Mathematical Sciences: Mathematical Models in Cell Biology:Responses to Molecular Signals

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The principal investigator will developed the mathematical theory of the theoretical/experimental collaboration aimed at identifying signal and response mechanisms in immediate allergic reactions. Biological cells sense their environment primarily through the interaction of cell surface receptors with specific extracellular ligands. These interactions serve as signals, initiating cell responses to hormones, neurotransmitters, immune response mediators, and other molecules. One response the principal investigator and her colleagues will study is the release, from intracellular granules, of molecules that cause allergic symptoms. The mathematics proposed here involves setting up systems of differential equations, and estimating parameters involved in these equations as well as estimating distributions using statistical techniques. The mathematical analysis will be necessary to interpret any but the simplest experiments. The combination of solid mathematical modeling and analysis expertise with the biological experimentation is a positive model for interdisciplinary research.