Parallel solutions to the phase problem in X-ray crystallography

The central problem of single crystal molecular structure determination via X-ray diffraction is the "phase problem." Associated with each diffraction maximum (a reflection) are a magnitude, which can be experimentally determined, and a phase angle, which is lost in the experiment. The goal of "direct methods" is to mathematically reconstruct the phase information from the magnitude information alone. Traditional direct methods are capable of determining structures of moderate complexity, but to extend them to problems of the size of macromolecules (proteins, etc.) requires developing new techniques that appear to be computationally intensive. Recently, a new formulation of the phasing process, dependent on a minimal function, has been proposed. Here we explore a number of different implementations of the principle to the solution of small molecular structures. The machines that we use include an Intel iPSC/2 hypercube, the Connection Machine CM- 2, and a network of Sun workstations.