Two-state model for outer hair cell stiffness and motility

With discovery of the protein prestin and the gathering evidence linking it to outer hair cell electromotility, the working mechanism of outer hair cells is becoming clearer. Recent experiments have established the voltage-dependent stiffness of outer hair cells and given an insight into the nature of variation of stiffness with respect to voltage. These and earlier experiments are used to analyze and develop models of outer hair cell response. In this article, recent modeling efforts have been reconciled and placed into a common mechanics-based framework. The constitutive models are analyzed with regard to their capability to replicate experimental results. We extend the area motor model to include elastic constants dependent on motor state. The modified model successfully captures stiffness variations of outer hair cells and capacitance changes with respect to voltage.     

Harmonics of outer hair cell motility.

The voltage-dependent mechanical activity of outer hair cells (OHC) from the organ of Corti is considered responsible for the peripheral auditory system's enhanced ability to detect and analyze sound. Nonlinear processes within the inner ear are presumed to be characteristic of this enhancement process. Harmonic distortion in the OHC mechanical response was analyzed under whole-cell voltage clamp. It is shown that the OHC produces DC, fundamental and second harmonic length changes in response to sinusoidal transmembrane voltage stimulation. Mechanical second harmonic distortion decreases with frequency, whereas the predicted transmembrane second harmonic voltage increases with frequency. Furthermore, the phase of the second harmonic distortion does not correspond to the phase of the predicted transmembrane voltage. In contradistinction, it has been previously shown (Santos-Sacchi, J. 1992. Neuroscience. 12:1906-1916) that fundamental voltage and evoked mechanical responses share magnitude and phase characteristics. OHC length changes are modeled as resulting from voltage-dependent cell surface area changes. The model suggests that the observed harmonic responses in the mechanical response are consistent with the nonlinearity of the voltage-to-length change (V-delta L) function. While these conclusions hold for the data obtained with the present voltage clamp protocol and help to understand the mechanism of OHC motility, modeling the electromechanical system of the OHC in the in vivo state indicates that the mechanical nonlinearity of the OHC contributes minimally to mechanical distortion. That is, in vivo, at moderate sound pressure levels and below, the dominant factor which contributes to nonlinearities of the OHC mechanical response resides within the nonlinear, voltage-generating, stereociliar transduction process.     

Cytoplasmic actin and cochlear outer hair cell motility

Summary Isolated outer hair cells of the guinea pig lacking a cuticular plate and its associated infracuticular network retain the ability to shorten longitudinally and become thinner. Membrane ghosts lacking cytoplasm retain the cylindrical shape of the hair-cell, and although they do not shorten, they retain the ability to constrict and become thinner. These data suggest that cytoplasmic components are associated with outer hair-cell longitudinal shortening and that the lateral wall is responsible for maintaing cell shape and for constriction. Actin, a protein associated with the cytoskeleton and cell motility, is thought to be involved in outer hair-cell motility. To study its role, actin was localized in isolated outer hair cells by use of phalloidin labeled with fluorescein and antibodies against actin coupled to colloidal gold. In permeabilized guinea-pig hair cells stained with phalloidin, actin filaments are found along the lateral wall. In frozen-fixed hair cells actin filaments are distributed uniformly throughout the cytoplasm. Electron-microscopic studies show that antibodies label actin throughout the outer hair-cell body. Thus cytoplasmic actin filaments may provide the structural basis for the contraction-like events.     

Prestin-based outer hair cell motility is necessary for mammalian cochlear amplification

It is a central tenet of cochlear neurobiology that mammalian ears rely on a local, mechanical amplification process for their high sensitivity and sharp frequency selectivity. While it is generally agreed that outer hair cells provide the amplification, two mechanisms have been proposed: stereociliary motility and somatic motility. The latter is driven by the motor protein prestin. Electrophysiological phenotyping of a prestin knockout mouse intimated that somatic motility is the amplifier. However, outer hair cells of knockout mice have significantly altered mechanical properties, making this mouse model unsatisfactory. Here, we study a mouse model without alteration to outer hair cell and organ of Corti mechanics or to mechanoelectric transduction, but with diminished prestin function. These animals have knockout-like behavior, demonstrating that prestin-based electromotility is required for cochlear amplification.     

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.     

The role of outer hair cell motility in cochlear tuning.

The mammalian cochlea's remarkable sensitivity and frequency selectivity are thought to be mediated by the mechanical feedback action of outer hair cells. New tools for measuring the movement of cochlear elements, and recent advances in modeling are increasing our knowledge of cochlear mechanics.     

A two-layer outer hair cell model with orthotropic piezoelectric properties: correlation of cell resonant frequencies with tuning in the cochlea

The frequency response of outer hair cells (OHCs) of different lengths is studied using a mathematical model of a two-layer cylindrical shell with orthotropic properties. Material properties in the model are determined from experimental measurements reported in the literature, and the variation of material properties with the cell length is studied. The cortical lattice's Poisson ratios are found to remain fairly constant with cell length, while its stiffness changes significantly with cell length. The natural frequencies corresponding to several modes of deformation of an OHC with intracellular and extracellular fluids are calculated from this model. Our results suggest that the best frequency in the cochlea at the position where the OHC is located corresponds to different modes of deformation of the OHC, depending on the OHC length. For short OHCs, the best frequency is close to the natural frequency of the axisymmetric mode; for long OHCs, it is close to the natural frequencies of the beam-like bending and pinched modes. Such a difference in resonant modes for short and long OHCs at the best frequency suggests that different modes of OHC elongation motility may be present in amplifying the basilar membrane motion in the high and low frequency regions of the cochlea.     

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.     

Rho GTPases mediate the regulation of cochlear outer hair cell motility by acetylcholine

Outer hair cells are the mechanical effectors of the cochlear amplifier, an active process that improves the sensitivity and frequency discrimination of the mammalian ear. In vivo, the gain of the cochlear amplifier is regulated by the efferent neurotransmitter acetylcholine through the modulation of outer hair cell motility. Little is known, however, regarding the molecular mechanisms activated by acetylcholine. In this study, intracellular signaling pathways involving the small GTPases RhoA, Rac1, and Cdc42 have been identified as regulators of outer hair cell motility. Changes in cell length (slow motility) and in the amplitude of electrically induced movement (fast motility) were measured in isolated outer hair cells patch clamped in whole-cell mode, internally perfused through the patch pipette with different inhibitors and activators of these small GTPases while being externally stimulated with acetylcholine. We found that acetylcholine induces outer hair cell shortening and a simultaneous increase in the amplitude of fast motility through Rac1 and Cdc42 activation. In contrast, a RhoA- and Rac1-mediated signaling pathway induces outer hair cell elongation and decreases fast motility amplitude. These two opposing processes provide the basis for a regulatory mechanism of outer hair cell motility.     

Evidence of piezoelectric resonance in isolated outer hair cells

Our results demonstrate high-frequency electrical resonances in outer hair cells (OHCs) exhibiting features analogous to classical piezoelectric transducers. The fundamental (first) resonance frequency averaged f(n) approximately 13 kHz (Q approximately 1.7). Higher-order resonances were also observed. To obtain these results, OHCs were positioned in a custom microchamber and subjected to stimulating electric fields along the axis of the cell (1-100 kHz, 4-16 mV/80 microm). Electrodes embedded in the side walls of the microchamber were used in a voltage-divider configuration to estimate the electrical admittance of the top portion of the cell-loaded chamber (containing the electromotile lateral wall) relative to the lower portion (containing the basal plasma membrane). This ratio exhibited resonance-like electrical tuning. Resonance was also detected independently using a secondary 1-MHz radio-frequency interrogation signal applied transversely across the cell diameter. The radio-frequency interrogation revealed changes in the transverse electric impedance modulated by the axial stimulus. Modulation of the transverse electric impedance was particularly pronounced near the resonant frequencies. OHCs used in our study were isolated from the apical region of the guinea pig cochlea, a region that responds exclusively to low-frequency acoustic stimuli. In this sense, electrical resonances we observed in vitro were at least an order of magnitude higher (ultrasonic) than the best physiological frequency of the same OHCs under acoustic stimuli in vivo. These resonance data further support the piezoelectric theory of OHC function, and implicate piezoelectricity in the broad-band electromechanical behavior of OHCs underlying mammalian cochlear function.     

Pivotal role of actin depolymerization in the regulation of cochlear outer hair cell motility

Cochlear outer hair cells undergo reversible changes in shape when externally stimulated. This response, known as OHC motility, is a central component of the cochlear amplifier, the mechanism responsible for the high sensitivity of mammalian hearing. We report that actin depolymerization, as regulated by activation/inhibition of LIMK/cofilin-mediated pathways, has a pivotal role in OHC motility. LIMK-mediated cofilin phosphorylation, which inhibits the actin depolymerizing activity of this protein, increases both electromotile amplitude and total length of guinea pig OHCs. In contrast, a decrease in cofilin phosphorylation reduces both OHC electromotile amplitude and OHC length. Experiments with acetylcholine and lysophosphatidic acid indicate that the effects of these agents on OHC motility are associated with regulation of cofilin phosphorylation via different signaling cascades. On the other hand, nonlinear capacitance measurements confirmed that all observed changes in OHC motile response were independent of the performance of the motor protein prestin. Altogether, these results strongly support the hypothesis that the cytoskeleton has a major role in the regulation of OHC motility, and identify actin depolymerization as a key process for modulating cochlear amplification.     

Mapping the distribution of the outer hair cell motility voltage sensor by electrical amputation.

The outer hair cell (OHC) possesses a nonlinear charge movement whose characteristics indicate that it represents the voltage sensor responsible for OHC mechanical activity. OHC mechanical activity is known to exist along a restricted extent of the cell's length. We have used a simultaneous partitioning microchamber and whole cell voltage clamp technique to electrically isolate sections of the OHC membrane and find that the nonlinear charge movement is also restricted along the cell's length. Apical and basal portions of the OHC are devoid of voltage sensors, corresponding to regions of the cell where the subsurface cisternae and/or the mechanical responses are absent. We conclude that the physical domain of the motility voltage sensor corresponds to that of the mechanical effector and speculate that sensor and effector reside within one intra membranous molecular species, perhaps an evolved nonconducting or poorly conducting voltage-dependent ion channel.     

Membrane tension directly shifts voltage dependence of outer hair cell motility and associated gating charge.

The unique electromotility of the outer hair cell (OHC) is believed to promote sharpening of the passive mechanical vibration of the mammalian basilar membrane. The cell also presents a voltage-dependent capacitance, or equivalently, a nonlinear gating current, which correlates well with its mechanical activity, suggesting that membrane-bound voltage sensor-motor elements control OHC length. We report that the voltage dependence of the gating charge and motility are directly related to membrane stress induced by intracellular pressure. A tracking procedure was devised to continuously monitor the voltage at peak capacitance (VpkCm) after obtaining whole cell voltage clamp configuration. In addition, nonlinear capacitance was more fully evaluated with a stair step voltage protocol. Upon whole cell configuration, VpkCm was typically near -20 mV. Negative patch pipette pressure caused a negative shift in VpkCm, which obtained a limiting value near the normal resting potential of the OHC (approximately -70 mV) at the point of cell collapse. Positive pressure in the pipette caused a positive shift that could reach values greater than 0 mV. Measures of the mechanical activity of the OHC mirrored those of charge movement. Similar membrane-tension dependent peak shifts were observed after the cortical cytoskeletal network was disrupted by intracellular dialysis of trypsin from the patch pipette. We conclude that unlike stretch receptors, which may sense tension through elastic cytoskeletal elements, the OHC motor senses tension directly. Furthermore, since the voltage dependence of the OHC nonlinear capacitance and motility is directly regulated by intracellular turgor pressure, we speculate that modification of intracellular pressure in vivo provides a mechanism for controlling the gain of the mammalian "cochlear amplifier".     

A two-state tension-displacement model for hemoglobin-ligand binding

Based on the Perutz view of hemoglobin co-operativity and the methodology of statistical physics, a two-state (t → r) model for the co-operative response is presented. The motion of the iron atom with respect to the heme plane is assumed to be the important feature of the binding process, and results in an expression for hemoglobin saturation as an explicit function of the internal tension of the hemoglobin molecule. Closure of the equation is achieved with the assumption of linearity between the internal tension and the displacement of the iron atom above the heme plane. The result is a linear dependence of log_e [(ψ/(1?ψ)/(1/X_L)] on the fractional saturation, ψ, the slope and intercept being expressed in terms of physically realizable parameters characteristic of the hemoglobin-ligand reaction. Agreement with experimental data for hemoglobin-oxygen and hemoglobin-carbon monoxide is obtained using parameter values that are reasonable in terms of the interactions they represent.     

An anion antiporter model of prestin, the outer hair cell motor protein

Cochlear amplification in mammalian hearing relies on an active mechanical feedback process generated by outer hair cells, driven by a protein, prestin (SLC26A5), in the lateral membrane. We have used kinetic models to understand the mechanism by which prestin might function. We show that the two previous hypotheses of prestin, which assume prestin cannot operate as a transporter, are insufficient to explain previously published data. We propose an alternative model of prestin as an electrogenic anion exchanger, exchanging one Cl(-) ion for one divalent or two monovalent anions. This model can reproduce the key aspects of previous experimental observations. The experimentally observed charge movements are produced by the translocation of one Cl(-) ion combined with intrinsic positively charged residues, while the transport of the counteranion is electroneutral. We tested the model with measurements of the Cl(-) dependence of charge movement, using SO(4)(2-) to replace Cl(-). The data was compatible with the predictions of the model, suggesting that prestin does indeed function as a transporter.     

A model for cell motility on soft bio-adhesive substrates

Mechanical stiffness of bio-adhesive substrates has been recognized as a major regulator of cell motility. We present a simple physical model to study the crawling locomotion of a contractile cell on a soft elastic substrate. The mechanism of rigidity sensing is accounted for using Schwarz's two-spring model Schwarz et al. (2006). The predicted dependency between the speed of motility and substrate stiffness is qualitatively consistent with experimental observations. The model demonstrates that the rigidity dependent motility of cells is rooted in the regulation of actomyosin contractile forces by substrate deformation at each anchorage point. On stiffer substrates, the traction forces required for cell translocation acquire larger magnitude but show weaker asymmetry which leads to slower cell motility. On very soft substrates, the model predicts a biphasic relationship between the substrate rigidity and the speed of locomotion, over a narrow stiffness range, which has been observed experimentally for some cell types.