Results and Discussion

To determine the fixed charge concentration of the TM, we recorded the electrical responses of the TM using a microaperture chamber in a patch clamp configuration (Fig. 2; Materials and Methods). The voltage measured between the baths represents the sum of the junction potentials at two TM surfaces (Fig. 2 A and B): one bathed in artificial endolymph (AE) and one bathed in a test solution. KCl concentration in the test solution was altered systematically to modulate the adjacent junction potential via changes in charge shielding. The resulting measurements were well fit by a model based on the Donnan relation (Materials and Methods) and provided an estimate of fixed charge density c_f of −7.1 ± 2.0 mmol/L at physiological pH, and 3.0 mmol/L at pH 3.5 (Fig. 2C). These results are consistent with predictions based on biochemical composition studies (27). The net charge of approximately −7.1 mmol/L at physiological pH is large, representing 1 fixed charge molecule for every ∼25 cations in endolymph.

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Fig. 2.

Fixed-charge density of the TM. (A) Schematic drawings of the microaperture setup showing side views of an isolated TM positioned over a circular microaperture. (Left) The microaperture creates a fluid path from the overlying bath of AE to the underlying microfluidics channel (test bath) perfused with AE-like solutions with variable KCl concentrations. (Right) The TM acts as an electrochemical barrier between the overlying bath and underlying fluid channel. The potential difference between the baths (V_D = V_T − V_B) was recorded with Ag/AgCl electrodes that were placed in contact with the two baths. (B) Schematic drawing of the microaperture setup showing the top view of the TM positioned over the microaperture in the region near Hensen’s stripe and the marginal zone. (Inset) TM segment overlying the microaperture using 40× magnification. (C) Voltage was plotted as a function of test bath KCl concentration. Best-fit estimates to the median voltages yielded c_f (–7.1 ± 2.0 mmol/L; n = 5 TM preparations). Vertical lines and boxes denote extreme values and the extent of the interquartile range, respectively. Horizontal lines through the boxes denote the median values. Reducing the bath pH from 7.3 to 3.5 caused voltage measurements to change polarity and decrease in magnitude (3.0 mmol/L).

To determine the mechanical contribution of charge in the TM, we analyzed a macrocontinuum model based on the stress–strain relation and Donnan equilibrium (27, 41). Internal pressures that arise from mechanical and electrostatic mechanisms resist external pressures on the TM (Fig. 1). The mechanical component is proportional to changes in TM volume and may be expressed as

where p_mech is the hydraulic pressure, κ is the bulk modulus, V is TM volume, and V_o is the volume in the absence of a hydraulic pressure. The electrostatic component depends on the concentration of fixed charge in the TM, which tends to concentrate mobile counterions to maintain electroneutrality. This concentration of counterions increases the osmotic pressure (p_elec) in the TM and may be expressed as

where R is the molar gas constant, T is absolute temperature, and C represents the concentration of monovalent ionic species (KCl) in the bath. This model predicts that electrostatic repulsion due to the −7.1 mmol/L of fixed charge density may contribute up to 0.35 kPa to the equilibrium bulk modulus κ, accounting for ∼70% of compressive rigidity of the TM at equilibrium (21). Under dynamic conditions, the contribution of charge to mechanical properties also is important. A recent study found that a shift to acidic pHs in the bath causes about a two- to threefold reduction in dynamic shear impedance of the TM (42). The density of charge in the TM thus is sufficient to be the basis of mechanical properties under both static and dynamic conditions, a striking finding given the fact that the TM is highly hydrated (27, 29, 30).

The presence of charge in the TM suggests the possibility that electrical stimuli might generate a mechanical response (43, 44). The application of oscillating electric fields at audio frequencies (1–1,000 Hz) directed along the transverse axis of the TM in the microaperture chamber (Fig. 3A) generated displacements of the TM near the marginal zone and Hensen’s stripe (n = 4 TM preparations) (Movie S1). Fig. 3B shows that TM displacements had peak amplitudes of 50 nm in response to 8 kV/m (at 10 Hz) at a position on the undersurface of the TM above the microaperture. Displacement amplitudes dropped significantly with distance away from the microaperture (Fig. 3B), increased with electric field strength (Fig. 3C), and decreased as a function of stimulus frequency with the phase angle approaching −π/2 radians (Fig. 3D), consistent with viscous dominated interactions. Similar motion behaviors were reproduced in a microfluidics chamber used to apply radial electric fields (SI Materials and Methods, Movie S2, and Fig. S1). Using this chamber, we measured the frequency response of the TM at very low frequencies (1–80 Hz) and exposed the TM to different perfusates in the microchannel environment. Perfusion of AE equilibrated at pH 3.5 led to a shift in phase angle of ∼π radians (Fig. S2A), indicating ionization of positively charged collagen groups (38) and neutralization of negatively charged GAGs.

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Fig. 3.

TM electrokinetic response. (A) The microaperture setup was used to deliver electric fields to the TM with a pair of Ag/AgCl-stimulating electrodes. Electrically evoked displacements were measured using computer microvision and DOCM systems (Materials and Methods). Voltages were delivered with Ag/AgCl electrodes positioned in the top bath and in a reservoir connecting to the underlying fluid channel. Electric fields were computed based on the geometry of the microaperture, and electrical current was measured across a resistor that was placed in series with the microaperture chamber during voltage application. (B) Transverse displacements were sinusoidal and largest in the regions of the TM directly overlying the microaperture and decreased with radial distance away from the microaperture. A typical TM segment excised from the middle turn exhibited electrically evoked displacements up to ∼45 nm in response to electrical stimuli applied in the middle zone region directly overlying the microaperture (10 Hz; 8 kV/m). Motion amplitudes varied depending on whether the TM sample was a basal or an apical segment. (C) Displacements scaled linearly with electric field magnitude for TM samples excised from the middle turn of the cochlea (n = 4 TM preparations). (D) (Upper) Displacement amplitudes decreased with increasing stimulus frequency (40–1,000 Hz) with a slope of –1 (solid line) for a typical apical TM segment. Black dots denote the mean value of TM displacement. (Lower) Phase angle of TM displacement as a function of frequency. Vertical lines with horizontal bars denote SEM.

The frequency dependence of TM displacement magnitude and phase (Fig. 3D and Fig. S2B) suggests an interplay between electrophoretic forces on the solid matrix and electro-osmotic forces on interstitial fluid (which carries a charge equal in magnitude but opposite in polarity to the fixed charge on TM macromolecules) (40). At low frequencies, these forces displace the fixed-charge groups attached to the elastic matrix of the TM to generate displacements, which scale with field strength and the radius of the microaperture (45). However, this process is viscosity limited (Fig. 3D) because of the small size of the pores (21). Therefore, as the frequency of the electrical stimulus increases, there is less time per period for fluid motion through the porous matrix and a proportional reduction in total fluid transport. The result is that electrokinetic displacements of the TM are larger at low frequencies than at high frequencies.

For asymptotically low frequencies, the solid and fluid phases separate, and electrokinetic displacements result from electrical forces acting on fixed charges embedded in the elastic matrix. To estimate the magnitude of these displacements, we modeled the TM as a semi-infinite, isotropic, elastic matrix, which overlies a circular aperture (25-μm diameter) through which current is passed. The mechanical properties of the matrix were represented by Young’s modulus (∼10⁵ Pa for a basal TM segment) (18, 23). The matrix was assumed to have a uniform electrical resistivity (0.3 Ω⋅m) and fixed charge density q (∼7 × 10⁵ C/m³), determined from the measurements in this study (c_f ∼7 mmol/L; Fig. 2). The equations of motion were solved using finite differences (SI Results), with the result that electric fields of 1 kV/m (generated by ∼2 μA of current) produced electrokinetic displacements on the order of 1.5 μm. This motion estimate is based on a quasistatic model of the TM, which is appropriate at asymptotically low frequencies. However, the motion measurements in Fig. 3D show strong frequency dependence of motion (with slope of –1) over the measured range of frequencies (which is limited at low frequencies by table vibrations and thermal drift). We expect the trend shown in Fig. 3D to continue (to lower frequencies) until the transition to quasistatic behavior occurs, at frequencies that correspond to the poroelastic relaxation time [which is on the order of tens of minutes, based on previous osmotic experiments (21, 27)]. Thus, the transition frequency is two to three orders of magnitude below our lowest measured frequency, and we expect the quasistatic motion estimate to be two to three orders of magnitude larger than the measured range of motions.

Under dynamic conditions, viscous forces increasingly couple electro-osmotic and electrophoretic forces, which are equal in magnitude but opposite in direction. To test the effect of pore size and interstitial fluids on TM electrokinetics, we measured TM motion in response to changes in viscosity by introducing different-sized PEG molecules in AE (SI Results and Materials and Methods). We altered the viscosity of the fluid surrounding the TM by perfusing AE mixed with large PEG molecules (10 μmol/L, 400 kDa), which could not penetrate the TM. To alter internal viscosity of the TM, we perfused AE mixed with small PEG molecules (10 mmol/L, 8 kDa), whose radius of gyration was sufficiently small to enter through TM nanopores (21). Adding small PEG molecules caused TM motion to decrease by ∼6.5 times, whereas, adding large PEG molecules caused relatively minor changes in TM motion (Fig. S2C). Changing internal viscosity of the TM is functionally equivalent to reducing TM pore size, suggesting a strong dependence of TM electrokinetic interactions on effective porosity and a weak dependence on external viscosity of the surrounding fluid. These results provide a framework for a general poroelastic model of the TM under both quasistatic (21) and dynamic conditions, thereby highlighting the important interplay between fixed-charge groups, porosity, and the internal water content of the TM at the nanoscale.

Electrically evoked displacements of the TM may have important implications for electrical stimulation of the cochlea (46⇓⇓⇓–50). Mechanical responses to electrical stimulation generally have been attributed to OHC somatic and hair bundle motility mechanisms. Although exogenous application of electrical currents undoubtedly excites sensory receptor cells, our results suggest that electrically induced TM motions also must be taken into account if electrical currents flow through the TM. Thus, electrically evoked motions of the cochlear partition may be stimulated at least partially by TM electrokinetics, especially at low audio frequencies.

Electrokinetic properties of the TM might interact directly with hair cell ion channels. Although the exact position of hair cell transduction channels relative to the TM remains unclear, it is well known that the undersurface of the TM is close (nanometer-scale separation) to the tallest rows of stereocilia (51⇓–53). Fig. 4 A and B shows the TM–hair bundle interface and highlights how transduction currents, driven predominantly by potassium and calcium ions, generate electric fields, which in turn might exert local force on TM macromolecules. Although it is unlikely that transduction currents generate bulk movements of the TM in vivo, it is possible that local electrically induced deformations of the TM might occur near single stereocilia ion channels.

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Fig. 4.

TM electrokinetics near hair cell ion channels. (A) Schematic drawing of a cochlear partition showing the orientation of the TM relative to OHC stereocilia and tip links. (B) Inset shows the OHC ion channel as a point source with radial electric fields (blue arrows) acting on TM fixed-charge macromolecules locally over small distances r. (C) Model predictions of electric field magnitudes as a function of radial distance r from the opening of the ion channel. Electric fields were estimated based on experimental values for single-channel transduction currents, resistivity of the ionic environment, and the radius of the ion channel from previous data (51⇓⇓⇓–55). The shaded region labeled “This study” denotes the range of electric field (10³–10⁴ V/m) magnitudes applied in the microaperture chamber with values corresponding to ∼7–30 nm from the ion channel opening. The shaded region labeled “Ref. 51” denotes electric fields (∼1 V/m) measured at ∼1 µm from the tips of hair bundles in the bullfrog’s sacculus (51). In both cases, radial distances r are significantly larger than the TM’s space charge layer thickness (34).

A previous study of electrical recordings from a bullfrog’s sacculus found electric field magnitudes of ∼1 V/m at distances ∼1 µm from the tips of the stereociliary hair bundles containing clusters of ion channels (51). These electric fields depend not only on the magnitude of the current but also on the spatial proximity of the TM relative to the ion channels. If we assume ∼20-pA transduction currents through a solitary ion channel (54, 55) and a distance of ∼1 µm from the channel opening, the electric fields would be in the range of those measured by Hudspeth (labeled “Ref. 51” in Fig. 4C). However, as the distance to the ion channel is decreased, the field strength increases rapidly. For example, at distances within 7–30 nm of an ion channel, the field strengths are 10³–10⁴ V/m, similar to those applied in the microaperture chamber (labeled “This study” in Fig. 4C).

Electrically evoked TM motions and forces produced by transduction electric fields depend on the material properties of the TM as well as the channel geometry. If we assume that a solitary ion channel is modeled as a single nanopore, then we can estimate the magnitude of TM displacements by scaling the measurements in the microaperture setup (Fig. 3). TM motion in the microaperture setup under quasistatic conditions (d_μ ∼1.5 μm) is proportional to the applied electric field strength (E_μ ∼10³ V/m), where the proportionality constant is the effective charge (q_μ) divided by TM stiffness (k_μ). The stiffness k_μ scales with the radius of the microaperture (45) and therefore is ∼10⁴ smaller near an ion channel (∼1-nm radius), whereas the quantity of charge q_μ scales with the volume of the TM overlying the microaperture. As a result, the proportionality between d_μ and E_μ changes by a factor of 10⁸ for a single ion channel relative to the microaperture. On that basis, we predict TM displacements (d_ch) near an ion channel to be ∼0.01 nm in response to E_ch adjacent to a nanochannel (Fig. 4C). Because the electric field strength depends linearly on the number of stereociliary channels, the aggregate TM motion for ∼75 channels (d_hb) for a given hair bundle would be ∼0.75 nm. TM displacements at the ion channel and bundle level scale linearly with electrical current I (SI Results). This linear dependence of TM motion on electrical current is consistent with a finite difference model (SI Results), which predicts TM motion estimates on the order of those based purely on scaling.

The total mechanical energy available from TM electrokinetic motions (SI Results) is the product of d_hb² and TM stiffness (k_TM ∼1.33 N/m for a basal TM segment over a 5-μm radius) (18, 23, 45), yielding ∼0.75 aJ for basal TM segments and on the order of ∼7.5 aJ for apical TM segments with lower stiffness (k_TM ∼0.13 N/m for an apical TM segment over a 5-μm radius) (18, 23, 45). These energy estimates are comparable with the amount of work needed to deflect hair bundles during calcium-driven bundle motility (∼2 aJ) and are significantly larger than the work performed against viscosity during bundle movements (∼0.1 aJ) (56, 57), suggesting that electrically evoked motions of the TM might interact with MET currents of the hair bundles. The direction of TM motion and the associated feedback mechanism at the level of the hair bundles depend on the location of the MET channels. If the ion channels face toward the inhibitory direction of bundle motion (i.e., if they are on the side closest to a shorter stereocilium), the net electric field caused by opening the channels will generate a force that will tend to close the channels, consistent with negative feedback. If, on the other hand, the ion channels face the tallest stereocilium (as in Fig. 4B), the net electric field would force TM negative charge groups in the direction of positive bundle deflection to open more ion channels, as the basis of a positive feedback mechanism for amplification.

Beyond cochlear mechanics, our findings have important implications for all sensory systems, which (with the exception of a few species of lizards) all contain accessory gelatinous structures overlying hair cells. Gels, such as the cupulae and otolithic membranes found in the vestibular system and those covering electrosensory hair cells on the skin of aquatic vertebrates, play a key role in hair cell stimulation (58⇓–60). Much like the TM, these gels are poised to undergo deformations in response to transduction currents. The effect of electrokinetics may be even greater in these sensory systems because their MET channels operate at significantly lower frequencies than those in the cochlea.