Pushing the boundaries of molecular replacement with maximum likelihood

The molecular-replacement method works well with good models and simple uni t cells, but often fails with more difficult problems. Experience with like lihood in other areas of crystallography suggests that it would improve per formance significantly. For molecular replacement, the form of the required likelihood function depends on whether there is ambiguity in the relative phases of the contributions from symmetry-related molecules (e.g. rotation versus translation searches). Likelihood functions used in structure refine ment are appropriate only for translation (or six-dimensional) searches, wh ere the correct translation will place all of the atoms in the model approx imately correctly. A new likelihood function that allows for unknown relati ve phases is suitable for rotation searches. It is shown that correlations between sequence identity and coordinate error can be used to calibrate par ameters for model quality in the likelihood functions. Multiple models of a molecule can be combined in a statistically valid way by setting up the jo int probability distribution of the true and model structure factors as a m ultivariate complex normal distribution, from which the conditional distrib ution of the true structure factor given the models can be derived. Tests i n a new molecular-replacement program, Beast, show that the likelihood-base d targets are more sensitive and more accurate than previous targets. The n ew multiple-model likelihood function has a dramatic impact on success.