Terman 9802339 The investigator and his colleagues develop mathematical tools for analyzing the population rhythms of biophysical models for neuronal networks. These models exhibit a rich structure of oscillatory behavior. The dynamics of even a single cell can be quite complicated; it may, for example, fire either periodic spikes or bursts of action potentials that are followed by a silent phase of near quiescent behavior. Examples of population rhythms include synchronous behavior, in which every cell in the network fires at the same time, and clustering, in which the entire population of cells breaks up into groups; cells within a single group fire synchronously and different groups are desynchronized from each other. Activity may propagate through the network in a wave-like manner. A network's population rhythm results from interactions between three separate components: the intrinsic properties of neurons, the synaptic properties of coupling between neurons, and the architecture of coupling. Each of these components may include numerous parameters and multiple time scales. The mathematical techniques that are developed by the investigator can help determine the role each of these components plays in shaping the emergent network behavior. This may lead to a classification of the possible rhythms that can emerge from a given network and help determine how complicated a model must be in order to display some observed dynamics. The types of rhythms that the investigator studies arise throughout the central nervous system. Consider, for example, thalamic networks: these have been implicated in the generation of sleep rhythms, certain forms of epilepsy, and Parkinson tremor. The investigator studies how the same set of neurons can exhibit the very different rhythms that take place during different stages of sleep and what changes must occur in the networks during the transition from one stage of sleep to another. Recent experiments have demons trated that neurons in the basal ganglia exhibit quite different population rhythms in normal and parkinsonian animals. The investigator develops and analyzes biophysical models for these networks in order to determine factors responsible for the generation of these rhythms.
