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".     

Mapping the distribution of outer hair cell voltage-dependent conductances by electrical amputation.

The mammalian outer hair cell (OHC) functions not only as sensory receptor, but also as mechanical effector; this unique union is believed to enhance our ability to discriminate among acoustic frequencies, especially in the kilohertz range. An electrical technique designed to isolate restricted portions of the plasma membrane was used to map the distribution of voltage-dependent conductances along the cylindrical extent of the cell. We show that three voltage-dependent currents, outward K, I(K,n), and I(Ca) are localized to the basal, synaptic pole of the OHC. Previously we showed that the lateral membrane of the OHC harbors a dense population of voltage sensor-motor elements responsible for OHC motility. This segregation of membrane molecules may have important implications for auditory function. The distribution of OHC conductances will influence the cable properties of the cell, thereby potentially controlling the voltage magnitudes experienced by the motility voltage sensors in the lateral membrane, and thus the output of the "cochlear amplifier."     

Loss of stability-a new model for stress relaxation in plant cell walls

This study addresses the mechanism of wall stress relaxation in growing plant cells. The current viscoelastic model of cell wall relaxation, which dates from the work of Preston, Cleland, Lockhart, and others in the 1960s, has serious shortcomings. It has been shown however that the theory of loss of stability (LOS) can be applied to materials in tension, leading to the conclusion that the relaxation of stresses in the walls of any pressure vessel is rigorously modeled using LOS. We propose that LOS also provides a more appropriate and versatile model of stress relaxation in growing plant cells. We argue that when treated as a manifestation of LOS, the regulation of cell turgor has a rigorous and demonstrable basis in the geometrical and physical properties of the cell wall and the cell's ability to import water. Thus plant cell growth can be regarded as an inherently self-limiting process, tunable by biochemical or structural means. Lastly, despite the current limitations of our model, we apply direct measurement of elastic modulus, wall thickness and cell radius obtained from cylindrical Chara corallina cells to generate an initial calculation of critical pressures in a hypothetical spherical cell with the same material properties.     

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.     

Effects of chlorpromazine on mechanical properties of the outer hair cell plasma membrane

An optical tweezers system was used to characterize the effects of chlorpromazine (CPZ) on the mechanical properties of the mammalian outer hair cell (OHC) through the formation of plasma membrane tethers. Such tethers exhibited force relaxation when held at a constant length for several minutes. We used a second-order generalized Kelvin body to model tether-force behavior from which several mechanical parameters were then calculated including stiffness, viscosity-associated measures, and force relaxation time constants. The results of the analysis portray a two-part relaxation process characterized by significantly different rates of force decay, which we propose is due to the local reorganization of lipids within the tether and the flow of external lipid into the tether. We found that CPZ's effect was limited to the latter phenomenon since only the second phase of relaxation was significantly affected by the drug. This finding coupled with an observed large reduction in overall tether forces implies a common basis for the drug's effects, the plasma membrane-cytoskeleton interaction. The CPZ-induced changes in tether viscoelastic behavior suggest that alterations in the mechanical properties of the OHC lateral wall could play a role in the modulation of OHC electromotility by CPZ.     

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.     

Evidence for outer hair cell driven oscillatory fluid flow in the tunnel of corti

Outer hair cell (OHC) somatic motility plays a key role in mammalian cochlear frequency selectivity and hearing sensitivity, but the mechanism of cochlear amplification is not well understood and remains a matter of controversy. We have visualized and quantified the effects of electrically evoked OHC somatic motility within the gerbil organ of Corti using an excised cochlear preparation. We found that OHC motility induces oscillatory motion of the medial olivocochlear fibers where they cross the tunnel of Corti (ToC) in their course to innervate the OHCs. We show that this motion is present at physiologically relevant frequencies and remains at locations distal to the OHC excitation point. We interpret this fiber motion to be the result of oscillatory fluid flow in the ToC. We show, using a simple one-dimensional hydromechanical model of the ToC, that a fluid wave within the tunnel can travel without significant attenuation for distances larger than the wavelength of the cochlear traveling wave at its peak. This ToC fluid wave could interact with the cochlear traveling wave to amplify the motion of the basilar membrane. The ToC wave could also provide longitudinal coupling between adjacent sections of the basilar membrane, and such coupling may be critical for cochlear amplification.     

Physical model for membrane protrusions during spreading

During cell spreading onto a substrate, the kinetics of the contact area is an observable quantity. This paper is concerned with a physical approach to modeling this process in the case of ameboid motility where the membrane detaches itself from the underlying cytoskeleton at the leading edge. The physical model we propose is based on previous reports which highlight that membrane tension regulates cell spreading. Using a phenomenological feedback loop to mimic stress-dependent biochemistry, we show that the actin polymerization rate can be coupled to the stress which builds up at the margin of the contact area between the cell and the substrate. In the limit of small variation of membrane tension, we show that the actin polymerization rate can be written in a closed form. Our analysis defines characteristic lengths which depend on elastic properties of the membrane-cytoskeleton complex, such as the membrane-cytoskeleton interaction, and on molecular parameters, the rate of actin polymerization. We discuss our model in the case of axi-symmetric and non-axi-symmetric spreading and we compute the characteristic time scales as a function of fundamental elastic constants such as the strength of membrane-cytoskeleton adherence.     

Chloride-driven Electromechanical Phase Lags at Acoustic Frequencies Are Generated by SLC26a5, the Outer Hair Cell Motor Protein

Outer hair cells (OHC) possess voltage-dependent membrane bound molecular motors, identified as the solute carrier protein SLC26a5, that drive somatic motility at acoustic frequencies. The electromotility (eM) of OHCs provides for cochlear amplification, a process that enhances auditory sensitivity by up to three orders of magnitude. In this study, using whole cell voltage clamp and mechanical measurement techniques, we identify disparities between voltage sensing and eM that result from stretched exponential electromechanical behavior of SLC26a5, also known as prestin, for its fast responsiveness. This stretched exponential behavior, which we accurately recapitulate with a new kinetic model, the meno presto model of prestin, influences the protein’s responsiveness to chloride binding and provides for delays in eM relative to membrane voltage driving force. The model predicts that in the frequency domain, these delays would result in eM phase lags that we confirm by measuring OHC eM at acoustic frequencies. These lags may contribute to canceling viscous drag, a requirement for many models of cochlear amplification.     

Exploring membrane mechanics: The role of membrane-cortex attachment in cell dynamics

The role of plasma membrane (PM) tension in cell dynamics has gained increasing interest in recent years to understand the mechanism by which individual cells regulate their dynamic behavior. Membrane-to-cortex attachment (MCA) is a component of apparent PM tension, and its assembly and disassembly determine the direction of cell motility, controlling the driving forces of migration. There is also evidence that membrane tension plays a role in malignant cancer cell metastasis and stem cell differentiation. Here, we review recent important discoveries that explore the role of membrane tension in the regulation of diverse cellular processes, and discuss the mechanisms of cell dynamics regulated by this physical parameter.     

Imaging electrically evoked micromechanical motion within the organ of corti of the excised gerbil cochlea

The outer hair cell (OHC) of the mammalian inner ear exhibits an unusual form of somatic motility that can follow membrane-potential changes at acoustic frequencies. The cellular forces that produce this motility are believed to amplify the motion of the cochlear partition, thereby playing a key role in increasing hearing sensitivity. To better understand the role of OHC somatic motility in cochlear micromechanics, we developed an excised cochlea preparation to visualize simultaneously the electrically-evoked motion of hundreds of cells within the organ of Corti (OC). The motion was captured using stroboscopic video microscopy and quantified using cross-correlation techniques. The OC motion at approximately 2-6 octaves below the characteristic frequency of the region was complex: OHC, Deiter's cell, and Hensen's cell motion were hundreds of times larger than the tectorial membrane, reticular lamina (RL), and pillar cell motion; the inner rows of OHCs moved antiphasic to the outer row; OHCs pivoted about the RL; and Hensen's cells followed the motion of the outer row of OHCs. Our results suggest that the effective stimulus to the inner hair cell hair bundles results not from a simple OC lever action, as assumed by classical models, but by a complex internal motion coupled to the RL.     

Optimal Electrical Properties of Outer Hair Cells Ensure Cochlear Amplification

The organ of Corti (OC) is the auditory epithelium of the mammalian cochlea comprising sensory hair cells and supporting cells riding on the basilar membrane. The outer hair cells (OHCs) are cellular actuators that amplify small sound-induced vibrations for transmission to the inner hair cells. We developed a finite element model of the OC that incorporates the complex OC geometry and force generation by OHCs originating from active hair bundle motion due to gating of the transducer channels and somatic contractility due to the membrane protein prestin. The model also incorporates realistic OHC electrical properties. It explains the complex vibration modes of the OC and reproduces recent measurements of the phase difference between the top and the bottom surface vibrations of the OC. Simulations of an individual OHC show that the OHC somatic motility lags the hair bundle displacement by ∼90 degrees. Prestin-driven contractions of the OHCs cause the top and bottom surfaces of the OC to move in opposite directions. Combined with the OC mechanics, this results in ∼90 degrees phase difference between the OC top and bottom surface vibration. An appropriate electrical time constant for the OHC membrane is necessary to achieve the phase relationship between OC vibrations and OHC actuations. When the OHC electrical frequency characteristics are too high or too low, the OHCs do not exert force with the correct phase to the OC mechanics so that they cannot amplify. We conclude that the components of OHC forward and reverse transduction are crucial for setting the phase relations needed for amplification.     

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.     

Extraction of prestin-dependent and prestin-independent components from complex motile responses in guinea pig outer hair cells

Electromotility of cochlear outer hair cells (OHC) is associated with conformational changes in the integral membrane protein prestin. We have recently reported that electrical stimulation evokes significant prestin-dependent changes in the length, width, and area of the longitudinal section of OHCs, but not in their volume. In contrast, prestin-independent responses elicited at constant membrane potential are associated with changes in cell length, width, and volume without significant changes in their longitudinal section area. In this report we describe a novel analytical technique, based on a simple theoretical model and continuous measurement of changes in cell length and longitudinal section area, to evaluate the contribution of each one of these mechanisms to the motile response of OHCs. We demonstrate that if the relative change in OHC length (L) during the motile response is expressed as L = A2 x V(-1) (with A and V being the relative changes in longitudinal section area and volume, respectively), A2 will describe the contribution of the prestin-dependent mechanism whereas V(-1) will describe the contribution of the prestin-independent mechanism. Thus, relative changes in any two of these cellular morphological parameters (L, A, or V) would be necessary and sufficient for characterizing any OHC motile response. This simple approach provides access to information previously unavailable, and may become a novel and important tool for increasing our understanding of the cellular and molecular mechanisms of OHC motility.     

The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet

We have recently demonstrated that the mitral valve anterior leaflet (MVAL) exhibited minimal hysteresis, no strain rate sensitivity, stress relaxation but not creep (Grashow et al., 2006, Ann Biomed Eng., 34(2), pp. 315-325; Grashow et al., 2006, Ann Biomed. Eng., 34(10), pp. 1509-1518). However, the underlying structural basis for this unique quasi-elastic mechanical behavior is presently unknown. As collagen is the major structural component of the MVAL, we investigated the relation between collagen fibril kinematics (rotation and stretch) and tissue-level mechanical properties in the MVAL under biaxial loading using small angle X-ray scattering. A novel device was developed and utilized to perform simultaneous measurements of tissue level forces and strain under a planar biaxial loading state. Collagen fibril D-period strain (epsilonD) and the fibrillar angular distribution were measured under equibiaxial tension, creep, and stress relaxation to a peak tension of 90 N/m. Results indicated that, under equibiaxial tension, collagen fibril straining did not initiate until the end of the nonlinear region of the tissue-level stress-strain curve. At higher tissue tension levels, epsilonD increased linearly with increasing tension. Changes in the angular distribution of the collagen fibrils mainly occurred in the tissue toe region. Using epsilonD, the tangent modulus of collagen fibrils was estimated to be 95.5+/-25.5 MPa, which was approximately 27 times higher than the tissue tensile tangent modulus of 3.58+/-1.83 MPa. In creep tests performed at 90 N/m equibiaxial tension for 60 min, both tissue strain and epsilonD remained constant with no observable changes over the test length. In contrast, in stress relaxation tests performed for 90 min epsilonD was found to rapidly decrease in the first 10 min followed by a slower decay rate for the remainder of the test. Using a single exponential model, the time constant for the reduction in collagen fibril strain was 8.3 min, which was smaller than the tissue-level stress relaxation time constants of 22.0 and 16.9 min in the circumferential and radial directions, respectively. Moreover, there was no change in the fibril angular distribution under both creep and stress relaxation over the test period. Our results suggest that (1) the MVAL collagen fibrils do not exhibit intrinsic viscoelastic behavior, (2) tissue relaxation results from the removal of stress from the fibrils, possibly by a slipping mechanism modulated by noncollagenous components (e.g. proteoglycans), and (3) the lack of creep but the occurrence of stress relaxation suggests a "load-locking" behavior under maintained loading conditions. These unique mechanical characteristics are likely necessary for normal valvular function.     

Modeling the effect of stretch and plasma membrane tension on Na+-K+-ATPase activity in alveolar epithelial cells

While a number of whole cell mechanical models have been proposed, few, if any, have focused on the relationship among plasma membrane tension, plasma membrane unfolding, and plasma membrane expansion and relaxation via lipid insertion. The goal of this communication is to develop such a model to better understand how plasma membrane tension, which we propose stimulates Na(+)-K(+)-ATPase activity but possibly also causes cell injury, may be generated in alveolar epithelial cells during mechanical ventilation. Assuming basic relationships between plasma membrane unfolding and tension and lipid insertion as the result of tension, we have captured plasma membrane mechanical responses observed in alveolar epithelial cells: fast deformation during fast cyclic stretch, slower, time-dependent deformation via lipid insertion during tonic stretch, and cell recovery after release from stretch. The model estimates plasma membrane tension and predicts Na(+)-K(+)-ATPase activation for a specified cell deformation time course. Model parameters were fit to plasma membrane tension, whole cell capacitance, and plasma membrane area data collected from the literature for osmotically swollen and shrunken cells. Predictions of membrane tension and stretch-stimulated Na(+)-K(+)-ATPase activity were validated with measurements from previous studies. As a proof of concept, we demonstrate experimentally that tonic stretch and consequent plasma membrane recruitment can be exploited to condition cells against subsequent cyclic stretch and hence mitigate stretch-induced responses, including stretch-induced cell death and stretch-induced modulation of Na(+)-K(+)-ATPase activity. Finally, the model was exercised to evaluate plasma membrane tension and potential Na(+)-K(+)-ATPase stimulation for an assortment of traditional and novel ventilation techniques.     

The nonlinear mechanical response of the red blood cell

We measure the dynamical mechanical properties of human red blood cells. A single cell response is measured with optical tweezers. We investigate both the stress relaxation following a fast deformation and the effect of varying the strain rate. We find a power-law decay of the stress as a function of time, down to a plateau stress, and a power-law increase of the cell's elasticity as a function of the strain rate. Interestingly, the exponents of these quantities violate the linear superposition principle, indicating a nonlinear response. We propose that this is due to the breaking of a fraction of the crosslinks during the deformation process. The soft glassy rheology model accounts for the relation between the exponents we observe experimentally. This picture is consistent with recent models of bond remodeling in the red blood cell's molecular structure. Our results imply that the blood cell's mechanical behavior depends critically on the deformation process.     

Regulation of outer hair cell cytoskeletal stiffness by intracellular Ca2+: underlying mechanism and implications for cochlear mechanics

Two Ca(2+)-dependent mechanisms have been proposed to regulate the mechanical properties of outer hair cells (OHCs), the sensory-motor receptors of the mammalian cochlea. One involves the efferent neurotransmitter, acetylcholine, decreasing OHC axial stiffness. The other depends on elevation of intracellular free Ca(2+) concentration ([Ca(2+)](i)) resulting in OHC elongation, a process known as Ca(2+)-dependent slow motility. Here we provide evidence that both these phenomena share a common mechanism. In whole-cell patch-clamp conditions, a fast increase of [Ca(2+)](i) by UV-photolysis of caged Ca(2+) or by extracellular application of Ca(2+)-ionophore, ionomycin, produced relatively slow (time constant approximately 20s) cell elongation. When OHCs were partially collapsed by applying minimal negative pressure through the patch pipette, elevation of the [Ca(2+)](i) up to millimole levels (estimated by Fura-2) was unable to restore the cylindrical shape of the OHC. Stiffness measurements with vibrating elastic probes showed that the increase of [Ca(2+)](i) causes a decrease of OHC axial stiffness, with time course similar to that of the Ca(2+)-dependent elongation, without developing any measurable force. We concluded that, contrary to a previous proposal, Ca(2+)-induced OHC elongation is unlikely to be driven by circumferential contraction of the lateral wall, but is more likely a passive mechanical reaction of the turgid OHC to Ca(2+)-induced decrease of axial stiffness. This may be the key phenomenon for controlling gain and operating point of the cochlear amplifier.     

Modulation of membrane dynamics and cell motility by membrane tension

The plasma membrane of most cells is drawn tightly over the cytoskeleton of the cell, resulting in a significant tension being developed in the membrane. The tension in the membrane can be calculated from the force required to separate it from the cytoskeleton; and the force itself can be measured rapidly by using laser tweezers. Recent observations indicate that decreasing membrane tension stimulates endocytosis and increasing tension stimulates secretion. Thus, membrane tension provides a simple physical mechanism to control the area of the plasma membrane. Here, we speculate that tension is a global parameter that the cell uses to control physically plasma membrane dynamics, cell shape and cell motility.     

Cell Blebbing and Membrane Area Homeostasis in Spreading and Retracting Cells

Cells remodel their plasma membrane and cytoskeleton during numerous physiological processes, including spreading and motility. Morphological changes require the cell to adjust its membrane tension on different timescales. While it is known that endo- and exocytosis regulate the cell membrane area in a timescale of 1 h, faster processes, such as abrupt cell detachment, require faster regulation of the plasma membrane tension. In this article, we demonstrate that cell blebbing plays a critical role in the global mechanical homeostasis of the cell through regulation of membrane tension. Abrupt cell detachment leads to pronounced blebbing (which slow detachment does not), and blebbing decreases with time in a dynamin-dependent fashion. Cells only start spreading after a lag period whose duration depends on the cell's blebbing activity. Our model quantitatively reproduces the monotonic decay of the blebbing activity and accounts for the lag phase in the spreading of blebbing cells.