20 results on '"Direct methods"'
Search Results
2. Novel phasing method using the origin-free modulus sum function expressed in terms of the absolute electron density
- Author
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Jordi Rius, Ministerio de Economía y Competitividad (España), and European Commission
- Subjects
Electron density ,Patterson function ,Modulo operation ,Probability density function ,02 engineering and technology ,010403 inorganic & nuclear chemistry ,Phasing methods ,01 natural sciences ,Biochemistry ,Coincidence ,Inorganic Chemistry ,symbols.namesake ,Structural Biology ,General Materials Science ,Physical and Theoretical Chemistry ,Physics ,Mathematical analysis ,Function (mathematics) ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,Research Papers ,Modulus sum function ,0104 chemical sciences ,Structure solution ,Fourier transform ,Direct methods ,symbols ,0210 nano-technology - Abstract
The origin-free modulus sum function SM refines the set Φ of phases of the structure factors by maximizing the coincidence between the experimental origin-free modulus function and the calculated one in terms of the ρ(Φ)2 density function [Rius, J. (1993). Acta Cryst. A49, 406–409]. Maximization is normally achieved through the recursive application of a Fourier-based algorithm. The purpose of the present study is: (i) to show that ρ(Φ)2 can be replaced by |ρ(Φ)| in SM; (ii) to illustrate the viability of the corresponding phasing algorithm with experimental data., MINECO & FEDER (grant No. RTI2018-098537-B-C21 ); Severo Ochoa Programme for Centres of Excellence in R&D (grant No. SEV-2015-0496). more...
- Published
- 2020
- Full Text
- View/download PDF
Catalog
3. Cannabidiol: a natural product structure in the mid-1970s. Weissenberg photos, four-circle diffractometry, direct methods and more
- Author
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Larry R. Falvello
- Subjects
Inorganic Chemistry ,Crystallography ,Materials science ,Structural Biology ,Direct methods ,medicine ,Structure (category theory) ,General Materials Science ,Physical and Theoretical Chemistry ,Condensed Matter Physics ,Biochemistry ,Cannabidiol ,medicine.drug - Published
- 2021
- Full Text
- View/download PDF
4. Determination of small crystal structures from a minimum set of diffraction intensities by homotopy continuation
- Author
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Oleg V. Tsodikov and Dimitri Leggas
- Subjects
Diffraction ,Polynomial ,Molecular Structure ,Mathematical analysis ,Probabilistic logic ,Phase problem ,Crystal structure ,Crystallography, X-Ray ,Condensed Matter Physics ,Biochemistry ,Inorganic Chemistry ,Combinatorics ,Set (abstract data type) ,Structural Biology ,Direct methods ,General Materials Science ,Physical and Theoretical Chemistry ,Algorithms ,Software ,Homotopy analysis method ,Mathematics - Abstract
No deterministic approach to obtaining a crystal structure from a set of diffraction intensities exists, despite significant progress in traditional probabilistic direct methods. One of the biggest hurdles in determining a crystal structure algebraically is solving a system of many polynomial equations of high power on intensities in terms of atomic coordinates. In this study, homotopy continuation is used for exhaustive investigation of such systems and an optimized homotopy continuation method is developed with random restarts to determine small (N< 5) crystal structures from a minimum set of error-free intensities. more...
- Published
- 2015
- Full Text
- View/download PDF
5. Applications of direct methods in protein crystallography for dealing with diffraction data down to 5 Å resolution
- Author
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Tao Zhang, Yao He, Deqiang Yao, Zheng-Jiong Lin, Yuanxin Gu, Hai-fu Fan, and Jiawei Wang
- Subjects
Models, Molecular ,Diffraction ,business.industry ,Chemistry ,Escherichia coli Proteins ,Resolution (electron density) ,Ab initio ,Membrane Transport Proteins ,Phase problem ,Crystallography, X-Ray ,Condensed Matter Physics ,Biochemistry ,Phaser ,Inorganic Chemistry ,Reciprocal lattice ,Optics ,Structural Biology ,Direct methods ,X-ray crystallography ,General Materials Science ,Physical and Theoretical Chemistry ,business ,Algorithm ,Algorithms - Abstract
Apart from solving the heavy-atom substructure in proteins andab initiophasing of protein diffraction data at atomic resolution, direct methods have also been successfully combined with other protein crystallographic methods in dealing with diffraction data far below atomic resolution, leading to significantly improved results. In this respect, direct methods provide phase constraints in reciprocal space within a dual-space iterative framework rather than solve the phase problem independently. Applications of this type of direct methods to difficult SAD phasing, model completion and low-resolution phase extension will be described in detail. more...
- Published
- 2014
- Full Text
- View/download PDF
6. A new density-modification procedure extending the application of the recent |ρ|-based phasing algorithm to larger crystal structures.
- Author
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Rius J and Torrelles X
- Abstract
The incorporation of the new peakness-enhancing fast Fourier transform compatible ipp procedure (ipp = inner-pixel preservation) into the recently published S
M algorithm based on |ρ| [Rius (2020). Acta Cryst A76, 489-493] improves its phasing efficiency for larger crystal structures with atomic resolution data. Its effectiveness is clearly demonstrated via a collection of test crystal structures (taken from the Protein Data Bank) either starting from random phase values or by using the randomly shifted modulus function (a Patterson-type synthesis) as initial ρ estimate. It has been found that in the presence of medium scatterers (e.g. S or Cl atoms) crystal structures with 1500 × c atoms in the unit cell (c = number of centerings) can be routinely solved. In the presence of strong scatterers like Fe, Cu or Zn atoms this number increases to around 5000 × c atoms. The implementation of this strengthened SM algorithm is simple, since it only includes a few easy-to-adjust parameters., (open access.) more...- Published
- 2021
- Full Text
- View/download PDF
7. Novel phasing method using the origin-free modulus sum function expressed in terms of the absolute electron density.
- Author
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Rius J
- Abstract
The origin-free modulus sum function S
M refines the set Φ of phases of the structure factors by maximizing the coincidence between the experimental origin-free modulus function and the calculated one in terms of the ρ(Φ)2 density function [Rius, J. (1993). Acta Cryst. A49, 406-409]. Maximization is normally achieved through the recursive application of a Fourier-based algorithm. The purpose of the present study is: (i) to show that ρ(Φ)2 can be replaced by |ρ(Φ)| in SM ; (ii) to illustrate the viability of the corresponding phasing algorithm with experimental data. more...- Published
- 2020
- Full Text
- View/download PDF
8. History of direct methods: a personal account
- Author
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Davide Viterbo
- Subjects
Inorganic Chemistry ,Personal account ,Structural Biology ,Direct methods ,General Materials Science ,Physical and Theoretical Chemistry ,Condensed Matter Physics ,Psychology ,Biochemistry ,Social psychology - Published
- 2016
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9. Updating direct methods.
- Author
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Giacovazzo C
- Abstract
The standard method of joint probability distribution functions, so crucial for the development of direct methods, has been revisited and updated. It consists of three steps: identification of the reflections which may contribute to the estimation of a given structure invariant or seminvariant, calculation of the corresponding joint probability distribution, and derivation of the conditional distribution of the invariant or seminvariant phase given the values of some diffracted amplitudes. In this article the conditional distributions are derived directly without passing through the second step. A good feature of direct methods is that they may work in the absence of any prior information: that is also their weakness. Different types of prior information have been taken into consideration: interatomic distances, interatomic vectors, Patterson peaks, structural model. The method of directly deriving the conditional distributions has been applied to those cases. Some new formulas have been obtained estimating two-, three- and four-phase invariants. Special attention has been dedicated to the practical aspects of the new formulas, in order to simplify their possible use in direct phasing procedures. more...
- Published
- 2019
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10. Application of Direct Methods to Inorganic Materials Characterization
- Author
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Jordi Rius
- Subjects
Inorganic Chemistry ,Materials science ,Structural Biology ,Direct methods ,General Materials Science ,Inorganic materials ,Nanotechnology ,Physical and Theoretical Chemistry ,Condensed Matter Physics ,Biochemistry ,Characterization (materials science) - Abstract
Although in the last years most attention has been paid to the development of direct methods (DM) in the macromolecular field, DM also play an important role in the characterization of inorganic materials. Very challenging is nowadays the structure solution of increasingly small crystals. Here the difficulty is not associated with the large number of atoms but with experimental limitations which may affect the data accuracy and the completeness of the data sets. It is obvious that DM have to adapt to this emerging scientific need. Particularly interesting has been the evolution of Patterson-function DM to cope with these objectives. The initial formulation based on the explicit use of triple-phase sums was modified to permit the calculation with Fourier transforms thus resulting in the more simple and accurate S-FFT algorithm [1]. Thanks to the resulting increased simplicity, this algorithm could be easily adapted to the treatment of powder diffraction data of complex inorganic materials [2]. The practical application of this algorithm is analyzed by using data of some synthetic and natural materials. Recently, the possibility of collecting good quality 3D intensity data from very small nanovolumes by new sophisticated electron diffraction (ED) techniques has become a reality. However, these data sets are often incomplete and, in addition, the intensities are not completely kinematical. The processing of these data sets represents a new challenge for DM. To this purpose a new (even more simple) Patterson-function DM (called delta-recycling) has been developed and tested on precession ED data from inorganic materials with variable degree of difficulty [3]. Phasing with delta-recycling proves to be highly efficient and from the interpretation of the results important practical conclusions can be drawn. more...
- Published
- 2014
- Full Text
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11. SHELXT: Integrating space group determination and structure solution
- Author
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G. Sheldrick
- Subjects
Computer science ,Group (mathematics) ,Dual space ,Structure (category theory) ,Condensed Matter Physics ,Space (mathematics) ,Biochemistry ,Inorganic Chemistry ,Superposition principle ,Structural Biology ,Simple (abstract algebra) ,Direct methods ,General Materials Science ,Physical and Theoretical Chemistry ,Element (category theory) ,Algorithm - Abstract
SHELXT is intended for robust routine solution of small molecule crystal structures. It makes the simple but powerful assumption that the structure consists of resolved atoms, but unlike classical direct methods it is not required that the atoms are 'equal'. This enables it to succeed with poor or incomplete data but makes it unsuitable for structures that are twinned, modulated or contain severe (e.g. 'whole molecule') disorder. SHELXT is a dual-space program that starts with a Patterson minimum superposition and iteratively applies the random omit procedure (also used in SHELXD) with data expanded to space group P1, but does not use phase probability relations or solvent flipping. In the SHELX system it will probably obsolete SHELXS but not SHELXD, which is better for large equal-atom and twinned structures. SHELXT reads any legal SHELX format .ins and (HKLF3 or 4) .hkl files. It extracts the Laue group and tries to find space groups in this Laue group and origin shifts to fit the phases from the best P1 solution, and makes an approximate assignment of element types using the elements specified on the SFAC instruction (and maybe a couple more). This is followed by an isotropic refinement and an attempt to assign the absolute structure if the space group is non-centrosymmetric. It is hoped to release SHELXT as part of the SHELX system (http://shelx.uni-ac.gwdg.de/SHELX/index.php) in time for the 2014 Montreal IUCr Meeting. more...
- Published
- 2014
- Full Text
- View/download PDF
12. Initial phases from phosphate SAD in the direct methods determination of RNA
- Author
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Victoria Mooers, Tina McKay, Akila Venkataramany, Tzanko Doukov, and Blaine Mooers
- Subjects
Inorganic Chemistry ,chemistry.chemical_compound ,Biochemistry ,Structural Biology ,Chemistry ,Direct methods ,RNA ,General Materials Science ,Physical and Theoretical Chemistry ,Condensed Matter Physics ,Phosphate - Abstract
Atomic resolution diffraction data from crystals of double-stranded RNAs can often resist automated structure determination by ab initio methods including charge flipping and traditional direct methods. Often it is possible to obtain quick success at direct methods structure determination by supplying the positions of one or more heavier atoms, which are used to calculate a starting set of phase angles. Long wavelength radiation such as that near the iron K absorption edge can be used to measure the weak anomalous diffraction data from phosphorous atoms in the RNA backbones. These anomalous diffraction data can be used to locate the positions of some of the phosphorous atoms. Next, the phosphorous positions can be used to provide initial phases for direct methods structure determination with atomic resolution diffraction data collected with shorter wavelength radiation. We tested this hybrid approach with two double-stranded RNAs, one with 31 unique phosphates and a second with 44 unique phosphates. We used a combination of programs including those in the CCP4, SHELX, and Sir program suites. We varied the number of sweeps of images collected at the iron edge to find the minimum number (and hence minimum exposure) required to find enough of the phosphate substructure for success at direct methods with the native data before collecting atomic resolution diffraction data with the short wavelength radiation. Our results suggest that diffraction data could be collected at these two wavelengths from a single crystal to avoid problems with non-isomorphism. more...
- Published
- 2014
- Full Text
- View/download PDF
13. Direct methods for the 21st century
- Author
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Veit Elser
- Subjects
Inorganic Chemistry ,History ,Structural Biology ,Management science ,Direct methods ,General Materials Science ,Physical and Theoretical Chemistry ,Condensed Matter Physics ,Biochemistry - Abstract
We describe a general method for obtaining structures from diffraction data that can be applied to non-crystalline and magnetic materials.
- Published
- 2014
- Full Text
- View/download PDF
14. Davide Viterbo (1939-2017).
- Author
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Mealli C and Milanesio M
- Published
- 2017
- Full Text
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15. MPF, a multipurpose figure of merit for phasing procedures.
- Author
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Burla MC, Carrozzini B, Cascarano GL, Giacovazzo C, and Polidori G
- Subjects
- Crystallography, X-Ray, Models, Structural
- Abstract
The efficient multipurpose figure of merit MPF has been defined and characterized. It may be very helpful in phasing procedures. Indeed, it might be used for establishing the centric or acentric nature of an unknown structure, for identifying the presence of some pseudotranslational symmetry, for recognizing the correct solution in multisolution approaches and for estimating the quality of structure models as they become available during the phasing process. Thus, phase improvement or deterioration may be monitored and useless models may be discarded to save computing time. It is also shown that MPF may be applied in different phasing approaches, no matter if ab initio or non ab initio. more...
- Published
- 2017
- Full Text
- View/download PDF
16. Determination of small crystal structures from a minimum set of diffraction intensities by homotopy continuation.
- Author
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Leggas D and Tsodikov OV
- Subjects
- Algorithms, Molecular Structure, Software, Crystallography, X-Ray methods
- Abstract
No deterministic approach to obtaining a crystal structure from a set of diffraction intensities exists, despite significant progress in traditional probabilistic direct methods. One of the biggest hurdles in determining a crystal structure algebraically is solving a system of many polynomial equations of high power on intensities in terms of atomic coordinates. In this study, homotopy continuation is used for exhaustive investigation of such systems and an optimized homotopy continuation method is developed with random restarts to determine small (N < 5) crystal structures from a minimum set of error-free intensities. more...
- Published
- 2015
- Full Text
- View/download PDF
17. SHELXT - integrated space-group and crystal-structure determination.
- Author
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Sheldrick GM
- Abstract
The new computer program SHELXT employs a novel dual-space algorithm to solve the phase problem for single-crystal reflection data expanded to the space group P1. Missing data are taken into account and the resolution extended if necessary. All space groups in the specified Laue group are tested to find which are consistent with the P1 phases. After applying the resulting origin shifts and space-group symmetry, the solutions are subject to further dual-space recycling followed by a peak search and summation of the electron density around each peak. Elements are assigned to give the best fit to the integrated peak densities and if necessary additional elements are considered. An isotropic refinement is followed for non-centrosymmetric space groups by the calculation of a Flack parameter and, if appropriate, inversion of the structure. The structure is assembled to maximize its connectivity and centred optimally in the unit cell. SHELXT has already solved many thousand structures with a high success rate, and is optimized for multiprocessor computers. It is, however, unsuitable for severely disordered and twinned structures because it is based on the assumption that the structure consists of atoms. more...
- Published
- 2015
- Full Text
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18. An alternative method for the calculation of joint probability distributions. Application to the expectation of the triplet invariant.
- Author
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Brosius J
- Abstract
This paper presents a completely new method for the calculation of expectations (and thus joint probability distributions) of structure factors or phase invariants. As an example, a first approximation of the expectation of the triplet invariant (up to a constant) is given and a complex number is obtained. Instead of considering the atomic vector positions or reciprocal vectors as the fundamental random variables, the method samples over all functions (distributions) with a given number of atoms and given Patterson function. The aim of this paper was to explore the feasibility of the method, so the easiest problem was chosen: the calculation of the expectation value of the triplet invariant in P1. Calculation of the joint probability distribution of the triplet is not performed here but will be done in the future. more...
- Published
- 2015
- Full Text
- View/download PDF
19. Ambiguity of structure determination from a minimum of diffraction intensities.
- Author
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Al-Asadi A, Leggas D, and Tsodikov OV
- Subjects
- Algorithms, Phase Transition, Scattering, Radiation, Crystallography methods
- Abstract
Although the ambiguity of the crystal structures determined directly from diffraction intensities has been historically recognized, it is not well understood in quantitative terms. Bernstein's theorem has recently been used to obtain the number of one-dimensional crystal structures of equal point atoms, given a minimum set of diffraction intensities. By a similar approach, the number of two- and three-dimensional crystal structures that can be determined from a minimum intensity data set is estimated herein. The ambiguity of structure determination from the algebraic minimum of data increases at least exponentially fast with the increasing structure size. Substituting lower-resolution intensities by higher-resolution ones in the minimum data set has little or no effect on this ambiguity if the number of such substitutions is relatively small. more...
- Published
- 2014
- Full Text
- View/download PDF
20. Applications of direct methods in protein crystallography for dealing with diffraction data down to 5 Å resolution.
- Author
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Fan H, Gu Y, He Y, Lin Z, Wang J, Yao D, and Zhang T
- Subjects
- Algorithms, Crystallography, X-Ray methods, Escherichia coli Proteins chemistry, Membrane Transport Proteins chemistry, Models, Molecular
- Abstract
Apart from solving the heavy-atom substructure in proteins and ab initio phasing of protein diffraction data at atomic resolution, direct methods have also been successfully combined with other protein crystallographic methods in dealing with diffraction data far below atomic resolution, leading to significantly improved results. In this respect, direct methods provide phase constraints in reciprocal space within a dual-space iterative framework rather than solve the phase problem independently. Applications of this type of direct methods to difficult SAD phasing, model completion and low-resolution phase extension will be described in detail. more...
- Published
- 2014
- Full Text
- View/download PDF
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