Table of Contents
ISRN Biomathematics
Volume 2013 (2013), Article ID 194239, 7 pages
http://dx.doi.org/10.1155/2013/194239
Research Article

Phase-Coupled Oscillations in the Brain: Nonlinear Phenomena in Cellular Signalling

1School of Computer and Systems Sciences, Jawaharlal Nehru University, New Delhi 110067, India
2Division of Neuroradiology, The Russell H. Morgan Department of Radiology and Radiological Science, School of Medicine, The Johns Hopkins University, Baltimore, MD 21287, USA
3Department of Medicinal Chemistry, College of Pharmacy, Qassim University, Qassim 51452, Saudi Arabia

Received 16 January 2013; Accepted 20 February 2013

Academic Editors: J. Chow, J. Crezee, and J. H. Wu

Copyright © 2013 Vikas Rai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Daan and C. Berde, “Two coupled oscillators: simulations of the circadian pacemaker in mammalian activity rhythms,” Journal of Theoretical Biology, vol. 70, no. 3, pp. 297–313, 1978. View at Google Scholar · View at Scopus
  2. B. Van der Pol and J. Van der Mark, “The heartbeat considered as a relaxation oscillation, and an electrical model of the heart,” Philosophical Magazine, vol. 6, pp. 763–775, 1928. View at Google Scholar
  3. A. M. Dos Santos, S. R. Lopes, and R. L. Viana, “Rhythm synchronization and chaotic modulation of coupled Van der Pol oscillators in a model for the heartbeat,” Physica A, vol. 338, no. 3-4, pp. 335–355, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. J. Hasty, D. McMillen, F. Isaacs, and J. J. Collins, “Computational studies of gene regulatory networks: in numero molecular biology,” Nature Reviews Genetics, vol. 2, no. 4, pp. 268–279, 2001. View at Publisher · View at Google Scholar · View at Scopus
  5. G. Buzsáki and A. Draguhn, “Neuronal olscillations in cortical networks,” Science, vol. 304, no. 5679, pp. 1926–1929, 2004. View at Publisher · View at Google Scholar · View at Scopus
  6. Z. Sands, A. Grottesi, and M. S. Sansom, “Voltage-gated ion channels,” Current Biology, vol. 15, no. 2, pp. R44–R47, 2005. View at Google Scholar · View at Scopus
  7. W. J. Freeman, “Tutorial on neurobiology: from single neurons to brain chaos,” International Journal of Bifurcation and Chaos, vol. 2, pp. 451–482, 1992. View at Google Scholar
  8. A. L. Hodgkin and A. F. Huxley, “The components of membrane conductance in the giant axon of Loligo,” The Journal of Physiology, vol. 116, no. 4, pp. 473–496, 1952. View at Google Scholar · View at Scopus
  9. C. Morris and H. Lecar, “Voltage oscillations in the barnacle giant muscle fiber,” Biophysical Journal, vol. 35, no. 1, pp. 193–213, 1981. View at Google Scholar · View at Scopus
  10. S. R. Nadar and V. Rai, “Transient periodicity in a morris lecar neural system,” ISRN Biomathematics, vol. 2012, Article ID 546315, 7 pages, 2012. View at Publisher · View at Google Scholar
  11. G. A. Carpenter, “A geometric approach to singular perturbation problems with applications to nerve impulse equations,” Journal of Differential Equations, vol. 23, no. 3, pp. 335–367, 1977. View at Google Scholar · View at Scopus
  12. N. Fenichel, “Geometric singular perturbation theory for ordinary differential equations,” Journal of Differential Equations, vol. 31, no. 1, pp. 53–98, 1979. View at Google Scholar · View at Scopus
  13. E. M. Izhikevich, “Neural excitability, spiking and bursting,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 10, no. 6, pp. 1171–1266, 2000. View at Google Scholar · View at Scopus
  14. E. M. Izhikevich, Dynamical Systems in Neuroscience: the Geometry of Excitability and Bursting, MIT Press, Cambridge, Mass, USA, 2007.
  15. M. Colombo and C. G. Gross, “Responses of inferior temporal cortex and hippocampal neurons during delayed matching to sample in monkeys (Macaca fascicularis),” Behavioral Neuroscience, vol. 108, no. 3, pp. 443–455, 1994. View at Publisher · View at Google Scholar · View at Scopus
  16. N. Axmacher, C. E. Elger, and J. Fell, “Working memory-related hippocampal deactivation interferes with long-term memory formation,” Journal of Neuroscience, vol. 29, no. 4, pp. 1052–1060, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. X. J. Wang, “Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory,” Journal of Neuroscience, vol. 19, no. 21, pp. 9587–9603, 1999. View at Google Scholar · View at Scopus
  18. S. Makeig, M. Westerfield, T. P. Jung et al., “Dynamic brain sources of visual evoked responses,” Science, vol. 295, no. 5555, pp. 690–694, 2002. View at Publisher · View at Google Scholar · View at Scopus
  19. B. Ermentrout, “Type I membranes, phase resetting curves, and synchrony,” Neural Computation, vol. 8, no. 5, pp. 979–1001, 1996. View at Google Scholar · View at Scopus
  20. H. Y. Jeong and B. Gutkin, “Synchrony of neuronal oscillations controlled by GABAergic reversal potentials,” Neural Computation, vol. 19, no. 3, pp. 706–729, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. F. Collette and M. Van Der Linden, “Brain imaging of the central executive component of working memory,” Neuroscience and Biobehavioral Reviews, vol. 26, no. 2, pp. 105–125, 2002. View at Publisher · View at Google Scholar · View at Scopus
  22. A. D. Baddeley, “Short-term memory for word sequences as a function of acoustic, semantic and formal similarity,” The Quarterly Journal of Experimental Psychology, vol. 18, no. 4, pp. 362–365, 1966. View at Google Scholar · View at Scopus
  23. A. D. Baddeley, Working Memory, Oxford University Press, Oxford, UK, 1986.
  24. P. Larimer and B. W. Strowbridge, “Representing information in cell assemblies: persistent activity mediated by semilunar granule cells,” Nature Neuroscience, vol. 13, no. 2, pp. 213–222, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. D. D. Fraser and B. A. MacVicar, “Cholinergic-dependent plateau potential in hippocampal CA1 pyramidal neurons,” Journal of Neuroscience, vol. 16, no. 13, pp. 4113–4128, 1996. View at Google Scholar · View at Scopus
  26. A. Gupta, F. S. Elqammal, A. Proddutur, S. Shah, and V. Shantakumar, “Decrease in tonic inhibition contributes to increase in dentate semilunar granule cell excitability after brain injury,” Journal of Neuroscience, vol. 32, no. 7, pp. 2523–2537, 2012. View at Google Scholar