Solution of organic crystal structures from powder diffraction by combining simulated annealing and direct methods

2003 ◽  
Vol 36 (2) ◽  
pp. 230-238 ◽  
Author(s):  
Angela Altomare ◽  
Rocco Caliandro ◽  
Carmelo Giacovazzo ◽  
Anna Grazia Giuseppina Moliterni ◽  
Rosanna Rizzi
Keyword(s):  
Monte Carlo ◽  
Simulated Annealing ◽  
Electron Density ◽  
Powder Diffraction ◽  
Direct Methods ◽  
Molecular Geometry ◽  
Molecular Structures ◽  
Chemical Information ◽  
Density Map ◽  
Electron Density Map

Theab initiocrystal structure solution from powder diffraction data can be attemptedviadirect methods. If heavy atoms are present, they are usually correctly located; then some crystal chemical information can be exploited to complete the partial structure model. Organic structures are more resistant to direct methods; as an alternative, their molecular geometry is used as prior information for Monte Carlo methods. In this paper, a new procedure is described which combines the information contained in the electron density map provided by direct methods with a Monte Carlo method which uses simulated annealing as a minimization algorithm. A figure of merit has been designed based on the agreement between the experimental and calculated profiles, and on the positions of the peaks in the electron density map. The procedure is completely automatic and has been included inEXPO; its performance has been validated and tested for a set of known molecular structures.

Charge flipping and VLD (vive la difference)

2013 ◽  
Author(s):  
Carmelo Giacovazzo
Keyword(s):  
Simulated Annealing ◽  
Electron Density ◽  
Simulated Annealing Algorithm ◽  
Fourier Transforms ◽  
Direct Methods ◽  
Efficient Charge ◽  
Density Map ◽  
Annealing Algorithm ◽  
The Fourier Transform ◽  
Electron Density Map

Direct methods procedures (see Chapter 6) or Patterson techniques (see Chapter 10), primarily the former, have been methods of choice for crystal structure solution of small- to medium-sized molecules from diffraction data. Over the last 30 years, several new phasing algorithms have been proposed, not requiring the use of triplet and quartet invariants, but based only on the properties of Fourier transforms. These were not competitive with direct methods and have never became popular, but they contain a nucleus for further advances. Among these we mention: (i) Bhat (1990) proposed a Metropolis technique (Metropolis et al., 1953; Kirkpatrick et al., 1983; Press et al., 1992), also known as simulated annealing (the reader is referred to Section 12.9 for details on the algorithm). From a random set of phases, an electron density map is calculated, modified, and inverted. The corresponding phases are altered according to the simulated annealing algorithm, and then used to calculate a new electron density map. The procedure is cyclic. (ii) A strictly related simulated annealing procedure has been proposed by Su (1995). The objective function to minimize was . . . R = ∑h (S|Fh|calc − |Fh|obs)2, . . . where S is the scale factor. The scheme is as follows: random atomic positions are generated and in succession shifted; the simulated annealing algorithm is applied to accept or reject atomic shifts. At the end, a new atomic structure is generated, whose positions are shifted in succession, and so on in a cyclic way. (iii) The forced coalescence method (FCP) was proposed by Drendel et al. (1995). Hybrid electron density maps (see Section 7.3.4) were actively used with different values of τ and ω. Even if never popular, the above algorithms opened the way to two other methods which are much more efficient, charge flipping and VLD (vive la difference), to which this chapter is dedicated. Both are based on the properties of the Fourier transform; they do not require the explicit use of structure invariants and seminvariants, or a deep knowledge of their properties. The reader should not, however, conclude that the invariance and seminvariance concepts are not necessary in the handling of these approaches, on the contrary, understanding these basic concepts is essential to the appreciation of these new methods.

COVMAP: a new algorithm for structure model optimization in theEXPOpackage

2012 ◽  
Vol 45 (4) ◽  
pp. 789-797 ◽  
Author(s):  
Angela Altomare ◽  
Corrado Cuocci ◽  
Carmelo Giacovazzo ◽  
Anna Moliterni ◽  
Rosanna Rizzi
Keyword(s):  
Electron Density ◽  
Weighted Least Squares ◽  
Direct Methods ◽  
Structure Model ◽  
Model Optimization ◽  
Full Structure ◽  
Density Map ◽  
Starting Model ◽  
Electron Density Map ◽  
Correct Structure

A new procedure (COVMAP) has been developed with the aim of recovering the full structure from very poor models, such as those provided by direct methods in unfavorable conditions. The procedure is based on the concept of covariance between points of an electron density map, mathematically set out by the authors in a recent paper:i.e.the density at one point depends on the density at another point of the map if their covariance is not vanishing. This concept suggested a procedure of electron density modification that uses pairs of model peaks to restrict the region where the density modification should be applied. Such modified densities lead to additional peaks, which in turn are submitted to two other important phasing tools present inEXPO2011, the resolution bias minimization and weighted least-squares procedures, which relocate, refine or reject these peaks. The procedure is cyclic and often leads to the correct structure even if the starting model is very poor.

Patterson methods and direct space properties

2013 ◽  
Author(s):  
Carmelo Giacovazzo
Keyword(s):  
Ab Initio ◽  
Electron Density ◽  
Direct Methods ◽  
Reciprocal Space ◽  
Phase Information ◽  
Basic Principles ◽  
Density Map ◽  
Electron Density Map ◽  
Space Phase ◽  
Phase Relationships

According to the basic principles of structural crystallography, stated in Section 1.6: (i) it is logically possible to recover the structure from experimental diffraction moduli; (ii) the necessary information lies in the diffraction amplitudes themselves, because they depend on interatomic vectors. The first systematic approach to structure determination based on the above principle was developed by Patterson (1934a,b). In the small molecule field related techniques, even if computerized (Mighell and Jacobson, 1963; Nordman and Nakatsu, 1963), were relegated to niche by the advent of direct methods. Conversely, in macromolecular crystallography, they survived and are still widely used today. Nowadays, Patterson techniques have been reborn as a general phasing approach, valid for small-, medium-, and large-sized molecules. The bases of Patterson methods are described in Section 10.2; in Section 10.3 some methods for Patterson deconvolution (i.e. for passing from the Patterson map to the correct electron density map) are described, and in Section 10.4 some applications to ab initio phasing are summarized. The use of Patterson methods in non-ab initio approaches like MR, SAD-MAD, or SIR-MIR are deferred to Chapters 13 to 15. We do not want to leave this chapter without mentioning some fundamental relations between direct space properties and reciprocal space phase relationships. Patterson, unlike direct methods, seek their phasing way in direct space; conversely, DM are the counterpart, in reciprocal space, of some direct space properties (positivity, atomicity, etc.). One may wonder if, by Fourier transform, it is possible to immediately derive phase information from such properties, without the heavy probabilistic machinery. In Appendix 10.A, we show some of many relations between electron density properties and phase relationships, and in Appendix 10.B, we summarize some relations between Patterson space and phase relationships. Patterson (1949) defined a second synthesis, known as the Patterson synthesis of the second kind. Even if theoretically interesting, it is of limited use in practice. We provide information on this in Appendix 10.C.

Direct methods and the solution of organic structures from powder data

2007 ◽  
Vol 40 (2) ◽  
pp. 344-348 ◽  
Author(s):  
Angela Altomare ◽  
Mercedes Camalli ◽  
Corrado Cuocci ◽  
Carmelo Giacovazzo ◽  
Anna Grazia Giuseppina Moliterni ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Organic Compounds ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Direct Methods ◽  
Structure Model ◽  
Powder Diffraction Data ◽  
Complete Structure ◽  
Density Map ◽  
Electron Density Map

The electron density map produced after the application of direct methods to powder diffraction data of organic compounds is usually very approximated: some atoms are missed, other atoms are in false positions, some atoms are imperfectly located and the connectivity is quite low. A new procedure able to recover the complete structure model is described. In this procedure, a better interpretation of the map is combined with geometrical techniques for generating new atomic positions. The application of the new procedure may lead to the recovery of the complete crystal structure.

A Comparison of Two Algorithms for Electron-Density Map Improvement by Introduction of Atomicity: Skeletonization, and Map Sorting Followed by Refinement

1998 ◽  
Vol 54 (1) ◽  
pp. 81-85 ◽  
Author(s):  
F. M. D. Vellieux
Keyword(s):  
Electron Density ◽  
Initial Density ◽  
Acta Cryst ◽  
Density Maps ◽  
Resolution Electron ◽  
Crystallographic Symmetry ◽  
Density Map ◽  
Ornithine Transcarbamoylase ◽  
Electron Density Map ◽  
Pseudo Atom

A comparison has been made of two methods for electron-density map improvement by the introduction of atomicity, namely the iterative skeletonization procedure of the CCP4 program DM [Cowtan & Main (1993). Acta Cryst. D49, 148–157] and the pseudo-atom introduction followed by the refinement protocol in the program suite DEMON/ANGEL [Vellieux, Hunt, Roy & Read (1995). J. Appl. Cryst. 28, 347–351]. Tests carried out using the 3.0 Å resolution electron density resulting from iterative 12-fold non-crystallographic symmetry averaging and solvent flattening for the Pseudomonas aeruginosa ornithine transcarbamoylase [Villeret, Tricot, Stalon & Dideberg (1995). Proc. Natl Acad. Sci. USA, 92, 10762–10766] indicate that pseudo-atom introduction followed by refinement performs much better than iterative skeletonization: with the former method, a phase improvement of 15.3° is obtained with respect to the initial density modification phases. With iterative skeletonization a phase degradation of 0.4° is obtained. Consequently, the electron-density maps obtained using pseudo-atom phases or pseudo-atom phases combined with density-modification phases are much easier to interpret. These tests also show that for ornithine transcarbamoylase, where 12-fold non-crystallographic symmetry is present in the P1 crystals, G-function coupling leads to the simultaneous decrease of the conventional R factor and of the free R factor, a phenomenon which is not observed when non-crystallographic symmetry is absent from the crystal. The method is far less effective in such a case, and the results obtained suggest that the map sorting followed by refinement stage should be by-passed to obtain interpretable electron-density distributions.

Electron-density maps

2002 ◽  
Author(s):  
David Blow
Keyword(s):  
Fourier Transform ◽  
Electron Density ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Unit Cell ◽  
Density Maps ◽  
Wave Cycle ◽  
Density Map ◽  
The Fourier Transform ◽  
Electron Density Map

When everything has been done to make the phases as good as possible, the time has come to examine the image of the structure in the form of an electron-density map. The electron-density map is the Fourier transform of the structure factors (with their phases). If the resolution and phases are good enough, the electron-density map may be interpreted in terms of atomic positions. In practice, it may be necessary to alternate between study of the electron-density map and the procedures mentioned in Chapter 10, which may allow improvements to be made to it. Electron-density maps contain a great deal of information, which is not easy to grasp. Considerable technical effort has gone into methods of presenting the electron density to the observer in the clearest possible way. The Fourier transform is calculated as a set of electron-density values at every point of a three-dimensional grid labelled with fractional coordinates x, y, z. These coordinates each go from 0 to 1 in order to cover the whole unit cell. To present the electron density as a smoothly varying function, values have to be calculated at intervals that are much smaller than the nominal resolution of the map. Say, for example, there is a protein unit cell 50 Å on a side, at a routine resolution of 2Å. This means that some of the waves included in the calculation of the electron density go through a complete wave cycle in 2 Å. As a rule of thumb, to represent this properly, the spacing of the points on the grid for calculation must be less than one-third of the resolution. In our example, this spacing might be 0.6 Å. To cover the whole of the 50 Å unit cell, about 80 values of x are needed; and the same number of values of y and z. The electron density therefore needs to be calculated on an array of 80×80×80 points, which is over half a million values. Although our world is three-dimensional, our retinas are two-dimensional, and we are good at looking at pictures and diagrams in two dimensions.

scholarly journals Electron density map as an aid in the sequencing of peptides.

1973 ◽  
Vol 70 (6) ◽  
pp. 1793-1794 ◽  
Author(s):  
M. J. Adams ◽  
G. C. Ford ◽  
P. J. Lentz ◽  
A. Liljas ◽  
M. G. Rossmann
Keyword(s):  
Electron Density ◽  
Density Map ◽  
Electron Density Map
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