Statistical density modification can make use of local patterns of density found in protein structures to improve crystallographic phases.
A method for improving crystallographic phases is presented that is based on the preferential occurrence of certain local patterns of electron density in macromolecular electron-density maps. The method focuses on the relationship between the value of electron density at a point in the map and the pattern of density surrounding this point. Patterns of density that can be superimposed by rotation about the central point are considered equivalent. Standard templates are created from experimental or model electron-density maps by clustering and averaging local patterns of electron density. The clustering is based on correlation coefficients after rotation to maximize the correlation. Experimental or model maps are also used to create histograms relating the value of electron density at the central point to the correlation coefficient of the density surrounding this point with each member of the set of standard patterns. These histograms are then used to estimate the electron density at each point in a new experimental electron-density map using the pattern of electron density at points surrounding that point and the correlation coefficient of this density to each of the set of standard templates, again after rotation to maximize the correlation. The method is strengthened by excluding any information from the point in question from both the templates and the local pattern of density in the calculation. A function based on the origin of the Patterson function is used to remove information about the electron density at the point in question from nearby electron density. This allows an estimation of the electron density at each point in a map, using only information from other points in the process. The resulting estimates of electron density are shown to have errors that are nearly independent of the errors in the original map using model data and templates calculated at a resolution of 2.6 Å. Owing to this independence of errors, information from the new map can be combined in a simple fashion with information from the original map to create an improved map. An iterative phase-improvement process using this approach and other applications of the image-reconstruction method are described and applied to experimental data at resolutions ranging from 2.4 to 2.8 Å.
density modification; pattern matching
A method for automated macromolecular side-chain model building and for aligning the sequence to the map is described.
An algorithm is described for automated building of side chains in an electron-density map once a main-chain model is built and for alignment of the protein sequence to the map. The procedure is based on a comparison of electron density at the expected side-chain positions with electron-density templates. The templates are constructed from average amino-acid side-chain densities in 574 refined protein structures. For each contiguous segment of main chain, a matrix with entries corresponding to an estimate of the probability that each of the 20 amino acids is located at each position of the main-chain model is obtained. The probability that this segment corresponds to each possible alignment with the sequence of the protein is estimated using a Bayesian approach and high-confidence matches are kept. Once side-chain identities are determined, the most probable rotamer for each side chain is built into the model. The automated procedure has been implemented in the RESOLVE software. Combined with automated main-chain model building, the procedure produces a preliminary model suitable for refinement and extension by an experienced crystallographer.
model building; template matching
We report a normal-mode method for anisotropic refinement of membrane-protein structures, based on a hypothesis that the global near-native-state disordering of membrane proteins in crystals follows low-frequency normal modes. Thus, a small set of modes is sufficient to represent the anisotropic thermal motions in X-ray crystallographic refinement. By applying the method to potassium channel KcsA at 3.2 Å, we obtained a structural model with an improved fit with the diffraction data. Moreover, the improved electron density maps allowed for large structural adjustments for 12 residues in each subunit, including the rebuilding of 3 missing side chains. Overall, the anisotropic KcsA structure at 3.2 Å was systematically closer to a 2.0 Å KcsA structure, especially in the selectivity filter. Furthermore, the anisotropic thermal ellipsoids from the refinement revealed functionally relevant structural flexibility. We expect this method to be a valuable tool for structural refinement of many membrane proteins with moderate-resolution diffraction data.
We propose a template-based method for correcting field inhomogeneity biases in magnetic resonance images (MRI) of the human brain. At each algorithm iteration, the update of a B-spline deformation between an unbiased template image and the subject image is interleaved with estimation of a bias field based on the current template-to-image alignment. The bias field is modeled using a spatially smooth thin-plate spline interpolation based on ratios of local image patch intensity means between the deformed template and subject images. This is used to iteratively correct subject image intensities which are then used to improve the template-to-image deformation. Experiments on synthetic and real data sets of images with and without Alzheimer’s disease suggest that the approach may have advantages over the popular N3 technique for modeling bias fields and narrowing intensity ranges of gray matter, white matter, and cerebrospinal fluid. This bias field correction method has the potential to be more accurate than correction schemes based solely on intrinsic image properties or hypothetical image intensity distributions.
The quality of model structures generated by contemporary protein structure prediction methods strongly depends on the degree of similarity between the target and available template structures. Therefore, the importance of improving template-based model structures beyond the accuracy available from template information has been emphasized in the structure prediction community. The GalaxyRefine web server, freely available at http://galaxy.seoklab.org/refine, is based on a refinement method that has been successfully tested in CASP10. The method first rebuilds side chains and performs side-chain repacking and subsequent overall structure relaxation by molecular dynamics simulation. According to the CASP10 assessment, this method showed the best performance in improving the local structure quality. The method can improve both global and local structure quality on average, when used for refining the models generated by state-of-the-art protein structure prediction servers.
MAIN is interactive software designed to interactively perform the complex tasks of macromolecular crystal structure determination and validation. The features of MAIN and its tools for electron-density map calculations, model building, refinement in real and reciprocal space, and validation exploiting noncrystallographic symmetry in single and multiple crystal forms are presented.
MAIN is software that has been designed to interactively perform the complex tasks of macromolecular crystal structure determination and validation. Using MAIN, it is possible to perform density modification, manual and semi-automated or automated model building and rebuilding, real- and reciprocal-space structure optimization and refinement, map calculations and various types of molecular structure validation. The prompt availability of various analytical tools and the immediate visualization of molecular and map objects allow a user to efficiently progress towards the completed refined structure. The extraordinary depth perception of molecular objects in three dimensions that is provided by MAIN is achieved by the clarity and contrast of colours and the smooth rotation of the displayed objects. MAIN allows simultaneous work on several molecular models and various crystal forms. The strength of MAIN lies in its manipulation of averaged density maps and molecular models when noncrystallographic symmetry (NCS) is present. Using MAIN, it is possible to optimize NCS parameters and envelopes and to refine the structure in single or multiple crystal forms.
molecular modelling; molecular graphics; macromolecular crystal structure determination; map calculation; computer programs
Automatic modeling methods using cryo-electron microscopy (cryoEM) density maps as constrains are promising approaches to building atomic models of individual proteins or protein domains. However, their application to large macromolecular assemblies has not been possible largely due to computational limitations inherent to such unsupervised methods. Here we describe a new method, EM-IMO, for building, modifying and refining local structures of protein models using cryoEM maps as a constraint. As a supervised refinement method, EM-IMO allows users to specify parameters derived from inspections, so as to guide, and as a consequence, significantly speed up the refinement. An EM-IMO-based refinement protocol is first benchmarked on a data set of 50 homology models using simulated density maps. A multi-scale refinement strategy that combines EM-IMO-based and molecular dynamics (MD)-based refinement is then applied to build backbone models for the seven conformers of the five capsid proteins in our near-atomic resolution cryoEM map of the grass carp reovirus (GCRV) virion, a member of the aquareovirus genus of the Reoviridae family. The refined models allow us to reconstruct a backbone model of the entire GCRV capsid and provide valuable functional insights that are described in the accompanying publication. Our study demonstrates that the integrated use of homology modeling and a multi-scale refinement protocol that combines supervised and automated structure refinement offers a practical strategy for building atomic models based on medium- to high-resolution cryoEM density maps.
cryo-electron microscopy; density fitting; homology modeling; structure refinement; protein structure prediction
An OMIT procedure is presented that has the benefits of iterative model building density modification and refinement yet is essentially unbiased by the atomic model that is built.
A procedure for carrying out iterative model building, density modification and refinement is presented in which the density in an OMIT region is essentially unbiased by an atomic model. Density from a set of overlapping OMIT regions can be combined to create a composite ‘iterative-build’ OMIT map that is everywhere unbiased by an atomic model but also everywhere benefiting from the model-based information present elsewhere in the unit cell. The procedure may have applications in the validation of specific features in atomic models as well as in overall model validation. The procedure is demonstrated with a molecular-replacement structure and with an experimentally phased structure and a variation on the method is demonstrated by removing model bias from a structure from the Protein Data Bank.
model building; model validation; macromolecular models; Protein Data Bank; refinement; OMIT maps; bias; structure refinement; PHENIX
The decision-making algorithms and software used in PDB_REDO to re-refine and rebuild crystallographic protein structures in the PDB are presented and discussed.
Developments of the PDB_REDO procedure that combine re-refinement and rebuilding within a unique decision-making framework to improve structures in the PDB are presented. PDB_REDO uses a variety of existing and custom-built software modules to choose an optimal refinement protocol (e.g. anisotropic, isotropic or overall B-factor refinement, TLS model) and to optimize the geometry versus data-refinement weights. Next, it proceeds to rebuild side chains and peptide planes before a final optimization round. PDB_REDO works fully automatically without the need for intervention by a crystallographic expert. The pipeline was tested on 12 000 PDB entries and the great majority of the test cases improved both in terms of crystallographic criteria such as R
free and in terms of widely accepted geometric validation criteria. It is concluded that PDB_REDO is useful to update the otherwise ‘static’ structures in the PDB to modern crystallographic standards. The publically available PDB_REDO database provides better model statistics and contributes to better refinement and validation targets.
validation; refinement; model building; automation; PDB
Corrective osteotomy using dorsal plates and structural bone graft usually has been used for treating symptomatic distal radius malunions. However, the procedure is technically demanding and requires an extensive dorsal approach. Residual deformity is a relatively frequent complication of this technique.
We evaluated the clinical applicability of a three-dimensional osteotomy using computer-aided design and manufacturing techniques with volar locking plates for distal radius malunions.
Patients and Methods
Ten patients with metaphyseal radius malunions were treated. Corrective osteotomy was simulated with the help of three-dimensional bone surface models created using CT data. We simulated the most appropriate screw holes in the deformed radius using computer-aided design data of a locking plate. During surgery, using a custom-made surgical template, we predrilled the screw holes as simulated. After osteotomy, plate fixation using predrilled screw holes enabled automatic reduction of the distal radial fragment. Autogenous iliac cancellous bone was grafted after plate fixation.
The median volar tilt, radial inclination, and ulnar variance improved from −20°, 13°, and 6 mm, respectively, before surgery to 12°, 24°, and 1 mm, respectively, after surgery. The median wrist flexion improved from 33° before surgery to 60° after surgery. The median wrist extension was 70° before surgery and 65° after surgery. All patients experienced wrist pain before surgery, which disappeared or decreased after surgery.
Surgeons can operate precisely and easily using this advanced technique. It is a new treatment option for malunion of distal radius fractures.
Level of Evidence
Level IV, therapeutic study. See Guidelines for Authors for a complete description of levels of evidence.
Electronic supplementary material
The online version of this article (doi:10.1007/s11999-010-1748-z) contains supplementary material, which is available to authorized users.
A physics-based method, aimed at determining protein structures by using NOE-derived distances together with observed and computed 13C chemical shifts, is proposed. The approach makes use of 13Cα chemical shifts, computed at the density functional level of theory, to obtain torsional constraints for all backbone and side-chain torsional angles without making a priori use of the occupancy of any region of the Ramachandran map by the amino acid residues. The torsional constraints are not fixed but are changed dynamically in each step of the procedure, following an iterative self-consistent approach intended to identify a set of conformations for which the computed 13Cα chemical shifts match the experimental ones. A test is carried out on a 76-amino acid all-α-helical protein, namely the B. Subtilis acyl carrier protein. It is shown that, starting from randomly generated conformations, the final protein models are more accurate than an existing NMR-derived structure model of this protein, in terms of both the agreement between predicted and observed 13Cα chemical shifts and some stereochemical quality indicators, and of similar accuracy as one of the protein models solved at a high level of resolution. The results provide evidence that this methodology can be used not only for structure determination but also for additional protein structure refinement of NMR-derived models deposited in the Protein Data Bank.
I-TASSER is an automated pipeline for protein tertiary structure prediction using multiple threading alignments and iterative structure assembly simulations. In CASP9 experiments, two new algorithms, QUARK and FG-MD, were added to the I-TASSER pipeline for improving the structural modeling accuracy. QUARK is a de novo structure prediction algorithm used for structure modeling of proteins that lack detectable template structures. For distantly homologous targets, QUARK models are found useful as a reference structure for selecting good threading alignments and guiding the I-TASSER structure assembly simulations. FG-MD is an atomic-level structural refinement program that uses structural fragments collected from the PDB structures to guide molecular dynamics simulation and improve the local structure of predicted model, including hydrogen-bonding networks, torsion angles and steric clashes. Despite considerable progress in both the template-based and template-free structure modeling, significant improvements on protein target classification, domain parsing, model selection, and ab initio folding of beta-proteins are still needed to further improve the I-TASSER pipeline.
protein structure prediction; threading; contact prediction; ab initio folding; CASP
A procedure is described for improvement of crystallographic phases by reciprocal-space maximization of a likelihood function including experimental phases and characteristics of the electron-density map.
Solvent flattening is a powerful tool for improving crystallographic phases for macromolecular structures obtained at moderate resolution, but uncertainties in the optimal weighting of experimental phases and modified phases make it difficult to extract all the phase information possible. Solvent flattening is essentially an iterative method for maximizing a likelihood function which consists of (i) experimental phase information and (ii) information on the likelihood of various arrangements of electron density in a map, but the likelihood function is generally not explicitly defined. In this work, a procedure is described for reciprocal-space maximization of a likelihood function based on experimental phases and characteristics of the electron-density map. The procedure can readily be applied to phase improvement based on solvent flattening and can potentially incorporate information on a wide variety of other characteristics of the electron-density map.
solvent flattening; reciprocal-space maximization; phase improvement
Statistical models of deformations (SMD) capture the variability of deformations from the template image onto a group of sample images and can be used to constrain the traditional deformable registration algorithms to improve their robustness and accuracy. This paper employs a wavelet-PCA-based SMD to constrain the traditional deformable registration based on the Bayesian framework. The template image is adaptively warped by an intermediate deformation field generated based on the SMD during the registration procedure, and the traditional deformable registration is performed to register the intermediate template image with the input subject image. Since the intermediate template image is much more similar to the subject image, and the deformation is relatively small and local, it is less likely to be stuck into undesired local minimum using the same deformable registration in this framework. Experiments show that the proposed statistically-constrained deformable registration framework is more robust and accurate than the conventional registration.
biomedical image processing; magnetic resonance imaging; image registration; statistical model
A method for automated macromolecular main-chain model building is described.
An algorithm for the automated macromolecular model building of polypeptide backbones is described. The procedure is hierarchical. In the initial stages, many overlapping polypeptide fragments are built. In subsequent stages, the fragments are extended and then connected. Identification of the locations of helical and β-strand regions is carried out by FFT-based template matching. Fragment libraries of helices and β-strands from refined protein structures are then positioned at the potential locations of helices and strands and the longest segments that fit the electron-density map are chosen. The helices and strands are then extended using fragment libraries consisting of sequences three amino acids long derived from refined protein structures. The resulting segments of polypeptide chain are then connected by choosing those which overlap at two or more Cα positions. The fully automated procedure has been implemented in RESOLVE and is capable of model building at resolutions as low as 3.5 Å. The algorithm is useful for building a preliminary main-chain model that can serve as a basis for refinement and side-chain addition.
model building; template matching; fragment extension
Three-dimensional RNA models fitted into crystallographic density maps exhibit pervasive conformational ambiguities, geometric errors, and steric clashes. To address these problems, we present Enumerative Real-space Refinement ASsisted by Electron density under Rosetta (ERRASER), coupled to PHENIX (Python-based Hierarchical Environment for Integrated Xtallography) diffraction-based refinement. On 24 datasets, ERRASER automatically corrects the majority of MolProbity-assessed errors, improves average Rfree factor, resolves functionally important discrepancies in non-canonical structure, and refines low-resolution models to better match higher resolution models.
This paper presents a generalized learning based framework for improving both speed and accuracy of the existing deformable registration method. The key of our framework involves the utilization of a support vector regression (SVR) to learn the correlation between brain image appearances and their corresponding shape deformations to a template, for helping significantly cut down the computation cost and improve the robustness to local minima by using the learned correlation to instantly predict a good subject-specific deformation initialization for any given subject under registration. Our framework consists of three major parts: 1) training of SVR models based on the statistics of image samples and their shape deformations to capture intrinsic image-deformation correlations, 2) deformation prediction for a new subject with the trained SVR models to generate a subject-resemblance intermediate template by warping the original template with the predicted deformations, and 3) estimating of the residual deformation from the intermediate template to the subject for refined registration. Any existing deformable registration methods can be easily employed for training the SVR models and estimating the residual deformation. We have tested in this paper the two widely used deformable registration algorithms, i.e., HAMMER  and diffeomorphic demons , for demonstration of our proposed frameowrk. Experimental results show that, compared to the registration using the original methods (with no deformation prediction), our framework achieves a significant speedup (6X faster than HAMMER, and 3X faster than diffeomorphic demons), while maintaining comparable (or even slighly better) registration accuracy.
Acireductone dioxygenase (ARD) from Klebsiella ATCC 8724 is a metalloenzyme that is capable of catalyzing different reactions with the same substrates (acireductone and O2) depending upon the metal bound in the active site. A model for the solution structure of the paramagnetic Ni2+-containing ARD has been refined using residual dipolar couplings (RDCs) measured in two media. Additional dihedral restraints based on chemical shift (TALOS) were included in the refinement, and backbone structure in the vicinity of the active site was modeled from a crystallographic structure of the mouse homolog of ARD. The incorporation of residual dipolar couplings into the structural refinement alters the relative orientations of several structural features significantly, and improves local secondary structure determination. Comparisons between the solution structures obtained with and without RDCs are made, and structural similarities and differences between mouse and bacterial enzymes are described. Finally, the biological significance of these differences is considered.
metalloenzyme; magnetic alignment; nickel enzyme; paramagnetic; homology modeling
A procedure for carrying out iterative model building, density modification and refinement is presented in which the density in an OMITregion is essentially unbiased by an atomic model. Density from a set of overlapping OMIT regions can be combined to create a composite ‘iterative-build’ OMIT map that is everywhere unbiased by an atomic model but also everywhere benefiting from the model-based information present elsewhere in the unit cell. The procedure may have applications in the validation of specific features in atomic models as well as in overall model validation. The procedure is demonstrated with a molecular-replacement structure and with an experimentally phased structure and a variation on the method is demonstrated by removing model bias from a structure from the Protein Data Bank.
Multiple Mapping Method with Multiple Templates (M4T) (http://www.fiserlab.org/servers/m4t) is a fully automated comparative protein structure modeling server. The novelty of M4T resides in two of its major modules, Multiple Templates (MT) and Multiple Mapping Method (MMM). The MT module of M4T selects and optimally combines the sequences of multiple template structures through an iterative clustering approach that takes into account the ‘unique’ contribution of each template, its sequence similarity to other template sequences and to the target sequences, and the quality of its experimental resolution. MMM module is a sequence-to-structure alignment method that is aimed at improving the alignment accuracy, especially at lower sequence identity levels. The current implementation of MMM takes inputs from three profile-to-profile-based alignment methods and iteratively compares and ranks alternatively aligned regions according to their fit in the structural environment of the template structure. The performance of M4T was benchmarked on CASP6 comparative modeling target sequences and on a larger independent test set and showed a favorable performance to current state-of-the-art methods.
In image-guided diagnosis and treatment of small peripheral lung lesions the alignment of the pre-procedural lung CT images and the intra-procedural images is an important step to accurately guide and monitor the interventional procedure. Registering the serial images often relies on correct segmentation of the images and, on the other hand, the segmentation results can be further improved by temporal alignment of the serial images. This paper presents a joint serial image registration and segmentation algorithm. In this algorithm, serial images are segmented based on the current deformations, and the deformations among the serial images are iteratively refined based on the updated segmentation results. No temporal smoothness about the deformation fields is enforced so that the algorithm can tolerate larger or discontinuous temporal changes that often appear during image-guided therapy. Physical procedure models could also be incorporated to our framework to better handle the temporal changes of the serial images during intervention. In experiments, we apply the proposed algorithm to align serial lung CT images. Results using both simulated and clinical images show that the new algorithm is more robust compared to the method that only uses deformable registration.
Template-based protein structure modeling is commonly used for protein structure prediction. Based on the observation that multiple template-based methods often perform better than single template-based methods, we further explore the use of a variable number of multiple templates for a given target in the latest variant of TASSER, TASSERVMT. We first develop an algorithm that improves the target-template alignment for a given template. The improved alignment, called the SP3 alternative alignment, is generated by a parametric alignment method coupled with short TASSER refinement on models selected using knowledge-based scores. The refined top model is then structurally aligned to the template to produce the SP3 alternative alignment. Templates identified using SP3 threading are combined with the SP3 alternative and HHEARCH alignments to provide target alignments to each template. These template models are then grouped into sets containing a variable number of template/alignment combinations. For each set, we run short TASSER simulations to build full-length models. Then, the models from all sets of templates are pooled, and the top 20–50 models selected using FTCOM ranking method. These models are then subjected to a single longer TASSER refinement run for final prediction. We benchmarked our method by comparison with our previously developed approach, pro-sp3-TASSER, on a set with 874 Easy and 318 Hard targets. The average GDT-TS score improvements for the first model are 3.5% and 4.3% for Easy and Hard targets, respectively. When tested on the 112 CASP9 targets, our method improves the average GDT-TS scores as compared to pro-sp3-TASSER by 8.2% and 9.3% for the 80 Easy and 32 Hard targets, respectively. It also shows slightly better results than the top ranked CASP9 Zhang-Server, QUARK and HHpredA methods. The program is available for download at http://cssb.biology.gatech.edu/.
template-based modeling; threading; alignment; SP3; TASSER
Electron cryo-microscopy (cryo-EM) experiments yield low-resolution (3–30Å) 3D-density maps of macromolecules. These density maps are segmented to identify structurally distinct proteins, protein domains, and sub-units. Such partitioning aids the inference of protein motions and guides fitting of high-resolution atomistic structures. Cryo-EM density map segmentation has traditionally required tedious and subjective manual partitioning or semi-supervised computational methods, while validation of resulting segmentations has remained an open problem in this field. Our network-based bias-free segmentation method for cryo-EM density map segmentation, Nhs (Network-based hierarchical segmentation), provides the user with a multi-scale partitioning, reflecting local and global clustering, while requiring no user input. This approach models each map as a graph, where map voxels constitute nodes and edges connect neighboring voxels. Nhs initiates Markov diffusion (or random walk) on the weighted graph. As Markov probabilities homogenize through diffusion, an intrinsic segmentation emerges. We validate the segmentations with ground-truth maps based on atomistic models. When implemented on density maps in the 2010 Cryo-EM Modeling Challenge, Nhs efficiently and objectively partitions macromolecules into structurally and functionally relevant sub-regions at multiple scales.
The I-TASSER algorithm for protein 3D structure prediction was tested in CASP8, with the procedure fully automated in both the Server and Human sections. The quality of the server models is close to that of human ones but incorporating more diverse templates from other servers improves the results of human predictions in the distant homology category. For the first time, the sequence-based contact predictions from machine learning techniques are found helpful for both template-based modeling (TBM) and template-free modeling (FM). In TBM, although the average accuracy of the sequence-based contact predictions is lower than that from template-based ones, the novel contacts in the sequence-based predictions, which are complementary to the threading templates in the weakly or unaligned regions, are important to improve the global and local packing of these regions. Moreover, the newly developed atomic structural refinement algorithm was tested in CASP8 and found to improve the hydrogen-bonding networks and the overall TM-score, which is mainly due to its ability of removing steric clashes so that the models can be generated from cluster centroids. Nevertheless, one of the major issues of the I-TASSER pipeline is the model selection where the best models could not be appropriately recognized when the correct templates are detected only by the minority of the threading algorithms. There are also problems related with domain-splitting and mirror image recognition which mainly influences the performance of I-TASSER modeling in the FM-based structure predictions.
Protein structure prediction; threading; I-TASSER; CASP8; contact prediction; free modeling
is one of the prime tools for high resolution protein structure
refinement. While its scoring function can distinguish native-like
from non-native-like conformations in many cases, the method is limited
by conformational sampling for larger proteins, that is, leaving a
local energy minimum in which the search algorithm may get stuck.
Here, we test the hypothesis that iteration of Rosetta with an orthogonal
sampling and scoring strategy might facilitate exploration of conformational
space. Specifically, we run short molecular dynamics (MD) simulations
on models created by de novo folding of large proteins
into cryoEM density maps to enable sampling of conformational space
not directly accessible to Rosetta and thus provide an escape route
from the conformational traps. We present a combined MD–Rosetta
protein structure refinement protocol that can overcome some
of these sampling limitations. Two of four benchmark proteins showed
incremental improvement through all three rounds of the iterative
refinement protocol. Molecular dynamics is most efficient in applying
subtle but important rearrangements within secondary structure elements
and is thus highly complementary to the Rosetta refinement, which
focuses on side chains and loop regions.