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Dritan Siliqi - One of the best experts on this subject based on the ideXlab platform.
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The method of joint probability distribution functions applied to MAD techniques. The two-wavelength case for acentric crystals.
Acta Crystallographica Section A Foundations of Crystallography, 2001Co-Authors: Carmelo Giacovazzo, Dritan SiliqiAbstract:MAD (multiple-wavelength anomalous dispersion) techniques are often considered as a special MIR (multiple Isomorphous Replacement) case. The rigorous method of the joint probability distribution functions is applied to solve the phase problem for acentric crystals, on the assumption that the anomalous scatterer's substructure is a priori known. The two-wavelength case is considered: errors in measurements and in the model substructure are handled. The probabilistic approach provides a very simple and efficient formula for estimating structure-factor phases.
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The method of joint probability distribution functions applied to MAD techniques. The centric case.
Acta Crystallographica Section A Foundations of Crystallography, 2001Co-Authors: Carmelo Giacovazzo, Dritan SiliqiAbstract:Traditional probabilistic approaches consider MAD (multiple-wavelength anomalous-dispersion) data as a special MIR (multiple Isomorphous Replacement) case. The rigorous method of the joint probability distribution functions has been applied to solve the phase problem, with the assumption that the anomalous scatterers' substructure is a priori known. The probabilistic approach is able to handle measurement errors: it has been applied to symmetry-restricted phases and provides simple and efficient formulas.
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on integrating direct methods and Isomorphous Replacement techniques the formula p10
Acta Crystallographica Section A, 1997Co-Authors: C Giacovazzo, Dritan Siliqi, G Cascarano, Rocco Caliandro, A MelidoroAbstract:The joint probability distribution of ten pairs of Isomorphous structure factors has been derived. Their indices correspond to the reflections contained in the second phasing shell of the triplet invariant, as described by the theory of representations [Giacovazzo (1977). Acta Cryst. A33, 934–944; Giacovazzo (1980). Acta Cryst. A36, 362–373]. The conclusive formula allows the estimation of triplet invariants via a second representation formula, called the P10 formula, which is more accurate than the traditional formula of Giacovazzo, Cascarano & Zheng [Acta Cryst. (1988), A44, 45–51]. The procedure is also able to take into consideration the prior information on the heavy-atom structure, when available.
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on integrating direct methods and Isomorphous Replacement techniques ii the quartet invariant estimate
Acta Crystallographica Section A, 1996Co-Authors: Carmelo Giacovazzo, Dritan SiliqiAbstract:In a preceding paper [Giacovazzo & Siliqi (1996). Acta Cryst. A52, 133-142], the joint probability distribution of seven pairs of Isomorphous structure factors was derived. Its complicated mathematical expressions are here simplified by introducing the assumption that isomorphism is due to heavy-atom addition to the native structure. The reliability of the conclusive formula for calculated error-free data perfectly agrees with expectations. The formula, however, is not robust against lack of isomorphism and errors in measurements: in the paper, theoretical reasons are given justifying this behaviour. The use of the prior information on the heavy-atom structure markedly improves the formula, which then proves suitable for practical applications.
H F Fan - One of the best experts on this subject based on the ideXlab platform.
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serial crystallographic analysis of protein Isomorphous Replacement data from a mixture of native and derivative microcrystals
Acta Crystallographica Section D-biological Crystallography, 2015Co-Authors: Tao Zhang, Deqiang Yao, Jiawei Wang, H F FanAbstract:A post-experimental identification/purification procedure similar to that described in Zhang et al. [(2015), IUCrJ, 2, 322-326] has been proposed for use in the treatment of multiphase protein serial crystallography (SX) diffraction snapshots. As a proof of concept, the procedure was tested using theoretical serial femtosecond crystallography (SFX) data from a mixture containing native and derivatized crystals of a protein. Two known proteins were taken as examples. Multiphase diffraction snapshots were subjected to two rounds of indexing using the program CrystFEL [White et al. (2012). J. Appl. Cryst. 45, 335-341]. In the first round, an ab initio indexing was performed to derive a set of approximate primitive unit-cell parameters, which are roughly the average of those from the native protein and the derivative. These parameters were then used in a second round of indexing as input to CrystFEL. The results were then used to separate the diffraction snapshots into two subsets corresponding to the native and the derivative. For each test sample, integration of the two subsets of snapshots separately led to two sets of three-dimensional diffraction intensities, one belonging to the native and the other to the derivative. Based on these two sets of intensities, a conventional single Isomorphous Replacement (SIR) procedure solved the structure easily.
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oasis a computer program for breaking phase ambiguity in one wavelength anomalous scattering or single Isomorphous substitution Replacement data
Journal of Applied Crystallography, 2000Co-Authors: Quan Hao, C D Zheng, H F FanAbstract:The phase problem is reduced to a sign problem once the anomalous-scatterer or the replacing-heavy-atom sites are located. OASIS adopts the CCP4 format [Collaborative Computational Project, Number 4 (1994). Acta Cryst. D50, 760–763]. It applies a direct-method procedure to break the phase ambiguity intrinsic to one-wavelength anomalous scattering (OAS) or single Isomorphous Replacement (SIR) data.
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combining direct methods with Isomorphous Replacement or anomalous scattering data viii phasing experimental sir data with the replacing atoms in a centrosymmetric arrangement
Acta Crystallographica Section D-biological Crystallography, 1999Co-Authors: Yudong Liu, Quan Hao, C D Zheng, H F FanAbstract:A multisolution direct method has been proposed to resolve the phase ambiguity intrinsic in single Isomorphous Replacement data of proteins with the replacing atoms in a centrosymmetric arrangement. The phase ambiguity of each reflection is in fact a `sign ambiguity' of the phase difference between the phase of the native protein and that of the replacing atoms, i.e. ± |Δφ| = φ − φ′. The P+ probability formula can be used to derive the signs. The multisolution phasing procedure is initiated using random starting values of P+. A cluster analysis is used instead of figures of merit to find the correct solution. The direct-method phases can be further improved by density-modification techniques. The method was tested with the experimental SIR data at 2 A resolution from a known protein aPP; satisfactory results were obtained.
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applications of direct methods with single Isomorphous Replacement or one wavelength anomalous scattering data
1998Co-Authors: H F Fan, Quan Hao, I Harvey, Samar S Hasnain, Y D Liu, C D ZhengAbstract:Recent developments of our study have been concentrated on the following topics: 1) the accuracy of our Cochran-distribution-based probability formula: it has been shown that the results of the formula are much more accurate than what people would usually predict; 2) an iterative procedure of combining direct methods with the solvent flattening technique: test on the experimental single Isomorphous Replacement (SIR) data of the known protein RNase Sa showed considerable improvement to the previous procedure; 3) direct-method phasing of the one-wavelength anomalous scattering (OAS) data of an unknown protein: the result leads to a traceable Fourier map and thus to the solution of the structure.
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use of single Isomorphous Replacement data of proteins resolving the phase ambiguity and a new procedure for phase extension
Acta Crystallographica Section D-biological Crystallography, 1997Co-Authors: X F Zheng, H F Fan, C D Zheng, Quan HaoAbstract:A procedure combining direct methods and solvent flattening to break the phase ambiguity intrinsic to the single Isomorphous Replacement (SIR) technique has been tested with the experimental SIR data of the known protein RNase Sa at 2.5 A resolution. The use of direct methods provided better initial phases for the solvent-flattening procedure, while the solvent-flattening procedure greatly improved direct-method phases leading to a traceable Fourier map. A small subset of known phases at low resolution makes direct phasing of SIR data much easier. Accordingly a method for extending low-resolution phases to high-resolution ones is proposed making use of additional SIR information. This reduces the problem of finding a value in the range of 0–2π for each unknown phase to that of just making a choice between two possible values. Tests with the known protein RNase Sa showed that the method is able to extend phases from a resolution of 6 to 2.5 A leading to an easily traceable Fourier map. The solvent-flattening technique and the combination of which with direct methods were used for the phase extension. Either procedure yielded reasonably good results, but on the whole, the result from the combination of direct methods with solvent flattening is better. Results of the latter procedure were further compared with that from direct phasing of the 2.5 A SIR data and with that from phase extension by solvent flattening without SIR information. An improvement gained by the use of SIR information is evident.
Carmelo Giacovazzo - One of the best experts on this subject based on the ideXlab platform.
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The method of joint probability distribution functions applied to MAD techniques. The two-wavelength case for acentric crystals.
Acta Crystallographica Section A Foundations of Crystallography, 2001Co-Authors: Carmelo Giacovazzo, Dritan SiliqiAbstract:MAD (multiple-wavelength anomalous dispersion) techniques are often considered as a special MIR (multiple Isomorphous Replacement) case. The rigorous method of the joint probability distribution functions is applied to solve the phase problem for acentric crystals, on the assumption that the anomalous scatterer's substructure is a priori known. The two-wavelength case is considered: errors in measurements and in the model substructure are handled. The probabilistic approach provides a very simple and efficient formula for estimating structure-factor phases.
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The method of joint probability distribution functions applied to MAD techniques. The centric case.
Acta Crystallographica Section A Foundations of Crystallography, 2001Co-Authors: Carmelo Giacovazzo, Dritan SiliqiAbstract:Traditional probabilistic approaches consider MAD (multiple-wavelength anomalous-dispersion) data as a special MIR (multiple Isomorphous Replacement) case. The rigorous method of the joint probability distribution functions has been applied to solve the phase problem, with the assumption that the anomalous scatterers' substructure is a priori known. The probabilistic approach is able to handle measurement errors: it has been applied to symmetry-restricted phases and provides simple and efficient formulas.
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on integrating direct methods and Isomorphous Replacement techniques ii the quartet invariant estimate
Acta Crystallographica Section A, 1996Co-Authors: Carmelo Giacovazzo, Dritan SiliqiAbstract:In a preceding paper [Giacovazzo & Siliqi (1996). Acta Cryst. A52, 133-142], the joint probability distribution of seven pairs of Isomorphous structure factors was derived. Its complicated mathematical expressions are here simplified by introducing the assumption that isomorphism is due to heavy-atom addition to the native structure. The reliability of the conclusive formula for calculated error-free data perfectly agrees with expectations. The formula, however, is not robust against lack of isomorphism and errors in measurements: in the paper, theoretical reasons are given justifying this behaviour. The use of the prior information on the heavy-atom structure markedly improves the formula, which then proves suitable for practical applications.
Quan Hao - One of the best experts on this subject based on the ideXlab platform.
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oasis a computer program for breaking phase ambiguity in one wavelength anomalous scattering or single Isomorphous substitution Replacement data
Journal of Applied Crystallography, 2000Co-Authors: Quan Hao, C D Zheng, H F FanAbstract:The phase problem is reduced to a sign problem once the anomalous-scatterer or the replacing-heavy-atom sites are located. OASIS adopts the CCP4 format [Collaborative Computational Project, Number 4 (1994). Acta Cryst. D50, 760–763]. It applies a direct-method procedure to break the phase ambiguity intrinsic to one-wavelength anomalous scattering (OAS) or single Isomorphous Replacement (SIR) data.
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combining direct methods with Isomorphous Replacement or anomalous scattering data viii phasing experimental sir data with the replacing atoms in a centrosymmetric arrangement
Acta Crystallographica Section D-biological Crystallography, 1999Co-Authors: Yudong Liu, Quan Hao, C D Zheng, H F FanAbstract:A multisolution direct method has been proposed to resolve the phase ambiguity intrinsic in single Isomorphous Replacement data of proteins with the replacing atoms in a centrosymmetric arrangement. The phase ambiguity of each reflection is in fact a `sign ambiguity' of the phase difference between the phase of the native protein and that of the replacing atoms, i.e. ± |Δφ| = φ − φ′. The P+ probability formula can be used to derive the signs. The multisolution phasing procedure is initiated using random starting values of P+. A cluster analysis is used instead of figures of merit to find the correct solution. The direct-method phases can be further improved by density-modification techniques. The method was tested with the experimental SIR data at 2 A resolution from a known protein aPP; satisfactory results were obtained.
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applications of direct methods with single Isomorphous Replacement or one wavelength anomalous scattering data
1998Co-Authors: H F Fan, Quan Hao, I Harvey, Samar S Hasnain, Y D Liu, C D ZhengAbstract:Recent developments of our study have been concentrated on the following topics: 1) the accuracy of our Cochran-distribution-based probability formula: it has been shown that the results of the formula are much more accurate than what people would usually predict; 2) an iterative procedure of combining direct methods with the solvent flattening technique: test on the experimental single Isomorphous Replacement (SIR) data of the known protein RNase Sa showed considerable improvement to the previous procedure; 3) direct-method phasing of the one-wavelength anomalous scattering (OAS) data of an unknown protein: the result leads to a traceable Fourier map and thus to the solution of the structure.
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use of single Isomorphous Replacement data of proteins resolving the phase ambiguity and a new procedure for phase extension
Acta Crystallographica Section D-biological Crystallography, 1997Co-Authors: X F Zheng, H F Fan, C D Zheng, Quan HaoAbstract:A procedure combining direct methods and solvent flattening to break the phase ambiguity intrinsic to the single Isomorphous Replacement (SIR) technique has been tested with the experimental SIR data of the known protein RNase Sa at 2.5 A resolution. The use of direct methods provided better initial phases for the solvent-flattening procedure, while the solvent-flattening procedure greatly improved direct-method phases leading to a traceable Fourier map. A small subset of known phases at low resolution makes direct phasing of SIR data much easier. Accordingly a method for extending low-resolution phases to high-resolution ones is proposed making use of additional SIR information. This reduces the problem of finding a value in the range of 0–2π for each unknown phase to that of just making a choice between two possible values. Tests with the known protein RNase Sa showed that the method is able to extend phases from a resolution of 6 to 2.5 A leading to an easily traceable Fourier map. The solvent-flattening technique and the combination of which with direct methods were used for the phase extension. Either procedure yielded reasonably good results, but on the whole, the result from the combination of direct methods with solvent flattening is better. Results of the latter procedure were further compared with that from direct phasing of the 2.5 A SIR data and with that from phase extension by solvent flattening without SIR information. An improvement gained by the use of SIR information is evident.
Thomas C Terwilliger - One of the best experts on this subject based on the ideXlab platform.
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30 multiwavelength anomalous diffraction phasing of macromolecular structures analysis of mad data as single Isomorphous Replacement with anomalous scattering data using the madmrg program
Methods in Enzymology, 1997Co-Authors: Thomas C TerwilligerAbstract:Publisher Summary Multiwavelength anomalous diffraction (MAD) technique is a widely used and important tool in macromolecular structure determination. In the MAD technique, intensities of Bijvoet pairs of reflections are measured at several X-ray wavelengths, near to and distant from an absorption edge for an anomalously scattering atom. The anomalous and dispersive differences among measurements of a reflection at several wavelengths, therefore, contain information about the structure of the anomalously scattering atoms, as well as the relation between the anomalously scattering atoms and the remainder of the structure. Several methods for the analysis of MAD data have been developed. An alternative approach is to make use of the similarity between the MAD and Isomorphous Replacement experiments. MAD data are either treated as if they are multiple Isomorphous Replacement with anomalous scattering (MIRAS) data or converted into a form that is equivalent to that obtained in a single Isomorphous Replacement with anomalous scattering (SIRAS) experiment. In either case, the MAD data are then employed for phasing using the robust techniques developed for the method of Isomorphous Replacement. The chapter discusses an approach for the conversion of MAD data to a form compatible with SIRAS analysis.
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mad phasing treatment of dispersive differences as Isomorphous Replacement information
Acta Crystallographica Section D-biological Crystallography, 1994Co-Authors: Thomas C TerwilligerAbstract:A framework analogous to that used for the analysis of data in the method of Isomorphous Replacement is applied to the analysis of multi-wavelength anomalous-diffraction (MAD) data. The present method is advantageous in that refinement of parameters describing the anomalously scattering atoms in the structure can be carried out using nearly all the data, and in that phase information can be readily combined. The procedure described here involves an approximation in which it is assumed that the magnitude of the structure factor corresponding to anomalously scattering atoms in the unit cell is small compared to that corresponding to all other atoms in the structure. A model calculation is applied to a protein crystal with 682 non-H atoms in the asymmetric unit and two Se atoms as the anomalous scatterers. It is shown using this model calculation that the approximation used in this analysis does not substantially affect the accuracy of phase calculations for this MAD data. The method is demonstrated by application to MAD data collected on gene V protein.
