Mathematical Analysis of Networks of Neurons with Multiple Time Scales

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Kopell 9706694 The investigator and her colleagues study the dynamics of networks of neurons, especially networks whose output is rhythmic. The research uses methods of dynamical systems to understand how properties at the cellular level (intrinsic membrane dynamics) and the interconnections among the cells (synaptic properties) affect the network behavior. The research focuses on two kinds of problems. The first concerns the mechanisms by which networks synchronize or partially synchronize. These problems mainly concern cortical networks in which there are large numbers of similar cells. The other class, motivated mainly by smaller invertebrate networks, is concerned with the determination and regulation of network frequency and relative phases among cells in the network. In both classes of problems, the work is motivated by specific networks of neurons, but the techniques are broad enough to allow generalization of the results beyond the motivating examples. The dynamical systems methods to be used and developed exploit the many different times scales associated with the intrinsic and synaptic dynamical processes of the cells. One goal is to understand how network behavior is modulated by changing parameters that alter which subset of dynamical processes is most important in producing the network output. Networks of neurons producing rhythmic output are found in neural systems governing motor control, sensory processing, and in both sleeping and awake states. Rhythmic activity in the nervous system is also seen in pathological states, such as epilepsy and Parkinson's disease. Though there is much detailed information about the physiology of participating cells, it is not understood how networks that make use of dynamically complicated components are constructed to carry out their appropriate tasks. This research aims to identify mechanisms by which coherence, frequency and phase relationships of the rhythmic network output are regulated. Such identification can potentially allow scientists a deeper understanding of how the nervous sytem uses rhythms to produce appropriate behavior, as well as techniques for removing rhythmic activity that produces pathological states, including tremor.