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.     

Normal mode refinement: crystallographic refinement of protein dynamic structure. II. Application to human lysozyme.

The dynamic structure of a protein, human lysozyme, is determined by the normal mode refinement of X-ray crystal structure. This method uses the normal modes of both internal and external motions to distinguish the real internal dynamics from the external terms such as lattice disorder, and gives an anisotropic and concerted picture of atomic fluctuations. The refinement is carried out with diffraction data of 5.0 to 1.8 A resolution, which are collected on an imaging plate. The results of the refinement show: (1) Debye-Waller factor consists of two parts, highly anisotropic internal fluctuations and almost isotropic external terms. The former is smaller than the latter by a factor of 0.72 in the scale of B-factor. Therefore, the internal dynamics cannot be recognized directly from the apparent electron density distribution. (2) The internal fluctuations show basically similar features as those predicted by the normal mode analysis, with almost the same amplitude and a similar level of anisotropy. (3) Correlations of fluctuations are detected between two lobes forming the active site cleft, which move simultaneously in opposite directions. This corresponds to the hinge-bending motion of lysozyme.     

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.     

Deriving correlated motions in proteins from X-ray structure refinement by using TLS parameters

Dynamic information in proteins may provide valuable information for understanding allosteric regulation of protein complexes or long-range effects of the mutations on enzyme activity. Experimental data such as X-ray B-factors or NMR order parameters provide a convenient estimate of atomic fluctuations (or atomic auto-correlated motions) in proteins. However, it is not as straightforward to obtain atomic cross-correlated motions in proteins — one usually resorts to more sophisticated computational methods such as Molecular Dynamics, normal mode analysis or atomic network models. In this report, we show that atomic cross-correlations can be reliably obtained directly from protein structure using X-ray refinement data. We have derived an analytic form of atomic correlated motions in terms of the original TLS parameters used to refine the B-factors of X-ray structures. The correlated maps computed using this equation are well correlated with those of the method based on a mechanical model (the correlation coefficient is 0.75) for a non-homologous dataset comprising 100 structures. We have developed an approach to compute atomic cross-correlations directly from X-ray protein structure. Being in analytic form, it is fast and provides a feasible way to compute correlated motions in proteins in a high throughput way. In addition, avoiding sophisticated computational operations; it provides a quick, reliable way, especially for non-computational biologists, to obtain dynamics information directly from protein structure relevant to its function.     

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.     

Response of dynamic structure to removal of a disulfide bond: normal mode refinement of C77A/C95A mutant of human lysozyme.

In order to investigate the response of dynamic structure to removal of a disulfide bond, the dynamic structure of human lysozyme has been compared to its C77A/C95A mutant. The dynamic structures of the wild type and mutant are determined by normal mode refinement of 1.5-A-resolution X-ray data. The C77A/C95A mutant shows an increase in apparent fluctuations at most residues. However, most of the change originates from an increase in the external fluctuations, reflecting the effect of the mutation on the quality of crystals. The effects of disulfide bond removal on the internal fluctuations are almost exclusively limited to the mutation site at residue 77. No significant change in the correlation of the internal fluctuations is found in either the overall or local dynamics. This indicates that the disulfide bond does not have any substantial role to play in the dynamic structure. A comparison of the wild-type and mutant coordinates suggests that the disulfide bond does not prevent the 2 domains from parting from each other. Instead, the structural changes are characteristic of a cavity-creating mutation, where atoms surrounding the mutation site move cooperatively toward the space created by the smaller alanine side chain. Although this produces tighter packing, more than half of the cavity volume remains unoccupied, thus destabilizing the native state.     

Temperature-dependent molecular dynamics and restrained X-ray refinement simulations of a Z-DNA hexamer

Molecular dynamics simulations of the Z-DNA hexamer 5BrdC-dG-5BrdC-dG-5BrdC-dG were performed at several temperatures between 100 K and 300 K. Above 250 K, a strong sequence-dependent flexibility in the nucleic acid is observed, with the guanine sugar and the phosphate of GpC sequences much more mobile than the cytosine sugar and phosphate of CpG sequences. At 300 K, the hexamer is in dynamic equilibrium between several Z forms, including the crystallographically determined ZI and ZII forms. The local base-pair geometry, however, is not very variable, except for the roll of the base-pairs. The hexamer molecular dynamics trajectories have been used to test the restrained parameter crystallographic refinement model for nucleic acids. X-ray diffraction intensities corresponding to observed diffraction data were computed. The average structures obtained from the simulations were then refined against the calculated intensities, using a restrained least-squares program developed for nucleic acids in order to analyse the effects of the refinement model on the derived quantities. In general, the temperature dependence of the atomic fluctuations determined directly from the refined Debye-Waller factors is in reasonably good agreement with the results obtained by calculating the atomic fluctuations directly from the Z-DNA molecular dynamics trajectories. The agreement is best for refinement of temperature factors without restraints. At the highest temperature studied (300 K), the effect of the refinement on the most mobile atoms (phosphates) is to significantly reduce the mean-square atomic fluctuations estimated from the refined Debye-Waller factors below the actual values (less than (delta r)2 greater than congruent to 0.5 A2). Analysis of the temperature-dependence of the mean-square atomic fluctuations provides information concerning the conformational potential within which the atoms move. The calculated temperature-dependence and anharmonicity of the Z-DNA helix are compared with the results observed for proteins. The average structures from the simulations were refined against the experimental X-ray intensities. It is found that low-temperature molecular dynamics simulations provide a useful tool for optimizing the refinement of X-ray structures.     

Low-resolution structure refinement in electron microscopy

A real-space structure refinement method, originally developed for macromolecular X-ray crystallography, has been applied to protein structure analysis by electron microscopy (EM). This method simultaneously optimizes the fit of an atomic model to a density map and the stereo-chemical properties of the model by minimizing an energy function. The performance of this method is characterized at different resolution and signal-to-noise ratio conditions typical for EM electron density maps. A multi-resolution scheme is devised to improve the convergence of the refinement on the global energy minimum. Applications of the method to various model systems are demonstrated here. The first case is the arrangement of FlgE molecules in the helical filament of flagellar hook, in which refinement with segmented rigid bodies improves the density correlation and reduces severe van der Waals contacts among the symmetry-related subunits. The second case is a conformational analysis of the NSF AAA ATPase in which a multi-conformer model is used in the refinement to investigate the arrangement of the two ATPase domains in the molecule. The third case is a docking simulation in which the crystal structure of actin and the NOE data from NMR experiments on the dematin headpiece are combined with a low-resolution EM density map to generate an atomic model of the F-actin-dematin headpiece structure.     

SymmRef: a flexible refinement method for symmetric multimers

Symmetric protein complexes are abundant in the living cell. Predicting their atomic structure can shed light on the mechanism of many important biological processes. Symmetric docking methods aim to predict the structure of these complexes given the unbound structure of a single monomer, or its model. Symmetry constraints reduce the search-space of these methods and make the prediction easier compared to asymmetric protein-protein docking. However, the challenge of modeling the conformational changes that the monomer might undergo is a major obstacle. In this article, we present SymmRef, a novel method for refinement and reranking of symmetric docking solutions. The method models backbone and side-chain movements and optimizes the rigid-body orientations of the monomers. The backbone movements are modeled by normal modes minimization and the conformations of the side-chains are modeled by selecting optimal rotamers. Since solved structures of symmetric multimers show asymmetric side-chain conformations, we do not use symmetry constraints in the side-chain optimization procedure. The refined models are re-ranked according to an energy score. We tested the method on a benchmark of unbound docking challenges. The results show that the method significantly improves the accuracy and the ranking of symmetric rigid docking solutions. SymmRef is available for download at http:// bioinfo3d.cs.tau.ac.il/SymmRef/download.html.     

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.     

Crystallographic refinement by knowledge-based exploration of complex energy landscapes

Although X-ray crystallography remains the most versatile method to determine the three-dimensional atomic structure of proteins and much progress has been made in model building and refinement techniques, it remains a challenge to elucidate accurately the structure of proteins in medium-resolution crystals. This is largely due to the difficulty of exploring an immense conformational space to identify the set of conformers that collectively best fits the experimental diffraction pattern. We show here that combining knowledge-based conformational sampling in RAPPER with molecular dynamics/simulated annealing (MD/SA) vastly improves the quality and power of refinement compared to MD/SA alone. The utility of this approach is highlighted by the automated determination of a lysozyme mutant from a molecular replacement solution that is in congruence with a model prepared independently by crystallographers. Finally, we discuss the implications of this work on structure determination in particular and conformational sampling and energy minimization in general.     

Ensemble refinement of protein crystal structures: validation and application

X-ray crystallography typically uses a single set of coordinates and B factors to describe macromolecular conformations. Refinement of multiple copies of the entire structure has been previously used in specific cases as an alternative means of representing structural flexibility. Here, we systematically validate this method by using simulated diffraction data, and we find that ensemble refinement produces better representations of the distributions of atomic positions in the simulated structures than single-conformer refinements. Comparison of principal components calculated from the refined ensembles and simulations shows that concerted motions are captured locally, but that correlations dissipate over long distances. Ensemble refinement is also used on 50 experimental structures of varying resolution and leads to decreases in R(free) values, implying that improvements in the representation of flexibility observed for the simulated structures may apply to real structures. These gains are essentially independent of resolution or data-to-parameter ratio, suggesting that even structures at moderate resolution can benefit from ensemble refinement.     

Protonation status of metal-bound ligands can be determined by quantum refinement

The protonation status of key residues and bound ligands are often important for the function of a protein. Unfortunately, protons are not discerned in normal protein crystal structures, so their positions have to be determined by more indirect methods. We show that the recently developed quantum refinement method can be used to determine the position of protons in crystal structures. By replacing the molecular-mechanics potential, normally used in crystallographic refinement, by more accurate quantum chemical calculations, we get information about the ideal structure of a certain protonation state. By comparing the refined structures of different protonation states, the one that fits the crystallographic raw data best can be decided using four criteria: the R factors, electron density maps, strain energy, and divergence from the unrestrained quantum chemical structure. We test this method on alcohol dehydrogenase, for which the pK(a) of the zinc-bound solvent molecule is experimentally known. We show that we can predict the correct protonation state for both a deprotonated alcohol and a neutral water molecule.     

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 ?.     

FireDock: fast interaction refinement in molecular docking

Here, we present FireDock, an efficient method for the refinement and rescoring of rigid-body docking solutions. The refinement process consists of two main steps: (1) rearrangement of the interface side-chains and (2) adjustment of the relative orientation of the molecules. Our method accounts for the observation that most interface residues that are important in recognition and binding do not change their conformation significantly upon complexation. Allowing full side-chain flexibility, a common procedure in refinement methods, often causes excessive conformational changes. These changes may distort preformed structural signatures, which have been shown to be important for binding recognition. Here, we restrict side-chain movements, and thus manage to reduce the false-positive rate noticeably. In the later stages of our procedure (orientation adjustments and scoring), we smooth the atomic radii. This allows for the minor backbone and side-chain movements and increases the sensitivity of our algorithm. FireDock succeeds in ranking a near-native structure within the top 15 predictions for 83% of the 30 enzyme-inhibitor test cases, and for 78% of the 18 semiunbound antibody-antigen complexes. Our refinement procedure significantly improves the ranking of the rigid-body PatchDock algorithm for these cases. The FireDock program is fully automated. In particular, to our knowledge, FireDock's prediction results are comparable to current state-of-the-art refinement methods while its running time is significantly lower. The method is available at http://bioinfo3d.cs.tau.ac.il/FireDock/.     

Progress and challenges in high-resolution refinement of protein structure models

Achieving atomic level accuracy in de novo structure prediction presents a formidable challenge even in the context of protein models with correct topologies. High-resolution refinement is a fundamental test of force field accuracy and sampling methodology, and its limited success in both comparative modeling and de novo prediction contexts highlights the limitations of current approaches. We constructed four tests to identify bottlenecks in our current approach and to guide progress in this challenging area. The first three tests showed that idealized native structures are stable under our refinement simulation conditions and that the refinement protocol can significantly decrease the root mean square deviation (RMSD) of perturbed native structures. In the fourth test we applied the refinement protocol to de novo models and showed that accurate models could be identified based on their energies, and in several cases many of the buried side chains adopted native-like conformations. We also showed that the differences in backbone and side-chain conformations between the refined de novo models and the native structures are largely localized to loop regions and regions where the native structure has unusual features such as rare rotamers or atypical hydrogen bonding between beta-strands. The refined de novo models typically have higher energies than refined idealized native structures, indicating that sampling of local backbone conformations and side-chain packing arrangements in a condensed state is a primary obstacle.