Anomalous Brownian motion discloses viscoelasticity in the ear’s mechanoelectrical-transduction apparatus

Abstract

The ear detects sounds so faint that they produce only atomic-scale displacements in the mechanoelectrical transducer, yet thermal noise causes fluctuations larger by an order of magnitude. Explaining how hearing can operate when the magnitude of the noise greatly exceeds that of the signal requires an understanding both of the transducer's micromechanics and of the associated noise. Using microrheology, we characterize the statistics of this noise; exploiting the fluctuation-dissipation theorem, we determine the associated micromechanics. The statistics reveal unusual Brownian motion in which the mean square displacement increases as a fractional power of time, indicating that the mechanisms governing energy dissipation are related to those of energy storage. This anomalous scaling contradicts the canonical model of mechanoelectrical transduction, but the results can be explained if the micromechanics incorporates viscoelasticity, a salient characteristic of biopolymers. We amend the canonical model and demonstrate several consequences of viscoelasticity for sensory coding.auditory system | hair cell | interferometry | vestibular system T he development of experimental and analytical tools has made possible high-resolution studies of the mechanical properties of biological macromolecules on time scales ranging from the picosecond fluctuations of single amide bonds in proteins, through the submillisecond dynamics of ion-channel gating and enzyme catalysis, to the much slower events involved in cell division and motility (1,2). These studies reveal that the energy landscapes in proteins are complex and that the associated hierarchy of time scales produces nonexponential temporal correlations (3,4). The absence of a single characteristic time scale implies stochastic processes with memory and therefore distinct from simple diffusion.Auditory physiology offers a unique perspective on biological micromechanics. The conversion of a sound's energy into an electrical signal in the ear is a molecular event that involves an ion channel linked mechanically to a gating spring, an elastic element whose tension is modulated by sound. The weakest sounds that we can hear extend the gating spring by less than a nanometer (5,6). Under these conditions, separating the signal from the intrinsic thermal noise is a formidable task, but one facilitated by the periodic structure of most sounds. Although random fluctuations are known to dominate hair-bundle kinematics and to influence signal detection through stochastic resonance (7), their origin and statistical properties have remained obscure. In this work we have experimentally characterized the random fluctuations of hair bundles by dual-beam differential interferometry, a technique that has allowed us to make large-bandwidth, high-resolution measurements of the nanometer-scale thermal motions of stereocilia in living hair bundles from the inner ear. We have interpreted the measurements by introducing a theoretical framework that incorporates viscoelasticity and the known principl...

An elastic element in the protocadherin-15 tip link of the inner ear

“…17). Moreover, while sound transduction is a fast process that can occur in microseconds, SMD simulations are performed at stretching velocities that match only part of the spectrum of physiological stimuli and that may not completely capture the viscoelastic response60 of tip link cadherins (see Supplementary Discussion). Yet our structure and simulations of PCDH15 EC8–10 points to a key mechanical component of the tip link that is elastic and that must be incorporated in hair-cell transduction models.…”

Integrating the active process of hair cells with cochlear function

“…There are at least four possible explanations for fast adaptation. First, the phenomenon might simply represent the viscoelastic relaxation of some element in series with the transduction channels 79,86,133 . Because this mechanism is passive, it could not supply energy useful for amplifying mechanical inputs.…”

“…An alternative prospect is that the tip link's stiffness has been overestimated owing to crystallization of the Ca 2+ -stabilized cadherin domains at a Ca 2+ concentration much greater than the 20 μM that prevails in mammalian endolymph 83,84 . Ca 2+ ions affect the stiffness of gating springs 85 , which additionally display complex viscoelastic properties 86 .…”

Transduction channels’ gating can control friction on vibrating hair-cell bundles in the ear

“…Here we introduced the frequency-dependent parameter α 4 n = i n ω 0 =ω S , with ω S = ω 1 =β 4 1 , ω 1 the angular cutoff frequency of thermal fluctuations of the fiber's tip (see previous paragraph), and in which β 1 ≅ 1:8751 is the smallest positive solution of cos β 1 × cosh β 1 = −1. Data analysis was performed with Matlab (the Mathworks, version R2011b).…”

“…First, viscous drag by the surrounding fluid provides a minimum source of damping (2,3). Second, viscoelasticity of the tip links, or of proteins in series with these links, may result in additional dissipation during hair-bundle deflections (4). Third, an intrinsic source of friction-called "channel friction" in the following-is related to thermal fluctuations of the transduction channels between their open and closed states (5).…”