A ratchet mechanism for amplification in low-frequency mammalian hearing

Abstract

The sensitivity and frequency selectivity of hearing result from tuned amplification by an active process in the mechanoreceptive hair cells. In most vertebrates, the active process stems from the active motility of hair bundles. The mammalian cochlea exhibits an additional form of mechanical activity termed electromotility: its outer hair cells (OHCs) change length upon electrical stimulation. The relative contributions of these two mechanisms to the active process in the mammalian inner ear is the subject of intense current debate. Here, we show that active hair-bundle motility and electromotility can together implement an efficient mechanism for amplification that functions like a ratchet: Sound-evoked forces, acting on the basilar membrane, are transmitted to the hair bundles, whereas electromotility decouples active hair-bundle forces from the basilar membrane. This unidirectional coupling can extend the hearing range well below the resonant frequency of the basilar membrane. It thereby provides a concept for lowfrequency hearing that accounts for a variety of unexplained experimental observations from the cochlear apex, including the shape and phase behavior of apical tuning curves, their lack of significant nonlinearities, and the shape changes of threshold tuning curves of auditory-nerve fibers along the cochlea. The ratchet mechanism constitutes a general design principle for implementing mechanical amplification in engineering applications.auditory system | cochlea | hair cell T he mammalian cochlea acts as a frequency analyzer in which high frequencies are detected at the organ's base and low frequencies at more apical positions. This frequency mapping is thought to be achieved by a position-dependent resonance of the elastic basilar membrane separating two fluid-filled compartments ( Fig. 1A) (1-3). When sound evokes a pressure wave that displaces the basilar membrane, the resultant traveling wave gradually increases in amplitude as it progresses to the position where the basilar membrane's resonant frequency coincides with that of the stimulus. Aided by mechanical energy provided by the active process, the wave peaks at a characteristic place slightly before the resonant position and then declines sharply (Fig. 1B). This mechanism is termed critical-layer absorption (1), for a wave cannot travel beyond its characteristic position on the basilar membrane but peaks and dissipates most of its energy there. The mechanism displays scale invariance: different stimulation frequencies induce traveling waves that display a common, strongly asymmetric form upon rescaling of the amplitude and spatial coordinate (4, 5).Two important aspects of the cochlea's mechanics remain problematical. First, the basilar membrane's resonant frequency apparently cannot span the entire range of audible frequencies. Experimental measurements of basilar-membrane stiffness suggest that high-frequency resonances are feasible but lowfrequency ones are inaccessible (6). This result accords with the analysis of threshold tuning curve...

Auditory Nerve Excitation via a Non-traveling Wave Mode of Basilar Membrane Motion

“…Between BM motion and ANF responses lies HC excitation. Several theoretical studies have explored the relationship between BM and hair bundle motion, and this relationship is far from well understood (Neely and Kim 1986;Steele and Lim 1999;Cai and Chadwick 2003;Cai et al 2004;Steele and Puria 2005;Reichenbach and Hudspeth 2010). These models and in vitro experimental results (Nowotny and Gummer 2006) indicate that BM motion is not a direct predictor of hair bundle motion.…”

Unidirectional Amplification as a Mechanism for Low-Frequency Hearing in Mammals

“…Amplification in the apical region, however, is unidirectional. The basilar membrane is no longer tuned to the characteristic frequency but the hair-bundle complex exhibits an independent resonance enabled by unidirectional coupling ( [16], Fig. 2).…”

“…We discuss recent theoretical work in which we have proposed a ratchet mechanism for spatial separation of low frequencies that employs a synergistic interplay between the two cellular processes [16]. The fundamental feature of this mechanism is unidirectional coupling, an important property of an ideal amplifier.…”

A novel cochlea partition model based on asynchronous bifurcation processor

“…The spiral ganglion cells encode the receptor potential V I of the inner hair cell into parallel spike-trains, which are transmitted to the central nervous system. Due to its high nonlinearities, the whole cochlea (i.e., connected compartments of cochlea partition) exhibits a huge variety of nonlinear responses such as nonlinear DC response [4], nonlinear band-pass filtering [5][6][7], adaptation of spike density [8], multi-tone suppression [9,10], spike density modulation [11], missing fundamental, first pitch shift, second pitch shift, and so on (see also reviews in [1][2][3]). Among them, the nonlinear DC response, the nonlinear band-pass filtering, and the adaptation of spike density are important research topics when the cochlea partition is to be investigated like this paper since the other nonlinear responses are caused by connections of the compartments of the cochlea partition.…”

“…Among them, the nonlinear DC response, the nonlinear band-pass filtering, and the adaptation of spike density are important research topics when the cochlea partition is to be investigated like this paper since the other nonlinear responses are caused by connections of the compartments of the cochlea partition. In order to understand such complicated nonlinear responses of the cochlea partition and the whole cochlea, many mathematical models have been presented and analyzed intensively [1][2][3][4][5][6][7][8][9][10][11].…”