International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by E. Arnold, D. M. Himmel and M. G. Rossmann © International Union of Crystallography 2012 |
International Tables for Crystallography (2012). Vol. F, ch. 15.3, pp. 411-412
Section 15.3.5.6. Averaging^{a}Department of Chemistry, University of York, York YO1 5DD, England,^{b}Division of Basic Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N., Seattle, WA 90109, USA, and ^{c}Department of Physics, University of York, York YO1 5DD, England |
Averaging is performed using a single-step approach (Rossmann et al., 1992), in which every copy of the molecule in a `virtual' asymmetric unit is averaged with every other copy. Density values are obtained at non-grid positions using a 27-point quadratic spectral spline interpolation. A sharpened map is first calculated by dividing by the Fourier transform of the quadratic spline function. The same spline function is then convoluted with the sharpened map to obtain the density value at an arbitrary coordinate (Cowtan & Main, 1998). This approach gives very accurate interpolation from a coarse grid map with relatively little computation and additionally provides gradient information for the refinement of averaging operators.
References
Cowtan, K. D. & Main, P. (1998). Miscellaneous algorithms for density modification. Acta Cryst. D54, 487–493.Rossmann, M. G., McKenna, R., Tong, L., Xia, D., Dai, J.-B., Wu, H., Choi, H.-K. & Lynch, R. E. (1992). Molecular replacement real-space averaging. J. Appl. Cryst. 25, 166–180.