Theoretical and computational investigations of single biomolecule and multicellular morphogenetic processes

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In this proposal, we investigate fundamental phenomena in biology from the viewpoint of physics, using analytical and computational tools. We are interested primarily in 3 research areas. One is in biologically inspired optimization problems. Often evolution seeks to optimize the fitness of an organism by modifying shape, motion, or molecules. In some cases such optimization may be understood mathematically, in others, through computer algorithms. We focus specifically on a problem important to understanding how a protein folds to its biologically functional structure, which involves generalizing the notion of distance, normally taken between points, to objects of higher dimension. Another optimization problem is related to phylogenetic trees, the tree of life, and involves the construction of high-dimensional networks of minimal length indicating how closely related living species are, as well as what their common ancestors may have looked like. We are interested in constructing such networks and understanding their universal properties.