Biomedical subjects

K Cowtan

Publications and source records attributed to K Cowtan.

4 recordsLinked to original sources

PubMed2000

Eigensystem analysis of the refinement of a small metalloprotein.

The eigenvalues and eigenvectors of the least-squares normal matrix for the full-matrix refinement problem contain a great deal of information about the quality of a model; in particular the precision of the model parameters and correlations between those parameters. They also allow the isolation of those parameters or combinations of parameters which are not determined by the available data. Since a protein refinement is usually under-determined without the application of geometric restraints, such indicators of the reliability of a model offer an important contribution to structural knowledge. Eigensystem analysis is applied to the normal matrices for the refinement of a small metalloprotein using two data sets and models determined at different resolutions. The eigenvalue spectra reveal considerable information about the conditioning of the problem as the resolution varies. In the case of a restrained refinement, it also provides information about the impact of various restraints on the refinement. Initial results support conclusions drawn from the free R factor. Examination of the eigenvectors provides information about which regions of the model are poorly determined. In the case of a restrained refinement, it is also possible to isolate places where X-ray and geometric restraints are in disagreement, usually indicating a problem in the model.

Least-Squares Analysis↗

PubMed1999

Error estimation and bias correction in phase-improvement calculations.

With the rise of Bayesian methods in crystallography, the error estimates attached to estimated phases are becoming as important as the phase estimates themselves. Phase improvement by density modification can cause problems in this environment because the quality of the resulting phases is usually overestimated. This problem is addressed by an extension of the gamma correction [Abrahams (1997). Acta Cryst. D53, 371-376] to arbitrary density-modification techniques. The degree to which the improved phases are biased by the features of the initial map is investigated in order to determine the limits of the resulting procedure and the quality of the phase-error estimates.

Bayes Theorem↗

PubMed1998

Modified phased translation functions and their application to molecular-fragment location.

Direct methods at high resolution have depended on the resolution of atomic like features in the map. At data resolutions more typical for protein structures (2-3 A) individual atoms may not be resolved, so larger features must be identified. At one extreme the whole molecule may be located using the diffraction magnitudes alone by the molecular-replacement method. At the other extreme it is possible to locate individual residues in a well phased map. In this paper an intermediate problem is addressed: the location of multi-residue fragments on the basis of weak phase information. An agreement function based on the mean-squared difference between model and map over a masked region is shown to be more effective than a simple overlap integral, and may be efficiently calculated by Fourier methods. The techniques are compared using poorly phased electron-density maps at approximately 3 A for the proteins RNAse and O6-methylguanine-DNA-methyltransferase.

Animals↗

PubMed1998

Miscellaneous algorithms for density modification.

Various algorithms are described, developed for the dm density modification package, which have not been described elsewhere. Methods are described for the following problems: determination of the absolute scale and overall temperature factor of a data set, by a method which is less dependent on data resolution than Wilson statistics; an efficient interpolation algorithm for averaging and its application to refinement of averaging operators; a method for the automatic determination of averaging masks.

Algorithms↗