Refinement of F-Actin Model against Fiber Diffraction Data by Long-Range Normal Modes

The atomic model of F-actin was refined against fiber diffraction data using long-range normal modes as adjustable parameters to account for the collective long-range filamentous deformations. To determine the effect of long-range deformations on the refinement, each of the four domains of G-actin was treated as a rigid body. It was found that among all modes, the bending modes make the most significant contributions to the improvement of the refinement. Inclusion of only 7–9 bending modes as adjustable parameters yielded a lowest R-factor of 6.3%. These results demonstrate that employing normal modes as refinement parameters has the advantage of using a small number of adjustable parameters to achieve a good fitting efficiency. Such a refinement procedure may therefore prevent the refinement from overfitting the structural model. More importantly, the results of this study demonstrate that, for any fiber diffraction data, a substantial amount of refinement error is due to long-range deformations, especially the bending, of the filaments. The effects of these intrinsic deformations cannot be easily compensated for by adjusting local structural parameters, and must be properly accounted for in the refinement to achieve improved fit of refined models with experimental diffraction data.     

Benchmarking of structure refinement methods for protein complex models

Protein structure docking is the process in which the quaternary structure of a protein complex is predicted from individual tertiary structures of the protein subunits. Protein docking is typically performed in two main steps. The subunits are first docked while keeping them rigid to form the complex, which is then followed by structure refinement. Structure refinement is crucial for a practical use of computational protein docking models, as it is aimed for correcting conformations of interacting residues and atoms at the interface. Here, we benchmarked the performance of eight existing protein structure refinement methods in refinement of protein complex models. We show that the fraction of native contacts between subunits is by far the most straightforward metric to improve. However, backbone dependent metrics, based on the Root Mean Square Deviation proved more difficult to improve via refinement.     

生物大分子结晶学中的刚体修正方法

刚体修正方法是修正生物大分子初结构的取向和位置的一个很有效的方法.本文简要地介绍了Fourier搜索法,CORELS刚体修正法及TRAREF刚体修正法三种方法,并给出了它们在不同的蛋白质结构测定中应用的结果.     

Driven to near-experimental accuracy by refinement via molecular dynamics simulations

Protein model refinement has been an essential part of successful protein structure prediction. Molecular dynamics simulation-based refinement methods have shown consistent improvement of protein models. There had been progress in the extent of refinement for a few years since the idea of ensemble averaging of sampled conformations emerged. There was little progress in CASP12 because conformational sampling was not sufficiently diverse due to harmonic restraints. During CASP13, a new refinement method was tested that achieved significant improvements over CASP12. The new method intended to address previous bottlenecks in the refinement problem by introducing new features. Flat-bottom harmonic restraints replaced harmonic restraints, sampling was performed iteratively, and a new scoring function and selection criteria were used. The new protocol expanded conformational sampling at reduced computational costs. In addition to overall improvements, some models were refined significantly to near-experimental accuracy.     

Refinement of the influenza virus hemagglutinin by simulated annealing

We have applied the method of simulated annealing to the refinement of the 3 A resolution crystal structure of the influenza virus hemagglutinin glycoprotein, using the program X-PLOR. Two different methods were introduced into X-PLOR to treat the non-crystallographic symmetry present in this and in other crystal structures. In the first, only the unique protomer atoms are refined; by application of the non-crystallographic symmetry operators to the protomer atoms, the X-ray structure factor derivatives are effectively averaged, and a non-bonded energy term models the interactions of the protomer with its neighbors in the oligomer without explicit refinement of the other protomers in the crystallographic asymmetric unit. In the second method, the entire asymmetric unit is refined, but an effective energy term is added to the empirical energy that restrains symmetry-related atomic positions to their average values after least-squares superposition. Several other modifications and additions were made to previously published X-PLOR protocols, including weighting of the X-ray terms, maintenance of the temperature of the molecular dynamics simulation, treatment of charged groups, changes in the values of certain empirical energy parameters, and the use of N-linked carbohydrate empirical energy parameters. The hemagglutinin refinement proceeded in several stages. An initial round of simulated annealing of the monomer was followed by rigid-body refinement of the 3-fold non-crystallographic symmetry axis position and a second round of monomer refinement. A third round was performed on the trimer using non-crystallographic symmetry restraints in all regions except those in lattice contacts showing obvious derivations from 3-fold symmetry. The refinement was completed with several rounds of conventional positional and isotropic temperature factor refinement needed to correct bad model geometry introduced by high-temperature molecular dynamics in regions of weak electron density. This structure was then used as the basis for refinement of three crystallographically isomorphous hemagglutinin structures, including complexes with the influenza virus receptor, sialic acid. Model geometry comparable to well-refined high-resolution structures was obtained with relatively little manual intervention, demonstrating the ability of simulated annealing refinement to produce highly idealized structures at moderate resolution.     

Application of statistical potentials to protein structure refinement from low resolution ab initio models

Recently ab initio protein structure prediction methods have advanced sufficiently so that they often assemble the correct low resolution structure of the protein. To enhance the speed of conformational search, many ab initio prediction programs adopt a reduced protein representation. However, for drug design purposes, better quality structures are probably needed. To achieve this refinement, it is natural to use a more detailed heavy atom representation. Here, as opposed to costly implicit or explicit solvent molecular dynamics simulations, knowledge-based heavy atom pair potentials were employed. By way of illustration, we tried to improve the quality of the predicted structures obtained from the ab initio prediction program TOUCHSTONE by three methods: local constraint refinement, reduced predicted tertiary contact refinement, and statistical pair potential guided molecular dynamics. Sixty-seven predicted structures from 30 small proteins (less than 150 residues in length) representing different structural classes (alpha, beta, alpha;/beta) were examined. In 33 cases, the root mean square deviation (RMSD) from native structures improved by more than 0.3 A; in 19 cases, the improvement was more than 0.5 A, and sometimes as large as 1 A. In only seven (four) cases did the refinement procedure increase the RMSD by more than 0.3 (0.5) A. For the remaining structures, the refinement procedures changed the structures by less than 0.3 A. While modest, the performance of the current refinement methods is better than the published refinement results obtained using standard molecular dynamics.     

i3Drefine Software for Protein 3D Structure Refinement and Its Assessment in CASP10

Protein structure refinement refers to the process of improving the qualities of protein structures during structure modeling processes to bring them closer to their native states. Structure refinement has been drawing increasing attention in the community-wide Critical Assessment of techniques for Protein Structure prediction (CASP) experiments since its addition in 8^th CASP experiment. During the 9^th and recently concluded 10^th CASP experiments, a consistent growth in number of refinement targets and participating groups has been witnessed. Yet, protein structure refinement still remains a largely unsolved problem with majority of participating groups in CASP refinement category failed to consistently improve the quality of structures issued for refinement. In order to alleviate this need, we developed a completely automated and computationally efficient protein 3D structure refinement method, i3Drefine, based on an iterative and highly convergent energy minimization algorithm with a powerful all-atom composite physics and knowledge-based force fields and hydrogen bonding (HB) network optimization technique. In the recent community-wide blind experiment, CASP10, i3Drefine (as ‘MULTICOM-CONSTRUCT’) was ranked as the best method in the server section as per the official assessment of CASP10 experiment. Here we provide the community with free access to i3Drefine software and systematically analyse the performance of i3Drefine in strict blind mode on the refinement targets issued in CASP10 refinement category and compare with other state-of-the-art refinement methods participating in CASP10. Our analysis demonstrates that i3Drefine is only fully-automated server participating in CASP10 exhibiting consistent improvement over the initial structures in both global and local structural quality metrics. Executable version of i3Drefine is freely available at http://protein.rnet.missouri.edu/i3drefine/.     

Real-space refinement with DireX: from global fitting to side-chain improvements

Single-particle cryo-electron microscopy (cryo-EM) has become an important tool to determine the structure of large biomolecules and assemblies thereof. However, the achievable resolution varies considerably over a wide range of about 3.5-20 ?. The interpretation of these intermediate- to low-resolution density maps in terms of atomic models is a big challenge and an area of active research. Here, we present our real-space structure refinement program DireX, which was developed primarily for cryo-EM-derived density maps. The basic principle and its main features are described. DireX employs Deformable Elastic Network (DEN) restraints to reduce overfitting by decreasing the effective number of degrees of freedom used in the refinement. Missing or reduced density due to flexible parts of the protein can lead to artifacts in the structure refinement, which is addressed through the concept of restrained grouped occupancy refinement. Furthermore, we describe the performance of DireX in the 2010 Cryo-EM Modeling Challenge, where we chose six density maps of four different proteins provided by the Modeling Challenge exemplifying typical refinement results at a large resolution range from 3 to 23 ?.     

Normal mode refinement: crystallographic refinement of protein dynamic structure. I. Theory and test by simulated diffraction data.

A dynamic structure refinement method for X-ray crystallography, referred to as the normal mode refinement, is proposed. The Debye-Waller factor is expanded in terms of the low-frequency normal modes whose amplitudes and eigenvectors are experimentally optimized in the process of the crystallographic refinement. In this model, the atomic fluctuations are treated as anisotropic and concerted. The normal modes of the external motion (TLS model) are also introduced to cover the factors other than the internal fluctuations, such as the lattice disorder and diffusion. A program for the normal mode refinement (NM-REF) has been developed. The method has first been tested against simulated diffraction data for human lysozyme calculated by a Monte Carlo simulation. Applications of the method have demonstrated that the normal mode refinement has: (1) improved the fitting to the diffraction data, even with fewer adjustable parameters; (2) distinguished internal fluctuations from external ones; (3) determined anisotropic thermal factors; and (4) identified concerted fluctuations in the protein molecule.     

The molecular signals that regulate activity-dependent synapse refinement in the brain

The formation of appropriate synaptic connections is critical for the proper functioning of the brain. Early in development, neurons form a surplus of immature synapses. To establish efficient, functional neural networks, neurons selectively stabilize active synapses and eliminate less active ones. This process is known as activity-dependent synapse refinement. Defects in this process have been implicated in neuropsychiatric disorders such as schizophrenia and autism. Here we review the manner and mechanisms by which synapse elimination is regulated through activity-dependent competition. We propose a theoretical framework for the molecular mechanisms of synapse refinement, in which three types of signals regulate the refinement. We then describe the identity of these signals and discuss how multiple molecular signals interact to achieve appropriate synapse refinement in the brain.     

Highly constrained multiple-copy refinement of protein crystal structures

In the course of refining atomic protein structures, one often encounters difficulty with molecules that are unusually flexible or otherwise disordered. We approach the problem by combining two relatively recent developments: simultaneous refinement of multiple protein conformations and highly constrained refinement. A constrained Langevin dynamics refinement is tested on two proteins: neurotrophin-3 and glutamine synthetase. The method produces closer agreement between the calculated and observed scattering amplitudes than standard, single-copy, Gaussian atomic displacement parameter refinement. This is accomplished without significantly increasing the number of fitting parameters in the model. These results suggest that loop motion in proteins within a crystal lattice can be extensive and that it is poorly modeled by isotropic Gaussian distributions for each atom. Proteins 29:426–432, 1997. © 1997 Wiley-Liss, Inc.     

Refinement of protein structure homology models via long, all-atom molecular dynamics simulations

Accurate computational prediction of protein structure represents a longstanding challenge in molecular biology and structure-based drug design. Although homology modeling techniques are widely used to produce low-resolution models, refining these models to high resolution has proven difficult. With long enough simulations and sufficiently accurate force fields, molecular dynamics (MD) simulations should in principle allow such refinement, but efforts to refine homology models using MD have for the most part yielded disappointing results. It has thus far been unclear whether MD-based refinement is limited primarily by accessible simulation timescales, force field accuracy, or both. Here, we examine MD as a technique for homology model refinement using all-atom simulations, each at least 100 μs long-more than 100 times longer than previous refinement simulations-and a physics-based force field that was recently shown to successfully fold a structurally diverse set of fast-folding proteins. In MD simulations of 24 proteins chosen from the refinement category of recent Critical Assessment of Structure Prediction (CASP) experiments, we find that in most cases, simulations initiated from homology models drift away from the native structure. Comparison with simulations initiated from the native structure suggests that force field accuracy is the primary factor limiting MD-based refinement. This problem can be mitigated to some extent by restricting sampling to the neighborhood of the initial model, leading to structural improvement that, while limited, is roughly comparable to the leading alternative methods.     

Constrained and restrained refinement in EXAFS data analysis with curved wave theory.

This paper describes methods of constrained and restrained refinement of EXAFS data which provide a means of substantially reducing the number of independent parameters compared to conventional least-squares methods commonly used. Constrained refinement allows a major reduction in the number of free parameters for a refinement of a structural model. In restrained refinement, additional structural information from well-characterized small molecules is used to provide additional observations in the data analysis. Even though these methods are of general application to the majority of complex systems, they are particularly valuable for biological molecules. The methods are of major advantage for ligands where significant multiple scattering is present, e.g., histidine, tyrosine, CO, CN, etc. The bases of these methods are described, and applications to some complex chemical and biological systems are given.     

Crystallographic structure refinement of Chromatium high potential iron protein at two Angstroms resolution.

The structure of Chromatium high potential iron protein (HiPIP) has been refined by semiautomatic Fo-Fc (observed minus calculated structure amplitude Fourier methods to a convential R index, R=sum of the absolute value of Fo-Fc divided by the sum of Fo, of 24.7% for a model in which bond distances and angles are constrained to standard values. Bond length and angle constraints were applied only intermittenly during the computations. At a late stage of the refinement, atomic parameters for only the Fe4S4 cluster plus the 4 associated cystein S-gamma atoms were adjusted by least squares methods and kept fixed during the rest of the refinement. The refined model consists of 625 of the 632 nonhydrogen atoms in the protein plus 75 water molecules. Seven side chain atoms could not be located in the final electron density map. A computer program rather than visual inspection was used wherever possible in the refinement: for locating water molecules, for removing water molecules that too closely approach other atoms, for deleting atoms that lay in regions of low electron density, and for evaluating the progress of refinement. Fo-Fc Fourier refinement is sufficiently economical to be applied routinely in protein crystal structure determinations. The complete HiPIP refinement required approximately 12 hours of CDC 3600 computer time and cost less than $3000 starting from a "trial structure," based upon multipe isomorphoous replacement phases, which gave an R of 43%...     

Effect of anisotropy and anharmonicity on protein crystallographic refinement. An evaluation by molecular dynamics

Molecular dynamics simulations are employed to determine the errors introduced by anharmonicity and anisotropy in the structure and temperature factors obtained for proteins by refinement of X-ray diffraction data. Simulations (25 ps and 300 ps) of metmyoglobin are used to generate time-averaged diffraction data at 1.5 A resolution. The crystallographic restrained-parameter least-squares refinement program PROLSQ is used to refine models against these simulated data. The resulting atomic positions and isotropic temperature factors are compared with the average structure and fluctuations calculated directly from the simulations. It is found that significant errors in the atomic positions and fluctuations are introduced by the refinement, and that the errors increase with the magnitude of the atomic fluctuations. Of particular interest is the fact that the refinement generally underestimates the atomic motions. Moreover, while the actual fluctuations go up to a mean-square value of about 5 A2, the X-ray results never go above approximately 2 A2. This systematic deviation in the motional parameters appears to be due to the use of a single-site isotropic model for the atomic fluctuations. Many atoms have multiple peaks in their probability distribution functions. For some atoms, the multiple peaks are seen in difference electron density maps and it is possible to include these in the refinement as disordered residues. However, for most atoms the refinement fits only one peak and neglects the rest, leading to the observed errors in position and temperature factor. The use of strict stereochemical restraints is inconsistent with the average dynamical structure; nevertheless, refinement with tight restraints results in structures that are comparable to those obtained with loose restraints and better than those obtained with no restraints. The results support the use of tight stereochemical restraints, but indicate that restraints on the variation of temperature factors are too restrictive.     

Normal-mode refinement of anisotropic thermal parameters for potassium channel KcsA at 3.2 A crystallographic resolution

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 A, 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 A was systematically closer to a 2.0 A 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.     

Biomolecular structure refinement using the GROMOS simulation software

For the understanding of cellular processes the molecular structure of biomolecules has to be accurately determined. Initial models can be significantly improved by structure refinement techniques. Here, we present the refinement methods and analysis techniques implemented in the GROMOS software for biomolecular simulation. The methodology and some implementation details of the computation of NMR NOE data, ³ J-couplings and residual dipolar couplings, X-ray scattering intensities from crystals and solutions and neutron scattering intensities used in GROMOS is described and refinement strategies and concepts are discussed using example applications. The GROMOS software allows structure refinement combining different types of experimental data with different types of restraining functions, while using a variety of methods to enhance conformational searching and sampling and the thermodynamically calibrated GROMOS force field for biomolecular simulation.     

Refinement of herpesvirus B-capsid structure on parallel supercomputers.

Electron cryomicroscopy and icosahedral reconstruction are used to obtain the three-dimensional structure of the 1250-A-diameter herpesvirus B-capsid. The centers and orientations of particles in focal pairs of 400-kV, spot-scan micrographs are determined and iteratively refined by common-lines-based local and global refinement procedures. We describe the rationale behind choosing shared-memory multiprocessor computers for executing the global refinement, which is the most computationally intensive step in the reconstruction procedure. This refinement has been implemented on three different shared-memory supercomputers. The speedup and efficiency are evaluated by using test data sets with different numbers of particles and processors. Using this parallel refinement program, we refine the herpesvirus B-capsid from 355-particle images to 13-A resolution. The map shows new structural features and interactions of the protein subunits in the three distinct morphological units: penton, hexon, and triplex of this T = 16 icosahedral particle.     

How noise in force fields can affect the structural refinement of protein models?

Structural refinement of predicted models of biological macromolecules using atomistic or coarse‐grained molecular force fields having various degree of error is investigated. The goal of this analysis is to estimate what is the probability for designing an effective structural refinement based on computations of conformational energies using force field, and starting from a structure predicted from the sequence (using template‐based or template‐free modeling), and refining it to bring the structure into closer proximity to the native state. It is widely believed that it should be possible to develop such a successful structure refinement algorithm by applying an iterative procedure with stochastic sampling and appropriate energy function, which assesses the quality (correctness) of protein decoys. Here, an analysis of noise in an artificially introduced scoring function is investigated for a model of an ideal sampling scheme, where the underlying distribution of RMSDs is assumed to be Gaussian. Sampling of the conformational space is performed by random generation of RMSD values. We demonstrate that whenever the random noise in a force field exceeds some level, it is impossible to obtain reliable structural refinement. The magnitude of the noise, above which a structural refinement, on average is impossible, depends strongly on the quality of sampling scheme and a size of the protein. Finally, possible strategies to overcome the intrinsic limitations in the force fields for impacting the development of successful refinement algorithms are discussed. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

Sampling of near-native protein conformations during protein structure refinement using a coarse-grained model, normal modes, and molecular dynamics simulations

Protein structure refinement from comparative models with the goal of predicting structures at near-experimental accuracy remains an unsolved problem. Structure refinement might be achieved with an iterative protocol where the most native-like structure from a set of decoys generated from an initial model in one cycle is used as the starting structure for the next cycle. Conformational sampling based on the coarse-grained SICHO model, atomic level of detail molecular dynamics simulations, and normal-mode analysis is compared in the context of such a protocol. All of the sampling methods can achieve significant refinement close to experimental structures, although the distribution of structures and the ability to reach native-like structures differs greatly. Implications for the practical application of such sampling methods and the requirements for scoring functions in an iterative refinement protocol are analyzed in the context of theoretical predictions for the distribution of protein-like conformations with a random sampling protocol.