Dáibhid Ó Maoiléidigh
Laboratory of Sensory Neuroscience
The Rockefeller University
Sensory transduction by active, noisy oscillators on the brink of self-oscillation
Hair bundles are the active oscillators that transduce mechanical stimuli into electrical signals in the auditory and balance organs of vertebrates. Their signal-detection ability is limited, however, by noise. Theory predicts that a bundle’s function is dictated by whether it operates near supercritical or subcritical Hopf bifurcations. We confirmed these predictions by employing a feedback system to change the operating point of individual hair bundles. We discuss how to identify and locate a Hopf bifurcation from experimental data possessing substantial environmental noise. For operating points corresponding to a balance organ, a hair bundle can determine the onset of a step force or the size of the step. Under conditions similar to those found in an auditory system, a bundle is frequency selective and amplifies periodic stimuli.
We additionally predict that an oscillator's phase-locked response and its degree of entrainment to a frequency-detuned stimulus are greatest when its control parameter lies near—but not precisely at—a Hopf bifurcation. As predicted, we found that the phase-locked response and the vector strength of hair bundles peaked for operating points near the bifurcation. These results imply that a hair bundle embedded in an auditory organ would optimally detect periodic stimuli within a band of frequencies around its best frequency if the system’s operating point were near but not at a Hopf bifurcation.