Active hair bundle movements in auditory hair cells

Abstract

The frequency selectivity of mammalian hearing depends on not only the passive mechanics of the basilar membrane but also an active amplification of the mechanical stimulus by the cochlear hair cells. The common view is that amplification stems from the somatic motility of the outer hair cells (OHCs), changes in their length impelled by voltage-dependent transitions in the membrane protein prestin. Whether this voltage-controlled mechanism, whose frequency range may be limited by the membrane time constant, has the band width to cover the entire auditory range of mammals is uncertain. However, there is ample evidence for an alternative mode of force generation by hair cells of non-mammals, such as frogs and turtles, which probably lack prestin. The latter process involves active motion of the hair bundle underpinned by conformational changes in the mechanotransducer (MT) channels and activation of one or more isoforms of myosin. This review summarizes evidence for active hair bundle motion and its connection to MT channel adaptation. Key factors for the hair bundle motor to play a role in the mammalian cochlea include the size and speed of force production.

Mechanoelectrical transduction and adaptation

The common substrates of both forward transduction and active hair bundle motion are the mechanotransducer (MT) channels located near the tips of ∼100 stereocilia that fashion the hair bundle. MT channels detect submicrometre displacements of the hair bundle by force thought to be transmitted via tip links between neighbouring stereocilia (Pickles et al. 1984; Assad et al. 1991). They are cation channels preferentially permeable to Ca²⁺ (Ohmori, 1985) with large unitary conductances of 100–300 pS under ionic conditions existing in vivo (Ricci et al. 2003; Géléoc et al. 1997; Beurg et al. 2006). In auditory end-organs, where hair cells at different locations respond to different characteristic frequencies (CF), the single-channel conductance varies systematically with CF. Both turtle hair cells and rat OHCs tuned to low frequencies possess small-conductance (∼100 pS) MT channels whereas cells tuned to high frequencies have larger conductance channels (Ricci et al. 2003; Beurg et al. 2006). The molecular composition of the MT channel has not yet been identified and the origin of the variable conductance is unknown. Owing to the high Ca²⁺ permeability of the MT channels, their opening by a mechanical stimulus promotes influx and intracellular accumulation of Ca²⁺. The local rise in Ca²⁺ acts as a feedback signal to implement adaptation or channel reclosure (Eatock, 2000; Fettiplace & Ricci, 2003). Adaptation is manifested as a decline in the transduction current during a sustained stimulus and a translation of the relationship between probability of opening (p_O) and displacement (X) along the X-axis in the direction of the stimulus (Fig. 1). One phase of adaptation occurs rapidly in a millisecond or two, but others take tens or hundreds of milliseconds. Whilst a general function of adaptation is to keep the MT channels within the most sensitive part of their operating range, fast adaptation may have a role in frequency tuning because in auditory organs its time constant varies inversely with hair cell CF (Ricci et al. 1998, 2003, 2005). The tonotopic variation in adaptation time constant is largely due to differences in MT channel unitary conductance: hair cells tuned to higher frequencies have larger single channel conductances permitting greater Ca²⁺ influx that will drive adaptation faster (Ricci et al. 2003).

Figure 1. Fast adaptation shifts the current–displacement relationship in a rat outer hair cell.

A, MT currents before (top) and immediately after (bottom) a 0.4 μm maintained adapting hair bundle step. Adaptation time constant for small responses is ∼100 μs. B, relationships between MT current (I) and bundle displacement (Δx) from A. Smooth curves calculated from a two state Boltzmann relation:

where X₀ = 0.26 μm, z₀ = 13 μm⁻¹ (control), X₀ = 0.55 μm, z₀ = 17 μm⁻¹ (after adaptation) and I_max = 0.9 nA for both. Holding potential −84 mV, CsCl intracellular. The control and test stimuli were interleaved, separated by a 35 ms delay as indicated by the time axes in A.

Slow adaptation is thought to require myosin-1c tugging on the top of the tip link to adjust the mechanical input to the channel (Gillespie & Cyr, 2004). During bundle deflection, an increase in intracellular Ca²⁺ causes myosin-1c to dissociate from actin, allowing the link's attachment point to slip down the stereocilium to produce adaptation. The role of myosin-1c in mouse vestibular hair cells is supported by experiments in which its ATP-binding site was mutated to confer susceptibility for inhibition by ADP analogues. Expression of mutant myosin-1c rendered slow adaptation vulnerable to block by ADP analogues introduced through the recording pipette (Holt et al. 2002). These same experiments have not yet been performed on cochlear hair cells and it is currently unknown whether OHCs have any slow adaptation based on myosin-1c. The mechanism of fast adaptation involves the MT channel or its anchoring to the cytoskeleton. Specific putative mechanisms include Ca²⁺ binding directly to the MT channel making it more difficult to open (Wu et al. 1999; Cheung & Corey, 2006) or Ca²⁺ slackening a series elastic element and hence relieving tension on the channel (Martin et al. 2003; Stauffer et al. 2005).

Passive and active components of hair bundle stiffness

Displacement of the hair bundle is produced in vivo by radial motion of the overlying tectorial membrane. Free-standing hair bundles can be manipulated by applying force stimuli with a calibrated flexible glass fibre that allows their stiffness to be quantified (Strelioff & Flock, 1984; Crawford & Fettiplace, 1985). These measurements have shown hair bundle stiffness to be non-linear with both passive and active components (Howard & Hudspeth, 1988; Russell et al. 1992; van Netten & Kros, 2000; Ricci et al. 2002; Cheung & Corey, 2006). The passive stiffness, K_p, stems from the flexibility of the stereociliary ankles, the interciliary connections, and the gating springs (Fig. 2). The active component is linked to the probability of opening (p_O) of the MT channels (Howard & Hudspeth, 1988) and contributes a negative term in the force equation. The relationship between the force, F_B, applied to the bundle and its displacement, X, is given by:

(1)

where A is the product of the single-channel gating force, z, and the number of channels per bundle, N. Typical values for N (100) and z (∼0.3 pN; Howard & Hudspeth, 1988; van Netten & Kros, 2000; Ricci et al. 2002) yield a value for A on the gating spring model of 30 pN. F_o is a constant force making F_B zero at the bundle's resting position, presumably attributable to the myosin motors tensioning the tip links.

Figure 2. Schematic diagram of hair cell mechanotransduction.

A, stereocilia along the excitatory axis of the hair bundle are connected by lateral links and tip links (Furness et al. 1997; Tsuprun & Santi, 2002). Radial deflection of the hair bundle bends the stereocilia at their ankles and increases tension in the tip links to activate one or two MT channels per tip link. The cap at the stereociliary tips represents the protein complex that anchors actin filaments to the plasma membrane. B, mechanical representation of hair bundle according to the gating spring model (Howard & Hudspeth, 1988). Force is delivered to the channel via gating springs whose tension is maintained by a myosin motor (M). Switching the channel from the open to closed state introduces a phenomenological compliance in series with the gating spring. K_S is the passive stiffness of the rootlets and lateral links, and R is the coefficient of viscous damping on the bundle that affects the time course of its motion.

The relative magnitudes of the passive and active components determine the prominence of the non-linearity (Fig. 3) which varies among preparations. At one extreme, the passive stiffness is much larger than the active one and the bundle approximates a simple spring (van Netten & Kros, 2000). At the other, the active component dominates the stiffness to the extent that over the range of displacements where the channel is gated, the stiffness becomes negative, a property that has been linked to spontaneous oscillations of the bundle (Martin et al. 2000). The diversity in force–displacement relationships at least partly reflects a difference in passive stiffness which, particularly in mammalian hair cells, is several millinewtons per metre, up to 10-fold larger than in frogs (Strelioff & Flock, 1984; van Netten & Kros, 2000; Kennedy et al. 2005). However, to produce non-linearity with a larger passive stiffness, the size of the channel component may also be larger than the 30 pN predicted from the gating spring model even in the turtle (Fig. 3B) where hair bundle mechanics should be similar to those in the frog for which the model was developed. Put another way, the maximum reduction in stiffness attributable to gating compliance using existing parameters is ∼0.6 mN m⁻¹, which would introduce a minor non-linearity in a bundle with a passive stiffness 5- to 10-fold larger. The reason for this departure from the model based on the frog measurements is unknown: it may reflect an underestimate in the single-channel gating force, z, or, especially in mammals, the recruitment of another mechanism of force generation associated with channel gating (Fig. 3C).

Figure 3. Probability of opening (p_o) of the MT channels and force versus bundle displacement relationships of hair bundles in different end organs.

A, frog saccular hair bundle (Martin et al. 2000) shows negative slope region for displacements in the range where the MT channels are gated. B, turtle auditory hair bundle (Ricci et al. 2002) with resting (black) and adapted (red) functions shows moderate non-linearity. C, rat OHC (Kennedy et al. 2005) showing the instantaneous (black) and time dependent (blue) relationship ∼1 ms after bundle deflection. p_O–Δx functions calculated from a two-state Boltzmann relation and force–Δx functions calculated from eqn (1). The p_O–Δx relationship for the rat OHC is broader probably because fast adaptation occurs during the stimulus onset. Passive stiffnesses: A, 0.5 mN m⁻¹; B, 3 mN m⁻¹; C, 3 mN m⁻¹.

Active hair bundle movements

The principal manifestations of active hair bundle movements are oscillations of free-standing bundles and non-linear responses to applied force stimuli. Spontaneous hair bundle oscillations have been reported in turtle and frog hair cells at frequencies of 5–80 Hz with amplitudes up to 50 nm (Crawford & Fettiplace, 1985; Howard & Hudspeth, 1987; Denk & Webb, 1992; Martin et al. 2003). The oscillation frequency can be increased by raising the external Ca²⁺ concentration, consistent with Ca²⁺ influx being a signal in the feedback pathway. Bundle oscillations are abolished (Martin et al. 2003) by blockers of the MT channel (e.g. gentamicin) and by agents that affected myosin motors (e.g. butanedione monoxime). Together these results have been used to argue that the oscillations arise from the negative stiffness of the hair bundle combined with the forces generated by the adaptation motors which bias the bundle towards its region of negative stiffness (Martin et al. 2000, 2003). The mechanism is reminiscent of spontaneous subthreshold oscillations in neuronal membrane potential (Jack et al. 1983; White et al. 1995), underpinned by an inward voltage-dependent Na⁺ or Ca²⁺ current (with a negative resistance region in the I–V relation analogous to the negative stiffness) and an outward voltage-dependent K⁺ current (providing negative feedback analogous to the hair bundle motor). In the intact cochlea, loading of the hair bundles by the tectorial membrane would increase the frequency and damping of their motion to the point where they would cease to be oscillatory but may still retain tuned resonant behaviour.

The bias forces supplied by the motors are evident when bundle movements are evoked by force stimuli imposed with a flexible fibre. Two time-dependent movements have been described with opposite polarity, and kinetics corresponding to fast and slow adaptation (Fig. 4A). For a positive stimulus that opens the MT channels, the fast response is in the negative direction and therefore opposes applied deflection of the bundle, whereas the slow movement is in the positive direction and reinforces the applied deflection. The slow movement may be a consequence of the myosin-based motor proposed to underlie slow adaptation (Howard & Hudspeth, 1987; Assad & Corey, 1992). Thus during a positive force stimulus to the bundle, the increase in tip link tension initially opens the channel but slipping of the upper attachment point of the link decreases the tension causing further displacement of the bundle. The fast movement, a recoil that opposes the stimulus (Benser et al. 1996; Ricci et al. 2000), is synchronous with channel reclosure attributed to fast adaptation. As with fast adaptation, the time constant of the fast recoil in turtle auditory hair cells is correlated with hair cell CF (Ricci et al. 2000).

Figure 4. Schematic hair bundle responses to force stimuli.

A, in frog and turtle hair cells, the MT current (middle) displays fast and slow phases of adaptation, the current declining from a peak with two time constants (1 and 15 ms). The fast phase is correlated with a rapid recoil in bundle position (Δx; bottom) followed by a slower positive creep. B, adaptation in a rat OHC is faster with a principal time constant of 0.2 ms correlated with a further positive motion in the same direction as the stimulus. Note that B has a 10-fold shorter time scale than A.

Active bundle movements in mammalian hair cells

Evidence for the existence and role of active bundle movements in mammalian cochlear hair cells is much sparser than in non-mammals, partly because of the greater difficulty of working with isolated mammalian preparations. Nevertheless, large transduction currents have been recorded from OHCs in such preparations (Kros et al. 1992; Kennedy et al. 2003; He et al. 2004; Ricci et al. 2005). These currents exhibit fast adaptation (Kros et al. 1992; Kennedy et al. 2003) with a time constant that, as in the turtle, decreases with CF (Ricci et al. 2005). However the kinetics of MT channel activation and adaptation are more than an order of magnitude faster than those in non-mammals (Ricci et al. 2005). Thus in excised preparations of rat cochlea, fast adaptation time constants of less than 100 microseconds have been measured in OHCs, while the time course of channel activation is too fast to be measured accurately. MT channel activation in vivo must occur within a few microseconds for hair cells to encode frequencies up to 100 kHz. Such performance would make it the ion channel with the fastest known kinetics.

The speed of transduction poses a problem because the fastest hair bundle deflection possible using an external glass probe still limits the activation kinetics. As a consequence, adaptation time constants are probably overestimated and the p_O–X relationship is broadened because the MT channels adapt during the slow rise time of the mechanical stimulus (at best ∼50 μs). Thus the p_O–X relation is shifting along the displacement axis even during channel activation. The problem is exacerbated when stimulating with a flexible fibre whose speed of attack is constrained by viscous drag. Force application with a laser trap may eventually circumvent this shortcoming but in its present mode the rise time is no faster than for a flexible fibre (Cheung & Corey, 2006). This kinetic limitation may explain why force stimulation has not so far revealed any fast mechanical recoil analogous to that seen in non-mammals. Nor is there any evidence for spontaneous bundle oscillations. However, when OHC hair bundles are deflected with a flexible fibre, a time-dependent creep in position resembling slow adaptation in frog saccular hair cells is seen, but with a time constant several orders of magnitude faster (Kennedy et al. 2005; Fig. 4B). Thus the force–displacement relationship becomes non-linear and acquires a negative slope region (Fig. 3C) with a submillisecond time constant comparable to fast adaptation. Also, like adaptation, it is sensitive to external Ca²⁺. The force–displacement relationship can be fitted with eqn (1) but requires a value of A that is time dependent and 100-fold larger than expected on the gating-spring model. The mechanism and significance of this process are still unknown. Taken at face value it implies that an OHC bundle can generate substantial force, 500–1000 pN, which might contribute positive mechanical feedback to reinforce motion of the tectorial membrane.

The magnitude of the force generated does not easily fit with the gating-spring models developed for frog hair cells and may involve a novel mechanism. An attempt to simulate the mammalian results (LeMasurier & Gillespie, 2005) required a much greater resting tension (F_O) of 500 pN that may be unrealistic. By comparison, the maximum tension exerted by the motors in frog hair cells has been estimated, by severing the tip-links with BAPTA, as up to ∼150 pN (Jaramillo & Hudspeth, 1993). It will be important to investigate whether the OHC bundles are held under high tension at rest, and explore possible mechanisms: does this resting tension involve larger clusters of myosin-1c, or another isoform such as myosin-7a which has also been implicated in OHC adaptation (Kros et al. 2002)? Nevertheless the finding that OHC hair bundles can generate significant force on the time scale of fast adaptation provides a mechanism for amplification. Moreover, since the time constant of fast adaptation varies with CF, the feedback force could occur in a frequency selective manner matched to the hair cell CF. Extrapolation of the adaptation time constants (τ_A) to conditions in vivo have suggested they correspond to corner frequencies (1/2πτ_A) close to the CF (Ricci et al. 2005).

Role of active bundle movements and cochlear amplification

Active bundle movements may be a byproduct of adaptation machinery whose primary role is to adjust the mechanical input and thereby set the operating range of a mechanically sensitive channel. Alternatively they might sum with the forces of the external stimulus providing amplification to enhance the signal-to-noise ratio of transduction especially near threshold. Amplification has been demonstrated by active motion of free standing hair bundles, but in the cochlea the bundles are restrained by attachment to the tectorial membrane. For the movements to fulfil a physiological role, the mechanical impedance of the hair bundle must be a significant fraction of the cochlear partition. In an in vitro gerbil cochlea, exposure of the hair bundles to 5 mm BAPTA, the main effect of which would be to destroy the tip links (Assad et al. 1991), caused a 20–40% reduction in the overall stiffness of the cochlear partition (Chan & Hudspeth, 2005b). This result implies that the OHC bundles, the only ones directly attached to the tectorial membrane, are a substantial fraction of the impedance of the partition. Consequently, stiffness changes or active motion of the bundles must affect the mechanics of the entire organ.

Direct evidence for the influence of the hair bundles on cochlear mechanics has come from measurements of their movements in the in vitro gerbil cochlea (Chan & Hudspeth, 2005a). The cochlea was sealed so that it could be acoustically stimulated to vibrate the basilar membrane, the motion of the cochlear partition being inferred by imaging inner hair cell bundles. The measured displacements were a saturating non-linear function of sound pressure that reflected low level amplification resembling that observed in the intact cochlea (Robles & Ruggero, 2001). The non-linearity was abolished by blocking the MT channels, but not by attenuating the receptor potentials by removing permeant monovalent cations, thus excluding the prestin motor as a source. Non-linear motion was also evoked in this preparation by applying voltage stimuli across the partition. The manoeuvre was assumed to evoke active hair bundle movements, as it does in non-mammals (Assad & Corey, 1992; Ricci et al. 2000), by hair cell depolarization reducing Ca²⁺ influx through the MET channels and thereby affecting the adaptation motors. However, the interpretation of these results is confounded in mammals by the additional effects of voltage on the prestin motor (Ashmore, 1987) to deform the organ of Corti (Mammano et al. 1995; Jia & He, 2005; Kennedy et al. 2006). Although electrical polarization of the hair cell epithelium has been previously deployed to study active force generation in the intact cochlea, it could work either by activating the prestin motor (Xue et al. 1995; Ren & Nuttall, 1995) or by evoking active hair bundle movements due to changing the driving force on current flowing through the MT channels (Yates & Kirk, 1998).

Conclusions

The large force developed by the hair bundle motor and its potential speed, if linked to fast adaptation, support a role in cochlear amplification. The kinetic limits of fast adaptation and force production have not yet been established, but in theory should be dictated by the rate of the MT channel transitions and by Ca²⁺ exit from the channel; to achieve frequencies of tens of kilohertz demands a very low affinity Ca²⁺-binding site. A faster mode of experimentally deflecting the bundle will be needed to define the kinetic limits of the process. An important difference between the two OHC motors is the phase of their force feedback. The bundle motor is in phase with the imposed deflection and produces the positive feedback necessary for amplification. In contrast, the somatic motor may supply negative feedback on the MT channels, equivalent to adaptation, to set their operating point. Thus depolarization induced by positive displacement of the hair bundle causes OHC shortening, pulling the reticular lamina towards the basilar membrane and reducing the angular deflection of bundles whose tips are fixed to the tectorial membrane (Dallos, 2003). The 180 deg phase lag of the somatic motor may strictly apply only to low frequencies of a few hundred Hertz where the OHC receptor potential is not low-pass filtered by the membrane time constant. Because both motors are in the feedback pathway, dissecting their contributions over different frequency ranges is not straightforward and manipulating one may influence the other. To address this question, new techniques (e.g. Fridberger et al. 2006) may be needed to visualize the cellular deformations and dynamic behaviour of the organ of Corti during acoustic stimulation.