A Critique of the Critical Cochlea: Hopf—a Bifurcation—Is Better Than None

Abstract

Hudspeth AJ, Jülicher F, Martin P. A critique of the critical cochlea: Hopf-a bifurcation-is better than none. J Neurophysiol 104: 1219-1229. First published June 10, 2010 doi:10.1152/jn.00437.2010. The sense of hearing achieves its striking sensitivity, frequency selectivity, and dynamic range through an active process mediated by the inner ear's mechanoreceptive hair cells. Although the active process renders hearing highly nonlinear and produces a wealth of complex behaviors, these various characteristics may be understood as consequences of a simple phenomenon: the Hopf bifurcation. Any critical oscillator operating near this dynamic instability manifests the properties demonstrated for hearing: amplification with a specific form of compressive nonlinearity and frequency tuning whose sharpness depends on the degree of amplification. Critical oscillation also explains spontaneous otoacoustic emissions as well as the spectrum and level dependence of the ear's distortion products. Although this has not been realized, several valuable theories of cochlear function have achieved their success by incorporating critical oscillators.The technical specifications of the human ear are remarkable. We can hear sounds that evoke mechanical vibrations of magnitudes comparable to those produced by thermal noise (de Vries 1948;Sivian and White 1933). Hearing is so sharply tuned to specific frequencies that trained musicians can distinguish tones differing in frequency by only 0.1% (Spiegel and Watson 1984). Finally, our ears can process sounds over a range of amplitudes encompassing six orders of magnitude, which corresponds to a trillionfold range in stimulus power (Knudsen 1923).These striking characteristics of our hearing emerge because the ear is not a passive sensory receptor, but possesses an active process that augments audition in three ways (reviewed in Hudspeth 2008;Manley 2000Manley , 2001. First, amplification renders hearing several hundred times as sensitive as would be expected for a passive system. The active process next exhibits tuning that sharpens our frequency discrimination. Finally, a compressive nonlinearity ensures that inputs spanning an enormous range of sound-pressure levels are systematically encoded by a modest range of mechanical vibrations and in turn of receptor potentials and nerve-fiber firing rates. The active process additionally exhibits the striking epiphenomenon of spontaneous otoacoustic emission, the production of sound by an ear in the absence of external stimulation. Although considerable attention has been devoted to these properties in mammalian and especially human hearing, the four defining features of the active process are equally characteristic of nonmammalian tetrapods (reviewed in Manley 2001).

Time-Domain Representation of Active Nonlinear Cochlear Waves

“…In mammals, manifestations of the so-called cochlear amplifier are the high sensitivity and frequency selectivity with respect to weak stimuli, the compressive nonlinearity, and the generation of oto-acoustic emissions. All aspects of the active process are consistent with the notion of nonlinear oscillators at work in the cochlea [2]. This regards in particular the properties of the active wave traveling in the cochlea, which could be generically described in terms of critical oscillators and has been explored previously in the frequency (Fourier) domain [1].…”

Sensory coding in oscillatory electroreceptors of paddlefish

“…33 In particular, recent works have shown that the "phase response curve," a metric of the dynamics of a neuronal oscillator perturbed by weak noise, is directly related to its linear transfer function, 25,69 so that a direct link can be made between dynamics and information encoding into neuronal spike timing. 69 Physiological studies on several species have shown and discussed essential nonlinearities of sensory encoding in auditory, 22,38 visual, 40,56,59 vestibular, 66 mechanosensory, 61 and electrosensory 14,16 systems. In many cases, nonlinearities were associated with non-weak stimuli or with the existence of bursting patterns of neural firing.…”

Comparative Aspects of Hearing in Vertebrates and Insects with Antennal Ears

“…Please cite this article in press as: Albert and Kozlov, Comparative Aspects of Hearing in Vertebrates and Insects with Antennal Ears, Current Biology (2016), http://dx.doi.org/10.1016/j.cub.2016 to maintain the system's control parameters in the desired range in order to benefit functionally from the oscillatory instability) [12]. Thus, natural selection has produced ears that operate close to a bifurcation [12], which produces amplification, frequency selectivity, and a gain control -characteristics that underlie sensitive hearing in vertebrates as well as in some insects.…”