Forced coalescence phasing: a method for ab initio determination of crystallographic phases

A method has been developed for ab initio determination of crystallographic phases. This technique, called forced coalescence phasing (FCP), is implemented on a computer and uses an automated iterative procedure that combines real space filtering with numerically seeded Fourier transforms to solve the crystallographic phase problem. This approach is fundamentally different from that of traditional direct methods of phasing, which rely on structure invariant probabilistic phase relationships. In FCP, the process begins with an appropriate set of atoms randomly distributed throughout the unit cell. In subsequent cycles of the program, these atoms undergo continual rearrangements ultimately forming the correct molecular structure(s) consistent with the observed x-ray data. In each cycle, the molecular rearrangement is directed by an electron density (Fourier) map calculated using specially formulated numerical seed coefficients that, along with the phase angles for the map, are derived from the arrangement of atoms in the preceding cycle. The method has been tested using actual x-ray data from three organic compounds. For each data set, 100 separate phase determination trials were conducted, each trial beginning with a different set of randomly generated starting phases. Correct phase sets were successfully determined in all of the trials with most trials requiring fewer than 50 cycles of the FCP program. In addition to its effectiveness in small molecule phase determination, FCP offers unexplored potential in the application of real-space methods to ab initio phasing of proteins and other macromolecule structures.