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Michael G. Rossmann - One of the best experts on this subject based on the ideXlab platform.
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International Tables for Crystallography - Patterson and Molecular‐Replacement techniques
International Tables for Crystallography, 2006Co-Authors: Michael G. Rossmann, Edward ArnoldAbstract:The Patterson function is a phaseless Fourier synthesis of diffraction intensities that corresponds to an autocorrelation of electron densities in a crystal cell. Prominent non-origin peaks in a Patterson function represent interatomic vectors; deconvolution of this information can be used to locate heavy atoms, known structures or structural fragments. Interpretation of Patterson maps lies at the foundation of most macroMolecular structure elucidation processes, both in determining the position of heavy atoms and/or anomalous scatterers for the isomorphous Replacement and anomalous scattering methods, and in determining the orientation and position of a homologous protein model for the Molecular-Replacement method. The Molecular-Replacement method also encompasses the use of noncrystallographic redundancy within a crystal or between crystal forms to phase and refine crystal structures. Applications of Patterson and Molecular-Replacement techniques to structure determination including Patterson interpretation methods, rotation functions, translation functions, symmetry averaging, density modification and phase extension are discussed.
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Molecular Replacement--historical background.
Acta Crystallographica Section D Biological Crystallography, 2001Co-Authors: Michael G. RossmannAbstract:A review is given of the mathematical procedures required for a Molecular-Replacement structure determination. These apply equally to the more frequently encountered situations where a known homologous structure can be used as a search model and to phase determination in the presence of non-crystallographic symmetry (NCS). In general, the former represents improper NCS between two different unit cells, whereas the latter occurs when there is proper NCS within one unit cell.
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Reciprocal-space Molecular-Replacement averaging.
Acta Crystallographica Section D Biological Crystallography, 1995Co-Authors: Liang Tong, Michael G. RossmannAbstract:The Molecular-Replacement equations, in which electron-density averaging and skew averaging have been unified, were used in reciprocal space to refine and extend the resolution of phased reflections. A procedure has been developed for the treatment of Molecular envelopes of general shape. The equations were successfully applied to the reflection data of bacteriophage phiX174 (60-fold redundancy). Truncation of the G diffraction function beyond the first few nodes did not have a significant effect on the quality of the Molecular-Replacement equations. Reciprocal-space Molecular-Replacement averaging should prove to be a useful alternative to real-space averaging. Strategies are discussed that are possible only in reciprocal space.
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The structure determination of Sindbis virus core protein using isomorphous Replacement and Molecular Replacement averaging between two crystal forms.
Acta Crystallographica Section A Foundations of Crystallography, 1992Co-Authors: Liang Tong, Hok-kin Choi, Wladek Minor, Michael G. RossmannAbstract:The structure of Sindbis virus core protein has been determined by a combination of multiple isomorphous Replacement and Molecular Replacement averaging techniques. The multiple isomorphous Replacement phase determinations were made for two crystal forms (P21 and P432~2 ) of the core protein. The real-space Molecular Replacement averaging was subsequently carded out between two copies of the protein per asymmetric unit in the monoclinic form and one copy in the tetragonal form. This greatly improved the quality of the electron density maps. The Sindbis virus core protein polypeptide could be
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The structure determination of Sindbis virus core protein using isomorphous Replacement and Molecular Replacement averaging between two crystal forms.
Acta crystallographica. Section A Foundations of crystallography, 1992Co-Authors: Liang Tong, Hok-kin Choi, Wladek Minor, Michael G. RossmannAbstract:The structure of Sindbis virus core protein has been determined by a combination of multiple isomorphous Replacement and Molecular Replacement averaging techniques. The multiple isomorphous Replacement phase determinations were made for two crystal forms (P2(1) and P4(3)2(1)2) of the core protein. The real-space Molecular Replacement averaging was subsequently carried out between two copies of the protein per asymmetric unit in the monoclinic form and one copy in the tetragonal form. This greatly improved the quality of the electron density maps. The Sindbis virus core protein polypeptide could be traced and related to the known amino acid sequence. The averaging procedure between different crystal forms, as described in this paper, should be generally applicable to other systems.
Liang Tong - One of the best experts on this subject based on the ideXlab platform.
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Combined Molecular Replacement
Acta Crystallographica Section A Foundations of Crystallography, 1996Co-Authors: Liang TongAbstract:Current Molecular-Replacement methods assume that the correct rotations to be applied to a search atomic model are close to peaks in the rotation function. In addition, generally only the top peaks in the rotation function are examined by the translation function. For difficult structures and for high-symmetry space groups, this assumption may no longer hold true. The more powerful approach is to examine not only the peaks but also other angles that have reasonable values in the rotation function to look for the Molecular-Replacement solutions. The combined Molecular-Replacement protocol is therefore a limited six-dimensional search, where the sampling of the rotational degrees of freedom is restricted by the rotation function. A packing check is used to eliminate solutions that cause steric clashes of the search atomic model in the crystal. Several new structures have been determined with this protocol.
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Reciprocal-space Molecular-Replacement averaging.
Acta Crystallographica Section D Biological Crystallography, 1995Co-Authors: Liang Tong, Michael G. RossmannAbstract:The Molecular-Replacement equations, in which electron-density averaging and skew averaging have been unified, were used in reciprocal space to refine and extend the resolution of phased reflections. A procedure has been developed for the treatment of Molecular envelopes of general shape. The equations were successfully applied to the reflection data of bacteriophage phiX174 (60-fold redundancy). Truncation of the G diffraction function beyond the first few nodes did not have a significant effect on the quality of the Molecular-Replacement equations. Reciprocal-space Molecular-Replacement averaging should prove to be a useful alternative to real-space averaging. Strategies are discussed that are possible only in reciprocal space.
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The structure determination of Sindbis virus core protein using isomorphous Replacement and Molecular Replacement averaging between two crystal forms.
Acta Crystallographica Section A Foundations of Crystallography, 1992Co-Authors: Liang Tong, Hok-kin Choi, Wladek Minor, Michael G. RossmannAbstract:The structure of Sindbis virus core protein has been determined by a combination of multiple isomorphous Replacement and Molecular Replacement averaging techniques. The multiple isomorphous Replacement phase determinations were made for two crystal forms (P21 and P432~2 ) of the core protein. The real-space Molecular Replacement averaging was subsequently carded out between two copies of the protein per asymmetric unit in the monoclinic form and one copy in the tetragonal form. This greatly improved the quality of the electron density maps. The Sindbis virus core protein polypeptide could be
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The structure determination of Sindbis virus core protein using isomorphous Replacement and Molecular Replacement averaging between two crystal forms.
Acta crystallographica. Section A Foundations of crystallography, 1992Co-Authors: Liang Tong, Hok-kin Choi, Wladek Minor, Michael G. RossmannAbstract:The structure of Sindbis virus core protein has been determined by a combination of multiple isomorphous Replacement and Molecular Replacement averaging techniques. The multiple isomorphous Replacement phase determinations were made for two crystal forms (P2(1) and P4(3)2(1)2) of the core protein. The real-space Molecular Replacement averaging was subsequently carried out between two copies of the protein per asymmetric unit in the monoclinic form and one copy in the tetragonal form. This greatly improved the quality of the electron density maps. The Sindbis virus core protein polypeptide could be traced and related to the known amino acid sequence. The averaging procedure between different crystal forms, as described in this paper, should be generally applicable to other systems.
Randy J. Read - One of the best experts on this subject based on the ideXlab platform.
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Factors influencing estimates of coordinate error for Molecular Replacement.
Acta Crystallographica Section D Structural Biology, 2020Co-Authors: Kaushik Hatti, Robert D. Oeffner, Airlie J. Mccoy, Sammito, Randy J. ReadAbstract:Good prior estimates of the effective root-mean-square deviation (r.m.s.d.) between the atomic coordinates of the model and the target optimize the signal in Molecular Replacement, thereby increasing the success rate in difficult cases. Previous studies using protein structures solved by X-ray crystallography as models showed that optimal error estimates (refined after structure solution) were correlated with the sequence identity between the model and target, and with the number of residues in the model. Here, this work has been extended to find additional correlations between parameters of the model and the target and hence improved prior estimates of the coordinate error. Using a graph database, a curated set of 6030 Molecular-Replacement calculations using models that had been solved by X-ray crystallography was analysed to consider about 120 model and target parameters. Improved estimates were achieved by replacing the sequence identity with the Gonnet score for sequence similarity, as well as by considering the resolution of the target structure and the MolProbity score of the model. This approach was extended by analysing 12 610 additional Molecular-Replacement calculations where the model was determined by NMR. The median r.m.s.d. between pairs of models in an ensemble was found to be correlated with the estimated r.m.s.d. to the target. For models solved by NMR, the overall coordinate error estimates were larger than for structures determined by X-ray crystallography, and were more highly correlated with the number of residues.
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coping with strong translational noncrystallographic symmetry and extreme anisotropy in Molecular Replacement with phaser human rab27a
Acta Crystallographica Section D Structural Biology, 2019Co-Authors: Mostafa Jamshidiha, Inmaculada Perezdorado, James W Murray, Edward W Tate, Ernesto Cota, Randy J. ReadAbstract:Data pathologies caused by effects such as diffraction anisotropy and translational noncrystallographic symmetry (tNCS) can dramatically complicate the solution of the crystal structures of macromolecules. Such problems were encountered in determining the structure of a mutant form of Rab27a, a member of the Rab GTPases. Mutant Rab27a constructs that crystallize in the free form were designed for use in the discovery of drugs to reduce primary tumour invasiveness and metastasis. One construct, hRab27aMut, crystallized within 24 h and diffracted to 2.82 A resolution, with a unit cell possessing room for a large number of protein copies. Initial efforts to solve the structure using Molecular Replacement by Phaser were not successful. Analysis of the data set revealed that the crystals suffered from both extreme anisotropy and strong tNCS. As a result, large numbers of reflections had estimated standard deviations that were much larger than their measured intensities and their expected intensities, revealing problems with the use of such data at the time in Phaser. By eliminating extremely weak reflections with the largest combined effects of anisotropy and tNCS, these problems could be avoided, allowing a Molecular-Replacement solution to be found. The lessons that were learned in solving this structure have guided improvements in the numerical analysis used in Phaser, particularly in identifying diffraction measurements that convey very little information content. The calculation of information content could also be applied as an alternative to ellipsoidal truncation. The post-mortem analysis also revealed an oversight in accounting for measurement errors in the fast rotation function. While the crystal of mutant Rab27a is not amenable to drug screening, the structure can guide new modifications to obtain more suitable crystal forms.
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On the application of the expected log-likelihood gain to decision making in Molecular Replacement.
Acta crystallographica. Section D Structural biology, 2018Co-Authors: Robert D. Oeffner, Pavel V Afonine, Randy J. Read, Claudia Millán, Massimo Sammito, Isabel Usón, Airlie J. MccoyAbstract:Molecular-Replacement phasing of macroMolecular crystal structures is often fast, but if a Molecular-Replacement solution is not immediately obtained the crystallographer must judge whether to pursue Molecular Replacement or to attempt experimental phasing as the quickest path to structure solution. The introduction of the expected log-likelihood gain [eLLG; McCoy et al. (2017), Proc. Natl Acad. Sci. USA, 114, 3637-3641] has given the crystallographer a powerful new tool to aid in making this decision. The eLLG is the log-likelihood gain on intensity [LLGI; Read & McCoy (2016), Acta Cryst. D72, 375-387] expected from a correctly placed model. It is calculated as a sum over the reflections of a function dependent on the fraction of the scattering for which the model accounts, the estimated model coordinate error and the measurement errors in the data. It is shown how the eLLG may be used to answer the question `can I solve my structure by Molecular Replacement?'. However, this is only the most obvious of the applications of the eLLG. It is also discussed how the eLLG may be used to determine the search order and minimal data requirements for obtaining a Molecular-Replacement solution using a given model, and for decision making in fragment-based Molecular Replacement, single-atom Molecular Replacement and likelihood-guided model pruning.
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X-ray structure determination using low-resolution electron microscopy maps for Molecular Replacement
Nature Protocols, 2015Co-Authors: Ryan N Jackson, Randy J. Read, Airlie J. Mccoy, Thomas C. Terwilliger, Blake WiedenheftAbstract:Structures of multisubunit macroMolecular machines are primarily determined either by electron microscopy (EM) or by X-ray crystallography. In many cases, a structure for a complex can be obtained at low resolution (at a coarse level of detail) with EM and at a higher resolution (with finer detail) by X-ray crystallography. The integration of these two structural techniques is becoming increasingly important for the generation of atomic models of macroMolecular complexes. A low-resolution EM image can be a powerful tool for obtaining the 'phase' information that is missing from an X-ray crystallography experiment; however, integration of EM and X-ray diffraction data has been technically challenging. Here we present a step-by-step protocol that explains how low-resolution EM maps can be placed in the crystallographic unit cell by Molecular Replacement, and how initial phases computed from the placed EM density are extended to high resolution by averaging maps over noncrystallographic symmetry. As the resolution gap between EM and X-ray crystallography continues to narrow, the use of EM maps to help with X-ray crystal structure determination, as described in this protocol, will become increasingly effective. Molecular Replacement is often used to solve the “phase problem” in X-ray crystallography. This protocol explains how low-resolution maps generated using electron microscopy can be used for the Molecular Replacement step in solving X-ray structures.
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Local Error Estimates Dramatically Improve the Utility of Homology Models for Solving Crystal Structures by Molecular Replacement
Structure (London England : 1993), 2015Co-Authors: Gabor Bunkoczi, Björn Wallner, Randy J. ReadAbstract:Predicted structures submitted for CASP10 have been evaluated as Molecular Replacement models against the corresponding sets of structure factor amplitudes. It has been found that the log-likelihood gain score computed for each prediction correlates well with common structure quality indicators but is more sensitive when the accuracy of the models is high. In addition, it was observed that using coordinate error estimates submitted by predictors to weight the model can improve its utility in Molecular Replacement dramatically, and several groups have been identified who reliably provide accurate error estimates that could be used to extend the application of Molecular Replacement for low-homology cases.
Airlie J. Mccoy - One of the best experts on this subject based on the ideXlab platform.
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Factors influencing estimates of coordinate error for Molecular Replacement.
Acta Crystallographica Section D Structural Biology, 2020Co-Authors: Kaushik Hatti, Robert D. Oeffner, Airlie J. Mccoy, Sammito, Randy J. ReadAbstract:Good prior estimates of the effective root-mean-square deviation (r.m.s.d.) between the atomic coordinates of the model and the target optimize the signal in Molecular Replacement, thereby increasing the success rate in difficult cases. Previous studies using protein structures solved by X-ray crystallography as models showed that optimal error estimates (refined after structure solution) were correlated with the sequence identity between the model and target, and with the number of residues in the model. Here, this work has been extended to find additional correlations between parameters of the model and the target and hence improved prior estimates of the coordinate error. Using a graph database, a curated set of 6030 Molecular-Replacement calculations using models that had been solved by X-ray crystallography was analysed to consider about 120 model and target parameters. Improved estimates were achieved by replacing the sequence identity with the Gonnet score for sequence similarity, as well as by considering the resolution of the target structure and the MolProbity score of the model. This approach was extended by analysing 12 610 additional Molecular-Replacement calculations where the model was determined by NMR. The median r.m.s.d. between pairs of models in an ensemble was found to be correlated with the estimated r.m.s.d. to the target. For models solved by NMR, the overall coordinate error estimates were larger than for structures determined by X-ray crystallography, and were more highly correlated with the number of residues.
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On the application of the expected log-likelihood gain to decision making in Molecular Replacement.
Acta crystallographica. Section D Structural biology, 2018Co-Authors: Robert D. Oeffner, Pavel V Afonine, Randy J. Read, Claudia Millán, Massimo Sammito, Isabel Usón, Airlie J. MccoyAbstract:Molecular-Replacement phasing of macroMolecular crystal structures is often fast, but if a Molecular-Replacement solution is not immediately obtained the crystallographer must judge whether to pursue Molecular Replacement or to attempt experimental phasing as the quickest path to structure solution. The introduction of the expected log-likelihood gain [eLLG; McCoy et al. (2017), Proc. Natl Acad. Sci. USA, 114, 3637-3641] has given the crystallographer a powerful new tool to aid in making this decision. The eLLG is the log-likelihood gain on intensity [LLGI; Read & McCoy (2016), Acta Cryst. D72, 375-387] expected from a correctly placed model. It is calculated as a sum over the reflections of a function dependent on the fraction of the scattering for which the model accounts, the estimated model coordinate error and the measurement errors in the data. It is shown how the eLLG may be used to answer the question `can I solve my structure by Molecular Replacement?'. However, this is only the most obvious of the applications of the eLLG. It is also discussed how the eLLG may be used to determine the search order and minimal data requirements for obtaining a Molecular-Replacement solution using a given model, and for decision making in fragment-based Molecular Replacement, single-atom Molecular Replacement and likelihood-guided model pruning.
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Acknowledging Errors: Advanced Molecular Replacement with Phaser
Methods in molecular biology (Clifton N.J.), 2017Co-Authors: Airlie J. MccoyAbstract:Molecular Replacement is a method for solving the crystallographic phase problem using an atomic model for the target structure. State-of-the-art methods have moved the field significantly from when it was first envisaged as a method for solving cases of high homology and completeness between a model and target structure. Improvements brought about by application of maximum likelihood statistics mean that various errors in the model and pathologies in the data can be accounted for, so that cases hitherto thought to be intractable are standardly solvable. As a result, Molecular Replacement phasing now accounts for the lion's share of structures deposited in the Protein Data Bank. However, there will always be cases at the fringes of solvability. I discuss here the approaches that will help tackle challenging Molecular Replacement cases.
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X-ray structure determination using low-resolution electron microscopy maps for Molecular Replacement
Nature Protocols, 2015Co-Authors: Ryan N Jackson, Randy J. Read, Airlie J. Mccoy, Thomas C. Terwilliger, Blake WiedenheftAbstract:Structures of multisubunit macroMolecular machines are primarily determined either by electron microscopy (EM) or by X-ray crystallography. In many cases, a structure for a complex can be obtained at low resolution (at a coarse level of detail) with EM and at a higher resolution (with finer detail) by X-ray crystallography. The integration of these two structural techniques is becoming increasingly important for the generation of atomic models of macroMolecular complexes. A low-resolution EM image can be a powerful tool for obtaining the 'phase' information that is missing from an X-ray crystallography experiment; however, integration of EM and X-ray diffraction data has been technically challenging. Here we present a step-by-step protocol that explains how low-resolution EM maps can be placed in the crystallographic unit cell by Molecular Replacement, and how initial phases computed from the placed EM density are extended to high resolution by averaging maps over noncrystallographic symmetry. As the resolution gap between EM and X-ray crystallography continues to narrow, the use of EM maps to help with X-ray crystal structure determination, as described in this protocol, will become increasingly effective. Molecular Replacement is often used to solve the “phase problem” in X-ray crystallography. This protocol explains how low-resolution maps generated using electron microscopy can be used for the Molecular Replacement step in solving X-ray structures.
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sceds protein fragments for Molecular Replacement in phaser
Acta Crystallographica Section D-biological Crystallography, 2013Co-Authors: Airlie J. Mccoy, Robert A Nicholls, Thomas R SchneiderAbstract:A method is described for generating protein fragments suitable for use as Molecular-Replacement (MR) template models. The template model for a protein suspected to undergo a conformational change is perturbed along combinations of low-frequency normal modes of the elastic network model. The unperturbed structure is then compared with each perturbed structure in turn and the structurally invariant regions are identified by analysing the difference distance matrix. These fragments are scored with SCEDS, which is a combined measure of the sphericity of the fragments, the continuity of the fragments with respect to the polypeptide chain, the equality in number of atoms in the fragments and the density of Cα atoms in the triaxial ellipsoid of the fragment extents. The fragment divisions with the highest SCEDS are then used as separate template models for MR. Test cases show that where the protein contains fragments that undergo a change in juxtaposition between template model and target, SCEDS can identify fragments that lead to a lower R factor after ten cycles of all-atom refinement with REFMAC5 than the original template structure. The method has been implemented in the software Phaser.
Hok-kin Choi - One of the best experts on this subject based on the ideXlab platform.
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The structure determination of Sindbis virus core protein using isomorphous Replacement and Molecular Replacement averaging between two crystal forms.
Acta Crystallographica Section A Foundations of Crystallography, 1992Co-Authors: Liang Tong, Hok-kin Choi, Wladek Minor, Michael G. RossmannAbstract:The structure of Sindbis virus core protein has been determined by a combination of multiple isomorphous Replacement and Molecular Replacement averaging techniques. The multiple isomorphous Replacement phase determinations were made for two crystal forms (P21 and P432~2 ) of the core protein. The real-space Molecular Replacement averaging was subsequently carded out between two copies of the protein per asymmetric unit in the monoclinic form and one copy in the tetragonal form. This greatly improved the quality of the electron density maps. The Sindbis virus core protein polypeptide could be
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The structure determination of Sindbis virus core protein using isomorphous Replacement and Molecular Replacement averaging between two crystal forms.
Acta crystallographica. Section A Foundations of crystallography, 1992Co-Authors: Liang Tong, Hok-kin Choi, Wladek Minor, Michael G. RossmannAbstract:The structure of Sindbis virus core protein has been determined by a combination of multiple isomorphous Replacement and Molecular Replacement averaging techniques. The multiple isomorphous Replacement phase determinations were made for two crystal forms (P2(1) and P4(3)2(1)2) of the core protein. The real-space Molecular Replacement averaging was subsequently carried out between two copies of the protein per asymmetric unit in the monoclinic form and one copy in the tetragonal form. This greatly improved the quality of the electron density maps. The Sindbis virus core protein polypeptide could be traced and related to the known amino acid sequence. The averaging procedure between different crystal forms, as described in this paper, should be generally applicable to other systems.