REFINEMENT OF MACROMOLECULAR STRUCTURES BY THE MAXIMUM-LIKELIHOOD METHOD

This paper reviews the mathematical basis of maximum likelihood. The l ikelihood function for macromolecular structures is extended to includ e prior phase information and experimental standard uncertainties. The assumption that different parts of a structure might have different e rrors is considered. A method for estimating sigma(A) using 'free' ref lections is described and its effects analysed. The derived equations have been implemented in the program REFMAC. This has been tested on s everal proteins at different stages of refinement (bacterial alpha-amy lase, cytochrome c', cross-linked insulin and oligopeptide binding pro tein). The results derived using the maximum-likelihood residual are c onsistently better than those obtained from least squares refinement.