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

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.

Complex dynamics of hair bundle of auditory nervous system (II): forced oscillations related to two cases of steady state

The forced oscillations of hair bundle of inner hair cells of auditory nervous system evoked by external force from steady state are related to the fast adaption of hair cells, which are very important for auditory amplification. In the present paper, comprehensive and deep understandings to nonlinear dynamics of forced oscillations are acquired in four aspects. Firstly, the complex dynamics underlying the twitch (fast recoil of displacement X which is fast variable) induced from Case-1 and Case-2 steady states by external pulse force are obtained. With help of vector fields and nullclines, the phase trajectory of forced oscillations is identified to be an evolution process between two equilibrium points corresponding to zero force and pulse force, respectively, and then the twitch is obtained as the behavior running along the nonlinear part of X-nullcline. Especially, twitch observed in experiment are classified into 6 types, which are induced by negative change of force, negative and positive changes of force, and positive change of force, respectively, and further build relationships to three subcases of Case-2 steady state with N-shaped X-nullcline (equilibrium point locates on the left, middle, and right branches of X-nullcline, respectively). Secondly, the experimental observation of fatigue of twitch induced by continual two pulse forces, i.e. the reduced amplitude of the latter twitch when interval between two forces is short, is also explained as a nonlinear behavior beginning from an initial value different from that of the former one. Thirdly, the experimental observation of transition between sustained oscillations and steady state induced by pulse force can be simulated for Case-1 steady state with Z-shaped X-nullcline instead of Case-2, due to that there exists bifurcations with respect to external force for Case-1 while no bifurcations for Case-2. Last, the threshold phenomenon induced by simple pulse stimulation exists for Case-1 steady state rather than Case-2, due to that the upper and lower branches of Z-shaped X-nullcline close to the middle branch exhibit coexisting behaviors of variable X while N-shaped X-nullcline does not. The nonlinear dynamics of forced oscillations are helpful for explanations to the complex experimental observations, which presents potential measures to modulate the functions of twitch such as the fast adaption.

Unloading outer hair cell bundles in vivo does not yield evidence of spontaneous oscillations in the mouse cochlea

Along with outer hair cell (OHC) somatic electromotility as the actuator of cochlear amplification, active hair bundle motility may be a complementary mechanism in the mammalian auditory system. Here, we searched the mouse cochlea for the presence of spontaneous bundle oscillations that have been observed in non-mammalian ears. In those systems, removal of the overlying membrane is necessary for spontaneous bundle oscillations to manifest. Thus, we used a genetic mouse model with a C1509G (cysteine-to-glycine) point mutation in the Tecta gene where the tectorial (TM) is lifted away from the OHC bundles, allowing us to explore whether unloaded bundles spontaneously oscillate. We used VOCTV in vivo to detect OHC length changes due to electromotility as a proxy for the spontaneous opening and closing of the mechanoelectrical transduction (MET) channels associated with bundle oscillation. In wild type mice with the TM attached to OHC bundles, we did find peaks in vibratory magnitude spectra. Such peaks were not observed in the mutants where the TM is detached from the OHC bundles. Statistical analysis of the time signals indicates that these peaks do not signify active oscillations. Rather, they are filtered responses of the sensitive wild type cochlea to weak background noise. We therefore conclude that, to the limits of our system (∼30 pm), there is no spontaneous mechanical activity that manifests as oscillations in OHC electromotility within the mouse cochlea, arguing that unloaded OHC bundles do not oscillate in vivo. This article is part of the Special Issue Outer hair cell Edited by Joseph Santos-Sacchi and Kumar Navaratnam.

Fast adaptation of cooperative channels engenders Hopf bifurcations in auditory hair cells

Since the pioneering work of Thomas Gold, published in 1948, it has been known that we owe our sensitive sense of hearing to a process in the inner ear that can amplify incident sounds on a cycle-by-cycle basis. Called the active process, it uses energy to counteract the viscous dissipation associated with sound-evoked vibrations of the ear's mechanotransduction apparatus. Despite its importance, the mechanism of the active process and the proximate source of energy that powers it have remained elusive, especially at the high frequencies characteristic of amniote hearing. This is partly due to our insufficient understanding of the mechanotransduction process in hair cells, the sensory receptors and amplifiers of the inner ear. It has been proposed previously that cyclical binding of Ca2+ ions to individual mechanotransduction channels could power the active process. That model, however, relied on tailored reaction rates that structurally forced the direction of the cycle. Here we ground our study on our previous model of hair-cell mechanotransduction, which relied on cooperative gating of pairs of channels, and incorporate into it the cyclical binding of Ca2+ ions. With a single binding site per channel and reaction rates drawn from thermodynamic principles, the current model shows that hair cells behave as nonlinear oscillators that exhibit Hopf bifurcations, dynamical instabilities long understood to be signatures of the active process. Using realistic parameter values, we find bifurcations at frequencies in the kilohertz range with physiological Ca2+ concentrations. The current model relies on the electrochemical gradient of Ca2+ as the only energy source for the active process and on the relative motion of cooperative channels within the stereociliary membrane as the sole mechanical driver. Equipped with these two mechanisms, a hair bundle proves capable of operating at frequencies in the kilohertz range, characteristic of amniote hearing.

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.

Active Biomechanics of Sensory Hair Bundles

During the detection of sound, hair bundles perform a crucial step by responding to mechanical deflections and converting them into changes in electrical potential that subsequently lead to the release of neurotransmitter. The sensory hair bundle response is characterized by an essential nonlinearity and an energy-consuming amplification of the incoming sound. The active response has been shown to enhance the hair bundle's sensitivity and frequency selectivity of detection. The biological phenomena shown by the bundle have been extensively studied in vitro, allowing comparisons to behaviors observed in vivo. The experimental observations have been well explained by numerical simulations, which describe the cellular mechanisms operant within the bundle, as well as by more sparse theoretical models, based on dynamical systems theory.

Noise-induced distortion of the mean limit cycle of nonlinear oscillators

We study the change in the size and shape of the mean limit cycle of a stochastically driven nonlinear oscillator as a function of noise amplitude. Such dynamics occur in a variety of nonequilibrium systems, including the spontaneous oscillations of hair cells of the inner ear. The noise-induced distortion of the limit cycle generically leads to its rounding through the elimination of sharp (high-curvature) features through a process we call corner cutting. We provide a criterion that may be used to identify limit cycle regions most susceptible to such noise-induced distortions. By using this criterion, one may obtain more meaningful parametric fits of nonlinear dynamical models from noisy experimental data, such as those coming from spontaneously oscillating hair cells.

A Bundle of Mechanisms: Inner-Ear Hair-Cell Mechanotransduction

In the inner ear, the deflection of hair bundles, the sensory organelles of hair cells, activates mechanically-gated channels (MGCs). Hair bundles monitor orientation of the head, its angular and linear acceleration, and detect sound. Force applied to MGCs is shaped by intrinsic hair-bundle properties, by the mechanical load on the bundle, and by the filter imparted by the environment of the hair bundle. Channel gating and adaptation, the ability of the bundle to reset its operating point, contribute to hair-bundle mechanics. Recent data from mammalian hair cells challenge longstanding hypotheses regarding adaptation mechanisms and hair-bundle coherence. Variations between hair bundles from different organs in hair-bundle mechanics, mechanical load, channel gating, and adaptation may allow a hair bundle to selectively respond to specific sensory stimuli.

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.

Bottom-up approach to torus bifurcation in neuron models

We study the quasi-periodicity phenomena occurring at the transition between tonic spiking and bursting activities in exemplary biologically plausible Hodgkin-Huxley type models of individual cells and reduced phenomenological models with slow and fast dynamics. Using the geometric slow-fast dissection and the parameter continuation approach, we show that the transition is due to either the torus bifurcation or the period-doubling bifurcation of a stable periodic orbit on the 2D slow-motion manifold near a characteristic fold. Various torus bifurcations including stable and saddle torus-canards, resonant tori, the co-existence of nested tori, and the torus breakdown leading to the onset of complex and bistable dynamics in such systems are examined too.

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.

Lipid bilayer mediates ion-channel cooperativity in a model of hair-cell mechanotransduction

Mechanoelectrical transduction in the inner ear is a biophysical process underlying the senses of hearing and balance. The key players involved in this process are mechanosensitive ion channels. They are located in the stereocilia of hair cells and opened by the tension in specialized molecular springs, the tip links, connecting adjacent stereocilia. When channels open, the tip links relax, reducing the hair-bundle stiffness. This gating compliance makes hair cells especially sensitive to small stimuli. The classical explanation for the gating compliance is that the conformational rearrangement of a single channel directly shortens the tip link. However, to reconcile theoretical models based on this mechanism with experimental data, an unrealistically large structural change of the channel is required. Experimental evidence indicates that each tip link is a dimeric molecule, associated on average with two channels at its lower end. It also indicates that the lipid bilayer modulates channel gating, although it is not clear how. Here, we design and analyze a model of mechanotransduction where each tip link attaches to two channels, mobile within the membrane. Their states and positions are coupled by membrane-mediated elastic forces arising from the interaction between the channels' hydrophobic cores and that of the lipid bilayer. This coupling induces cooperative opening and closing of the channels. The model reproduces the main properties of hair-cell mechanotransduction using only realistic parameters constrained by experimental evidence. This work provides an insight into the fundamental role that membrane-mediated ion-channel cooperativity can play in sensory physiology.

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.