Gating Spring Research Articles

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.

Molecular Organization of the Distal Cilium, a Potential Mechanotransduction Site, in Campaniform Receptor of Drosophila Melanogaster

The observation of a very short latency between stimulus and cell response in mechanosensation led to the gating-spring concept. The central idea is that the gating of mechanosensitive channels is directly controlled by a compliant structure, the gating spring. This model suggests a transduction apparatus based on the physical organization of several molecular components. We are studying the identities and organization of these molecular components by using campaniform receptor in fly as a model system. The distal cilium of campaniform receptor is in close proximity to the cuticle and directly connects to the extracellular matrix. We found that NOMPC, a candidate of the mechanotransduction channel, exclusively localizes to this region by immunofluorescence with an antibody against N-terminal of NOMPC. We also found that the electrical response of campaniform receptors is absent in nompC mutant. These observations suggest that the distal cilium is the transduction site in the campaniform receptor. Transmission EM of this region reveals a particular microtubule-based structure and membrane-microtubule connection (MMC), which we have analyzed quantitatively using image analysis software. This method was applied to several mutants. First, ultrastructural defects in both microtubule-based structure and MMC in this region were found in a nompC mutant, suggesting an important role of NOMPC in the structural organization of this region. Second, the microtubule-based structure in DCX-EMAP mutant is disrupted. Although the localization of NOMPC seems normal, the electrical response of campaniform receptor in DCX-EMAP mutant is altered in both amplitude and time course, suggesting that microtubule structure is involved in shaping the electrical response. In summary, our data provide further information about the general architecture of the transduction site in campaniform receptor and the possible roles of several molecular components in its organization.

Harmonin-b, an actin-binding scaffold protein, is involved in the adaptation of mechanoelectrical transduction by sensory hair cells

We assessed the involvement of harmonin-b, a submembranous protein containing PDZ domains, in the mechanoelectrical transduction machinery of inner ear hair cells. Harmonin-b is located in the region of the upper insertion point of the tip link that joins adjacent stereocilia from different rows and that is believed to gate transducer channel(s) located in the region of the tip link's lower insertion point. In Ush1c dfcr-2J/dfcr-2J mutant mice defective for harmonin-b, step deflections of the hair bundle evoked transduction currents with altered speed and extent of adaptation. In utricular hair cells, hair bundle morphology and maximal transduction currents were similar to those observed in wild-type mice, but adaptation was faster and more complete. Cochlear outer hair cells displayed reduced maximal transduction currents, which may be the consequence of moderate structural anomalies of their hair bundles. Their adaptation was slower and displayed a variable extent. The latter was positively correlated with the magnitude of the maximal transduction current, but the cells that showed the largest currents could be either hyperadaptive or hypoadaptive. To interpret our observations, we used a theoretical description of mechanoelectrical transduction based on the gating spring theory and a motor model of adaptation. Simulations could account for the characteristics of transduction currents in wild-type and mutant hair cells, both vestibular and cochlear. They led us to conclude that harmonin-b operates as an intracellular link that limits adaptation and engages adaptation motors, a dual role consistent with the scaffolding property of the protein and its binding to both actin filaments and the tip link component cadherin-23.Electronic supplementary materialThe online version of this article (doi:10.1007/s00424-009-0711-x) contains supplementary material, which is available to authorized users.

A mechanical model of the gating spring mechanism of stereocilia

The stereocilium is the basic sensory unit of nature's mechanotransducers, which include the cochlear and vestibular organs. In noisy environments, stereocilia display high sensitivity to miniscule stimuli, effectively dealing with a situation that is a design challenge in micro systems. The gating spring hypothesis suggests that the mechanical stiffness of stereocilia bundle is softened by tip-link gating in combination with active bundle movement, contributing to the nonlinear amplification of miniscule stimuli. To demonstrate that the amplification is induced mechanically by the gating as hypothesized, we developed a biomimetic model of stereocilia and fabricated the model at the macro scale. The model consists of an inverted pendulum array with bistable buckled springs at its tips, which represent the mechanically gated ion channel. Model simulations showed that at the moment of gating, instantaneous stiffness softening generates an increase in response magnitude, which then sequentially occurs as the number of gating increases. This amplification mechanism appeared to be robust to the change of model parameters. Experimental data from the fabricated macro model also showed a significant increase in the open probability and pendulum deflection at the region having a smaller input magnitude. The results demonstrate that the nonlinear amplification of miniscule stimuli is mechanically produced by stiffness softening from channel gating.

The Frequency Range of the Ear Supported by Hair Bundle Motility

The sensitivity of the ear depends on the mechanical feedback in hair cells. Here we examine two models of hair bundle motility by assuming that the energy gained by the hair bundle motor is greater than the energy loss due to viscous drag in the subtectorial gap. The channel re-closure (CRC) model (Choe et al., Proc. Natl. Acad. Sci. USA, 1998) leads to a frequency limit (kgxg)2ΦFm, where kg and xg are gating spring stiffness and gating distance of the mechanoelectric transducer (MET) channel, respectively, Φ the factor that depends on channel kinetics, and Fm(=Ns2/(hA)) the morphological factor with the number N of tip-links per hair cell, the rootlet separation s, the height h of the tallest cilia, and the area A of the gap. Tinevez-Jülicher-Martin (TJM) model (Tinevez et al., Biophys. J., 2007) leads to the frequency limit of the form a[bFm-1]1/2 with both a and b depend on transducer stiffness kg[1-kgxg2Po(1-Po)/(kBT)], which is required to be negative, and friction coefficient of the motor among others. The limiting frequency estimated for the mammalian ear under realistic conditions is up to 1.2 kHz based on CRC model and is up to 2.8 kHz based on TJM model, lower than the mammalian auditory range. If the mechanical characteristics of the MET channel and the adaptation motor are similar, the limiting frequency could be described by the morphological factor in both models, although TJM model is much more sensitive to the operating point. This feature could be used to explain the auditory range of the avian ears and their tonotopic maps by the morphological factor.

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 Ca 2+ 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 Ca 2+ 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 Ca 2+ binding kinetics. Spontaneous oscillations persisted, becoming very narrow-band, when the hair bundle was loaded with a tectorial membrane mass.

Transducer-Based Force Generation Explains Active Process in Drosophila Hearing

Like vertebrate hair cells, Drosophila auditory neurons are endowed with an active, force-generating process that boosts the macroscopic performance of the ear. The underlying force generator may be the molecular apparatus for auditory transduction, which, in the fly as in vertebrates, seems to consist of force-gated channels that occur in series with adaptation motors and gating springs. This molecular arrangement explains the active properties of the sensory hair bundles of inner-ear hair cells, but whether it suffices to explain the active macroscopic performance of auditory systems is unclear. To relate transducer dynamics and auditory-system behavior, we have devised a simple model of the Drosophila hearing organ that consists only of transduction modules and a harmonic oscillator that represents the sound receiver. In vivo measurements show that this model explains the ear's active performance, quantitatively capturing displacement responses of the fly's antennal sound receiver to force steps, this receiver's free fluctuations, its response to sinusoidal stimuli, nonlinearity, and activity and cycle-by-cycle amplification, and properties of electrical compound responses in the afferent nerve. Our findings show that the interplay between transduction channels and adaptation motors accounts for the entire macroscopic phenomenology of the active process in the Drosophila auditory system, extending transducer-based amplification from hair cells to fly ears and demonstrating that forces generated by transduction modules can suffice to explain active processes in ears.

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.

Chapter 14 - Models of Hair Cell Mechanotransduction

Hair cell mechanotransduction is based on a finely tuned machinery residing in the hair bundle, the hair cell's receptive organelle. The machinery consists of a transduction channel, an adaptation motor, the tip link, and many other components that reside in the stereocilia. The transduction channel is connected to and opened by a gating spring, for which there are several molecular candidates. The interplay among the motor, the spring, the channel, and the tip link assures that the channel is always working at its most sensitive point of this machine, allowing very fast responses to a force stimulus. This chapter addresses the mechanisms and molecular components underlying mechanotransduction, adaptation, and motility in the hair bundle. Bundle deflection in the excitatory direction is thought to increase tension in the tip link, which leads to an opening of the mechanoelectrical transduction channel, located close to the insertion site of the tip link.

A Conceptual Model of Micro Inertial Sensor Mimicking Amplifying Mechanism of the Hair Cells

The inner ear hair cells, the receptors sensing mechanical stimuli such as acoustic vibration and acceleration, achieve remarkably high sensitivity to miniscule stimuli by selectively amplifying small inputs. The gating springs hypothesis proposes that a phenomenon called negative stiffness is responsible for the nonlinear sensitivity. According to the hypothesis, the bundle becomes more sensitive in certain region as its stiffness changes due to the opening or closing of transduction channels, which in turn exert force in the same direction of the bundle’s displacement. In this study, we developed a conceptual model of an inertial sensor inspired by the inner ear hair cells, focusing on the hair cell’s amplifying mechanism known as negative stiffness. The negative stiffness was applied to a simple mass-spring-damper system with nonlinear spring derived from gating springs hypothesis. Sinusoidal stimuli of 0.1Hz~10Hz with magnitude of 1pN to 1000pN were applied to the system to match the dynamic range of vestibular organs. Simulation on this nonlinear model was performed on MATLAB, and power transfers and sensitivities in both transient and steady states were obtained and compared with those from the system with linear spring. Parameters were chosen in relation to those of the hair bundle to reproduce operating conditions of both the hair cells and micro inertial sensors. The suggested model displayed compressive nonlinear sensitivity resulting from selective amplification of smaller stimuli despite the energy loss due to large viscous damping typical in micro systems.

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 5300 pN/ μm, and the combined stiffness of shaft links binding two adjacent stereocilia of 750 ∼ 2250 pN/ μm. 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.

Mechano-electrical Transduction: New Insights into Old Ideas

The gating-spring theory of hair cell mechanotransduction channel activation was first postulated over twenty years ago. The basic tenets of this hypothesis have been reaffirmed in hair cells from both auditory and vestibular systems and across species. In fact, the basic findings have been reproduced in every hair cell type tested. A great deal of information regarding the structural, mechanical, molecular and biophysical properties of the sensory hair bundle and the mechanotransducer channel has accumulated over the past twenty years. The goal of this review is to investigate new data, using the gating spring hypothesis as the framework for discussion. Mechanisms of channel gating are presented in reference to the need for a molecular gating spring or for tethering to the intra- or extracellular compartments. Dynamics of the sensory hair bundle and the presence of motor proteins are discussed in reference to passive contributions of the hair bundle to gating compliance. And finally, the molecular identity of the channel is discussed in reference to known intrinsic properties of the native transducer channel.

Aminoglycoside ototoxicity: permeant drugs cause permanent hair cell loss

Aminoglycoside ototoxicity: permeant drugs cause permanent hair cell loss

Fast Adaptation in Vestibular Hair Cells Requires Myosin-1c Activity

In sensory hair cells of the inner ear, mechanical amplification of small stimuli requires fast adaptation, the rapid closing of mechanically activated transduction channels. In frog and mouse vestibular hair cells, we found that the rate of fast adaptation depends on both channel opening and stimulus size and that it is modeled well as a release of a mechanical element in series with the transduction apparatus. To determine whether myosin-1c molecules of the adaptation motor are responsible for the release, we introduced the Y61G mutation into the Myo1c locus and generated mice homozygous for this sensitized allele. Measuring transduction and adaptation in the presence of NMB-ADP, an allele-specific inhibitor, we found that the inhibitor not only blocked slow adaptation, as demonstrated previously in transgenic mice, but also inhibited fast adaptation. These results suggest that mechanical activity of myosin-1c is required for fast adaptation in vestibular hair cells.

In Search of the Hair-Cell Gating Spring

Mechanotransduction in vertebrate hair cells involves a biophysically defined elastic element (the "gating spring") that pulls on the transduction channels. The tip link, a fine filament made of cadherin 23 linking adjacent stereocilia in hair-cell bundles, has been suggested to be the gating spring. However, TRP channels that mediate mechanotransduction in Drosophila, zebrafish, and mice often have cytoplasmic domains containing a large number of ankyrin repeats that are also candidates for the gating spring. We have explored the elastic properties of cadherin and ankyrin repeats through molecular dynamics simulations using crystallographic structures of proteins with one cadherin repeat or 4 and 12 ankyrin repeats, and using models of 17 and 24 ankyrin repeats. The extension and stiffness of large ankyrin-repeat structures were found to match those predicted by the gating-spring model. Our results suggest that ankyrin repeats of TRPA1 and TRPN1 channels serve as the gating spring for mechanotransduction.

Myo1c is designed for the adaptation response in the inner ear.

The molecular motor, Myo1c, a member of the myosin family, is widely expressed in vertebrate tissues. Its presence at strategic places in the stereocilia of the hair cells in the inner ear and studies using transgenic mice expressing a mutant Myo1c that can be selectively inhibited implicate it as the mediator of slow adaptation of mechanoelectrical transduction, which is required for balance. Here, we have studied the structural, mechanical and biochemical properties of Myo1c to gain an insight into how this molecular motor works. Our results support a model in which Myo1c possesses a strain-sensing ADP-release mechanism, which allows it to adapt to mechanical load.

Hypothesis: A helix of ankyrin repeats of the NOMPC-TRP ion channel is the gating spring of mechanoreceptors

The authors thank Vann Bennett for an illuminating discussion on the mechanics of ankyrin, Mayte Pisabarro for help with molecular modeling, and Peter Gillespie, A.J. Hudspeth and M. Landolfa for comments on an earlier draft of the manuscript.

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.

High-resolution structure of hair-cell tip links.

Transduction-channel gating by hair cells apparently requires a gating spring, an elastic element that transmits force to the channels. To determine whether the gating spring is the tip link, a filament interconnecting two stereocilia along the axis of mechanical sensitivity, we examined the tip link's structure at high resolution by using rapid-freeze, deep-etch electron microscopy. We found that the tip link is a right-handed, coiled double filament that usually forks into two branches before contacting a taller stereocilium; at the other end, several short filaments extend to the tip link from the shorter stereocilium. The structure of the tip link suggests that it is either a helical polymer or a braided pair of filamentous macromolecules and is thus likely to be relatively stiff and inextensible. Such behavior is incompatible with the measured elasticity of the gating spring, suggesting that the gating spring instead lies in series with the helical segment of the tip link.

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.