The Competition between the Noise and Shear Motion Sensitivity of Cochlear Inner Hair Cell Stereocilia

Comments on "What is silence? Therefore, what is sound?" - A discussion of Brownian motion and the threshold of hearing (L)

This Letter to the editor is a comment on an article in the JASA Forum by William Yost. It pertains to a reference he made to prior work that indicates the possibility that the human threshold of hearing in the most sensitive region may be limited by Brownian motion of the air molecules, also called thermal noise. I present additional data and my own observations that support this contention.

Noise within: Signal-to-noise enhancement via coherent wave amplification in the mammalian cochlea

The extraordinary sensitivity of the mammalian inner ear has captivated scientists for decades, largely due to the crucial role played by the outer hair cells (OHCs) and their unique electromotile properties. Typically arranged in three rows along the sensory epithelium, the OHCs work in concert via mechanisms collectively referred to as the "cochlear amplifier" to boost the cochlear response to faint sounds. While simplistic views attribute this enhancement solely to the OHC-based increase in cochlear gain, the inevitable presence of internal noise requires a more rigorous analysis. Achieving a genuine boost in sensitivity through amplification requires that signals be amplified more than internal noise, and this requirement presents the cochlea with an intriguing challenge. Here we analyze the effects of spatially distributed cochlear-like amplification on both signals and internal noise. By combining a straightforward mathematical analysis with a simplified model of cochlear mechanics designed to capture the essential physics, we generalize previous results about the impact of spatially coherent amplification on signal degradation in active gain media. We identify and describe the strategy employed by the cochlea to amplify signals more than internal noise and thereby enhance the sensitivity of hearing. For narrow-band signals, this effective, wave-based strategy consists of spatially amplifying the signal within a localized cochlear region, followed by rapid attenuation. Location-dependent wave amplification and attenuation meet the necessary conditions for amplifying near-characteristic frequency (CF) signals more than internal noise components of the same frequency. Our analysis reveals that the sharp wave cutoff past the CF location greatly reduces noise contamination. The distinctive asymmetric shape of the "cochlear filters" thus underlies a crucial but previously unrecognized mechanism of cochlear noise reduction.

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.

Coupling between the Stereocilia of Rat Sensory Inner-Hair-Cell Hair Bundles Is Weak, Shaping Their Sensitivity to Stimulation

The hair bundle is the universal mechanosensory organelle of auditory, vestibular, and lateral-line systems. A bundle comprises mechanically coupled stereocilia, whose displacements in response to stimulation activate a receptor current. The similarity of stereociliary displacements within a bundle regulates fundamental properties of the receptor current like its speed, magnitude, and sensitivity. However, the dynamics of individual stereocilia from the mammalian cochlea in response to a known bundle stimulus has not been quantified. We developed a novel high-speed system, which dynamically stimulates and tracks individual inner-hair-cell stereocilia from male and female rats. Stimulating two to three of the tallest stereocilia within a bundle (nonuniform stimulation) caused dissimilar stereociliary displacements. Stereocilia farther from the stimulator moved less, but with little delay, implying that there is little slack in the system. Along the axis of mechanical sensitivity, stereocilium displacements peaked and reversed direction in response to a step stimulus. A viscoelastic model explained the observed displacement dynamics, which implies that coupling between the tallest stereocilia is effectively viscoelastic. Coupling elements between the tallest inner-hair-cell stereocilia were two to three times stronger than elements anchoring stereocilia to the surface of the cell but were 100-10,000 times weaker than those of a well-studied noncochlear hair bundle. Coupling was too weak to ensure that stereocilia move similarly in response to nonuniform stimulation at auditory frequencies. Our results imply that more uniform stimulation across the tallest stereocilia of an inner-hair-cell bundle in vivo is required to ensure stereociliary displacement similarity, increasing the speed, sensitivity, and magnitude of the receptor current.SIGNIFICANCE STATEMENT Generation of the receptor current of the hair cell is the first step in electrically encoding auditory information in the hearing organs of all vertebrates. The receptor current is shaped by mechanical coupling between stereocilia in the hair bundle of each hair cell. Here, we provide foundational information on the mechanical coupling between stereocilia of cochlear inner-hair cells. In contrast to other types of hair cell, coupling between inner-hair-cell stereocilia is weak, causing slower, smaller, and less sensitive receptor currents in response to stimulation of few, rather than many, stereocilia. Our results imply that inner-hair cells need many stereocilia to be stimulated in vivo to ensure fast, large, and sensitive receptor currents.

A flexible anatomical set of mechanical models for the organ of Corti

We build a flexible platform to study the mechanical operation of the organ of Corti (OoC) in the transduction of basilar membrane (BM) vibrations to oscillations of an inner hair cell bundle (IHB). The anatomical components that we consider are the outer hair cells (OHCs), the outer hair cell bundles, Deiters cells, Hensen cells, the IHB and various sections of the reticular lamina. In each of the components we apply Newton's equations of motion. The components are coupled to each other and are further coupled to the endolymph fluid motion in the subtectorial gap. This allows us to obtain the forces acting on the IHB, and thus study its motion as a function of the parameters of the different components. Some of the components include a nonlinear mechanical response. We find that slight bending of the apical ends of the OHCs can have a significant impact on the passage of motion from the BM to the IHB, including critical oscillator behaviour. In particular, our model implies that the components of the OoC could cooperate to enhance frequency selectivity, amplitude compression and signal to noise ratio in the passage from the BM to the IHB. Since the model is modular, it is easy to modify the assumptions and parameters for each component.

Unified cochlear model for low- and high-frequency mammalian hearing

The spatial variations of the intricate cytoarchitecture, fluid scalae, and mechano-electric transduction in the mammalian cochlea have long been postulated to provide the organ with the ability to perform a real-time, time-frequency processing of sound. However, the precise manner by which this tripartite coupling enables the exquisite cochlear filtering has yet to be articulated in a base-to-apex mathematical model. Moreover, while sound-evoked tuning curves derived from mechanical gains are excellent surrogates for auditory nerve fiber thresholds at the base of the cochlea, this correlation fails at the apex. The key factors influencing the divergence of both mechanical and neural tuning at the apex, as well as the spatial variation of mechanical tuning, are incompletely understood. We develop a model that shows that the mechanical effects arising from the combination of the taper of the cochlear scalae and the spatial variation of the cytoarchitecture of the cochlea provide robust mechanisms that modulate the outer hair cell-mediated active response and provide the basis for the transition of the mechanical gain spectra along the cochlear spiral. Further, the model predicts that the neural tuning at the base is primarily governed by the mechanical filtering of the cochlear partition. At the apex, microscale fluid dynamics and nanoscale channel dynamics must also be invoked to describe the threshold neural tuning for low frequencies. Overall, the model delineates a physiological basis for the difference between basal and apical gain seen in experiments and provides a coherent description of high- and low-frequency cochlear tuning.