Mathematical Modeling of Neural Populations

When we reach toward a visual object, there is a precise and continuous flow of information from the visual areas to the motor circuits that control arm and hand movements. But a moment later, we may be engaged in scratching an ear, with the same motor circuits now guided by tactile sensation and uncoupled from vision. This research project asks fundamental questions about how neural circuits perform such complex switching functions to re-route the flow of information during controlled and adaptive behaviors. A critical role in functional switching may be played by gain modulation, in which a type of "volume-control" mechanism at synapses adjusts neural responses. An important novel component is a testable hypothesis of a specific biophysical mechanism for gain modulation. Mathematical models of neurons and neural populations will be constructed based on detailed anatomical and physiological data, and the results arising from these models will be compared with experiments involving visual, discrimination, and motor tasks. Results of the proposed research will shed light on some of the complex features of neural circuitry that allow animals and people to control their actions and modify and tune their behaviors to specific conditions. The scientific goal is to relate these behavioral aspects of neural circuitry to the underlying cellular and biophysical mechanisms that generate them, using mathematical modeling to bridge the gaps between our knowledge at the cellular and behavioral levels. In addition, the proposed research will play a critical role integrating mathematics and biology into the education and training of undergraduate and graduate students, through classroom work, honors and rotation projects, and thesis research. This project is jointly supported between Computational Neuroscience (BIO) and Applied Mathematics (MPS).