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.

Abstract

We report the existence of phase-coupled oscillations in a model neural system. The model consists of a group of excitatory principal cells in interaction with local inhibitory interneurons. The voltages across the membranes of excitatory cells are governed primarily by calcium and potassium ion conductivities. The number of potassium channels open at any given instant changes in accordance with a deterministic law. The time scale of this change is set by a constant which depends on midpoint potentials at which potassium and calcium currents are half-activated. The growth of mean membrane potential of excitatory principal cells is controlled by that of the inhibitory interneurons. Nonlinear oscillatory system associated with these limit cycles starting from two different initial conditions maintain a definite phase relationship. The phase-coupled oscillations in electrical activity of the neuronal cells carry together amplitude, phase, and time information for cellular signaling. This mechanism supports an energy efficient way of information processing in the central nervous system. The information content is encoded as persistent periodic oscillations represented by stable limit cycles in the phase space.