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Neuronal Models for Sleep-Wake Regulation and Synaptic Reorganization in the Sleeping Hippocampus

Department of Mathematics and Mathematical Biosciences Institute, Ohio State University, Columbus, OH

Cecilia Diniz Behn

Division of Sleep Medicine, Harvard Medical School and Brigham & Women's Hospital, Boston, MA, Department of Neurology, Beth Israel Deaconess Medical Center, Boston, MA

Gina R. Poe

Department of Anesthesiology, University of Michigan, Ann Arbor, MI, Department of Molecular and Integrative Physiology, University of Michigan, Ann Arbor, MI

Victoria Booth

Department of Anesthesiology, University of Michigan, Ann Arbor, MI, vbooth{at}umich.edu, Department of Mathematics, University of Michigan, Ann Arbor, MI

In this article, we discuss mathematical models that address the control of sleep-wake behavior in the infant and adult rodent and a model that addresses changes in single-cell firing patterns in the hippocampus across wake and rapid eye movement (REM) sleep states. Each of the models describes the dynamics of experimentally identified neuronal components—either the firing activity of wake-and sleep-promoting neuronal populations or the spiking activity of hippocampal pyramidal neurons. Our discussion of each model illustrates how a mathematical model that describes the temporal dynamics of the modeled neuronal components can reveal specifics about proposed neuronal mechanisms that underlie sleep-wake regulation or sleep-specific firing patterns. For example, the dynamics of the models developed for sleep-wake regulation in the infant rodent lend insight into the involved brain-stem neuronal populations and the evolution of the network during maturation. The results of the model for sleep-wake regulation in the adult rodent suggest distinct properties of the involved neuronal populations and their interactions that account for long-lasting and brief waking bouts. The dynamics of the model for sleep-specific hippocampal neural activity proposes neural mechanisms to account for observed activity changes that can invoke synaptic reorganization associated with learning and memory consolidation.

Key Words: sleep-wake transitions • development • REM sleep • hippocampus • learning

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