Mathematics and the gap junctions: In-phase synchronization of identical neurons

International Journal of Neuroscience

Volumn 113, Issue 8, 2003, Pages 1095-1101

  Perez Velazquez, Jose L ^a  

^a HOSPITAL FOR SICK CHILDREN   (Canada)

Author keywords

Coupled oscillators; Gap junctions; Inteneurons; Synchrony

Indexed keywords

ARTICLE; CELL INTERACTION; CELL SYNCHRONIZATION; ELECTRIC POTENTIAL; GAP JUNCTION; MATHEMATICAL ANALYSIS; NERVE CELL; NEUROTRANSMISSION; OSCILLATION;

ACTION POTENTIALS; ANIMALS; GAP JUNCTIONS; HUMANS; MODELS, NEUROLOGICAL; NEURONS;

EID: 0041695564     PISSN: 00207454     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207450390212069     Document Type: Article

References (16)

1. Deans, M. R., Gibson, J. R., Sellitto, C., Connors, B. W., & Paul, D. L. (2001). Synchronous activity of inhibitory networks in neocortex requires electrical synapses containing connexin36. Neuron, 31, 477-485
2. Draguhn, A., Traub, R. D., Schmitz, D., & Jefferys, J. G. (1998). Electrical coupling underlies high-frequency oscillations in the hippocampus in vitro. Nature, 394, 189-192.
3. Galarreta, M., & Hestrin, S. (1999). A network of fast-spiking cells in the neocortex connected by electrical synapses. Nature, 402, 72-75.
4. Galarreta, M., & Hestrin, S. (2001). Electrical synapses between GABA-releasing interneurons. Nature Reviews Neuroscience, 2, 425-433.
5. Gibson, J. R., Beierlein, M., & Connors, B. W. (1999). Two networks of electrically coupled inhibitory neurons in neocortex. Nature, 402, 75-79.
6. Hoppensteadt, F. C., & Izhikevich, E. M. (1997). Weakly connected neural networks. In Applied mathematical sciences (Vol. 126). New York: Springer Verlag.
7. Hormuzdi, S. G., Pais, I., LeBeau, F. E. N., Towers, S. K., Rozov, A., Buhl, E. H., Whittington, M. A., & Monyer, H. (2001). Impaired electrical signalling disrupts gamma frequency oscillations in connexin 36-deficient mice. Neuron, 31, 487-495.
8. Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Berlin: Springer.
9. Landisman, C. E., Long, M. A., Beierlein, M., Deans, M. R., Paul, D. L., & Connors, B. W. (2002). Electrical synapses in the thalamic reticular nucleus. Journal of Neuroscience, 22, 1002-1009.
10. MacVicar, B. A., & Dudek, F. E. (1982). Electrotonic coupling between granule cells of rat dentate gyrus: Physiological and anatomical evidence. Journal of Neurophysiology, 47, 579-592.
11. Pecora, L. M., Carroll, T. L., Johnson, G. A., & Mar, D. J. (1997). Fundamentals of synchronization in chaotic systems, concepts and applications. Chaos, 7, 520-543.
12. Perez Velazquez, J. L., & Carlen, P. L. (2000). Gap junctions, synchrony and seizures. Trends in Neurosciences, 23, 68-74.
13. Perez Velazquez, J. L., Carlen, P. L., & Skinner, F. (2001). Artificial electrotonic coupling affects neuronal firing patterns depending upon intrinsic cellular characteristics. Neuroscience, 103, 841-849.
14. Sherman, A., & Rinzel, J. (1992). Rhythmogenic effects of weak electrotonic coupling in neuronal models. Proceedings of the National Academy of Sciences USA, 89, 2471-2474.
15. Strogatz, S. H. (2000). From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators. Physica D, 143, 1-20.
16. Venance, L., Rozov, A., Biatow, M., Burnashev, N., Feldmeyer, D., & Monyer, H. (2000). Connexin expression in electrically coupled postnatal rat brain neurons. Proceedings of the National Academy of Sciences USA, 97, 10260-10265.