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

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Postnov D. E., Zhirin R. A., Serdobinceva J. A. Noise-induced coherent firing patterns in small neural ensembles with ionic coupling. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 4, pp. 83-100. DOI: 10.18500/0869-6632-2008-16-4-83-100

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577.38
DOI: 
10.18500/0869-6632-2008-16-4-83-100

Noise-induced coherent firing patterns in small neural ensembles with ionic coupling

Autors: 
Postnov Dmitry E, Saratov State University
Zhirin Roman Andreevich, Saratov State University
Serdobinceva Julija Aleksandrovna, Saratov State University
Abstract: 

By means of modeling and numeric simulation we consider, how the rise of extracellular potassium concentration due to the neuronal activity can affect the firing patterns of the neighboring neurons. To take into account mentioned above effects, we suggest simple extension of Hodgkin-Huxley model. We consider the behavior of 2, 4, and 8 excitable neurons being forced by external noisy stimulus. We reveal the main effects being the attributes of ionic coupling that are include the emergence of new time scales and spatially-ordered firing patterns.

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Reference: 
  1. Nicholls JG, Martin AR, Wallas BJ, Fuchs PA. From Neuron to Brain. Sinauer Associates; 2001. 672 p.
  2. Rubin AB. Biophysics. Moscow: Vysshaya Shkola; 1987. 464 p. (in Russian).
  3. Keener J, Sneyd J. Mathematical Physiology. Springer, New York, Inc; 2001. 547 p. DOI: 10.1007/978-0-387-75847-3.
  4. Sykov E. Extracellular K+ accumulation in the central nervous system. Prog. Biophys. Mol. Biol. 1983;42(2–3):135–189. DOI: 10.1016/0079-6107(83)90006-8.
  5. Deitmer JW, Rose CR, Munsch T, Schmidt J, Nett W, Schneider HP, Lohr C. Leech giant glial cell. Functional Role in a Simple Nervous System GLIA. 1999;28(3):175–182.
  6. Hansen AJ. The extracellular potassium concentration in brain cortex following oschemia in hypo- and hyperglycemic rats. Acta Physiol. Scand. 1978;102(3):324–329. DOI: 10.1111/j.1748-1716.1978.tb06079.x.
  7. Yan GX, Chen J, Yamada KA, Kleber AG, and Corr PG. Contribution of shrinkage of extracellular space to extracellular K+ accumulation in myocardial ischemia at the rabbit. J.Physiol. 1996;490(1):215–228. DOI: 10.1113/jphysiol.1996.sp021137.
  8. Yi CS, Fogelson AL, Keener JP, and Peskin CS. A mathematical study of volume shifts and ionic concentration changes during ischemia and hypoxia. Journal of Theoretical Biology. 2003;220(1):83–106. DOI: 10.1006/jtbi.2003.3154.
  9. Bazhenov M, Timofeev I, Steriade M, and Sejnowski TJ. Potassium model for slow (2-3 Hz) neocortical paroxysmal oscillations in vivo. Journal of Neurophisiology. 2004;92(2):1116–1132. DOI: 10.1152/jn.00529.2003.
  10. Park EH, Durand DM. Role of potassium lateral diffusion in non-synaptic epilepsy: A computational study. Journal of Theoretical Biology. 2006;238(3):666–682. DOI: 10.1016/j.jtbi.2005.06.015.
  11. Postnov DE, Ryazanova LS, Sosnovtseva OS, Mosekilde E. Neural synchronization via potassium signaling. International Journal of Neural Systems. 2006;16(2):99–109. DOI: 10.1142/s0129065706000536.
  12. Lee SG, Neiman A, Kim S. Coherence resonance in a Hodgkin–Huxley neuron. Phys. Rev. E. 1998;57(3):3292–3297. DOI: 10.1103/PhysRevE.57.3292.
  13. Pikovsky A, Kurth J. Coherence resonance in a noise–driven excitable systems. Phys. Rev. Lett. 1997;78(5):775–778. DOI: 10.1103/PhysRevLett.78.775.
  14. Han SK, Yim TG, Postnov DE, and Sosnovtseva OV. Interacting coherence resonance oscillators. Phys. Rev. Lett. 1999;83(9):1771–1774. DOI: 10.1103/PhysRevLett.83.1771.
  15. Postnov DE, Sosnovtseva OV, Han SK, and Kim WS. Noise-induced multimode behavior in excitable systems. Phys. Rev. 2002;66(1):016203. DOI: 10.1103/physreve.66.016203.
  16. Mosekilde E, Sosnovtseva OV, Postnov D, Braun HA, and Huber MT. Noise-activated and noise-induced rhythms in neural systems. Nonlinear Science. 2004;11(3):449–467.
  17. Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in a nerve. J. Physiol. 1952;117(4):500–544. DOI: 10.1113/jphysiol.1952.sp004764.
  18. Guantes R and de Polavieja GG. Variability in noise-driven integrator neurons. Phys. Rev. E. 2005;71(1):011911. DOI: 10.1103/PhysRevE.71.011911.
  19. Baccus S.A. Synaptic facilitation by reflected action potentials: Enhancement of transmission when nerve impulses reverse direction at axon branch points. Proc. Natl. Acad. Sci. USA. 1998;95(14):8345–8350. DOI: 10.1073/pnas.95.14.8345.
  20. Postnov DE, Zhirin RA. Modeling oscillatory and wave processes in two-dimensional media of arbitrary geometry. Certificate of Official Registration of the Computer Program 2007614145 dated 28.09.2007 (in Russian).
Received: 
11.12.2007
Accepted: 
13.03.2008
Published: 
31.10.2008
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