short communications\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Journal logoBIOLOGICAL
CRYSTALLOGRAPHY
ISSN: 1399-0047
Volume 63| Part 11| November 2007| Pages 1194-1197

On macromolecular refinement at subatomic resolution with interatomic scatterers

CROSSMARK_Color_square_no_text.svg

aLawrence Berkeley National Laboratory, One Cyclotron Road, BLDG 64R0121, Berkeley, CA 94720, USA, bInstitute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino 142290, Russia, cIGMBC, 1 Rue L. Fries, 67404 Illkirch and IBMC, 15 Rue R. Descartes, 67084 Strasbourg, France, and dFaculty of Sciences, Nancy University, 54506 Vandoeuvre-lès-Nancy, France
*Correspondence e-mail: pafonine@lbl.gov

(Received 18 June 2007; accepted 20 September 2007)

This paper is dedicated to the memory of Niels Hansen.

A study of the accurate electron-density distribution in molecular crystals at subatomic resolution (better than ∼1.0 Å) requires more detailed models than those based on independent spherical atoms. A tool that is conventionally used in small-molecule crystallography is the multipolar model. Even at upper resolution limits of 0.8–1.0 Å, the number of experimental data is insufficient for full multipolar model refinement. As an alternative, a simpler model composed of conventional independent spherical atoms augmented by additional scatterers to model bonding effects has been proposed. Refinement of these mixed models for several benchmark data sets gave results that were comparable in quality with the results of multipolar refinement and superior to those for conventional models. Applications to several data sets of both small molecules and macromolecules are shown. These refinements were performed using the general-purpose macromolecular refinement module phenix.refine of the PHENIX package.

1. Introduction

The growing number of macromolecular crystals diffracting to subatomic resolution (53 models in 2003; currently 270) requires the development of appropriate methods and software to model them best. The new information obtained from such macromolecular studies has been discussed in a number of articles (see, for example, the reviews by Dauter et al., 1995[Dauter, Z., Lamzin, V. S. & Wilson, K. S. (1995). Curr. Opin. Struct. Biol. 5, 784-790.], 1997[Dauter, Z., Lamzin, V. S. & Wilson, K. S. (1997). Curr. Opin. Struct. Biol. 7, 681-688.]; Vrielink & Sampson, 2003[Vrielink, A. & Sampson, N. (2003). Curr. Opin. Struct. Biol. 13, 709-715.]; Petrova & Podjarny, 2004[Petrova, T. E. & Podjarny, A. D. (2004). Rep. Prog. Phys. 67, 1565-1605.], and numerous references therein). Afonine et al. (2004[Afonine, P. V., Lunin, V. Y., Muzet, N. & Urzhumtsev, A. (2004). Acta Cryst. D60, 260-274.]) have shown that information about the density deformation of individual atoms can be extracted from macromolecular data at resolutions of 0.9 Å or better. As a consequence, conventional models for macromolecular structures, in which the electron density of the molecule is a simple sum of contributions from spherical atoms smeared by individual anisotropic displacements, are incomplete and provide inaccurate values for ADPs (atomic displace­ment parameters). Following previous publications, we refer to these models as IAM (independent-atom models).

Model refinement of small molecules at subatomic resolution largely uses the multipolar formalism of Hansen & Coppens (1978[Hansen, N. K. & Coppens, P. (1978). Acta Cryst. A34, 909-921.]). For these models, the electron density is a sum of atomic contributions in which the density is no longer spherical but depends upon the chemical environment. Such a nonspherical distribution is described by a linear combination of spherical harmonics (Hansen & Coppens, 1978[Hansen, N. K. & Coppens, P. (1978). Acta Cryst. A34, 909-921.]). Refinement of parameters of multipolar models is monitored mainly by decrease of the crystallographic R factor, improvement of the residual Fourier syntheses, the rigid-bond test (RBT) and other characteristics.

Lecomte and coworkers have reported a number of multipolar refinements of amino acids and nucleic acids to determine a database of multipole parameters and have described several cases of polypeptide and protein refinement using this database (for a review, see Jelsch et al., 2005[Jelsch, C., Guillot, B., Lagoutte, A. & Lecomte, C. (2005). J. Appl. Cryst. 38, 38-54.]). Recently, the group of Coppens (Volkov et al., 2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]) also reported an application of the multipolar refinement to polypeptides, but using their own database of multipolar parameters.

Volkov et al. (2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]) concluded that the applicability of multipolar models in macromolecular studies `is in general not warranted, unless exceptionally high-resolution data of ∼0.6 Å or better with satisfactory completeness' are available. Also it was stated that `for macromolecular crystal such data are generally not available, … the number of reflections is not sufficient'. A possible solution to overcome this obstacle is a direct transfer of library parameters without their refinement as discussed by Brock et al. (1991[Brock, C. P., Dunitz, J. D. & Hirshfeld, F. L. (1991). Acta Cryst. B47, 789-797.]), Pichon-Pesme et al. (1995[Pichon-Pesme, V., Lecomte, C. & Lachekar, H. (1995). J. Phys. Chem. 99, 6242-6250.]), Jelsch et al. (1998[Jelsch, C., Pichon-Pesme, V., Lecomte, C. & Aubry, A. (1998). Acta Cryst. D54, 1306-1318.]), Dittrich et al. (2005[Dittrich, B., Hübschle, C. B., Messerschmidt, M., Kalinowski, R., Girnt, D. & Luger, P. (2005). Acta Cryst. A61, 314-320.]), Volkov et al. (2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]) and Zarychta et al. (2007[Zarychta, B., Pichon-Pesme, V., Guillot, B., Lecomte, C. & Jelsch, C. (2007). Acta Cryst. A63, 108-125.]). However, since the quality of macromolecular X-ray data is generally lower than that for small-molecule crystals, an alternative solution is to introduce a model of intermediate complexity that is more detailed than IAM but simpler than a multipolar model (Afonine et al., 2004[Afonine, P. V., Lunin, V. Y., Muzet, N. & Urzhumtsev, A. (2004). Acta Cryst. D60, 260-274.]). A possible approach is to complete the IAM with spherical scatterers between the atoms (IAS, interatomic scatterers). It should be noted that the use of the IAM–IAS model is much more runtime-efficient and can be straightforwardly implemented in macromolecular crystallographic packages. Here, we use IAS instead of the previous name DBE (dummy bond electron model; Afonine et al., 2004[Afonine, P. V., Lunin, V. Y., Muzet, N. & Urzhumtsev, A. (2004). Acta Cryst. D60, 260-274.]), as it better reflects the features of the model.

In this paper, we compare the results obtained with different types of electron-density models for several benchmark data sets. The implementation of IAS modelling into the general-purpose crystallographic program suite PHENIX (Adams et al., 2002[Adams, P. D., Grosse-Kunstleve, 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.]) has allowed the corresponding refinements with phenix.refine (Afonine et al., 2005[Afonine, P. V., Grosse-Kunstleve, R. W. & Adams, P. D. (2005). CCP4 Newsl. 42, contribution 8.]) to be performed quickly and in a fully automated fashion.

2. Comparative refinement at subatomic resolution

The modelling of structures at subatomic resolution with multipolar models takes into account the delocalization of electron density from atomic centres owing to the formation of interatomic bonds. The IAM–IAS model (Afonine et al., 2004[Afonine, P. V., Lunin, V. Y., Muzet, N. & Urzhumtsev, A. (2004). Acta Cryst. D60, 260-274.]) instead treats this delocalized density as spherical Gaussian scatterers located at the centroid of the delocalized density and keeps the conventional spherical atoms unchanged. The multipolar model requires that existing IAM atoms be replaced, while the IAS models complete them with specifically constructed scatterers. Also, the IAM–IAS model may be gradually extended once the new features become visible. Some details of the construction and refinement of IAM–IAS models and the development of the corresponding library of parameters were originally outlined by Afonine et al. (2004[Afonine, P. V., Lunin, V. Y., Muzet, N. & Urzhumtsev, A. (2004). Acta Cryst. D60, 260-274.]). The current tests were aimed to demonstrate that IAM–IAS models can improve conventional IAM models by lowering the R and Rfree factors, correcting the ADP parameters and producing clearer residual maps to the same degree as multipolar models and yet are significantly simpler to work with. In this short communication, we do not have the possibility of discussing applications other than map improvement (see, for example, Afonine et al., 2002[Afonine, P. V., Pichon-Pesme, V., Muzet, N., Jelsch, C., Lecomte, C. & Urzhumtsev, A. (2002). CCP4 Newsl. 41, contribution 6.]). For the same reason, the complete methodology and implementation details of IAS in PHENIX, including the choice of refinement targets, the role of data completeness and the efficient resolution, will be discussed separately in a full-length paper (Afonine et al., in preparation).

To estimate the quality of IAM–IAS models, we built and refined such models for YGG and P2A4 (Table 1[link]), for which a comparative refinement has been reported by Volkov et al. (2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]). Similarly to Volkov et al. (2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]), refinement was performed at two different resolutions. The highest available resolution (0.44 and 0.37 Å, respectively; for YGG the data completeness is below 50% at a resolution higher than 0.57 Å) was considered as `high resolution', where the data-to-parameter ratio is high enough even for the use of a multipolar model, and a resolution of 0.80 Å was the `low resolution' where this ratio becomes too low. In addition to the standard R factor and rigid-bond test (Hirshfeld, 1976[Hirshfeld, F. L. (1976). Acta Cryst. A32, 239-244.]), Rfree (Brünger, 1992[Brünger, A. (1992). Nature (London), 355, 472-475.]) was used as a refinement-quality indicator.

Table 1
Data used for refinements

NnonH, NH and NIAS give the number of non-H, H and IAS atoms in corresponding models. dhigh is the highest resolution for the data set, Nhigh is the corresponding number of reflections. Nlow is the number of reflections for the data sets truncated to lower resolution (dlow = 0.80 Å; YGG and P2A4 only).

Molecule Space group and unit-cell parameters (Å, °) NnonH NH NIAS dhigh (Å) Nhigh Nlow Reference
YGG P212121, a = 7.98, b = 9.54, c = 18.32 22 19 39 0.43 4766 1358 Volkov et al. (2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.])
P2A4 P212121, a = 10.13, b = 12.50, c = 19.50 35 36 71 0.37 21475 2513 Volkov et al. (2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.])
Antifreeze protein (KW03) P212121, a = 32.50, b = 39.50, c = 44.64 650 518 367 0.62 118501 Ko et al. (2003[Ko, T.-P., Robinson, H., Gao, Y.-G., Cheng, C.-H. C., DeVries, A. L. & Wang, A. H.-J. (2003). Biophys. J. 84, 1228-1237.])
Trypsin P1, a = 32.87, b = 37.02, c = 39.78, α = 102.89, β = 104.59, γ = 102.37 2231 1515 1362 0.80 163918 Schmidt et al. (2003[Schmidt, A., Jelsch, C., Østergaard, P., Rypniewski, W. & Lamzin, V. S. (2003). J. Biol. Chem. 278, 43357-43362.])
Phospholipase C2, a = 44.73, b = 59.09, c = 45.31, α = 90.00, β = 117.43, γ = 90.00 1324 956 679 0.80 77695 Liu et al. (2003[Liu, Q., Huang, Q., Teng, M., Weeks, C. M., Jelsch, C., Zhang, R. & Niu, L. (2003). J. Biol. Chem. 278, 41400-41408.])
Scorpion toxin P212121, a = 45.90, b = 40.70, c = 30.10 647 441 335 0.96 31001 Housset et al. (2000[Housset, D., Benabicha, F., Pichon-Pesme, V., Jelsch, C., Maierhofer, A., David, S., Fontecilla-Camps, J. C. & Lecomte, C. (2000). Acta Cryst. D56, 151-160.])

Unfortunately, the YGG and P2A4 models had been refined previously against the full set of data [in fact, the set selected with I > 3σ(I), which is not explicitly stated in Volkov et al., 2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]], making the conventional Rfree analysis biased. Therefore, when performing the IAS refinements we only note that Rfree is lower than the corresponding values for the refined IAM models.

The IAM–IAS models were generated and refined completely automatically in PHENIX. Table 2[link] shows principal refinement information. All stereochemical and ADP restraints on atomic parameters were removed for both the small molecules and macromolecules used in this study (Dauter et al., 1997[Dauter, Z., Lamzin, V. S. & Wilson, K. S. (1997). Curr. Opin. Struct. Biol. 7, 681-688.]; Schmidt et al., 2003[Schmidt, A., Jelsch, C., Østergaard, P., Rypniewski, W. & Lamzin, V. S. (2003). J. Biol. Chem. 278, 43357-43362.]; Petrova et al., 2006[Petrova, T., Ginell, S., Mitschler, A., Hazemann, I., Schneider, T., Cousido, A., Lunin, V. Y., Joachimiak, A. & Podjarny, A. (2006). Acta Cryst. D62, 1535-1544.]). Since the starting models were previously refined to a high quality, no stereochemical distortions arising from the unrestrained refinement were observed. A decrease in the Rfree shows that refinement of IAS did not overfit the experimental data and indeed improved the models. When refining at `low resolution', the ADP values obtained with the IAS are smaller than those from the refinement of corresponding IAMs. Based on previous work (Afonine et al., 2004[Afonine, P. V., Lunin, V. Y., Muzet, N. & Urzhumtsev, A. (2004). Acta Cryst. D60, 260-274.]; Petrova et al., 2006[Petrova, T., Ginell, S., Mitschler, A., Hazemann, I., Schneider, T., Cousido, A., Lunin, V. Y., Joachimiak, A. & Podjarny, A. (2006). Acta Cryst. D62, 1535-1544.]), we believe that they are closer to the correct values of the ADPs, which will otherwise tend to increase to model the deformation density along the bonds (Coppens, 1967[Coppens, P. (1967). Science, 158, 1577-1579.]; Dunitz & Seiler, 1973[Dunitz, J. D. & Seiler, P. (1973). Acta Cryst. B29, 589-595.]). The rigid-bond test also confirms that the introduction of IAS improved the model. In fact, the IAS refinement with the maximum-likelihood target (Lunin et al., 2002[Lunin, V. Y., Afonine, P. V. & Urzhumtsev, A. G. (2002). Acta Cryst. A58, 270-­282.]; to our knowledge never previously applied in this context) improved the models further as measured by the rigid-bond test; however, analysis of this is beyond the scope of this paper. For `high-resolution refinement', mean ADP values are similar with and without IAS, as noted previously by Afonine et al. (2004[Afonine, P. V., Lunin, V. Y., Muzet, N. & Urzhumtsev, A. (2004). Acta Cryst. D60, 260-274.]). This indicates that the highest resolution data contain sufficient information to deconvolute the deformation-density and atomic uncertainty effects and to estimate the ADPs correctly even without IAS.

Table 2
Comparative statistics for refinement of IAS and multipolar models

Mt and Mr represent multipolar models with transferred and refined parameters (refinements `3' and `5' in Volkov et al., 2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]). 〈BnonH〉 is the mean value of the equivalent isotropic ADP calculated for non-H atoms. RBT is the rigid-bond-test value (the same as DMSDA, differences in mean-squared displacement amplitudes, in Volkov et al., 2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]). Rwork and Rfree are the standard crystallographic R and Rfree factors between experimental Fobs and model-based calculated structure-factor magnitudes Fmodel (Afonine et al., 2005[Afonine, P. V., Grosse-Kunstleve, R. W. & Adams, P. D. (2005). CCP4 Newsl. 42, contribution 8.]) calculated as [\textstyle \sum_{s}|F_{s}^{\rm obs} - kF_{s}^{\rm model}|/][\textstyle \sum_{s}F_{s}^{\rm obs}].

Data set Model Ndata/Npar Rwork Rfree BnonH〉 (Å2) RBT (104 Å2)
YGG, low resolution IAM 4.9 2.16 17.76
  Mt 6.2 1.22 12.85
  IAM 6.2 2.35 2.62 1.23 18.99
  IAS 4.0 1.57 2.00 1.05 12.23
YGG, high resolution IAM 17.3 4.51 8.77
  Mt 21.9 3.66 7.38
  Mr 10.6§ 3.42 6.38
  IAM 21.9 4.57 4.72 1.04 8.62
  IAS 14.2 3.75 4.06 1.07 7.68
P2A4, low resolution IAM 5.5 2.98 15.64
  Mt 7.1 1.84 7.09
  IAM 7.1 3.51 3.79 1.24 20.77
  IAS 4.5 2.45 3.27 1.07 16.77
P2A4, high resolution IAM 46.7 3.44 3.67
  Mt 61.0 2.67 2.65
  Mr 43.6§ 2.53 3.09
  IAM 61.1 3.72 3.63 1.14 3.66
  IAS 38.1 3.06 3.23 1.14 4.79
Antifreeze protein IAM 18.6 12.77 15.37 7.84 208.4
  IAS 14.3 11.76 14.44 7.40 195.7
Trypsin IAM 7.6 10.30 13.79 5.79 149.3
  IAS 5.8 9.19 13.35 5.52 126.0
Phospholipase IAM 6.0 8.99 12.80 9.88 250.6
  IAS 4.7 8.31 12.64 9.11 213.5
Scorpion toxin IAM 4.9 9.40 15.47 10.30 365.8
  IAS 3.9 8.78 15.23 10.42 363.1
†For multipolar refinement a number of parameters were fixed or linked by constraints. Npar is the number of parameters at each step and does not include the number of parameters refined previously. In contrast to Volkov et al. (2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]), in the current project the ratio Ndata/Npar was calculated for the total number of refined parameters even when at each particular moment only a subset of them were refined; a direct comparison of this information with that reported in Volkov et al. (2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]) is not straightforward.
‡Refined by Volkov et al. (2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]); corresponding numbers are cited from there.
§An estimate obtained if the same set of parameters were used for refinement at `high' resolution.

Fig. 1[link] illustrates the improvement of the difference FobsFcalc maps, reducing the residual peaks to the same level as for multipolar models (compare with Figs. 2 and 3 in Volkov et al., 2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]). Overall, for the whole set of monitoring parameters the results show the comparable quality of the IAM–IAS and multipolar models despite the simplicity of the former.

[Figure 1]
Figure 1
Residual Fourier maps calculated on an absolute scale. IAS are shown as small spheres in magenta (IAS with positive occupancy) and in brown (IAS with negative occupancy). (a, b) Maps at 0.43 Å resolution for YGG. Left and middle, IAM-phased maps; right, IAM–IAS-phased maps. Contour colours are +0.20 e Å−3 (marine), +0.10 e Å−3 (cyan), −0.10 e Å−3 (yellow) and −0.20 e Å−3 (red). Views are similar to those in Figs. 2 and 3 of Volkov et al. (2007[Volkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160-­170.]). (c) Maps at 0.62 Å resolution for the antifreeze protein RD1. Left and middle, IAM-phased maps shown at cutoff levels of 0.40 e Å−3 (green) and 0.25 e Å−3 (light blue); right, IAM–IAS-phased map shown at a cutoff level of 0.25 e Å−3 (light blue). The sulfate ion inserted instead of the previously located water nicely fits the residual density (shown in brown).

Several macromolecular structures were used as another benchmark (Table 1[link]). Previously, refinement at subatomic resolution using multipolar models has been reported for crambin (Fernandez-Serra et al., 2000[Fernandez-Serra, M. V., Junquera, J., Jelsch, C., Lecomte, C. & Artacho, E. (2000). Solid State Commun. 116, 395-400.]; 0.54 Å), trypsin (Schmidt et al., 2003[Schmidt, A., Jelsch, C., Østergaard, P., Rypniewski, W. & Lamzin, V. S. (2003). J. Biol. Chem. 278, 43357-43362.]; 0.80 Å), phospholipase (Liu et al., 2003[Liu, Q., Huang, Q., Teng, M., Weeks, C. M., Jelsch, C., Zhang, R. & Niu, L. (2003). J. Biol. Chem. 278, 41400-41408.]; 0.80 Å; for resolution higher than 0.86 Å the data completeness is below 50%) and scorpion toxin (Housset et al., 2000[Housset, D., Benabicha, F., Pichon-Pesme, V., Jelsch, C., Maierhofer, A., David, S., Fontecilla-Camps, J. C. & Lecomte, C. (2000). Acta Cryst. D56, 151-160.]; 0.96 Å). The corresponding models were extracted from the PDB (Bernstein et al., 1977[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.]; Berman et al., 2000[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.]). Unfortunately, the models available in the PDB did not allow exact reproduction of the results reported, making comparative analysis of the IAS refinement impossible. In particular, this completely excluded the crambin data from our tests. To complete the picture at higher resolution, we additionally performed an IAS refinement of the antifreeze protein RD1 at 0.62 Å (Ko et al., 2003[Ko, T.-P., Robinson, H., Gao, Y.-G., Cheng, C.-H. C., DeVries, A. L. & Wang, A. H.-J. (2003). Biophys. J. 84, 1228-1237.]). Table 2[link] summarizes the results of the refinement of these models. In all cases, the residual maps became much clearer. In particular, this map improvement highlighted the double conformation of the S—S bonds for the phospholipase and trypsin structures, which were otherwise hidden in the noise, and identified two ions previously interpreted as waters (Fig. 1[link]c illustrates this for RD1).

In all cases, the full round of completely automated IAS model building and IAS–IAM refinement, with no manual intervention, took from a few minutes to 1 h on a modern Linux computer. For all protein refinements, completing IAM by IAS decreases the R factors; the Rfree factors are lower for IAS–IAM than for IAM. The RBT value systematically decreases after the introduction of IAS. We observe that the mean ADP slightly increased for the scorpion toxin data, which may indicate that the resolution (0.96 Å) approaches the limit for the use of the IAM–IAS method.

3. Conclusion

Currently, multipolar modelling is the most precise and powerful tool for crystallographic studies at subatomic resolution when the crystals diffract to ultrahigh resolution of about 0.6 Å or higher and the data-to-parameter ratio justifies refinement of the model parameters. At a resolution near 0.8–0.9 Å, which is more common for macromolecular crystals at sub-angstrom resolutions, multipolar modelling typically requires too many parameters to be refined. As an alternative to the multipolar method, IAM–IAS models may be used, where IAM atoms are augmented by small interatomic scatterers. This approach makes model building and refinement a very transparent and easily monitored procedure. The results of automated refinement of such models for both small molecules and macromolecules at subatomic resolution confirm the efficiency of these models both in terms of model quality and CPU resources required. The tests show that these models can be used even at ultrahigh resolution, producing results that are comparable with those obtained with multipolar models.

Acknowledgements

This work was supported in part by the US Department of Energy under Contract No. DE-AC03-76SF00098 and a grant to PDA from NIH/NIGMS (1P01GM063210). VYL was supported by RFBR grants 05-01-22002_CNRS-a and 07-07-00313-A. All results presented are based on the CCI Apps source-code bundle with version tag 2007_08_10_0051. PyMOL (DeLano, 2002[DeLano, W. L. (2002). The PyMOL Molecular Graphics System. DeLano Scientific, San Carlos, CA, USA. https://www.pymol.org .]) was used to present the maps and structures.

References

First citationAdams, P. D., Grosse-Kunstleve, 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
First citationAfonine, P. V., Grosse-Kunstleve, R. W. & Adams, P. D. (2005). CCP4 Newsl. 42, contribution 8.  Google Scholar
First citationAfonine, P. V., Lunin, V. Y., Muzet, N. & Urzhumtsev, A. (2004). Acta Cryst. D60, 260–274.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationAfonine, P. V., Pichon-Pesme, V., Muzet, N., Jelsch, C., Lecomte, C. & Urzhumtsev, A. (2002). CCP4 Newsl. 41, contribution 6.  Google Scholar
First citationBernstein, 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
First citationBerman, 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
First citationBrock, C. P., Dunitz, J. D. & Hirshfeld, F. L. (1991). Acta Cryst. B47, 789–797.  CrossRef CAS Web of Science IUCr Journals Google Scholar
First citationBrünger, A. (1992). Nature (London), 355, 472–475.  PubMed Web of Science Google Scholar
First citationCoppens, P. (1967). Science, 158, 1577–1579.  CSD CrossRef PubMed CAS Web of Science Google Scholar
First citationDauter, Z., Lamzin, V. S. & Wilson, K. S. (1995). Curr. Opin. Struct. Biol. 5, 784–790.  CrossRef CAS PubMed Web of Science Google Scholar
First citationDauter, Z., Lamzin, V. S. & Wilson, K. S. (1997). Curr. Opin. Struct. Biol. 7, 681–688.  CrossRef CAS PubMed Web of Science Google Scholar
First citationDeLano, W. L. (2002). The PyMOL Molecular Graphics System. DeLano Scientific, San Carlos, CA, USA. https://www.pymol.orgGoogle Scholar
First citationDittrich, B., Hübschle, C. B., Messerschmidt, M., Kalinowski, R., Girnt, D. & Luger, P. (2005). Acta Cryst. A61, 314–320.  Web of Science CSD CrossRef CAS IUCr Journals Google Scholar
First citationDunitz, J. D. & Seiler, P. (1973). Acta Cryst. B29, 589–595.  CrossRef CAS IUCr Journals Web of Science Google Scholar
First citationFernandez-Serra, M. V., Junquera, J., Jelsch, C., Lecomte, C. & Artacho, E. (2000). Solid State Commun. 116, 395–400.  Web of Science CrossRef CAS Google Scholar
First citationHansen, N. K. & Coppens, P. (1978). Acta Cryst. A34, 909–921.  CrossRef CAS IUCr Journals Web of Science Google Scholar
First citationHirshfeld, F. L. (1976). Acta Cryst. A32, 239–244.  CrossRef IUCr Journals Web of Science Google Scholar
First citationHousset, D., Benabicha, F., Pichon-Pesme, V., Jelsch, C., Maierhofer, A., David, S., Fontecilla-Camps, J. C. & Lecomte, C. (2000). Acta Cryst. D56, 151–160.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationJelsch, C., Guillot, B., Lagoutte, A. & Lecomte, C. (2005). J. Appl. Cryst. 38, 38–54.  Web of Science CrossRef IUCr Journals Google Scholar
First citationJelsch, C., Pichon-Pesme, V., Lecomte, C. & Aubry, A. (1998). Acta Cryst. D54, 1306–1318.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationJelsch, C., Teeter, M. M., Lamzin, V. S., Pichon-Pesme, V., Blessing, R. H. & Lecomte, C. (2000). Proc. Natl Acad. Sci. USA, 97, 31731–3176.  Web of Science CrossRef Google Scholar
First citationKo, T.-P., Robinson, H., Gao, Y.-G., Cheng, C.-H. C., DeVries, A. L. & Wang, A. H.-J. (2003). Biophys. J. 84, 1228–1237.  CrossRef PubMed CAS Google Scholar
First citationLiu, Q., Huang, Q., Teng, M., Weeks, C. M., Jelsch, C., Zhang, R. & Niu, L. (2003). J. Biol. Chem. 278, 41400–41408.  Web of Science CrossRef PubMed CAS Google Scholar
First citationLunin, V. Y., Afonine, P. V. & Urzhumtsev, A. G. (2002). Acta Cryst. A58, 270–­282.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationPetrova, T., Ginell, S., Mitschler, A., Hazemann, I., Schneider, T., Cousido, A., Lunin, V. Y., Joachimiak, A. & Podjarny, A. (2006). Acta Cryst. D62, 1535–1544.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationPetrova, T. E. & Podjarny, A. D. (2004). Rep. Prog. Phys. 67, 1565–1605.  Web of Science CrossRef CAS Google Scholar
First citationPichon-Pesme, V., Lecomte, C. & Lachekar, H. (1995). J. Phys. Chem. 99, 6242–6250.  CrossRef CAS Web of Science Google Scholar
First citationSchmidt, A., Jelsch, C., Østergaard, P., Rypniewski, W. & Lamzin, V. S. (2003). J. Biol. Chem. 278, 43357–43362.  Web of Science CrossRef PubMed CAS Google Scholar
First citationVolkov, A., Messerschmidt, M. & Coppens, P. (2007). Acta Cryst. D63, 160–­170.  Web of Science CrossRef CAS IUCr Journals Google Scholar
First citationVrielink, A. & Sampson, N. (2003). Curr. Opin. Struct. Biol. 13, 709–715.  Web of Science CrossRef PubMed CAS Google Scholar
First citationZarychta, B., Pichon-Pesme, V., Guillot, B., Lecomte, C. & Jelsch, C. (2007). Acta Cryst. A63, 108–125.  Web of Science CrossRef CAS IUCr Journals Google Scholar

This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.

Journal logoBIOLOGICAL
CRYSTALLOGRAPHY
ISSN: 1399-0047
Volume 63| Part 11| November 2007| Pages 1194-1197
Follow Acta Cryst. D
Sign up for e-alerts
Follow Acta Cryst. on Twitter
Follow us on facebook
Sign up for RSS feeds