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.     

Stimulus coding in crayfish antennal mechanoreceptors estimated by noise analysis

Two different kinds of mechanoreceptive hairs (smooth and feathered) on the second antennae of the freshwater crayfish, Orconectes virilis, have been investigated for their stimulus coding propertics. These mechanoreceptors show a great deal of non-linear behaviour both in threshold and in directionality. An effective appraoch for the investigation of such systems is noise analysis in the frequency domain. This method has been used here to calculate zero-, first- and second-order kernels. Sensory cells reveal different first- and second-order kernels, depending on which type of hair is being stimulated. The first-order kernel has a pronounced peak in the frequency response at 110 Hz if a feathered hair is stimulated and at 60 Hz if a smooth hair is stimulated. The second-order kernel shows a number of pronounced peaks in the frequency response between 40 and 110 Hz, but only if a feathered hair is stimulated. Smooth hair stimulation results in less sharp peaks but in higher gain for the same range of stimulus frequencies.     

β4-subunit increases Slo responsiveness to physiological Ca2+ concentrations and together with β1 reduces surface expression of Slo in hair cells

Changing kinetics of large-conductance potassium (BK) channels in hair cells of nonmammalian vertebrates, including the chick, plays a critical role in electrical tuning, a mechanism used by these cells to discriminate between different frequencies of sound. BK currents are less abundant in low-frequency hair cells and show large openings in response to a rise in intracellular Ca(2+) at a hair cell's operating voltage range (spanning -40 to -60 mV). Although the molecular underpinnings of its function in hair cells are poorly understood, it is established that BK channels consist of a pore-forming α-subunit (Slo) and a number of accessory subunits. Currents from the α (Slo)-subunit alone do not show dramatic increases in response to changes in Ca(2+) concentrations at -50 mV. We have cloned the chick β(4)- and β(1)-subunits and show that these subunits are preferentially expressed in low-frequency hair cells, where they decrease Slo surface expression. The β(4)-subunit in particular is responsible for the BK channel's increased responsiveness to Ca(2+) at a hair cell's operating voltage. In contrast, however, the increases in relaxation times induced by both β-subunits suggest additional mechanisms responsible for BK channel function in hair cells.     

Myosin light-chain kinase is necessary for membrane homeostasis in cochlear inner hair cells

The structural homeostasis of the cochlear hair cell membrane is critical for all aspects of sensory transduction, but the regulation of its maintenance is not well understood. In this report, we analyzed the cochlear hair cells of mice with specific deletion of myosin light chain kinase (MLCK) in inner hair cells. MLCK-deficient mice showed impaired hearing, with a 5- to 14-dB rise in the auditory brainstem response (ABR) thresholds to clicks and tones of different frequencies and a significant decrease in the amplitude of the ABR waves. The mutant inner hair cells produced several ball-like structures around the hair bundles in vivo, indicating impaired membrane stability. Inner hair cells isolated from the knockout mice consistently displayed less resistance to hypoosmotic solution and less membrane F-actin. Myosin light-chain phosphorylation was also reduced in the mutated inner hair cells. Our results suggest that MLCK is necessary for maintaining the membrane stability of inner hair cells.     

Limiting Frequency of the Cochlear Amplifier Based on Electromotility of Outer Hair Cells

Outer hair cells are the critical element for the sensitivity and sharpness of frequency selectivity of the ear. It is believed that fast motility (electromotility) of these cells is essential for this function. Indeed, force produced by outer hair cells follows their membrane potential very closely at least up to 60 kHz. However, it has been pointed out that the cell's receptor potential is attenuated by a low-pass RC circuit inherent to these cells, with the RC roll-off frequencies significantly lower than their operating frequencies. This would render electromotility ineffective in producing force. To address this issue, we assume that multiple degrees of freedom and vibrational modes due to the complex structure of the organ of Corti provide optimal phases for outer hair cells' force to cancel viscous drag. Our derived frequency limit depends on the drag-capacitance product, not directly on the RC time constant. With a reasonable assumption for the viscous drag, the estimated limit is 10–13 kHz, exceeding the RC corner frequency. Our analysis shows that a fast-activating potassium current can substantially extend the frequency limit by counteracting the capacitive current.     

Hair canopy of cricket sensory system tuned to predator signals

Filiform hairs located on the cerci of crickets are among the most sensitive sensors in the animal world and enable crickets to sense the faintest air movements generated by approaching predators. While the neurophysiological and biomechanical aspects of this sensory system have been studied independently for several decades, their integration into a coherent framework was wanting. In order to evaluate the hair canopy tuning to predator signals, we built a model of cercal population coding of oscillating air flows by the hundreds of hairs on the cerci of the sand cricket Gryllus bimaculatus (Insecta: Orthoptera). A complete survey of all hairs covering the cerci was done on intact cerci using scanning electronic microscopy. An additive population coding of sinusoid signals of varying frequencies and velocities taking into account hair directionality delivered the cercal canopy tuning curve. We show that the range of frequencies and velocities at which the cricket sensory system is best tuned corresponds to the values of signals produced by approaching predators. The relative frequencies of short (< 0.5 x 10(-3) m) and long hairs and their differing responses to oscillating air flows therefore enable crickets to detect predators in a time-frequency-intensity space both as far as possible and at close range.     

Modeling Hair Cell Tuning by Expression Gradients of Potassium Channel β Subunits

The receptor potential of sensory hair cells arises from the gating of mechanosensitive cation channels, but its amplitude and time course also depend on the number and kinetics of voltage-gated ion channels in each cell. Prominent among these are “BK” potassium channels encoded by the slo gene that support electrical tuning in some hair cells. Hair cells tuned to low frequencies have slowly gating BK channels, whereas those of higher-frequency hair cells gate more rapidly. Alternative splicing of the slo gene mRNA that encodes the pore-forming α subunit can alter BK channel kinetics, and gating is dramatically slowed by coexpression with modulatory β subunits. The effect of the β subunit is consistent with low-frequency tuning, and β mRNA is expressed at highest levels in the low frequency apex of the bird’s auditory epithelium. How might an expression gradient of β subunits contribute to hair cell tuning? The present work uses a computational model of hair cell-tuning based on the functional properties of BK channels expressed from hair cell α and βslo cDNA. The model reveals that a limited tonotopic gradient could be achieved simply by altering the fraction of BK channels in each hair cell that are combined with β subunits. However, complete coverage of the tuning spectrum requires kinetic variants in addition to those modeled here.     

A common origin of voltage noise and generator potentials in statocyst hair cells

Voltage noise, generator potentials, and hair movements in the Hermissenda statocyst were analyzed. Motile hairs on the cyst's luminal surface moved as rods through +/- 10 degrees Hz when free and at 7 Hz when loaded with the weight of the statoconia (at 120 degrees C). For hair cells oriented opposite to a centrifugal force vector, rotation caused depolarization and increase of voltage noise variance. The depolarizing generator potential and the increase in voltage noise variance were similarly reduced by perfusion with zero external sodium or chloral hydrate. Cooling, perfusion with zero external sodium or chloral hydrate reduced the movement frequencies of the hairs but increased their range of motion. The same treatments reduced voltage noise variance and increased input resistance of the hair cell membrane. The results indicate that voltage noise and hair cell generator potential have a common origin: exertion of force on statocyst hairs by the weight of statoconia. The collision of statoconia with the motile hairs, not the hairs' bending, produces most of the voltage noise.     

Follicular epithelia and dermal papillae of mouse vibrissal follicles qualitatively change their hair-forming ability during anagen

We studied the hair-forming ability of epithelium and the relevant activity of dermal papilla (DP) in mouse vibrissal follicles during the hair cycle. Follicles were transversely cut into four pieces and each of them was associated with an isolated DP and grafted beneath the kidney capsule to induce hair formation. Various hair-cycle combinations of the fragments and DPs were examined. Hairs were generated not only in the follicle fragment containing the bulge (fragment III) but also in the fragment between the bulge and hair bulb (fragment II). The hair-forming frequencies were affected by the hair cycle stages of both the follicle fragments and DPs. Fragment III at late anagen (LA) and fragment II at catagen frequently generated hairs when associated with early anagen (EA)-DPs, but infrequently with mid-anagen (MA)-DPs. Oppositely, anagen fragment II produced hairs at a high frequency with MA-DPs and at a low frequency with EA-DPs. Hair generation in anagen fragment II is an unexpected finding because previous studies suggested that, during anagen, this region does not contain clonogenic epithelial cells that have been believed to be crucial for hair formation. Therefore, non-clonogenic epithelial cells would be able to generate hairs as well as clonogenic ones, and they should have a latent hair-forming ability that could be more effectively awakened by MA-DP than by EA-DP stimuli. Non-clonogenic epithelial cells might be a dormant phase of hair precursor cells. Proliferating follicular epithelial cells were detected in the middle and lower outer root sheath throughout the hair cycle but scarcely at LA. These findings suggest that the hair inductivity of DPs should be altered between EA and MA, and follicular epithelial cells would change their DP stimuli-directed hair-forming ability around LA, probably linked to the proliferative activity.     

Hair Cells – Beyond the Transducer

Overview This review considers the “tween twixt and twain” of hair cell physiology, specifically the signaling elements and membrane conductances which underpin forward and reverse transduction at the input stage of hair cell function and neurotransmitter release at the output stage. Other sections of this review series outline the advances which have been made in understanding the molecular physiology of mechanoelectrical transduction and outer hair cell electromotility. Here we outline the contributions of a considerable array of ion channels and receptor signaling pathways that define the biophysical status of the sensory hair cells, contributing to hair cell development and subsequently defining the operational condition of the hair cells across the broad dynamic range of physiological function.     

Glutamate Transporters EAAT4 and EAAT5 Are Expressed in Vestibular Hair Cells and Calyx Endings

Glutamate is the neurotransmitter released from hair cells. Its clearance from the synaptic cleft can shape neurotransmission and prevent excitotoxicity. This may be particularly important in the inner ear and in other sensory organs where there is a continually high rate of neurotransmitter release. In the case of most cochlear and type II vestibular hair cells, clearance involves the diffusion of glutamate to supporting cells, where it is taken up by EAAT1 (GLAST), a glutamate transporter. A similar mechanism cannot work in vestibular type I hair cells as the presence of calyx endings separates supporting cells from hair-cell synapses. Because of this arrangement, it has been conjectured that a glutamate transporter must be present in the type I hair cell, the calyx ending, or both. Using whole-cell patch-clamp recordings, we demonstrate that a glutamate-activated anion current, attributable to a high-affinity glutamate transporter and blocked by DL-TBOA, is expressed in type I, but not in type II hair cells. Molecular investigations reveal that EAAT4 and EAAT5, two glutamate transporters that could underlie the anion current, are expressed in both type I and type II hair cells and in calyx endings. EAAT4 has been thought to be expressed almost exclusively in the cerebellum and EAAT5 in the retina. Our results show that these two transporters have a wider distribution in mice. This is the first demonstration of the presence of transporters in hair cells and provides one of the few examples of EAATs in presynaptic elements.     

Sensory transduction and frequency selectivity in the basal turn of the guinea-pig cochlea.

Receptor potentials recorded from outer hair cells (OHC) and inner hair cells (IHC) in the basal high-frequency turn were compared. The DC component of the IHC receptor potential is maximized to ensure that IHCS can signal a voltage response to high-frequency tones. The OHC DC component is minimized so that OHCS transduce in the most sensitive region of their operating range. The phase and magnitude of OHC receptor potentials were recorded as an indicator of the magnitude and phase of the energy which is fed back to the basilar membrane to provide the basis for the sharp tuning and fine sensitivity of the cochlea to tones. IHC receptor potentials were recorded to assess the net effect of the feedback on the mechanics of the cochlea. It was concluded that OHCS generate feedback which enhances the IHC responses only at the best frequency. At frequencies below CF, IHC DC responses are elicited only when the OHC AC responses begin to saturate.     

Voltage oscillations and ionic conductances in hair cells isolated from the alligator cochlea

Summary Tall hair cells were isolated by enzymatic and mechanical dissociation from selected regions of the apical half of the alligator (A. mississippiensis) cochlea. Single cells were subjected to voltage-clamp and current-clamp using the tight-seal whole-cell recording technique. Most hair cells isolated from the apex of the cochlea produced slowly regenerative depolarizations or Na action potentials during current injection, whereas hair cells isolated from more basal regions usually produced voltage oscillations (ringing) in response to depolarizing current injection, an indication of electrical resonance. Resonant frequencies ranged from 50 to 157 Hz in different cells. The higher-frequency cells tended to have larger and more rapidly activating outward currents than did the lower-frequency cells. An inward Ca current and an outward Ca-activated K current were present in all hair cells. In addition, an inwardly rectifying current and a small, transient outward current were often seen. Thus, we conclude that an electrical tuning mechanism is present in alligator hair cells. The role of the ionic conductances in shaping hair cell responses to current injection, and the possible contributions of these electrical responses to cochlear function are discussed.     

Isolation and culture of hair cell progenitors from postnatal rat cochleae

Cochlear hair cells are a terminally differentiated cell population that is crucial for hearing. Although recent work suggests that there are hair cell progenitors in postnatal mammalian cochleae, isolation and culture of pure hair cell progenitors from a well-defined cochlear area have not been reported. Here we present an experimental method that allows isolation and culture of hair cell progenitors from postnatal rat cochleae. These progenitor cells are isolated from the lesser epithelial ridge (LER, or outer spiral sulcus cell) area of pre-plated neonatal rat cochlear segments. They express the same markers as LER cells in vivo, including ZO1, Islet1, Hes1, and Hes5. When these cells are induced to express Hath1, they show the potential to differentiate into hair cell-like cells. Interestingly, these cells can be lifted from monolayer cultures and maintained in aggregate cultures in which spheres can be formed. Hair cell progenitors in the spheres display their proliferating capability and express only epithelial markers. Furthermore, when these spheres are mixed with dissociated mesenchymal cells prepared from postnatal rat utricular whole mounts, and replated onto a collagen substratum, the epithelial progenitor cells are able to differentiate into cells expressing markers of hair cells and supporting cells in epithelial islands, which mirrors the inner ear sensory epithelium in vivo. Successful isolation and culture of hair cell progenitors from the mammalian cochlea will facilitate studies on gene expression profiling and mechanism of differentiation/regeneration of hair cells, which are crucial for repairing hearing loss.     

Temperature dependency of cupular mechanics and hair cell frequency selectivity in the fish canal lateral line organ

The mechanical frequency selectivity of the cupula located in the supraorbital lateral line canal and the frequency selectivity of the hair cells driven by the cupula were measured simultaneously in vivo. Laser interferometry was used to measure cupular mechanics and extracellular receptor potentials were recorded to determine hair cell frequency selectivity. Results were obtained from two teleost fish species, the ruffe (Acerina cernua L.), a European temperate zone freshwater fish, and the tropical African knife fish (Xenomiystus nigri). In both species cupular displacement grows with increasing frequency of canal fluid displacement, reaching a maximum at 115 Hz in the ruffe and at 460 Hz in the African knife fish. Cupular best frequencies were independent of temperature. Cut-off frequencies of hair cell frequency selectivity were found to depend on temperature with a Q10 of 1.75, ranging from 116 Hz (4 degrees C) to 290 Hz (20 degrees C), as established in the ruffe. At normal habitat temperatures of the two fish species (ruffe, 4 degrees C; African knife fish, 28 degrees C), this results in hair cell cut-off frequencies that match the two different cupular best frequencies remarkably well. This match suggests adjusted signal transfer in these two peripheral stages of canal lateral line transduction.     

Dynamic tuning of hair bundle mechanoreceptors in a sea anemone during predation

The sea anemone Haliplanella luciae (Cnidaria, Anthozoa) detects chemical and mechanical stimuli from prey. Hair bundle mechanoreceptors on the tentacles participate in regulating discharge of microbasic p-mastigophore nematocysts. Properly stimulated hair bundles sensitize the anemone to discharge nematocysts into objects that contact the tentacles. The hair bundle mechanoreceptors are composed of stereocilia derived from a multicellular complex. This complex consists of a single sensory neuron surrounded by two to four supporting cells. The mechanoreceptor is similar in many ways to vertebrate hair cells of the acousticolateralis system. However, anemone hair bundles are adjustable in structure and responsiveness according to the activity of two different chemoreceptors. One chemoreceptor binds N -acetylated sugars and the other binds amino compounds including proline. N -acetylated sugars induce lengthening of the hair bundle and a downward shift in frequencies that elicit maximal discharge of microbasic p-mastigophore nematocysts. Furthermore, N -acetylated sugars shift maximal discharge to smaller amplitude vibrations. Thus, N -acetylated sugars likely tune hair bundles so that small, swimming zooplankton stimulate maximal discharge. Proline leaks into the seawater from the hemolymph of wounded prey. Proline induces shortening of the hair bundle and shifts maximal discharge of nematocysts to higher frequencies and to larger amplitude vibrations. Thus, proline likely tunes hair bundles so that small, wounded, prey stimulate maximal discharge of nematocysts as they struggle to escape. Thus, suitably sized prey stimulate maximal discharge of microbasic p-mastigophore nematocysts upon first contacting the anemone tentacle and again upon attempting to escape.     

Molecular basis of hair cell loss

Mechanisms that lead to the death of hair cells are reviewed. Exposure to noise, the use of ototoxic drugs that damage the cochlea and old age are accompanied by hair cell death. Outer hair cells are often more susceptible than inner hair cells, partly because of an intrinsically greater susceptibility; high frequency cells are also more vulnerable. A common factor in hair cell loss following age-related changes and exposure to ototoxic drugs or high noise levels is the generation of reactive oxygen species, which can trigger intrinsic apoptosis (the mitochondrial pathway). However, hair cell death is sometimes produced via an extracellular signal pathway triggering extrinsic apoptosis. Necrosis and necroptosis also play a role and, in various situations in which cochlear damage occurs, a balance exists between these possible routes of cell death, with no one mechanism being exclusively activated. Finally, the numerous studies on these mechanisms of hair cell death have led to the identification of many potential therapeutic agents, some of which have been used to attempt to treat people exposed to damaging events, although clinical trials are not yet conclusive. Continued work in this area is likely to lead to clinical treatments that could be used to prevent or ameliorate hearing loss.     

Supporting Evidence from Single Unit Experiments for the Cochlea as an Addressed Delay Line

WE have already outlined the principles of a theory of cochlear organization^{1, 2} whereby acoustic signal components in the low and mid frequency range—-that is to say, frequencies for which good or moderate phase locking of unit response is possible—are detected by the cochlea using an approximate cross-correlation mechanism which operates on the time varying signal displayed along the basilar membrane, the latter acting as an acoustic exponential delay line. The running correlations are performed using fixed patterns of control fibres addressed to the outer hair cells, the pattern of addressing for each control fibre group corresponding to an instantaneous wave pattern for a specific frequency defined by the location of the fibre system along the length of the membrane. The fibres of each control system synapse with the afferent dendrites associated with a definite inner hair cell and act as a frequency sensitive gate, the inner hair cell of the assembly providing generator current related to signal amplitude.     

Peripheral auditory processing in the bobtail lizard Tiliqua rugosa

Summary We have labelled single physiologically-characterized primary auditory neurones in the bobtail lizard and traced them to their innervation sites within the basilar papilla. The distribution of stained fibre terminals shows that low frequencies (up to a characteristic frequency, CF, of about 0.8 kHz) are processed in the smaller apical segment of the papilla and medium to high frequencies in the much longer basal segment. It is possible that the frequency ranges of these segments partly overlap in individual animals.The tonotopic organization of the basal segment is well described by an exponential relationship; the CF increases towards the basal end. Systematic, peripheral recordings from the auditory nerve very close to the papilla confirm this tonotopicity for the basal segment.The apical segment of the papilla shows an unusual tonotopic organization in that the CF appears to increase across the epithelium, from abneural to neural. A tonotopicity in this direction has not previously been demonstrated in vertebrates.All stained neurones branched within the basilar papilla to innervate, typically, between 4 and 14 hair cells. The branching patterns of fibres innervating in the apical and basal papillar segment, respectively, show characteristic differences. Apical fibres tend to innervate hair cells with the same morphological polarity and often branch extensively along the segment. Basal fibres, in contrast, typically innervate about equal numbers of hair cells of opposing polarity and are more restricted in their longitudinal branching.Abbreviation CF characteristic frequency     

Multifrequency forcing of a Hopf oscillator model of the inner ear

In response to a sound stimulus, the inner ear emits sounds called otoacoustic emissions. While the exact mechanism for the production of otoacoustic emissions is not known, active motion of individual hair cells is thought to play a role. Two possible sources for otoacoustic emissions, both localized within individual hair cells, include somatic motility and hair bundle motility. Because physiological models of each of these systems are thought to be poised near a Hopf bifurcation, the dynamics of each can be described by the normal form for a system near a Hopf bifurcation. Here we demonstrate that experimental results from three-frequency suppression experiments can be predicted based on the response of an array of noninteracting Hopf oscillators tuned at different frequencies. This supports the idea that active motion of individual hair cells contributes to active processing of sounds in the ear. Interestingly, the model suggests an explanation for differing results recorded in mammals and nonmammals.