research papers
Surprises and pitfalls arising from (pseudo)symmetry
^{a}Berkeley Center for Structural Biology, Lawrence Berkeley National Laboratory, One Cyclotron Road, Building 6R2100, Berkeley, CA 94720, USA,^{b}Lawrence Berkeley National Laboratory, One Cyclotron Road, Building 64R0121, Berkeley, CA 94720, USA, and ^{c}Structural Biology Laboratory, Chemistry Department, University of York, Heslington, York YO10 5YW, England
^{*}Correspondence email: phzwart@lbl.gov
It is not uncommon for protein crystals to crystallize with more than a single molecule per
When more than a single molecule is present in the various pathological situations such as modulated crystals and pseudo translational or rotational symmetry can arise. The presence of can lead to uncertainties about the correct especially in the presence of The background to certain common pathologies is presented and a new notation for space groups in unusual settings is introduced. The main concepts are illustrated with several examples from the literature and the Protein Data Bank.Keywords: pathology; twinning; pseudosymmetry.
1. Introduction
With the advent of automated methods in crystallography (Adams et al., 2002, 2004; Brunzelle et al., 2003; Lamzin & Perrakis, 2000; Lamzin et al., 2000; Snell et al., 2004), it is possible to solve a structure without visual inspection of the diffraction images (Winter, 2008; Holton & Alber, 2004), interpretation of the output of a molecularreplacement program (Read, 2001; Navaza, 1994; Vagin & Teplyakov, 2000) or, in extreme cases, manually building a model or even looking at the electrondensity map (Emsley & Cowtan, 2004; Terwilliger, 2002a,b; Morris et al., 2003, 2004; Holton et al., 2000; Ioerger et al., 1999; McRee, 1999; Perrakis et al., 1999). Although automated methods often handle many routine structuresolution scenarios, pitfalls arising from certain pathologies are still outside the scope of most automated methods and often require human intervention to ensure smooth progress of structure solution or refinement.
This manuscript studies situations that arise when et al., 2005), since a large number of proteins crystallize with more than a single copy in the or in various space groups.
(NCS) operators are close to true a situation known as pseudosymmetry. Pathologies of this type are often seen in protein crystallography (DauterThe distinction between `simple' NCS and ^{α} atoms of the actual structure and the putative structure in which the pseudosymmetry is an exact symmetry. If the resulting r.m.s.d. is below a certain threshold value (say 3 Å), the structure can be called pseudosymmetric. Using this definition, we find that about 6% of the structures deposited in the PDB exhibit This observation is in line with the observations of Wang & Janin (1993), who concluded that the alignment of NCS axes is biased towards axes. On a yeartoyear basis, there has been a slow increase in the fraction of new structures that exhibit pseudosymmetry (Fig. 1). This small increase is most likely to be the consequence of improvements in hardware and software that allow more routine detection, solution and of structures with as well as a general tendency to focus on more challenging proteins or protein complexes.
can be made in a number of ways. One way of defining is by idealizing NCS operators to crystallographic operators and determining the rootmeansquare displacement (r.m.s.d.) between CIn order to develop a better understanding of the consequences of via graphs similar to those generated by the Bilbao crystallographic server (Ivanchev et al., 2000). In contrast to these, the graphs presented here include the point groups or space groups in all orientations in which they occur in the supergroups, rather than just one representative per pointgroup or spacegroup type. This results in a more informative and complete overview of the relations between different groups.
we review some basic concepts and introduce an efficient way of describing space groups in unusual settings. We furthermore `visualize' relations between space groupsA number of examples from the PDB (Berman et al., 2000; Bernstein et al., 1977) and literature are provided to illustrate common surprises and pitfalls arising from (pseudo) symmetry. We will describe structures with suspected incorrect symmetry, give an example of of twinned data with ambiguous spacegroup choices and illustrate the uses of group–subgroup relations.
2. Space groups, symmetry and approximate symmetry
2.1. Space groups in unusual settings
The standard reference for crystallographic spacegroup symmetry is International Tables for Crystallography Volume A (Hahn, 2002). In the following, we will use ITVA to refer to this work. ITVA Table 4.3.1 defines Hermann–Mauguin spacegroup symbols for 530 conventional settings of the 230 spacegroup types. This means that in general there are multiple settings for a given spacegroup type. For example, assume we are given an Xray data set that can be integrated and scaled in P222. Further analysis of the data reveals for (0, k, 0) with k odd. This suggests the is P22_{1}2. It may be useful or necessary (e.g. for compatibility with older software) to reindex the data set so that the twofold screw axis is parallel to a new c axis to obtain P222_{1}. The space groups and unit cells before and after reindexing are said to be in different settings.
In the context of group–subgroup analysis with respect to a given metric (unitcell parameters), unusual settings not tabulated in ITVA arise frequently. To be able to represent these with concise symbols, we have introduced universal Hermann–Mauguin symbols by borrowing an idea introduced in Shmueli et al. (2001): a changeofbasis symbol is appended to the conventional Hermann–Mauguin symbol. To obtain short symbols, two notations are used. For example (compare with Fig. 4 below),
These two symbols are equivalent, i.e. encode the same unconventional setting of No. 5. The changeofbasis matrix encoded with the x, y, z notation is the inverse transpose of the matrix encoded with the a, b, c notation. Often, for a given change of basis, one notation is significantly shorter than the other. The shortest symbol is used when composing the universal Hermann–Mauguin symbol.
Note that both changeofbasis notations have precedence in ITVA. The x, y, z notation is used to symbolize symmetry operators which act on coordinates. Similarly, the x, y, z changeofbasis symbol encodes a matrix that transforms coordinates from the reference setting to the unconventional setting. The a, b, c notation appears in ITVA §4.3, where it encodes basisvector transformations. Our a, b, c notation is compatible with this convention. The a, b, c changeofbasis symbol encodes a matrix that transforms basis vectors from the reference setting to the unconventional setting. A comprehensive overview of transformation relations is given in and around Table 2.E.1 of Giacovazzo (1992).
2.2. Relations between groups
A H of a group G is a subset of the elements of G which also forms a (smaller) group. For instance, the symmetry operators of P222 can be described by {(x, y, z), (−x, y, −z), (x, −y, −z), (−x, −y, z)}. Subgroups of P222 can be constructed by selecting only certain operators. The full list of subgroups of P222 and the set of `remaining operators' for each with respect to P222 are given in Table 1.

Note that if the operators of P211 are combined with one of the `remaining' operators (−x, y, −z) or (−x, −y, z), the other operator is generated by group multiplication, leading to P222. A depiction of the relations between all subgroups of P222 is shown in Fig. 2. In this figure, nodes representing space groups are linked with arrows. The arrows between the space groups indicate that the multiplication of a single symmetry operator into a group results in the other group. For example, the arrow in Fig. 2 from P1 to P211 indicates that a single [in this case (x, −y, −z)] combined with P1 results in the P211.
2.3. Pseudosymmetry
As mentioned before, it is not uncommon that noncrystallographic symmetry can be approximated by et al., 2001; Poulsen et al., 2001; Parsons, 2003).
A change of the spacegroup symmetry of a known crystal form, either a reduction or an increase of the symmetry, is often induced by ligand binding, the introduction of selenomethionine residues, halide or heavymetal soaking or crystal growth under different conditions (DauterGroup–subgroup relations and their graphical representations as outlined in §2.2 are a useful tool for understanding approximate symmetry and the resulting relations between the space groups of different crystal forms. The graphical representations can often provide an easy way of enumerating and illustrating all possible subgroups of a This enumeration of possible space or point groups can be useful in the case of perfect twinning.
Constructing artificial structures with P222, generate a symmetryequivalent copy using the operator (−x, y, −z) or (−x, −y, z). If small random perturbations are applied to this new copy (e.g. a small overall rotation or small random shifts), then the two copies together can be considered as the of a P211 structure with P222 These two molecules are then related by an NCS operator that is close to a perfect twofold crystallographic rotation.
is straightforward. For example, given the of a protein inNote that in the previous example can be seen as NCS operators that are approximately equal to the listed operators.
operators were transformed into an NCS operator by the application of a small perturbation of the coordinates. The `remaining operators' in Table 13. Common pathologies
3.1. Rotational pseudosymmetry
Rotational 1q43 (Zagotta et al., 2003). The structure crystallizes in I4, with two molecules per (ASU). The r.m.s.d. between the two copies in the ASU is 0.27 Å. The following NCS operator (in fractional coordinates) that relates one molecule to the other is
(RPS) can arise if the (approximate) pointgroup symmetry of the lattice is higher than the pointgroup symmetry of the crystal. RPS is generated by an NCS operator parallel to a symmetry operator of the lattice that is not also a symmetry operator of the crystal A prime example of such a case can be found in PDB entryThe rotational part R of the NCS operator can be recognized as being almost identical to a twofold axis in the xy plane. If the idealized operator (−y + ½, −x + ½, −z + 0.31) is combined with I4m we obtain I422 with an arbitrary origin shift along z, which is a polar axis in I4.
The R value between pseudosymmetryrelated intensities as calculated from the coordinates is equal to 44%. For unrelated (independent) intensities, the R value is expected to be equal to 50% (Lebedev et al., 2006). In this case, it is clear that the correct symmetry is I4 rather than I422. However, there is a `grey area' where it may be possible to merge the data with reasonable statistics in the higher symmetry. While this has the advantage of reducing the number of model parameters, overidealization of the symmetry may lead to problems in structure solution and particularly Furthermore, information about biologically significant differences may be lost. In case of doubt, the best approach is to process and refine in both the lower and the higher symmetry and to compare the resulting R_{free} values and model quality indicators.
3.2. Translational and pseudocentring
Translational 1sct (Royer et al., 1995), where an NCS operator (x + ½, y + ½, z) mimics a Ccentring operator. In this particular case, the true is P2_{1}2_{1}2_{1}, but pseudosymmetric C222_{1}.
(TPS) is generated by an NCS operator whose rotational part is close to a unit matrix. If a TPS operator or a combination of TPS operators is very similar to a group of latticecentring operators, it can be denoted as pseudocentring. An example is PDB entryIn e.g. Chook et al., 1998) and is most easily detected by inspection of the (e.g. Zwart et al., 2005). The subset of reflections that would be systematically absent given idealized centring operators will have systematically low intensities. If these intensities are sufficiently low, dataprocessing programs may index and reduce the diffraction images in a that is too small. This situation is very similar to the case of higher rotational symmetry as discussed in the previous section. The `grey area' considerations of the previous section also apply to TPS.
the presence of pseudocentring operators translates into a systematic modulation of the observed intensities (An interesting crystallographic pathology can arise when pseudocentring is present. An example is given by Isupov & Lebedev (2008). In this case, the is P2_{1} with a pseudotranslation (x + ½, y, z). Consider two P2_{1} cells stacked side by side on the bc face of the The resulting symmetry is described by the universal Hermann–Mauguin symbol P12_{1}1 (2a, b, c). A full list of symmetry operators in this setting is shown in Table 2. From this set of operators, a number of subgroups can be constructed (Fig. 3). Operators not used in the construction of the can be regarded as NCS operators. If operators A and B are designated as the is P2_{1} and operators C and D are NCS operators. If, however, operators A and D are designated to be crystallographic, the is P2_{1} with an origin shift of (¼, 0, 0) and B and C are NCS operators. Both choices produce initially reasonable R values, but only choice one is correct and eventually leads to the best model.

3.3. Twinning
et al. (2006). Prime examples of problems with spacegroup assignment owing to the presence of and are described by Abrescia & Subirana (2002), Lee et al. (2003), RudiñoPiñera et al. (2004) and MacRae et al. (2006).
is the partial or full overlap of multiple reciprocal lattices. Each measured intensity is therefore the sum of the intensities of the individual domains with different orientations. The presence of in an Xray data set usually reveals itself by intensity statistics that deviate from theoretical distributions. However, the presence of pseudorotational symmetry (especially when parallel to the twin axis) or pseudotranslational symmetry can offset the on the intensity statistics, making it more difficult to detect the Basic intensity statistics elucidating the problems of in combination with are explained thoroughly by LebedevThe relative sizes of the twin domains building up the crystal are the twin fractions. The sum of the twin fractions is 1. The situation where all twin fractions are all equal is called perfect ; Parsons, 2003; Yeates, 1997; Yeates & Fam, 1999), as well as case studies of particular proteins (Barends et al., 2005; Barends & Dijkstra, 2003; Lehtiö et al., 2005; Rudolph et al., 2003, 2004; Wittmann & Rudolph, 2007; Yang et al., 2000).
A twin with an arbitrary ratio of twin fractions is denoted as a partial twin. A number of papers are available from the literature that deal with a basic introduction to (Dauter, 20033.3.1. and pseudomerohedral twins
Merohederal or
is a form of in which the (primitive) lattice has a higher symmetry than the symmetry of the unitcell content. If this occurs, the arrangement of reciprocallattice points will have a higher symmetry than the symmetry of the intensities associated with the reciprocallattice points. The symmetry operators that belong to the of the but not to the symmetry of the of the intensities, are potential twin laws. is perfectly invariant under a given (merohedral twinning), the presence of can only be detected by inspection of the intensity statistics or modelbased techniques. However, if the is only approximately invariant under a given (pseudomerohedral twinning), twinrelated intensities may be identified as individual reflections in the diffraction pattern. Examples of a number of (pseudo)merohedrally twinned structures are given in Table 3

The presence of an NCS operator that is an approximate crystallographic operator provides a structural basis for the presence of et al., 2006; HerbstIrmer & Sheldrick, 1998; Parsons, 2003) or by other external influences such as inclusion of a ligand or heavyatom soaks. An example of such a is described by Dauter et al. (2001). In that particular case, however, the occurred in the other direction: the symmetry of the crystals before a halide soak had a lower symmetry than after the soak, eliminating the possibility of twinning.
Twindomain interfaces have molecular contacts that are very similar to interfaces seen in nontwinned domains, which allows or promotes the growth of twinned crystals in general. In a similar manner, can be introduced by the breaking of symmetry owing to a temperaturedependent (HelliwellNote that when a crystal is perfectly twinned or almost perfectly twinned, the data will scale well in a 3.3) is that structure solution is possible once the correct has been found. Incorrect assignment of the for data sets with close to perfect seems to be the most important factor hampering structure solution.
that is incorrect. The use of an incorrect often impedes a successful structuresolution procedure. A general theme in most cases studies involving difficulties with (see references in §3.3.2. by reticular merohedry
Reticular ). In this type of only a fraction of the reflections will overlap with their twinrelated counterpart. This results in a diffraction pattern that consists of intensity sums with contributions from a variable number of twin domains. A well known example of is the obverse–reverse in rhombohedral space groups. An excellent introduction to is given by Parsons (2003). Examples of diffraction patterns can be found in Dauter (2003).
can be understood as on a collection of unit cells, a socalled (Rutherford, 20063.3.3. Order–disorder twinning
Order–disorder ; DornbergerSchiff & GrellNiemann, 1961; DornbergerSchiff, 1956, 1966) is a less well classified type of but has been observed for protein structures in a number of cases (Trame & McKay, 2001; Wang et al., 2005; Rye et al., 2007). Order–disorder can occur when a is built up of successive layers of molecules, in such a manner that two or more different stacking vectors can relate neighboring layers to form geometrically identical interfaces between them. An irregular sequence of stacking vectors results in ODtwinning or partial crystal disorder dependent on the frequency of the defects. Such irregularity introduces a modulation of the intensities of specific reflections. A correction for this effect can be vital for structure solution and can result in lower R values during (Trame & McKay, 2001). As noted by Nespolo et al. (2004), order–disorder phenomena in combination with may easily go unnoticed during structure solution and refinement.
(DornbergerSchiff & Dunitz, 19653.4. Common pitfalls
3.4.1. Misindexing
If the beam centre has not been defined accurately enough, autoindexing programs can return an indexing solution in which the (0, 0, 0) reflection (the direct beam) is, for instance, indexed as (0, 0, 1). Subsequent merging of the data will fail if the et al., 2004).
are not corrected. Misindexing can be avoided by obtaining the position of the direct beam on the detector using powder methods or by using more robust autoindexing routines (Sauter3.4.2. Incorrect unit cell
When more than one single crystal is present or when the diffraction images are noisy in general, it is possible that autoindexing procedures will produce a
that is too large. In the integrated and merged data, this issue can reveal itself as a prominent peak in the In contrast, if the structure under investigation has a strong pseudotranslation, it can occur that the indexing solution corresponds to a that is too small. In such a case, reflections that are systematically weak owing to the pseudotranslation are ignored and the pseudotranslation is mistaken for a lattice translation.3.4.3. Incorrect space group
If an approximately correct phenix.xtriage (Zwart et al., 2005), XPREP (Sheldrick, 2000), POINTLESS (Evans, 2006) or LABELIT (Sauter et al., 2006). Assigning an incorrect can result in a number of difficulties. If the assigned symmetry is too low, structure solution and is made artificially difficult because of the larger number of molecules in the Furthermore, differences between molecules can subsequently be overinterpreted, resulting in incorrect biological conclusions.
has been obtained, the has to be determined based on the intensities. The presence of pseudosymmetry can make this choice difficult, but it can often be made automatically by programs such asIf the data are twinned and as a result the assigned symmetry is too high, it may not be possible to solve the structure. An excellent example that illustrates this (and other) pitfalls is given by Lee et al. (2003), where the presence of pseudotranslational symmetry and perfect resulted in an incorrect choice of both the and the space group.
4. Examples
4.1. Interesting cases from the PDB
A number of data sets in the PDB show interesting pathologies such as
and pseudorotational and or pseudotranslational symmetry. A few examples are highlighted here.4.1.1. 2bd1 : incorrect symmetry
The structure of phospholipase A_{2} (Sekar et al., 2006) was indexed in C2 with unitcell parameters a = 74.58, b = 48.69, c = 67.55 Å, α = 90, β = 102.3, γ = 90°. The reveals a peak at (0, ½, 0) with a height approximately equal to that of the origin (99%). Correspondingly, the intensities of the reflections with that would be equal to zero if the NCS operator was crystallographic barely rise above the noise as judged from their associated standard deviations. The r.m.s.d. between the C^{α} atoms of the two molecules related by the translational NCS operator obtained from the is very small (0.08 Å). In comparison, the crossvalidated estimate of the coordinate error is 0.19 Å, which strongly suggests that the is in fact too large.
4.1.2. 2a8y : incorrect symmetry
The unitcell parameters for this structure are a = 96.60, b = 96.56, c = 96.63 Å, α = 91.57, β = 91.23, γ = 91.52°. The deposited is P1 (Zhang et al., 2006). Cursory analysis of the unitcell parameters suggests that the highest possible symmetry is rhombohedral. An analysis of the merged intensities with phenix.xtriage reveals that the intensity symmetry corresponds to the C2, with unitcell parameters a = 135.2, b = 138.1, c = 96.6 Å, α = 90, β = 92.2, γ = 90°. In this particular case, the authors did attempt to merge the data in various point groups (including C2), but the data only scaled well in P1 (Zhang et al., 2006). Given the pseudosymmetric nature of the lattice (pseudorhombohedral), C2 can be embedded in the higher symmetry lattice in three different ways (see Fig. 4), corresponding to the three orientations of the twofold axis in R32. The integration suite used to initially process the data only gave a single indexing choice for C2, which was unfortunately incorrect. Currently, the structure is being rerefined in the higher symmetry C2 (Ealick, private communication).
4.1.3. 1upp : pseudotranslational symmetry and twinning
The structure of a spinach Rubisco complex (Karkehabadi et al., 2003) has associated unitcell parameters a = 155.9, b = 156.3, c = 199.8 Å, α = 90, β = 90, γ = 90° and C222_{1}. Obviously, a is approximately equal to b, resulting in the presence of the (k, h, −l). Furthermore, the indicates a translational NCS vector (½, 0, ½) with a height of 40% of the origin. The presence of pseudotranslational symmetry can make the detection of difficult, but the results of the L test (Padilla & Yeates, 2003) are quite clear (Table 4). of the twin fraction given the deposited structure indicates that the twin fraction is approximately 45%. Including in the Rvalue calculations (while keeping the model fixed) reduces the R value from 0.25 to 0.17.

4.2. using twinned data
Using artificially twinned data, it can be demonstrated that the contrast of the rotation function decreases in proportion to the twin fraction (Fig. 5). A similar observation is made for the translation function (Fig. 6). However, from practical experience we know that based on twinned data is often successful if the quality of the search model is reasonable (e.g. Wittmann & Rudolph, 2007).
In the case of perfect 3.3.1). In this situation it is unlikely that will produce a solution, as the ASU is typically too small to contain the true contents of the crystal. Working with the data reprocessed in the lower symmetry may be successful, even though the data are perfectly twinned. This is illustrated by the following example.
a datareduction program may pick a symmetry that is too high (see §The Xray data set of Dicer crystals (MacRae et al., 2006; MacRae & Doudna, 2007) was initially processed in P422, but failed to give interpretable maps using experimental phasing methods in all P4_{x}2_{y}2 groups. Intensity statistics revealed that the data were twinned and reprocessing the data in P4 resulted in partially interpretable SAD maps in P4_{1}, assuming a twofold along b. However, a complete and refinable model could not be obtained in any tetragonal Collecting data from a new specimen revealed that the pointgroup symmetry was equal to P222 with almost perfect leading to a pseudotetragonal system. A successful structure solution via and SAD methods was obtained in P2_{1}22_{1}. Here, we repeat the structure solution using to determine the effect of different prior spacegroup hypotheses. To this end, data submitted to the PDB with accession code 2qwv were reindexed from P2_{1}2_{1}2 to P2_{1}22_{1} with operator (−a, c, b) to obtain a setting that corresponds to the standard setting if the data were merged in P422. The data with intensity symmetry P222 were then merged in P422. These merged data were then expanded out to point groups P4, C222 and P222, the three point groups directly `below' P422 (see Fig. 1 in the supplementary material^{1}). with chain A of the deposited model was used to determine the structure in all possible space groups of the given point groups. The rotation function gave two clear solutions in P422 and four clear solutions in point groups P4, C222 and P222 (Table 5). Subsequent translation functions and of the twin fraction resulted in three likely possible solutions in space groups P4_{1}, P2_{1}22_{1} and P22_{1}2_{1} (Table 6). Further rigidbody and group ADP lowered the R values of the spacegroup candidates in the orthorhombic system to 25%, while the model in P4_{1} had an R value of 29%.


Note that it is not surprising that P2_{1}22_{1} and P22_{1}2_{1} are both possible solutions since the data are perfectly twinned in P222 with (−k, −h, −l) and the solutions correspond to the two different twin domains. Data with a lower twin fraction or the presence of anomalous differences can be used to determine the space group.
4.3. Manual using group–subgroup relations
It is not uncommon that protein molecules crystallize in various space groups (polymorphs). In some cases, the polymorphs are related and one can use the structure of one polymorph to solve the other without the aid of automated molecularreplacement software (Di Costanzo et al., 2003). An example structure solution utilizing group–subgroup relations is presented here.
The crystals of 1eix and 1jjk (Poulsen et al., 2001) were grown under similar conditions, but 1eix is a native protein structure while 1jjk is a selenomethionine derivative. The unitcell parameters are listed in Table 7. The ratio of the unitcell volumes is 2.12, suggesting the possibility of a relation between the two unit cells. Another piece of evidence suggesting a relation is found in the of 1jjk : a large peak is located at (½, 0, ½), which can be interpreted as pseudocentring (translational NCS). If this NCS operator is idealized to a crystallographic operator, the unitcell parameters of 1jjk become equal to the unitcell parameters of 1eix (apart from a permutation of the basis vectors). It is thus clear that 1jjk is related to 1eix via pseudotranslational symmetry (as seen from the Patterson peak) and pseudorotational/screw symmetry (P2_{1} versus P2_{1}2_{1}2_{1}).

A relation between the two unit cells was identified with the tool iotbx.explore_metric_symmetry (Zwart et al., 2006) and is depicted in Fig. 7. The procedure used to solve the structure of 1jjk with the model of 1eix via group–subgroup relations is described in Di Costanzo et al. (2003). Firstly, the appropriate ASU is constructed by applying a twofold screw axis to the ASU of 1eix . Subsequently, a lattice translation along a is applied to these two molecules. An appropriate change of basis to bring the model into the correct orientation and a subsequent origin shift generates a possible solution. In this particular case, a group theoretical analysis reveals that two origin shifts are possible (see §3.2 and Fig. 2 in the supplementary material^{1}). Rigidbody of the two possible solutions, taking into account the presence of resulted in a single clear solution (Table 8).

Using the same group–subgroup relations, one can test the presence of a relation between crystal forms by computing intensity correlations between reindexed data sets. If the crystal form with the smaller et al., 2005). This allows one to verify a possible relationship between two crystal forms before attempting manual molecular replacement.
is reindexed to a that is related to the larger cell, the intensities can be compared relatively straightforwardly (GrosseKunstleve5. Discussion and conclusions
There are numerous special cases and pitfalls arising from the interplay of crystallographic and ; Sheldrick, 2000; Vaguine et al., 1999; Zwart et al., 2005). In some situations it is possible to correct for the problem; in others, use of the appropriate algorithms in subsequent structure solution and can lead to accurate final models that are suitable for biological interpretation. Experience suggests that it is initially best to treat all experimental data with suspicion and apply all available tests to identify possible pathologies as soon as possible after data collection and processing. In an ideal world, data would be stored in an unmerged form in P1 and certain decisions made automatically as more information becomes available. In the case of (close to) perfect knowledge of the proper can for instance only be available when a partial model has been built. A similar argument can be made for the detection of and dealing with order–disorder Note that this scheme assumes that the correct has been found by the autoindexing software. Incorporating decisionmaking schemes that include changes in the primitive unitcell parameters will most likely require access to the raw data.
in macromolecular crystals. Clearly, this paper only touches the tip of the iceberg. Fortunately, there are now a number of tools that make it possible to identify many of the most common problems (Evans, 2006Although access to the raw data is preferred for decisionmaking procedures, the Dicer example (§4.2) illustrates that integrating the expansion of data into a lower in a molecularreplacement procedure can in some cases lead to a successful structure solution. Similar arguments can probably be made for structuresolution routes via experimental phasing techniques.
Acknowledgements
The authors would like to thank the NIH for generous support of the PHENIX project (1P01 GM063210). This work was partially supported by the US Department of Energy under Contract No. DEAC0205CH11231 (PHZ, RWGK and PDA), the Wellcome Trust (064405/Z/01/A, GNM) and NIH (1RO1GM06975803, AAL) The programs mentioned here are available in the PHENIX (https://www.phenixonline.org ) and CCP4 (https://www.ccp4.ac.uk ) software suites.
References
Abrescia, N. G. A. & Subirana, J. A. (2002). Acta Cryst. D58, 2205–2208. CrossRef CAS IUCr Journals Google Scholar
Adams, P. D., Gopal, K., GrosseKunstleve, R. W., Hung, L.W., Ioerger, T. R., McCoy, A. J., Moriarty, N. W., Pai, R. K., Read, R. J., Romo, T. D., Sacchettini, J. C., Sauter, N. K., Storoni, L. C. & Terwilliger, T. C. (2004). J. Synchrotron Rad. 11, 53–55. Web of Science CrossRef CAS IUCr Journals Google Scholar
Adams, P. D., GrosseKunstleve, R. W., Hung, L.W., Ioerger, T. R., McCoy, A. J., Moriarty, N. W., Read, R. J., Sacchettini, J. C., Sauter, N. K. & Terwilliger, T. C. (2002). Acta Cryst. D58, 1948–1954. Web of Science CrossRef CAS IUCr Journals Google Scholar
Barends, T. R. M., de Jong, R. M., van Straaten, K. E., Thunnissen, A.M. W. H. & Dijkstra, B. W. (2005). Acta Cryst. D61, 613–621. CrossRef CAS IUCr Journals Google Scholar
Barends, T. R. M. & Dijkstra, B. W. (2003). Acta Cryst. D59, 2237–2241. CrossRef CAS IUCr Journals Google Scholar
Berman, H. M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T. N., Weissig, H., Shindyalov, I. N. & Bourne, P. E. (2000). Nucleic Acids Res. 28, 235–242. Web of Science CrossRef PubMed CAS Google Scholar
Bernstein, F. C., Koetzle, T. F., Williams, G. J., Meyer, E. F. Jr, Brice, M. D., Rodgers, J. R., Kennard, O., Shimanouchi, T. & Tasumi, M. (1977). J. Mol. Biol. 112, 535–542. CrossRef CAS PubMed Web of Science Google Scholar
Brunzelle, J. S., Shafaee, P., Yang, X., Weigand, S., Ren, Z. & Anderson, W. F. (2003). Acta Cryst. D59, 1138–1144. Web of Science CrossRef CAS IUCr Journals Google Scholar
Chook, Y. M., Lipscomb, W. N. & Ke, H. (1998). Acta Cryst. D54, 822–827. Web of Science CrossRef CAS IUCr Journals Google Scholar
Dauter, Z. (2003). Acta Cryst. D59, 2004–2016. Web of Science CrossRef CAS IUCr Journals Google Scholar
Dauter, Z., Botos, I., LaRondeLeBlanc, N. & Wlodawer, A. (2005). Acta Cryst. D61, 967–975. Web of Science CrossRef CAS IUCr Journals Google Scholar
Dauter, Z., Li, M. & Wlodawer, A. (2001). Acta Cryst. D57, 239–249. Web of Science CrossRef CAS IUCr Journals Google Scholar
Di Costanzo, L., Forneris, F., Geremia, S. & Randaccio, L. (2003). Acta Cryst. D59, 1435–1439. Web of Science CrossRef CAS IUCr Journals Google Scholar
DornbergerSchiff, K. (1956). Acta Cryst. 9, 593–601. CrossRef CAS IUCr Journals Web of Science Google Scholar
DornbergerSchiff, K. (1966). Acta Cryst. 21, 311–322. CrossRef CAS IUCr Journals Web of Science Google Scholar
DornbergerSchiff, K. & Dunitz, J. D. (1965). Acta Cryst. 19, 471–472. CrossRef IUCr Journals Web of Science Google Scholar
DornbergerSchiff, K. & GrellNiemann, H. (1961). Acta Cryst. 14, 167–177. CrossRef IUCr Journals Web of Science Google Scholar
Emsley, P. & Cowtan, K. (2004). Acta Cryst. D60, 2126–2132. Web of Science CrossRef CAS IUCr Journals Google Scholar
Evans, P. (2006). Acta Cryst. D62, 72–82. Web of Science CrossRef CAS IUCr Journals Google Scholar
Giacovazzo, C. (1992). Fundamentals of Crystallography. Oxford University Press. Google Scholar
GrosseKunstleve, R. W., Afonine, P. V., Sauter, N. K. & Adams, P. D. (2005). IUCr Comput. Commission Newsl. 5, 69–91. Google Scholar
Hahn, T. (2002). International Tables for Crystallography, Vol. A, 5th ed. Dordrecht: Kluwer Academic Publishers. Google Scholar
Helliwell, M., Collison, D., John, G. H., May, I., Sarsfield, M. J., Sharrad, C. A. & Sutton, A. D. (2006). Acta Cryst. B62, 68–85. Web of Science CSD CrossRef CAS IUCr Journals Google Scholar
HerbstIrmer, R. & Sheldrick, G. M. (1998). Acta Cryst. B54, 443–449. Web of Science CSD CrossRef CAS IUCr Journals Google Scholar
Holton, J. & Alber, T. (2004). Proc. Natl Acad. Sci. USA, 101, 1537–1542. Web of Science CrossRef PubMed CAS Google Scholar
Holton, T., Ioerger, T. R., Christopher, J. A. & Sacchettini, J. C. (2000). Acta Cryst. D56, 722–734. Web of Science CrossRef CAS IUCr Journals Google Scholar
Ioerger, T. R., Holton, T., Christopher, J. A. & Sacchettini, J. C. (1999). Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology, pp. 130–137. Menlo Park: AAAI. Google Scholar
Isupov, M. N. & Lebedev, A. A. (2008). Acta Cryst. D64, 90–98. Web of Science CrossRef CAS IUCr Journals Google Scholar
Ivantchev, S., Kroumova, E., Madariaga, G., PérezMato, J. M. & Aroyo, M. I. (2000). J. Appl. Cryst. 33, 1190–1191. Web of Science CrossRef CAS IUCr Journals Google Scholar
Karkehabadi, S., Taylor, T. C. & Andersson, I. (2003). J. Mol. Biol. 334, 65–73. Web of Science CrossRef PubMed CAS Google Scholar
Lamzin, V. S. & Perrakis, A. (2000). Nature Struct. Biol. 7, Suppl., 978–981. Google Scholar
Lamzin, V. S., Perrakis, A., Bricogne, G., Jiang, J., Swaminathan, S. & Sussman, J. L. (2000). Acta Cryst. D56, 1510–1511. CrossRef CAS IUCr Journals Google Scholar
Lebedev, A. A., Vagin, A. A. & Murshudov, G. N. (2006). Acta Cryst. D62, 83–95. Web of Science CrossRef CAS IUCr Journals Google Scholar
Lee, S., Sawaya, M. R. & Eisenberg, D. (2003). Acta Cryst. D59, 2191–2199. Web of Science CrossRef CAS IUCr Journals Google Scholar
Lehtiö, L., Fabrichniy, I., Hansen, T., Schönheit, P. & Goldman, A. (2005). Acta Cryst. D61, 350–354. CrossRef IUCr Journals Google Scholar
MacRae, I. J. & Doudna, J. A. (2007). Acta Cryst. D63, 993–999. Web of Science CrossRef IUCr Journals Google Scholar
MacRae, I. J., Zhou, K., Li, F., Repic, A., Brooks, A. N., Cande, W. Z., Adams, P. D. & Doudna, J. A. (2006). Science, 311, 195–198. Web of Science CrossRef PubMed CAS Google Scholar
McRee, D. E. (1999). J. Struct. Biol. 125, 156–165. Web of Science CrossRef PubMed CAS Google Scholar
Morris, R. J., Perrakis, A. & Lamzin, V. S. (2003). Methods Enzymol. 374, 229–244. Web of Science CrossRef PubMed CAS Google Scholar
Morris, R. J., Zwart, P. H., Cohen, S., Fernandez, F. J., Kakaris, M., Kirillova, O., Vonrhein, C., Perrakis, A. & Lamzin, V. S. (2004). J. Synchrotron Rad. 11, 56–59. Web of Science CrossRef CAS IUCr Journals Google Scholar
Navaza, J. (1994). Acta Cryst. A50, 157–163. CrossRef CAS Web of Science IUCr Journals Google Scholar
Nespolo, M., Ferraris, G., Durovic, S. & Takeuchi, Y. (2004). Z. Kristallogr. 219, 773–778. Web of Science CrossRef CAS Google Scholar
Padilla, J. E. & Yeates, T. O. (2003). Acta Cryst. D59, 1124–1130. Web of Science CrossRef CAS IUCr Journals Google Scholar
Parsons, S. (2003). Acta Cryst. D59, 1995–2003. Web of Science CrossRef CAS IUCr Journals Google Scholar
Perrakis, A., Morris, R. & Lamzin, V. S. (1999). Nature Struct. Biol. 6, 458–463. Web of Science CrossRef PubMed CAS Google Scholar
Poulsen, J.C. N., Harris, P., Jensen, K. F. & Larsen, S. (2001). Acta Cryst. D57, 1251–1259. Web of Science CrossRef CAS IUCr Journals Google Scholar
Read, R. J. (2001). Acta Cryst. D57, 1373–1382. Web of Science CrossRef CAS IUCr Journals Google Scholar
Royer, W. E. Jr, Heard, K. S., Harrington, D. J. & Chiancone, E. (1995). J. Mol. Biol. 253, 168–186. CrossRef CAS PubMed Web of Science Google Scholar
RudiñoPiñera, E., SchwarzLinek, U., Potts, J. R. & Garman, E. F. (2004). Acta Cryst. D60, 1341–1345. CrossRef IUCr Journals Google Scholar
Rudolph, M. G., Kelker, M. S., Schneider, T. R., Yeates, T. O., Oseroff, V., Heidary, D. K., Jennings, P. A. & Wilson, I. A. (2003). Acta Cryst. D59, 290–298. Web of Science CrossRef CAS IUCr Journals Google Scholar
Rudolph, M. G., Wingren, C., Crowley, M. P., Chien, Y. & Wilson, I. A. (2004). Acta Cryst. D60, 656–664. Web of Science CrossRef CAS IUCr Journals Google Scholar
Rutherford, J. S. (2006). Acta Cryst. A62, 93–97. Web of Science CrossRef CAS IUCr Journals Google Scholar
Rye, C. A., Isupov, M. N., Lebedev, A. A. & Littlechild, J. A. (2007). Acta Cryst. D63, 926–930. Web of Science CrossRef CAS IUCr Journals Google Scholar
Sauter, N. K., GrosseKunstleve, R. W. & Adams, P. D. (2004). J. Appl. Cryst. 37, 399–409. Web of Science CrossRef CAS IUCr Journals Google Scholar
Sauter, N. K., GrosseKunstleve, R. W. & Adams, P. D. (2006). J. Appl. Cryst. 39, 158–168. Web of Science CrossRef CAS IUCr Journals Google Scholar
Sekar, K., Yogavel, M., Kanaujia, S. P., Sharma, A., Velmurugan, D., Poi, M.J., Dauter, Z. & Tsai, M.D. (2006). Acta Cryst. D62, 717–724. Web of Science CrossRef CAS IUCr Journals Google Scholar
Sheldrick, G. M. (2000). XPREP Version 6.0. Bruker AXS Inc., Madison, Wisconsin, USA. Google Scholar
Shmueli, U., Hall, S. R. & GrosseKunstleve, R. W. (2001). International Tables for Crystallography, Vol. B, edited by U. Shmueli, pp. 107–119. Dordrecht: Kluwer Academic Publishers. Google Scholar
Snell, G., Cork, C., Nordmeyer, R., Cornell, E., Meigs, G., Yegian, D., Jaklevic, J., Jin, J., Stevens, R. C. & Earnest, T. (2004). Structure, 12, 537–545. Web of Science CrossRef PubMed CAS Google Scholar
Terwilliger, T. (2002a). Acta Cryst. A58, C57. CrossRef IUCr Journals Google Scholar
Terwilliger, T. C. (2002b). Acta Cryst. D58, 1937–1940. Web of Science CrossRef CAS IUCr Journals Google Scholar
Trame, C. B. & McKay, D. B. (2001). Acta Cryst. D57, 1079–1090. Web of Science CrossRef CAS IUCr Journals Google Scholar
Vagin, A. & Teplyakov, A. (2000). Acta Cryst. D56, 1622–1624. Web of Science CrossRef CAS IUCr Journals Google Scholar
Vaguine, A. A., Richelle, J. & Wodak, S. J. (1999). Acta Cryst. D55, 191–205. Web of Science CrossRef CAS IUCr Journals Google Scholar
Wang, J., Kamtekar, S., Berman, A. J. & Steitz, T. A. (2005). Acta Cryst. D61, 67–74. Web of Science CrossRef CAS IUCr Journals Google Scholar
Wang, X. & Janin, J. (1993). Acta Cryst. D49, 505–512. CrossRef CAS Web of Science IUCr Journals Google Scholar
Winter, G. M. (2008). In preparation. Google Scholar
Wittmann, J. G. & Rudolph, M. G. (2007). Acta Cryst. D63, 744–749. Web of Science CrossRef IUCr Journals Google Scholar
Yang, F., Dauter, Z. & Wlodawer, A. (2000). Acta Cryst. D56, 959–964. Web of Science CrossRef CAS IUCr Journals Google Scholar
Yeates, T. O. (1997). Methods Enzymol. 276, 344–358. CrossRef CAS PubMed Web of Science Google Scholar
Yeates, T. O. & Fam, B. C. (1999). Structure, 7, R25–R29. Web of Science CrossRef PubMed CAS Google Scholar
Zagotta, W. N., Olivier, N. B., Black, K. D., Young, E. C., Olson, R. & Gouaux, E. (2003). Nature (London), 425, 200–205. Web of Science CrossRef PubMed CAS Google Scholar
Zhang, Y., Porcelli, M., Cacciapuoti, G. & Ealick, S. E. (2006). J. Mol. Biol. 357, 252–262. Web of Science CrossRef PubMed CAS Google Scholar
Zwart, P. H., GrosseKunstleve, R. W. & Adams, P. D. (2005). CCP4 Newsl. 42, contribution 10. Google Scholar
Zwart, P. H., GrosseKunstleve, R. W. & Adams, P. D. (2006). CCP4 Newsl. 44, contribution 8. Google Scholar
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