States of arousal, or consciousness with the brain are regulated largely by the neurotransmitter acetylcholine (ACh). Specifically, ACh is likely responsible for the transition between slow wave sleep (SWS; where ACh is absent) and rapid eye movement sleep or waking states (where ACh is high). Patterns of neural activity within the cerebral cortex corresponding to these states are markedly different. During SWS there are traveling waves of intense activity in the cortex while in other states locally organized stationary patterns occur . From a functional perspective, stationary patterns are likely to be important for working memory and attention dynamics while traveling waves could lead to synaptic renormalization . The mechanism for how changes on the cellular level are translated to patterns on the network level is not understood. In this work we give a model for the action of ACh on a network of neurons of the Hodgkin-Huxley type with a current that is regulated by ACh that induces spike-frequency adaptation (SFA) .
1 Neuroscience Graduate Program, University of Michigan, Ann Arbor, MI, 48109, U.S.A. 2 School of Physics and Astronomy, Tel-Aviv University, Tel Aviv, 69978, Israel. 3 Center for Theoretical Biological Physics, and Department of Biochemistry and Cell Biology, Rice University, Houston, TX, 77005, USA.