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

Vestibular Drop Attacks and Meniere's Disease as Results of Otolithic Membrane Damage-A Numerical Model

Meniere's disease (MD) is a condition of the inner ear with symptoms affecting both vestibular and hearing functions. Some patients with MD experience vestibular drop attacks (VDAs), which are violent falls caused by spurious vestibular signals from the utricle and/or saccule. Recent surgical work has shown that patients who experience VDAs also show disrupted utricular otolithic membranes. The objective of this study is to determine if otolithic membrane damage alone is sufficient to induce spurious vestibular signals, thus potentially eliciting VDAs and the vestibular dysfunction seen in patients with MD. We use a previously developed numerical model to describe the nonlinear dynamics of an array of active, elastically coupled hair cells. We then reduce the coupling strength of a selected region of the membrane to model the effects of tissue damage. As we reduce the coupling strength, we observe large and abrupt spikes in hair bundle position. As bundle displacements from the equilibrium position have been shown to lead to depolarization of the hair-cell soma and hence trigger neural activity, this spontaneous activity could elicit false detection of a vestibular signal. The results of this numerical model suggest that otolithic membrane damage alone may be sufficient to induce VDAs and the vestibular dysfunction seen in patients with MD. Future experimental work is needed to confirm these results in vitro.

Fluid Jet Stimulation of Auditory Hair Bundles Reveal Spatial Non-uniformities and Two Viscoelastic-Like Mechanisms

Hair cell mechanosensitivity resides in the sensory hair bundle, an apical protrusion of actin-filled stereocilia arranged in a staircase pattern. Hair bundle deflection activates mechano-electric transduction (MET) ion channels located near the tops of the shorter rows of stereocilia. The elicited macroscopic current is shaped by the hair bundle motion so that the mode of stimulation greatly influences the cell’s output. We present data quantifying the displacement of the whole outer hair cell bundle using high-speed imaging when stimulated with a fluid jet. We find a spatially non-uniform stimulation that results in splaying, where the hair bundle expands apart. Based on modeling, the splaying is predominantly due to fluid dynamics with a small contribution from hair bundle architecture. Additionally, in response to stimulation, the hair bundle exhibited a rapid motion followed by a slower motion in the same direction (creep) that is described by a double exponential process. The creep is consistent with originating from a linear passive system that can be modeled using two viscoelastic processes. These viscoelastic mechanisms are integral to describing the mechanics of the mammalian hair bundle.

Volterra-series approach to stochastic nonlinear dynamics: Linear response of the Van der Pol oscillator driven by white noise

The Van der Pol equation is a paradigmatic model of relaxation oscillations. This remarkable nonlinear phenomenon of self-sustained oscillatory motion underlies important rhythmic processes in nature and electrical engineering. Relaxation oscillations in a real system are usually coupled to environmental noise, which further enriches their dynamics, but makes theoretical analysis of such systems and determination of the equation parameter values a difficult task. In a companion paper we have proposed an analytic approach to a similar problem for another classical nonlinear model-the bistable Duffing oscillator. Here we extend our techniques to the case of the Van der Pol equation driven by white noise. We analyze the statistics of solutions and propose a method to estimate parameter values from the oscillator's time series. We use experimental data of active oscillations in a biophysical system to demonstrate how our method applies to real observations and can be generalized for more complex models.

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.

Oscillations in the auditory system and their possible role

GOURÉVITCH, B., C. Martin, O. Postal, J.J. Eggermont. Oscillations in the auditory system, their possible role. NEUROSCI BIOBEHAV REV XXX XXX-XXX, 2020. - Neural oscillations are thought to have various roles in brain processing such as, attention modulation, neuronal communication, motor coordination, memory consolidation, decision-making, or feature binding. The role of oscillations in the auditory system is less clear, especially due to the large discrepancy between human and animal studies. Here we describe many methodological issues that confound the results of oscillation studies in the auditory field. Moreover, we discuss the relationship between neural entrainment and oscillations that remains unclear. Finally, we aim to identify which kind of oscillations could be specific or salient to the auditory areas and their processing. We suggest that the role of oscillations might dramatically differ between the primary auditory cortex and the more associative auditory areas. Despite the moderate presence of intrinsic low frequency oscillations in the primary auditory cortex, rhythmic components in the input seem crucial for auditory processing. This allows the phase entrainment between the oscillatory phase and rhythmic input, which is an integral part of stimulus selection within the auditory system.

Effects of Efferent Activity on Hair Bundle Mechanics

Hair cells in both the auditory and vestibular systems receive efferent innervation. A number of prior studies have indicated that efferent regulation serves to diminish the overall sensitivity of the auditory system. The efferent pathway is believed to affect the sensitivity and frequency selectivity of the hair cell by modulating its membrane potential. However, its effect on the mechanical response of the hair cell has not been established. We explored how stimulation of the efferent neurons affects the mechanical responsiveness of an individual hair bundle. We tested this effect on in vitro preparations of hair cells in the sacculi of American bullfrogs of both genders. Efferent stimulation routinely resulted in an immediate increase of the frequency of hair bundle spontaneous oscillations for the duration of the stimulus. Enlarging the stimulus amplitude and pulse length, or conversely, decreasing the interpulse interval led to oscillation suppression. Additionally, we tested the effects of efference on the hair bundle response to mechanical stimulation. The receptive field maps of hair cells undergoing efferent actuation demonstrated an overall desensitization with respect to those of unstimulated cells.SIGNIFICANCE STATEMENT The efferent system is an important aide for the performance of the auditory system. It has been seen to contribute to sound detection and localization, ototoxicity prevention, and speech comprehension. Although measurements have demonstrated that efference suppresses basilar membrane movement, there is still much unknown about how efferent activity affects hearing mechanics. Here, we explore the mechanical basis for the efferent system's capabilities at the level of the hair bundle. We present optical recordings, receptive field maps, and sensitivity curves that show a hair bundle is desensitized by efferent stimulation. This supports the hypothesis that efferent regulation may be a biological control parameter for tuning the hair bundle's mechanical sensitivity.

Hair Bundle Stimulation Mode Modifies Manifestations of Mechanotransduction Adaptation

Sound detection in auditory sensory hair cells depends on the deflection of the stereocilia hair bundle which opens mechano-electric transduction (MET) channels. Adaptation is hypothesized to be a critical property of MET that contributes to the auditory system's wide dynamic range and sharp frequency selectivity. Our recent work using a stiff probe to displace hair bundles showed that the fastest adaptation mechanism (fast adaptation) does not require calcium entry. Using fluid-jet stimuli, others obtained data showing only a calcium-dependent fast adaptation response. Because cochlear stereocilia do not move coherently and the hair cell response depends critically on the magnitude and time course of the hair bundle deflection, we developed a high-speed imaging technique to quantify this deflection in rat cochlear hair cells. The fluid jet delivers a force stimulus, and force steps lead to a complex time course of hair bundle displacement (mechanical creep), which affects the hair cell's macroscopic MET current response by masking the time course of the fast adaptation response. Modifying the fluid-jet stimulus to generate a hair bundle displacement step produced rapidly adapting currents that did not depend on membrane potential, confirming that fast adaptation does not depend on calcium entry. MET current responses differ with stimulus modality and will shape receptor potentials of different hair cell types based on their in vivo stimulus mode. These transformations will directly affect how stimuli are encoded.SIGNIFICANCE STATEMENT Mechanotransduction by sensory hair cells represents a key first step for the sound sensing ability in vertebrates. The sharp frequency tuning and wide dynamic range of sound sensation are hypothesized to require a mechanotransduction adaptation mechanism. Recent work indicated that the apparent calcium dependence of the fastest adaptation differs with the method of cochlear hair cell stimulation. Here, we reconcile existing data and show that calcium entry does not drive the fastest adaptation process, independent of the stimulation method. With force stimulation of the hair bundle, adaptation manifests differently than with displacement stimulation, indicating that the stimulation mode of the hair bundle will affect the hair cell receptor current and stimulus coding.

Friction from Transduction Channels' Gating Affects Spontaneous Hair-Bundle Oscillations

Hair cells of the inner ear can power spontaneous oscillations of their mechanosensory hair bundle, resulting in amplification of weak inputs near the characteristic frequency of oscillation. Recently, dynamic force measurements have revealed that delayed gating of the mechanosensitive ion channels responsible for mechanoelectrical transduction produces a friction force on the hair bundle. The significance of this intrinsic source of dissipation for the dynamical process underlying active hair-bundle motility has remained elusive. The aim of this work is to determine the role of friction in spontaneous hair-bundle oscillations. To this end, we characterized key oscillation properties over a large ensemble of individual hair cells and measured how viscosity of the endolymph that bathes the hair bundles affects these properties. We found that hair-bundle movements were too slow to be impeded by viscous drag only. Moreover, the oscillation frequency was only marginally affected by increasing endolymph viscosity by up to 30-fold. Stochastic simulations could capture the observed behaviors by adding a contribution to friction that was 3-8-fold larger than viscous drag. The extra friction could be attributed to delayed changes in tip-link tension as the result of the finite activation kinetics of the transduction channels. We exploited our analysis of hair-bundle dynamics to infer the channel activation time, which was ∼1 ms. This timescale was two orders-of-magnitude shorter than the oscillation period. However, because the channel activation time was significantly longer than the timescale of mechanical relaxation of the hair bundle, channel kinetics affected hair-bundle dynamics. Our results suggest that friction from channel gating affects the waveform of oscillation and that the channel activation time can tune the characteristic frequency of the hair cell. We conclude that the kinetics of transduction channels' gating plays a fundamental role in the dynamic process that shapes spontaneous hair-bundle oscillations.

Nonequilibrium limit-cycle oscillators: Fluctuations in hair bundle dynamics

We develop a framework for the general interpretation of the stochastic dynamical system near a limit cycle. Such quasiperiodic dynamics are commonly found in a variety of nonequilibrium systems, including the spontaneous oscillations of hair cells of the inner ear. We demonstrate quite generally that in the presence of noise, the phase of the limit cycle oscillator will diffuse, while deviations in the directions locally orthogonal to that limit cycle will display the Lorentzian power spectrum of a damped oscillator. We identify two mechanisms by which these stochastic dynamics can acquire a complex frequency dependence and discuss the deformation of the mean limit cycle as a function of temperature. The theoretical ideas are applied to data obtained from spontaneously oscillating hair cells of the amphibian sacculus.

Amphibian sacculus and the forced Kuramoto model with intrinsic noise and frequency dispersion

The amphibian sacculus (AS) is an end organ that specializes in the detection of low-frequency auditory and vestibular signals. In this paper, we propose a model for the AS in the form of an array of phase oscillators with long-range coupling, subject to a steady load that suppresses spontaneous oscillations. The array is exposed to significant levels of frequency dispersion and intrinsic noise. We show that such an array can be a sensitive and robust subthreshold detector of low-frequency stimuli, though without significant frequency selectivity. The effects of intrinsic noise and frequency dispersion are contrasted. Intermediate levels of intrinsic noise greatly enhance the sensitivity through stochastic resonance. Frequency dispersion, on the other hand, only degrades detection sensitivity. However, frequency dispersion can play a useful role in terms of the suppression of spontaneous activity. As a model for the AS, the array parameters are such that the system is poised near a saddle-node bifurcation on an invariant circle. However, by a change of array parameters, the same system also can be poised near an emergent Andronov-Hopf bifurcation and thereby function as a frequency-selective detector.

Signal Processing in Periodically Forced Gradient Frequency Neural Networks

Oscillatory instability at the Hopf bifurcation is a dynamical phenomenon that has been suggested to characterize active non-linear processes observed in the auditory system. Networks of oscillators poised near Hopf bifurcation points and tuned to tonotopically distributed frequencies have been used as models of auditory processing at various levels, but systematic investigation of the dynamical properties of such oscillatory networks is still lacking. Here we provide a dynamical systems analysis of a canonical model for gradient frequency neural networks driven by a periodic signal. We use linear stability analysis to identify various driven behaviors of canonical oscillators for all possible ranges of model and forcing parameters. The analysis shows that canonical oscillators exhibit qualitatively different sets of driven states and transitions for different regimes of model parameters. We classify the parameter regimes into four main categories based on their distinct signal processing capabilities. This analysis will lead to deeper understanding of the diverse behaviors of neural systems under periodic forcing and can inform the design of oscillatory network models of auditory signal processing.

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.

Magnetic nanoparticles for ultrafast mechanical control of inner ear hair cells

We introduce cubic magnetic nanoparticles as an effective tool for precise and ultrafast control of mechanosensitive cells. The temporal resolution of our system is ∼1000 times faster than previously used magnetic switches and is comparable to the current state-of-the-art optogenetic tools. The use of a magnetism-gated switch reported here can address the key challenges of studying mechanotransduction in biological systems. The cube-shaped magnetic nanoparticles are designed to bind to components of cellular membranes and can be controlled with an electromagnet to exert pico-Newtons of mechanical force on the cells. The cubic nanoparticles can thus be used for noncontact mechanical control of the position of the stereocilia of an inner ear hair cell, yielding displacements of tens of nanometers, with sub-millisecond temporal resolution. We also prove that such mechanical stimulus leads to the influx of ions into the hair cell. Our study demonstrates that a magnetic switch can yield ultrafast temporal resolution, and has capabilities for remote manipulation and biological specificity, and that such magnetic system can be used for the study of mechanotransduction processes of a wide range of sensory systems.

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.

Enhanced signal-to-noise ratios in frog hearing can be achieved through amplitude death

In the ear, hair cells transform mechanical stimuli into neuronal signals with great sensitivity, relying on certain active processes. Individual hair cell bundles of non-mammals such as frogs and turtles are known to show spontaneous oscillation. However, hair bundles in vivo must be quiet in the absence of stimuli, otherwise the signal is drowned in intrinsic noise. Thus, a certain mechanism is required in order to suppress intrinsic noise. Here, through a model study of elastically coupled hair bundles of bullfrog sacculi, we show that a low stimulus threshold and a high signal-to-noise ratio (SNR) can be achieved through the amplitude death phenomenon (the cessation of spontaneous oscillations by coupling). This phenomenon occurs only when the coupled hair bundles have inhomogeneous distribution, which is likely to be the case in biological systems. We show that the SNR has non-monotonic dependence on the mass of the overlying membrane, and find out that the SNR has maximum value in the region of amplitude death. The low threshold of stimulus through amplitude death may account for the experimentally observed high sensitivity of frog sacculi in detecting vibration. The hair bundles' amplitude death mechanism provides a smart engineering design for low-noise amplification.

Phase slips in oscillatory hair bundles

Hair cells of the inner ear contain an active amplifier that allows them to detect extremely weak signals. As one of the manifestations of an active process, spontaneous oscillations arise in fluid immersed hair bundles of in vitro preparations of selected auditory and vestibular organs. We measure the phase-locking dynamics of oscillatory bundles exposed to low-amplitude sinusoidal signals, a transition that can be described by a saddle-node bifurcation on an invariant circle. The transition is characterized by the occurrence of phase slips, at a rate that is dependent on the amplitude and detuning of the applied drive. The resultant staircase structure in the phase of the oscillation can be described by the stochastic Adler equation, which reproduces the statistics of phase slip production.

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.

Coupling and elastic loading affect the active response by the inner ear hair cell bundles

Active hair bundle motility has been proposed to underlie the amplification mechanism in the auditory endorgans of non-mammals and in the vestibular systems of all vertebrates, and to constitute a crucial component of cochlear amplification in mammals. We used semi-intact in vitro preparations of the bullfrog sacculus to study the effects of elastic mechanical loading on both natively coupled and freely oscillating hair bundles. For the latter, we attached glass fibers of different stiffness to the stereocilia and observed the induced changes in the spontaneous bundle movement. When driven with sinusoidal deflections, hair bundles displayed phase-locked response indicative of an Arnold Tongue, with the frequency selectivity highest at low amplitudes and decreasing under stronger stimulation. A striking broadening of the mode-locked response was seen with increasing stiffness of the load, until approximate impedance matching, where the phase-locked response remained flat over the physiological range of frequencies. When the otolithic membrane was left intact atop the preparation, the natural loading of the bundles likewise decreased their frequency selectivity with respect to that observed in freely oscillating bundles. To probe for signatures of the active process under natural loading and coupling conditions, we applied transient mechanical stimuli to the otolithic membrane. Following the pulses, the underlying bundles displayed active movement in the opposite direction, analogous to the twitches observed in individual cells. Tracking features in the otolithic membrane indicated that it moved in phase with the bundles. Hence, synchronous active motility evoked in the system of coupled hair bundles by external input is sufficient to displace large overlying structures.

Multiple-timescale dynamics underlying spontaneous oscillations of saccular hair bundles

Spontaneous oscillations displayed by hair bundles of the bullfrog sacculus have complex temporal profiles, not fully captured by single limit-cycle descriptions. Quiescent intervals are typically interspersed with oscillations, leading to a bursting-type behavior. Temporal characteristics of the oscillation are strongly affected by imposing a mechanical load or by the application of a steady-state deflection to the resting position of the bundle. Separate spectral components of the spontaneous motility are differently affected by increases in the external calcium concentration. We use numerical modeling to explore the effects of internal parameters on the oscillatory profiles, and to reproduce the experimental modulation induced by mechanical or ionic manipulation.

Magnetic actuation of hair cells

The bullfrog sacculus contains mechanically sensitive hair cells whose stereociliary bundles oscillate spontaneously when decoupled from the overlying membrane. Steady-state offsets on the resting position of a hair bundle can suppress or modulate this native motility. To probe the dynamics of spontaneous oscillation in the proximity of the critical point, we describe here a method for mechanical actuation that avoids loading the bundles or contributing to the viscous drag. Magnetite beads were attached to the tips of the stereocilia, and a magnetic probe was used to impose deflections. This technique allowed us to observe the transition from multi-mode to single-mode state in freely oscillating bundles, as well as the crossover from the oscillatory to the quiescent state.

Coupling a sensory hair-cell bundle to cyber clones enhances nonlinear amplification

The vertebrate ear benefits from nonlinear mechanical amplification to operate over a vast range of sound intensities. The amplificatory process is thought to emerge from active force production by sensory hair cells. The mechano-sensory hair bundle that protrudes from the apical surface of each hair cell can oscillate spontaneously and function as a frequency-selective, nonlinear amplifier. Intrinsic fluctuations, however, jostle the response of a single hair bundle to weak stimuli and seriously limit amplification. Most hair bundles are mechanically coupled by overlying gelatinous structures. Here, we assayed the effects of mechanical coupling on the hair-bundle amplifier by combining dynamic force clamp of a hair bundle from the bullfrog's saccule with real-time stochastic simulations of hair-bundle mechanics. This setup couples the hair bundle to two virtual hair bundles, called cyber clones, and mimics a situation in which the hair bundle is elastically linked to two neighbors with similar characteristics. We found that coupling increased the coherence of spontaneous hair-bundle oscillations. By effectively reducing noise, the synergic interplay between the hair bundle and its cyber clones also enhanced amplification of sinusoidal stimuli. All observed effects of coupling were in quantitative agreement with simulations. We argue that the auditory amplifier relies on hair-bundle cooperation to overcome intrinsic noise limitations and achieve high sensitivity and sharp frequency selectivity.

Spikes and membrane potential oscillations in hair cells generate periodic afferent activity in the frog sacculus

To look for membrane potential oscillations that may contribute to sensory coding or amplification in the ear, we made whole-cell and perforated-patch recordings from hair cells and postsynaptic afferent neurites in the explanted frog sacculus, with mechanoelectrical transduction (MET) blocked. Small depolarizing holding currents, which may serve to replace the in vivo resting MET current, evoked all-or-none calcium spikes (39-75 mV amplitude) in 37% of hair cells tested, and continuous membrane potential oscillations (14-28 mV; 15-130 Hz) in an additional 14% of cells. Spiking hair cells were on average taller and thinner than nonspiking hair cells, and had smaller outward currents through delayed rectifier channels (I(KV)) and noninactivating calcium-activated potassium channels (I(BK,steady)), and larger inward rectifier currents (I(K1)). Some spiking hair cells fired only a brief train at the onset of a current step, but others could sustain repetitive firing (3-70 Hz). Partial blockade of I(BK) changed the amplitude and frequency of oscillations and spikes, and converted some nonspiking cells into spiking cells. Oscillatory hair cells preferentially amplified sinusoidal stimuli at frequencies near their natural oscillation frequency. Postsynaptic recordings revealed regularly timed bursts of EPSPs in some afferent neurites. EPSP bursts were able to trigger afferent spikes, which may be initiated at the sodium channel cluster located adjacent to the afferent axon's most peripheral myelin segment. These results show that some frog saccular hair cells can generate spontaneous rhythmic activity that may drive periodic background activity in afferent axons.