MATHEMATICAL THEORY OF OSCILLATORY NEURAL NETWORKS

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DESCRIPTION (Adapted from applicant's abstract): Oscillatory behavior is found in many parts of the nervous system of both vertebrates and invertebrates. In many cases, there is much known about the participating neurons. However, it is not understood how networks that make use of dynamically complicated components are constructed in order to be able to carry out their appropriate tasks. The aim of the proposal is to continue to develop a body of technique relevant to addressing this question, and to use this technique to further the understanding of particular neural networks. The neural networks to be investigated fall into three classes to be described below. Together, they permit investigation of a range of closely related questions about how oscillations are produced and how networks maintain their particular timing relationships. Linearly organized networks include the central pattern generators for locomotion in lamprey, leech and Xenopus tadpoles. These systems have many features in common, but are different in details of anatomy and cell physiology. Investigation of the different design constraints of the different networks can yield general principles governing all of these, and an understanding of the different mechanisms that can produce similar behavior. The small network studies will focus on the crustacean STG. Of special interest are mechanisms for regulating such quantities as phase differences between the firing of neurons within the network and the frequency of the network activity when it is oscillatory. The ultimate aim is to understand how networks can be constructed to be flexible in their outputs under a variety of modulatory influences, yet still be able to regulate those quantities which must be preserved for the appropriate functioning of the network. This work is part of a larger project involving modeling and experiments. Cortical and cortical-like networks are capable of very complex dynamics. This part of the project focuses on how properties of cells and synapses affect the emergent behavior of the network. The studies will be grounded in data from a simple cortical-like network, the olfactory system of the locust. One long-term goal is to understand how rhythmic behavior participates in sensory coding, processing and learning.