Probing hair cell's mechano-transduction using two-tone suppression measurements

Rate Dependent Cochlear Outer Hair Cell Force Generation: Models and Parameter Estimation

The outer hair cells (OHCs) of the mammalian cochlea are the mediators of an active, nonlinear electromechanical process necessary for sensitive, frequency specific hearing. The membrane protein prestin conveys to the OHC a piezoelectric-like behavior hypothesized to actuate a high frequency, cycle-by-cycle conversion of electrical to mechanical energy to boost cochlear responses to low-level sound. This hypothesis has been debated for decades, and we address two key remaining issues: the influence of the rate dependence of conformal changes in prestin and the OHC transmembrane impedance. We develop a theoretical electromechanical model of the OHC that explicitly includes rate dependence of conformal transitions, viscoelasticity, and piezoelectricity. Using this theory, we show the influence of rate dependence and viscoelasticity on electromechanical force generation. Further, we stress the importance of using the correct mechanical boundary conditions when estimating the transmembrane capacitance. Finally, a set of experiments is described to uniquely estimate the constitutive properties of the OHC from whole-cell measurements.

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.

Deiters Cells Act as Mechanical Equalizers for Outer Hair Cells

The outer hair cells in the mammalian cochlea are cellular actuators essential for sensitive hearing. The geometry and stiffness of the structural scaffold surrounding the outer hair cells will determine how the active cells shape mammalian hearing by modulating the organ of Corti (OoC) vibrations. Specifically, the tectorial membrane and the Deiters cell are mechanically in series with the hair bundle and soma, respectively, of the outer hair cell. Their mechanical properties and anatomic arrangement must determine the relative motion among different OoC structures. We measured the OoC mechanics in the cochleas acutely excised from young gerbils of both sexes at a resolution fine enough to distinguish the displacement of individual cells. A three-dimensional finite element model of fully deformable OoC was exploited to analyze the measured data in detail. As a means to verify the computer model, the basilar membrane deformations because of static and dynamic stimulations were measured and simulated. Two stiffness ratios have been identified that are critical to understand cochlear physics, which are the stiffness of the tectorial membrane with respect to the hair bundle and the stiffness of the Deiters cell with respect to the outer hair cell body. Our measurements suggest that the Deiters cells act like a mechanical equalizer so that the outer hair cells are constrained neither too rigidly nor too weakly.SIGNIFICANCE STATEMENT Mammals can detect faint sounds thanks to the action of mammalian-specific receptor cells called the outer hair cells. It is getting clearer that understanding the interactions between the outer hair cells and their surrounding structures such as the tectorial membrane and the Deiters cell is critical to resolve standing debates. Depending on theories, the stiffness of those two structures ranges from negligible to rigid. Because of their perceived importance, their properties have been measured in previous studies. However, nearly all existing data were obtained ex situ (after they were detached from the outer hair cells), which obscures their interaction with the outer hair cells. We quantified the mechanical properties of the tectorial membrane and the Deiters cell in situ.

Complex dynamics of hair bundle of auditory nervous system (I): spontaneous oscillations and two cases of steady states

The hair bundles of inner hair cells in the auditory nervous exhibit spontaneous oscillations, which is the prerequisite for an important auditory function to enhance the sensitivity of inner ear to weak sounds, otoacoustic emission. In the present paper, the dynamics of spontaneous oscillations and relationships to steady state are acquired in a two-dimensional model with fast variable X (displacement of hair bundles) and slow variable X a . The spontaneous oscillations are derived from negative stiffness modulated by two biological factors (S and D) and are identified to appear in multiple two-dimensional parameter planes. In (S, D) plane, comprehensive bifurcations including 4 types of codimension-2 bifurcation and 5 types of codimension-1 bifurcation related to the spontaneous oscillations are acquired. The spontaneous oscillations are surrounded by supercritical and subcritical Hopf bifurcation curves, and outside of the curves are two cases of steady state. Case-1 and Case-2 steady states exhibit Z-shaped (coexistence of X) and N-shaped (coexistence of X a ) X-nullclines, respectively. In (S, D) plane, left and right to the spontaneous oscillations are two subcases of Case-1, which exhibit the stable equilibrium point locating on the upper and lower branches of X-nullcline, respectively, resembling that of the neuron. Lower to the spontaneous oscillations are 3 subcases of Case-2 from left to right, which manifest stable equilibrium point locating on left, middle, and right branches of X-nullcline, respectively, differing from that of the neuron. The phase plane for steady state is divided into four parts by nullclines, which manifest different vector fields. The phase trajectory of transient behavior beginning from a phase point in the four regions to the stable equilibrium point exhibits different dynamics determined by the vector fields, which is the basis to identify dynamical mechanism of complex forced oscillations induced by external signal. The results present comprehensive viewpoint and deep understanding for dynamics of the spontaneous oscillations and steady states of hair bundles, which can be used to well explain the experimental observations and to modulate functions of spontaneous oscillations.

The Elusive Cochlear Filter: Wave Origin of Cochlear Cross-Frequency Masking

The mammalian cochlea achieves its remarkable sensitivity, frequency selectivity, and dynamic range by spatially segregating the different frequency components of sound via nonlinear processes that remain only partially understood. As a consequence of the wave-based nature of cochlear processing, the different frequency components of complex sounds interact spatially and nonlinearly, mutually suppressing one another as they propagate. Because understanding nonlinear wave interactions and their effects on hearing appears to require mathematically complex or computationally intensive models, theories of hearing that do not deal specifically with cochlear mechanics have often neglected the spatial nature of suppression phenomena. Here we describe a simple framework consisting of a nonlinear traveling-wave model whose spatial response properties can be estimated from basilar-membrane (BM) transfer functions. Without invoking jazzy details of organ-of-Corti mechanics, the model accounts well for the peculiar frequency-dependence of suppression found in two-tone suppression experiments. In particular, our analysis shows that near the peak of the traveling wave, the amplitude of the BM response depends primarily on the nonlinear properties of the traveling wave in more basal (high-frequency) regions. The proposed framework provides perhaps the simplest representation of cochlear signal processing that accounts for the spatially distributed effects of nonlinear wave propagation. Shifting the perspective from local filters to non-local, spatially distributed processes not only elucidates the character of cochlear signal processing, but also has important consequences for interpreting psychophysical experiments.

Model of cochlear microphonic explores the tuning and magnitude of hair cell transduction current

The mammalian cochlea relies on the active forcing of sensory outer hair cells (OHCs) to amplify traveling wave responses along the basilar membrane. These forces are the result of electromotility, wherein current through the OHCs leads to conformational changes in the cells that provide stresses on surrounding structures. OHC transducer current can be detected via the voltage in the scala tympani (the cochlear microphonic, CM), and the CM can be used as an indicator of healthy cochlear operation. The CM represents a summation of OHC currents (the inner hair cell contribution is known to be small) and to use CM to probe the properties of OHC transduction requires a model that simulates that summation. We developed a finite element model for that purpose. The pattern of current generators (the model input) was initially based on basilar membrane displacement, with the current size based on in vitro data. The model was able to reproduce the amplitude of experimental CM results reasonably well when the input tuning was enhanced slightly (peak increased by ∼6 dB), which can be regarded as additional hair bundle tuning, and with a current/input value of 200-260 pA/nm, which is ∼4 times greater than the largest in vitro measures.

Intracochlear distortion products are broadly generated by outer hair cells but their contributions to otoacoustic emissions are spatially restricted

Detection of low-level sounds by the mammalian cochlea requires electromechanical feedback from outer hair cells (OHCs). This feedback arises due to the electromotile response of OHCs, which is driven by the modulation of their receptor potential caused by the stimulation of mechano-sensitive ion channels. Nonlinearity in these channels distorts impinging sounds, creating distortion-products that are detectable in the ear canal as distortion-product otoacoustic emissions (DPOAEs). Ongoing efforts aim to develop DPOAEs, which reflects the ear's health, into diagnostic tools for sensory hearing loss. These efforts are hampered by limited knowledge on the cochlear extent contributing to DPOAEs. Here, we report on intracochlear distortion products (IDPs) in OHC electrical responses and intracochlear fluid pressures. Experiments and simulations with a physiologically motivated cochlear model show that widely generated electrical IDPs lead to mechanical vibrations in a frequency-dependent manner. The local cochlear impedance restricts the region from which IDPs contribute to DPOAEs at low to moderate intensity, which suggests that DPOAEs may be used clinically to provide location-specific information about cochlear damage.

Mechanically facilitated micro-fluid mixing in the organ of Corti

The cochlea is filled with two lymphatic fluids. Homeostasis of the cochlear fluids is essential for healthy hearing. The sensory epithelium called the organ of Corti separates the two fluids. Corti fluid space, extracellular fluid space within the organ of Corti, looks like a slender micro-tube. Substantial potassium ions are constantly released into the Corti fluid by sensory receptor cells. Excess potassium ions in the Corti fluid are resorbed by supporting cells to maintain fluid homeostasis. Through computational simulations, we investigated fluid mixing within the Corti fluid space. Two assumptions were made: first, there exists a longitudinal gradient of potassium ion concentration; second, outer hair cell motility causes organ of Corti deformations that alter the cross-sectional area of the Corti fluid space. We hypothesized that mechanical agitations can accelerate longitudinal mixing of Corti fluid. Corti fluid motion was determined by solving the Navier–Stokes equations incorporating nonlinear advection term. Advection–diffusion equation determined the mixing dynamics. Simulating traveling boundary waves, we found that advection and diffusion caused comparable mixing when the wave amplitude and speed were 25 nm and 7 m/s, respectively. Higher-amplitude and faster waves caused stronger advection. When physiological traveling waves corresponding to 70 dB sound pressure level at 9 kHz were simulated, advection speed was as large as 1 mm/s in the region basal to the peak responding location. Such physiological agitation accelerated longitudinal mixing by more than an order of magnitude, compared to pure diffusion. Our results suggest that fluid motion due to outer hair cell motility can help maintain longitudinal homeostasis of the Corti fluid.

Utricular Sensitivity during Hydrodynamic Displacements of the Macula

To explore the effects of cochlear hair cell displacement, researchers have previously monitored functional and mechanical responses during low-frequency (LF) acoustic stimulation of the cochlea. The induced changes are believed to result from modulation of the conductance of mechano-electrical transduction (MET) channels on cochlear hair cells, along with receptor potential modulation. It is less clear how, or if, vestibular hair cell displacement affects vestibular function. Here, we have used LF (<20 Hz) hydrodynamic modulation of the utricular macula position, whilst recording functional and mechanical responses, to investigate the effects of utricular macula displacement. Measured responses included the Utricular Microphonic (UM), the vestibular short-latency evoked potential (VsEP), and laser Doppler vibrometry recordings of macular position. Over 1 cycle of the LF bias, the UM amplitude and waveform were cyclically modulated, with Boltzmann analysis suggesting a cyclic modulation of the vestibular MET gating. The VsEP amplitude was cyclically modulated throughout the LF bias, demonstrating a relative increase (~20-50 %; re baseline) and decrease (~10-20 %; re baseline), which is believed to be related to the MET conductance and vestibular hair cell sensitivity. The relationship between macular displacement and changes in UM and VsEP responses was consistent within and across animals. These results suggest that the sensory structures underlying the VsEP, often thought to be a cranial jerk-sensitive response, are at least partially sensitive to LF (and possibly static) pressures or motion. Furthermore, these results highlight the possibility that some of the vestibular dysfunction related to endolymphatic hydrops may be due to altered vestibular transduction following mechanical (or morphological) changes in the labyrinth.

Interactions between Passive and Active Vibrations in the Organ of Corti In Vitro

High sensitivity and selectivity of hearing require an active cochlea. The cochlear sensory epithelium, the organ of Corti, vibrates because of external and internal excitations. The external stimulation is acoustic pressures mediated by the scala fluids, whereas the internal excitation is generated by a type of sensory receptor cells (the outer hair cells) in response to the acoustic vibrations. The outer hair cells are cellular actuators that are responsible for cochlear amplification. The organ of Corti is highly structured for transmitting vibrations originating from acoustic pressure and active outer hair cell force to the inner hair cells that synapse on afferent nerves. Understanding how the organ of Corti vibrates because of acoustic pressure and outer hair cell force is critical for explaining cochlear function. In this study, cochleae were freshly isolated from young gerbils. The organ of Corti in the excised cochlea was subjected to mechanical and electrical stimulation that are analogous to acoustic and cellular stimulation in the natural cochlea. Organ of Corti vibrations, including those of individual outer hair cells, were measured using optical coherence tomography. Respective vibration patterns due to mechanical and electrical stimulation were characterized. Interactions between the two vibration patterns were investigated by applying the two forms of stimulation simultaneously. Our results show that the interactions could be either constructive or destructive, which implies that the outer hair cells can either amplify or reduce vibrations in the organ of Corti. We discuss a potential consequence of the two interaction modes for cochlear frequency tuning.

Nonlinear cochlear mechanics without direct vibration-amplification feedback

Recent in vivo recordings from the mammalian cochlea indicate that although the motion of the basilar membrane appears actively amplified and nonlinear only at frequencies relatively close to the peak of the response, the internal motions of the organ of Corti display these same features over a much wider range of frequencies. These experimental findings are not easily explained by the textbook view of cochlear mechanics, in which cochlear amplification is controlled by the motion of the basilar membrane (BM) in a tight, closed-loop feedback configuration. This study shows that a simple phenomenological model of the cochlea inspired by the work of Zweig [J. Acoust. Soc. Am. 138, 1102 (2015)] can account for recent data in mouse and gerbil. In this model, the active forces are regulated indirectly, through the effect of BM motion on the pressure field across the cochlear partition, rather than via direct coupling between active-force generation and BM vibration. The absence of strong vibration-amplification feedback in the cochlea also provides a compelling explanation for the observed intensity invariance of fine time structure in the BM response to acoustic clicks.