The investigators investigate mathematical and algorithmic problems arising in studies of the flexibility and mobility of biomolecules, which include proteins and protein complexes. Many proteins exist in their native state with enough rigidity to maintain their three dimensional structure, but with sufficient flexibility to function. In other words, native state proteins exist right at the transition from rigid to flexible, where small stimuli can produce large functional responses. To study this behavior, the investigators propose a new category of constrained simulations, called geometric simulations since they enforce equality and inequality constraints of a geometric nature. They are designed to produce realistic motions of kinematic linkages of bodies, which obey length and angle constraints (covalent bonds, locked peptide double bonds and hydrogen bonds), and van der Waals hard core radii associated with various atom types, as well as hydrophobic tethers. The project team's joint expertise will be devoted to identify new techniques for efficient, robust and mathematically rigorous geometric simulations, inspired by and applied to real biological problems.
The investigators' study of the properties of biomolecules brings together concepts from mathematics, chemistry, engineering, computer science and physics to unify the various manifestations of structural flexibility, and to better understand their roles in determining observable properties. This mixing of concepts from different disciplines is likely to produce new insights, and shed light on problems arising in other areas (besides biology) where many bodies are interconnected by linkages and exclusion zones, as in material science, cell dynamics and crowd motion. This kind of interdisciplinary approach is particularly valuable to graduate and advanced undergraduate students, who can see unexpected connections between seemingly disparate areas of science. The software that is being developed through our work is freely available to the academic community via Flexweb, which has been made user-friendly and is promoted through discussion forums and monthly net-meetings. This software should also be useful in research involved in detecting biomolecules that are potential biohazards. This project, conducted in part at an all-women college with a sustained reputation in the sciences, has the potential for becoming a model of integration of high-caliber research and education in an era of interdisciplinarity.
