DIRECT PHASE DETERMINATION BY ENTROPY MAXIMIZATION AND LIKELIHOOD RANKING - STATUS-REPORT AND PERSPECTIVES

A new multisolution phasing method based on entropy maximization and l ikelihood ranking, proposed for the specific purpose of extending prob abilistic direct methods to the field of macromolecules, has been impl emented in two different computer programs and applied to a wide varie ty of problems. The latter comprise the determination of small crystal structures from X-ray diffraction data obtained from single crystals or from powders, and from electron diffraction data partially phased b y image processing of electron micrographs; the ab initio generation a nd ranking of phase sets for small proteins; and the improvement of po or quality phases for a larger protein at medium resolution under cons traint of solvent flatness. These applications show that the primary g oal of this new method - namely increasing the accuracy and sensitivit y of probabilistic phase indications compared with conventional direct methods - has been achieved. The main components of the method are (1 ) a tree-directed search through a space of trial phase sets; (2) the saddle-point method for calculating joint probabilities of structure f actors, using entropy maximization; (3) likelihood-based scores to ran k trial phase sets and prune the search tree; (4) efficient schemes, b ased on error-correcting codes, for sampling trial phase sets; (5) a s tatistical analysis of the scores for automatically selecting reliable phase indications. They have been implemented to varying degrees of c ompleteness in a computer program (BUSTER) and tested on two small str uctures as well as on the small protein crambin. The main obstructions to successful ab initio phasing in the latter case seem to reside in the accumulation of phase sampling errors and in die lack of a properl y defined molecular envelope, both of which can be remedied within die methods proposed. A review of the Bayesian statistical theory encompa ssing all phasing procedures, proposed earlier as an extension of the initial theory, shows that the techniques now available in BUSTER brin g closer a number of major enhancements of standard macromolecular pha sing techniques, namely isomorphous replacement, molecular replacement , solvent flattening and non-crystallographic symmetry averaging. The gradual implementation of the successive stages of this 'Bayesian prog ramme' should lead to an increasingly integrated, effective and depend able phasing procedure for macromolecular structure determination.