Neural synchronization at tonic-to-bursting transitions

Journal of Biological Physics

Volumn 33, Issue 2, 2007, Pages 129-143

  Postnova, Svetlana ^a   Voigt, Karlheinz ^a   Braun, Hans A ^a  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

Author keywords

Gap junction; Neural synchronization; Tonic to bursting transition

Indexed keywords

ARTICLE; CELL ACTIVITY; CELL FUNCTION; CELL SYNCHRONIZATION; CHAOTIC DYNAMICS; MOLECULAR DYNAMICS; NERVE CELL; PRIORITY JOURNAL;

EID: 40149084958     PISSN: 00920606     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10867-007-9048-x     Document Type: Article

References (34)

1. Singer, W.: Synchronization of cortical activity and its putative role in information processing and learning. Annu. Rev. Physiol. 5, 349-374 (1993)
2. McCormick, D.A., Feeser, H.R.: Functional implications of burst firing and single spike activity in lateral geniculate relay neurons. Neuroscience 39, 103-113 (1990)
3. Mormann, F., Kreuz, T., Andrzejak, R.G., David, P., Lehnertz, K., Elger, C.E.: Epileptic seizures are preceded by a decrease in synchronization. Epilepsy Res. 53(3), 173-185 (2003)
4. Levy, R.: High-frequency synchronization of neuronal activity in the subthalamic nucleus of parkinsonian patients with limb tremor. J. Neurosci. 20(20), 7766-7775 (2000)
5. Baufreton, J., Zhu, Z.T., Garret, M., Bioulac, B., Jonson, S.W., Taupingon, A.I.: Dopamine receptors set the pattern of activity generated in subthalamic neurons. FASEB J. 19, 1771-1777 (2005)
6. Merello, M., Tenca, E., Cerquetti, D.: Neuronal activity of the zona incerta in Parkinson's disease patients. Mov. Disord. 21(7), 937-943 (2006)
7. Silva, L., Blanes, F., Kalitzin, W., Parra, S.N., Suffczynski, J., Velis, D.N.: Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity. Epilepsia 44, 72-83 (2003)
8. Braun, H.A., Bade, H., Hensel, H.: Static and dynamic discharge patterns of bursting cold fibers related to hypothetical receptor mechanisms. Eur. J. Physiol. 386, 1-9 (1980)
9. Dutton, A., Dyball, R.E.J.: Phasic firing enhances vasopressin release from the rat neurohypophysis. J. Physiol. (Lond) 290, 433-440 (1979)
10. Atwater, I., Dawson, C.M., Scott, A., Eddlestone, G., Rojas, E.: The nature of the oscillatory behavior in electrical activity for the pancreatic beta cell. In: Malaisse, W.J., Taljedal, I.B. (eds.) Biochemistry and Biophysics of the Pancreatic Beta Cell, Hormone and Metabolic Research Supplement Series 10, pp. 100-107. Georg Thiem Verlag, Stuttgart (1980)
11. Dewald, M., Braun, H., Huber, M., Zwingmann, D., Roth, J., Voigt, K.: Interactions of temperature and angiotensin II in paraventricular neurons of rats in vitro. Eur. J. Physiol. 444, 117-125 (2002)
12. Sherman, A., Rinzel, J.: Model for synchronization of pancreatic beta-cells by gap junction coupling. Biophys. J. 59, 547-559 (1991)
13. Chow, C.C., Kopell, N.: Dynamics of spiking neurons with electrical coupling. Neural Comput. 12, 1643-1678 (2000)
14. Ermentrout, G.B.: Type I membranes, phase resetting curves, and synchrony. Neural Comput. 8, 979-1001 (1996)
15. Izhikevich, E.M.: Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models. IEEE Trans. Neural Netw. 10, 499-507 (1999)
16. Hoppensteadt, F.C., Izhikevich, E.M.: Weakly Connected Neural Networks. Springer, New York (1997)
17. Hansel, D., Mato, G., Meunier, C.: Synchrony in excitatory neural networks. Neural Comput. 7, 307-335 (1995)
18. Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization-A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge (2001)
19. Postnov, D.E., Sosnovtseva, O.V., Malova, S.Y., Mosekilde, E.: Complex phase dynamics in coupled bursters. Phys. Rev. E 67, 016215-016225 (2003)
20. Izhikevich, E.M.: Synchronization of elliptic bursters. SIAM Rev. 43(2), 315-344 (2001)
21. Belykh, V.N., Belykh, I.V., Colding-Jørgensen, M., Mosekilde, E.: Homoclinic bifurcations leading to bursting oscillations in cell models. Eur. Phys. J. 3, 205-219 (2000)
22. Hansel, D., Sompolinsky, H.: Synchronization and computation in a chaotic neural network. Phys. Rev. Lett. 68(5), 718-721 (1992)
23. Dhamala, M., Jirsa, V.K., Ding, M.: Transitions to synchrony in coupled bursting neurons. Phys. Rev. Lett. 92(2), 028101 (2004)
24. Xia, S., Qi-Shao, L.: Firing patterns and complete synchronization of coupled Hindmarsh-Rose neurons. Chin. Phys. 14(1), 77-85 (2005)
25. Bahar, S.: Burst-enhanced synchronization in an array of noisy coupled neurons. FNL 4(1), L87-L96 (2004)
26. Rulkov, N.F.: Modeling of spiking-bursting neural behavior using two-dimensional map. Phys. Rev. E 65, 041922-041930 (2002)
27. Wang, X.J.: Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle. Physica D 62, 263-274 (1993)
28. Shilnikov, A., Cymbalyuk, G.: Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. Phys. Rev. Lett. 94, 048101-041930 (2005)
29. de Vries, G., Sherman, A.: From spikers to bursters via coupling: help from heterogeneity. Bull. Math. Biol. 63, 371-391 (2001)
30. Braun, H.A., Voigt, K., Huber, M.T.: Oscillation, resonances and noise: basis of flexible neuronal pattern generation. Biosystems 71, 39-50 (2003)
31. Rinzel, J.: A formal classification of bursting mechanisms in excitable systems. In: Gleason, A.M. (ed.) Proceedings of the International Congress of Mathematicians, pp. 135-169. AMS, Providence (1987)
32. Feudel, U., Neiman, A., Pei, X., Wojtenek, W., Braun, H.A., Huber, M.T.: Homoclinic bifurcations in a Hodgkin-Huxley model of thermally sensitive neurons. Chaos 10, 231-239 (2000)
33. Postnova, S., Nekrasov, A., Sosnovtseva, O.: Noise induced effects in dynamics of coupled bursters. Proc. SPIE 5696, 183-192 (2005)
34. Postnov, D., Han, S.K., Kook, H.: Synchronization of diffusively coupled oscillators near the homoclinic bifurcation. Phys. Rev. E 60(3), 2799-2807 (1999)