The JCSG MR pipeline: optimized alignments, multiple models and parallel searches
The success rate of molecular replacement (MR) falls considerably when search models share less than 35% sequence identity with their templates, but can be improved significantly by using fold-recognition methods combined with exhaustive MR searches. Models based on alignments calculated with fold-recognition algorithms are more accurate than models based on conventional alignment methods such as FASTA or BLAST, which are still widely used for MR. In addition, by designing MR pipelines that integrate phasing and automated refinement and allow parallel processing of such calculations, one can effectively increase the success rate of MR. Here, updated results from the JCSG MR pipeline are presented, which to date has solved 33 MR structures with less than 35% sequence identity to the closest homologue of known structure. By using difficult MR problems as examples, it is demonstrated that successful MR phasing is possible even in cases where the similarity between the model and the template can only be detected with fold-recognition algorithms. In the first step, several search models are built based on all homologues found in the PDB by fold-recognition algorithms. The models resulting from this process are used in parallel MR searches with different combinations of input parameters of the MR phasing algorithm. The putative solutions are subjected to rigid-body and restrained crystallographic refinement and ranked based on the final values of free R factor, figure of merit and deviations from ideal geometry. Finally, crystal packing and electron-density maps are checked to identify the correct solution. If this procedure does not yield a solution with interpretable electron-density maps, then even more alternative models are prepared. The structurally variable regions of a protein family are identified based on alignments of sequences and known structures from that family and appropriate trimmings of the models are proposed. All combinations of these trimmings are applied to the search models and the resulting set of models is used in the MR pipeline. It is estimated that with the improvements in model building and exhaustive parallel searches with existing phasing algorithms, MR can be successful for more than 50% of recognizable homologues of known structures below the threshold of 35% sequence identity. This implies that about one-third of the proteins in a typical bacterial proteome are potential MR targets.
Molecular replacement (MR; Rossmann, 2001) has an advantage over experimental phasing techniques because it requires only one data set of reflections obtained from a native protein crystal, which is considerably less resource-intensive than multiple-wavelength experiments with substituted protein crystals.
Because of advances in structural biology, more and more structures are available through the Protein Data Bank (PDB; Berman et al., 2000). As the number of known protein structures grows rapidly, the main interest shifts from studying individual structures to studying protein complexes, which are fundamental to our understanding of protein interactions in biological mechanisms such as metabolism, the cell cycle or apoptosis. MR is the method of choice for solving the structures of protein complexes because the structures of individual proteins are often known. As a result, the number of protein structures determined by MR increases every year, so any improvements in the method can save considerable time and resources.
The MR phasing algorithms pioneered by Hoppe (1957) and Rossmann & Blow (1962) require the identification of the correct orientation and position of the structural model in the asymmetric unit of a new crystal. Currently, several automated computational algorithms for solving this problem are available in popular programs such as Phaser (Storoni et al., 2004), AMoRe (Navaza, 2001), X-PLOR/CNS (Brünger et al., 1998), MOLREP (Vagin & Teplyakov, 2000), EPMR (Kissinger et al., 1999) and Queen of Spades (Glykos & Kokkinidis, 2000). The success of these MR methods depends critically on the quality of the model used and different ways of preparing models are still being explored. MR has been accomplished with models that cover only a small fraction (<30%) of the molecule (Bernstein et al., 1997), but experience has shown that in order for the procedure to be successful a significant portion of the molecule (>60%) is required and the differences between the coordinates of the model and the molecule must be small [usually with a root-mean-square distance of Cα atoms (CαRMSD) below 2.5 Å]. The requirements for optimal search models for MR are still being explored. Several interesting ideas regarding search models have been proposed or tested on individual cases or on small sets of structures (Kleywegt, 1998). These ideas include removing or cutting back residues or regions with high temperature factors, the omission of regions where sequence conservation is low, using composite search models (Chen, 2001) and building alternative models based on suboptimal alignments (Jones, 2001). Recently, the analysis of several difficult MR problems from our center has demonstrated that the alignment accuracy and side-chain modeling have a significant impact on MR success rates (Schwarzenbacher et al., 2004). Some of the methods of model preparation have been implemented in the CHAINSAW program, written by Norman Stein and included in the CCP4 suite (Collaborative Computational Project, Number 4, 1994). CHAINSAW prepares different variants of pruned (mixed) search models for MR.
The most effective methods of protein structure prediction are based on establishing a homology between a protein of interest and an already characterized protein. However, the standard sequence-comparison methods rapidly lose sensitivity in the `twilight zone' where there is below 30% sequence identity between the protein of interest and the closest known structure (Holm et al., 1992). The sensitivity of fold recognition can be improved by using evolutionary information, which can be extracted from large families of protein sequences. Instead of comparing two sequences, one compares a protein sequence with sequences from an entire protein family represented by a sequence profile as implemented in PSI-BLAST (Altschul et al., 1997) or by hidden Markov model (HMM; Eddy, 1998). A logical next step in this strategy is to compare two sequence profiles as introduced in FFAS (Rychlewski et al., 2000) or two hidden Markov models as implemented in HHSEARCH (Soding, 2005).
The application of sequence profiles has a significant impact on the number of fold predictions one can make from a given set of known structures. A widely accepted way of testing homology-prediction methods is to apply them to representative sets of known structures and to calculate the number of correct predictions and false positives for different score thresholds corresponding to different error levels. Using this procedure, we re-evaluated the sensitivity of remote homology detection using three different methods. We used the ASTRAL resource (Chandonia et al., 2004) based on the SCOP database (Murzin et al., 1995) to construct a benchmark set of 5868 protein domain structures with less than 25% sequence identity to each other. The predictions obtained with BLAST, PSI-BLAST and FFAS for this benchmark clearly illustrate the advantage of using sequence profiles for the detection of distant homologues (see Fig. 1). At the 5% error level the profile–sequence comparison method PSI-BLAST (Altschul et al., 1997) gives almost twice as many correct predictions as the sequence–sequence comparison algorithm BLAST (Altschul et al., 1990). The profile–profile comparison method FFAS improves the sensitivity by another 20%.
Other advanced fold-recognition methods based on sequences profiles or similar methods of using evolutionary information include 3D-PSSM (Kelley et al., 2000), FUGUE (Shi et al., 2001), BIOINBGU (Fischer, 2000), PROSPECT (Xu & Xu, 2000) and SAMT98 (Karplus et al., 1998). These methods are more sensitive than sequence–sequence alignment methods such as BLAST and are usually more sensitive than profile–sequence alignment methods such as PSI-BLAST.
Besides the accuracy of the model, for more difficult MR problems, the success may critically depend on certain settings of the phasing algorithm, such as the low- and high-resolution limit applied to the crystallographic data. The strong dependence on the resolution limit and cutoff is especially evident for MR phasing algorithms, which are not based on the maximum-likelihood principle. It is rather difficult to propose any useful rules of thumb for selecting optimal low- and high-resolution cutoffs and, as suggested by the authors of MR programs, it is beneficial to test several combinations of these cutoffs. Usually, in difficult MR cases multiple phasing trials with different models and input parameters are performed manually, which imposes practical limits on the number of tested combinations.
We demonstrated that it is possible to extend the limits of the MR method by using several specifically designed protein models based on profile–profile fold recognition and exhaustive MR searches in a parallelized and automated MR pipeline (Schwarzenbacher et al., 2004) built at the Joint Center for Structural Genomics (Lesley et al., 2002).
At least three other groups are also involved in the development of advanced and publicly available MR pipelines, including CaspR (Claude et al., 2004), MrBUMP (Keegan & Winn, 2008) and BALBES (Long et al., 2008). Interesting attempts have also been made to go beyond the `rigid search model' and generate search models using normal-mode analysis (Suhre & Sanejouand, 2004; Jeong et al. 2006).
In this manuscript, we provide a short description of the JCSG MR pipeline, discuss the advantages of using sensitive fold-recognition algorithms and show the benefits of applying parameter-space screening to MR searches. We also give an update on the statistics of the results of the pipeline and further explore methods of generating alternative models for MR.
The parallelized MR pipeline used in the JCSG automatically performs all steps from homology detection through model preparation and MR searches to automated refinement. The pipeline includes the following steps (see Fig. 2).
The MR pipeline provided solutions for 33 protein structures with less than 35% sequence identity to their modeling templates (column P in Table 1). These results were compared with results from `simple' MR runs (column S in Table 1) in which one model based on a BLAST alignment was used in an MR search with default parameters. The same model was also used in exhaustive MR searches (column E in Table 1) with a wide range of parameters. By using different types of models based on accurate alignments combined with parallel processing, we can practically double the number of protein structures which can be solved by MR. Our results indicate that MR is usually straightforward if models share more than 30–35% identical residues with their templates (Schwarzenbacher et al., 2004), which is in good agreement with the widely accepted limit of highly accurate homology modeling (Vogt et al., 1995). Almost all MR cases with more than 35% sequence identity between the model and the structure were solved with the `simple approach' and unsolved problems are most likely to indicate problems with the crystallographic data rather than with model accuracy. Below 35% sequence identity the `simple approach' was ineffective and successful in only ten out of 33 cases (column S in Table 1). Exhaustive MR searches with standard templates resulted in six additional MR solutions (column E, Table 1). Exhaustive MR searches with different types of models including biologically relevant oligomers, mixed and all-atom homology models based on FFAS alignments (column P, Table 1) solved 17 additional structures with less than 35% sequence identity to their templates. Despite exhaustive searches with multiple models, 14 structures with less than 35% sequence identity remained unsolved.
The procedure of exhaustive testing of different input parameters of crystallographic software has been called parameter-space screening (Liu et al., 2005). In order to complete calculations in a reasonable time, parameter-space screening is usually performed in a parallel way using computer clusters. The results of MR phasing algorithms often depend on several input parameters connected to filters applied to the data and to the anticipated accuracy of the search model. In our pipeline, we relied on the program MOLREP (Vagin & Teplyakov, 2000) from the CCP4 suite (Collaborative Computational Project, Number 4, 1994) because of its robustness, speed and simple usage. Two of the input parameters of the program are related to the expected completeness of the search model and its expected similarity to the structure being solved. The completeness parameter (COMPL) is linked to the soft low-resolution cutoff applied to the crystallographic data and the similarity parameter (SIM) is linked to the high-resolution cutoff. Since we do not have exact information about the accuracy of the model before the actual structure is solved, different combinations of these two parameters are exhaustively tested, as suggested by the authors of the program. In particular, low-resolution reflections and the low-resolution cutoff are known to play important roles in MR phasing. However, instead of examining the low-resolution part of the data and trying to find the optimal low-resolution cutoff, we applied different low-resolution cutoffs by changing the COMPL parameter and tested the correctness of all solutions by refining them. In fact, our tests indicated that in several cases the success of phasing with MOLREP was dependent on these input parameters in an unpredictable way, which underscores the importance of exhaustive parameter-space screening. For example, parameter-space screening was used for MR phasing of orotidine 5′-phosphate decarboxylase (TM0332) from Thermotoga maritima. FFAS detected similarity to the structure of orotidine 5′-phosphate decarboxylase from Escherichia coli (PDB code 1eix ) with a score of −60, a sequence identity of 24% and the alignment covering 98% of the sequence with six gaps. Fig. 3 shows a contour map of final Rfree values after restrained refinement obtained for MR solutions calculated with different values of the similarity and completeness parameters. The MR solutions obtained for different input parameters of the program MOLREP led to final Rfree values from REFMAC5 ranging from 0.464 to 0.546. The solution with the lowest Rfree value was manually refined and deposited in the PDB (PDB code 1vqt ). The CαRMSD between fully refined TM0332 structure and 1eix is 2.27 Å. A detailed analysis of the solutions with different final Rfree values showed that most of the solutions with Rfree values higher than 0.5 were incorrect, underscoring the significance of parameter-space screening for this case.
For difficult cases in which the application of exhaustive parameter-space screening combined with multiple models based on different templates does not yield a solution, it is possible to increase the variability of the models used in the pipeline by using models with different combinations of trimmings of possibly unreliable regions.
It is widely accepted that an optimal model for MR phasing should contain all atoms that can be predicted with sufficient accuracy and should not contain any atoms with high coordinate errors. Unreliable regions of the model usually include loops, gaps and fragments of low sequence similarity between the model and the template. Such regions are more likely to contain significant errors. Therefore, by removing such regions from the model one can significantly increase its overall accuracy, but some accurately predicted regions can also be removed, since the exact locations of inaccurate regions are not known before the structure is solved. The level of accuracy required for MR models is also not obvious and may vary for different data sets. A brute-force solution to this problem is to use the capabilities of a parallelized MR pipeline and test all combinations of possible trimmings of the model. This procedure allowed MR phasing of the structure of NADH dehydrogenase subunit C from Thermobifida fusca (GenBank accession code YP_290749). According to FFAS, the only structure homologous to this protein is subunit 5 of an oligomeric domain in respiratory complex I from Thermus thermophilus (PDB code 2fug ). FFAS aligned 66% of the sequence of YP_290749 with the sequence of 2fug , with a score of −79 and a sequence identity of 27%. Residues 213–249 of the target sequence were aligned with the region of 2fug subunit 5 which extends from its globular domain and binds to another subunit in the complex. However, since the present crystals only contained the isolated domain, we expected that this particular region may have a different conformation and removed it from the model. This resulted in a decrease in the sequence identity to 22% and in the sequence coverage by the model to 50% (see Fig. 4a). Since the asymmetric unit of 2fug contains four slightly different copies of subunit 5 (chains 5, E, N, W), each of them was used to build models of the target. Model trimmings were proposed based on the sequence alignment, in which six potentially unreliable regions of the model were identified. We applied up to four alternative trimmings in each of these regions (see Fig. 4a). By applying all combinations of these trimmings, we produced 540 trimmed models from each copy of subunit 5, yielding a total of 2160 models. All search models were submitted to the MR pipeline. MR searches were completed in about 5 h on a 50 CPU Linux cluster. Because of time limitations, parameter-space screening was not used and MR solutions obtained with default MOLREP parameters went directly to 30 cycles of restrained refinement in REFMAC5.
The JCSG MR pipeline increases the success rate of MR by using accurate modeling methods, large numbers of alternative models and applying parameter-space screening to phasing algorithms. We observed that MR was relatively straightforward when the sequences of the target and the template were more than 35% identical. Based on our results, we tend to accept 35% as a limit of straightforward MR, since almost all cases in this range could be solved using the standard approach.
This situation changes when the sequence identity drops below 35%: standard alignment methods start to be less accurate and CαRMSD values between structures of related proteins increase significantly (Chothia & Lesk, 1986). Although the relationship between the sequence identity of pairs of protein structures and their CαRMSD values is well established, the character of this relationship varies significantly among protein families, as it becomes apparent when structural alignments of large families are calculated and analyzed (Reeves et al., 2006). Therefore, one can expect that the limit of accurate homology modeling (which is also the limit of feasible MR) may be different for different protein families. In some cases, the chances of successful MR phasing can be estimated based on the structural variability observed among known structures from a protein family of interest. If known structures from a family show only small differences in the protein core, then unknown structures from this family are also likely to have a well conserved core. Members of such protein families could be suitable for MR, even when the sequence identity to the closest known structure is very low. Therefore, as an element of experiment design one may perform homology searches in the PDB database using sensitive fold-recognition methods such as the FFAS server (Jaroszewski et al., 2005; available at https://ffas.burnham.org ). Then, if homologous structures are found one can assess the structural similarity between them using a multiple structural alignment method such as POSA (Ye & Godzik, 2005; available at https://fatcat.burnham.org/POSA ). The POSA server provides a quantitative measure of the structural similarities between submitted structures along with a graphical interface, which we found very helpful in determining the extent of the conserved structural core in the family. At this point it is rather difficult to provide general quantitative limits of the applicability of MR based on such analyses, but in many cases it is possible to tell whether MR phasing is worth considering.
Below 35% sequence identity models based on BLAST alignments had a lower success rate, since in most cases they are shorter and less accurate than the alignments from PSI-BLAST and FFAS. Furthermore, in two cases (targets 17134165 and TM0603) BLAST could not detect a homologous structure at all, while remote similarity detected using FFAS led to successful MR phasing. This observation implies that some difficult MR problems can be solved by using publicly available fold-recognition servers.
Because of its high computational cost, the method of combinatorial model trimming was only applied to a few unsolved MR problems. The example of the phasing of NADH dehydrogenase subunit C using this method is interesting because the distribution of Rfree values for trimmed models has a very narrow minimum. It is impossible to make general conclusions based on one example, but this observation suggests that the results of MR and refinement are highly susceptible to the ratio of correctly and incorrectly predicted atoms in the search model. This implies that combinatorial trimming, which allows maximization of this ratio in some models, may provide solutions to problems that are beyond the reach of models based on one optimal alignment. It has to be noted that the method of combinatorial trimming is currently only partly automated and requires manual intervention. For example, the model regions to be trimmed were proposed based on visual inspection of the alignment. In principle, one can imagine full automation of such a procedure by using known methods of assessing the local accuracy of the model. The method needs to be tested on more examples before it can be fully automated.
The results obtained for 47 data sets still do not allow a thorough statistical analysis of the feasibility of MR, which depends on too many features of the data and the model. Nevertheless, we can roughly estimate that the success rate is about 50% for proteins with an FFAS score better (lower) than −15, a sequence identity in the range 15–35% and a model which covers at least two-thirds of the sequence.
The main conclusion of our tests is that search models based on alignments from sensitive fold-recognition algorithms together with the latest MR phasing techniques in combination with parameter-space screening do improve the success rate of MR phasing. This improvement will be critical for solving protein complexes and may save a considerable amount of time and resources, especially for structural genomics projects.
It has to be noted that the procedures described above are very CPU demanding and in most cases impractical without a computer cluster. At JCSG we used 25–50 CPUs of a Linux cluster for most calculations. Completion of most searches still took several hours.
The FFAS program is available as a web server at https://ffas.burnham.org and is linked to a modeling server which can produce all-atom and mixed models based on FFAS alignments. The authors are preparing a distribution version of the JCSG MR pipeline scripts and it will be made available to the academic community on request.
The results presented in this publication were possible thanks to the effort of the entire JCSG team. The authors are especially grateful to their colleagues from the JCSG Structure Determination Core at Stanford Synchrotron Radiation Laboratory, who obtained all data sets used in this work and helped with their crystallographic expertise. The JCSG is supported by the NIH Protein Structure Initiative grant U54 GM074898 from the National Institute of General Medical Sciences (https://www.nigms.nih.gov ). RS is supported by EC grant MEXT-CT-2006-033534.
Altschul, S. F., Gish, W., Miller, W., Myers, E. W. & Lipman, D. J. (1990). J. Mol. Biol. 215, 403–410. CrossRef CAS PubMed Web of Science Google Scholar
Altschul, S. F., Madden, T. L., Schaffer, A. A., Zhang, J., Zhang, Z., Miller, W. & Lipman, D. J. (1997). Nucleic Acids Res. 25, 3389–3402. CrossRef CAS PubMed Web of Science 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, B. E., Michels, P. A. & Hol, W. G. (1997). Nature (London), 385, 275–278. CrossRef CAS PubMed Web of Science Google Scholar
Brünger, A. T., Adams, P. D., Clore, G. M., DeLano, W. L., Gros, P., Grosse-Kunstleve, R. W., Jiang, J.-S., Kuszewski, J., Nilges, M., Pannu, N. S., Read, R. J., Rice, L. M., Simonson, T. & Warren, G. L. (1998). Acta Cryst. D54, 905–921. Web of Science CrossRef IUCr Journals Google Scholar
Chandonia, J. M., Hon, G., Walker, N. S., Lo Conte, L., Koehl, P., Levitt, M. & Brenner, S. E. (2004). Nucleic Acids Res. 32, D189–D192. Web of Science CrossRef PubMed CAS Google Scholar
Chen, Y. W. (2001). Acta Cryst. D57, 1457–1461. Web of Science CrossRef CAS IUCr Journals Google Scholar
Chothia, C. & Lesk, A. M. (1986). EMBO J. 4, 823–826. Google Scholar
Claude, J. B., Suhre, K., Notredame, C., Claverie, J. M. & Abergel, C. (2004). Nucleic Acids Res. 32, W606–W609. Web of Science CrossRef PubMed CAS Google Scholar
Collaborative Computational Project, Number 4 (1994). Acta Cryst. D50, 760–763. CrossRef IUCr Journals Google Scholar
Eddy, S. R. (1998). Bioinformatics, 14, 755–763. Web of Science CrossRef CAS PubMed Google Scholar
Fischer, D. (2000). Pac. Symp. Biocomput. 5, 119–130. Google Scholar
Glykos, N. M. & Kokkinidis, M. (2000). Acta Cryst. D56, 169–174. Web of Science CrossRef CAS IUCr Journals Google Scholar
Holm, L., Ouzounis, C., Sander, C., Tuparev, G. & Vriend, G. (1992). Protein Sci. 12, 1691–1698. CrossRef Google Scholar
Hoppe, W. (1957). Acta Cryst. 10, 750–751. Google Scholar
Jaroszewski, L., Rychlewski, L., Li, Z., Li, W. & Godzik, A. (2005). Nucleic Acids Res. 33, W284–W288. Web of Science CrossRef PubMed CAS Google Scholar
Jeong, J. I., Lattman, E. E. & Chirikjian, G. S. (2006). Acta Cryst. D62, 398–409. Web of Science CrossRef CAS IUCr Journals Google Scholar
Jones, D. T. (2001). Acta Cryst. D57, 1428–1434. CrossRef CAS IUCr Journals Google Scholar
Karplus, K., Barrett, C. & Hughey, R. (1998). Bioinformatics, 14, 846–856. Web of Science CrossRef CAS PubMed Google Scholar
Keegan, R. M. & Winn, M. D. (2008). Acta Cryst. D64, 119–124. Web of Science CrossRef CAS IUCr Journals Google Scholar
Kelley, L. A., MacCallum, R. M. & Sternberg, M. J. E. (2000). J. Mol. Biol. 299, 501–522. CrossRef Google Scholar
Kissinger, C. R., Gehlhaar, D. K. & Fogel, D. B. (1999). Acta Cryst. D55, 484–491. Web of Science CrossRef CAS IUCr Journals Google Scholar
Kleywegt, G. J. (1998). News From The Uppsala Software Factory. https://xray.bmc.uu.se/usf/factory_6.html Google Scholar
Lesley, S. A. et al. (2002). Proc. Natl Acad. Sci. USA, 99, 11664–11669. Web of Science CrossRef PubMed CAS Google Scholar
Liu, Z.-J., Lin, D., Tempel, W., Praissman, J. L., Rose, J. P. & Wang, B.-C. (2005). Acta Cryst. D61, 520–527. Web of Science CrossRef CAS IUCr Journals Google Scholar
Long, F., Vagin, A. A., Young, P. & Murshudov, G. N. (2008). Acta Cryst. D64, 125–132. Web of Science CrossRef CAS IUCr Journals Google Scholar
Murshudov, G. N., Vagin, A. A. & Dodson, E. J. (1997). Acta Cryst. D53, 240–255. CrossRef CAS Web of Science IUCr Journals Google Scholar
Murzin, A. G., Brenner, S. E., Hubbard, T. & Chothia, C. (1995). J. Mol. Biol. 247, 536–540. CrossRef CAS PubMed Web of Science Google Scholar
Navaza, J. (2001). Acta Cryst. D57, 1367–1372. Web of Science CrossRef CAS IUCr Journals Google Scholar
Reeves, G. A., Dallman, T. J., Redfern, O. C., Akpor, A. & Orengo, C. A. (2006). J. Mol. Biol. 360, 725–741. Web of Science CrossRef PubMed CAS Google Scholar
Rossmann, M. G. (2001). Acta Cryst. D57, 1360–1366. Web of Science CrossRef CAS IUCr Journals Google Scholar
Rossmann, M. G. & Blow, D. M. (1962). Acta Cryst. 15, 24–31. CrossRef CAS IUCr Journals Web of Science Google Scholar
Rychlewski, L., Jaroszewski, L., Li, W. & Godzik, A. (2000). Protein Sci. 9, 232–241. Web of Science CrossRef PubMed CAS Google Scholar
Shi, J., Blundell, T. L. & Mizuguchi, K. (2001). J. Mol. Biol. 310, 243–257. Web of Science CrossRef PubMed CAS Google Scholar
Schwarzenbacher, R., Godzik, A., Grzechnik, S. K. & Jaroszewski, L. (2004). Acta Cryst. D60, 1229–1236. Web of Science CrossRef CAS IUCr Journals Google Scholar
Soding, J. (2005). Bioinformatics, 21, 951–960. Web of Science CrossRef PubMed Google Scholar
Storoni, L. C., McCoy, A. J. & Read, R. J. (2004). Acta Cryst. D60, 432–438. Web of Science CrossRef CAS IUCr Journals Google Scholar
Suhre, K. & Sanejouand, Y.-H. (2004). Acta Cryst. D60, 796–799. 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
Vogt, G., Etzold, T. & Argos, P. (1995). J. Mol. Biol. 249, 816–831. CrossRef CAS PubMed Web of Science Google Scholar
Vriend, G. J. (1990). J. Mol. Graph. 8, 52–56. CrossRef CAS PubMed Web of Science Google Scholar
Xu, Y. & Xu, D. (2000). Proteins, 40, 343–354. Web of Science CrossRef PubMed CAS Google Scholar
Ye, Y. & Godzik, A. (2005). Bioinformatics, 21, 2362–2369. Web of Science CrossRef PubMed CAS Google Scholar
© International Union of Crystallography. Prior permission is not required to reproduce short quotations, tables and figures from this article, provided the original authors and source are cited. For more information, click here.