Mathematical Modeling of the Nervous System of the Leech

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This IGMS project will deepen and extend the preparation of PI Carl Cowen to undertake research in mathematical neuroscience by working in the Purdue University Dept. of Biological Sciences with Prof. Chris Sahley and her postdocs Brian Burrell and Brenda Moss. Professor Sahley's group studies the cellular and molecular mechanisms of behavioral plasticity, especially associative learning and non-associative learning using the medicinal leech, Hirudo medicinalis, as a model organism. Cowen proposes to spend the year of the project working in Sahley's lab, observing the experimental techniques used, learning about the underlying cellular and molecular mechanisms of learning, working closely with the biologists in developing mathematical and computational models of the processes, analyzing the dynamics of the models, working with the biologists to understand the models' predictions, and using the predictions to deepen understanding of the cellular and molecular mechanisms involved or design experiments to test new hypotheses. The project will develop the close working relationships between Cowen and biologists at Purdue that are expected to lead to successful interdisciplinary collaboration. The specific cellular mechanisms proposed for study, interactions between S-cells and P-cells in the neurosystem of the leech, are both simple enough to afford detailed investigation and also representative of an important class of neuronal interactions in both invertebrates and higher animals, including humans. The project centers on learning, including Cowen's learning in the area of neurobiology and modeling and the learning of some related mathematics and modeling by his collaborators. In addition, in Spring 2004, Cowen will offer a course in the Purdue Biology Department on the differential equations and dynamical systems involved in modeling neuronal systems that will be suitable for advanced undergraduates or beginning graduate students in biology or other sciences. Moreover, Cowen will direct two undergraduate students during summer of 2004 in research projects involved with modeling neurosystems. This project willprovide the foundation for Cowen to begin research in collaboration with Purdue's neurobiologists and to mentor graduate and undergraduate students, including women and members of underrepresented minority groups, in mathematical neuroscience.This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).