Study Weekend Program... UP


Statistical and Optimisation Aspects of Structure Refinement and Completion

Gérard Bricogne (a), Eric Blanc (a,b) and Pietro Roversi (a,c)
(a) Global Phasing Ltd, Sheraton House, Castle Park, Cambridge CB3 0AX, UK.
(b) European Bioinformatics Institute, Wellcome Trust Genome Campus, Hinxton, Cambridge CB10 1SD, UK.
(c) Laboratory of Molecular Biophysics, Biochemistry Department, Oxford
University, South Parks Road, Oxford OX1 3HQ, UK.

The original aim of the BUSTER program [1] was to investigate the use of joint (jpd's) probability distributions of structure factors emanating from non-uniform distributions of random atoms, in conjunction with the maximum- entropy method [2,3]. It was then used, in conjunction with TNT [4], as a test bed for the maximum-likelihood refinement of partial structures [5], in which both of these capabilities could be exploited. The jpd methods were (under)used to describe quantitatively the statistical distribution of structure factor contributions from atoms known to be present in an unknown structure but not included in the atomic model, thus allowing the refinement of that incomplete model. The technique of maximum-entropy modulation of a prior spatial distribution for the missing atoms was then available to assist in the completion of that model by producing maps which were more contrasted than the conventional ones, yet still relatively unbiased. The BUSTER-TNT program has been used successfully to deal with such situations, for instance in finding missing loops (see the companion talk by Pietro Roversi et al.).

This talk will describe the various tools used to define and manipulate non-uniform distributions of random atoms, approximate the corresponding distributions of structure factors, turn these into likelihood functions by consulting measured amplitude data as well as experimental phase information, and optimise likelihood under geometric restraints or constraints.

Numerous questions related to sharpening these tools and improving refinement methodology will be discussed.

[1] G. Bricogne, Acta Cryst. (1993) D49, 37-60
[2] G. Bricogne, Acta Cryst. (1984) A40, 410-445
[3] G. Bricogne, Acta Cryst. (1988) A44, 517-545
[4] D.E. Tronrud, L.F. Ten Eyck & B.W. Matthews, Acta Cryst. (1987) A43, 489-501
[5] G. Bricogne & J.J. Irwin (1996). In "Macromolecular Refinement", edited by M. Moore and E.J. Dodson, 85-92. Daresbury Laboratory, Warrington.