Improved Structure Refinement Through Maximum Likelihood

When crystal structures of proteins or small molecules are used to address questions of scientific relevance, the accuracy and precision of the atomic coordinates are crucial. Accordingly, the atomic model is generally improved by refining it to improve agreement with the observed diffraction data. The refinement of crystal structures is conventionally based on least-squares methods but such procedures are handicapped since conditions necessary for the use of the least-squares target are not satisfied. It is proposed here that refinement should be based on maximum likelihood and two maximum-likelihood targets have been implemented in the program XPLOR. Preliminary tests with protein structures give dramatic results. Compared to least-squares refinement, maximum-likelihood refinement can achieve more than twice the improvement in average phase error. The resulting electron-density maps are correspondingly clearer and suffer less from model bias.