Analysis of outer hair cell electromechanics reveals power delivery at the upper-frequency limits of hearing

Abstract

Outer hair cells are the cellular motors in the mammalian inner ear responsible for sensitive high-frequency hearing. Motor function over the frequency range of human hearing requires expression of the protein prestin in the OHC lateral membrane, which imparts piezoelectric properties to the cell membrane. In the present report, electrical power consumption and mechanical power output of the OHC membrane-motor complex are determined using previously published voltage-clamp data from isolated OHCs and membrane patches. Results reveal that power output peaks at a best frequency much higher than implied by the low-pass character of nonlinear capacitance, and much higher than the whole-cell resistive-capacitive corner frequency. High frequency power output is enabled by a -90° shift in the phase of electrical charge displacement in the membrane, manifested electrically as emergence of imaginary-valued nonlinear capacitance.

Keywords: biological motor; cochlea; electromotility; imaginary capacitance; piezoelectricity; prestin.

Figure 1.

OHC mechanical power output in the dish. (a). Schematic of a micro-chamber used to apply sinusoidal voltage stimuli to the base of the cell with the OHC partially extending into media. (b,c) Magnitude and phase of the displacement X measured by Frank et al. (open symbols: open green circles, open purple squares) [27] and Santos-Sacchi & Tan (inverted triangles) [26]. Solid curves are curve-fits to equation (2.8) used to estimate the dissipation parameters ‘c’ and ‘n’. (d) Mechanical power output was determined from equation (2.9) and measured displacement X. Power output computed from the Frank et al. data peaked at frequencies as high as 74 kHz, when the phase of the displacement was −90° relative to the peak sinusoidal voltage. Power output computed from the Santos-Sacchi & Tan data (triangles: filled triangle, open triangle) was continuing to increase up to the highest frequency tested.

Figure 2.

Membrane patch electrical power consumption. (a) Real NLC, Re(C^V), recorded from OHC membrane macro-patches from data reported by Santos-Sacchi et al. (thick black) [24]. The right axis shows NLC recorded using an alternative approach by Gale & Ashmore (blue symbols) [23] for comparison. (b) Imaginary NLC, Im(C^V), recorded from OHC membrane macro-patches from data reported by Santos-Sacchi et al. (thick black). (c) Electrical power consumed by the prestin-motor complex (thick black) computed using equation (2.6) and Im(C^V) reported by Santos-Sacchi et al. (thick black, b). (a–c) Thin grey curves are predictions of PZT theory [31]. (d) Voltage and frequency dependence of PZT theory, with frequency-dependence of the peaks corresponding to the solid grey curves in panels a–c.