Molecular Structure: Dynamics, Geometry, and Topology

The design or redesign of macromolecules to perform biological or industrial functions requires quantum mechanical models to be solved. Various approximate models are currently being refined and further developed as the power of available computers increases. Monte Carlo techniques are also becoming feasible for this class of problem. The workshop will combine researchers involved in the development of these diverse techniques and identify mathematical problems for further study.

The structure of macromolecules can often be described as a linear sequence of bonded atoms (e.g. a DNA nucleotide sequence) yet the three-dimensional structure (and resulting function) remain elusive. The ``protein folding problem'' is one of the simplest to state and yet impossible to solve for molecules of substantial size. Different approaches are being proposed for attacking this problem, ranging from topology, geometry, mechanics, and even artificial intelligence. The workshop will focus on the various mathematical approaches available. Fundamental to the three dimensional structure is the quantum-mechanically determined local bond structure.