The Critical Thing about the Ear's Sensory Hair Cells

Abstract

The capabilities of the human ear are remarkable. We can normally detect acoustic stimuli down to a threshold sound-pressure level of 0 dB (decibels) at the entrance to the external ear, which elicits eardrum vibrations in the picometer range. From this threshold up to the onset of pain, 120 dB, our ears can encompass sounds that differ in power by a trillionfold. The comprehension of speech and enjoyment of music result from our ability to distinguish between tones that differ in frequency by only 0.2%. All these capabilities vanish upon damage to the ear's receptors, the mechanoreceptive sensory hair cells. Each cochlea, the auditory organ of the inner ear, contains some 16,000 such cells that are frequency-tuned between ∼20 Hz (cycles per second) and 20,000 Hz. Remarkably enough, hair cells do not simply capture sound energy: they can also exhibit an active process whereby sound signals are amplified, tuned, and scaled. This article describes the active process in detail and offers evidence that its striking features emerge from the operation of hair cells on the brink of an oscillatory instability-one example of the critical phenomena that are widespread in physics.

Keywords: auditory system; cochlea; gating spring; hair bundle; transduction; vestibular system.

Figure 1.

Hair cells: the sensory receptors of the inner ear and potential substrate for critical behavior. A, The hair bundle that protrudes from the apical surface of a cochlear outer hair cell is a palisade of ∼85 stereocilia, each of which is an enlarged microvillus with a core of cross-linked actin filaments. B, A schematic figure depicts the mechanoelectrical transduction process. In the undisturbed hair bundle (left), most ion channels (red) at the stereociliary tips are closed, as represented here by gates (blue). When mechanical stimulation from a sound moves the bundle in the positive direction, toward its tall edge (right), the shear between adjacent stereocilia increases the tension in tip links (orange) that interconnect the stereocilia. As a result, the channels are opened, cations enter the cell and depolarize it, and the cell communicates this excitation to an afferent nerve fiber. C, This scanning electron micrograph of a short cochlear segment from a young mouse shows hair bundles in the organ of Corti. The 10 straight bundles near the bottom belong to inner hair cells, which send electrical signals into the brain. Threefold as many bundles near the top extend from outer hair cells, the sites of the cochlear active process. In addition to protruding from a common sheet of hair cells, the bundles are ordinarily surmounted by a continuous tectorial membrane that has been removed during preparation. These two interconnections among the bundles constitute a potential means of eliciting cooperative and critical behaviors.

Figure 2.

The ear's daily task. A sonogram, which depicts the frequency content of a 3 s sample of human speech as a function of time, demonstrates the complexity of the auditory signals. Sound intensity is represented on a scale from blue, for the weakest signals, to red and finally yellow for the most intense. The auditory system uses frequency, intensity, and timing information to decode the utterance as “The Journal of Neuroscience.” Some words, such as “the” and “of,” garner only rudimentary representation. Note the precise timing of the hard “j” at the onset of “journal.” Equally striking are the high-frequency sibilants at the beginning and conclusion of “science.” The protracted vowel sounds in “journal,” “neuro,” and “science” involve distinctive stacks of low frequencies, the formants.

Figure 3.

Signature of criticality in the cochlea. An idealized “level function” portrays the logarithm of a cochlear response to the sound-pressure level—also a logarithmic measure—that elicits it. The response represents the oscillatory movement of the basilar membrane or of some component of the organ of Corti for a frequency of stimulation—the characteristic frequency—that accords with the tonotopic map. In the present instance, the response above the noise floor (gray) covers three orders of magnitude, a much narrower range than the six orders of magnitude in sound-pressure level that are characteristic of human hearing. Over most of the range, the slope of the level function is 1/3 (pink), indicating a power law relationship with this exponent. This form of compressive nonlinearity is characteristic of a system operating near a Hopf bifurcation and provides strong evidence for critical oscillators in the cochlea. The response is instead linear (slope 1) for signals so weak that Brownian motion is comparable with the movements elicited by the stimulus, which limits the sensitivity of hearing. When the active process fails, and one becomes “hard of hearing,” the passive response of the cochlea is nearly linear at all sound-pressure levels (blue dashed line) and hearing is confined to a narrow range of quite strong stimuli. At each sound intensity, the magnitude ratio between the active response (solid pink line) and the passive one (dashed blue line) quantifies amplification by the active process. Amplification is highest when we need it most, for faint stimuli, and decreases progressively at increasing sound-pressure levels. For very strong stimuli that overwhelm active force production by the hair cells, the response of the organ of Corti is dictated by its passive mechanics. Nonlinear amplification of cochlear vibrations lowers the threshold of hearing by 40–50 dB (red arrow).

Figure 4.

Critical behavior at a Hopf bifurcation. A, A bifurcation diagram shows the amplitude of spontaneous oscillations as a function of a control parameter, $\epsilon$, in an active dynamical system that undergoes an oscillatory instability—a Hopf bifurcation—at the critical value $\epsilon =0$. At positive values of the control parameter, the system is endowed with a stable fixed point: it relaxes to this point in response to an external perturbation (right inset). When the control parameter crosses zero and becomes negative, the fixed point becomes unstable and the system reaches a limit cycle oscillation (left inset). Near the bifurcation point, the magnitude of the limit cycle grows as the square root of the distance, $-\epsilon$, to the critical point. This behavior is analogous to that of the spontaneous magnetization that appears in ferromagnetic materials below the Curie temperature, an example of a second-order phase transition (Kardar, 2007). B, When the system approaches criticality, $\epsilon \to 0$, the sensitivity to vanishing amplitudes $(F\to 0)$ of an external periodic stimulus at the characteristic frequency of spontaneous oscillation becomes arbitrarily large. This critical behavior mirrors that of the magnetic susceptibility of a material operating at the paramagnetic-to-ferromagnetic transition. In both cases, criticality expands the dynamical range of responsiveness (Kardar, 2007). C, The decimal logarithm of the sensitivity of a critical oscillator $(\epsilon =0)$ is depicted as a function of the ratio of the frequency, $\omega$, of a sinusoidal stimulus and the characteristic frequency, ${\omega }_0$, of the oscillator. The sensitivity is tuned at $\omega ={\omega }_0$. The peak sensitivity decreases and the bandwidth increases with the stimulus level (by a factor of 64 from red to blue) according to generic power laws (Eq. 4). Away from the characteristic frequency, the sensitivity is low and all the curves superimpose: the output is proportional to the input and the system thus evinces a linear behavior.