Neuronal Dynamics

点击翻译按钮获取中文摘要

A primary goal of the proposed research is to develop mathematical tools for analyzing activity patterns in biophysical, conductance-based models for a broad class of neuronal systems. Specific issues are motivated by models for activity patterns in three systems. The first model arises in the study of the basal ganglia, a part of the brain that plays an important role in the generation of movements. Dysfunction of the basal ganglia is associated with movement disorders such as Parkinson's disease and Huntington's chorea. Experiments have demonstrated that neurons within the basal ganglia display a variety of dynamic behaviors; moreover, patterns of activity differ between normal and pathological states. The principal investigator is developing mathematical methods for analyzing the origins and mechanisms underlying these firing patterns. The principal investigator will also consider models of the insect antennal lobe. These neurons exhibit complex oscillatory dynamics in response to odors; however, the mechanisms underlying both single-cell and population rhythms are not fully understood. The principal investigator will develop mathematical models to explore mechanisms underlying odor representations in the insect antennal lobe and their modification with learning. Finally, the principal investigator is considering models of respiratory rhythm generation. Breathing movements in mammals are generated by networks of neurons in the lower brain stem that produce rhythmic oscillations of neural activity. One interesting feature of this network is the apparent high degree of heterogeneity among cells. The principal investigator will develop analytic tools to understand how a network of heterogeneous cells can exhibit synchronized activity and how synchronization is lost as parameters in the model are varied. Oscillations and other patterns of neuronal activity arise throughout the central nervous system. These oscillations have been implicated in the generation of sleep rhythms, epilepsy, parkinsonian tremor, sensory processing, and learning. Oscillatory behavior also arises in such physiological processes as respiration, movement, and secretion. Models for the relevant neuronal networks often exhibit a rich structure of dynamic behavior. Examples of population rhythms include synchronized oscillations, propagating waves and chaotic dynamics. Computational models and mathematical analysis can be extremely useful in understanding the mechanisms underlying this complex dynamics and predicting how the dynamics may change with respect to parameters. Specific neuronal systems to be studied in this project include the basal ganglia, a part of the brain implicated in the generation of Parkinsonian rhythms, the insect antennal lobe and the pre-Botzinger complex, a brain nuclei believed to be the origin of respiratory rhythm generation.