(IUCr) Recent advances in the CRANK software suite for experimental phasing

research papers

BIOLOGICAL
CRYSTALLOGRAPHY

ISSN: 1399-0047

Volume 67| Part 4| April 2011| Pages 331-337

doi:10.1107/S0907444910052224

Open

access

Recent advances in the CRANK software suite for experimental phasing

Navraj S. Pannu,^a ^* Willem-Jan Waterreus,^a Pavol Skubák,^a Irakli Sikharulidze,^a Jan Pieter Abrahams ^a and Rudolf A. G. de Graaff ^a

^aBiophysical Structural Chemistry, Leiden University, PO Box 9502, 2300 RA Leiden, The Netherlands
^*Correspondence e-mail: raj@chem.leidenuniv.nl

(Received 2 August 2010; accepted 13 December 2010)

For its first release in 2004, CRANK was shown to effectively detect and phase anomalous scatterers from single-wavelength anomalous diffraction data. Since then, CRANK has been significantly improved and many more structures can be built automatically with single- or multiple-wavelength anomalous diffraction or single isomorphous replacement with anomalous scattering data. Here, the new algorithms that have been developed that have led to these substantial improvements are discussed and CRANK's performance on over 100 real data sets is shown. The latest version of CRANK is freely available for download at https://www.bfsc.leidenuniv.nl/software/crank/ and from CCP4 (https://www.ccp4.ac.uk/ ).

Keywords: CRANK; experimental phasing.

1. Introduction

Currently, many software packages are available to automatically solve structures. The main aim of CRANK is to provide a user-friendly and automated system incorporating the latest computational developments in all stages of structure solution by experimental phasing. CRANK is not a monolithic system: users can define pipelines from a choice of many different programs. Fig. 1 shows the current steps that CRANK can perform and the programs that users can select to perform the task. The externally developed programs that CRANK can interface with are SHELXC (Sheldrick, 2008 ), SHELXD (Schneider & Sheldrick, 2002 ), SHELXE (Sheldrick, 2002 ), DM (Cowtan, 1994 ), Parrot (Cowtan, 2010 ), Pirate (Cowtan, 2000 ), Buccaneer (Cowtan, 2006 ) and ARP/wARP (Langer et al., 2008 ), the latter two of which both iterate with REFMAC (Murshudov et al., 2011 ), and RESOLVE (Terwilliger, 2000 ).

Figure 1
Flowchart showing the programs that CRANK can use and the steps that it can perform.

We are the main authors of the programs AFRO (Pannu et al., in preparation) for F_A calculation, CRUNCH2 (de Graaff et al., 2001 ) for substructure detection, BP3 (Pannu & Read, 2004 ) for substructure phasing, SOLOMON (Abrahams & Leslie, 1996 ) for density modification and MULTICOMB (Skubák, Waterreus et al., 2010 ) for phase combination and are co-authors of the program REFMAC (Murshudov et al., 2011). These programs use multivariate maximum-likelihood methods that allow the observed diffraction data and any current models to be considered simultaneously at any stage in the structure-solution process. Thus, the wealth of information contained in the observed diffraction data can be used directly throughout the structure-solution process and not approximated or ignored as current approaches do after constructing an initial electron-density map.

Below, we provide a brief intuitive description of the novel methods in various steps in experimental phasing that we have developed since our first publication on CRANK (Ness et al., 2004 ). We show the power of combining all of these new methods on over 100 real single-wavelength anomalous diffraction (SAD), multiple-wavelength anomalous diffraction (MAD) and single isomorphous replacement with anomalous scattering (SIRAS) data sets run automatically with minimal user input in CRANK.

The programs and methods we develop are not only available in CRANK, but also in AutoRickshaw (Panjikar et al., 2005 ) and ARP/wARP. Furthermore, the original methods that we have developed have also been rewritten in mathematically identical forms in both phenix.refine and Phaser (Adams et al., 2010 ).

2. Recent developments in CRANK

2.1. Substructure determination

After the diffraction data have been indexed and merged, F_A values are calculated for input to substructure-detection programs. |F_A| values are the amplitudes of structure factors corresponding to the heavy atoms to be located. For SAD data, most programs use the absolute value of Bijvoet differences, ΔF = $[\big| |F^+| - |F^-|\big |]$ , as an estimate of |F_A|. Burla et al. (2002 ) proposed employing multivariate joint probability distributions to obtain the expected value for |F_A| in an equation that contains three integrals. In order to obtain an analytical solution to the integrals, Burla et al. (2002) assume that the `Bijvoet phases' are equal. We have obtained an expression requiring only one numerical integration without making this assumption. This approach has been implemented in the program AFRO and performs satisfactorily. Details of the implementation and test results will be given elsewhere (Pannu et al., in preparation). The development version of AFRO containing the multivariate |F_A| calculation is available in the latest version of CRANK and can be used as input for either CRUNCH2 or SHELXD.

Within CRANK, methods exist to validate whether a correct substructure has been determined and to terminate the substructure-detection step early. If a threshold value for a statistic used by the substructure-detection program has been reached or if a significant deviation exists between the best and worst score in different trials, the substructure-detection program will successfully terminate before running all trials. CRANK also provides an alternate and independent assessment of whether a correct substructure solution has been located: an option exists to run the substructure-phasing program BP3 quickly in `check' mode and examine likelihood-based statistics to determine whether a correct and complete substructure has been found. The statistic that CRANK uses is a Luzzati parameter (Luzzati, 1952 ): if the average Luzzati parameter is greater than a threshold value (the default is 0.7) it is assumed that the full substructure has been found and substructure detection is terminated. Using likelihood methods to validate substructure detection has been available in CRANK for over three years (Pannu et al., 2007 ) and this approach has been appreciated by PHENIX developers, who recently adopted it in their own suite (Paul Adams, CCP4 bulletin board, 31 July 2010).

2.2. Substructure phasing

To incorporate anomalous phase information, heavy-atom refinement programs such as SHARP (Bricogne et al., 2003 ) or MLPHARE (Otwinowski, 1991 ; Collaborative Computational Project, Number 4, 1994 ) use a Gaussian function on observed Bijvoet differences (ΔF = |F⁺| − |F⁻|) centred on the `calculated' Bijvoet difference that is determined from an assumed value of the `true' structure factor and the heavy-atom structure factor (North, 1965 ; Matthews, 1966 ). Since, in general, the `true' structure factor is not known for a SAD or MAD experiment, SHARP integrates out the amplitude and phase of the true structure factor. Furthermore, the estimate of measurement error for Bijvoet differences is determined by merging the measurement errors for Friedel pairs [σ_ΔF = $[(\sigma_{F^+}^2 + \sigma_{F^-}^2)^{1/2}]$ ], leading to suboptimal use of experimental information.

To input the observed structure factors directly, it is necessary to consider a joint probability of all observations given a current model. We have previously shown that this method provides better results compared with other approaches for the case of SAD (Pannu & Read, 2004; Ness et al., 2004) as implemented in BP3. We have recently shown that better results may be obtained by deriving a multivariate function for SIRAS (Skubák et al., 2009 ), which will be released in the next version of CRANK.

2.3. Density modification

In the density-modification procedure, the density-modified map is iteratively combined with the initial map obtained from experimental phasing. Current methods assume that these two maps are independent and propagate the initial map's phase information indirectly through Hendrickson–Lattman coefficients (Hendrickson & Lattman, 1970 ). We have applied a multivariate analysis that considers the observed Friedel pairs directly for a SAD experiment, accounts for the correlation between the initial and density-modified maps and refines the errors that can occur in a single-wavelength anomalous diffraction experiment. Results on many test cases show a significant improvement over the current state of the art (Skubák, Waterreus et al., 2010): the maps produced by the multivariate phase-combination algorithm lead to many more structures being built automatically.

Despite the improvements in the quality of electron-density maps, the figures of merit remained escalated after density modification. To obtain more accurate figures of merit, we have recently developed and implemented a new cross-validated scheme for accurate error-parameter estimation in likelihood-based phase combination. This method leads to more reliable phase probability statistics from density modification and results in a further improvement in subsequent model building. In addition, the more accurate figures of merit enable a more reliable hand determination or identification of incorrect NCS operators used in density modification (Skubák & Pannu, 2011 ). These developments have been implemented in a new phase-combination program called MULTICOMB and can be used in conjunction with either SOLOMON or Parrot.

2.4. Automated model building and refinement

The incorporation of experimental phase information has previously been shown to improve refinement (Pannu et al., 1998 ). However, the likelihood function developed, typically denoted MLHL, propagates the external phase information via Hendrickson–Lattman coefficients. Thus, the MLHL function is dependent on the accuracy and reliability of the coefficients that are input. Furthermore, in its derivation the MLHL function assumes that the experimental phase information (represented by Hendrickson–Lattman coefficients) is independent of the calculated structure factor. This assumption is questionable, as the experimental phase information is used to build an initial model. To overcome these issues, we considered and derived a multivariate likelihood function for SAD (Skubák et al., 2004 , 2005 ) and SIRAS (Skubák et al., 2009) experiments. The likelihood functions take as input the diffraction data directly, the heavy-atom coordinates and the calculated structure factors and account for correlation between them. Compared with the other likelihood functions in REFMAC, more models are built automatically in ARP/wARP with the multivariate functions. The SAD and SIRAS functions in REFMAC are available in CRANK in model building with both ARP/wARP and Buccaneer.

2.5. Integration of programs and steps

To support the integration of the different programs that it interfaces with, CRANK has a plug-in architecture and communicates between plug-ins via an XML file. At the moment, there are two methods available to generate an XML file that CRANK uses to run a pipeline: the program GCX and the ccp4i graphical user interface. Both interfaces to CRANK can be run with only minimal input: an MTZ file with the relevant column labels specified, a sequence file and the name, expected number and f′ and f′′ values for the heavy atoms. However, users can customize the settings for individual programs, define custom-made pipelines using any programs at each step and define the start and end step for a particular pipeline. Fig. 2 shows the ccp4i graphical user interface with its few required fields.

Figure 2
Screen shot of the ccp4i GUI for CRANK.

The program GCX allows CRANK to be run from a command line with a simple Unix script: more information on this can be obtained from the program's documentation (https://www.ccp4.ac.uk/html/gcx.html ). The test cases that are described below were run with GCX. Most users are likely to run CRANK via the ccp4i interface. The most convenient way to view a CRANK logfile is via the Baubles system, which can be initiated with the `View Annotated Logfile in a Web Browser' option in ccp4i. Documentation for CRANK can be found at the the CCP4 wiki (https://www.ccp4wiki.org/ ), which includes information on how to best interpret the log files.

3. Methods

Here, we test the new methods described above on a wide range of real SAD, MAD and SIRAS merged diffraction data sets. For our tests, only the intensities or structure-factor amplitudes, along with the sequence for a protein monomer, the number of substructure atoms expected per monomer and the f′ and f′′ values for the substructure atoms were input. CRANK used AFRO and CRUNCH2 for substructure detection, BP3 for substructure phasing and SOLOMON with MULTICOMB for density modification. Three cycles of Buccaneer iterated with REFMAC were used for automated model building with iterative refinement. The default options or parameters were used in all programs. The defaults set by CRANK depend upon the particular experiment: for SAD data, AFRO uses the multivariate |F_A| value calculation and MULTICOMB uses the multivariate SAD function for phase combination in density modification, while Buccaneer uses the SAD function implemented in REFMAC. For SIRAS data, AFRO calculates |F_A| from either the anomalous signal or using isomorphous differences by determining which signal is greater. BP3 uses the uncorrelated SIRAS function described previously (Pannu et al., 2003 ) and SOLOMON uses MLHL phase combination in MULTICOMB, while Buccaneer uses the multivariate SIRAS function in REFMAC. Finally, for MAD data AFRO chooses the wavelength with the greatest anomalous signal and calculates multivariate F_A values from it. Similar to SIRAS data, SOLOMON uses MLHL phase combination in MULTICOMB to perform density modification and Buccaneer uses the MLHL likelihood function in REFMAC for model refinement.

In the test cases below, the previous version of CRANK, version 1.3, is tested with the current version, version 1.4. The main differences between the two versions are the development version of AFRO that calculates multivariate |F_A| values given SAD data and the use of MULTICOMB for phase combination in density modification, which were both introduced in version 1.4.

In total, we report results from 116 real data sets from several different sources listed in Appendix A. The data sets cover a wide range of resolutions (from 0.94 to 3.29 Å) and anomalous scatterers, including selenium, sulfur, chloride, sulfate, manganese, bromide, calcium and zinc. Of the 116 data sets, 63 are MAD data sets, 46 are SAD data sets and seven are SIRAS data sets.

4. Results and discussion

Fig. 3 shows the fraction of the backbone built within 1 Å of the final deposited structure for each of these data sets for the current version of CRANK (version 1.4) versus the previous version (version 1.3). In total, 77 of 116 structures have greater than 60% of the structure built correctly; of these 77 structures, 66 are built to over 80% completeness. An example of an automatically built structure with a weak signal is GerE (Ducros et al., 2001 ). The structure of GerE was originally solved with a four-wavelength selenomethionine MAD data set collected at 2.7 Å resolution and a native data set to 2.1 Å resolution. CRANK version 1.3 could build the structure using just the peak data set to a high degree, but failed to build the structure using just the SAD inflection data set. CRANK version 1.4 can build the structure to a high degree using either the peak or inflection data set. We are unaware of any other automated package or collection of algorithms that can build GerE using either the peak or inflection data set automatically. To give an indication of the anomalous signal, Fig. 4 plots the Bijvoet ratio (i.e. |ΔF|/|F|) as a function of resolution bin for the GerE peak and inflection data: the overall Bijvoet ratios for the peak and inflection data are 0.167 and 0.139, respectively.

Figure 3
Graph of the fraction of the model automatically built with CRANK version 1.3 versus CRANK version 1.4. MAD data sets are shown as blue squares, SAD data sets are shown as red circles and SIRAS data sets are shown as green triangles.

Figure 4
Graph of the Bijvoet ratios from the peak-wavelength and inflection-wavelength data from the GerE test case as a function of resolution. The peak wavelength is shown as blue squares and the inflection wavelength is shown as red circles.

For the 77 structures that were built automatically, substructure determination successfully terminated early in 69 of the cases. For 33 of the 69 cases the Luzzati parameter statistics in Bp3 allowed early termination, while in the remaining 36 cases the complete substructure was validated by an analysis of the CRUNCH2 statistics.

4.1. Analysis of data sets that were not automatically built

39 of the 116 data sets could not be built automatically by CRANK. 19 of the 39 data sets failed at substructure detection and could be built automatically if the resolution cutoff in CRUNCH2 was changed or if SHELXC and SHELXD were used in substructure detection. It should also be noted that the five cases that could not be built in version 1.4 but were successful in version 1.3 were all a consequence of the changes in the substructure-detection algorithm. These tests will be used to further debug and improve the development version of the multivariate |F_A| calculation in AFRO.

For five of the 39 cases, CRANK in conjunction with a new SIRAS function for phasing leads to building when the current `uncorrelated' function in BP3 had failed to produce an automatically traceable map. The multivariate SIRAS function for phasing will be released in the next version of CRANK.

The remaining 15 cases could not be built automatically or manually in CRANK. For seven of theses cases, Mueller-Dieckmann et al. (2007 ) had also failed to build the structures. Similarly, four other cases consisted of SAD experiments using derivative data sets from SIRAS experiments also containing a very weak signal. It is very likely that no currently available methods can build these structures and new methods need to be developed to build structures from such weak data. The remaining four cases that could not be built are from the JCSG repository: these structures can be built with currently available methods and the given data. The reasons why CRANK fails to build these data sets have yet to be determined.

5. Conclusions and future developments

Because of the new methods that we have developed, CRANK can build many more structures automatically and can build structures where current methods fail. CRANK's robustness is shown by the large number of data sets that we use in this test that require very minimal input.

CRANK's ccp4i interface is easy to use but does have some limitations: log files are only updated once a particular step in the pipeline has finished and users cannot manually stop a current step and proceed to a next step; the pipeline can only be terminated and the CRANK run must be restarted from the the beginning. Furthermore, although CRANK has an interface to Coot (Emsley et al., 2010 ), it cannot show real-time updates of a model as a CRANK run proceeds. All of these shortcomings are being addressed and a new PyQt (https://www.riverbankcomputing.co.uk/software/pyqt/intro ) interface for CRANK is currently being developed in collaboration with CCP4.

Although having an easy-to-use and powerful interface is important, the first priority for CRANK will always be the development of better methods to solve data sets that elude current methods. In the case of MAD data, current approaches in CRANK and elsewhere use univariate uncorrelated likelihood functions for F_A calculation, substructure phasing and the MLHL function for density modification and automated model building and refinement. Obviously, a multivariate MAD function could address the shortcomings in current approaches and could lead to structure solutions where current methods fail.

In the case of SAD data, the multivariate functions used in substructure phasing, density modification and model refinement only differ in the number of input variables and the parameterization. Although current algorithms separate these steps, the common mathematical framework suggests that all the information could be used simultaneously and combined optimally in a unified process using a single mathematical function, possibly resulting in substantial improvements.

APPENDIX A

Data sets

A total of 132 data sets were used and were composed of 78 data sets from the Joint Center for Structural Genomics (JCSG; https://www.jcsg.org/ ), 1vjn, 1vjr, 1vjz, 1vk4, 1vkm, 1vlm, 1vqr, 1z82, 1zy9, 1zyb, 2a2m, 2a2o, 2a3n, 2a6b, 2aml, 2avn, 2b8m, 2etd, 2etj, 2ets, 2etv, 2evr, 2f4p, 2fea, 2ffj, 2fg0, 2fg9, 2fna, 2fqp, 2fur, 2fzt, 2g0t, 2g42, 2gc9, 2nlv, 2nuj, 2nwv, 2o08, 2o1q, 2o2x, 2o2z, 2o3l, 2o62, 2o7t, 2o8q, 2obp, 2oc5, 2od5, 2od6, 2oh3, 2okc, 2okf, 2ooj, 2opk, 2osd, 2otm, 2ozg, 2ozj, 2p10, 2p4o, 2p7h, 2p7i, 2p97, 2pg3, 2pg4, 2pgc, 2pim, 2pn1, 2pnk, 2ppv, 2pr7, 2prr, 2prv, 2prx, 2pv4, 2pw4, 2b78 and 2b79; 23 data sets from Mueller-Dieckmann et al. (2007), 2g4h, 2g4i, 2g4j, 2g4k, 2g4p, 2g4q, 2g4l, 2g4n, 2g4o, 2g4r, 2g4s, 2g4t, 2g4u, 2g4v, 2g4w, 2g4x, 2g4y, 2g4z, 2ill, 2g51, 2g52, 2g54 and 2g55; and 31 from various other individual data-set contributors, 1e42 (Owen, Vallis et al., 2000 ), 1e6i (Owen, Ornaghi et al., 2000 ), 1hf8 (Ford et al., 2001 ), 2ahy (Shi et al., 2006 ), 2hba (J.-H. Cho, S. Sato, E. Y. Kim, H Schindelin & D. P. Raleigh, unpublished work), 2o0h (Sun et al., 2007 ), 2rkk (Xiao et al., 2008 ), 3bpj (L. Nedyalkova, B. Hong, W. Tempel, F. MacKenzie, C. H. Arrowsmith, A. M. Edwards, J. Weigelt, A. Bochkarev & H. Park, unpublished work), 2fdn (Dauter et al., 1997 ), 1of3 (Boraston et al., 2003 ), 1i4u (Gordon et al., 2001 ), 1dw9 (Walsh et al., 2000 ), 1v0o (Holton et al., 2003 ), 1fse (Ducros et al., 2001), 1xib (Carrell et al., 1989 ), 1fj2 (Devedjiev et al., 2000 ), 1h29 (Matias et al., 2002 ), 1c8u (Jia et al., 2000 ), 1lvy (Schiltz et al., 1997 ), 1lz8 (Dauter et al., 1999 ), 1e3m (Lamers et al., 2000 ), 1ga1 (Dauter et al., 2001 ), 1djl (White et al., 2000 ), 1dtx (Skarzynski, 1992 ), 1dpx (Weiss, 2001 ), 1mso (Smith et al., 2003 ), 1ocy (Thomassen et al., 2003 ), 1rju (Calderone, 2004 ), 1rgg (Sevcik et al., 1996 ), 1m32 (Chen et al., 2002 ) and a subtilisin data set (Betzel et al., 1988 ; Dauter et al., 2002 ). Data where a program terminated abnormally in either pipeline were excluded from the statistics and graphs presented, resulting in 116 data sets.

Acknowledgements

Steven Ness provided an initial implementation of the plug-in architecture. We thank all authors who kindly provided us with data sets, including the JCSG (https://www.jcsg.org/ ), M. Weiss, C. Mueller-Dieckmann and Z. Dauter. Funding for this work was provided by Leiden University, the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO; https://www.nwo.nl/ ) and Cyttron (https://www.cyttron.org/ ). CRANK is distributed as free open-source software via the website https://www.bfsc.leidenuniv.nl/software/crank/ and in CCP4 (https://www.ccp4.ac.uk/ ).

References

Abrahams, J. P. & Leslie, A. G. W. (1996). Acta Cryst. D52, 30–42. CrossRef CAS Web of Science IUCr Journals Google Scholar
Adams, P. D. et al. (2010). Acta Cryst. D66, 213–221. Web of Science CrossRef CAS IUCr Journals Google Scholar
Betzel, C., Dauter, Z., Dauter, M., Ingelman, M., Papendorf, G., Wilson, K. S. & Branner, S. (1988). J. Mol. Biol. 204, 803–804. CrossRef PubMed Web of Science Google Scholar
Boraston, A. B., Revett, T. J., Boraston, C. M., Nurizzo, D. & Davies, G. J. (2003). Structure, 11, 665–675. Web of Science CrossRef PubMed CAS Google Scholar
Bricogne, G., Vonrhein, C., Flensburg, C., Schiltz, M. & Paciorek, W. (2003). Acta Cryst. D59, 2023–2030. Web of Science CrossRef CAS IUCr Journals Google Scholar
Burla, M. C., Carrozzini, B., Cascarano, G. L., Giacovazzo, C., Polidori, G. & Siliqi, D. (2002). Acta Cryst. D58, 928–935. Web of Science CrossRef CAS IUCr Journals Google Scholar
Calderone, V. (2004). Acta Cryst. D60, 2150–2155. CrossRef CAS IUCr Journals Google Scholar
Carrell, H. L., Glusker, J. P., Burger, V., Manfre, F., Tritsch, D. & Biellmann, J. F. (1989). Proc. Natl Acad. Sci. USA, 86, 4440–4444. CrossRef CAS PubMed Web of Science Google Scholar
Chen, C. C., Zhang, H., Kim, A. D., Howard, A., Sheldrick, G. M., Mariano-Dunaway, D. & Herzberg, O. (2002). Biochemistry, 41, 13162–13169. Web of Science CrossRef PubMed CAS Google Scholar
Collaborative Computational Project, Number 4 (1994). Acta Cryst. D50, 760–763. CrossRef IUCr Journals Google Scholar
Cowtan, K. (1994). Jnt CCP4/ESF–EACBM Newsl. Protein Crystallogr. 31, 34–38. Google Scholar
Cowtan, K. (2000). Acta Cryst. D56, 1612–1621. Web of Science CrossRef CAS IUCr Journals Google Scholar
Cowtan, K. (2006). Acta Cryst. D62, 1002–1011. Web of Science CrossRef CAS IUCr Journals Google Scholar
Cowtan, K. (2010). Acta Cryst. D66, 470–478. Web of Science CrossRef CAS IUCr Journals Google Scholar
Dauter, Z., Dauter, M., de La Fortelle, E., Bricogne, G. & Sheldrick, G. M. (1999). J. Mol. Biol. 289, 83–92. Web of Science CrossRef PubMed CAS Google Scholar
Dauter, Z., Dauter, M. & Dodson, E. J. (2002). Acta Cryst. D58, 494–506. 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
Dauter, Z., Wilson, K. S., Sieker, L. C., Meyer, J. & Moulis, J. M. (1997). Biochemistry, 36, 16065–16073. Web of Science CrossRef CAS PubMed Google Scholar
Devedjiev, Y., Dauter, Z., Kuznetsov, S. R., Jones, T. L. & Derewenda, Z. S. (2000). Structure, 8, 1137–1146. Web of Science CrossRef PubMed CAS Google Scholar
Ducros, V. M., Lewis, R. J., Verma, C. S., Dodson, E. J., Leonard, G., Turkenburg, J. P., Murshudov, G. N., Wilkinson, A. J. & Brannigan, J. A. (2001). J. Mol. Biol. 306, 759–771. Web of Science CrossRef PubMed CAS Google Scholar
Emsley, P., Lohkamp, B., Scott, W. G. & Cowtan, K. (2010). Acta Cryst. D66, 486–501. Web of Science CrossRef CAS IUCr Journals Google Scholar
Ford, M. G., Pearse, B. M., Higgins, M. K., Vallis, Y., Owen, D. J., Gibson, A., Hopkins, C. R., Evans, P. R. & McMahon, H. T. (2001). Science, 291, 1051–1055. Web of Science CrossRef PubMed CAS Google Scholar
Gordon, E. J., Leonard, G. A., McSweeney, S. & Zagalsky, P. F. (2001). Acta Cryst. D57, 1230–1237. Web of Science CrossRef CAS IUCr Journals Google Scholar
Graaff, R. A. G. de, Hilge, M., van der Plas, J. L. & Abrahams, J. P. (2001). Acta Cryst. D57, 1857–1862. Web of Science CrossRef IUCr Journals Google Scholar
Hendrickson, W. A. & Lattman, E. E. (1970). Acta Cryst. B26, 136–143. CrossRef CAS IUCr Journals Google Scholar
Holton, S., Merckx, A., Burgess, D., Doerig, C., Noble, M. & Endicott, J. (2003). Structure, 11, 1329–1337. Google Scholar
Jia, L., Derewenda, U., Dauter, Z., Smith, S. & Derewenda, Z. S. (2000). Nature Struct. Biol. 7, 555–559. CrossRef PubMed Google Scholar
Lamers, M. H., Perrakis, A., Enzlin, J. H., Winterwerp, H. H., de Wind, N. & Sixma, T. K. (2000). Nature (London), 407, 711–717. Web of Science PubMed CAS Google Scholar
Langer, G., Cohen, S. X., Lamzin, V. S. & Perrakis, A. (2008). Nature Protoc. 3, 1171–1179. Web of Science CrossRef CAS Google Scholar
Luzzati, V. (1952). Acta Cryst. 5, 802–810. CrossRef IUCr Journals Web of Science Google Scholar
Matias, P. M., Coelho, A. V., Valente, F. M., Placido, D., LeGall, J., Xavier, A. V., Pereira, I. A. & Carrondo, M. A. (2002). J. Biol. Chem. 277, 47907–47916. Web of Science CrossRef PubMed CAS Google Scholar
Matthews, B. W. (1966). Acta Cryst. 20, 82–86. CrossRef IUCr Journals Web of Science Google Scholar
Mueller-Dieckmann, C., Panjikar, S., Schmidt, A., Mueller, S., Kuper, J., Geerlof, A., Wilmanns, M., Singh, R. K., Tucker, P. A. & Weiss, M. S. (2007). Acta Cryst. D63, 366–380. Web of Science CrossRef CAS IUCr Journals Google Scholar
Murshudov, G. N., Skubák, P., Lebedev, A. A., Pannu, N. S., Steiner, R. A., Nicholls, R. A., Winn, M. D., Long, F. & Vagin, A. A. (2011). Acta Cryst. D67, 355–367. Web of Science CrossRef CAS IUCr Journals Google Scholar
Ness, S. R., de Graaff, R. A. G., Abrahams, J. P. & Pannu, N. S. (2004). Structure, 12, 1753–1761. Web of Science CrossRef PubMed CAS Google Scholar
North, A. C. T. (1965). Acta Cryst. 18, 212–216. CrossRef IUCr Journals Web of Science Google Scholar
Otwinowski, Z. (1991). Proceedings of the CCP4 Study Weekend. Isomorphous Replacement and Anomalous Scattering, edited by W. Wolf, P. R. Evans & A. G. W. Leslie, pp. 80–86. Warrington: Daresbury Laboratory. Google Scholar
Owen, D. J., Ornaghi, P., Yang, J.-C., Lowe, N., Evans, P. R., Ballario, P., Neuhaus, D., Filetici, P. & Travers, A. A. (2000). EMBO J. 19, 6141–6149. Web of Science CrossRef PubMed CAS Google Scholar
Owen, D. J., Vallis, Y., Pearse, B. M., McMahon, H. T. & Evans, P. R. (2000). EMBO J. 19, 4216–4227. Web of Science CrossRef PubMed CAS Google Scholar
Panjikar, S., Parthasarathy, V., Lamzin, V. S., Weiss, M. S. & Tucker, P. A. (2005). Acta Cryst. D61, 449–457. Web of Science CrossRef CAS IUCr Journals Google Scholar
Pannu, N. S., McCoy, A. J. & Read, R. J. (2003). Acta Cryst. D59, 1801–1808. Web of Science CrossRef CAS IUCr Journals Google Scholar
Pannu, N. S., Murshudov, G. N., Dodson, E. J. & Read, R. J. (1998). Acta Cryst. D54, 1285–1294. Web of Science CrossRef CAS IUCr Journals Google Scholar
Pannu, N. S. & Read, R. J. (2004). Acta Cryst. D60, 22–27. Web of Science CrossRef CAS IUCr Journals Google Scholar
Pannu, N. S., Skubak, P., Sikharulidze, I., Abrahams, J. P. & de Graaff, R. A. G. (2007). Acta Cryst. A63, s116. CrossRef IUCr Journals Google Scholar
Schiltz, M., Shepard, W., Fourme, R., Prangé, T., de La Fourtelle, E. & Bricogne, G. (1997). Acta Cryst. D53, 78–92. CrossRef CAS Web of Science IUCr Journals Google Scholar
Schneider, T. R. & Sheldrick, G. M. (2002). Acta Cryst. D58, 1772–1779. Web of Science CrossRef CAS IUCr Journals Google Scholar
Sevcik, J., Dauter, Z., Lamzin, V. S. & Wilson, K. S. (1996). Acta Cryst. D52, 327–344. CrossRef CAS IUCr Journals Google Scholar
Sheldrick, G. M. (2002). Z. Krystallogr. 217, 644–650. CrossRef CAS Google Scholar
Sheldrick, G. M. (2008). Acta Cryst. A64, 112–122. Web of Science CrossRef CAS IUCr Journals Google Scholar
Shi, N., Ye, S., Alam, A., Chen, L. & Jiang, Y. (2006). Nature (London), 440, 570–574. Web of Science CrossRef PubMed CAS Google Scholar
Skarzynski, T. (1992). J. Mol. Biol. 224, 671–683. CrossRef PubMed CAS Web of Science Google Scholar
Smith, G. D., Pangborn, W. A. & Blessing, R. H. (2003). Acta Cryst. D59, 474–482. Web of Science CrossRef CAS IUCr Journals Google Scholar
Skubák, P., Murshudov, G. N. & Pannu, N. S. (2004). Acta Cryst. D60, 2196–2201. Web of Science CrossRef IUCr Journals Google Scholar
Skubák, P., Murshudov, G. & Pannu, N. S. (2009). Acta Cryst. D65, 1051–1061. Web of Science CrossRef IUCr Journals Google Scholar
Skubák, P., Ness, S. & Pannu, N. S. (2005). Acta Cryst. D61, 1626–1635. Web of Science CrossRef IUCr Journals Google Scholar
Skubák, P. & Pannu, N. S. (2011). Acta Cryst. D67, 345–354. Web of Science CrossRef IUCr Journals Google Scholar
Skubák, P., Waterreus, W.-J. & Pannu, N. S. (2010). Acta Cryst. D66, 783–788. Web of Science CrossRef IUCr Journals Google Scholar
Sun, S., Kondabagil, K., Gentz, P. M., Rossmann, M. G. & Rao, V. B. (2007). Mol. Cell, 25, 943–949. Web of Science CrossRef PubMed CAS Google Scholar
Terwilliger, T. C. (2000). Acta Cryst. D56, 965–972. Web of Science CrossRef CAS IUCr Journals Google Scholar
Thomassen, E., Gielen, G., Schutz, M., Schoehn, G., Abrahams, J. P., Miller, S. & van Raaij, M. J. (2003). J. Mol. Biol. 331, 361–373. Web of Science CrossRef PubMed CAS Google Scholar
Xiao, J., Xia, H., Zhou, J., Azmi, I. F., Davies, B. A., Katzmann, D. J. & Xu, Z. (2008). Dev. Cell, 14, 37–49. Web of Science CrossRef PubMed CAS Google Scholar
Walsh, M. A., Otwinowski, Z., Perrakis, A., Anderson, P. M. & Joachimiak, A. (2000). Structure, 8, 505–514. Web of Science CrossRef PubMed CAS Google Scholar
Weiss, M. S. (2001). J. Appl. Cryst. 34, 130–135. Web of Science CrossRef CAS IUCr Journals Google Scholar
White, S. A., Peake, S. J., McSweeney, S., Leonard, G., Cotton, N. P. & Jackson, J. B. (2000). Structure, 8, 1–12. Web of Science CrossRef PubMed CAS Google Scholar