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. 13.4, p. 360   | 1 | 2 |

Section 13.4.12. Ab initio phasing starts

M. G. Rossmanna* and E. Arnoldb

aDepartment of Biological Sciences, Purdue University, West Lafayette, IN 47907–1392, USA, and  bBiomolecular Crystallography Laboratory, CABM & Rutgers University, 679 Hoes Lane, Piscataway, NJ 08854–5638, USA
Correspondence e-mail:

13.4.12. Ab initio phasing starts

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Some initial low-resolution model is required to initiate phasing at very low resolution. The use of cryo-EM reconstructions or available homologous structures is now quite usual. However, a phase determination using a sphere or hollow shell is also possible. In the case of a spherical virus, such an approximation is often very reasonable, as is evident when plotting the mean intensities at low resolution. These often show the anticipated distribution of a Fourier transform of a uniform sphere (Fig.[link]). Thus, initiating phasing using a spherical model does require the prior determination of the average radius of the spherical virus. This can be done either by using an R-factor search (Tsao, Chapman & Rossmann, 1992[link]) or by using low-angle X-ray scattering data (Chapman et al., 1992[link]). A minimal model would be to estimate the value of F(000) on the same relative scale as the observed amplitudes. This structure factor must always have a positive value. Such a limited initial start was first explored by Rossmann & Blow (1963)[link].


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Structure amplitudes of the type II crystals of southern bean mosaic virus, averaged within shells of reciprocal space, shown in relation to the Fourier transform of a 284 Å diameter sphere. The inset shows the complete spherical transform from infinity to 30 Å resolution. [Reproduced with permission from Johnson et al. (1976[link]). Copyright (1976) Academic Press.]

In surprisingly many cases (Valegård et al., 1990[link]; Chapman et al., 1992[link]; McKenna, Xia, Willingmann, Ilag, Krishnaswamy et al., 1992[link]; McKenna, Xia, Willingmann, Ilag & Rossmann, 1992[link]; Tsao, Chapman & Rossmann, 1992[link]; Tsao, Chapman, Wu et al., 1992[link]), it has been found that initiating phasing by using a very low resolution model results in a phase solution of the Babinet inverted structure ([\alpha \rightarrow \alpha + \pi]), where the desired density is negative instead of positive. Presumably, this is the result of phase convergence in a region where the assumed spherical transform is π out of step with reality. As long as this possibility is kept in mind with a watchful eye, such an inversion does not hamper good phase determination. In the case of phase extension, stepping too far in resolution can also lead to analogous problems (Arnold et al., 1987[link]).

Similar errors can occur due to lack of information on the correct enantiomorph in the initial phasing model. In some cases, where spherical envelopes are used and the distribution of NCS elements is also centric, there will be no decision on hand, and the phases will remain centric (Johnson et al., 1975[link]). However, in general, the enantiomorphic ambiguity (hand assignment) can be resolved by providing a model that has some asymmetry or by arbitrarily selecting the phase of a large-amplitude structure factor away from its centric value.

The progress of phase refinement away from false solutions has been the subject of `post mortem' examinations (Valegård et al., 1990[link]; Chapman et al., 1992[link]; McKenna, Xia, Willingmann, Ilag, Krishnaswamy et al., 1992[link]; McKenna, Xia, Willingmann, Ilag & Rossmann, 1992[link]; Tsao, Chapman & Rossmann, 1992[link]; Tsao, Chapman, Wu et al., 1992[link]; Dokland et al., 1998[link]). The main lesson learned from these observations is that phase determination using NCS is amazingly powerful. Most initial errors in phasing gradually work themselves out with subsequent iterations and phase extension.

Perhaps the power of NCS phase determination should not be overly surprising. When phases are determined by multiple isomorphous replacement, the amount of data collected for the given molecular weight is [(N + 1)], where N is the number of derivatives and is usually 3 or 4. Similarly, for multiwavelength anomalous-dispersion data collection, there might be measurements at four different wavelengths, essentially giving [N = 8] data points for each reflection. However, icosahedral virus determination frequently provides [N = 60] data points for the equivalent resolution.


Arnold, E., Vriend, G., Luo, M., Griffith, J. P., Kamer, G., Erickson, J. W., Johnson, J. E. & Rossmann, M. G. (1987). The structure determination of a common cold virus, human rhinovirus 14. Acta Cryst. A43, 346–361.Google Scholar
Chapman, M. S., Tsao, J. & Rossmann, M. G. (1992). Ab initio phase determination for spherical viruses: parameter determination for spherical-shell models. Acta Cryst. A48, 301–312.Google Scholar
Dokland, T., McKenna, R., Sherman, D. M., Bowman, B. R., Bean, W. F. & Rossmann, M. G. (1998). Structure determination of the ϕX174 closed procapsid. Acta Cryst. D54, 878–890.Google Scholar
Johnson, J. E., Argos, P. & Rossmann, M. G. (1975). Rotation function studies of southern bean mosaic virus at 22 Å resolution. Acta Cryst. B31, 2577–2583.Google Scholar
McKenna, R., Xia, D., Willingmann, P., Ilag, L. L., Krishnaswamy, S., Rossmann, M. G., Olson, N. H., Baker, T. S. & Incardona, N. L. (1992). Atomic structure of single-stranded DNA bacteriophage ϕX174 and its functional implications. Nature (London), 355, 137–143.Google Scholar
McKenna, R., Xia, D., Willingmann, P., Ilag, L. L. & Rossmann, M. G. (1992). Structure determination of the bacteriophage ϕX174. Acta Cryst. B48, 499–511.Google Scholar
Rossmann, M. G. & Blow, D. M. (1963). Determination of phases by the conditions of non-crystallographic symmetry. Acta Cryst. 16, 39–45.Google Scholar
Tsao, J., Chapman, M. S. & Rossmann, M. G. (1992). Ab initio phase determination for viruses with high symmetry: a feasibility study. Acta Cryst. A48, 293–301.Google Scholar
Tsao, J., Chapman, M. S., Wu, H., Agbandje, M., Keller, W. & Rossmann, M. G. (1992). Structure determination of monoclinic canine parvovirus. Acta Cryst. B48, 75–88.Google Scholar
Valegård, K., Liljas, L., Fridborg, K. & Unge, T. (1990). The three-dimensional structure of the bacterial virus MS2. Nature (London), 345, 36–41.Google Scholar

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