Mathematical Modeling of Neural Populations

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L.F.Abbott IBN 98-17194Mathematical Modeling of Neural PopulationsABSTRACTThe proposed research is part of a general program that uses mathematical modeling and computational analysis to reveal how the functional characteristics of neuronal circuits arise from basic cellular mechanisms. The research is theoretical, but it is based on anatomical and physiological data, and the results suggest directions and provide predictions for future experiments. The proposed work focuses primarily on the visual system. The goal is to determine how the circuits of the primary visual cortex generate responses to visual images, and to study how the necessary circuit elements could develop on the basis of activity-dependent processes.Much is known about how neurons in the primary visual cortex respond to the spatial pattern of a visual image, but less is known about the temporal characteristics of responses to changing images. One project in the proposed research will address this issue by constructing models that accurately duplicate visual responses to transient, moving, and oscillating images. A number of mechanisms that affect temporal response characteristics will be studied, compared, and contrasted. Responses of cells in primary visual cortex often depend on the direction that a visual image is moving, and a model of this phenomenon will be developed and investigated in depth.Some cells in the primary visual cortex exhibit an interesting property that may represent the first stage in our ability to identify objects irrespective of their position in the visual field, so-called invariant object recognition. Another research project proposes a new model for how transitionally invariant visual responses are generated by cortical circuitry. The model is based on the structure and strength of interconnections between cortical cells and makes definite predictions about what happens if these connections are modulated or disrupted. The predictions of the model can be tested experimentally. The development of the synaptic interconnections needed in the model through activity-dependent processes will also be studied.The proposed research serves an important educational function by training graduate students to apply mathematical and computation techniques to the analysis and understanding of neuronal circuits of the brain. This education is cross-disciplinary, involving skills in mathematics, physics, computer science, and neurobiology.