Notes on ambiguities encountered in phasing

Indexing ambiguities

Indexing ambiguity type 1

In space groups where the symmetry of the Bravais lattice is higher than the point group symmetry, there are several choices of indexing a diffraction pattern. When confronted with several indexing possibilities, autoindexing programs like Denzo, MOSFLM and d*trek can only make a random choice. However, if data from two or more crystals are to be merged or combined in some other way (for example to compute isomorphous differences), it is important that the indexing choices are compatible.

The CCP4 documentation (reindexing.doc) and the Scalepack manual (Scenario 5: Reindexing) give practical advise for resolving the indexing ambiguity. The general idea is that the indexing choice of some reference data set is kept fixed, and all possible indexing choices are tested for the other data sets. For each indexing choice, a data set is reindexed, scaled and merged with the reference data set. The correct indexing choice is characterized by the lowest Rmerge or Chi2.

Indexing ambiguity type 2

Another problem arises if anomalous scattering leads to the breakdown of Friedel's law. If the data are correctly indexed on a right handed basis system, the assignment of "F+" and "F-" is such that the experimental electron density map will show amino acids and helices with the correct hand. However, if by accident a left handed system was chosen (for example if the sign of Y SCALE in Denzo was chosen incorrectly), the experimental electron density map will have the wrong hand.

If anomalous data are used and the experimental MAD or SAD map shows amino acids and helices with the wrong hand, the Friedel mates have to be flipped in order to arrive at a right handed indexing basis. This means, "F+" becomes "F-" and vice versa. At the same time, the hand of the heavy atom configuration has to be changed (see below).

Use the flip_friedels.inp task file to flip the Friedel mates.
Use the flip_sites.inp task file to flip the heavy atom configuration.

Enantiomorph ambiguity

 A given 3-dimensionally periodic configuration of atoms and its inverse image give rise to identical diffraction patterns. For crystals with a centrosymmetric space group this is trivially true. For non-centrosymmetric space groups this gives rise to a hand ambiguity or enantiomorph ambiguity (Protein Crystallography, Blundell & Johnson, 1976, page 374).

For non-centrosymmetric space groups, there always exists a centre of inversion which maps the given atom configuration onto its inverse image. For most non-centrosymmetric space groups, this centre of inversion is at the origin of the coordinate system (i.e. at 0,0,0) and the inverse image is obtained simply by flipping the signs of the atomic coordinates. However, there can be two kinds of difficulties:

  1. The centre of inversion is not at the origin of the coordinate system.
    This is the case for space groups Fdd2, I41, I4122, I41md, I41cd, I-42d, and F4132.
    In these space groups, the inverse image is obtained by a combination of flipping the signs of the coordinates and a translation (International Tables for Crystallography, Volume A, 1983, Table 15.3.2, column 6).

  2. The centre of inversion changes the space group.
    This is the case for the 22 enantiomorphic space groups.
    The 22 enantiomorphic space groups can be grouped into 11 pairs:

    P41 P4122 P41212 P31 P3112 P3121 P61 P62 P6122 P6222 P4132
    P43 P4322 P43212 P32 P3212 P3221 P63 P64 P6322 P6422 P4332

    The atomic coordinates of the inverse image are obtained by flipping the signs of the original coordinates. If the space group of the original atom configuration is listed in the top row of the table, the space group of the inverse image is given in the same column in the bottom row, and vice versa.

The flip_sites.inp task file can be used to flip an atom configuration. The two kinds of difficulties outlined above are correctly taken care of.

In isomorphous replacement (SIR/MIR) experiments, the enantiomorph ambiguity can be resolved by inspection of the experimental electron density map. If the amino acids and helices have the wrong hand, the heavy atom configuration has to be flipped.

In anomalous diffraction (SAD/MAD) experiments, the enantiomorph ambiguity can be resolved by SAD/MAD phasing with both choices, followed by inspection of the resulting electron density maps. Only the correct enantiomorph will produce an interpretable map.

For a clarification of the terms enantiomorph and enantiomorphic space group refer to the International Tables for Crystallography, Volume A, 1983, section 10.5, Enantiomorphism, enantiomerism, chirality, dissymmetry.

Phase ambiguity

 In Single Isomorphous Replacement (SIR) or Single Anomalous Diffraction (SAD) experiments, the resulting phase probability distributions are bimodal, i.e. there are two maxima in the probablity distribution for each reflection. This is explained in detail in many textbooks, for example Protein Crystallography, Blundell & Johnson, 1976, or Principles of Protein X-ray Crystallography, Drenth, 1994.

In many cases, density modification can be used to resolve the phase ambiguity. In CNS, use the task file density_modify.inp.

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