A TEST OF MAXIMUM-LIKELIHOOD REFINEMENT OF MACROMOLECULAR STRUCTURES WITH BUSTER & TNT. John Irwin and Gérard Bricogne, MRC Laboratory of Molecular Biology, Hills Road, Cambridge CB2 2QH, UK.

The Bayesian viewpoint [1,2,3,4] has long suggested that structure refinement should be carried out by maximising the log-likelihood gain (LLG) rather than by minimising the conventional least-squares residual, as only the maximum-likelihood (ML) method can take into account the uncertainty of the phases associated to model incompleteness and model imperfection by suitably downweighting the corresponding amplitude constraints. It was predicted [3] that ML refinement would allow the refinement of an incomplete model by using the structure factor statistics of randomly distributed scatterers to represent the effects of the missing atoms, in such a way that the latter would not be wiped out; and that the final would then provide indications about the location of these missing atoms.

These predictions have now been confirmed by actual tests carried out by combined use of BUSTER [4] and TNT [5] on an incomplete (60% of molecule) and imperfect (1Å rms positional error) model. The maximum-likelihood result is more accurate than that from least-squares, and the final LLG gradient map is much more informative than the usual difference map, thus greatly increasing the chances of success in "bootstrapping" from an unpromising molecular replacement starting point to a complete structure.

We will also discuss the two main concerns at the moment in the fields of structure refinement and validation where Bayesian methods have much to offer, namely (1) getting better reliability indicators for the final results of structure refinement, and (2) ensuring that these indicators are effectively optimised during refinement.

References

[1] G. Bricogne (1984). Acta Cryst. A40, 410-445.

[2] G. Bricogne (1988). Acta Cryst. A44, 517-545.

[3] G. Bricogne (1992). In The Molecular Replacement Method, edited by W. Wolf, E.J. Dodson and S. Gover, pp. 62-75. Warrington: Daresbury Laboratory.

[4] G. Bricogne, Acta Cryst. D49, 37-60 (1993).

[5] D.E. Tronrud (1987). L.F. Ten Eyck, and B.W. Matthews, Acta Cryst. A43, 489-501.