Mark Ospeck

Piezoelectric Reciprocal Relationship of the Membrane Motor in the Cochlear Outer Hair Cell

It has been shown that the membrane motor in the outer hair cell is driven by the membrane potential. Here we examine whether the motility satisfies the reciprocal relationship, the characteristic of piezoelectricity, by measuring charge displacement induced by stretching the cell with known force. The efficiency of inducing charge displacement was membrane potential dependent. The maximum efficiency of inducing charge displacement by force was approximately 20 fC/nN for 50-microm-long lateral membrane. The efficiency per cell stretching was 0.1 pC/microm. We found that these values are consistent with the reciprocal relationship based on the voltage sensitivity of approximately 20 nm/mV for 50-microm-long cell and force production of 0.1 nN/mV by the cell. We can thus conclude that the membrane motor in the outer hair cell satisfies a necessary condition for piezoelectricity and that the hair cells piezoelectric coefficient of 20 fC/nN is four orders of magnitude greater than the best man-made material.

Evidence of a Hopf Bifurcation in Frog Hair Cells

The membrane potential of hair cells in the low-frequency hearing organ of the bullfrog, the amphibian papilla, sinusoidally oscillates at small amplitude in the absence of acoustical input. We stimulate the cell with a series of periodic currents close to this natural frequency and observe that its current-to-voltage transfer function is compressively nonlinear, having a large gain for small stimuli and a smaller gain for larger currents. Along with the spontaneous oscillation, this implies that the cell is poised close to a dynamical instability such as a Hopf bifurcation, because distant from the instability the transfer function becomes linear. The cells frequency selectivity is enhanced for small stimuli. Simulations show that the cells membrane capacitance is effectively reduced due to a current gain provided by this dynamical instability. We propose that the Hopf resonance is widely used by transducer cells on the sensory periphery to achieve small-signal amplification.

How Close Should the Outer Hair Cell RC Roll-Off Frequency Be to the Characteristic Frequency?

Recent experiments have shown a much larger conductance in outer hair cells, the central components of the mammalian cochlear amplifier. The report used only the cells linear capacitance, which together with increased conductance, raised the cells RC corner frequency so that voltage-dependent motility was better able to amplify high-frequency sounds. We construct transfer functions for a simple model of a high characteristic frequency (CF) local cochlear resonance. These show that voltage roll-off does not occur above the RC corner. Instead, it is countered by high-pass filtering that is intrinsic to the mammals electromechanical resonance. Thus, the RC corner of a short outer hair cell used for high-frequency amplification does not have to be close to the CF, but depending on the drag, raised only above 0.1 CF. This high-pass filter, built in to the mammalian amplifier, allows for sharp frequency selectivity at very high CF.

Electromotility in outer hair cells: a supporting role for fast potassium conductance.

Motility of outer hair cells underlies the cochlear amplifier, which is critical for the ear’s sensitivity and fine tuning. Of the two motile mechanisms present in these cells, electromotility at the lateral wall depends on the receptor potential and thus depends on currents through the cell body. We found that, in the guinea pig cochlea, basal turn outer hair cells have a fast-activating ion current (τ < 0.3 ms at 23°C), which is absent in apical turn cells. This finding is consistent with our previous theoretical analysis that a fast-activating potassium current is required only in the basal turn to counteract the capacitive current and thereby to enhance the effectiveness of electromotility. Thus, our finding is consistent with the functional significance of electromotility. We conjecture therefore that the current reduces the capacitance of the outer hair cell in order to increase hearing bandwidth.

Noise in the Outer Hair Cell and Gain Control in the Ear

We present a minimal model of a local resonance inside the mammalian cochlea in which a feedback loop containing an outer hair cell is poised on a dynamical instability. This model results in an amplifier essentially equivalent to a van der Pol oscillator in its weakly nonlinear limit. The feedback loop automatically seeks the instability where gain and gain compression are optimized. The outer hair cell’s average membrane potential is the control parameter which sets amplifier gain. We briefly investigate noise sources inside the outer hair cell which contribute to the feedback loop oscillating in a noise‐driven limit‐cycle. Experimentally this limit‐cycle is increased by 3 to 5 times in high external noise environments. A half millivolt shift due to efferent stimulation can account for the observed 50 percent reduction in both the size of the noisy limit‐cycle oscillation and the feedback loop gain.