ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Mosekilde E., Sosnovtseva O. V., Postnov D. E., Braun H., Huber M. Noisy neural rhythm generators. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 3, pp. 95-109. DOI: 10.18500/0869-6632-2003-11-3-95-109

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Language: 
English
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
532.517, 517.9, 621.373
DOI: 
10.18500/0869-6632-2003-11-3-95-109

Noisy neural rhythm generators

Autors: 
Mosekilde Erik, Technical University of Denmark
Sosnovtseva Olga Vladimirovna, Danmarks Tekniske Universitet
Postnov Dmitry E, Saratov State University
Braun Hans Albert, Philipps-University Marburg
Huber Martin Tobias, Philipps-University Marburg
Abstract: 

The dynamical features of spike train generation in the presence of noise are investigated for three different models of neural rhythm generators: а single neuron model that simulates impulse pattern modulation for temperature encoding in mammalian cold receptors, а minimal neural network that describes transitions between beta and gamma rthythms in the brain and аn electronic switching device that represents а simple breathing rhythm generator for а snail. We show that noise can explain а number оf peculiarities in the observed spike trains, cause coherent switchings between different states, and induce new rhythms in small neural ensembles.

Key words: 
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Acknowledgments: 
This work was partly supported by INTAS grant 01-2061 and RFBR grant 01-02-16709. O.S. acknowledges INTAS (Grant YSF 01/1-0023) and the Lundbeck Foundation.
Reference: 
  1. Anishchenko VS. Dynamical Chaos: Models and Experiments. Singapore: World Scientific; 1995. 400 p.
  2. Anishchenko VS, Astakhov VV, Neiman AB, Vadivasova TE, Schimansky-Geier L. Nonlinear Dynamics of Chaotic and Stochastic Systems. Berlin: Springer Verlag; 2002. 446 p.
  3. Eckhorn R, Bauer R, Jordan W, Brosch M, Kruse W, Munk W, Reitboeck HJ. Coherent oscillations: A mechanism оf feature linking in the visual cortex? Biol. Cybern. 1988;60(2):121–130. DOI: 10.1007/bf00202899.
  4. Gray CM, Kénig Р, Engel AK, Singer W. Oscillatory responses in саt visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 1989;338(6213):334–337. DOI: 10.1038/338334a0.
  5. Braun HA, Bade H, Hensel H. Static and dynamic discharge patterns of bursting cold fibers related to hypothetical receptor mechanisms. Pfligers Arch. 1980;386(1):1–9. DOI: 10.1007/bf00584180.
  6. Braun HA, Schéfer K, Wissing H, Hensel H. Periodic transduction processes in thermosensitive receptors. In: Hamann W, Iggo A, editors. Sensory Receptor Mechanisms. Singapore: World Scientific; 1984. P. 147–156.
  7. Braun HA, Huber MT, Dewald M, Schifer K, Voigt K. Computer simulations of neuronal signal transduction: The role оf nonlinear dynamics and noise. Int. J. Bifurc. Chaos.1998;8(5):881–889. DOI: 10.1142/S021812749800067X.
  8. Braun W, Eckhardt B, Braun HA, Huber МТ. Phase space structure оf а thermoreceptor. Phys. Rev. Е. 2000;62(5):6352–6360. DOI: 10.1103/PhysRevE.62.6352.
  9. Feudel U, Neiman A, Pei X, Wojtenek W, Braun HA, Huber MT. Homoclinic bifurcations in а Hodgkin-Huxley model оf thermally sensitive neurons. Chaos. 2000;10(1):231–239. DOI: 10.1063/1.166488.
  10. Tuckwell HC. Stochastic Processes in the Neurosciences. Philadelphia: SIAM; 1989. 129 p.; Taylor JG. Neurodynamics. In: Faseman E, Doebner HD, editors. Singapore: World Scientific; 1991. P. 129–164.
  11. Braun HA, Wissing H, Schfer K, Hirsch MC. Oscillation and noise determine signal transduction in shark multimodal sensory cells. Nature. 1994;367(6460):270–273. DOI: 10.1038/367270a0.
  12. Russell DF, Wilkens LA, Moss Е. Use of behavioural stochastic resonance by paddle fish for feeding. Nature. 1999;402(6759):291–294. DOI: 10.1038/46279.
  13. Nakamura K. Stochastic Resonance in the FitzHugh-Nagumo Neuron Model. Proc. Inst. Natural Sci. 2000;35:179–185.
  14. Pikovsky AS, Kurth J. Coherence resonance in a noise-driven excitable system. Phys. Rev. Lett. 1997;78(5):775–778. DOI: 10.1103/PhysRevLett.78.775.
  15. Neiman А, Pei X, Russell Р, Wojtenek W, Wilkens L, Moss F, Braun НА, Huber MT, Voigt K. Synchronization of the noise electrosensitive cells in the paddlefish. Phys. Rev. Lett. 1999;82(3):660–663. DOI: 10.1103/PhysRevLett.82.660.
  16. Kopell N, Ermentrout GB, Whittington МА, Traub RD. Gamma rhythms and beta rhythms have different synchronization properties. Proc. Nat. Acad. Sci. USA. 2000;97(4):1867–1872. DOI: 10.1073/pnas.97.4.1867.
  17. Bressler SL, Coppola R, Nakamura R. Episodic multiregional cortical coherence at multiple frequencies during visual task performance. Nature. 1993;366(6451):153–156. DOI: 10.1038/366153a0.
  18. Braun HA, Huber MT, Anthes N, Voigt K, Neiman A, Pei X, Moss F. Interaction between slow and fast conductances in the Huber/Braun model of cold-receptor discharges. Neurocomputing. 2000;32–33:51–59. DOI: 10.1016/S0925-2312(00)00143-0.
  19. Fox RF, Gatland LR, Roy R, Vemuri С. Fast accurate algorithm for numerical simulation оf exponentially correlated colored noise. Phys. Rev. А. 1988;38(11):5938–5940. DOI: 10.1103/PhysRevA.38.5938.
  20. 1) Equilibrium potentials: Esd=Ed=50, Vsr=Vr=-90, V1=-60 (mV); 2) ionic conductances: g1=0.1, gd=1.5, gr=2.0, gsd=0.25, gsr=0.4 (mS/cm2), 3) membrane capacitance: C=1 (mF/cm2) gives a passive time constant tm=Clg1=10 (ms); 4) activation time constants: tr=2, tsd=2, tsr=2 (ms); 5) slope оf steady state activation: sd=sr=0.25, ssd=0.09; 6) half activation potentials V0d=V0r=-25, V0ds=-40 (mV); 7) coupling an relaxation constants for Isr:n=0.012, k=0.17 8) reference temperature: T0=25°(C).
  21. Hodgkin AL, Huxley АЕ. A quantitative description оf membrane current and its application to conduction ап excitation in nerve. J. Physiol. 1952;117(4):500–544. DOI: 10.1113/jphysiol.1952.sp004764.
  22. Fausboll А. Analysis оf а Minimal Network оf Cortical Neurons. MSc. Thesis. Denmark: DTU; 2001.
  23. Мооте GP, Perkel DH, Segundo JP. Statistical analysis and functional interpretation of neuronal spike data. Ann. Rev. Physiol. 1966;28:493–522. DOI: 10.1146/annurev.ph.28.030166.002425.
  24. Lee S-G, Neiman А, Kim S. Coherence resonance in а Hodgkin-Huxley neuron. Phys. Rev. Е. 1998;57(3):3292–3297. DOI: 10.1103/PhysRevE.57.3292.
  25. Postnov DE, Setsinsky DV, Sosnovtseva ОМ. Stochastic synchronization and the growth in regularity оf the noise-induced oscillations. Tech. Phys. Lett. 2001;27(6):49–55. DOI: 10.1134/1.1383826.
  26. Rosenzweig MR, Leiman AL, Breedlove SM. Biological Psychology. Sinaur Associated, Inc. Sunderland, Massachusetts; 1996. 624 p.
  27. Postnov DE, Han SK, Yim T, Sosnovtseva OV. Experimental observation оf coherence resonance in cascaded excitable systems. Phys. Rev. Е. 1999;59(4):R3791–R3794. DOI: 10.1103/PhysRevE.59.R3791; Han SK, Yim T, Postnov DE, Sosnovtseva OV. Interacting coherence resonance oscillators. Phys. Rev. Lett. 1999;83(9):1771–1774. DOI: 10.1103/PhysRevLett.83.1771.
  28. Sosnovtseva ОМ, Setsinsky D, Fausboll А, Mosekilde Е. Transitions between beta and gamma rhythms in neural systems. Phys. Rev. Е. 2002;66(4):041901. DOI: 10.1103/PhysRevE.66.041901.
  29. Postnov DE, Sosnovtseva OV, Han SK, Kim WS. Noise-induced multimode behavior in excitable systems. Phys. Rev. E. 2002;66(1):016203. DOI: 10.1103/PhysRevE.66.016203.
Received: 
31.07.2003
Accepted: 
04.09.2003
Available online: 
23.11.2023
Published: 
31.12.2003
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