Skip to main content
PMC home page
Biophysical Journal logoLink to Biophysical Journal
. 2001 Jun;80(6):2597–2607. doi: 10.1016/S0006-3495(01)76230-3

Evidence of a Hopf bifurcation in frog hair cells.

M Ospeck 1, V M Eguíluz 1, M O Magnasco 1
PMCID: PMC1301448  PMID: 11371437

Abstract

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.

Full Text

The Full Text of this article is available as a PDF (178.0 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Camalet S., Duke T., Jülicher F., Prost J. Auditory sensitivity provided by self-tuned critical oscillations of hair cells. Proc Natl Acad Sci U S A. 2000 Mar 28;97(7):3183–3188. doi: 10.1073/pnas.97.7.3183. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Corey D. P., Hudspeth A. J. Ionic basis of the receptor potential in a vertebrate hair cell. Nature. 1979 Oct 25;281(5733):675–677. doi: 10.1038/281675a0. [DOI] [PubMed] [Google Scholar]
  3. Crawford A. C., Fettiplace R. An electrical tuning mechanism in turtle cochlear hair cells. J Physiol. 1981 Mar;312:377–412. doi: 10.1113/jphysiol.1981.sp013634. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Crawford A. C., Fettiplace R. Non-linearities in the responses of turtle hair cells. J Physiol. 1981 Jun;315:317–338. doi: 10.1113/jphysiol.1981.sp013750. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Crawford A. C., Fettiplace R. The frequency selectivity of auditory nerve fibres and hair cells in the cochlea of the turtle. J Physiol. 1980 Sep;306:79–125. doi: 10.1113/jphysiol.1980.sp013387. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Eatock R. A., Corey D. P., Hudspeth A. J. Adaptation of mechanoelectrical transduction in hair cells of the bullfrog's sacculus. J Neurosci. 1987 Sep;7(9):2821–2836. doi: 10.1523/JNEUROSCI.07-09-02821.1987. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Eguíluz V. M., Ospeck M., Choe Y., Hudspeth A. J., Magnasco M. O. Essential nonlinearities in hearing. Phys Rev Lett. 2000 May 29;84(22):5232–5235. doi: 10.1103/PhysRevLett.84.5232. [DOI] [PubMed] [Google Scholar]
  8. HERMANN H. T., STARK L. Single unit responses in a primitive photoreceptor organ. J Neurophysiol. 1963 Mar;26:215–228. doi: 10.1152/jn.1963.26.2.215. [DOI] [PubMed] [Google Scholar]
  9. Holt J. R., Eatock R. A. Inwardly rectifying currents of saccular hair cells from the leopard frog. J Neurophysiol. 1995 Apr;73(4):1484–1502. doi: 10.1152/jn.1995.73.4.1484. [DOI] [PubMed] [Google Scholar]
  10. Hudspeth A. J., Corey D. P. Controlled bending of high-resistance glass microelectrodes. Am J Physiol. 1978 Jan;234(1):C56–C57. doi: 10.1152/ajpcell.1978.234.1.C56. [DOI] [PubMed] [Google Scholar]
  11. Hudspeth A. J., Lewis R. S. A model for electrical resonance and frequency tuning in saccular hair cells of the bull-frog, Rana catesbeiana. J Physiol. 1988 Jun;400:275–297. doi: 10.1113/jphysiol.1988.sp017120. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Hudspeth A. J., Lewis R. S. Kinetic analysis of voltage- and ion-dependent conductances in saccular hair cells of the bull-frog, Rana catesbeiana. J Physiol. 1988 Jun;400:237–274. doi: 10.1113/jphysiol.1988.sp017119. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Jørgensen F., Ohmori H. Amiloride blocks the mechano-electrical transduction channel of hair cells of the chick. J Physiol. 1988 Sep;403:577–588. doi: 10.1113/jphysiol.1988.sp017265. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Kros C. J., Ruppersberg J. P., Rüsch A. Expression of a potassium current in inner hair cells during development of hearing in mice. Nature. 1998 Jul 16;394(6690):281–284. doi: 10.1038/28401. [DOI] [PubMed] [Google Scholar]
  15. Lewis R. S., Hudspeth A. J. Voltage- and ion-dependent conductances in solitary vertebrate hair cells. Nature. 1983 Aug 11;304(5926):538–541. doi: 10.1038/304538a0. [DOI] [PubMed] [Google Scholar]
  16. Martin P., Hudspeth A. J. Active hair-bundle movements can amplify a hair cell's response to oscillatory mechanical stimuli. Proc Natl Acad Sci U S A. 1999 Dec 7;96(25):14306–14311. doi: 10.1073/pnas.96.25.14306. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Meyer J. H., Zakon H. H. Androgens alter the tuning of electroreceptors. Science. 1982 Aug 13;217(4560):635–637. doi: 10.1126/science.217.4560.635. [DOI] [PubMed] [Google Scholar]
  18. Rieke F., Bodnar D. A., Bialek W. Naturalistic stimuli increase the rate and efficiency of information transmission by primary auditory afferents. Proc Biol Sci. 1995 Dec 22;262(1365):259–265. doi: 10.1098/rspb.1995.0204. [DOI] [PubMed] [Google Scholar]
  19. Rosenblatt K. P., Sun Z. P., Heller S., Hudspeth A. J. Distribution of Ca2+-activated K+ channel isoforms along the tonotopic gradient of the chicken's cochlea. Neuron. 1997 Nov;19(5):1061–1075. doi: 10.1016/s0896-6273(00)80397-9. [DOI] [PubMed] [Google Scholar]
  20. Smotherman M. S., Narins P. M. The electrical properties of auditory hair cells in the frog amphibian papilla. J Neurosci. 1999 Jul 1;19(13):5275–5292. doi: 10.1523/JNEUROSCI.19-13-05275.1999. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES