Crystallography is the primary method employed to determine 3-dimensional structures of large biological molecules, namely proteins and nucleic acids. The principal tool for studying single crystals is Xray diffraction, which yields an image of a molecule's electron density, or more precisely, an average electron density of all the molecules in the crystal. The average electron density contains not only the information about the position of atoms, but also information about the possible spread of atomic positions. The range of protein motions in the crystal is a dynamic property that can be studied by Xray diffraction. The difficulty is not in generating possible solutions to the problem, but rather in estimating the reliability of the result. Mathematically, the above problem is related to the "phase problem" in X-ray diffraction. Our research addresses all aspects of phase estimates through interference measurements, direct methods, and dynamic simulations in the crystal lattice.

The methods for the generation of a 3-dimensional molecular image will combine diverse sources of information, namely experimental (e.g., Multiple Anomalous Diffraction) and theoretical (predictions of the expected result). This combined process has mathematical similarity to the process of automated reasoning and pattern recognition.

The particular biological process of interest to this laboratory is protein folding. Proteins function in the globular, folded state; but they are produced in the elongated, unfolded state. For many proteins, the transition to folded state is accomplished with help from chaperonin proteins. Understanding the structure and function of the 800 kilodalton chaperonin GroEL requires finding out how this chaperonin can bind a large class of unfolded proteins. The structural challenge is to explain how a disordered state can be bound specifically.