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Processing of two-tone stimuli by the auditory system introduces prominent masking of one frequency component by the other as well as additional "phantom" tones that are absent in the sound input. Mechanical correlates of these psychophysical phenomena have been observed in sound-evoked mechanical vibrations of the mammalian cochlea and are thought to originate in sensory hair cells from the intrinsic nonlinearity associated with mechano-electrical transduction by ion channels. However, nonlinearity of the transducer is not sufficient to explain the rich phenomenology of two-tone interferences in hearing. Here we show that active oscillatory movements of single hair-cell bundles elicit two-tone suppression and distortions that are shaped by nonlinear amplification of periodic stimuli near the characteristic frequency of spontaneous oscillations. When both stimulus frequencies enter the bandwidth of the hair-bundle amplifier, two-tone interferences display level functions that are characteristic both of human psychoacoustics and of in vivo mechanical measurements in auditory organs. Our work distinguishes the frequency-dependent nonlinearity that emerges from the active process that drives the hair bundle into spontaneous oscillations from the passive nonlinear compliance associated with the direct gating of transduction channels by mechanical force. Numerical simulations based on a generic description of an active dynamical system poised near an oscillatory instability--a Hopf bifurcation--account quantitatively for our experimental observations. In return, we conclude that the properties of two-tone interferences in hearing betray the workings of self-sustained "critical" oscillators, which function as nonlinear amplifying elements in the inner ear.

Phantom tones and suppressive masking by active nonlinear oscillation of the hair-cell bundle