Correcting resolution bias in electron density maps of organic molecules derived by direct methods from powder data

2008 ◽  
Vol 41 (3) ◽  
pp. 592-599 ◽  
Author(s):  
Angela Altomare ◽  
Corrado Cuocci ◽  
Carmelo Giacovazzo ◽  
Anna Moliterni ◽  
Rosanna Rizzi
Keyword(s):  
Electron Density ◽  
Direct Methods ◽  
Large Set ◽  
Acta Cryst ◽  
Pattern Decomposition ◽  
Density Maps ◽  
Decomposition Procedure ◽  
Data Resolution ◽  
Current Electron ◽  
The Difference

Fourier syntheses providing electron density maps are usually affected by truncation effects due to the limited data resolution. A recent theoretical approach [Altomare, Cuocci, Giacovazzo, Kamel, Moliterni & Rizzi (2008).Acta Cryst.A64, 326–336] suggests that the resolution bias may be reduced by correcting the current electron density maps in accordance with the physics of the diffraction experiment. We have implemented the approach inEXPO2004[Altomare, Caliandro, Camalli, Cuocci, Giacovazzo, Moliterni & Rizzi (2004).J. Appl. Cryst.37, 1025–1028], a program devoted to the solution of crystal structures from powder data. The new algorithm was applied at the end of the direct methods modulus, to verify if the reduction of the resolution bias is able to improve the electron density maps and to provide additional power to direct methods. Application of this method to a large set of test structures indicates that resolution-bias correction often makes the difference between success and failure, and thus constitutes a new tool for reducing the dependence of modern crystallography on resolution effects. The chances of failure are expected to depend on the quality of the experimental data (e.g.the accuracy of the full-pattern decomposition procedure and the data resolution), on the size of the structure and on its chemical composition.

The revenge of the Patterson methods. II. Substructure applications

2007 ◽  
Vol 40 (2) ◽  
pp. 211-217 ◽  
Author(s):  
Maria Cristina Burla ◽  
Rocco Caliandro ◽  
Benedetta Carrozzini ◽  
Giovanni Luca Cascarano ◽  
Liberato De Caro ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Ab Initio ◽  
Electron Density ◽  
Direct Methods ◽  
Large Set ◽  
Common Belief ◽  
Anomalous Diffraction ◽  
Density Maps ◽  
Structure Solution ◽  
The Common

The Patterson techniques, recently developed by the same authors for theab initiocrystal structure solution of proteins, have been applied to single and multiple anomalous diffraction (SAD and MAD) data to find the substructure of the anomalous scatterers. An automatic procedure has been applied to a large set of test structures, some of which were originally solved with remarkable difficulty. In all cases, the procedure automatically leads to interpretable electron density maps. Patterson techniques have been compared with direct methods; the former seem to be more efficient than the latter, so confirming the results obtained forab initiophasing, and disproving the common belief that they could only be applied to determine large equal-atom substructures with difficulty.

Is single-wavelength anomalous scattering sufficient for solving phases? A comparison of different methods for a 2.1 Å structure solution

1999 ◽  
Vol 55 (9) ◽  
pp. 1620-1622 ◽  
Author(s):  
Liu Yu-dong ◽  
I. Harvey ◽  
Gu Yuan-xin ◽  
Zheng Chao-de ◽  
He Yi-zong ◽  
...  
Keyword(s):  
Electron Density ◽  
Phase Error ◽  
Direct Methods ◽  
Anomalous Scattering ◽  
Refined Model ◽  
Native Protein ◽  
Acta Cryst ◽  
Density Maps ◽  
Structure Solution ◽  
Unknown Structure

The structure of rusticyanin is the largest unknown structure (Mr = 16.8 kDa) which has been recently solved by the direct-methods approach using only single-wavelength anomalous scattering (SAS) data from the native protein [Harvey et al. (1998). Acta Cryst. D54, 629–635]. Here, the results of the Sim distribution approach [Hendrickson & Teeter (1981). Nature (London), 290, 107–113] and of the CCP4 procedure MLPHARE [Collaborative Computational Project, Number 4 (1994). Acta Cryst. D50, 760–763] are compared with those from direct methods. Analysis against the final refined model shows that direct methods produced significantly better phases (average phase error 56°) and therefore significantly better electron-density maps than the Sim distribution and MLPHARE approaches (average phase error was around 63° in both cases).

From a random to the correct structure: the VLD algorithm

2010 ◽  
Vol 43 (4) ◽  
pp. 825-836 ◽  
Author(s):  
Maria Cristina Burla ◽  
Carmelo Giacovazzo ◽  
Giampiero Polidori
Keyword(s):  
Electron Density ◽  
Random Model ◽  
Good Representation ◽  
Large Set ◽  
Target Structure ◽  
Difference Electron Density ◽  
Fourier Synthesis ◽  
Acta Cryst ◽  
The Difference ◽  
Difference Term

A recent probabilistic reformulation of the difference electron-density Fourier synthesis [Burla, Caliandro, Giacovazzo & Polidori (2010).Acta Cryst.A66, 347–361] suggested that the most suitable Fourier coefficients are the sum of the classical difference term (mF−DFp) with a flipping term, depending on the model and on its quality. The flipping term is dominant when the model is poor and is negligible when the model is a good representation of the target structure. In the case of a random model the Fourier coefficient does not vanish and therefore could allow the recovery of the target structure from a random model. This paper describes a new phasing algorithm which does not require use of the concept of structure invariants or semi-invariants: it is based only on the properties of the new difference electron density and of the observed Fourier synthesis. The algorithm is cyclic and very easy to implement. It has been applied to a large set of small-molecule structures to verify the suitability of the approach.

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.

scholarly journals σ2 R , a reciprocal-space measure of the quality of macromolecular electron-density maps

1999 ◽  
Vol 55 (6) ◽  
pp. 1174-1178 ◽  
Author(s):  
Thomas C. Terwilliger
Keyword(s):  
Standard Deviation ◽  
Ab Initio ◽  
Electron Density ◽  
Reciprocal Space ◽  
Rapid Evaluation ◽  
Reliable Measure ◽  
Similar Measure ◽  
Acta Cryst ◽  
Density Maps

It has previously been shown that the presence of distinct regions of solvent and protein in macromolecular crystals leads to a high value of the standard deviation of local r.m.s. electron density and that this can in turn be used as a reliable measure of the quality of macromolecular electron-density maps [Terwilliger & Berendzen (1999a). Acta Cryst. D55, 501–505]. Here, it is demonstrated that a similar measure, \sigma_{R}^{2}, the variance of the local roughness of the electron density, can be calculated in reciprocal space. The formulation is suitable for rapid evaluation of macromolecular crystallographic phases, for phase improvement and for ab initio phasing procedures.

Synergy among phase-refinement techniques in macromolecular crystallography

2017 ◽  
Vol 73 (11) ◽  
pp. 877-888 ◽  
Author(s):  
Maria Cristina Burla ◽  
Giovanni Luca Cascarano ◽  
Carmelo Giacovazzo ◽  
Giampiero Polidori
Keyword(s):  
Ab Initio ◽  
Electron Density ◽  
Molecular Model ◽  
Experimental Tests ◽  
Protein Chemistry ◽  
Sources Of Information ◽  
Density Maps ◽  
Structure Solution ◽  
Molecular Interpretation ◽  
The Difference

Ab initioand non-ab initiophasing methods are often unable to provide phases of sufficient quality to allow the molecular interpretation of the resulting electron-density maps. Phase extension and refinement is therefore a necessary step: its success or failure can make the difference between solution and nonsolution of the crystal structure. Today phase refinement is trusted to electron-density modification (EDM) techniques, and in practice to dual-space methods which try,viasuitable constraints in direct and in reciprocal space, to generate higher quality electron-density maps. The most popular EDM approaches, denoted here as mainstream methods, are usually part of packages which assist crystallographers in all of the structure-solution steps from initial phasing to the point where the molecular model perfectly fits the known features of protein chemistry. Other phase-refinement approaches that are based on different sources of information, denoted here as out-of-mainstream methods, are not frequently employed. This paper aims to show that mainstream and out-of-mainstream methods may be combined and may lead to dramatic advances in the present state of the art. The statement is confirmed by experimental tests using molecular-replacement, SAD–MAD andab initiotechniques.

The maximum entropy distribution consistent with observed structure amplitudes

1989 ◽  
Vol 45 (2) ◽  
pp. 200-203 ◽  
Author(s):  
E. Prince
Keyword(s):  
Maximum Entropy ◽  
Electron Density ◽  
Direct Methods ◽  
Positive Definite ◽  
Sufficient Information ◽  
Large Set ◽  
Unique Structure ◽  
Structure Factors ◽  
The Matrix ◽  
Maximum Entropy Distribution

It is shown that an electron density distribution of the formρk= exp [Σfj(rk)xj] has maximum entropy under the constraint that the expected values of a set of functions,fj(r), are constant. For a Fourier map the functionsfj(r) are the magnitudes of the structure factors for a set of reflectionshjincludingF(000). The values of the parametersxjfor which [(exp (2πihj. r))] = [Fobs(hj)[ for an arbitrarily large set of reflections may be found by an iterative algorithm in whichxi+ 1=xi+Hi-1Δi, where the matrixHis positive definite. Because the distributionρ(r) is everywhere positive, if non-negativity of electron density is sufficient information to determine a unique structure by direct methods, it follows that the maximum entropy procedure must lead to the same unique structure. Maximum entropy is thus an efficient way of expressing the phase implications of a large set of structure amplitudes.

scholarly journals Statistical quality indicators for electron-density maps

2012 ◽  
Vol 68 (4) ◽  
pp. 454-467 ◽  
Author(s):  
Ian J. Tickle
Keyword(s):  
Electron Density ◽  
Statistical Significance ◽  
Significance Test ◽  
Real Space ◽  
Structure Model ◽  
Space Correlation ◽  
The Real ◽  
Difference Density ◽  
Density Maps ◽  
The Difference

The commonly used validation metrics for the local agreement of a structure model with the observed electron density, namely the real-space R (RSR) and the real-space correlation coefficient (RSCC), are reviewed. It is argued that the primary goal of all validation techniques is to verify the accuracy of the model, since precision is an inherent property of the crystal and the data. It is demonstrated that the principal weakness of both of the above metrics is their inability to distinguish the accuracy of the model from its precision. Furthermore, neither of these metrics in their usual implementation indicate the statistical significance of the result. The statistical properties of electron-density maps are reviewed and an improved alternative likelihood-based metric is suggested. This leads naturally to a χ2 significance test of the difference density using the real-space difference density Z score (RSZD). This is a metric purely of the local model accuracy, as required for effective model validation and structure optimization by practising crystallographers prior to submission of a structure model to the PDB. A new real-space observed density Z score (RSZO) is also proposed; this is a metric purely of the model precision, as a substitute for other precision metrics such as the B factor.

VLD algorithm and hybrid Fourier syntheses

2012 ◽  
Vol 45 (6) ◽  
pp. 1287-1294 ◽  
Author(s):  
Maria Cristina Burla ◽  
Benedetta Carrozzini ◽  
Giovanni Luca Cascarano ◽  
Carmelo Giacovazzo ◽  
Giampiero Polidori
Keyword(s):  
Electron Density ◽  
Standard Procedure ◽  
Joint Probability ◽  
Distribution Functions ◽  
Medium Size ◽  
Joint Probability Distribution ◽  
Fourier Synthesis ◽  
Acta Cryst ◽  
The Difference ◽  
Difference Fourier

The VLD (vive la difference) phasing algorithm combines the model electron density with the difference electron densityviareciprocal space relationships to obtain new phase values and drive them to the correct values. The process is iterative and has been applied to small and medium-size structures and to proteins. Hybrid Fourier syntheses show properties that are intermediate between those of the observed synthesis (whose peaks should correspond to the most probable atomic positions) and those of the difference synthesis (whose positive and negative peaks should correspond to missed atomic positions and to false atoms of the model, respectively). Thanks to these properties some hybrid syntheses can be used in the phase extension and refinement step, to reduce the model bias and more rapidly move to the target structure. They have been recently revisitedviathe method of joint probability distribution functions [Burla, Carrozzini, Cascarano, Giacovazzo & Polidori (2011).Acta. Cryst. A67, 447–455]. The results suggested that VLD could be usefully combined, forab initiophasing, with the hybrid rather than with the difference Fourier synthesis. This paper explores the feasibility of such a combination and shows that the original VLD algorithm is only one of several variants, all with relevant phasing capacity. The study explores the role of several parameters in order to design a standard procedure with optimized phasing power.

Peak labelling in electron density maps from powder data: the use of crystal chemical information

2002 ◽  
Vol 35 (1) ◽  
pp. 21-27 ◽  
Author(s):  
Angela Altomare ◽  
Carmelo Giacovazzo ◽  
Massimo Ianigro ◽  
Anna Grazia Giuseppina Moliterni ◽  
Rosanna Rizzi
Keyword(s):  
Electron Density ◽  
Structure Refinement ◽  
Random Phase ◽  
Series Representation ◽  
Direct Methods ◽  
Chemical Information ◽  
Heavy Atoms ◽  
Phase Errors ◽  
Density Maps ◽  
Alternative Techniques

Direct methods applied to powder diffraction data often provide electron density maps of which the quality is usually affected by systematic and/or random phase errors, by amplitude truncation effects in the series representation of the electron density,etc. The frequent incorrect labelling of the peaks can strongly affect the efficiency of the procedures used for crystal structure refinement. For example, the success of alternative techniques, such asPOLPO[Altomareet al. (2000).J. Appl. Cryst.33, 1305–1310], requires that all the heavy atoms be positioned and exactly labelled.

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