Using Phase Response Curves to Understand Neuronal Synchronization and Sleep.

Abstract

The phase response curve (PRC) is a mathematical tool used to characterize the dynamics of individual neurons. It is useful for understanding the synchronization properties of neuronal networks, though until now most work has focused upon networks either with very few neurons or with very simple connectivity structure. This thesis investigates to what degree the predictions of PRC theory hold in complex, large-scale neuronal networks, paying particular attention to the phenomenon of frequency-dependent synchronization. This phenomenon is explored using both a simplified neuron model (Morris-Lecar) and a more complex, Hodgkin-Huxley type model. This last model is based upon experiments which showed that the PRCs of cortical cells were dramatically altered by the neuromodulator acetylcholine. This thesis explores a possible role for such cholinergically-induced PRC switching in helping to explain the function of sleep.