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Copyright © International Union of Crystallography 2008
AMoRe: classical and modern Correspondence e-mail: stefano.trapani/at/cbs.cnrs.fr ConferenceMolecular replacement Received February 16, 2007; Accepted September 11, 2007. This is an open-access article distributed under the terms described at http://journals.iucr.org/services/termsofuse.html. | |||||||||||||||||||||||||||
Abstract An account is given of the latest developments of the AMoRe package: new rotational search algorithms, exploitation of noncrystallographic symmetry, generation and use of ensemble models and interactive graphical molecular replacement. Keywords: AMoRe, molecular replacement | |||||||||||||||||||||||||||
In this paper, we give an account of the latest developments of the AMoRe package. The newly introduced features follow the general guidelines that determined the success of the AMoRe molecular-replacement (MR) strategy (Navaza, 1994
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The rotation function Methods for an optimal and rapid sampling of the rotation function have long been an object of study (for a review, see Navaza, 2001 A natural way of representing the rotation function is to expand it in terms of the complete set of Wigner functions, i.e. the elements of the rotation-group irreducible-representation matrices
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![]() ![]() ![]() 2.1. Three-dimensional FFT sampling of the rotation function (4) requires the evaluation of the reduced Wigner functions ![]() ![]() ![]()
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![]() ![]() ![]() According to Navaza (1993 2.2. Metric based FFT sampling of the rotation function The Wigner expansion in (1) and the Fourier expansion in (6) are of quite general validity for functions defined on the domain of rotations, although they were obtained for the specific case of the Patterson-overlap rotation function. The summation limit ![]() ![]() ![]() ![]() The choice of a suitable set of samples for the rotation function is a nontrivial issue if the actual distance between sampling points is to be taken into account. Since the metric of the rotation group, independent of its parametrization, cannot be reduced to a Euclidean metric, FFT sampling based on (6) will result in an unevenly distributed set of points in the rotation domain. The problem can be partially solved in two-dimensional β-sections, where the rotation metric becomes equivalent to a Euclidean metric (Burdina, 1971
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It seems physically reasonable to assume that if a sample spacing Δ (as defined above) permits the recovery of one β-section from its samples, then the same sample spacing should also be applicable to any other β-section. Δ would then represent the angular resolution of the rotation function. Under this hypothesis, however, the number of Fourier coefficients of a β-section should vary according to sinβ, while, after (3) and (4), the number of S
m,m′ coefficients is dictated uniquely by the value of
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If in (3) we limit the summation to those indices that satisfy inequality (10), then one can sample the rotation function on economic grids with sinβ fewer points than in the classical Crowther’s development, while still computing it by FFT techniques, and recover distortion-free sections, which facilitates peak-searching procedures. In Fig. 1 | |||||||||||||||||||||||||||
When several copies of the same molecule are present in the asymmetric unit, each molecule can in principle be superimposed on another of the same type by a rigid-body movement, although the structural correspondence between the two molecules may not be exact owing to the different crystalline environments. This movement is not an element of the crystal symmetry space group; it defines a noncrystallographic symmetry operation (see Rossmann, 1990 The knowledge of the NCS operations can be exploited to help the MR search when the standard procedures fail.
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The number of protein structures available from the PDB has grown to a point where many of the known protein folds are currently over-represented. As a consequence, it is often possible to find families of homologues that are potentially exploitable as probes for a given MR problem. In these cases, the logical choice of a model must clearly favour a very closely related molecule, if one is available. On the other hand, it may be necessary to test several trial models when only medium/low-similarity homologues are available. Accumulated experience shows that even if structural homology is certain, models are likely to fail if similarity is not high enough. When the MR search using each member of a whole family of structures fails, it may be worthwhile to combine information from all available models in order to take into account structural variability within the family and thus improve the effectiveness of the model. Hybrid models can be built up on the basis of structure and sequence alignments. Their use has indeed led to positive results in some difficult MR cases. The outcome, however, depends highly on the quality of the alignment employed for model construction (Schwarzenbacher et al., 2004 As an alternative to hybrid models, one can treat a whole ensemble of superposed homologous structures as an MR probe. In this way, regions of structural variability/flexibility are implicitly weighted within the model itself. This type of model closely resembles NMR-based models, whose usability as MR probes has previously been examined (Chen, 2001 In a recent study (the results of which are briefly summarized in Table 1
In order to superpose molecular structures and thus generate ensembles, it is common practice to use algorithms which optimize a certain set of interatomic distances. In the work described above, we used a different approach based on the maximization of the electron-density correlation (EDC). By expressing the EDC in terms of the molecular Fourier transforms, the superposition problem can be straightforwardly reduced to an MR-like problem. Exploiting the existing AMoRe procedures, an automatic EDC-based model-superposition utility, SUPER, has been developed and is now available as part of the software package. A somewhat related technique has been implemented in MOLREP (Vagin & Isupov, 2001
According to our experience, ensemble-based MR searches have the potential to combine and exploit the richness of structural information in the PDB in a relatively easy though effective way. EDC-based ensembles of structures should be considered by developers of databases for automatic structure-solution pipelines as a valuable alternative to homology-based representative models. | |||||||||||||||||||||||||||
A molecular-graphics interface has been developed to assist the AMoRe user in the interpretation and interactive manipulation of the MR search results. The program permits the following.
A foreseen use of the program, in addition to facilitating crystal-packing analysis, is for the specific cases in which one wants to position small-size components of molecular complexes, especially when there is some prior knowledge of the regions of interaction between the components. | |||||||||||||||||||||||||||
Acknowledgments We acknowledge Alberto Podjarny for kindly providing the Fab Q11 B13 crystal structure factors. | |||||||||||||||||||||||||||
References
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