Modeling electrically active viscoelastic membranes

The membrane protein prestin is native to the cochlear outer hair cell that is crucial to the ear's amplification and frequency selectivity throughout the whole acoustic frequency range. The outer hair cell exhibits interrelated dimensional changes, force generation, and electric charge transfer. Cells transfected with prestin acquire unique active properties similar to those in the native cell that have also been useful in understanding the process. Here we propose a model describing the major electromechanical features of such active membranes. The model derived from thermodynamic principles is in the form of integral relationships between the history of voltage and membrane resultants as independent variables and the charge density and strains as dependent variables. The proposed model is applied to the analysis of an active force produced by the outer hair cell in response to a harmonic electric field. Our analysis reveals the mechanism of the outer hair cell active (isometric) force having an almost constant amplitude and phase up to 80 kHz. We found that the frequency-invariance of the force is a result of interplay between the electrical filtering associated with prestin and power law viscoelasticity of the surrounding membrane. Paradoxically, the membrane viscoelasticity boosts the force balancing the electrical filtering effect. We also consider various modes of electromechanical coupling in membrane with prestin associated with mechanical perturbations in the cell. We consider pressure or strains applied step-wise or at a constant rate and compute the time course of the resulting electric charge. The results obtained here are important for the analysis of electromechanical properties of membranes, cells, and biological materials as well as for a better understanding of the mechanism of hearing and the role of the protein prestin in this mechanism.     

Prestin-prestin and prestin-GLUT5 interactions in HEK293T cells

The remarkable hearing sensitivity and frequency selectivity in mammals is attributed to cochlear amplifier in the outer hair cells (OHCs). Prestin, a membrane protein in the lateral wall of OHC plasma membrane, is required for OHC electromotility and cochlear amplifier. In addition, GLUT5, a fructose transporter, is reported to be abundant in the plasma membrane of the OHC lateral wall and has been originally proposed as the OHC motor protein. Here we provide evidence of interactions between prestin/prestin and prestin/GLUT5 in transiently transfected HEK293T cells. We used a combination of techniques: (1) membrane colocalization by confocal microscopy, (2) fluorescence resonance energy transfer (FRET) by fluorescence activated cell sorting (FACS), (3) FRET by acceptor photobleaching, (4) FRET by fluorescence lifetime imaging (FRET-FLIM), and (5) coimmunoprecipitation. Our results suggest that homomeric and heteromeric prestin interactions occur in native OHCs to facilitate its electromotile function and that GLUT5 interacts with prestin for its elusive function.     

Modeling 3-D deformation of outer hair cells and their production of the active force in the cochlea

 We analyze the deformation of the outer hair cell and its production of active force under physiological conditions. The active force has two components. One results from the strain caused by loading in the organ of Corti in the cochlea and depends on the level of the acoustic signal; the other is related to the intrinsic active properties of the cell membrane. We demonstrate our approach by considering, as a basic model of an outer hair cell in the organ of Corti, a cylindrical shell that is filled with an incompressible fluid and located between two planes that move relative to each other. These planes represent the basilar membrane and tectorial membrane complexes. We show that the deformed state of the cell has a 3-D nature, including bending and twisting components. This is different from the experimental conditions in which the active force is usually measured. We estimate the active force as a function of the relative position of the planes, angle of the cell's inclination, and the cell length. Received: 25 October 2001 / Accepted: 30 May 2002 We thank Drs. Aleksander Popel and William Brownell for constructive discussions of the results. This work was supported by research grants DC02775 and DC00354 from NIDCD and AG014748 from NIA.     

A membrane bending model of outer hair cell electromotility

We propose a new mechanism for outer hair cell electromotility based on electrically induced localized changes in the curvature of the plasma membrane (flexoelectricity). Electromechanical coupling in the cell's lateral wall is modeled in terms of linear constitutive equations for a flexoelectric membrane and then extended to nonlinear coupling based on the Langevin function. The Langevin function, which describes the fraction of dipoles aligned with an applied electric field, is shown to be capable of predicting the electromotility voltage displacement function. We calculate the electrical and mechanical contributions to the force balance and show that the model is consistent with experimentally measured values for electromechanical properties. The model rationalizes several experimental observations associated with outer hair cell electromotility and provides for constant surface area of the plasma membrane. The model accounts for the isometric force generated by the cell and explains the observation that the disruption of spectrin by diamide reduces force generation in the cell. We discuss the relation of this mechanism to other proposed models of outer hair cell electromotility. Our analysis suggests that rotation of membrane dipoles and the accompanying mechanical deformation may be the molecular mechanism of electromotility.     

Lateral wall protein content mediates alterations in cochlear outer hair cell mechanics before and after hearing onset

Specialized outer hair cells (OHCs) housed within the mammalian cochlea exhibit active, nonlinear, mechanical responses to auditory stimulation termed electromotility. The extraordinary frequency resolution capacity of the cochlea requires an exquisitely equilibrated mechanical system of sensory and supporting cells. OHC electromotile length change, stiffness, and force generation are responsible for a 100-fold increase in hearing sensitivity by augmenting vibrational input to non-motile sensory inner hair cells. Characterization of OHC mechanics is crucial for understanding and ultimately preventing permanent functional deficits due to overstimulation or as a consequence of various cochlear pathologies. The OHCs' major structural assembly is a highly-specialized lateral wall. The lateral wall consists of three structures; a plasma membrane highly-enriched with the motor-protein prestin, an actin-spectrin cortical lattice, and one or more layers of subsurface cisternae. Technical difficulties in independently manipulating each lateral wall constituent have constrained previous attempts to analyze the determinants of OHCs' mechanical properties. Temporal separations in the accumulation of each lateral wall constituent during postnatal development permit associations between lateral wall structure and OHC mechanics. We compared developing and adult gerbil OHC axial stiffness using calibrated glass fibers. Alterations in each lateral wall component and OHC stiffness were correlated as a function of age. Reduced F-actin labeling was correlated with reduced OHC stiffness before hearing onset. Prestin incorporation into the PM was correlated with increased OHC stiffness at hearing onset. Our data indicate lateral wall F-actin and prestin are the primary determinants of OHC mechanical properties before and after hearing onset, respectively.     

Tuning of the outer hair cell motor by membrane cholesterol

Cholesterol affects diverse biological processes, in many cases by modulating the function of integral membrane proteins. We observed that alterations of cochlear cholesterol modulate hearing in mice. Mammalian hearing is powered by outer hair cell (OHC) electromotility, a membrane-based motor mechanism that resides in the OHC lateral wall. We show that membrane cholesterol decreases during maturation of OHCs. To study the effects of cholesterol on hearing at the molecular level, we altered cholesterol levels in the OHC wall, which contains the membrane protein prestin. We show a dynamic and reversible relationship between membrane cholesterol levels and voltage dependence of prestin-associated charge movement in both OHCs and prestin-transfected HEK 293 cells. Cholesterol levels also modulate the distribution of prestin within plasma membrane microdomains and affect prestin self-association in HEK 293 cells. These findings indicate that alterations in membrane cholesterol affect prestin function and functionally tune the outer hair cell.     

ROCK-dependent and ROCK-independent control of cochlear outer hair cell electromotility

Outer hair cell electromotility is crucial for the proper function of the cochlear amplifier, the active process that enhances sensitivity and frequency discrimination of the mammalian ear. Previous work (Kalinec, F., Zhang, M., Urrutia, R., and Kalinec, G. (2000) J. Biol. Chem. 275, 28000-28005) has suggested a role for Rho GTPases in the regulation of outer hair cell electromotility, although the signaling pathways mediated by these enzymes remain to be established. Here we have investigated the cellular and molecular mechanisms underlying the homeostatic regulation of the electromotile response of guinea pig outer hair cells. Our findings defined a ROCK-mediated signaling cascade that continuously modulates outer hair cell electromotility by selectively targeting the cytoskeleton. A distinct ROCK-independent pathway functions as a fast resetting mechanism for this system. Neither pathway affects the function of prestin, the unique molecular motor of outer hair cells. These results extend our understanding of a basic mechanism of both normal human hearing and deafness, revealing the key role of the cytoskeleton in the regulation of outer hair cell electromotility and suggesting ROCK as a molecular target for modulating the function of the cochlear amplifier.     

Effect of membrane mechanics on charge transfer by the membrane protein prestin

Prestin was found in the membrane of outer hair cells (OHCs) located in the cochlea of the mammalian inner ear. These cells convert changes in the membrane potential into dimensional changes and (if constrained) to an active electromechanical force. The OHCs provide the ear with the mechanism of amplification and frequency selectivity that is effective up to tens of kHz. Prestin is a crucial part of the motor complex driving OHCs. Other cells transfected with prestin acquire electromechanical properties similar to those in the native cell. While the mechanism of prestin has yet to be fully understood, the charge transfer is its critical component. Here we investigate the effect of the mechanics of the surrounding membrane on electric charge transfer by prestin. We simulate changes in the membrane mechanics via the corresponding changes in the free energy of the prestin system. The free energy gradient enters a Fokker-Planck equation that describes charge transfer in our model. We analyze the effects of changes in the membrane tension and membrane elastic moduli. In the case of OHC, we simulate changes in the longitudinal and/or circumferential stiffness of the cell’s orthotropic composite membrane. In the case of cells transfected with prestin, we vary the membrane areal modulus. As a result, we show the effects of the membrane mechanics on the probabilistic characteristics of prestin-associated charge transfer for both stationary and high-frequency conditions. We compare our computational results with the available experimental data and find good agreement with the experiment.     

Tension sensitivity of prestin: comparison with the membrane motor in outer hair cells

The membrane motor in outer hair cells undergoes conformational transitions involving charge displacement of approximately 0.8 e across the membrane and changes of approximately 4 nm(2) in its membrane area. Previous reports have established that the charge transfer in the membrane motor and that in prestin, a membrane protein in the plasma membrane of outer hair cells, are approximately equal. Here, we determine the membrane area changes based on its sensitivity to membrane tension. We found that prestin does undergo area changes and that the magnitude is approximately 1 nm(2), smaller than the value 4 nm(2) for outer hair cell motor. This result confirms that prestin is a protein that functions as a membrane motor based on piezoelectricity. The discrepancy in the magnitude could suggest a prestin-containing complex in outer hair cells.     

Modeling the mechanics of tethers pulled from the cochlear outer hair cell membrane

Cell membrane tethers are formed naturally (e.g., in leukocyte rolling) and experimentally to probe membrane properties. In cochlear outer hair cells, the plasma membrane is part of the trilayer lateral wall, where the membrane is attached to the cytoskeleton by a system of radial pillars. The mechanics of these cells is important to the sound amplification and frequency selectivity of the ear. We present a modeling study to simulate the membrane deflection, bending, and interaction with the cytoskeleton in the outer hair cell tether pulling experiment. In our analysis, three regions of the membrane are considered: the body of a cylindrical tether, the area where the membrane is attached and interacts with the cytoskeleton, and the transition region between the two. By using a computational method, we found the shape of the membrane in all three regions over a range of tether lengths and forces observed in experiments. We also analyze the effects of biophysical properties of the membrane, including the bending modulus and the forces of the membrane adhesion to the cytoskeleton. The model's results provide a better understanding of the mechanics of tethers pulled from cell membranes.     

Protein- and Lipid-Reactive Agents Alter Outer Hair Cell Lateral Membrane Motor Charge Movement

Outer hair cells from the mamma*lian cochlea are mechanically active cells that rely on charged voltage sensors within their lateral plasma membrane to gate the integral membrane motor protein, prestin, into one of two area states. Here we use protein and lipid reactive reagents to probe the influence of these bilayer components on motor-induced nonlinear membrane capacitance. Of the protein-reactive reagents tested, cross-linking and sulfhydryl reagents were most effective in altering steady state and time-varying motor activity. Of the lipid-altering agents, chloroform and HePC were most effective. Chloroform, in particular, drastically modified the susceptibility of the motor to prior voltage (initial conditions). Our data suggest that outer hair cell motor activity derives substantially from interactions with its lipid environment.This revised version was published online in June 2005 with a corrected cover date.     

Effectiveness, active energy produced by molecular motors, and nonlinear capacitance of the cochlear outer hair cell

Cochlear outer hair cells are crucial for active hearing. These cells have a unique form of motility, named electromotility, whose main features are the cell's length changes, active force production, and nonlinear capacitance. The molecular motor, prestin, that drives outer hair cell electromotility has recently been identified. We reveal relationships between the active energy produced by the outer hair cell molecular motors, motor effectiveness, and the capacitive properties of the cell membrane. We quantitatively characterize these relationships by introducing three characteristics: effective capacitance, zero-strain capacitance, and zero-resultant capacitance. We show that zero-strain capacitance is smaller than zero-resultant capacitance, and that the effective capacitance is between the two. It was also found that the differences between the introduced capacitive characteristics can be expressed in terms of the active energy produced by the cell's molecular motors. The effectiveness of the cell and its molecular motors is introduced as the ratio of the motors'active energy to the energy of the externally applied electric field. It is shown that the effectiveness is proportional to the difference between zero-strain and zero-resultant capacitance. We analyze the cell and motor's effectiveness within a broad range of cellular parameters and estimate it to be within a range of 12%-30%.     

Outer Hair Cell Lateral Wall Structure Constrains the Mobility of Plasma Membrane Proteins

Nature’s fastest motors are the cochlear outer hair cells (OHCs). These sensory cells use a membrane protein, Slc26a5 (prestin), to generate mechanical force at high frequencies, which is essential for explaining the exquisite hearing sensitivity of mammalian ears. Previous studies suggest that Slc26a5 continuously diffuses within the membrane, but how can a freely moving motor protein effectively convey forces critical for hearing? To provide direct evidence in OHCs for freely moving Slc26a5 molecules, we created a knockin mouse where Slc26a5 is fused with YFP. These mice and four other strains expressing fluorescently labeled membrane proteins were used to examine their lateral diffusion in the OHC lateral wall. All five proteins showed minimal diffusion, but did move after pharmacological disruption of membrane-associated structures with a cholesterol-depleting agent and salicylate. Thus, our results demonstrate that OHC lateral wall structure constrains the mobility of plasma membrane proteins and that the integrity of such membrane-associated structures are critical for Slc26a5’s active and structural roles. The structural constraint of membrane proteins may exemplify convergent evolution of cellular motors across species. Our findings also suggest a possible mechanism for disorders of cholesterol metabolism with hearing loss such as Niemann-Pick Type C diseases.     

Multiple quantitative trait loci modify cochlear hair cell degeneration in the Beethoven (Tmc1Bth) mouse model of progressive hearing loss DFNA36

Dominant mutations of transmembrane channel-like gene 1 (TMC1) cause progressive sensorineural hearing loss in humans and Beethoven (Tmc1Bth/+) mice. Here we show that Tmc1Bth/+ mice on a C3HeB/FeJ strain background have selective degeneration of inner hair cells while outer hair cells remain structurally and functionally intact. Inner hair cells primarily function as afferent sensory cells, whereas outer hair cells are electromotile amplifiers of auditory stimuli that can be functionally assessed by distortion product otoacoustic emission (DPOAE) analysis. When C3H-Tmc1Bth/Bth is crossed with either C57BL/6J or DBA/2J wild-type mice, F1 hybrid Tmc1Bth/+ progeny have increased hearing loss associated with increased degeneration of outer hair cells and diminution of DPOAE amplitudes but no difference in degeneration of inner hair cells. We mapped at least one quantitative trait locus (QTL), Tmc1m1, for DPOAE amplitude on chromosome 2 in [(C/B)F1xC]N2-Tmc1Bth/+ backcross progeny, and three other QTL on chromosomes 11 (Tmc1m2), 12 (Tmc1m3), and 5 (Tmc1m4) in [(C/D)F1xC]N2-Tmc1Bth/+ progeny. The polygenic basis of outer hair cell degeneration in Beethoven mice provides a model system for the dissection of common, complex hearing loss phenotypes, such as presbycusis, that involve outer hair cell degeneration in humans.     

Force Transmission in the Organ of Corti Micromachine

Auditory discrimination is limited by the performance of the cochlea whose acute sensitivity and frequency tuning are underpinned by electromechanical feedback from the outer hair cells. Two processes may underlie this feedback: voltage-driven contractility of the outer hair cell body and active motion of the hair bundle. Either process must exert its mechanical effect via deformation of the organ of Corti, a complex assembly of sensory and supporting cells riding on the basilar membrane. Using finite element analysis, we present a three-dimensional model to illustrate deformation of the organ of Corti by the two active processes. The model used available measurements of the properties of structural components in low-frequency and high-frequency regions of the rodent cochlea. The simulations agreed well with measurements of the cochlear partition stiffness, the longitudinal space constant for point deflection, and the deformation of the organ of Corti for current injection, as well as displaying a 20-fold increase in passive resonant frequency from apex to base. The radial stiffness of the tectorial membrane attachment was found to be a crucial element in the mechanical feedback. Despite a substantial difference in the maximum force generated by hair bundle and somatic motility, the two mechanisms induced comparable amplitudes of motion of the basilar membrane but differed in the polarity of their feedback on hair bundle position. Compared to the hair bundle motor, the somatic motor was more effective in deforming the organ of Corti than in displacing the basilar membrane.     

Modeling the active process of the cochlea: phase relations, amplification, and spontaneous oscillation.

The high sensitivity and sharp frequency selectivity of acoustical signal transduction in the cochlea suggest that an active process pumps energy into the basilar membrane's oscillations. This function is generally attributed to outer hair cells, but its exact mechanism remains uncertain. Several classical models of amplification represent the load upon the basilar membrane as a single mass. Such models encounter a fundamental difficulty, however: the phase difference between basilar-membrane movement and the force generated by outer hair cells inhibits, rather than amplifies, the modeled basilar-membrane oscillations. For this reason, modelers must introduce artificially either negative impedance or an appropriate phase shift, neither of which is justified by physical analysis of the system. We consider here a physical model based upon the recent demonstration that the basilar membrane and reticular lamina can move independently, albeit with elastic coupling through outer hair cells. The mechanical model comprises two resonant masses, representing the basilar membrane and the reticular lamina, coupled through an intermediate spring, the outer hair cells. The spring's set point changes in response to displacement of the reticular lamina, which causes deflection of the hair bundles, variation of outer hair cell length and, hence, force production. Depending upon the frequency of the acoustical input, the basilar membrane and reticular lamina can oscillate either in phase or in counterphase. In the latter instance, the force produced by hair cells leads basilar-membrane oscillation, energy is pumped into basilar-membrane movement, and an external input can be strongly amplified. The model is also capable of producing spontaneous oscillation. In agreement with experimental observations, the model describes mechanical relaxation of the basilar membrane after electrical stimulation causes outer hair cells to change their length.     

Modes and balance of energy in the piezoelectric cochlear outer hair cell wall

Here, we analyze energy transformations in the outer hair cell and its effectiveness as a piezoelectric-type actuator in the cochlea. The major modes of energy are introduced, and a method to estimate the coefficients of their tension-dependence is proposed. Next, we derive balance of the mechanical and electrical parts of energy, and show two forms of the active energy associated with the motors driving electromotility. The two forms of the active energy, stored mechanical energy, and external electrical work are then introduced as functions of voltage and applied force. We use the energy balance to introduce and estimate the effectiveness of the cell's electromotile response.     

Piezoelectric reciprocal relationship of the membrane motor in the cochlear outer hair cell

It has been shown that the membrane motor in the outer hair cell is driven by the membrane potential. Here we examine whether the motility satisfies the reciprocal relationship, the characteristic of piezoelectricity, by measuring charge displacement induced by stretching the cell with known force. The efficiency of inducing charge displacement was membrane potential dependent. The maximum efficiency of inducing charge displacement by force was approximately 20 fC/nN for 50-microm-long lateral membrane. The efficiency per cell stretching was 0.1 pC/microm. We found that these values are consistent with the reciprocal relationship based on the voltage sensitivity of approximately 20 nm/mV for 50-microm-long cell and force production of 0.1 nN/mV by the cell. We can thus conclude that the membrane motor in the outer hair cell satisfies a necessary condition for piezoelectricity and that the hair cell's piezoelectric coefficient of 20 fC/nN is four orders of magnitude greater than the best man-made material.     

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.     

Chloride and Salicylate Influence Prestin-dependent Specific Membrane Capacitance: SUPPORT FOR THE AREA MOTOR MODEL*

The outer hair cell is electromotile, its membrane motor identified as the protein SLC26a5 (prestin). An area motor model, based on two-state Boltzmann statistics, was developed about two decades ago and derives from the observation that outer hair cell surface area is voltage-dependent. Indeed, aside from the nonlinear capacitance imparted by the voltage sensor charge movement of prestin, linear capacitance (C_lin) also displays voltage dependence as motors move between expanded and compact states. Naturally, motor surface area changes alter membrane capacitance. Unit linear motor capacitance fluctuation (δC_sa) is on the order of 140 zeptofarads. A recent three-state model of prestin provides an alternative view, suggesting that voltage-dependent linear capacitance changes are not real but only apparent because the two component Boltzmann functions shift their midpoint voltages (V_h) in opposite directions during treatment with salicylate, a known competitor of required chloride binding. We show here using manipulations of nonlinear capacitance with both salicylate and chloride that an enhanced area motor model, including augmented δC_sa by salicylate, can accurately account for our novel findings. We also show that although the three-state model implicitly avoids measuring voltage-dependent motor capacitance, it registers δC_sa effects as a byproduct of its assessment of C_lin, which increases during salicylate treatment as motors are locked in the expanded state. The area motor model, in contrast, captures the characteristics of the voltage dependence of δC_sa, leading to a better understanding of prestin.