Study Weekend Program...

## 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.