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 low-frequency 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.

Fig. 1.

Principles of cochlear mechanics. (A) In a schematic diagram of the mammalian cochlea, the basilar membrane (BM) is displaced by sound stimuli acting on the stapes (Upper Left). (B) In the classical theory of cochlear mechanics, sound evokes a pressure wave that causes a longitudinal traveling wave of basilar-membrane displacement (Thick Line). The motion of the basilar membrane and the displacements of the associated hair bundles are approximately equal. As the wave approaches the position where its frequency matches the basilar membrane’s resonant frequency, the wave’s amplitude (Thin Line) increases and its wavelength and velocity decline. The wave peaks at a characteristic place slightly before the resonant position and then declines sharply, yielding a strongly asymmetric envelope of the traveling wave (Shading). Experiments confirm this behavior in the basal, high-frequency part of the cochlea. (C) We propose an alternative theory for the cochlea’s mechanics at low frequencies. The basilar membrane near the cochlear apex does not resonate, but the traveling wave on the basilar membrane propagates along the entire cochlea without a strong variation in amplitude, wavelength, and velocity (Black). However, the interplay of electromotility and active hair-bundle motility fosters an independent resonance of the complex formed by the hair bundles, reticular lamina, and tectorial membrane. The hair-bundle displacement (Red) at the characteristic place can therefore exhibit an approximately symmetric peak, exceeding basilar membrane motion by orders of magnitude.

Fig. 2.

The ratchet mechanism. (A) The organ of Corti rests upon the basilar membrane (BM). Three OHCs are connected to Deiters’ cells (DC) that together couple the basilar membrane to the reticular lamina (Dark Green, top of the OHCs) and through the hair bundles to the overlying tectorial membrane (TM). Sound-evoked external forces (Black Arrow) displace the basilar membrane, here upwards, and produce shearing (Black Arrow) of the hair bundles of OHCs (Red Asterisk) and the inner hair cell (IHC) (Cyan Asterisk). Two forms of motility underlie the active process: active hair-bundle motility (Single-Headed Red Arrow) and membrane-based electromotility (Double-Headed Red Arrow). (B) The two fundamental degrees of freedom are the basilar-membrane displacement X_BM and the displacement X_HB of the hair-bundle complex (circle) that comprises the hair bundles, reticular lamina (RL), and tectorial-membrane. Coupling stems from the impedance Z_D of the combined OHCs and Deiters’ cells as well as the impedance Z_C of the remaining organ of Corti. (C) In the ratchet mechanism, displacements of the basilar membrane caused by external forces are communicated to the hair-bundle complex. Internal forces (Red Arrow) in the hair bundles increase the shearing motion that decouples from basilar-membrane displacement through appropriate length changes of the OHCs (Dotted Red Arrow). For an animated representation of the model, see Movie S1.

Fig. 3.

Cochlear model. (A) The ratchet mechanism operates when the mechanomotility coefficient α (Green) coincides with the critical value α_∗ (gray). Although electromotility is negligible to the basal side of f_H, it underlies the ratchet mechanism apical to the position of f_L. (B) The resonant frequency of the hair-bundle complex (HB, Red) agrees with that of the basilar membrane (BM, Blue) only for frequencies above f_L. (C) A high-frequency sound stimulus (f₁ = 8 kHz) induces a traveling wave that peaks in the basal region. The displacements of the hair bundles (Red) coincide with that of the basilar membrane (Blue). Elimination of active hair-bundle motility decreases the sensitivity by a factor of 90,000 (Green, hair bundles; Black, basilar membrane) indicative of a strong nonlinearity. A low-frequency stimulus (f₂ = 200 Hz) triggers a traveling wave that does not peak on the basilar membrane, but the hair-bundle displacement exhibits a resonance enabled by the ratchet mechanism (same color code). Without active hair-bundle motion the hair-bundle displacement decreases by a factor of only 10, indicative of a weak nonlinearity. (D) The phase of the basilar-membrane displacement for f₁ has a strongly increasing slope near the resonant position and thus shows a wave traveling to the resonant position but not beyond. For f₂ the slope of the phase remains almost constant, corresponding to a wave traveling beyond the characteristic place.

Fig. 4.

Threshold tuning curves of auditory-nerve fibers. (A) The tuning curve at each position along the cochlea has a characteristic frequency f₀ corresponding to the resonant frequency of the hair-bundle complex. When tuning curves are rescaled such that the frequency is measured in octaves relative to the characteristic frequency f₀ and the threshold is measured relative to that at the characteristic frequency, characteristic shape changes are seen to occur between curves of different characteristic frequencies. (B) Tuning curves for high characteristic frequencies, above f_H, fall onto a universal curve that exhibits the strongly asymmetric form and high-frequency cutoff characteristic of a peaked traveling wave. (C) As the characteristic frequency declines from f_H to f_L, the left limb falls (Arrow), indicating the emerging influence of electromotility and the ratchet mechanism. (D) As the characteristic frequency diminishes below f_L, the right limb falls steeply (Arrow), pointing to the breakdown of the peaked-wave mechanism and the dominance of ratchet amplification.