Mechanical overstimulation of hair bundles: suppression and recovery of active motility

Active Biomechanics of Sensory Hair Bundles

During the detection of sound, hair bundles perform a crucial step by responding to mechanical deflections and converting them into changes in electrical potential that subsequently lead to the release of neurotransmitter. The sensory hair bundle response is characterized by an essential nonlinearity and an energy-consuming amplification of the incoming sound. The active response has been shown to enhance the hair bundle's sensitivity and frequency selectivity of detection. The biological phenomena shown by the bundle have been extensively studied in vitro, allowing comparisons to behaviors observed in vivo. The experimental observations have been well explained by numerical simulations, which describe the cellular mechanisms operant within the bundle, as well as by more sparse theoretical models, based on dynamical systems theory.

Homeostatic enhancement of sensory transduction

Our sense of hearing boasts exquisite sensitivity, precise frequency discrimination, and a broad dynamic range. Experiments and modeling imply, however, that the auditory system achieves this performance for only a narrow range of parameter values. Small changes in these values could compromise hair cells' ability to detect stimuli. We propose that, rather than exerting tight control over parameters, the auditory system uses a homeostatic mechanism that increases the robustness of its operation to variation in parameter values. To slowly adjust the response to sinusoidal stimulation, the homeostatic mechanism feeds back a rectified version of the hair bundle's displacement to its adaptation process. When homeostasis is enforced, the range of parameter values for which the sensitivity, tuning sharpness, and dynamic range exceed specified thresholds can increase by more than an order of magnitude. Signatures in the hair cell's behavior provide a means to determine through experiment whether such a mechanism operates in the auditory system. Robustness of function through homeostasis may be ensured in any system through mechanisms similar to those that we describe here.

Frequency locking in auditory hair cells: Distinguishing between additive and parametric forcing

- The auditory system displays remarkable sensitivity and frequency discrimination, attributes shown to rely on an amplification process that involves a mechanical as well as a biochemical response. Models that display proximity to an oscillatory onset (also known as Hopf bifurcation) exhibit a resonant response to distinct frequencies of incoming sound, and can explain many features of the amplification phenomenology. To understand the dynamics of this resonance, frequency locking is examined in a system near the Hopf bifurcation and subject to two types of driving forces: additive and parametric. Derivation of a universal amplitude equation that contains both forcing terms enables a study of their relative impact on the hair cell response. In the parametric case, although the resonant solutions are 1 : 1 frequency locked, they show the coexistence of solutions obeying a phase shift of π, a feature typical of the 2 : 1 resonance. Different characteristics are predicted for the transition from unlocked to locked solutions, leading to smooth or abrupt dynamics in response to different types of forcing. The theoretical framework provides a more realistic model of the auditory system, which incorporates a direct modulation of the internal control parameter by an applied drive. The results presented here can be generalized to many other media, including Faraday waves, chemical reactions, and elastically driven cardiomyocytes, which are known to exhibit resonant behavior.

Magnetic Force Nanoprobe for Direct Observation of Audio Frequency Tonotopy of Hair Cells

Sound perception via mechano-sensation is a remarkably sensitive and fast transmission process, converting sound as a mechanical input to neural signals in a living organism. Although knowledge of auditory hair cell functions has advanced over the past decades, challenges remain in understanding their biomechanics, partly because of their biophysical complexity and the lack of appropriate probing tools. Most current studies of hair cells have been conducted in a relatively low-frequency range (<1000 Hz); therefore, fast kinetic study of hair cells has been difficult, even though mammalians have sound perception of 20 kHz or higher. Here, we demonstrate that the magnetic force nanoprobe (MFN) has superb spatiotemporal capabilities to mechanically stimulate spatially-targeted individual hair cells with a temporal resolution of up to 9 μs, which is equivalent to approximately 50 kHz; therefore, it is possible to investigate avian hair cell biomechanics at different tonotopic regions of the cochlea covering a full hearing frequency range of 50 to 5000 Hz. We found that the variation of the stimulation frequency and amplitude of hair bundles creates distinct mechanical responsive features along the tonotopic axis, where the kinetics of the hair bundle recovery motion exhibits unique frequency-dependent characteristics: basal, middle, and apical hair bundles can effectively respond at their respective ranges of frequency. We revealed that such recovery kinetics possesses two different time constants that are closely related to the passive and active motilities of hair cells. The use of MFN is critical for the kinetics study of free-standing hair cells in a spatiotemporally distinct tonotopic organization.

Voltage-Mediated Control of Spontaneous Bundle Oscillations in Saccular Hair Cells

Hair cells of the vertebrate vestibular and auditory systems convert mechanical inputs into electrical signals that are relayed to the brain. This transduction involves mechanically gated ion channels that open following the deflection of mechanoreceptive hair bundles that reside on top of these cells. The mechano-electrical transduction includes one or more active feedback mechanisms to keep the mechanically gated ion channels in their most sensitive operating range. Coupling between the gating of the mechanosensitive ion channels and this adaptation mechanism leads to the occurrence of spontaneous limit-cycle oscillations, which indeed have been observed in vitro in hair cells from the frog sacculus and the turtle basilar papilla. We obtained simultaneous optical and electrophysiological recordings from bullfrog saccular hair cells with such spontaneously oscillating hair bundles. The spontaneous bundle oscillations allowed us to characterize several properties of mechano-electrical transduction without artificial loading the hair bundle with a mechanical stimulus probe. We show that the membrane potential of the hair cell can modulate or fully suppress innate oscillations, thus controlling the dynamic state of the bundle. We further demonstrate that this control is exerted by affecting the internal calcium concentration, which sets the resting open probability of the mechanosensitive channels. The auditory and vestibular systems could use the membrane potential of hair cells, possibly controlled via efferent innervation, to tune the dynamic states of the cells.

Synchronization of Spontaneous Active Motility of Hair Cell Bundles

Hair cells of the inner ear exhibit an active process, believed to be crucial for achieving the sensitivity of auditory and vestibular detection. One of the manifestations of the active process is the occurrence of spontaneous hair bundle oscillations in vitro. Hair bundles are coupled by overlying membranes in vivo; hence, explaining the potential role of innate bundle motility in the generation of otoacoustic emissions requires an understanding of the effects of coupling on the active bundle dynamics. We used microbeads to connect small groups of hair cell bundles, using in vitro preparations that maintain their innate oscillations. Our experiments demonstrate robust synchronization of spontaneous oscillations, with either 1:1 or multi-mode phase-locking. The frequency of synchronized oscillation was found to be near the mean of the innate frequencies of individual bundles. Coupling also led to an improved regularity of entrained oscillations, demonstrated by an increase in the quality factor.

Magnetic nanoparticles for ultrafast mechanical control of inner ear hair cells

We introduce cubic magnetic nanoparticles as an effective tool for precise and ultrafast control of mechanosensitive cells. The temporal resolution of our system is ∼1000 times faster than previously used magnetic switches and is comparable to the current state-of-the-art optogenetic tools. The use of a magnetism-gated switch reported here can address the key challenges of studying mechanotransduction in biological systems. The cube-shaped magnetic nanoparticles are designed to bind to components of cellular membranes and can be controlled with an electromagnet to exert pico-Newtons of mechanical force on the cells. The cubic nanoparticles can thus be used for noncontact mechanical control of the position of the stereocilia of an inner ear hair cell, yielding displacements of tens of nanometers, with sub-millisecond temporal resolution. We also prove that such mechanical stimulus leads to the influx of ions into the hair cell. Our study demonstrates that a magnetic switch can yield ultrafast temporal resolution, and has capabilities for remote manipulation and biological specificity, and that such magnetic system can be used for the study of mechanotransduction processes of a wide range of sensory systems.

Low frequency entrainment of oscillatory bursts in hair cells

Sensitivity of mechanical detection by the inner ear is dependent upon a highly nonlinear response to the applied stimulus. Here we show that a system of differential equations that support a subcritical Hopf bifurcation, with a feedback mechanism that tunes an internal control parameter, captures a wide range of experimental results. The proposed model reproduces the regime in which spontaneous hair bundle oscillations are bistable, with sporadic transitions between the oscillatory and the quiescent state. Furthermore, it is shown, both experimentally and theoretically, that the application of a high-amplitude stimulus to the bistable system can temporarily render it quiescent before recovery of the limit cycle oscillations. Finally, we demonstrate that the application of low-amplitude stimuli can entrain bundle motility either by mode-locking to the spontaneous oscillation or by mode-locking the transition between the quiescent and oscillatory states.