V curves with a low membrane conductance flanked by large inward and outward rectifying potassium conductances, the inward rectifier (K(IR)), the delayed outward rectifier (K(V)) and the large conductance, calcium-sensitive, voltage-gated potassium channel (BK(Ca)) were all activated at rest. Under current clamp conditions, the outward current through these channels balanced the inward current through mechano-electrical transduction (MET) and Ca2+ channels. In 45% (22/49) of the cells, the membrane potential fluctuated spontaneously between two voltage levels determined by the voltage extent of the low membrane conductance range. These fluctuations were not influenced by blocking the MET channels but could be reversibly stopped by increasing [K+]o or by blocking of K(IR) channels. Blocking the BK(Ca) channels induced regular voltage oscillations.

CONCLUSIONS

Two intrinsic dynamical instabilities of V(m) are present in hair cells. One of these is observed as spontaneous voltage fluctuations by currents through K(IR), K(V) and h-channels in combination with a steady current through MET channels. The other instability shows as regenerative voltage changes involving Ca2+ and K(V) channels. The BK(Ca) channels prevent the spontaneous voltage fluctuations from activating the regenerative system.

Stochastic resonance in the mechanoelectrical transduction of hair cells

In transducing mechanical stimuli into electrical signals, at least some hair cells in vertebrate auditory and vestibular systems respond optimally to weak periodic signals at natural, nonzero noise intensities. We understand this stochastic resonance by constructing a faithful mechanical model reflecting the hair cell geometry and described by a nonlinear stochastic differential equation. This Langevin description elucidates the mechanism of hair cell stochastic resonance while supporting the hypothesis that noise plays a functional role in hearing.

Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro

An active process in the inner ear expends energy to enhance the sensitivity and frequency selectivity of hearing. Two mechanisms have been proposed to underlie this process in the mammalian cochlea: receptor potential-based electromotility and Ca(2+)-driven active hair-bundle motility. To link the phenomenology of the cochlear amplifier with these cellular mechanisms, we developed an in vitro cochlear preparation from Meriones unguiculatus that affords optical access to the sensory epithelium while mimicking its in vivo environment. Acoustic and electrical stimulation elicited microphonic potentials and electrically evoked hair-bundle movement, demonstrating intact forward and reverse mechanotransduction. The mechanical responses of hair bundles from inner hair cells revealed a characteristic resonance and a compressive nonlinearity diagnostic of the active process. Blocking transduction with amiloride abolished nonlinear amplification, whereas eliminating all but the Ca(2+) component of the transduction current did not. These results suggest that the Ca(2+) current drives the cochlear active process, and they support the hypothesis that active hair-bundle motility underlies cochlear amplification.

BAPTA Induces Frequency Shifts in vivo of Spontaneous Otoacoustic Emissions of the Bobtail Lizard

Spontaneous otoacoustic emissions (SOAEs) are indicators of active processes in the inner ear and are found in all classes of land vertebrates. In the Australian bobtail lizard, earlier work showed that otoacoustic emissions are generated by an active motility process in the hair-cell bundle. This is likely to be driven by calcium-sensitive mechanisms implicated in other non-mammalian hair cell systems. If so, it should be fundamentally influenced by the extracellular calcium concentration. In in vitro studies, the rate of force generation in hair cell stereovilli is linked to the extracellular calcium concentration. In such preparations, low-calcium solutions, buffered by the calcium chelator BAPTA, were reported to change the frequency of hair cell bundle oscillations. In the present study, BAPTA was iontophoresed into the endolymph of the bobtail skink in vivo, and SOAEs were monitored. Application of BAPTA resulted in a prolonged downward shift in the frequency of individual SOAE spectral peaks. Recovery took more than 1 h, consistent with a slow clearance of BAPTA from endolymph. SOAE peak amplitudes were most often enhanced, suggesting there was no functional disruption of tip links. The direction and degree of frequency shifts were consistent with in vitro and in vivo data showing the effects of changing calcium concentrations in the endolymph directly.

Spontaneous low-frequency voltage oscillations in frog saccular hair cells

Spontaneous membrane voltage oscillations were found in 27 of 130 isolated frog saccular hair cells. Voltage oscillations had a mean peak-to-peak amplitude of 23 mV and a mean oscillatory frequency of 4.6 Hz. When compared with non-oscillatory cells, oscillatory cells had significantly greater hyperpolarization-activated and lower depolarization-activated current densities. Two components, the hyperpolarization-activated cation current, I(h), and the K(+)-selective inward-rectifier current, I(K1), contributed to the hyperpolarization-activated current, as assessed by the use of the I(K1)-selective inhibitor Ba(2+) and the I(h)-selective inhibitor ZD-7288. Five depolarization-activated currents were present in these cells (transient I(BK), sustained I(BK), I(DRK), I(A), and I(Ca)), and all were found to have significantly lower densities in oscillatory cells than in non-oscillatory cells (revealed by using TEA to block I(BK), 4-AP to block I(DRK), and prepulses at different voltages to isolate I(A)). Bath application of either Ba(2+) or ZD-7288 suppressed spontaneous voltage oscillations, indicating that I(h) and I(K1) are required for generating this activity. On the contrary, TEA or Cd(2+) did not inhibit this activity, suggesting that I(BK) and I(Ca) do not contribute. A mathematical model has been developed to test the interpretation derived from the pharmacological and biophysical data. This model indicates that spontaneous voltage oscillations can be generated when the electrophysiological features of oscillatory cells are used. The oscillatory behaviour is principally driven by the activity of I(K1) and I(h), with I(A) playing a modulatory role. In addition, the model indicates that the high densities of depolarization-activated currents expressed by non-oscillatory cells help to stabilize the resting membrane potential, thus preventing the spontaneous oscillations.

Hair-cell versus afferent adaptation in the semicircular canals

The time course and extent of adaptation in semicircular canal hair cells was compared to adaptation in primary afferent neurons for physiological stimuli in vivo to study the origins of the neural code transmitted to the brain. The oyster toadfish, Opsanus tau, was used as the experimental model. Afferent firing-rate adaptation followed a double-exponential time course in response to step cupula displacements. The dominant adaptation time constant varied considerably among afferent fibers and spanned six orders of magnitude for the population ( approximately 1 ms to >1,000 s). For sinusoidal stimuli (0.1-20 Hz), the rapidly adapting afferents exhibited a 90 degrees phase lead and frequency-dependent gain, whereas slowly adapting afferents exhibited a flat gain and no phase lead. Hair-cell voltage and current modulations were similar to the slowly adapting afferents and exhibited a relatively flat gain with very little phase lead over the physiological bandwidth and dynamic range tested. Semicircular canal microphonics also showed responses consistent with the slowly adapting subset of afferents and with hair cells. The relatively broad diversity of afferent adaptation time constants and frequency-dependent discharge modulations relative to hair-cell voltage implicate a subsequent site of adaptation that plays a major role in further shaping the temporal characteristics of semicircular canal afferent neural signals.

Active hair-bundle motility harnesses noise to operate near an optimum of mechanosensitivity

The ear relies on nonlinear amplification to enhance its sensitivity and frequency selectivity to oscillatory mechanical stimuli. It has been suggested that this active process results from the operation of dynamical systems that operate in the vicinity of an oscillatory instability, a Hopf bifurcation. In the bullfrog's sacculus, a hair cell can display spontaneous oscillations of its mechanosensory hair bundle. The behavior of an oscillatory hair bundle resembles that of a critical oscillator. We present here a theoretical description of the effects of intrinsic noise on active hair-bundle motility. An oscillatory instability can result from the interplay between a region of negative stiffness in the bundle's force-displacement relation and the Ca(2+)-regulated activity of molecular motors. We calculate a state diagram that describes the possible dynamical states of the hair bundle in the absence of fluctuations. Taking into account thermal fluctuations, the stochastic nature of transduction channels' gating, and of the forces generated by molecular motors, we discuss conditions that yield a response function and spontaneous noisy movements of the hair bundle in quantitative agreement with previously published experiments. We find that the magnitude of the fluctuations resulting from the active processes that mediate mechanical amplification remains just below that of thermal fluctuations. Fluctuations destroy the phase coherence of spontaneous oscillations and restrict the bundle's sensitivity as well as frequency selectivity to small oscillatory stimuli. We show, however, that a hair bundle studied experimentally operates near an optimum of mechanosensitivity in our state diagram.