Dynamics of freely oscillating and coupled hair cell bundles under mechanical deflection

Criticality and chaos in auditory and vestibular sensing

The auditory and vestibular systems exhibit remarkable sensitivity of detection, responding to deflections on the order of angstroms, even in the presence of biological noise. The auditory system exhibits high temporal acuity and frequency selectivity, allowing us to make sense of the acoustic world around us. As the acoustic signals of interest span many orders of magnitude in both amplitude and frequency, this system relies heavily on nonlinearities and power-law scaling. The vestibular system, which detects ground-borne vibrations and creates the sense of balance, exhibits highly sensitive, broadband detection. It likewise requires high temporal acuity so as to allow us to maintain balance while in motion. The behavior of these sensory systems has been extensively studied in the context of dynamical systems theory, with many empirical phenomena described by critical dynamics. Other phenomena have been explained by systems in the chaotic regime, where weak perturbations drastically impact the future state of the system. Using a Hopf oscillator as a simple numerical model for a sensory element in these systems, we explore the intersection of the two types of dynamical phenomena. We identify the relative tradeoffs between different detection metrics, and propose that, for both types of sensory systems, the instabilities giving rise to chaotic dynamics improve signal detection.

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.

Modeling the tonotopic map using a two-dimensional array of neural oscillators

We present a model of a tonotopic map known as the Oscillatory Tonotopic Self-Organizing Map (OTSOM). It is a 2-dimensional, self-organizing array of Hopf oscillators, capable of performing a Fourier-like decomposition of the input signal. While the rows in the map encode the input phase, the columns encode frequency. Although Hopf oscillators exhibit resonance to a sinusoidal signal when there is a frequency match, there is no obvious way to also achieve phase tuning. We propose a simple method by which a pair of Hopf oscillators, unilaterally coupled through a coupling scheme termed as modified power coupling, can exhibit tuning to the phase offset of sinusoidal forcing input. The training of OTSOM is performed in 2 stages: while the frequency tuning is adapted in Stage 1, phase tuning is adapted in Stage 2. Earlier tonotopic map models have modeled frequency as an abstract parameter unconnected to any oscillation. By contrast, in OTSOM, frequency tuning emerges as a natural outcome of an underlying resonant process. The OTSOM model can possibly be regarded as an approximation of the tonotopic map found in the primary auditory cortices of mammals, particularly exemplified in the studies of echolocating bats.

Complex dynamics of hair bundle of auditory nervous system (I): spontaneous oscillations and two cases of steady states

The hair bundles of inner hair cells in the auditory nervous exhibit spontaneous oscillations, which is the prerequisite for an important auditory function to enhance the sensitivity of inner ear to weak sounds, otoacoustic emission. In the present paper, the dynamics of spontaneous oscillations and relationships to steady state are acquired in a two-dimensional model with fast variable X (displacement of hair bundles) and slow variable X a . The spontaneous oscillations are derived from negative stiffness modulated by two biological factors (S and D) and are identified to appear in multiple two-dimensional parameter planes. In (S, D) plane, comprehensive bifurcations including 4 types of codimension-2 bifurcation and 5 types of codimension-1 bifurcation related to the spontaneous oscillations are acquired. The spontaneous oscillations are surrounded by supercritical and subcritical Hopf bifurcation curves, and outside of the curves are two cases of steady state. Case-1 and Case-2 steady states exhibit Z-shaped (coexistence of X) and N-shaped (coexistence of X a ) X-nullclines, respectively. In (S, D) plane, left and right to the spontaneous oscillations are two subcases of Case-1, which exhibit the stable equilibrium point locating on the upper and lower branches of X-nullcline, respectively, resembling that of the neuron. Lower to the spontaneous oscillations are 3 subcases of Case-2 from left to right, which manifest stable equilibrium point locating on left, middle, and right branches of X-nullcline, respectively, differing from that of the neuron. The phase plane for steady state is divided into four parts by nullclines, which manifest different vector fields. The phase trajectory of transient behavior beginning from a phase point in the four regions to the stable equilibrium point exhibits different dynamics determined by the vector fields, which is the basis to identify dynamical mechanism of complex forced oscillations induced by external signal. The results present comprehensive viewpoint and deep understanding for dynamics of the spontaneous oscillations and steady states of hair bundles, which can be used to well explain the experimental observations and to modulate functions of spontaneous oscillations.

Chimera states and frequency clustering in systems of coupled inner-ear hair cells

Coupled hair cells of the auditory and vestibular systems perform the crucial task of converting the energy of sound waves and ground-borne vibrations into ionic currents. We mechanically couple groups of living, active hair cells with artificial membranes, thus mimicking in vitro the coupled dynamical system. We identify chimera states and frequency clustering in the dynamics of these coupled nonlinear, autonomous oscillators. We find that these dynamical states can be reproduced by our numerical model with heterogeneity of the parameters. Furthermore, we find that this model is most sensitive to external signals when poised at the onset of synchronization, where chimera and cluster states are likely to form. We, therefore, propose that the partial synchronization in our experimental system is a manifestation of a system poised at the verge of synchronization with optimal sensitivity.

Otolith adaptive responses to altered gravity

The force of gravity has remained constantly present over the course of animal evolution and forms our frame of reference with the environment, including spatial orientation, navigation, gaze and postural stability. Inertial head accelerations occur within this gravity frame of reference naturally during voluntary movements and perturbations. Execution of movements of aquatic, terrestrial and flight species widely differ, but the sensory systems detecting acceleration forces, including gravity, have remained remarkably conserved among vertebrates. The utricular organ senses the sum of inertial force due to head translation and head tilt relative to gravitational vertical. A sudden or persistent change in gravitational force would be expected to have profound and global effects on an organism. Physiological data collected immediately after orbital missions, after short and extended increases in gravity load via centrifugation, and after readaptation to normal gravity exist in the toadfish model. This review focuses on the otolith adaptive responses to changes in gravity in a number of model organisms and their potential impact on human space travel.

Challenges to the central nervous system during human spaceflight missions to Mars

Space travel presents a number of environmental challenges to the central nervous system, including changes in gravitational acceleration that alter the terrestrial synergies between perception and action, galactic cosmic radiation that can damage sensitive neurons and structures, and multiple factors (isolation, confinement, altered atmosphere, and mission parameters, including distance from Earth) that can affect cognition and behavior. Travelers to Mars will be exposed to these environmental challenges for up to 3 years, and space-faring nations continue to direct vigorous research investments to help elucidate and mitigate the consequences of these long-duration exposures. This article reviews the findings of more than 50 years of space-related neuroscience research on humans and animals exposed to spaceflight or analogs of spaceflight environments, and projects the implications and the forward work necessary to ensure successful Mars missions. It also reviews fundamental neurophysiology responses that will help us understand and maintain human health and performance on Earth.

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.

Influence of Magnitude and Duration of Altered Gravity and Readaptation to 1 g on the Structure and Function of the Utricle in Toadfish, Opsanus tau

Gravity has remained constant during animal evolution and the neural sensory systems detecting acceleration forces have remained remarkably conserved among vertebrates. The utricular organ senses the sum of inertial force due to head translation and head tilt relative to gravitational vertical. Change in gravitational force would be expected to have profound effects on how an organism maintains equilibrium. We characterize the physiology of utricular afferents to applied accelerations in the oyster toadfish, Opsanus tau, in normal 1 g to establish benchmarks, after 1–32-day exposures to 2.24 g (resultant) via centrifugation (hypergravity, HG), after 4- and 16-day exposures to 1.12 g (resultant), and following 1–8 days recovery to HG exposures to study re-adaptation to 1 g. Afferents were also examined during activation of efferent vestibular pathway. Centrifugation at 2.24 g included 228°/s constant angular velocity component, and thus horizontal canal afferent responses to yaw rotation were recorded as an internal control in each fish. Afferents studied after 228°/s rotation for 4 and 16 days without centripetal acceleration, called On-Center-Control, were indistinguishable from their control counterparts. Principal response to HG was an adjustment of afferent sensitivity as a function of magnitude and duration of exposure: an initial robust increase at 3–4 days followed by a significant decrease from 16 to 32 days. Initial increase observed after 4 days of HG took >4 days in 1 g to recover, and the decrease observed after 16 days of HG took >2 days to readapt to 1 g. Hair cells in striola and medial extrastriola macula regions were serially reconstructed in 3D from thin sections using transmission electron microscopy in control fish and fish exposed to 4 and 16 days of HG. Despite the highly significant differences in afferent physiology, synaptic body counts quantified in the same fish were equivalent in their inter-animal variability and averages. No clear role of the efferent pathway as a feedback mechanism regulating afferent behavior to HG was found. Transfer from 1 g to HG imparts profound effects on gravitational sensitivity of utricular afferents and the accompanying transfer from the HG back to the 1 g resembles in part (as an analog) the transfer from 1 g to the micrograms.

Identification of Bifurcations from Observations of Noisy Biological Oscillators

Hair bundles are biological oscillators that actively transduce mechanical stimuli into electrical signals in the auditory, vestibular, and lateral-line systems of vertebrates. A bundle’s function can be explained in part by its operation near a particular type of bifurcation, a qualitative change in behavior. By operating near different varieties of bifurcation, the bundle responds best to disparate classes of stimuli. We show how to determine the identity of and proximity to distinct bifurcations despite the presence of substantial environmental noise. Using an improved mechanical-load clamp to coerce a hair bundle to traverse different bifurcations, we find that a bundle operates within at least two functional regimes. When coupled to a high-stiffness load, a bundle functions near a supercritical Hopf bifurcation, in which case it responds best to sinusoidal stimuli such as those detected by an auditory organ. When the load stiffness is low, a bundle instead resides close to a subcritical Hopf bifurcation and achieves a graded frequency response—a continuous change in the rate, but not the amplitude, of spiking in response to changes in the offset force—a behavior that is useful in a vestibular organ. The mechanical load in vivo might therefore control a hair bundle’s responsiveness for effective operation in a particular receptor organ. Our results provide direct experimental evidence for the existence of distinct bifurcations associated with a noisy biological oscillator, and demonstrate a general strategy for bifurcation analysis based on observations of any noisy system.

Electrophysiological Measurements of Peripheral Vestibular Function-A Review of Electrovestibulography

Electrocochleography (EcochG), incorporating the Cochlear Microphonic (CM), the Summating Potential (SP), and the cochlear Compound Action Potential (CAP), has been used to study cochlear function in humans and experimental animals since the 1930s, providing a simple objective tool to assess both hair cell (HC) and nerve sensitivity. The vestibular equivalent of ECochG, termed here Electrovestibulography (EVestG), incorporates responses of the vestibular HCs and nerve. Few research groups have utilized EVestG to study vestibular function. Arguably, this is because stimulating the cochlea in isolation with sound is a trivial matter, whereas stimulating the vestibular system in isolation requires significantly more technical effort. That is, the vestibular system is sensitive to both high-level sound and bone-conducted vibrations, but so is the cochlea, and gross electrical responses of the inner ear to such stimuli can be difficult to interpret. Fortunately, several simple techniques can be employed to isolate vestibular electrical responses. Here, we review the literature underpinning gross vestibular nerve and HC responses, and we discuss the nomenclature used in this field. We also discuss techniques for recording EVestG in experimental animals and humans and highlight how EVestG is furthering our understanding of the vestibular system.

High-order synchronization of hair cell bundles

Auditory and vestibular hair cell bundles exhibit active mechanical oscillations at natural frequencies that are typically lower than the detection range of the corresponding end organs. We explore how these noisy nonlinear oscillators mode-lock to frequencies higher than their internal clocks. A nanomagnetic technique is used to stimulate the bundles without an imposed mechanical load. The evoked response shows regimes of high-order mode-locking. Exploring a broad range of stimulus frequencies and intensities, we observe regions of high-order synchronization, analogous to Arnold Tongues in dynamical systems literature. Significant areas of overlap occur between synchronization regimes, with the bundle intermittently flickering between different winding numbers. We demonstrate how an ensemble of these noisy spontaneous oscillators could be entrained to efficiently detect signals significantly above the characteristic frequencies of the individual cells.

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.

Mechanical amplification exhibited by quiescent saccular hair bundles

Spontaneous oscillations exhibited by free-standing hair bundles from the Bullfrog sacculus suggest the existence of an active process that might underlie the exquisite sensitivity of the sacculus to mechanical stimulation. However, this spontaneous activity is suppressed by coupling to an overlying membrane, which applies a large mechanical load on the bundle. How a quiescent hair bundle utilizes its active process is still unknown. We studied the dynamics of motion of individual hair bundles under different offsets in the bundle position, and observed the occurrence of spikes in hair-bundle motion, associated with the generation of active work. These mechanical spikes can be evoked by a sinusoidal stimulus, leading to an amplified movement of the bundle with respect to the passive response. Amplitude gain reached as high as 100-fold at small stimulus amplitudes. Amplification of motion decreased with increasing amplitude of stimulation, ceasing at ∼6–12 pN stimuli. Results from numerical simulations suggest that the adaptation process, mediated by myosin 1c, is not required for the production of mechanical spikes.

Control of a hair bundle's mechanosensory function by its mechanical load

Hair cells, the sensory receptors of the internal ear, subserve different functions in various receptor organs: they detect oscillatory stimuli in the auditory system, but transduce constant and step stimuli in the vestibular and lateral-line systems. We show that a hair cell's function can be controlled experimentally by adjusting its mechanical load. By making bundles from a single organ operate as any of four distinct types of signal detector, we demonstrate that altering only a few key parameters can fundamentally change a sensory cell's role. The motions of a single hair bundle can resemble those of a bundle from the amphibian vestibular system, the reptilian auditory system, or the mammalian auditory system, demonstrating an essential similarity of bundles across species and receptor organs.

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.

Integrating the active process of hair cells with cochlear function

Uniquely among human senses, hearing is not simply a passive response to stimulation. Our auditory system is instead enhanced by an active process in cochlear hair cells that amplifies acoustic signals several hundred-fold, sharpens frequency selectivity and broadens the ear's dynamic range. Active motility of the mechanoreceptive hair bundles underlies the active process in amphibians and some reptiles; in mammals, this mechanism operates in conjunction with prestin-based somatic motility. Both individual hair bundles and the cochlea as a whole operate near a dynamical instability, the Hopf bifurcation, which accounts for the cardinal features of the active process.

The physics of hearing: fluid mechanics and the active process of the inner ear

Most sounds of interest consist of complex, time-dependent admixtures of tones of diverse frequencies and variable amplitudes. To detect and process these signals, the ear employs a highly nonlinear, adaptive, real-time spectral analyzer: the cochlea. Sound excites vibration of the eardrum and the three miniscule bones of the middle ear, the last of which acts as a piston to initiate oscillatory pressure changes within the liquid-filled chambers of the cochlea. The basilar membrane, an elastic band spiraling along the cochlea between two of these chambers, responds to these pressures by conducting a largely independent traveling wave for each frequency component of the input. Because the basilar membrane is graded in mass and stiffness along its length, however, each traveling wave grows in magnitude and decreases in wavelength until it peaks at a specific, frequency-dependent position: low frequencies propagate to the cochlear apex, whereas high frequencies culminate at the base. The oscillations of the basilar membrane deflect hair bundles, the mechanically sensitive organelles of the ear's sensory receptors, the hair cells. As mechanically sensitive ion channels open and close, each hair cell responds with an electrical signal that is chemically transmitted to an afferent nerve fiber and thence into the brain. In addition to transducing mechanical inputs, hair cells amplify them by two means. Channel gating endows a hair bundle with negative stiffness, an instability that interacts with the motor protein myosin-1c to produce a mechanical amplifier and oscillator. Acting through the piezoelectric membrane protein prestin, electrical responses also cause outer hair cells to elongate and shorten, thus pumping energy into the basilar membrane's movements. The two forms of motility constitute an active process that amplifies mechanical inputs, sharpens frequency discrimination, and confers a compressive nonlinearity on responsiveness. These features arise because the active process operates near a Hopf bifurcation, the generic properties of which explain several key features of hearing. Moreover, when the gain of the active process rises sufficiently in ultraquiet circumstances, the system traverses the bifurcation and even a normal ear actually emits sound. The remarkable properties of hearing thus stem from the propagation of traveling waves on a nonlinear and excitable medium.

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.