Evidence of a Hopf bifurcation in frog hair cells.
The membrane potential of hair cells in the low-frequency hearing organ of the bullfrog, the amphibian papilla, sinusoidally oscillates at small amplitude in the absence of acoustical input. We stimulate the cell with a series of periodic currents close to this natural frequency and observe that its current-to-voltage transfer function is compressively nonlinear, having a large gain for small stimuli and a smaller gain for larger currents. Along with the spontaneous oscillation, this implies that the cell is poised close to a dynamical instability such as a Hopf bifurcation, because distant from the instability the transfer function becomes linear. The cell's frequency selectivity is enhanced for small stimuli. Simulations show that the cell's membrane capacitance is effectively reduced due to a current gain provided by this dynamical instability. We propose that the Hopf resonance is widely used by transducer cells on the sensory periphery to achieve small-signal amplification.
Ospeck
M
M
Biophysics Section, Laboratory of Cellular Biology, National Institute on Deafness and Other Communication Disorders, National Institutes of Health, Bethesda, Maryland 20892-0922, USA. ospeckm@nidcd.nih.gov
Eguíluz
V M
VM
Magnasco
M O
MO
D000161:Acoustic Stimulation; D000818:Animals; D004553:Electric Conductivity; D004710:Endolymph / Q000378:metabolism; D006198:Hair Cells, Auditory / Q000502:physiology*; D008564:Membrane Potentials; D008858:Microscopy, Phase-Contrast; D008954:Models, Biological; D011188:Potassium / Q000378:metabolism; D015221:Potassium Channels / Q000378:metabolism; D011892:Rana catesbeiana / Q000502:physiology*
D015221:Potassium Channels; D011188:Potassium