Regulation of free Ca2+ concentration in hair-cell stereocilia

A functional study of plasma-membrane calcium-pump isoform 2 mutants causing digenic deafness

Ca2+ enters the stereocilia of hair cells through mechanoelectrical transduction channels opened by the deflection of the hair bundle and is exported back to endolymph by an unusual splicing isoform (w/a) of plasma-membrane calcium-pump isoform 2 (PMCA2). Ablation or missense mutations of the pump cause deafness, as described for the G283S mutation in the deafwaddler (dfw) mouse. A deafness-inducing missense mutation of PMCA2 (G293S) has been identified in a human family. The family also was screened for mutations in cadherin 23, which accentuated hearing loss in a previously described human family with a PMCA2 mutation. A T1999S substitution was detected in the cadherin 23 gene of the healthy father and affected son but not in that of the unaffected mother, who presented instead the PMCA2 mutation. The w/a isoform was overexpressed in CHO cells. At variance with the other PMCA2 isoforms, it became activated only marginally when exposed to a Ca2+ pulse. The G293S and G283S mutations delayed the dissipation of Ca2+ transients induced in CHO cells by InsP3. In organotypic cultures, Ca2+ imaging of vestibular hair cells showed that the dissipation of stereociliary Ca2+ transients induced by Ca2+ uncaging was compromised in the dfw and PMCA2 knockout mice, as was the sensitivity of the mechanoelectrical transduction channels to hair bundle displacement in cochlear hair cells.

3p-- syndrome defines a hearing loss locus in 3p25.3

Deletions affecting the terminal end of chromosome 3p result in a characteristic set of clinical features termed 3p-- syndrome. Bilateral, sensorineural hearing loss (SNHL) has been found in some but not all cases, suggesting the possibility that it is due to loss of a critical gene in band 3p25. To date, no genetic locus in this region has been shown to cause human hearing loss. However, the ATP2B2 gene is located in 3p25.3, and haploinsufficiency of the mouse homolog results in SNHL with similar severity. We compared auditory test results with fine deletion mapping in seven previously unreported 3p-- syndrome patients and identified a 1.38Mb region in 3p25.3 in which deletions were associated with moderate to severe, bilateral SNHL. This novel hearing loss locus contains 18 genes, including ATP2B2. ATP2B2 encodes the plasma membrane calcium pump PMCA2. We used immunohistochemistry in human cochlear sections to show that PMCA2 is located in the stereocilia of hair cells, suggesting its function in the auditory system is conserved between humans and mice. Although other genes in this region remain candidates, we conclude that haploinsufficiency of ATP2B2 is the most likely cause of SNHL in 3p-- syndrome.

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

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

Hair cell mechanotransduction: the dynamic interplay between structure and function

Hair cells are capable of detecting mechanical vibrations of molecular dimensions at frequencies in the 10s to 100s of kHz. This remarkable feat is accomplished by the interplay of mechanically gated ion channels located near the top of a complex and dynamic sensory hair bundle. The hair bundle is composed of a series of actin-filled stereocilia that has both active and passive mechanical components as well as a highly active turnover process, whereby the components of the hair bundle are rapidly and continually recycled. Hair bundle mechanical properties have significant impact on the gating of the mechanically activated channels, and delineating between attributes intrinsic to the ion channel and those imposed by the channel's microenvironment is often difficult. This chapter describes what is known and accepted regarding hair-cell mechanotransduction and what remains to be explored, particularly, in relation to the interplay between hair bundle properties and mechanotransducer channel response. The interplay between hair bundle dynamics and mechanotransduction are discussed.

Calcium microdomains: organization and function

Microdomains of Ca(2+), which are formed at sites where Ca(2+) enters the cytoplasm either at the cell surface or at the internal stores, are a key element of Ca(2+) signalling. The term microdomain includes the elementary events that are the basic building blocks of Ca(2+) signals. As Ca(2+) enters the cytoplasm, it produces a local plume of Ca(2+) that has been given different names (sparks, puffs, sparklets and syntillas). These elementary events can combine to produce larger microdomains. The significance of these localized domains of Ca(2+) is that they can regulate specific cellular processes in different regions of the cell. Such microdomains are particularly evident in neurons where both pre- and postsynaptic events are controlled by highly localized pulses of Ca(2+). The ability of single neurons to process enormous amounts of information depends upon such miniaturization of the Ca(2+) signalling system. Control of cardiac cell contraction and gene transcription provides another example of how the parallel processing of Ca(2+) signalling can occur through microdomains of intracellular Ca(2+).

Atp2b2, encoding plasma membrane Ca2+-ATPase type 2, (PMCA2) exhibits tissue-specific first exon usage in hair cells, neurons, and mammary glands of mice

Atp2b2 encodes the plasma membrane Ca(2+)-ATPase type 2 (PMCA2) expressed in various tissues, including stereocilia of cochlear and vestibular hair cells, cerebellar Purkinje cells, and lactating mammary epithelia. Mutations of the gene lead to deafness, ataxia, and reduced Ca(2+) levels in milk. Heterozygous mutants also have abnormal hearing, suggesting that precise regulation of Atp2b2 is required for normal function. In this study, we describe Atp2b2 5'-untranslated region genomic structure and transcript usage in mice. Using 5'-rapid amplification of cDNA ends, we observed four transcripts: types alpha, beta, mu and delta, each splicing into a common ATG-containing exon. Types alpha and beta correspond to previously published mammalian cDNA sequences. Types mu and delta constitute novel 5'-untranslated region sequences, and were observed at high levels only in lactating mammary gland. Using real-time reverse transcriptase polymerase chain reaction, we quantified relative transcript usage across several tissues. We show that alpha and beta are abundant throughout the CNS, as well as the cochlea. When we microdissected the cochlea into hair cell and spiral ganglion containing fractions, we found that cochlear hair cell expression is mediated through the type alpha transcript. In situ hybridization studies in cerebellum using exon-specific probes revealed that alpha dominates in Purkinje neurons, while beta is enriched in cerebellar granule neurons. We compared 5'-untranslated region sequence across multiple species, and found high conservation around the first exons for alpha and beta in mammals, but not other species. The regions around the mu and delta first exons are highly conserved between rat and mouse, but less so with other species. Our results show that expression of Atp2b2 is highly regulated, using four different transcriptional start regions, two of which are differentially expressed in neuronal tissue. This suggests that unique regulatory mechanisms are used to control Atp2b2 expression in different types of cells.

Calcium concentration changes during sensory transduction in spider mechanoreceptor neurons

Most mechanoreceptor neurons encode mechanical signals into action potential trains within the same cell. Evidence suggests that intracellular calcium ion concentration, [Ca2+], increases during mechanotransduction, either by direct entry through mechanically activated channels or indirectly through voltage-activated calcium channels. However, little is known about the amounts of calcium involved or its roles in mechanotransduction. We estimated [Ca2+] in mechanoreceptor neurons of the spider, Cupiennius salei, during mechanical stimulation using Oregon Green BAPTA-1, and a single-compartment model of [Ca2+] as a function of action potential firing rate. Resting [Ca2+] was approximately 400 nM and increased to up to 2 microM at 30 action potentials/s. Similar levels of resting and stimulated [Ca2+] were obtained in the cell soma, axon and two parts of the sensory dendrite, including the region immediately adjacent to the site of sensory transduction. The time constant of rise and fall of [Ca2+] was 1-5 s in the dendrite and axon, but up to 15 s in the soma. Calcium elevation was dependent on action potentials and could not be induced by the receptor potential alone. Blockade of voltage-activated calcium channels by nickel ions prevented calcium increase, but thapsigargin, which empties intracellular calcium stores, had no effect. Estimates of calcium entry per action potential from fluorescence changes agreed approximately with estimates based on action potential voltage-time profile and previous reports of calcium channel properties. This first report of calcium levels during transduction in spiking mechanoreceptors suggests that calcium signaling plays important roles in primary somatosensory neurons.

Ca2+ changes the force sensitivity of the hair-cell transduction channel

The mechanically gated transduction channels of vertebrate hair cells tend to close in approximately 1 ms after their activation by hair bundle deflection. This fast adaptation is correlated with a quick negative movement of the bundle (a "twitch"), which can exert force and may mediate an active mechanical amplification of sound stimuli in hearing organs. We used an optical trap to deflect bullfrog hair bundles and to measure bundle movement while controlling Ca(2+) entry with a voltage clamp. The twitch elicited by repolarization of the cell varied with force applied to the bundle, going to zero where channels were all open or closed. The force dependence is quantitatively consistent with a model in which a Ca(2+)-bound channel requires approximately 3 pN more force to open, and rules out other models for the site of Ca(2+) action. In addition, we characterized a faster, voltage-dependent "flick", which requires intact tip links but not current through transduction channels.

Voltage-clamp errors cause anomalous interaction between independent ion channels

In voltage-clamp, uncompensated series resistance results in steady-state voltage errors that scale with the amplitude of the elicited current and are often correctable offline. However, while investigating mechanoelectric transduction currents at hair cells' resting potential, voltage-gated calcium channels and calcium-activated potassium channels (BK) were activated in voltage-clamp by displacing the sensory hair bundle. This resulted from steady-state voltage errors (<1.5 mV) induced by series resistance changing the holding potential. Thus, uncompensated series resistance, interacting with an elicited current, resulted in a voltage error that could induce the erroneous activation of other currents. This error is not correctable offline. Recognizing this type of error is critical when investigating multiple voltage-dependent conductances with steep voltage dependence.

Intracellular Ca2+ buffers can dramatically affect Ca2+ conductances in hair cells

The effects of endogenous and exogenous Ca(2+) buffers on Ca(2+) current kinetics have been investigated by patch clamp in hair cells mechanically isolated from frog semicircular canals. This preparation displays at least three different Ca(2+) channel types: transient currents flow through a drug-resistant channel ("R1"), while non-inactivating channels sustain a steady, plateau current comprised of a large L component and a small drug-resistant fraction ("R2"). In the perforated-patch condition a large and stable Ca(2+) current was recorded, with all three components. In whole-cell, a buffer-free pipette solution did not prevent a complete Ca(2+) response. The size of the transient and plateau current fractions were greatly reduced, but the ratio between the two fractions, as well as the activation, inactivation and deactivation kinetics, were substantially unmodified. Current amplitude partially recovered with 5 mM EGTA in the pipette solution. With 50 mM EGTA all the kinetic parameters were slowed down and the transient component, but not the plateau component, markedly increased in size. Response kinetics slowed down even more with 30 mM Cs-BAPTA and the Ca(2+) waveform was substantially modified. The transient component was very large and inactivated slowly; the remaining very small plateau fraction deactivated along a slow, single exponential time. Under this condition nifedipine (10 microM) produced a great reduction of the transient current, leaving plateau and deactivation phase unaltered. This suggests that only R2 channels were still active at the end of the test and that the minor remaining transient component flowed through slowly but completely inactivating R1 channels. These results confirm the presence of several channel types in semicircular canal receptors, at difference with cochlear hair cells, and highlight a dramatic alteration of L-type channel behavior when intracellular Ca(2+) buffers are sufficiently concentrated and fast to interfere with rapid and local changes in Ca(2+) levels.

Haplo-insufficiency revealed in deafwaddler mice when tested for hearing loss and ataxia

The auditory and vestibular systems rely on the plasma membrane calcium ATPase, isoform 2 (PMCA2) to extrude calcium that enters the stereocilia during transduction. Mutations in the gene encoding this protein result in recessive sensorineural deafness and ataxia in the deafwaddler mouse. In this study, we report the identification of a new allele of deafwaddler, dfw(3j). This allele contains a 4-nucleotide deletion resulting in a frame-shift and predicted truncation of PMCA2. No protein is detected in dfw(3j) homozygotes. To examine the dependence of auditory and vestibular function on PMCA2 activity, we compared dfw(3j) with another functional null allele, dfw(2j), and the partial loss-of-function allele, dfw. All mice studied were in the good-hearing CBA/CaJ background. Heterozygotes of either functional null allele displayed highly significant hearing loss by auditory-evoked brainstem responses relative to controls (P < 0.0001), particularly at high frequencies (> 24 kHz). Ataxia was also apparent in these mice on an accelerating rotarod (P < 0.05). In contrast, +/dfw mice were not measurably different from controls in either behavioral test. dfw/dfw mice were deaf, but showed less ataxia than dfw(2j)/dfw(2j) or dfw(3j)/dfw(3j) mice. These results demonstrate that hearing loss and ataxia are dependent on gene dosage and PMCA2 dysfunction.

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

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

Hair cells require phosphatidylinositol 4,5-bisphosphate for mechanical transduction and adaptation

After opening in response to mechanical stimuli, hair cell transduction channels adapt with fast and slow mechanisms that each depend on Ca(2+). We demonstrate here that transduction and adaptation require phosphatidylinositol 4,5-bisphosphate (PIP(2)) for normal kinetics. PIP(2) has a striking distribution in hair cells, being excluded from the basal region of hair bundles and apical surfaces of frog saccular hair cells. Localization of a phosphatidylinositol lipid phosphatase, Ptprq, to these PIP(2)-free domains suggests that Ptprq maintains low PIP(2) levels there. Depletion of PIP(2) by inhibition of phosphatidylinositol 4-kinase or sequestration by aminoglycosides reduces the rates of fast and slow adaptation. PIP(2) and other anionic phospholipids bind directly to the IQ domains of myosin-1c, the motor that mediates slow adaptation, permitting a strong interaction with membranes and likely regulating the motor's activity. PIP(2) depletion also causes a loss in transduction current. PIP(2) therefore plays an essential role in hair cell adaptation and transduction.

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

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

Myosin-1c, the hair cell's adaptation motor

Given their prominent actin-rich subcellular specializations, it is no surprise that mechanosensitive hair cells of the inner ear exploit myosin molecules-the only known actin-dependent molecular motors-to carry out exotic but essential tasks. Recent experiments have confirmed that an unconventional myosin isozyme, myosin-1c, is a component of the hair cell's adaptation-motor complex. This complex carries out slow adaptation, provides tension to sensitize transduction channels, and may participate in assembly of the transduction apparatus. This review focuses on the detailed operation of the adaptation motor and the functional consequences of the incorporation of this specific myosin isozyme into the motor complex.

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

The hair cells of the vertebrate inner ear convert mechanical stimuli to electrical signals. Two adaptation mechanisms are known to modify the ionic current flowing through the transduction channels of the hair bundles: a rapid process involves Ca(2+) ions binding to the channels; and a slower adaptation is associated with the movement of myosin motors. We present a mathematical model of the hair cell which demonstrates that the combination of these two mechanisms can produce "self-tuned critical oscillations", i.e., maintain the hair bundle at the threshold of an oscillatory instability. The characteristic frequency depends on the geometry of the bundle and on the Ca(2+) dynamics, but is independent of channel kinetics. Poised on the verge of vibrating, the hair bundle acts as an active amplifier. However, if the hair cell is sufficiently perturbed, other dynamical regimes can occur. These include slow relaxation oscillations which resemble the hair bundle motion observed in some experimental preparations.

Spontaneous oscillation by hair bundles of the bullfrog's sacculus

One prominent manifestation of mechanical activity in hair cells is spontaneous otoacoustic emission, the unprovoked emanation of sound by an internal ear. Because active hair bundle motility probably constitutes the active process of nonmammalian hair cells, we investigated the ability of hair bundles in the bullfrog's sacculus to produce oscillations that might underlie spontaneous otoacoustic emissions. When maintained in the normal ionic milieu of the ear, many bundles oscillated spontaneously through distances as great as 80 nm at frequencies of 5-50 Hz. Whole-cell recording disclosed that the positive phase of movement was associated with the opening of transduction channels. Gentamicin, which blocks transduction channels, reversibly arrested oscillation; drugs that affect the cAMP phosphorylation pathway and might influence the activity of myosin altered the rate of oscillation. Increasing the Ca 2+ concentration rendered oscillations faster and smaller until they were suppressed; lowering the Ca 2+ concentration moderately with chelators had the opposite effect. When a bundle was offset with a stimulus fiber, oscillations were transiently suppressed but gradually resumed. Loading a bundle by partial displacement clamping, which simulated the presence of the accessory structures to which a bundle is ordinarily attached, increased the frequency and diminished the magnitude of oscillation. These observations accord with a model in which oscillations arise from the interplay of the hair bundle's negative stiffness with the activity of adaptation motors and with Ca 2+-dependent relaxation of gating springs.

Vertebrate and invertebrate TRPV-like mechanoreceptors

Our senses of touch, hearing, and balance are mediated by mechanosensitive ion channels. In vertebrates, little is known about the molecular composition of these mechanoreceptors, an example of which is the transduction channel of the inner ear's receptor cells, hair cells. Members of the TRP family of ion channels are considered candidates for the vertebrate hair cell's mechanosensitive transduction channel and here we review the evidence for this candidacy. We start by examining the results of genetic screens in invertebrates that identified members of the TRP gene family as core components of mechanoreceptors. In particular, we discuss the Caenorhabditis elegans OSM-9 channel, an invertebrate TRPV channel, and the Drosophila melanogaster TRP channel NOMPC. We then evaluate basic features of TRPV4, a vertebrate member of the TRPV subfamily, which is gated by a variety of physical and chemical stimuli including temperature, osmotic pressure, and ligands. Finally, we compare the characteristics of all discussed mechanoreceptive TRP channels with the biophysical characteristics of hair cell mechanotransduction, speculating about the possible make-up of the elusive inner ear mechanoreceptor.

Intracellular calcium regulation in inner hair cells from neonatal mice

The mechanisms that regulate the concentration of ionized intracellular calcium (Ca(2+)(i)) in the base of neonatal mouse inner hair cells, close to synaptic sites, were investigated using confocal microscopy combined with conventional patch-clamp electrophysiology. Cells were depolarized under whole-cell voltage clamp to load the cell with C a(2+) through voltage-activated Ca(2+) channels. Repeated depolarizations produced Ca(2+)(i) increases with similar amplitudes and time-courses of recovery. The rate of recovery from depolarization-induced Ca(2+)(i) loads was used to assess the mechanisms responsible for Ca(2+)(i) regulation. Removal of extracellular sodium had no effect on resting Ca(2+)(i) or the rate of recovery of Ca(2+)(i) suggesting no role for Na:Ca exchange in these cells. Inhibitors of intracellular store uptake such as thapsigargin, 2,5-di(tert-butyl)hydroquinone (BHQ) and cyclopiazonic acid (CPA) caused an increase in resting Ca(2+)(i) and slowed the rate of recovery, indicating that Ca(2+) can be taken up intracellularly. However, 5mM caffeine failed to cause a detectable release of Ca(2+) from intracellular stores. FCCP, a mitochondrial inhibitor, slowed the rate of recovery from Ca(2+)(i) loads, indicating a role for mitochondrial Ca(2+) uptake. The largest effects were seen with intracellular vanadate (1mM) which caused an irreversible rise in resting Ca(2+)(i) and depolarization-induced increases in Ca(2+)(i) failed to recover fully. Together, these data indicate that both thapsigargin-sensitive stores and mitochondria can take up Ca(2+)(i), but that Ca(2+) efflux from the cell occurs solely via a plasma membrane Ca(2+)-ATPase.

Role of microvillar cell surfaces in the regulation of glucose uptake and organization of energy metabolism

Experimental evidence suggesting a type of glucose uptake regulation prevailing in resting and differentiated cells was surveyed. This type of regulation is characterized by transport-limited glucose metabolism and depends on segregation of glucose transporters on microvilli of differentiated or resting cells. Earlier studies on glucose transport regulation and a recently presented general concept of influx regulation for ions and metabolic substrates via microvillar structures provide the basic framework for this theory. According to this concept, glucose uptake via transporters on microvilli is regulated by changes in the structural organization of the microfilament bundle, which is acting as a diffusion barrier between the microvillar tip compartment and the cytoplasm. Both microvilli formation and the switch of glucose metabolism from "metabolic regulation" to "transport limitation" occur during differentiation. The formation of microvillar cell surfaces creates the essential preconditions to establish the characteristic functions of specialized tissue cells including the coordination between glycolysis and oxidative phosphorylation, regulation of cellular functions by external signals, and Ca(2+) signaling. The proposed concept integrates various aspects of glucose uptake regulation into a ubiquitous cellular mechanism involved in regulation of transmembrane ion and substrate fluxes.

Characterization of the deafwaddler mutant of the rat plasma membrane calcium-ATPase 2

The deafwaddler mutant in mice was the first spontaneous mutant discovered in the plasma membrane Ca(2+) pump (PMCA) [Street, V.A. et al., 1998, Nat. Genet. 19, 390-394]. A nucleotide substitution in deafwaddler results in a Gly to Ser transition at amino acid 283 in the small cytoplasmic loop of PMCA isoform 2 (PMCA2). PMCA2 is abundant in the stereocilia of auditory and vestibular hair cells, neurons of the spiral ganglion, and participates in inner ear development. Mice that are homozygous for deafwaddler are deaf and have poor balance. However, the balance and hearing disorders of the deafwaddler mice appear to be less severe than homozygotes for a functionally null frameshift mutant or homozygous PMCA2 knockout mice, suggesting that deafwaddler PMCA2 retains some biological activity. To examine the enzymic effects of the deafwaddler mutant, PMCA2 wild-type and deafwaddler were produced by transient expression in COS cells as well as baculovirus-mediated expression in Sf9 insect cells. Membrane preparations were assayed for calcium transport and ATPase activity. No significant differences in the regulation by calmodulin of the wild-type and deafwaddler PMCA2b were found. Steady-state transport assays and pre-steady-state ATPase assays of these two proteins revealed that the K(0.5) for Ca(2+), K(0.5) for calmodulin, degree of activation by calmodulin and rate of activation by Ca-calmodulin were nearly identical. However, calcium transport of the deafwaddler pump was reduced to 30% of the wild-type activity. Although calcium transport activity was reduced in the deafwaddler pump, total phosphoenzyme formation from ATP was slightly higher for deafwaddler than for wild-type. 50 microM LaCl3 (which blocks the E(1)P to E(2)P conformational transition) increased the steady-state level of phosphoenzyme 3-fold for the wild-type but had no effect on the deafwaddler. Taken together, the kinetic data suggest that the deafwaddler mutation affects PMCA2 by slowing the E(1)P to E(2)P transition, resulting in approximately 70% reduction in the PMCA2-mediated Ca(2+) export.

Wavelets of excitability in sensory neurons

We have investigated variations in the excitability of mammalian cutaneous mechanoreceptor neurons. We focused on the phase dynamics of an action potential relative to a periodic stimulus, showing that the excitability of these sensory neurons has interesting nonstationary oscillations. Using a wavelet analysis, these oscillations were characterized through the depiction of their period as a function of time. It was determined that the induced oscillations are weakly dependent on the stimulus frequency, and that lower temperatures significantly reduce the frequency of the phase response. Our results reveal novel excitability properties in sensory neurons, and, more generally, could prove significant in the deduction of mechanistic attributes underlying the nonstationary excitability in neuronal systems. Since peripheral neurons feed information to the CNS, variable responses observed in higher regions may be generated in part at the site of sensory detection.

Dynamics of intracellular calcium in hair cells isolated from the semicircular canal of the frog

Changes in cytosolic free Ca(2+) concentration ([Ca(2+)]i) were monitored optically in hair cells mechanically isolated from frog semicircular canals using the membrane-impermeant form of the Ca(2+)-selective dye Oregon Green 488 BAPTA-1 (OG, 100 microM). Cells stimulated by depolarization under whole-cell voltage clamp conditions revealed Ca(2+) entry at selected sites (hotspots) located mostly in the lower (synaptic) half of the cell body. [Ca(2+)]i at individual hotspots rose with a time constant tau1 approximately 70 ms and decayed with a bi-exponential time-course (tau2 approximately 160, tau3 approximately 2500 ms) following a 160 ms depolarization to -20 mV. With repeated stimulation [Ca(2+)]i underwent independent amplitude changes at distinct hotspots, suggesting that the underlying Ca(2+) channel clusters can be regulated differentially by intracellular signalling pathways. Block by nifedipine indicated that the L-type Ca(2+)channels are distributed at different densities in distinct hotspots. No diffusion barrier other than the nuclear region was found in the cytosol, so that, during a prolonged depolarization (lasting up to 1s), Ca(2+) was able to reach the cell apical ciliated pole. The effective Ca(2+) diffusion constant, measured from the progression of Ca(2+) wavefronts in the cytosol, was approximately 57 microm(2)/s. Our results indicate that in these hair cells, buffered diffusion of Ca(2+) proceeds evenly from the source point to the cell interior and is dominated by the diffusion constant of the endogenous mobile buffers.

Plasma membrane Ca2+-ATPase isoform 2a is the PMCA of hair bundles

Mechanoelectrical transduction channels of hair cells allow for the entry of appreciable amounts of Ca(2+), which regulates adaptation and triggers the mechanical activity of hair bundles. Most Ca(2+) that enters transduction channels is extruded by the plasma membrane Ca(2+)-ATPase (PMCA), a Ca(2+) pump that is highly concentrated in hair bundles and may be essential for normal hair cell function. Because PMCA isozymes and splice forms are regulated differentially and have distinct biochemical properties, we determined the identity of hair bundle PMCA in frog and rat hair cells. By screening a bullfrog saccular cDNA library, we identified abundant PMCA1b and PMCA2a clones as well as rare PMCA2b and PMCA2c clones. Using immunocytochemistry and immunoprecipitation experiments, we showed in bullfrog sacculus that PMCA1b is the major isozyme of hair cell and supporting cell basolateral membranes and that PMCA2a is the only PMCA present in hair bundles. This complete segregation of PMCA1 and PMCA2 isozymes holds for rat auditory and vestibular hair cells; PMCA2a is the only PMCA isoform in hair bundles of outer hair cells and vestibular hair cells and is the predominant PMCA of hair bundles of inner hair cells. Our data suggest that hair cells control plasma membrane Ca(2+)-pumping activity by targeting specific PMCA isozymes to distinct subcellular locations. Because PMCA2a is the only Ca(2+) pump present at appreciable levels in hair bundles, the biochemical properties of this pump must account fully for the physiological features of transmembrane Ca(2+) pumping in bundles.

Delayed activation of the plasma membrane calcium pump by a sudden increase in Ca2+: fast pumps reside in fast cells

There are four genes encoding isoforms of the plasma membrane Ca(2+) pump (PMCA). PMCA variability is increased by the presence of two splicing sites. Functional differences between the variants of PMCA have been described, but little is known about the adaptive advantages of this great diversity of pumps. In this paper we studied how the different isoforms respond to a sudden increase in Ca(2+) concentration. We found that different PMCAs are activated by Ca(2+) at different rates, PMCA 3f and 2a being the fastest, and 4b the slowest. The rate of activation by Ca(2+) depends both on the rate of calmodulin binding and the magnitude of the activation by calmodulin. We found that 2a is located in heart and the stereocilia of inner ear hair cells, 3f in skeletal muscle and 4b was identified in Jurkat cells. Both cardiac and skeletal muscle, and stereocilia recover very rapidly after a cytoplasmic Ca(2+)peak, while in Jurkat cells the recovery takes up to a minute. In stereocilia, 2a is the only method for export of Ca(2+), making the analysis of them unusually straightforward. This indicates that these rates of PMCA activation by Ca(2+) are correlated with the speed of Ca(2+) concentration decay after a Ca2 spike in the cells in which these variants of PMCA are expressed. The results suggest that the type of PMCA expressed will correspond with the speed of Ca(2+) signals in the cell.

Predicted profiles of ion concentrations in olfactory cilia in the steady state

The role of ciliary geometry for transduction events was explored by numerical simulation. The changes in intraciliary ion concentrations, suspected to occur during transduction, could thus be estimated. The case of a single excised cilium, having a uniform distribution of membrane channels, voltage clamped to -80 mV, was especially investigated. The axial profile of membrane voltage was that of a leaky cable. The Ca(2+) concentration profile tended to show a maximum in proximal segments, due to a preponderance of Ca(2+) inflow over Ca(2+) export at those locations. The local increase in Ca(2+) concentration activated Cl(-) channels. The resulting current caused a local drop in Cl(-) concentration, especially at the tip of the cilium and in distal segments, accompanied by a drop in ciliary K(+) concentration. In consequence, the membrane Cl(-) current was low in distal segments but stronger in proximal segments, where resupply was sufficient. The model predicts that the Cl(-) depletion will codetermine the time course of the receptor potential or current and the ciliary stimulus-response curve. In conclusion, when modeling with transduction elements presently known to participate, the ciliary geometry has large effects on ion distributions and transduction currents because ciliary ion transport is limited by axial electrodiffusion.

Immuno-electron microscopic localization of the alpha(1) and beta(1)-subunits of soluble guanylyl cyclase in the guinea pig organ of corti

Guanylyl cyclases (GC) catalyze the formation of the intracellular signal molecule cyclic GMP from GTP. For some years it has been known that the heme-containing soluble guanylyl cyclase (sGC) is stimulated by NO and NO-containing compounds. The sGC enzyme consists of two subunits (alpha(1) and beta(1)). In the present study, the alpha(1) and beta(1)-subunits were identified in the guinea pig cochlea at the electron microscopic level using a post-embedding immuno-labeling procedure. Ultrathin sections of LR White embedded specimens were incubated with various concentrations of two rabbit polyclonal antibodies to the alpha(1)- and beta(1)-subunit, respectively. The immunoreactivity was visualized by a gold-labeled secondary antibody in an energy-filtering transmission electron microscope (EFTEM). Marked immunoreactivity for both antibodies was found in the inner and outer hair cells, with numerous gold particles at the border of the cuticular plates, associated with the cell nuclei or attached to electron-dense parts of the cytoplasm. In the pillar cells and apical Deiters cells, soluble guanylyl cyclase immunoreactivity was located at the rim of the cuticular plates and between the microtubuli bundles. Together with the recently identified nitric oxide synthase isoforms [Eur. Arch. Otorhinolaryngol. 254 (1997) 396; Eur. Arch. Otorhinolaryngol. 255 (1998) 483], the soluble guanylyl cyclase may be involved in signalling processes in the organ of Corti.

Two mechanisms for transducer adaptation in vertebrate hair cells

Deflection of the hair bundle atop a sensory hair cell modulates the open probability of mechanosensitive ion channels. In response to sustained deflections, hair cells adapt. Two fundamentally distinct models have been proposed to explain transducer adaptation. Both models support the notion that channel open probability is modulated by calcium that enters via the transduction channels. Both also suggest that the primary effect of adaptation is to shift the deflection-response [I(X)] relationship in the direction of the applied stimulus, thus maintaining hair bundle sensitivity. The models differ in several respects. They operate on different time scales: the faster on the order of a few milliseconds or less and the slower on the order of 10 ms or more. The model proposed to explain fast adaptation suggests that calcium enters and binds at or near the transduction channels to stabilize a closed conformation. The model proposed to explain the slower adaptation suggests that adaptation is mediated by an active, force-generating process that regulates the effective stimulus applied to the transduction channels. Here we discuss the evidence in support of each model and consider the possibility that both may function to varying degrees in hair cells of different species and sensory organs.

Putting ion channels to work: mechanoelectrical transduction, adaptation, and amplification by hair cells

As in other excitable cells, the ion channels of sensory receptors produce electrical signals that constitute the cellular response to stimulation. In photoreceptors, olfactory neurons, and some gustatory receptors, these channels essentially report the results of antecedent events in a cascade of chemical reactions. The mechanoelectrical transduction channels of hair cells, by contrast, are coupled directly to the stimulus. As a consequence, the mechanical properties of these channels shape our hearing process from the outset of transduction. Channel gating introduces nonlinearities prominent enough to be measured and even heard. Channels provide a feedback signal that controls the transducer's adaptation to large stimuli. Finally, transduction channels participate in an amplificatory process that sensitizes and sharpens hearing.

Negative hair-bundle stiffness betrays a mechanism for mechanical amplification by the hair cell

Hearing and balance rely on the ability of hair cells in the inner ear to sense miniscule mechanical stimuli. In each cell, sound or acceleration deflects the mechanosensitive hair bundle, a tuft of rigid stereocilia protruding from the cell's apical surface. By altering the tension in gating springs linked to mechanically sensitive transduction channels, this deflection changes the channels' open probability and elicits an electrical response. To detect weak stimuli despite energy losses caused by viscous dissipation, a hair cell can use active hair-bundle movement to amplify its mechanical inputs. This amplificatory process also yields spontaneous bundle oscillations. Using a displacement-clamp system to measure the mechanical properties of individual hair bundles from the bullfrog's ear, we found that an oscillatory bundle displays negative slope stiffness at the heart of its region of mechanosensitivity. Offsetting the hair bundle's position activates an adaptation process that shifts the region of negative stiffness along the displacement axis. Modeling indicates that the interplay between negative bundle stiffness and the motor responsible for mechanical adaptation produces bundle oscillation similar to that observed. Just as the negative resistance of electrically excitable cells and of tunnel diodes can be embedded in a biasing circuit to amplify electrical signals, negative stiffness can be harnessed to amplify mechanical stimuli in the ear.

Regulation of cell volume via microvillar ion channels

A novel mechanism of cellular volume regulation is presented, which ensues from the recently introduced concept of transport and ion channel regulation via microvillar structures (Lange K, 1999, J Cell Physiol 180:19-35). According to this notion, the activity of ion channels and transporter proteins located on microvilli of differentiated cells is regulated by changes in the structural organization of the bundle of actin filaments in the microvillar shaft region. Cells with microvillar surfaces represent two-compartment systems consisting of the cytoplasm on the one side and the sum of the microvillar tip (or, entrance) compartments on the other side. The two compartments are separated by the microvillar actin filament bundle acting as diffusion barrier ions and other solutes. The specific organization of ion and water channels on the surface of microvillar cell types enables this two-compartment system to respond to hypo- and hyperosmotic conditions by activation of ionic fluxes along electrochemical gradients. Hypotonic exposure results in swelling of the cytoplasmic compartment accompanied by a corresponding reduction in the length of the microvillar diffusion barrier, allowing osmolyte efflux and regulatory volume decrease (RVD). Hypertonic conditions, which cause shortening of the diffusion barrier via swelling of the entrance compartment, allow osmolyte influx for regulatory volume increase (RVI). Swelling of either the cytoplasmic or the entrance compartment, by using membrane portions of the microvillar shafts for surface enlargement, activates ion fluxes between the cytoplasm and the entrance compartment by shortening of microvilli. The pool of available membrane lipids used for cell swelling, which is proportional to length and number of microvilli per cell, represents the sensor system that directly translates surface enlargements into activation of ion channels. Thus, the use of additional membrane components for osmotic swelling or other types of surface-expanding shape changes (such as the volume-invariant cell spreading or stretching) directly regulates influx and efflux activities of microvillar ion channels. The proposed mechanism of ion flux regulation also applies to the physiological main functions of epithelial cells and the auxiliary action of swelling-induced ATP release. Furthermore, the microvillar entrance compartment, as a finely dispersed ion-accessible peripheral space, represents a cellular sensor for environmental ionic/osmotic conditions able to detect concentration gradients with high lateral resolution. Volume regulation via microvillar surfaces is only one special aspect of the general property of mechanosensitivity of microvillar ionic pathways.

Adaptation in hair cells

Hair cells adapt to sustained deflections of the hair bundle via Ca(2+)-dependent negative feedback on the open probability of the mechanosensitive transduction channels. A model posits that adaptation relieves the input to the transduction channels--force applied by elastic tip links between stereocilia--by repositioning the insertions of the links in the stereocilium. The tip link insertion and transduction channel are dragged by myosins moving on the stereocilium's actin core. This model accounts for many aspects of adaptation in hair cells of the frog saccule, where adaptation time constants are tens of milliseconds. Adaptation in hair cells of the turtle cochlea is much faster, possibly reflecting a more direct mechanism such as Ca2+ binding to the transduction channel. Adaptation mechanisms attenuate the transduction current at low frequencies and may be tuned to different corner frequencies according to the stimulus demands of the inner ear organ. Other sites of adaptation in the inner ear include accessory structures, voltage-dependent properties of hair cells, and afferent transmitter release. A remaining challenge is to understand how these processes work together to shape the output of the inner ear to natural stimuli.

The deaf jerker mouse has a mutation in the gene encoding the espin actin-bundling proteins of hair cell stereocilia and lacks espins

The espins are actin-bundling proteins of brush border microvilli and Sertoli cell-spermatid junctions. We have determined that espins are also present in hair cell stereocilia and have uncovered a connection between the espin gene and jerker, a recessive mutation that causes hair cell degeneration, deafness, and vestibular dysfunction. The espin gene maps to the same region of mouse chromosome 4 as jerker. The tissues of jerker mice do not accumulate espin proteins but contain normal levels of espin mRNAs. The espin gene of jerker mice has a frameshift mutation that affects the espin C-terminal actin-bundling module. These data suggest that jerker mice are, in effect, espin null and that the jerker phenotype results from a mutation in the espin gene.

Medial efferent effects on auditory-nerve responses to tail-frequency tones II: alteration of phase

It is often assumed that at frequencies in the tuning-curve tail there is a passive, constant coupling of basilar-membrane motion to inner hair cell (IHC) stereocilia. This paper shows changes in the phase of auditory-nerve-fiber (ANF) responses to tail-frequency tones and calls into question whether basilar-membrane-to-IHC coupling is constant. In cat ANFs with characteristic frequencies > or = 10 kHz, efferent effects on the phase of ANF responses to tail-frequency tones were measured. Efferent stimulation caused substantial changes in ANF phase (deltaphi) (range -80 degrees to +60 degrees, average -15 degrees, a phase lag) with the largest changes at sound levels near threshold and 3-4 octaves below characteristic frequency (CF). At these tail frequencies, efferent stimulation had much less effect on the phase of the cochlear microphonic (CM) than on ANF phase. Thus, since CM is synchronous with basilar-membrane motion for low-frequency stimuli in the cochlear base, the efferent-induced change in ANF phase is unlikely to be due entirely to a change in basilar-membrane phase. At tail frequencies, ANF phase changed with sound level (often by 90 degrees-180 degrees) and the deltaphi from a fiber was positively correlated with the slope of its phase-versus-sound-level function at the same frequency, as if deltaphi were caused by a 2-4 dB increase in sound level. This correlation suggests that the processes that produce the change in ANF phase with sound level at tail frequencies are also involved in producing deltaphi. It is hypothesized that both efferent stimulation and increases in sound level produce similar phase changes because they both produce a similar mix of cochlear vibrational modes.

Hair cells, hearing and hopping: a field guide to hair cell physiology in the frog

For more than four decades, hearing in frogs has been an important source of information for those interested in auditory neuroscience, neuroethology and the evolution of hearing. Individual features of the frog auditory system can be found represented in one or many of the other vertebrate classes, but collectively the frog inner ear represents a cornucopia of evolutionary experiments in acoustic signal processing. The mechano-sensitive hair cell, as the focal point of transduction, figures critically in the encoding of acoustic information in the afferent auditory nerve. In this review, we provide a short description of how auditory signals are encoded by the specialized anatomy and physiology of the frog inner ear and examine the role of hair cell physiology and its influence on the encoding of sound in the frog auditory nerve. We hope to demonstrate that acoustic signal processing in frogs may offer insights into the evolution and biology of hearing not only in amphibians but also in reptiles, birds and mammals, including man.

Essential nonlinearities in hearing

Our hearing organ, the cochlea, evidently poises itself at a Hopf bifurcation to maximize tuning and amplification. We show that in this condition several effects are expected to be generic: compression of the dynamic range, infinitely sharp tuning at zero input, and generation of combination tones. These effects are "essentially" nonlinear in that they become more marked the smaller the forcing: there is no audible sound soft enough not to evoke them. All the well-documented nonlinear aspects of hearing therefore appear to be consequences of the same underlying mechanism.

Calcium transients in the rhabdomeres of dark- and light-adapted fly photoreceptor cells

The light response of fly photoreceptor cells is modulated by changes in free Ca(2+) concentration. Fly phototransduction and most processes regulating it take place in or very close to the rhabdomere. We therefore measured the kinetics and the absolute values of the free Ca(2+) concentration in the rhabdomere of fly photoreceptor cells in vivo by making use of the natural optics of the fly's eye. We show that Ca(2+) flowing into the rhabdomere after light stimulation of dark-adapted cells causes fast Ca(2+) transients that reach peak values higher than 200 microM in <20 msec. Approximately 500 msec later, the free Ca(2+) concentration has declined again to approximately 20 microM. The duration of the Ca(2+) transients becomes still shorter, and their size reduced, when the photoreceptor cell is light-adapted. This reduction in duration and size of the Ca(2+) transients is graded with the intensity of the adapting light. The kinetics and absolute values of the free calcium concentration found to occur in the rhabdomere are suitable to mediate the fast feedback signals known to act on the fly phototransduction cascade.

Chemical and physiological characterization of fluo-4 Ca(2+)-indicator dyes

We have developed fluo-4, a new fluorescent dye for quantifying cellular Ca2+ concentrations in the 100 nM to 1 microM range. Fluo-4 is similar in structure and spectral properties to the widely used fluorescent Ca(2+)-indicator dye, fluo-3, but it has certain advantages over fluo-3. Due to its greater absorption near 488 nm, fluo-4 offers substantially brighter fluorescence emission when used with excitation by argon-ion laser or other sources in conjunction with the standard fluorescein filter set. In vitro, fluo-4 exhibited high fluorescence emission, a high rate of cell permeation, and a large dynamic range for reporting [Ca2+] around a Kd(Ca2+) of 345 nM. We have also developed several Ca(2+)-indicators related to fluo-4 having lower affinities for Ca2+ that are useful in cellular studies requiring quantification of higher [Ca2+]. In a variety of physiological studies of live cells, fluo-4 labeled cells more brightly than did fluo-3, when challenged with procedures designed to elevate calcium levels. Fluo-4 is well suited for photometric and imaging applications that make use of confocal laser scanning microscopy, flow cytometry, or spectrofluorometry, or in fluorometric high-throughput microplate screening assays. Because of its higher fluorescence emission intensity, fluo-4 can be used at lower intracellular concentrations, making its use a less invasive practice.

Two components of transducer adaptation in auditory hair cells

Mechanoelectrical transducer currents in turtle auditory hair cells adapted to maintained stimuli via a Ca(2+)-dependent mechanism characterized by two time constants of approximately 1 and 15 ms. The time course of adaptation slowed as the stimulus intensity was raised because of an increased prominence of the second component. The fast component of adaptation had a similar time constant for both positive and negative displacements and was unaffected by the myosin ATPase inhibitors, vanadate and butanedione monoxime. Adaptation was modeled by a scheme in which Ca(2+) ions, entering through open transducer channels, bind at two intracellular sites to trigger independent processes leading to channel closure. It was assumed that the second site activates a modulator with 10-fold slower kinetics than the first site. The model was implemented by computing Ca(2+) diffusion within a single stereocilium, incorporating intracellular calcium buffers and extrusion via a plasma membrane CaATPase. The theoretical results reproduced several features of the experimental responses, including sensitivity to the concentration of external Ca(2+) and intracellular calcium buffer and a dependence on the onset speed of the stimulus. The model also generated damped oscillatory transducer responses at a frequency dependent on the rate constant for the fast adaptive process. The properties of fast adaptation make it unlikely to be mediated by a myosin motor, and we suggest that it may result from Ca(2+) binding to the transducer channel or a nearby cytoskeletal element.

ATP-Induced Ca(2+) release in cochlear outer hair cells: localization of an inositol triphosphate-gated Ca(2+) store to the base of the sensory hair bundle

We used a high-performance fluorescence imaging system to visualize rapid changes in intracellular free Ca(2+) concentration ([Ca(2+)](i)) evoked by focal applications of extracellular ATP to the hair bundle of outer hair cells (OHCs): the sensory-motor receptors of the cochlea. Simultaneous recordings of the whole-cell current and Calcium Green-1 fluorescence showed a two-component increase in [Ca(2+)](i). After an initial entry of Ca(2+) through the apical membrane, a second and larger, inositol triphosphate (InsP(3))-gated, [Ca(2+)](i) surge occurred at the base of the hair bundle. Electron microscopy of this intracellular Ca(2+) release site showed that it coincides with the localization of a unique system of endoplasmic reticulum (ER) membranes and mitochondria known as Hensen's body. Using confocal immunofluorescence microscopy, we showed that InsP(3) receptors share this location. Consistent with a Ca(2+)-mobilizing second messenger system linked to ATP-P2 receptors, we also determined that an isoform of G-proteins is present in the stereocilia. Voltage-driven cell shape changes and nonlinear capacitance were monitored before and after ATP application, showing that the ATP-evoked [Ca(2+)](i) rise did not interfere with the OHC electromotility mechanism. This second messenger signaling mechanism bypasses the Ca(2+)-clearance power of the stereocilia and transiently elevates [Ca(2+)](i) at the base of the hair bundle, where it can potentially modulate the action of unconventional myosin isozymes involved in maintaining the hair bundle integrity and potentially influence mechanotransduction.

Differential subcellular immunolocalization of voltage-gated calcium channel alpha1 subunits in the chinchilla cristae ampullaris

The immunohistochemical localization of alpha1A, alpha1B, alpha1C, alpha1D and alpha1E voltage-gated calcium channel subunits was investigated in the chinchilla cristae ampullaris and Scarpa's ganglia at the light and electron microscopy level with the use of specific antipeptide antibodies directed against these subunits. The stereocilia membrane of type I and type II hair cells was immunoreactive for alpha1B along its entire length. The basolateral membrane of both types of hair cells was alpha1B, alpha1C and alpha1D immunoreactive. Neurons in the Scarpa's ganglia and afferent nerve terminals in the cristae were immunoreactive for alpha1C and alpha1B. No specific immunoreactivity to alpha1A or alpha1E was seen in the sensory epithelia or ganglia. These findings are consistent with the presence of alpha1B (N-type channel), alpha1C and alpha1D (L-type channels) in the vestibular hair cells, and alpha1B (N-type channel) and alpha1C (L-type channel) in primary vestibular neurons.

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system's behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken's cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.