- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Models of stochastic biperiodic oscillations and extended serial correlations in electroreceptors of paddlefish

Alexander B. Neiman*

David F. Russell†

  • Department of Physics and Astronomy, Ohio University, Ohio 45701, USA

  • Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121, USA

  • *Electronic address: neiman@helios.phy.ohiou.edu
  • †Electronic address: drussell@admiral.umsl.edu
PDF

Phys. Rev. E 71, 061915 – Published 23 June, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.061915

Abstract

Two types of minimal models were used to study stochastic oscillations in sensory receptors composed of two coupled oscillators, as in the electroreceptors of paddlefish. They have populations of cells in sensory epithelia undergoing ≈26Hz oscillations. These are coupled unidirectionally via synaptic excitation to a few afferent neurons, each of whose terminal contains a 30–70Hz oscillator, expressed as a dominant peak in the power spectra of spontaneous afferent firing, corresponding to the mean firing rate. The two distinct types of internal noisy oscillators result in stochastic biperiodic firing patterns of the primary afferent sensory neurons. However, the functions of the oscillations have remained elusive, motivating this study. The models we used here are based on the circle map, or on the Ermentraut-Koppell canonical phase (theta neuron) model. Parameters were chosen according to experimental data. We used the models to demonstrate that the presence of epithelial oscillations leads to extended negative correlations of afferent interspike intervals, and to show that the correlation structure depends crucially on the ratio of the afferent to epithelial oscillation frequencies, being most pronounced when this ratio is close to 2, as observed in experiments. Our studies of stochastic versions of these models are of general interest for a wide range of coupled excitable systems, especially for understanding the functional roles of noisy oscillations in auditory and other types of “hair cell–primary afferent” sensory receptors.

View figure in article

Article Text

References (46)

  1. A. C. Crawford and R. Fettiplace, J. Physiol. (London) 364, 359 (1985).
  2. A. Rüsch and U. Thurm, Hear. Res. 48, 247 (1990).
  3. P. Martin, A. J. Hudspeth, and F. Jülicher, Proc. Natl. Acad. Sci. U.S.A. 98, 14380 (2001).
  4. M. Ospeck, V. M. Eguiluz, and M. O. Magnasco, Biophys. J. 80, 2597 (2001).
  5. S. Camelet, T. Duke, F. Jülicher, and J. Prost, Proc. Natl. Acad. Sci. U.S.A. 97, 3183 (2000).
  6. H. Bade, H. A. Braun, and H. Hensel, Pfluegers Arch. 382, 1 (1979).
  7. H. A. Braun, H. Wissing, K. Schäfer, and M. C. Hirsch, Nature (London) 367, 270 (1979).
  8. H. A. Braun, M. T. Huber, M. Dewald, K. Schäfer, and K. Voigt, Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 881 (1998).
  9. A. B. Neiman and D. F. Russell, Phys. Rev. Lett. 86, 3443 (2001).
  10. A. B. Neiman and D. F. Russell, J. Neurophysiol. 92, 492 (2004).
  11. A. Neiman, X. Pei, D. Russell, W. Wojtenek, L. Wilkens, F. Moss, H. Braun, M. Huber, and K. Voigt, Phys. Rev. Lett. 82, 660 (1999).
  12. D. F. Russell, L. A. Wilkens, and F. Moss, Nature (London) 402, 291 (1999).
  13. A. B. Neiman and D. F. Russell, Phys. Rev. Lett. 88, 138103 (2002).
  14. L. A. Wilkens, D. F. Russell, X. Pei, and C. Gurgens, Proc. R. Soc. London, Ser. B 264, 1723 (1997).
  15. J. M. Jørgensen, A. Flock, and J. Wersäll, Z. Zellforsch Mikrosk Anat. 130, 362 (1972).
  16. E. M. Izhikevich, Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, 1171 (2000).
  17. R. Ratnam and M. Nelson, J. Neurosci. 20, 6672 (2000).
  18. M. J. Chacron, A. Longtin, and L. Maler, J. Neurosci. 21, 5328 (2001).
  19. J. B. M. Goense and R. Ratnam, J. Comp. Physiol., A 189, 741 (2003).
  20. X.-J. Wang, J. Neurophysiol. 79, 1549 (1998).
  21. B. Lindner and A. Longtin, Proc. SPIE 5114, 209 (2003).
  22. L. Schimansky-Geier and C. Zülicke, Z. Phys. B: Condens. Matter 79, 451 (1990).
  23. J. Rinzel and G. B. Ermentrout, Analysis of Neural Excitability and Oscillations (MIT Press, Cambridge, MA, 1998), pp. 313–360.
  24. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, 1981).
  25. K. Schäfer, H. A. Braun, R. C. Peters, and F. Bretschnider, Pfluegers Arch. 429, 378 (1995).
  26. M. C. Teich and S. B. Lowen, IEEE Eng. Med. Biol. Mag. 13, 197 (1994).
  27. M. J. Chacron, B. Lindner, and A. Longtin, Phys. Rev. Lett. 92, 080601 (2004).
  28. S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, MA, 1995).
  29. L. Glass and M. C. Mackey, From Clocks to Chaos: The Rythms of Life (Princeton University Press, Princeton, NJ, 1988).
  30. A. S. Pikovsky, M. G. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, U.K., 2001).
  31. M. J. Chacron, K. Pakdaman, and A. Longtin, Neural Comput. 15, 253 (2003).
  32. M. Zeller, M. Bauer, and W. Martienssen, Chaos, Solitons Fractals 5, 885 (1995).
  33. J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures (J. Wiley and Sons, New York, 2000).
  34. A. B. Neiman, U. Feudel, and J. Kurths, J. Phys. A 28, 2471 (1995).
  35. D. R. Cox and P. A. Lewis, The Statistical Analysis of Series of Events (Methuren, London, 1966).
  36. J. W. Middleton, M. J. Chacron, B. Lindner, and A. Longtin, Phys. Rev. E 68, 021920 (2003).
  37. G. B. Ermentrout and N. Kopell, SIAM J. Appl. Math. 46, 233 (1986).
  38. G. B. Ermentrout, Neural Comput. 8, 979 (1996).
  39. F. C. Hoppensteadt and E. M. Izhikevich, Weakly Connected Neural Networks (Springer, Berlin, 1997).
  40. B. S. Gutkin and G. B. Ermentrout, Neural Comput. 10, 1047 (1998).
  41. B. Lindner, A. Longtin, and A. Bulsara, Neural Comput. 15, 1761 (2003).
  42. G. B. Ermentrout, Neural Comput. 10, 1721 (1998).
  43. J. H. Shin, Neurocomputing 44, 167 (2002).
  44. M. J. Chacron, A. Longtin, M. St-Hilaire, and L. Maler, Phys. Rev. Lett. 85, 1576 (2000).
  45. S. Bahar, J. W. Kantelhardt, A. B. Neiman, H. Rego, D. F. Russell, L. A. Wilkens, A. Bunde, and F. Moss, Europhys. Lett. 56, 454 (2001).
  46. W. Wojtenek, M. H. Hofmann, and L. A. Wilkens, Neurocomputing 38–40, 451 (2001).

Outline

Information

Phys. Rev. E 71, 061915– Published 23 June, 2005
  • Received 3 February 2005

© 2005 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation