A virtual hair cell, II: evaluation of mechanoelectric transduction parameters

The virtual hair cell we have proposed utilizes a set of parameters related to its mechanoelectric transduction. In this work, we observed the effect of such channel gating parameters as the gating threshold, critical tension, resting tension, and Ca(2+) concentration. The gating threshold is the difference between the resting and channel opening tension exerted by the tip link assembly on the channel. The critical tension is the tension in the tip link assembly over which the channel cannot close despite Ca(2+) binding. Our results show that 1), the gating threshold dominated the initial sensitivity of the hair cell; 2), the critical tension minimally affects the peak response, (I), but considerably affects the time course of response, I(t), and the force-displacement, F-X, relationship; and 3), higher intracellular [Ca(2+)] resulted in a smaller fast adaptation time constant. Based on the simulation results we suggest a role of the resting tension: to help overcome the viscous drag of the hair bundle during the oscillatory movement of the bundle. Also we observed the three-dimensional bundle effect on the hair cell response by varying the number of cilia forced. These varying forcing conditions affected the hair cell response.     

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.     

The calcium-activated potassium channels of turtle hair cells

A major factor determining the electrical resonant frequency of turtle cochlear hair cells is the time course of the Ca-activated K current (Art, J. J., and R. Fettiplace. 1987. Journal of Physiology. 385:207- 242). We have examined the notion that this time course is dictated by the K channel kinetics by recording single Ca-activated K channels in inside-out patches from isolated cells. A hair cell's resonant frequency was estimated from its known correlation with the dimensions of the hair bundle. All cells possess BK channels with a similar unit conductance of approximately 320 pS but with different mean open times of 0.25-12 ms. The time constant of relaxation of the average single- channel current at -50 mV in 4 microM Ca varied between cells from 0.4 to 13 ms and was correlated with the hair bundle height. The magnitude and voltage dependence of the time constant agree with the expected behavior of the macroscopic K(Ca) current, whose speed may thus be limited by the channel kinetics. All BK channels had similar sensitivities to Ca which produced half-maximal activation for a concentration of approximately 2 microM at +50 mV and 12 microM at -50 mV. We estimate from the voltage dependence of the whole-cell K(Ca) current that the BK channels may be fully activated at -35 mV by a rise in intracellular Ca to 50 microM. BK channels were occasionally observed to switch between slow and fast gating modes which raises the possibility that the range of kinetics of BK channels observed in different hair cells reflects a common channel protein whose kinetics are regulated by an unidentified intracellular factor. Membrane patches also contained 30 pS SK channels which were approximately 5 times more Ca-sensitive than BK channels at -50 mV. The SK channels may underlie the inhibitory synaptic potential produced in hair cells by efferent stimulation.     

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.     

Friction from Transduction Channels’ Gating Affects Spontaneous Hair-Bundle Oscillations

Hair cells of the inner ear can power spontaneous oscillations of their mechanosensory hair bundle, resulting in amplification of weak inputs near the characteristic frequency of oscillation. Recently, dynamic force measurements have revealed that delayed gating of the mechanosensitive ion channels responsible for mechanoelectrical transduction produces a friction force on the hair bundle. The significance of this intrinsic source of dissipation for the dynamical process underlying active hair-bundle motility has remained elusive. The aim of this work is to determine the role of friction in spontaneous hair-bundle oscillations. To this end, we characterized key oscillation properties over a large ensemble of individual hair cells and measured how viscosity of the endolymph that bathes the hair bundles affects these properties. We found that hair-bundle movements were too slow to be impeded by viscous drag only. Moreover, the oscillation frequency was only marginally affected by increasing endolymph viscosity by up to 30-fold. Stochastic simulations could capture the observed behaviors by adding a contribution to friction that was 3?8-fold larger than viscous drag. The extra friction could be attributed to delayed changes in tip-link tension as the result of the finite activation kinetics of the transduction channels. We exploited our analysis of hair-bundle dynamics to infer the channel activation time, which was ～1 ms. This timescale was two orders-of-magnitude shorter than the oscillation period. However, because the channel activation time was significantly longer than the timescale of mechanical relaxation of the hair bundle, channel kinetics affected hair-bundle dynamics. Our results suggest that friction from channel gating affects the waveform of oscillation and that the channel activation time can tune the characteristic frequency of the hair cell. We conclude that the kinetics of transduction channels’ gating plays a fundamental role in the dynamic process that shapes spontaneous hair-bundle oscillations.     

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.     

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.     

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.     

Effectiveness of Hair Bundle Motility as the Cochlear Amplifier

The effectiveness of hair bundle motility in mammalian and avian ears is studied by examining energy balance for a small sinusoidal displacement of the hair bundle. The condition that the energy generated by a hair bundle must be greater than energy loss due to the shear in the subtectorial gap per hair bundle leads to a limiting frequency that can be supported by hair-bundle motility. Limiting frequencies are obtained for two motile mechanisms for fast adaptation, the channel re-closure model and a model that assumes that fast adaptation is an interplay between gating of the channel and the myosin motor. The limiting frequency obtained for each of these models is an increasing function of a factor that is determined by the morphology of hair bundles and the cochlea. Primarily due to the higher density of hair cells in the avian inner ear, this factor is ∼10-fold greater for the avian ear than the mammalian ear, which has much higher auditory frequency limit. This result is consistent with a much greater significance of hair bundle motility in the avian ear than that in the mammalian ear.     

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.     

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.     

Linker-gating ring complex as passive spring and Ca(2+)-dependent machine for a voltage- and Ca(2+)-activated potassium channel

Ion channels are proteins that control the flux of ions across cell membranes by opening and closing (gating) their pores. It has been proposed that channels gated by internal agonists have an intracellular gating ring that extracts free energy from agonist binding to open the gates using linkers that directly connect the gating ring to the gates. Here we find for a voltage- and Ca(2+)-activated K+ (BK) channel that shortening the linkers increases channel activity and lengthening the linkers decreases channel activity, both in the presence and absence of intracellular Ca2+. These observations are consistent with a mechanical model in which the linker-gating ring complex forms a passive spring that applies force to the gates in the absence of Ca2+ to modulate the voltage-dependent gating. Adding Ca2+ then changes the force to further activate the channel. Both the passive and Ca(2+)-induced forces contribute to the gating of the channel.     

Crystal structures of a ligand-free MthK gating ring: insights into the ligand gating mechanism of K+ channels

MthK is a prokaryotic Ca(2+)-gated K(+) channel that, like other ligand-gated channels, converts the chemical energy of ligand binding to the mechanical force of channel opening. The channel's eight ligand-binding domains, the RCK domains, form an octameric gating ring in which Ca(2+) binding induces conformational changes that open the channel. Here we present the crystal structures of the MthK gating ring in closed and partially open states at 2.8 A, both obtained from the same crystal grown in the absence of Ca(2+). Furthermore, our biochemical and electrophysiological analyses demonstrate that MthK is regulated by both Ca(2+) and pH. Ca(2+) regulates the channel by changing the equilibrium of the gating ring between closed and open states, while pH regulates channel gating by affecting gating-ring stability. Our findings, along with the previously determined open MthK structure, allow us to elucidate the ligand gating mechanism of RCK-regulated K(+) channels.     

Single-channel, macroscopic, and gating currents from sodium channels in the squid giant axon.

Single-channel, macroscopic ionic, and macroscopic gating currents were recorded from the voltage-dependent sodium channel using patch-clamp techniques on the cut-open squid giant axon. To obtain a complete set of physiological measurements of sodium channel gating under identical conditions, and to facilitate comparison with previous work, comparison was made between currents recorded in the absence of extracellular divalent cations and in the presence of physiological concentrations of extracellular Ca2+ (10 mM) and Mg2+ (50 mM). The single-channel currents were well resolved when divalent cations were not included in the extracellular solution, but were decreased in amplitude in the presence of Ca2+ and Mg2+ ions. The instantaneous current-voltage relationship obtained from macroscopic tail current measurements similarly was depressed by divalents, and showed a negative slope-conductance region for inward current at negative potentials. Voltage dependent parameters of channel gating were shifted 9-13 mV towards depolarized potentials by external divalent cations, including the peak fraction of channels open versus voltage, the time constant of tail current decline, the prepulse inactivation versus voltage relationship, and the charge-voltage relationship for gating currents. The effects of divalent cations are consistent with open channel block by Ca2+ and Mg2+ together with divalent screening of membrane charges.     

Effects of permeant ion concentrations on the gating of L-type Ca2+ channels in hair cells

We determined the gating and permeation properties of single L-type Ca(2+) channels, using hair cells and varying concentrations (5-70 mM) of the charge carriers Ba(2+) and Ca(2+). The channels showed distinct gating modes with high- and low-open probability. The half-activation voltage (V(1/2)) shifted in the hyperpolarizing direction from high to low permeant ion concentrations consistent with charge screening effects. However, the differences in the slope of the voltage shifts (in VM(-1)) between Ca(2+) (0.23) and Ba(2+) (0.13), suggest that channel-ion interaction may also contribute to the gating of the channel. We examined the effect of mixtures of Ba(2+) and Ca(2+) on the activation curve. In 5 mM Ca(2+), the V(1/2) was, -26.4 +/- 2.0 mV compared to Ba(2+), -34.7 +/- 2.9 mV, as the charge carrier. However, addition of 1 mM Ba(2+) in 4 mM Ca(2+), a molar ratio, which yielded an anomalous-mole fraction effect, was sufficient to shift the V(1/2) to -34.7 +/- 1.5 mV. Although Ca(2+)-dependent inactivation of the L-type channels in hair cells can yield the present findings, we provide evidence that the anomalous gating of the channel may stem from the closed interaction between ion permeation and gating.     

Localization of the calcium channel subunits Cav1.2 (alpha1C) and Cav2.3 (alpha1E) in the mouse organ of Corti

Voltage-activated Ca2+ channels play an important role in synaptic transmission, signal processing and development. The immunohistochemical localization of Cav1.2 (alpha1C) and Cav2.3 (alpha1E) Ca2+ channels was studied in the developing and adult mouse organ of Corti using subunit-specific antibodies and fluorescent secondary antibodies with cochlear cryosections. Cav1.2 immunoreactivity has been detected from postnatal day 14 (P14) onwards at the synapses between cholinergic medial efferents and outer hair cells as revealed by co-staining with anti-synaptophysin and anti-choline acetyltransferase. Most likely the Cav1.2 immunoreactivity was located presynaptically at the site of contact of the efferent bouton with the outer hair cell which suggests a role for class C L-type Ca2+ channels in synaptic transmission of the medial efferent system. The localization of the second Ca2+ channel tested, Cav2.3, showed a pronounced change during cochlear development. From P2 until P10, Cav2.3 immunoreactivity was found in the outer spiral bundle followed by the inner spiral bundle, efferent endings and by medial efferent fibers. Around P14, Cav2.3 immunoreactivity disappeared from these structures and from P19 onwards it was observed in the basal poles of the outer hair cell membranes.     

Inwardly rectifying current-voltage relationship of small-conductance Ca2+-activated K+ channels rendered by intracellular divalent cation blockade

Small conductance Ca2+-activated K+ channels (SK(Ca) channels) are a group of K+-selective ion channels activated by submicromolar concentrations of intracellular Ca2+ independent of membrane voltages. We expressed a cloned SK(Ca) channel, rSK2, in Xenopus oocytes and investigated the effects of intracellular divalent cations on the current-voltage (I-V) relationship of the channels. Both Mg2+ and Ca2+ reduced the rSK2 channel currents in voltage-dependent manners from the intracellular side and thus rectified the I-V relationship at physiological concentration ranges. The apparent affinity of Mg2+ was changed as a function of both transmembrane voltage and intracellular Ca2+ concentration. Extracellular K+ altered the voltage dependence as well as the apparent affinities of Mg2+ binding from intracellular side. Thus, the inwardly rectifying I-V relationship of SK(Ca) channels is likely due to the voltage-dependent blockade of intracellular divalent cations and that the binding site is located within the ion-conducting pathway. Therefore, intracellular Ca2+ modulates the permeation characteristics of SK(Ca) channels by altering the I-V relationship as well as activates the channel by interacting with the gating machinery, calmodulin, and SK(Ca) channels can be considered as Ca2+-activated inward rectifier K+ channels.     

Open channel block by Ca2+ underlies the voltage dependence of drosophila TRPL channel

The light-activated channels of Drosophila photoreceptors transient receptor potential (TRP) and TRP-like (TRPL) show voltage-dependent conductance during illumination. Recent studies implied that mammalian members of the TRP family, which belong to the TRPV and TRPM subfamilies, are intrinsically voltage-gated channels. However, it is unclear whether the Drosophila TRPs, which belong to the TRPC subfamily, share the same voltage-dependent gating mechanism. Exploring the voltage dependence of Drosophila TRPL expressed in S2 cells, we found that the voltage dependence of this channel is not an intrinsic property since it became linear upon removal of divalent cations. We further found that Ca(2+) blocked TRPL in a voltage-dependent manner by an open channel block mechanism, which determines the frequency of channel openings and constitutes the sole parameter that underlies its voltage dependence. Whole cell recordings from a Drosophila mutant expressing only TRPL indicated that Ca(2+) block also accounts for the voltage dependence of the native TRPL channels. The open channel block by Ca(2+) that we characterized is a useful mechanism to improve the signal to noise ratio of the response to intense light when virtually all the large conductance TRPL channels are blocked and only the low conductance TRP channels with lower Ca(2+) affinity are active.