Phase-locked spiking of inner ear hair cells and the driven noisy Adler equation

Abstract

The inner ear constitutes a remarkably sensitive mechanical detector. This detection occurs in a noisy and highly viscous environment, as the sensory cells—the hair cells—are immersed in a fluid-filled compartment and operate at room or higher temperatures. We model the active motility of hair cell bundles of the vestibular system with the Adler equation, which describes the phase degree of freedom of bundle motion. We explore both analytically and numerically the response of the system to external signals, in the presence of white noise. The theoretical model predicts that hair bundles poised in the quiescent regime can exhibit sporadic spikes—sudden excursions in the position of the bundle. In this spiking regime, the system exhibits stochastic resonance, with the spiking rate peaking at an optimal level of noise. Upon the application of a very weak signal, the spikes occur at a preferential phase of the stimulus cycle. We compare the theoretical predictions of our model to experimental measurements obtained in vitro from individual hair cells. Finally, we show that an array of uncoupled hair cells could provide a sensitive detector that encodes the frequency of the applied signal.

Mechanical Amplification Exhibited by Quiescent Saccular Hair Bundles

“…The addition of an offset term leads to a time-dependent modulation of the barrier height. It was shown that such a model leads to the occurrence of spikes, which can be entrained by a weak signal (31). Our data confirm the existence of spikes, and show that this entrainment occurs at extremely weak signals, before any effects on spike amplitude or rate are observed.…”

“…The characteristics of spiking behavior shown here are consistent with theoretical studies of hair bundle motility (18,31). In a recent study, hair cell motion was modeled with a time-dependent Adler equation, which describes a system moving in a tilted washboard potential.…”

Targeted assembly and synchronization of self-spinning microgears

“…In the absence of noise, the phase is trapped in a potential well at high coupling, 3δω/ε < 1, and slides down the corrugated energy landscape at low coupling 33 . This qualitatively describes the phase-locking observed for contra-rotating rotors, for which δω ~ 0, and the slow revolution at Ω of co-rotating pairs, for which δω ~ 2ω.…”

High-order synchronization of hair cell bundles

“…4d). The presence of noise therefore helps the ensemble to encode high frequencies, analogous to stochastic resonance predicted for individual hair bundles38. Extracting the intensity of physiological noise from our data, and comparing it to results of the simulations, we found that the innate biological noise is in the range that offers a compromise between the enhancement of detection of high frequencies and maintaining the detection of low frequencies (see SI.…”

“…Variation of internal control parameters poises hair cells near different bifurcations, leading to different phase-locking characteristics133638. Hair bundle exhibits a regime of spontaneous limit cycle oscillation15, the frequency of which reveals an internal time scale defined by the active processes within the bundle.…”