lifelines : Ears how

PHILIP BALL

Now researchers are proposing that these and other strange properties of our hearing apparatus are due to the fact that it operates at a delicate threshold, like a balance poised to tip one way or the other.

Hearing relies on an organ in the ear called the cochlea, encased in a spiral-shaped minaret of bone. In the cochlea the oscillating air pressure of a sound wave is transformed into a nerve signal and sent to the brain. The vibrations of the air stimulate oscillations in a thin membrane in the cochlea, which pulls on tiny hair-like protrusions called 'stereocilia' attached to the membrane. The other ends of the stereocilia are anchored in cells called hair cells, which produce nerve impulses when tugged.

In the 1980s, biologists David Corey and James Hudspeth suggested that stereocilia are connected via a spring mechanism to tiny channels that, when pulled open, admit calcium ions through the membranes of the hair cells. This influx of ions triggers the nerve signal. Hudspeth, working at the Rockefeller University in New York, has now teamed up with physicist Marcelo Magnasco and others to work out how this mechanism might generate some of the ear's peculiarities. They present their findings in Physical Review Letters¹.

The researchers suggest that hearing relies on a feedback mechanism: the ear tunes its response to optimize its sensitivity to the acoustic stimulus. The tuning enables the cochlea to poise itself at a threshold called a 'Hopf bifurcation'. So its response is extremely nonlinear: the output signal from the cochlea does not vary in direct proportion to the input signal.

A Hopf bifurcation is like, "a sound technician adjusting the volume at an amplifier to the loudest possible setting before feedback oscillation ensues" say Magnasco's team. In short, it is a kind of behaviour that is on the brink of tipping over into a different kind. Typically, at a Hopf bifurcation the output changes from a steady signal to an oscillating one as the input rises above the threshold.

When the input signal is itself oscillating, as sound waves are in the cochlea, the behaviour of a system poised thus looks very much like that of the cochlea. Low-amplitude signals (that is, low-volume sounds) are finely tuned to a particular resonant frequency of the system: the response is large at this frequency but falls quickly to zero for an off-resonance input. Experiments conducted in the past few years have shown that the cochlea does indeed seem to respond this way to sounds near the threshold of hearing.

At high volume, sound produces a quite different response. The output signal is less finely tuned: the cochlea will react to sound waves of a frequency quite different to the resonant frequency. And the response at the resonant frequency itself is 'compressed', so that the output becomes self-limiting as the driving signal gets louder. These characteristics are also signatures of a Hopf bifurcation.

But where does the feedback, needed to tune the cochlea to a Hopf bifurcation, come from in the mechanism postulated by Corey and Hudspeth? One possibility, the researchers suggest, is that the calcium ions mobilized as a membrane channel is opened by the stereocilia have an influence on the 'molecular springs' that promote channel reclosure. In other words, the opening of a channel affects its propensity to close. Mathematical models of this feedback process can produce Hopf bifurcations at resonant frequencies that span the range of the sound frequencies a human can hear. 

1. Eguíluz, V. M., Ospeck, M., Choe, Y., Hudspeth, A. J. & Magnasco, M. O. Essential nonlinearities in hearing. Physical Review Letters 84, 5232-5235 (2000).