IMPROVED STRUCTURE REFINEMENT THROUGH MAXIMUM-LIKELIHOOD

When crystal structures of proteins or small molecules are used to add ress questions of scientific relevance, the accuracy and precision of the atomic coordinates are crucial. Accordingly, the atomic model is g enerally improved by refining it to improve agreement with the observe d diffraction data. The refinement of crystal structures is convention ally based on least-squares methods but such procedures are handicappe d since conditions necessary for the use of the least-squares target a re not satisfied. It is proposed here that refinement should be based on maximum likelihood and two maximum-likelihood targets have been imp lemented in the program XPLOR. Preliminary tests with protein structur es give dramatic results. Compared to least-squares refinement, maximu m-likelihood refinement can achieve more than twice the improvement in average phase error. The resulting electron-density maps are correspo ndingly clearer and suffer less from model bias.