The brain regions devoted to the processing of sensory information are remarkable for their two-dimensional map-like (topographic) organization. Recent evidence suggests that this property can be maintained down to the subcellular level, in the form of topographically organized inputs onto the extended arborizations (dendrites) of single cells (neurons). The goal of this project is to identify the key principles underlying the processing of such topographic inputs in the dendrites of a prototypical neuron. The project focuses on a nerve cell that is most sensitive to objects approaching on a collision course with the animal and that is implicated in generating collision avoidance behaviors. The investigators use tools developed to study partial differential equations to determine the detailed dendritic distribution of the cell's ion channels. Next, techniques designed to reduce the complexity of mathematical models are used, as well as to simultaneously respect the topography of inputs, to extract a simplified representation of the neuron?s signal processing characteristics. This allows the investigators to characterize the role played by the neuron's dendrites in generating the responses of the neuron to objects approaching on a collision course. Particular focus is on understanding the invariance of responses to objects approaching from different directions.

The survival of all animals, including humans, critically depends on the neuronal processing of impending dangers. This project sheds light on how the brain accomplishes this feat in a particular model system ideally suited for this purpose. Mathematical tools are generated and are made available to other researchers to analyze neurons with similar properties in other contexts. Additionally, the project contributes to our basic understanding of brain function that may eventually lead to better cures for diseases affecting sensory perception. Finally, the results of this project could potentially find applications in the design of autonomous robots.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Mary Ann Horn
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Baylor College of Medicine
United States
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