Negative membrane capacitance of outer hair cells: electromechanical coupling near resonance

Multiple Modes of Motion for the Effectiveness of Outer Hair Cells at High Frequencies

Outer hair cells (OHCs) are essential for the sensitivity and frequency specificity of the mammalian ear. To perform this function, OHCs need to amplify the motion of the basilar membrane (BM), which is much stiffer than themselves. If OHCs and the BM are components of a single oscillator, this impedance mismatch seriously limits the effectiveness of OHCs. However, the elaborated structure of the organ of Corti can support multiple modes of motion. Here, systems of two coupled oscillators are examined as the simplest models of the system with multiple modes of motion. It is found that some of these model systems have conditions, under which an OHC can function as an effective amplifier, overcoming the impedance mismatch. The present examination suggests that the presence of multiple modes of motion is a key to the exquisite performance of the mammalian ear.

Intracochlear overdrive: Characterizing nonlinear wave amplification in the mouse apex

In this study, we explore nonlinear cochlear amplification by analyzing basilar membrane (BM) motion in the mouse apex. Through in vivo, postmortem, and mechanical suppression recordings, we estimate how the cochlear amplifier nonlinearly shapes the wavenumber of the BM traveling wave, specifically within a frequency range where the short-wave approximation holds. Our findings demonstrate that a straightforward mathematical model, depicting the cochlear amplifier as a wavenumber modifier with strength diminishing monotonically as BM displacement increases, effectively accounts for the various experimental observations. This empirically derived model is subsequently incorporated into a physics-based "overturned" framework of cochlear amplification [see Altoè, Dewey, Charaziak, Oghalai, and Shera (2022), J. Acoust. Soc. Am. 152, 2227-2239] and tested against additional experimental data. Our results demonstrate that the relationships established within the short-wave region remain valid over a much broader frequency range. Furthermore, the model, now exclusively calibrated to BM data, predicts the behavior of the opposing side of the cochlear partition, aligning well with recent experimental observations. The success in reproducing key features of the experimental data and the mathematical simplicity of the resulting model provide strong support for the "overturned" theory of cochlear amplification.

The Remarkable Outer Hair Cell: Proceedings of a Symposium in Honour of W. E. Brownell

In 1985, Bill Brownell and colleagues published the remarkable observation that cochlear outer hair cells (OHCs) express voltage-driven mechanical motion: electromotility. They proposed OHC electromotility as the mechanism for the elusive "cochlear amplifier" required to explain the sensitivity of mammalian hearing. The finding and hypothesis stimulated an explosion of experiments that have transformed our understanding of cochlear mechanics and physiology, the evolution of hair cell structure and function, and audiology. Here, we bring together examples of current research that illustrate the continuing impact of the discovery of OHC electromotility.

The Long Outer-Hair-Cell RC Time Constant: A Feature, Not a Bug, of the Mammalian Cochlea

The cochlea of the mammalian inner ear includes an active, hydromechanical amplifier thought to arise via the piezoelectric action of the outer hair cells (OHCs). A classic problem of cochlear biophysics is that the RC (resistance-capacitance) time constant of the hair-cell membrane appears inconveniently long, producing an effective cut-off frequency much lower than that of most audible sounds. The long RC time constant implies that the OHC receptor potential-and hence its electromotile response-decreases by roughly two orders of magnitude over the frequency range of mammalian hearing, casting doubt on the hypothesized role of cycle-by-cycle OHC-based amplification in mammalian hearing. Here, we review published data and basic physics to show that the "RC problem" has been magnified by viewing it through the wrong lens. Our analysis finds no appreciable mismatch between the expected magnitude of high-frequency electromotility and the sound-evoked displacements of the organ of Corti. Rather than precluding significant OHC-based boosts to auditory sensitivity, the long RC time constant appears beneficial for hearing, reducing the effects of internal noise and distortion while increasing the fidelity of cochlear amplification.

Of mice and chickens: Revisiting the RC time constant problem

Avian hair cells depend on electrical resonance for frequency selectivity. The upper bound of the frequency range is limited by the RC time constant of hair cells because the sharpness of tuning requires that the resonance frequency must be lower than the RC roll-off frequency. In contrast, tuned mechanical vibration of the inner ear is the basis of frequency selectivity of the mammalian ear. This mechanical vibration is supported by outer hair cells (OHC) with their electromotility (or piezoelectricity), which is driven by the receptor potential. Thus, it is also subjected to the RC time constant problem. Association of OHCs with a system with mechanical resonance leads to piezoelectric resonance. This resonance can nullify the membrane capacitance and solves the RC time constant problem for OHCs. Therefore, avian and mammalian ears solve the same problem in the opposite way.

Kinetic Membrane Model of Outer Hair Cells

The effectiveness of outer hair cells (OHCs) in amplifying the motion of the organ of Corti, and thereby contributing to the sensitivity of mammalian hearing, depends on the mechanical power output of these cells. Electromechanical coupling in OHCs, which enables these cells to convert electrical energy into mechanical energy, has been analyzed in detail using isolated cells using primarily static membrane models. The mechanical output of OHCs was previously evaluated by developing a kinetic theory based on a simplified one-dimensional model for OHCs. Here, a kinetic description of OHCs is extended by using the membrane model, which was used for analyzing in vitro experiments. This theory predicts, for systems without inertial load, that elastic load enhances positive shift of voltage dependence of the membrane capacitance because of turgor pressure. The effect of turgor pressure increases with increasing elastic load. For systems with inertia, the magnitude of mechanical power output could be ∼5% higher than the value predicted by the one-dimensional model at the optimal turgor pressure.

Timing of the reticular lamina and basilar membrane vibration in living gerbil cochleae

Auditory sensory outer hair cells are thought to amplify sound-induced basilar membrane vibration through a feedback mechanism to enhance hearing sensitivity. For optimal amplification, the outer hair cell-generated force must act on the basilar membrane at an appropriate time at every cycle. However, the temporal relationship between the outer hair cell-driven reticular lamina vibration and the basilar membrane vibration remains unclear. By measuring sub-nanometer vibrations directly from outer hair cells using a custom-built heterodyne low-coherence interferometer, we demonstrate in living gerbil cochleae that the reticular lamina vibration occurs after, not before, the basilar membrane vibration. Both tone- and click-induced responses indicate that the reticular lamina and basilar membrane vibrate in opposite directions at the cochlear base and they oscillate in phase near the best-frequency location. Our results suggest that outer hair cells enhance hearing sensitivity through a global hydromechanical mechanism, rather than through a local mechanical feedback as commonly supposed.

What is the quietest sound the ear can detect? All sounds begin as vibrating air molecules, which enter the ear and cause the eardrum to vibrate. We can detect vibrations that move the eardrum by a distance of less than one picometer. That’s one thousandth of a nanometer, or about 100 times smaller than a hydrogen atom. But how does the ear achieve this level of sensitivity?

Vibrations of the eardrum cause three small bones within the middle ear to vibrate. The vibrations then spread to the cochlea, a fluid-filled spiral structure in the inner ear. Tiny hair cells lining the cochlea move as a result of the vibrations. There are two types of hair cells: inner and outer. Outer hair cells amplify the vibrations. It is this amplification that enables us to detect such small movements of the eardrum. Inner hair cells then convert the amplified vibrations into electrical signals, which travel via the auditory nerve to the brain.

The bases of outer hair cells are connected to a structure called the basilar membrane, while their tops are anchored to a structure called the reticular lamina. It was generally assumed that outer hair cells amplify vibrations of the basilar membrane via a local positive feedback mechanism that requires the hair cells to vibrate first. But by comparing the timing of reticular lamina and basilar membrane vibrations in gerbils, He et al. show that this is not the case. Outer hair cells vibrate after the basilar membrane, not before. This indicates that outer hair cells use a mechanism other than commonly assumed local feedback to amplify sounds.

The results presented by He et al. change our understanding of how the cochlea works, and may help bioengineers to design better hearing aids and cochlea implants. Millions of patients worldwide who suffer from hearing loss may ultimately stand to benefit.

The Frequency Response of Outer Hair Cell Voltage-Dependent Motility Is Limited by Kinetics of Prestin

The voltage-dependent protein SLC26a5 (prestin) underlies outer hair cell electromotility (eM), which is responsible for cochlear amplification in mammals. The electrical signature of eM is a bell-shaped nonlinear capacitance (NLC), deriving from prestin sensor-charge (Qp) movements, which peaks at the membrane voltage, Vh, where charge is distributed equally on either side of the membrane. Voltage dependencies of NLC and eM differ depending on interrogation frequency and intracellular chloride, revealing slow intermediate conformational transitions between anion binding and voltage-driven Qp movements. Consequently, NLC exhibits low-pass characteristics, substantially below prevailing estimates of eM frequency response. Here we study in guinea pig and mouse of either sex synchronous prestin electrical (NLC, Qp) and mechanical (eM) activity across frequencies under voltage clamp (whole cell and microchamber). We find that eM and Qp magnitude and phase correspond, indicating tight piezoelectric coupling. Electromechanical measures (both NLC and eM) show dual-Lorentzian, low-pass behavior, with a limiting (τ2) time constant at Vh of 32.6 and 24.8 μs, respectively. As expected for voltage-dependent kinetics, voltage excitation away from Vh has a faster, flatter frequency response, with our fastest measured τ2 for eM of 18.2 μs. Previous observations of ultrafast eM (τ ≈ 2 μs) were obtained at offsets far removed from Vh We hypothesize that trade-offs in eM gain-bandwith arising from voltage excitation at membrane potentials offset from Vh influence the effectiveness of cochlear amplification across frequencies.SIGNIFICANCE STATEMENT Of two types of hair cells within the organ of Corti, inner hair cells and outer hair cells, the latter evolved to boost sensitivity to sounds. Damage results in hearing loss of 40-60 dB, revealing amplification gains of 100-1000× that arise from voltage-dependent mechanical responses [electromotility (eM)]. eM, driven by the membrane protein prestin, may work beyond 70 kHz. However, this speed exceeds, by over an order of magnitude, kinetics of typical voltage-dependent membrane proteins. We find eM is actually low pass in nature, indicating that prestin bears kinetics typical of other membrane proteins. These observations highlight potential difficulties in providing sufficient amplification beyond a cutoff frequency near 20 kHz. Nevertheless, observed trade-offs in eM gain-bandwith may sustain cochlear amplification across frequency.