Effects of cochlear loading on the motility of active outer hair cells

Abstract

Outer hair cells (OHCs) power the amplification of sound-induced vibrations in the mammalian inner ear through an active process that involves hair-bundle motility and somatic motility. It is unclear, though, how either mechanism can be effective at high frequencies, especially when OHCs are mechanically loaded by other structures in the cochlea. We address this issue by developing a model of an active OHC on the basis of observations from isolated cells, then we use the model to predict the response of an active OHC in the intact cochlea. We find that active hair-bundle motility amplifies the receptor potential that drives somatic motility. Inertial loading of a hair bundle by the tectorial membrane reduces the bundle's reactive load, allowing the OHC's active motility to influence the motion of the cochlear partition. The system exhibits enhanced sensitivity and tuning only when it operates near a dynamical instability, a Hopf bifurcation. This analysis clarifies the roles of cochlear structures and shows how the two mechanisms of motility function synergistically to create the cochlear amplifier. The results suggest that somatic motility evolved to enhance a preexisting amplifier based on active hair-bundle motility, thus allowing mammals to hear high-frequency sounds.adaptation | electromotility | hearing | nonlinear dynamics O ur ears are amazing signal detectors that reconcile great sensitivity with an enormous dynamic range. The faintest sounds that we can hear vibrate our eardrums by less than 1 pm and are a trillion times less intense than the loudest sounds that we can tolerate (1, 2). We can distinguish pure tones that differ in frequency by less than 0.2%, yet the frequency range of our ears exceeds a thousandfold (2). These features are all the more remarkable given that the mechanoreceptive organ of Corti operates in liquid and is therefore highly damped (3).An active process enhances the performance of the mammalian ear by augmenting sound-induced vibrations in the cochlea (2-6). This process results from the action of specialized outer hair cells (OHCs) whose motility boosts the motion of the cochlea in response to sounds, thus amplifying the signal transmitted to the brain. These cells counteract the damping that would otherwise limit the cochlea's sensitivity and frequency discrimination (3, 7). OHCs exhibit two forms of mechanical activity, hair-bundle motility and somatic motility, which may both contribute to the cochlear amplifier.Named for the mechanosensitive hair bundles protruding from their apices, hair cells transduce vibrations of their bundles into an electrical response. Cochlear hair cells are housed in the cochlear partition, which includes the organ of Corti sandwiched between the tectorial and basilar membranes (Fig. 1A). The hair bundle of each OHC is connected at its tip to the acellular tectorial membrane, and the soma of each OHC is linked to the basilar membrane through a rigid Deiters' cell (8). These membranes mechanically load each OHC with mass, damping, and stiffness....

Vibrational modes and damping in the cochlear partition

“…Active hair-bundle motility in turn amplifies the receptor potential driving somatic motility, thus solving the problem of the RC time constant [15]. That issue was predicated on the assumption that the current driving the receptor potential was frequency-independent.…”

“…The damping and stiffness of the partition, however, can render active hair-bundle motility ineffective by mechanically loading the bundle and suppressing the loop of Hopf bifurcations. These loads are counteracted respectively by feedback from somatic motility and mass loading by the tectorial membrane [13][14][15], allowing active hair-bundle motility to occur at frequencies exceeding 10 kHz.…”

“…Most of the values required to parameterize the model are known for a only few locations in the cochlea [12,15]. The values for the damping coefficients associated with the dashpots are unknown, however, as are the exact values for K a and α in Eq.…”

“…1B). The parameter values used in the description of hair-bundle motility are chosen such that the modeled bundle reproduces observations from outer hair cells under physiological conditions [7,15]. The current through the outer hair cell is described by a set of resistors, capacitors, and a piezoelectric element (Fig.…”

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

“…Indeed, experimental measurements have been performed and revealed complex dynamics in the transition from spontaneous oscillation into the resonance regime [31,64,65]. Experimental results have raised conjectures on the possible presence of both super-and sub-critical forms of the Hopf instability [1].…”