The cochlear outer hair cell speed paradox

Abstract

Cochlear outer hair cells (OHCs) are among the fastest known biological motors and are essential for high-frequency hearing in mammals. It is commonly hypothesized that OHCs amplify vibrations in the cochlea through cycle-by-cycle changes in length, but recent data suggest OHCs are low-pass filtered and unable to follow high-frequency signals. The fact that OHCs are required for high-frequency hearing but appear to be throttled by slow electromotility is the “OHC speed paradox.” The present report resolves this paradox and reveals origins of ultrafast OHC function and power output in the context of the cochlear load. Results demonstrate that the speed of electromotility reflects how fast the cell can extend against the load, and does not reflect the intrinsic speed of the motor element itself or the nearly instantaneous speed at which the coulomb force is transmitted. OHC power output at auditory frequencies is revealed by emergence of an imaginary nonlinear capacitance reflecting the phase of electrical charge displacement required for the motor to overcome the viscous cochlear load.

State dependent effects on the frequency response of prestin’s real and imaginary components of nonlinear capacitance

“…Here we find experimentally that prestin’s complex NLC displays a partially reciprocal trade-off between real and imaginary components across interrogating frequency that follows predictions based on the PZE model of prestin 21 . However, we find that similar behavior is found with a simple 2-state kinetic model that is not piezoelectric, but solely voltage-dependent.…”

“…1 C). Superimposed lines in green and magenta are the PZE model responses at V h from Rabbitt 21 , which shows general agreement within this bandwidth. Figure 1 D shows the absolute magnitude of NLC that continuously decreases across frequency.…”

“…Rabbitt 21 modeled prestin and its NLC as a piezoelectric process based on first principles. NLC can be deconstructed into real and imaginary components 23 , since it is defined as the frequency-dependent membrane admittance ( Y* m (ω)) divided by iω , where , providing a real capacitive component and an imaginary conductive component.…”

“…Indeed, combining measures across a number of studies, we arrived at a collective estimate of NLC (absolute magnitude) frequency response that led us to suggest that prestin activity could not drive eM to sufficiently influence cochlear mechanics at very high acoustic frequencies (> 50 kHz), where cochlear amplification is expected to work best 7 . Recently, Rabbitt 21 , expanding on earlier modelling investigations 16 , 43 – 45 , has modelled OHC NLC as a piezoelectric process whose imaginary complex component takes on special significance, namely, signifying power output associated with prestin charge displacement. He modelled that as the real component of NLC decreases across frequency, the imaginary component increases—a frequency-dependent, reciprocal trade-off in magnitudes.…”

“…Recently, Rabbitt 21 suggested that the PZE nature of prestin provides power to the cochlear amplifier that correlates with the imaginary component of NLC, that component of charge movement that alters phase in response to viscous load. Such modelled behavior of prestin sensor charge movement, which for a piezo component is coupled to imposed stress, was predicted to account for the apparent incongruity of prestin’s low-pass roll-off in the absolute magnitude of complex NLC 7 and the expected high frequency behavior of prestin required by cochlear modelers to account for high frequency cochlear amplification.…”