Phase Problem In X-ray Crystallography Research Articles

Molecular-replacement phasing using predicted protein structures from AWSEM-Suite.

The phase problem in X-ray crystallography arises from the fact that only the intensities, and not the phases, of the diffracting electromagnetic waves are measured directly. Molecular replacement can often estimate the relative phases of reflections starting with those derived from a template structure, which is usually a previously solved structure of a similar protein. The key factor in the success of molecular replacement is finding a good template structure. When no good solved template exists, predicted structures based partially on templates can sometimes be used to generate models for molecular replacement, thereby extending the lower bound of structural and sequence similarity required for successful structure determination. Here, the effectiveness is examined of structures predicted by a state-of-the-art prediction algorithm, the Associative memory, Water-mediated, Structure and Energy Model Suite (AWSEM-Suite), which has been shown to perform well in predicting protein structures in CASP13 when there is no significant sequence similarity to a solved protein or only very low sequence similarity to known templates. The performance of AWSEM-Suite structures in molecular replacement is discussed and the results show that AWSEM-Suite performs well in providing useful phase information, often performing better than I-TASSER-MR and the previous algorithm AWSEM-Template.

Bayesian machine learning improves single-wavelength anomalous diffraction phasing.

Single-wavelength X-ray anomalous diffraction (SAD) is a frequently employed technique to solve the phase problem in X-ray crystallography. The precision and accuracy of recovered anomalous differences are crucial for determining the correct phases. Continuous rotation (CR) and inverse-beam geometry (IBG) anomalous data collection methods have been performed on tetragonal lysozyme and monoclinic survivin crystals and analysis carried out of how correlated the pairs of Friedel's reflections are after scaling. A multivariate Bayesian model for estimating anomalous differences was tested, which takes into account the correlation between pairs of intensity observations and incorporates the a priori knowledge about the positivity of intensity. The CR and IBG data collection methods resulted in positive correlation between I(+) and I(-) observations, indicating that the anomalous difference dominates between these observations, rather than different levels of radiation damage. An alternative pairing method based on near simultaneously observed Bijvoet's pairs displayed lower correlation and it was unsuccessful for recovering useful anomalous differences when using the multivariate Bayesian model. In contrast, multivariate Bayesian treatment of Friedel's pairs improved the initial phasing of the two tested crystal systems and the two data collection methods.

Protein topology classification using two-stage support vector machines.

The determination of the first 3-D model of a protein from its sequence alone is a non-trivial problem. The first 3-D model is the key to the molecular replacement method of solving phase problem in x-ray crystallography. If the sequence identity is more than 30%, homology modelling can be used to determine the correct topology (as defined by CATH) or fold (as defined by SCOP). If the sequence identity is less than 25%, however, the task is very challenging. In this paper we address the topology classification of proteins with sequence identity of less than 25%. The input information to the system is amino acid sequence, the predicted secondary structure and the predicted real value relative solvent accessibility. A two stage support vector machine (SVM) approach is proposed for classifying the sequences to three different structural classes (alpha, beta, alpha+beta) in the first stage and 39 topologies in the second stage. The method is evaluated using a newly curated dataset from CATH with maximum pairwise sequence identity less than 25%. An impressive overall accuracy of 87.44% and 83.15% is reported for class and topology prediction, respectively. In the class prediction stage, a sensitivity of 0.77 and a specificity of 0.91 is obtained. Data file, SVM implementation (SVMHEAVY) and result files can be downloaded from http://www.ee.unimelb.edu.au/ISSNIP/downloads/.

Decavanadate Inhibits Mycobacterial Growth More Potently Than Other Oxovanadates.

51V NMR spectroscopy is used to document, using speciation analysis, that one oxometalate is a more potent growth inhibitor of two Mycobacterial strains than other oxovanadates, thus demonstrating selectivity in its interaction with cells. Historically, oxometalates have had many applications in biological and medical studies, including study of the phase-problem in X-ray crystallography of the ribosome. The effect of different vanadate salts on the growth of Mycobacterium smegmatis (M. smeg) and Mycobacterium tuberculosis (M. tb) was investigated, and speciation was found to be critical for the observed growth inhibition. Specifically, the large orange-colored sodium decavanadate (V10) anion was found to be a stronger inhibitor of growth of two mycobacterial species than the colorless oxovanadate prepared from sodium metavanadate. The vanadium(V) speciation in the growth media and conversion among species under growth conditions was monitored using 51V NMR spectroscopy and speciation calculations. The findings presented in this work is particularly important in considering the many applications of polyoxometalates in biological and medical studies, such as the investigation of the phase-problem in X-ray crystallography for the ribosome. The findings presented in this work investigate the interactions of oxometalates with other biological systems.

A convenient tool for gas derivatization using fine-needle capillary mounting for protein crystals

Gas derivatization of protein crystals is useful not only to analyse gas-binding proteins but also to solve the phase problem of X-ray crystallography by using noble gases. However, the gas pressurization tools for these experiments are often elaborate and need to release the gas before flash-cooling. To simplify this step, a procedure using a fine-needle capillary to mount and flash-cool protein crystals under the pressurization of gases has been developed. After the crystals are picked up with the capillary, the capillary is sealed with an adhesive and then connected directly to a gas regulator. The quality of the diffraction data using this method is comparable with that of data from conventional pressurization procedures. The preparation of xenon-derivatives of hen egg-white lysozyme using this method was a success. In the derivatives, two new xenon binding sites were found and one of their sites vanished by releasing the gas. This observation shows the availability of flash-cooling under gas pressurization. This procedure is simple and useful for preparing gas-derivative crystals.

Synthesis of novel di-Se-containing thymidine and Se-DNAs for structure and function studies

The selenium derivatization of nucleic acids and nucleic acid-protein complexes has provided a powerful tool to solve phase problem in X-ray crystallography. Selenium atoms in the nucleotides can serve as fine scattering centers in crystal diffraction. Towards the synthesis of multiple selenium atom-containing nucleotides, which offers strong phasing power to facilitate crystal structure determination, we report here the synthesis of the thymidine analogue containing two Se atoms in one nucleobase. The novel Se-containing nucleoside and oligonucleotide DNAs were synthesized and found with the red-shifted UV spectrum and yellow color. Their unique properties are useful in phase determination, nucleic acid-based detection as well as spectroscopic studies of nucleic acids and nucleic acid-protein complexes.

Improved Technologies Now Routinely Provide Protein NMR Structures Useful for Molecular Replacement

Molecular replacement (MR) is widely used for addressing the phase problem in X-ray crystallography. Historically, crystallographers have had limited success using NMR structures as MR search models. Here, we report a comprehensive investigation of the utility of protein NMR ensembles as MR search models, using data for 25 pairs of X-ray and NMR structures solved and refined using modern NMR methods. Starting from NMR ensembles prepared by an improved protocol, FindCore, correct MR solutions were obtained for 22 targets. Based on these solutions, automatic model rebuilding could be done successfully. Rosetta refinement of NMR structures provided MR solutions for another two proteins. We also demonstrate that such properly prepared NMR ensembles and X-ray crystal structures have similar performance when used as MR search models for homologous structures, particularly for targets with sequence identity >40%.

Solution of the Phase Problem of X-Ray Crystallography

We have developed interferometric systems to measure nanosize structures and freeze their motion in time. Researchers have also suggested a method to extract both phase and amplitude information for crystallography.

News

News

Lanthanide-tagged proteins—an illuminating partnership

Lanthanide-tagged proteins are valuable for exploiting the unique properties of Ln ions for investigating protein structure, function, and dynamics. Introduction of the Ln into the target is accomplished via chemical modification with synthetic lanthanide-chelating prosthetic groups or by coexpression with peptide-based binding tags. Complexed Ln-tags offer a heavy-atom site for solving the phase problem in X-ray crystallography. In NMR, paramagnetic lanthanide ions induce residual dipolar couplings and pseudo-contact shifts that yield valuable distance constraints for structural analysis. Lanthanide luminescence-based techniques and Ln-tagged proteins are valuable for investigating the functions and dynamics of large proteins and protein complexes and have been applied in vivo. Overall, the reach of Ln-tagged proteins will increase our ability to understand cellular functions on the molecular level.

Protein Structure Determination by Molecular Replacement using High-Accuracy Protein Structure Modeling

Molecular replacement (MR) technique is to solve the phase problem in x-ray crystallography. Currently, many computational methods are available and they can provide MR solutions when a suitable 3D model of the target molecule is available. In practice, the success of the MR method is limited by various factors including unavailability of suitable 3D models and the ambiguity of crystallographic parameters. Accurate 3D modeling of the target molecule can provide a breakthrough in these cases. Recently, we have developed a protein 3D modeling method which can provide accurate protein 3D models both in backbones and side-chains. In addition, the method provides a variety of protein 3D models with structural variation. In recent blind tests, CASP7 and CASP8 experiments, the method produced the very top quality protein 3D models for high-accuracy template-based modeling targets. We combined this modeling method with a MR technique and successfully determined two protein structures, which could not be determined using conventional methods with available protein templates. It appears that high-accuracy protein 3D modeling for backbones as well as side-chains can boost up the success rate of molecular replacement technique allowing us to solve the phase problem in x-ray crystallography without requiring additional experiments with high cost efforts.

Old fold in a new X‐ray diffraction dataset? Low‐resolution molecular replacement using representative structural templates can provide phase information

The advent of structural genomics has led to a dramatic increase in the number of structures deposited in the Protein Data Bank. The number of new folds, however, still remains a very small fraction of the total number of deposited structures. Recent data on the progress of the structural genomics initiative reveals that more than 85% of target proteins that progress to the stage of data collection and structure determination have a known fold. Enzymes, which tend to exploit reaction space while adopting a common stable scaffold, contribute significantly to this observation. Herein, we evaluate a method to examine the "old fold in a new dataset" scenario likely to be encountered in the structural genomics pipeline. We demonstrate that a fold detection strategy based on secondary structure signatures followed by molecular replacement using a minimalist model can be effectively used to solve the phase problem in X-ray crystallography without further recourse to heavy atom derivatives or multiple anomalous dispersion techniques. Three common folds-the triosephosphate isomerase (TIM), adenine nucleotide alpha hydrolase-like (HUP), and RNA recognition motif (RRM)-were examined using this approach. The results presented herein also provide an estimate of the extent of phase information that can be derived from a single domain in a large multidomain structure.

Optimizing statisticalShake-and-Bakefor Se-atom substructure determination

A novel statistical approach to the phase problem in X-ray crystallography was introduced in a recent paper [Xu & Hauptman (2004), Acta Cryst. A60, 153-157]. In this approach, a new minimal function based on the statistical distribution of structure-invariant values serves as the foundation of an optimization procedure called statistical Shake-and-Bake. Favorable application of this procedure to Se-atom substructure determination depends on the choice of the statistical interval over which the function is defined. The effects of interval variation have been studied for 19 Se-atom substructures ranging in size from five to 70 Se atoms in the asymmetric unit and the results have shown an overall improvement in success rate relative to traditional Shake-and-Bake. Statistical Shake-and-Bake is being incorporated as the default optimization procedure in newly distributed versions of the SnB and BnP computer programs.

Research challenges, opportunities and synergism in systems engineering and computational biology

During the last three decades, the research area of systems engineering has emerged as a domain of fundamental importance and major impact within chemical engineering, as well as a cornerstone area in interdisciplinary research initiatives with computer science, operations research, applied mathematics, materials and life sciences. This is attributed to the unique characteristics of systems engineering which are the combination of analysis and synthesis for the design, optimization, and operation of processes and products. The product and process discovery research efforts are founded on fundamental advances in mathematical modeling, optimization theory and algorithms, and insights derived either from existing operations and/or from biology, chemistry, and physics. The fundamental advances are epitomized through new theoretical, algorithmic, and modeling frameworks for (a) mixed-integer linear and nonlinear optimization, (b) deterministic global optimization, and (c) dynamic simulation and optimization. The proposed modeling and optimization approaches have multiscale applications ranging from macroscopic to mesoscopic to microscopic systems, and which provide a natural and fundamental link between systems engineering, computational chemistry, computational biology and systems biology. Approaches based on mixed-integer linear and nonlinear optimization which were typically identified with process synthesis, scheduling and planning applications, have entered the domains of gene regulatory networks, metabolic networks, signal transduction networks, beta-sheet topology prediction in proteins, de novo peptide and protein design, DNA recombination, phase problem in X-ray crystallography, side chain optimization in protein prediction, peptide identification via tandem mass spectroscopy. Approaches based on deterministic global optimization associated with process design, synthesis, scheduling, and pooling/blending applications, are now in the main stream of product design, structure prediction in protein folding, dynamics of protein folding, NMR protein structure refinement, and de novo protein design. Approaches based on dynamic models and large scale optimization which were identified with process models and their applications, are suited for metabolic and signal transduction networks. As a result, a synergism between systems engineering, computational biology, and systems biology has evolved gradually, opened new research avenues and has reached the stage where fascinating research contributions address important questions in computational biology with methods and tools from systems engineering which combine mathematical rigor with key biological insights. This article provides a perspective on the challenges and opportunities that emerge from the fundamental developments in the research fields of systems engineering and computational biology. The advances in the areas of deterministic global optimization and process scheduling are introduced first, followed by their respective research opportunities. The revolution of genomics is discussed next with a particular focus on the advances and challenges in the areas of structure prediction in protein folding, de novo peptide and protein design, and peptide and protein identification via tandem mass spectroscopy. This article is based on material presented as an invited talk at the session on “The Future of Chemical Engineering Research III” during the 2004 annual AIChE meeting.

The phase problem of X-ray crystallography

The phase problem of X-ray crystallography

A new approach to phase retrieval of a wave front

The main thrust of this project was to develop a process including data-gathering and processing techniques that would consistently and without fail discover the phase distribution of a wave front. In the course of the work, new thoughts on data gathering evolved to the point where a novel type of intensity picture bearing little or no resemblance to the wave front or its phase distribution was required for mathematical processing to achieve the phase distribution. For convenience these information images have been dubbed phasorgrams. Phasorgrams are recorded in the diffractive plane or in the image plane of an application device. Additional data, while helpful, are not required, thus eliminating the need for data from two Fourier conjugate planes as in the well-known method of Gerchberg and Saxton. The mathematical processing of these data is carried out by an iterative algorithm which also is new. This algorithm, given good data, has not failed to achieve the phase distribution. Contemporary devices have not been designed to measure the new kinds of data required for the process. Therefore, several novel devices are suggested. The new process could have major implications for the phase problem of X-ray crystallography.

A Fast Newton Algorithm for Entropy Maximization in Phase Determination

A long-standing issue in the Bayesian statistical approach to the phase problem in X-ray crystallography is to solve an entropy maximization subproblem efficiently in every iteration of phase estimation. The entropy maximization problem is a semi-infinite convex program and can be solved in a finite dual space by using a standard Newton method. However, the Newton method is too expensive for this application since it requires O(n3) floating point operations per iteration, where n corresponds to the number of phases to be estimated. Other less expensive methods have been used, but they cannot guarantee fast convergence. In this paper, we present a fast Newton algorithm for the entropy maximization problem, which uses the Sherman--Morrison--Woodbury formula and the fast Fourier transform to compute the Newton step and requires only O(n log n) floating point operations per iteration, yet has the same convergence rate as the standard Newton. We describe the algorithm and discuss related computational issues. Numerical results on simple test cases will also be presented to demonstrate the behavior of the algorithm.

Direct measurements of Bragg-reflection phases in x-ray crystallography

We present a reference-beam x-ray-diffraction technique applied to a good-quality protein crystal. The technique is based on a multiple-beam diffraction principle and employs a modified oscillation camera in a Bragg inclined geometry, which allows a simultaneous measurement of both magnitudes and triplet phases of a large number of Bragg reflections from the sample. This work demonstrates that the reference-beam method can be a simple practical solution to the phase problem in x-ray crystallography.

The Relation Between the Phase of the Electron Wave (Which is Lost When an Em Image is Recorded) and the Preserved Crystallographic Structure Factor Phases

The phase problem in X-ray crystallography is one of the most interesting and most studied mathematical problems that exist. There is still today no general solution of the phase problem, but partial solutions have resulted in at least 8 Nobel Prizes, even though one of the most prominent solutions, the Patterson function, was not awarded the Prize.It has frequently been claimed that there should be a phase problem also in electron microscopy. It may be more correct to say that there is no phase problem, only a phase confusion problem in electron microscopy. The phase confusion problem has arisen since the word phase is used for (at least) two very different physical entities in the field of electron microscopy. When crystallographers speak about phases, they mean the crystallographic structure factor phases, while physicists mean the wave front phases. In order to resolve the phase confusion problem, it is necessary to define clearly which phases are meant.

A more general expression for the average X-ray diffraction intensity of crystals with an incommensurate one-dimensional modulation

Statistical methods are used to derive an expression for the average X-ray diffraction intensity, as a function of (sinθ)/λ, of crystals with an incommensurate one-dimensional modulation. Displacive and density modulations are considered, as well as a combination of these two. The atomic modulation functions are given by truncated Fourier series that may contain higher-order harmonics. The resulting expression for the average X-ray diffraction intensity is valid for main reflections and low-order satellite reflections. The modulation of individual atoms is taken into account by the introduction of overall modulation amplitudes. The accuracy of this expression for the average X-ray diffraction intensity is illustrated by comparison with model structures. A definition is presented for normalized structure factors of crystals with an incommensurate one-dimensional modulation that can be used in direct-methods procedures for solving the phase problem in X-ray crystallography. A numerical fitting procedure is described that can extract a scale factor, an overall temperature parameter and overall modulation amplitudes from experimental reflection intensities.