Tables for
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 15.3, pp. 411-412   | 1 | 2 |

Section Averaging

K. D. Cowtan,a* K. Y. J. Zhangb and P. Mainc

aDepartment of Chemistry, University of York, York YO1 5DD, England,bDivision of Basic Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N., Seattle, WA 90109, USA, and cDepartment of Physics, University of York, York YO1 5DD, England
Correspondence e-mail: Averaging

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Averaging is performed using a single-step approach (Rossmann et al., 1992[link]), 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[link]). 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.


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.

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