LEAST-SQUARES REFINEMENT OF SMALL-MOIETY AND MACROMOLECULAR STRUCTURES

George M. Sheldrick

Institut für Anorganische Chemie, Universität Göttingen, Tammanstr. 4, D-37077 Göttingen, Germany; gsheldr@shelx.uni-ac.gwdg.de

Keywords: Least-squares, Structure refinement, Restraints, Disorder, Anisotropy, Twinning, Standard uncertainties

Once upon a time, small-moiety and macromolecular structures were refined using entirely different philosophies and computer programs. For macromolecules, the limited number of data per positional parameter made it essential to supplement the diffraction data with chemical information, e.g. in the form of restraints, and anisotropic refinement was out of the question. In the last few years, synchrotrons, cryogenic techniques and advances in detector technology have led to an explosion in the number of protein datasets collected to atomic resolution; small molecules have also been getting larger, and the gap between the two no longer exists.

The chemical restraints that were required for the refinement of macromolecules are also very powerful for the refinement of disordered solvent regions in small molecules, and restrained anisotropic refinement is proving to be an appropriate model in both cases when the limiting resolution is in the 0.9-1.5 Å range [1]. It is now possible to use full-matrix and similar techniques to estimate standard uncertainties in smaller macromolecules, and the availablity of effective techniques for refinement against twinned data, first developed for small molecules, has led to an apparent increase in the percentage of protein crystals that are twinned.

Although often (mis)used for the purpose, classical least-squares refinement is not the most appropriate techniqe for the extension of incomplete or partially erroneous structures. Maximum likelihood [2], simulated annealing [3] and simulation of the missing part of the structure by refinable dummy atoms (wARP) [4] are superior alternatives for this purpose.

For latest details of a least-squares refinement program [1] that attempts to unify both the small-moiety and macromolecular approaches see the SHELX homepage at: http://shelx.uni-ac.gwdg.de/SHELX/

1. G.M. Sheldrick & T.R. Schneider, SHELXL: High Resolution Refinement, Methods in Enzymology, 277 (1997) 319-343.
2. G. Bricogne, Bayesian Statistical Viewpoint on Structure Determination: Basic Concepts and Examples. Methods in Enzymology, 276 (1997) 361-423.
3. A.T. Brünger & L.M. Rice, Crystallographic Refinement by Simulated Annealing: Methods and Applications, Methods in Enzymology, 277 (1997) 243-269.
4. A. Perrakis, T.K. Sixma, K.S. Wilson & V.S. Lamzin, wARP: Improvement and Extension of Crystallographic Phases by Weighted Averaging of Multiple-Refined Dummy Atomic Models. Acta Cryst., D53 (1997) 448-455.