Stereocilia membrane deformation: implications for the gating spring and mechanotransduction channel

In hair cells, although mechanotransduction channels have been localized to tips of shorter stereocilia of the mechanically sensitive hair bundle, little is known about how force is transmitted to the channel. Here, we use a biophysical model of the membrane-channel complex to analyze the nature of the gating spring compliance and channel arrangement. We use a triangulated surface model and Monte Carlo simulation to compute the deformation of the membrane under the action of tip link force. We show that depending on the gating spring stiffness, the compliant component of the gating spring arises from either the membrane alone or a combination of the membrane and a tether that connects the channel to the actin cytoskeleton. If a bundle is characterized by relatively soft gating springs, such as those of the bullfrog sacculus, the need for membrane reinforcement by channel tethering then depends on membrane parameters. With stiffer gating springs, such as those from rat outer hair cells, the channel must be tethered for all biophysically realistic parameters of the membrane. We compute the membrane forces (resultants), which depend on membrane tension, bending modulus, and curvature, and show that they can determine the fate of the channel.     

Mechanical properties and consequences of stereocilia and extracellular links in vestibular hair bundles

Although knowledge of the fine structure of vestibular hair bundles is increasing, the mechanical properties and functional significance of those structures remain unclear. In 2004, Bashtanov and colleagues reported the contribution of different extracellular links to bundle stiffness. We simulated Bashtanov's experimental protocol using a three-dimensional finite element bundle model with geometry measured from a typical striolar hair cell. Unlike any previous models, we separately consider two types of horizontal links: shaft links and upper lateral links. Our most important results are as follows. First, we identified the material properties required to match Bashtanov's experiment: stereocilia Young's modulus of 0.74 GPa, tip link assembly (gating spring) stiffness of 5,300 pN/microm, and the combined stiffness of shaft links binding two adjacent stereocilia of 750 approximately 2,250 pN/microm. Second, we conclude that upper lateral links are likely to have nonlinear mechanical properties: they have minimal stiffness during small bundle deformations but stiffen as the bundle deflects further. Third, we estimated the stiffness of the gating spring based on our realistic three-dimensional bundle model rather than a conventional model relying on the parallel arrangement assumption. Our predicted stiffness of the gating spring was greater than the previous estimation.     

Theoretical conditions for high-frequency hair bundle oscillations in auditory hair cells

Substantial evidence exists for spontaneous oscillations of hair cell stereociliary bundles in the lower vertebrate inner ear. Since the oscillations are larger than expected from Brownian motion, they must result from an active process in the stereociliary bundle suggested to underlie amplification of the sensory input as well as spontaneous otoacoustic emissions. However, their low frequency (<100 Hz) makes them unsuitable for amplification in birds and mammals that hear up to 5 kHz or higher. To examine the possibility of high-frequency oscillations, we used a finite-element model of the outer hair cell bundle incorporating previously measured mechanical parameters. Bundle motion was assumed to activate mechanotransducer channels according to the gating spring hypothesis, and the channels were regulated adaptively by Ca²⁺ binding. The model generated oscillations of freestanding bundles at 4 kHz whose sharpness of tuning depended on the mechanotransducer channel number and location, and the Ca²⁺ concentration. Entrainment of the oscillations by external stimuli was used to demonstrate nonlinear amplification. The oscillation frequency depended on channel parameters and was increased to 23 kHz principally by accelerating Ca²⁺ binding kinetics. Spontaneous oscillations persisted, becoming very narrow-band, when the hair bundle was loaded with a tectorial membrane mass.     

Unconventional Mechanics of Lipid Membranes: A Potential Role for Mechanotransduction of Hair Cell Stereocilia

A force-conveying role of the lipid membrane across various mechanoreceptors is now an accepted hypothesis. However, such a mechanism is still not fully understood for mechanotransduction in the hair bundle of auditory sensory hair cells. A major goal of this theoretical assessment was to investigate the role of the lipid membrane in auditory mechanotransduction, especially in generating nonlinear bundle force versus displacement measurements, one of the main features of auditory mechanotransduction. To this end, a hair bundle model that generates lipid membrane tented deformation in the stereocilia was developed. A computational analysis of the model not only reproduced nonlinear bundle force measurements but also generated membrane energy that is potentially sufficient to activate the mechanosensitive ion channel of the hair cell. In addition, the model provides biophysical insight into 1) the likelihood that the channel must be linked in some way to the tip link; 2) how the interplay of the bending and stretching of the lipid bilayer may be responsible for the nonlinear force versus displacement response; 3) how measurements of negative stiffness may be a function of the rotational stiffness of the rootlets; and 4) how the standing tension of the tip link is required to interpret migration of the nonlinear force versus displacement and activation curves. These are all features of hair cell mechanotransduction, but the underlying biophysical mechanism has proved elusive for the last three decades.     

Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell

Mechanical stimuli are thought to open the transduction channels of a hair cell by tensing elastic components, the gating springs, that pull directly on the channels. To test this model, we measured the stiffness of hair bundles during mechanical stimulation. A bundle's compliance increased by about 40% at the position where half of the channels opened. This we attribute to conformational changes of transduction channels as they open and close. The magnitude and displacement dependence of the gating compliance provide quantitative information about the molecular basis of mechanoelectrical transduction: the force required to open each channel, the number of transduction channels per hair cell, the stiffness of a gating spring, and the swing of a channel's gate as it opens.     

Gating of Two Mechanoelectrical Transducer Channels Associated with a Single Tip Link

Although gating of mechanoelectrical transducer (MET) channels has been successfully described by assuming that one channel is associated with a tip link in the hair bundle, recent reports indicate that a single tip link is associated with more than one channel. To address the consistency of the model with the observations, gating of MET channels is described here by assuming that each tip link is associated with two identical MET channels, which are connected either in series or in parallel. We found that series connection does not lead to a single minimum of stiffness with respect to hair bundle displacement unless the minimum is above a certain positive value. Thus, negative stiffness must appear in pairs in the displacement axis. In contrast, parallel connection of the two channels predicts gating compliance similar to that predicted by the one-channel-per-tip-link model of channel gating, within the physiological range of parameters. Parallel connection of MET channels is, therefore, a reasonable assumption to explain most experimental observations. However, the compatibility with series connection cannot be ruled out for experimental data on turtle hair cells.     

Sound-evoked deflections of outer hair cell stereocilia arise from tectorial membrane anisotropy

The exceptional performance of mammalian hearing is due to the cochlea's amplification of sound-induced mechanical stimuli. During acoustic stimulation, the vertical motion of the outer hair cells relative to the tectorial membrane (TM) is converted into the lateral motion of their stereocilia. The actual mode of this conversion, which represents a fundamental step in hearing, remains enigmatic, as it is unclear why the stereocilia are deflected when pressed against the TM, rather than penetrating it. In this study we show that deflection of the stereocilia is a direct outcome of the anisotropic material properties of the TM. Using force spectroscopy, we find that the vertical stiffness of the TM is significantly larger than its lateral stiffness. As a result, the TM is more resistant to the vertical motion of stereocilia than to their lateral motion, and so they are deflected laterally when pushed against the TM. Our findings are confirmed by finite element simulations of the mechanical interaction between the TM and stereocilia, which show that the vertical outer hair cells motion is converted into lateral stereocilia motion when the experimentally determined stiffness values are incorporated into the model. Our results thus show that the material properties of the TM play a central and previously unknown role in mammalian hearing.     

The Local Forces Acting on the Mechanotransduction Channel in Hair Cell Stereocilia

In hair cells, mechanotransduction channels are located in the membrane of stereocilia tips, where the base of the tip link is attached. The tip-link force determines the system of other forces in the immediate channel environment, which change the channel open probability. This system of forces includes components that are out of plane and in plane relative to the membrane; the magnitude and direction of these components depend on the channel environment and arrangement. Using a computational model, we obtained the major forces involved as functions of the force applied via the tip link at the center of the membrane. We simulated factors related to channels and the membrane, including finite-sized channels located centrally or acentrally, stiffness of the hypothesized channel-cytoskeleton tether, and bending modulus of the membrane. Membrane forces are perpendicular to the directions of the principal curvatures of the deformed membrane. Our approach allows for a fine vectorial picture of the local forces gating the channel; membrane forces change with the membrane curvature and are themselves sufficient to affect the open probability of the channel.     

The Local Forces Acting on the Mechanotransduction Channel in Hair Cell Stereocilia

In hair cells, mechanotransduction channels are located in the membrane of stereocilia tips, where the base of the tip link is attached. The tip-link force determines the system of other forces in the immediate channel environment, which change the channel open probability. This system of forces includes components that are out of plane and in plane relative to the membrane; the magnitude and direction of these components depend on the channel environment and arrangement. Using a computational model, we obtained the major forces involved as functions of the force applied via the tip link at the center of the membrane. We simulated factors related to channels and the membrane, including finite-sized channels located centrally or acentrally, stiffness of the hypothesized channel-cytoskeleton tether, and bending modulus of the membrane. Membrane forces are perpendicular to the directions of the principal curvatures of the deformed membrane. Our approach allows for a fine vectorial picture of the local forces gating the channel; membrane forces change with the membrane curvature and are themselves sufficient to affect the open probability of the channel.     

Stereocilium injury mediates hair bundle stiffness loss and recovery following intense water-jet stimulation

Inner ear hair cells exhibit many pathologies following exposure to intense sound, and the hair bundle is a major site of damage. This paper measures in vitro hair bundle motion on chick cochlear hair cells after intense in vitro and in vivo stimulation to explore the nature of hair bundle injury. Hair bundle stiffness, as well as relative and asymmetric motion of individual stereocilia, is controlled largely by the extracellular tip links, and a change in hair bundle motion was used to assess tip-link destruction following overstimulation. Intense in vitro stimulation caused a loss in stiffness that fully recovered within 10 min post-exposure. Relative and asymmetric stereocilia motion, however, were unchanged following the exposure, implying that tip links remained intact while the core or rootlet of the stereocilia were damaged and subsequently repaired. Intense and prolonged in vivo sound exposures produced stereocilia movements, measured in vitro, that were indicative of damage to stereocilia and tip links. Finally, the relative susceptibility of hair bundles to overstimulation was addressed by comparing stiffness loss with morphological features in the hair bundles. The loss of stiffness significantly increased as the amount of curvature in the hair bundle contour increased.     

The actions of calcium on hair bundle mechanics in mammalian cochlear hair cells

Sound stimuli excite cochlear hair cells by vibration of each hair bundle, which opens mechanotransducer (MT) channels. We have measured hair-bundle mechanics in isolated rat cochleas by stimulation with flexible glass fibers and simultaneous recording of the MT current. Both inner and outer hair-cell bundles exhibited force-displacement relationships with a nonlinearity that reflects a time-dependent reduction in stiffness. The nonlinearity was abolished, and hair-bundle stiffness increased, by maneuvers that diminished calcium influx through the MT channels: lowering extracellular calcium, blocking the MT current with dihydrostreptomycin, or depolarizing to positive potentials. To simulate the effects of Ca²⁺, we constructed a finite-element model of the outer hair cell bundle that incorporates the gating-spring hypothesis for MT channel activation. Four calcium ions were assumed to bind to the MT channel, making it harder to open, and, in addition, Ca²⁺ was posited to cause either a channel release or a decrease in the gating-spring stiffness. Both mechanisms produced Ca²⁺ effects on adaptation and bundle mechanics comparable to those measured experimentally. We suggest that fast adaptation and force generation by the hair bundle may stem from the action of Ca²⁺ on the channel complex and do not necessarily require the direct involvement of a myosin motor. The significance of these results for cochlear transduction and amplification are discussed.     

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.     

Mechano-electrical transducer currents in hair cells of the cultured neonatal mouse cochlea.

The first step towards the generation of the receptor potential in hair cells is the gating of the transducer channels and subsequent flow of transducer current, induced by deflection of the stereocilia. We describe properties of the transducer current in outer hair cells of neonatal mice. Less extensive observations on inner hair cells suggest that their transducer currents have similar characteristics. The hair bundles were stimulated by force from a fluid jet. The transducer currents in outer hair cells are the largest found so far in any hair cell, with a chord conductance of up to 9.2 nS at -84 mV. The transfer function suggests that the channel has at least two closed states and one open state. The permeabilities for sodium, potassium and caesium are similar, consistent with the channel being a fairly non-selective cation channel. At negative potentials the currents adapt in most cells, although never as completely as in hair cells of lower vertebrates. If the unit conductance of the transducer channel is similar to that of the turtle's auditory hair cells (100 pS), then there are about 90 channels per hair bundle, or one channel between every pair of adjacent stereocilia in neighbouring rows.     

Simulation of the response of the inner hair cell stereocilia bundle to an acoustical stimulus

Mammalian hearing relies on a cochlear hydrodynamic sensor embodied in the inner hair cell stereocilia bundle. It is presumed that acoustical stimuli induce a fluid shear-driven motion between the tectorial membrane and the reticular lamina to deflect the bundle. It is hypothesized that ion channels are opened by molecular gates that sense tension in tip-links, which connect adjacent stepped rows of stereocilia. Yet almost nothing is known about how the fluid and bundle interact. Here we show using our microfluidics model how each row of stereocilia and their associated tip links and gates move in response to an acoustical input that induces an orbital motion of the reticular lamina. The model confirms the crucial role of the positioning of the tectorial membrane in hearing, and explains how this membrane amplifies and synchronizes the timing of peak tension in the tip links. Both stereocilia rotation and length change are needed for synchronization of peak tip link tension. Stereocilia length change occurs in response to accelerations perpendicular to the oscillatory fluid shear flow. Simulations indicate that nanovortices form between rows to facilitate diffusion of ions into channels, showing how nature has devised a way to solve the diffusive mixing problem that persists in engineered microfluidic devices.     

H bonding at the helix-bundle crossing controls gating in Kir potassium channels

Specific stimuli such as intracellular H+ and phosphoinositides (e.g., PIP2) gate inwardly rectifying potassium (Kir) channels by controlling the reversible transition between the closed and open states. This gating mechanism underlies many aspects of Kir channel physiology and pathophysiology; however, its structural basis is not well understood. Here, we demonstrate that H+ and PIP2 use a conserved gating mechanism defined by similar structural changes in the transmembrane (TM) helices and the selectivity filter. Our data support a model in which the gating motion of the TM helices is controlled by an intrasubunit hydrogen bond between TM1 and TM2 at the helix-bundle crossing, and we show that this defines a common gating motif in the Kir channel superfamily. Furthermore, we show that this proposed H-bonding interaction determines Kir channel pH sensitivity, pH and PIP2 gating kinetics, as well as a K+-dependent inactivation process at the selectivity filter and therefore many of the key regulatory mechanisms of Kir channel physiology.     

Putative immunolocalization of the mechanoelectrical transduction channels in mammalian cochlear hair cells.

Hair cells bear an apical bundle of stereocilia arranged in serried rows. Deflection of the bundle controls the opening and closing of mechanoelectrical transduction channels, thereby altering the conductance across the apical plasma membrane. Two locations for these channels have been proposed in the bundle, either near the bases of the stereocilia or towards their tips. One hypothesis that is consistent with the latter possibility suggests that fine extracellular filaments, which run between the tips of the shorter stereocilia and the sides of the taller stereocilia behind, operate the channels. Determining the precise position of the channels is essential to test this hypothesis. We have therefore attempted to localize them immunocytochemically. Because hair-cell transduction is amiloride sensitive, the channels may have an amiloride-binding site associated with them. We have therefore used a polyclonal antibody raised against another amiloride-sensitive ion channel to hunt for them. This antibody recognizes a 62-64 kDa band in immunoblots of cochlear tissue, and produces discrete labelling in the hair bundle. This is most concentrated just below the tips of the shorter stereocilia, coinciding with a region of specialization in the closely apposed membranes of the short and tall stereocilia but not with either end of the tip link.     

Coupling active hair bundle mechanics, fast adaptation, and somatic motility in a cochlear model

One of the central questions in the biophysics of the mammalian cochlea is determining the contributions of the two active processes, prestin-based somatic motility and hair bundle (HB) motility, to cochlear amplification. HB force generation is linked to fast adaptation of the transduction current via a calcium-dependent process and somatic force generation is driven by the depolarization caused by the transduction current. In this article, we construct a global mechanical-electrical-acoustical mathematical model of the cochlea based on a three-dimensional fluid representation. The global cochlear model is coupled to linearizations of nonlinear somatic motility and HB activity as well as to the micromechanics of the passive structural and electrical elements of the cochlea. We find that the active HB force alone is not sufficient to power high frequency cochlear amplification. However, somatic motility can overcome resistor-capacitor filtering by the basolateral membrane and deliver sufficient mechanical energy for amplification at basal locations. The results suggest a new theory for high frequency active cochlear mechanics, in which fast adaptation controls the transduction channel sensitivity and thereby the magnitude of the energy delivered by somatic motility.     

Lateral mechanical coupling of stereocilia in cochlear hair bundles

For understanding the gating process of transduction channels in the inner ear it is essential to characterize and examine the functional properties of the ultrastructure of stereociliary bundles. There is strong evidence that transduction channels in hair cells are gated by directly pulling at the so-called tip links. In addition to these tip links a second class of filamentous structures was identified in the scanning and transmission electron microscope: the side-to-side links. These links laterally connect stereocilia of the same row of a hair bundle. This study concentrates on mechanical coupling of stereocilia of the tallest row connected by side-to-side links. Atomic Force microscopy (AFM) was used to investigate hair bundles of outer hair cells (OHCs) from postnatal rats (day 4). Although hair bundles of postnatal rats are still immature at day 4 and interconnecting cross-links do not show preferential direction yet, hair bundles of investigated OHCs already showed the characteristic V-shape of mature hair cells. In a first experiment, the stiffness of stereocilia was investigated scanning individual stereocilia with an AFM tip. The spring constant for the excitatory direction was 2.5 +/- 0.6 x 10(-3) N/m whereas a higher spring constant (3.1 +/- 1.5 x 10(-3) N/m) was observed in the inhibitory direction. In a second set of experiments, the force transmission between stereocilia of the tallest row was measured using AFM in combination with a thin glass fiber. This fiber locally displaced a stereocilium while the force laterally transmitted to the neighboring untouched taller stereocilia was measured by AFM. The results show a weak force interaction between tallest stereocilia of postnatal rats. The force exerted to an individual stereocilium declines to 36% at the nearest adjacent stereocilium of the same row not touched with the fiber. It is suggested that the amount of force transmitted from a taller stereocilium to an adjacent one of the same row depends on the orientation of links. Maximum force transmission is expected to appear along the axis of interconnecting side links. In our studies it is suggested that transmitted forces are small because connecting side links are oriented very close to an angle of 90 degrees with respect of the scan direction (excitatory-inhibitory direction).     

Molecular mechanisms underlying function of hair bundle: study on genetic deafness in mouse models

Although the basic principles for the function of peripheral auditory system have been known for many years, the molecular mechanisms which affect deafness are not clear. In recent years, the study of hereditary deafness associated mouse models has revealed the molecular basis which is related with the formation and function of the hair bundle and the mechanosensory organelle of hair cell. This review focused on the role of protein network, which is formed by the proteins encoded by the Usher syndrome type 1 genes, in hair-bundle development and mechanotransducer channel gating. And the review also showed how the stereocilia rootlets contribute to the hair bundle's mechanical properties and how the hair bundle produces suppressive masking. Finally, the review revealed multiple roles of the tectorial membrane and extracellular matrix in the hair bundles stimulating in the cochlea.     

Dynamic compartmentalization of protein tyrosine phosphatase receptor Q at the proximal end of stereocilia: implication of myosin VI-based transport

Hair cell stereocilia are apical membrane protrusions filled with uniformly polarized actin filament bundles. Protein tyrosine phosphatase receptor Q (PTPRQ), a membrane protein with extracellular fibronectin repeats has been shown to localize at the stereocilia base and the apical hair cell surface, and to be essential for stereocilia integrity. We analyzed the distribution of PTPRQ and a possible mechanism for its compartmentalization. Using immunofluorescence we demonstrate that PTPRQ is compartmentalized at the stereocilia base with a decaying gradient from base to apex. This distribution can be explained by a model of transport directed toward the stereocilia base, which counteracts diffusion of the molecules. By mathematical analysis, we show that this counter transport is consistent with the minus end-directed movement of myosin VI along the stereocilia actin filaments. Myosin VI is localized at the stereocilia base, and exogenously expressed myosin VI and PTPRQ colocalize in the perinuclear endosomes in COS-7 cells. In myosin VI-deficient mice, PTPRQ is distributed along the entire stereocilia. PTPRQ-deficient mice show a pattern of stereocilia disruption that is similar to that reported in myosin VI-deficient mice, where the predominant features are loss of tapered base, and fusion of adjacent stereocilia. Thin section and freeze-etching electron microscopy showed that localization of PTPRQ coincides with the presence of a dense cell surface coat. Our results suggest that PTPRQ and myosin VI form a complex that dynamically maintains the organization of the cell surface coat at the stereocilia base and helps maintain the structure of the overall stereocilia bundle.