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1.  Hirshfeld atom refinement 
IUCrJ  2014;1(Pt 5):361-379.
The new automated iterative Hirshfeld atom refinement method is explained and validated through comparison of structural models of Gly–l-Ala obtained from synchrotron X-ray and neutron diffraction data at 12, 50, 150 and 295 K. Structural parameters involving hydrogen atoms are determined with comparable precision from both experiments and agree mostly to within two combined standard uncertainties.
Hirshfeld atom refinement (HAR) is a method which determines structural parameters from single-crystal X-ray diffraction data by using an aspherical atom partitioning of tailor-made ab initio quantum mechanical molecular electron densities without any further approximation. Here the original HAR method is extended by implementing an iterative procedure of successive cycles of electron density calculations, Hirshfeld atom scattering factor calculations and structural least-squares refinements, repeated until convergence. The importance of this iterative procedure is illustrated via the example of crystalline ammonia. The new HAR method is then applied to X-ray diffraction data of the dipeptide Gly–l-Ala measured at 12, 50, 100, 150, 220 and 295 K, using Hartree–Fock and BLYP density functional theory electron densities and three different basis sets. All positions and anisotropic displacement parameters (ADPs) are freely refined without constraints or restraints – even those for hydrogen atoms. The results are systematically compared with those from neutron diffraction experiments at the temperatures 12, 50, 150 and 295 K. Although non-hydrogen-atom ADPs differ by up to three combined standard uncertainties (csu’s), all other structural parameters agree within less than 2 csu’s. Using our best calculations (BLYP/cc-pVTZ, recommended for organic molecules), the accuracy of determining bond lengths involving hydrogen atoms from HAR is better than 0.009 Å for temperatures of 150 K or below; for hydrogen-atom ADPs it is better than 0.006 Å2 as judged from the mean absolute X-ray minus neutron differences. These results are among the best ever obtained. Remarkably, the precision of determining bond lengths and ADPs for the hydrogen atoms from the HAR procedure is comparable with that from the neutron measurements – an outcome which is obtained with a routinely achievable resolution of the X-ray data of 0.65 Å.
doi:10.1107/S2052252514014845
PMCID: PMC4174878  PMID: 25295177
aspherical atom partitioning; quantum mechanical molecular electron densities; X-ray structure refinement; hydrogen atom modelling; anisotropic displacement parameters
2.  REFMAC5 for the refinement of macromolecular crystal structures 
The general principles behind the macromolecular crystal structure refinement program REFMAC5 are described.
This paper describes various components of the macromolecular crystallographic refinement program REFMAC5, which is distributed as part of the CCP4 suite. REFMAC5 utilizes different likelihood functions depending on the diffraction data employed (amplitudes or intensities), the presence of twinning and the availability of SAD/SIRAS experimental diffraction data. To ensure chemical and structural integrity of the refined model, REFMAC5 offers several classes of restraints and choices of model parameterization. Reliable models at resolutions at least as low as 4 Å can be achieved thanks to low-resolution refinement tools such as secondary-structure restraints, restraints to known homologous structures, automatic global and local NCS restraints, ‘jelly-body’ restraints and the use of novel long-range restraints on atomic displacement parameters (ADPs) based on the Kullback–Leibler divergence. REFMAC5 additionally offers TLS parameterization and, when high-resolution data are available, fast refinement of anisotropic ADPs. Refinement in the presence of twinning is performed in a fully automated fashion. REFMAC5 is a flexible and highly optimized refinement package that is ideally suited for refinement across the entire resolution spectrum encountered in macromolecular crystallography.
doi:10.1107/S0907444911001314
PMCID: PMC3069751  PMID: 21460454
REFMAC5; refinement
3.  Refinement of macromolecular structures against neutron data with SHELXL2013  
Journal of Applied Crystallography  2013;47(Pt 1):462-466.
SHELXL2013 contains improvements over the previous versions that facilitate the refinement of macromolecular structures against neutron data. This article highlights several features of particular interest for this purpose and includes a list of restraints for H-atom refinement.
Some of the improvements in SHELX2013 make SHELXL convenient to use for refinement of macromolecular structures against neutron data without the support of X-ray data. The new NEUT instruction adjusts the behaviour of the SFAC instruction as well as the default bond lengths of the AFIX instructions. This work presents a protocol on how to use SHELXL for refinement of protein structures against neutron data. It includes restraints extending the Engh & Huber [Acta Cryst. (1991), A47, 392–400] restraints to H atoms and discusses several of the features of SHELXL that make the program particularly useful for the investigation of H atoms with neutron diffraction. SHELXL2013 is already adequate for the refinement of small molecules against neutron data, but there is still room for improvement, like the introduction of chain IDs for the refinement of macromolecular structures.
doi:10.1107/S1600576713027659
PMCID: PMC3937812  PMID: 24587788
single-crystal neutron diffraction; macromolecular structure refinement; hydrogen restraints; SHELXL2013
4.  On the temperature dependence of H-U iso in the riding hydrogen model 
The temperature dependence of hydrogen U iso and parent U eq in the riding hydrogen model is investigated by neutron diffraction, aspherical-atom refinements and QM/MM and MO/MO cluster calculations. Fixed values of 1.2 or 1.5 appear to be underestimated, especially at temperatures below 100 K.
The temperature dependence of H-U iso in N-acetyl-l-4-hydroxyproline monohydrate is investigated. Imposing a constant temperature-independent multiplier of 1.2 or 1.5 for the riding hydrogen model is found to be inaccurate, and severely underestimates H-U iso below 100 K. Neutron diffraction data at temperatures of 9, 150, 200 and 250 K provide benchmark results for this study. X-ray diffraction data to high resolution, collected at temperatures of 9, 30, 50, 75, 100, 150, 200 and 250 K (synchrotron and home source), reproduce neutron results only when evaluated by aspherical-atom refinement models, since these take into account bonding and lone-pair electron density; both invariom and Hirshfeld-atom refinement models enable a more precise determination of the magnitude of H-atom displacements than independent-atom model refinements. Experimental efforts are complemented by computing displacement parameters following the TLS+ONIOM approach. A satisfactory agreement between all approaches is found.
doi:10.1107/S2053273314010626
PMCID: PMC4075069
riding hydrogen model; QM/MM computations; neutron diffraction; invariom refinement; Hirshfeld-atom refinement; synchrotron radiation
5.  The active site of hen egg-white lysozyme: flexibility and chemical bonding 
Chemical bonding at the active site of lysozyme is analyzed on the basis of a multipole model employing transferable multipole parameters from a database. Large B factors at low temperatures reflect frozen-in disorder, but therefore prevent a meaningful free refinement of multipole parameters.
Chemical bonding at the active site of hen egg-white lysozyme (HEWL) is analyzed on the basis of Bader’s quantum theory of atoms in molecules [QTAIM; Bader (1994 ▶), Atoms in Molecules: A Quantum Theory. Oxford University Press] applied to electron-density maps derived from a multipole model. The observation is made that the atomic displacement parameters (ADPs) of HEWL at a temperature of 100 K are larger than ADPs in crystals of small biological molecules at 298 K. This feature shows that the ADPs in the cold crystals of HEWL reflect frozen-in disorder rather than thermal vibrations of the atoms. Directly generalizing the results of multipole studies on small-molecule crystals, the important consequence for electron-density analysis of protein crystals is that multipole parameters cannot be independently varied in a meaningful way in structure refinements. Instead, a multipole model for HEWL has been developed by refinement of atomic coordinates and ADPs against the X-ray diffraction data of Wang and coworkers [Wang et al. (2007), Acta Cryst. D63, 1254–1268], while multipole parameters were fixed to the values for transferable multipole parameters from the ELMAM2 database [Domagala et al. (2012), Acta Cryst. A68, 337–351] . Static and dynamic electron densities based on this multipole model are presented. Analysis of their topological properties according to the QTAIM shows that the covalent bonds possess similar properties to the covalent bonds of small molecules. Hydrogen bonds of intermediate strength are identified for the Glu35 and Asp52 residues, which are considered to be essential parts of the active site of HEWL. Furthermore, a series of weak C—H⋯O hydrogen bonds are identified by means of the existence of bond critical points (BCPs) in the multipole electron density. It is proposed that these weak interactions might be important for defining the tertiary structure and activity of HEWL. The deprotonated state of Glu35 prevents a distinction between the Phillips and Koshland mechanisms.
doi:10.1107/S1399004714001928
PMCID: PMC3975892  PMID: 24699657
hen egg-white lysozyme; multipole model; multipole parameters
6.  JLigand: a graphical tool for the CCP4 template-restraint library 
The CCP4 template-restraint library defines restraints for biopolymers, their modifications and ligands that are used in macromolecular structure refinement. JLigand is a graphical editor for generating descriptions of new ligands and covalent linkages.
Biological macromolecules are polymers and therefore the restraints for macromolecular refinement can be subdivided into two sets: restraints that are applied to atoms that all belong to the same monomer and restraints that are associated with the covalent bonds between monomers. The CCP4 template-restraint library contains three types of data entries defining template restraints: descriptions of monomers and their modifications, both used for intramonomer restraints, and descriptions of links for intermonomer restraints. The library provides generic descriptions of modifications and links for protein, DNA and RNA chains, and for some post-translational modifications including glycosylation. Structure-specific template restraints can be defined in a user’s additional restraint library. Here, JLigand, a new CCP4 graphical interface to LibCheck and REFMAC that has been developed to manage the user’s library and generate new monomer entries is described, as well as new entries for links and associated modifications.
doi:10.1107/S090744491200251X
PMCID: PMC3322602  PMID: 22505263
macromolecular refinement; restraint library; molecular graphics
7.  Atomic modeling of cryo-electron microscopy reconstructions – Joint refinement of model and imaging parameters 
Journal of structural biology  2013;182(1):10-21.
When refining the fit of component atomic structures into electron microscopic reconstructions, use of a resolution-dependent atomic density function makes it possible to jointly optimize the atomic model and imaging parameters of the microscope. Atomic density is calculated by one-dimensional Fourier transform of atomic form factors convoluted with a microscope envelope correction and a low-pass filter, allowing refinement of imaging parameters such as resolution, by optimizing the agreement of calculated and experimental maps. A similar approach allows refinement of atomic displacement parameters, providing indications of molecular flexibility even at low resolution. A modest improvement in atomic coordinates is possible following optimization of these additional parameters. Methods have been implemented in a Python program that can be used in stand-alone mode for rigid-group refinement, or embedded in other optimizers for flexible refinement with stereochemical restraints. The approach is demonstrated with refinements of virus and chaperonin structures at resolutions of 9 through 4.5 Å, representing regimes where rigid-group and fully flexible parameterizations are appropriate. Through comparisons to known crystal structures, flexible fitting by RSRef is shown to be an improvement relative to other methods and to generate models with all-atom rms accuracies of 1.5–2.5 Å at resolutions of 4.5–6 Å.
doi:10.1016/j.jsb.2013.01.003
PMCID: PMC3662558  PMID: 23376441
Fitting; Optimization; Structure; Resolution; Restraint; B-factor; Flexibility
8.  Crystal structure of di­chlorido­(2,2′:6′,2′′-terpyridine-κ3 N,N′,N′′)zinc: a redeter­min­ation 
The crystal structure of the title compound, [ZnCl2(C15H11N3)], was redetermined based on modern CCD data. In comparison with the previous determination from photographic film data [Corbridge & Cox (1956 ▶). J. Chem. Soc. 159, 594–603; Einstein & Penfold (1966 ▶). Acta Cryst. 20, 924–926], all non-H atoms were refined with anisotropic displacement parameters, leading to a much higher precision in terms of bond lengths and angles [e.g. Zn—Cl = 2.2684 (8) and 2.2883 (11) compared to 2.25 (1) and 2.27 (1) Å]. In the title mol­ecule, the ZnII atom is five-coordinated in a distorted square-pyramidal mode by two Cl atoms and by the three N atoms from the 2,2′:6′,2′′-terpyridine ligand. The latter is not planar and shows dihedral angles between the least-squares planes of the central pyridine ring and the terminal rings of 3.18 (8) and 6.36 (9)°. The mol­ecules in the crystal structure pack with π–π inter­actions [centroid–centroid distance = 3.655 (2) Å] between pyridine rings of neighbouring terpyridine moieties. These, together with inter­molecular C—H⋯Cl inter­actions, stablize the three-dimensional structure.
doi:10.1107/S1600536814023605
PMCID: PMC4257341  PMID: 25484786
crystal structure; redetermination; 2,2′:6′,2′′-terpyridine; zinc complex; π–π inter­actions
9.  Redetermination of Zn2Mo3O8  
The crystal structure of dizinc trimolybdenum(IV) octa­oxide, Zn2Mo3O8, has been redetermined from single-crystal X-ray data. The structure has been reported previously based on neutron powder diffraction data [Hibble et al. (1999 ▶). Acta Cryst. B55, 683-697] and single-crystal data [McCarroll et al. (1957 ▶). J. Am. Chem. Soc. 79, 5410–5414; Ansell & Katz (1966 ▶) Acta Cryst. 21, 482–485]. The results of the current redetermination show an improvement in the precision of the structural and geometric parameters with all atoms refined with anisotropic displacement parameters. The crystal structure consists of distorted hexa­gonal-close-packed oxygen layers with stacking sequence abac along [001] and is held together by alternating zinc and molybdenum layers. The Zn atoms occupy both tetra­hedral and octa­hedral inter­stices with a ratio of 1:1. The Mo atoms occupy octa­hedral sites and form strongly bonded triangular clusters involving three MoO6 octa­hedra that are each shared along two edges, forming a Mo3O13 unit. All atoms lie on special positions. The Zn atoms are in 2b Wyckoff positions with 3m. site symmetry, the Mo atoms are in 6c Wyckoff positions with . m. site symmetry and the O atoms are in 2a, 2b and 6c Wyckoff positions with 3m. and . m. site symmetries, respectively.
doi:10.1107/S1600536809021928
PMCID: PMC2969349  PMID: 21582645
10.  “Conditional Restraints”: Restraining the Free Atoms in ARP/wARP 
Structure(London, England:1993)  2009;17(2-3):183-189.
Summary
The automated building of a protein model into an electron density map remains a challenging problem. In the ARP/wARP approach, model building is facilitated by initially interpreting a density map with free atoms of unknown chemical identity; all structural information for such chemically unassigned atoms is discarded. Here, this is remedied by applying restraints between free atoms, and between free atoms and a partial protein model. These are based on geometric considerations of protein structure and tentative (conditional) assignments for the free atoms. Restraints are applied in the REFMAC5 refinement program and are generated on an ad hoc basis, allowing them to fluctuate from step to step. A large set of experimentally phased and molecular replacement structures showcases individual structures where automated building is improved drastically by the conditional restraints. The concept and implementation we present can also find application in restraining geometries, such as hydrogen bonds, in low-resolution refinement.
doi:10.1016/j.str.2008.12.011
PMCID: PMC2670983  PMID: 19217389
PROTEINS; CELLBIO
11.  Tools for macromolecular model building and refinement into electron cryo-microscopy reconstructions 
A description is given of new tools to facilitate model building and refinement into electron cryo-microscopy reconstructions.
The recent rapid development of single-particle electron cryo-microscopy (cryo-EM) now allows structures to be solved by this method at resolutions close to 3 Å. Here, a number of tools to facilitate the interpretation of EM reconstructions with stereochemically reasonable all-atom models are described. The BALBES database has been repurposed as a tool for identifying protein folds from density maps. Modifications to Coot, including new Jiggle Fit and morphing tools and improved handling of nucleic acids, enhance its functionality for interpreting EM maps. REFMAC has been modified for optimal fitting of atomic models into EM maps. As external structural information can enhance the reliability of the derived atomic models, stabilize refinement and reduce overfitting, ProSMART has been extended to generate interatomic distance restraints from nucleic acid reference structures, and a new tool, LIBG, has been developed to generate nucleic acid base-pair and parallel-plane restraints. Furthermore, restraint generation has been integrated with visualization and editing in Coot, and these restraints have been applied to both real-space refinement in Coot and reciprocal-space refinement in REFMAC.
doi:10.1107/S1399004714021683
PMCID: PMC4304694  PMID: 25615868
model building; refinement;  electron cryo-microscopy reconstructions; LIBG
12.  To B or not to B: a question of resolution? 
A simple rule of thumb based on resolution is not adequate to identify the best treatment of atomic displacements in macromolecular structural models. The choice to use isotropic B factors, anisotropic B factors, TLS models or some combination of the three should be validated through statistical analysis of the model refinement.
In choosing and refining any crystallographic structural model, there is tension between the desire to extract the most detailed information possible and the necessity to describe no more than what is justified by the observed data. A more complex model is not necessarily a better model. Thus, it is important to validate the choice of parameters as well as validating their refined values. One recurring task is to choose the best model for describing the displacement of each atom about its mean position. At atomic resolution one has the option of devoting six model parameters (a ‘thermal ellipsoid’) to describe the displacement of each atom. At medium resolution one typically devotes at most one model parameter per atom to describe the same thing (a ‘B factor’). At very low resolution one cannot justify the use of even one parameter per atom. Furthermore, this aspect of the structure may be described better by an explicit model of bulk displacements, the most common of which is the translation/libration/screw (TLS) formalism, rather than by assigning some number of para­meters to each atom individually. One can sidestep this choice between atomic displacement parameters and TLS descriptions by including both treatments in the same model, but this is not always statistically justifiable. The choice of which treatment is best for a particular structure refinement at a particular resolution can be guided by general considerations of the ratio of model parameters to the number of observations and by specific statistics such as the Hamilton R-­factor ratio test.
doi:10.1107/S0907444911028320
PMCID: PMC3322606  PMID: 22505267
atomic displacements; B factors; TLS models; model parameters
13.  Use of knowledge-based restraints in phenix.refine to improve macromolecular refinement at low resolution 
Recent developments in PHENIX are reported that allow the use of reference-model torsion restraints, secondary-structure hydrogen-bond restraints and Ramachandran restraints for improved macromolecular refinement in phenix.refine at low resolution.
Traditional methods for macromolecular refinement often have limited success at low resolution (3.0–3.5 Å or worse), producing models that score poorly on crystallographic and geometric validation criteria. To improve low-resolution refinement, knowledge from macromolecular chemistry and homology was used to add three new coordinate-restraint functions to the refinement program phenix.refine. Firstly, a ‘reference-model’ method uses an identical or homologous higher resolution model to add restraints on torsion angles to the geometric target function. Secondly, automatic restraints for common secondary-structure elements in proteins and nucleic acids were implemented that can help to preserve the secondary-structure geometry, which is often distorted at low resolution. Lastly, we have implemented Ramachandran-based restraints on the backbone torsion angles. In this method, a ϕ,ψ term is added to the geometric target function to minimize a modified Ramachandran landscape that smoothly combines favorable peaks identified from non­redundant high-quality data with unfavorable peaks calculated using a clash-based pseudo-energy function. All three methods show improved MolProbity validation statistics, typically complemented by a lowered R free and a decreased gap between R work and R free.
doi:10.1107/S0907444911047834
PMCID: PMC3322597  PMID: 22505258
macromolecular crystallography; low resolution; refinement; automation
14.  Atomic resolution studies of carbonic anhydrase II 
The structure of human carbonic anhydrase II has been solved with a sulfonamide inhibitor at 0.9 Å resolution. Structural variation and flexibility is seen on the surface of the protein and is consistent with the anisotropic ADPs obtained from refinement. Comparison with 13 other atomic resolution carbonic anhydrase structures shows that surface variation exists even in these highly ordered isomorphous crystals.
Carbonic anhydrase has been well studied structurally and functionally owing to its importance in respiration. A large number of X-ray crystallographic structures of carbonic anhydrase and its inhibitor complexes have been determined, some at atomic resolution. Structure determination of a sulfonamide-containing inhibitor complex has been carried out and the structure was refined at 0.9 Å resolution with anisotropic atomic displacement parameters to an R value of 0.141. The structure is similar to those of other carbonic anhydrase complexes, with the inhibitor providing a fourth nonprotein ligand to the active-site zinc. Comparison of this structure with 13 other atomic resolution (higher than 1.25 Å) isomorphous carbonic anhydrase structures provides a view of the structural similarity and variability in a series of crystal structures. At the center of the protein the structures superpose very well. The metal complexes superpose (with only two exceptions) with standard deviations of 0.01 Å in some zinc–protein and zinc–ligand bond lengths. In contrast, regions of structural variability are found on the protein surface, possibly owing to flexibility and disorder in the individual structures, differences in the chemical and crystalline environments or the different approaches used by different investigators to model weak or complicated electron-density maps. These findings suggest that care must be taken in interpreting structural details on protein surfaces on the basis of individual X-ray structures, even if atomic resolution data are available.
doi:10.1107/S0907444910006554
PMCID: PMC2865367  PMID: 20445237
carbonic anhydrase; structure comparison; metalloproteins; atomic resolution
15.  An introduction to stereochemical restraints 
A brief summary of the types of restraint defined in refinement dictionaries.
At the resolution available from most macromolecular crystals, the X-ray data alone are insufficient to lead to a chemically reasonable structure, so stereochemical restraints are essential. These usually restrain bond lengths, bond angles, planes and chiral volumes. The definition of these restraints and where the values come from are described. A dictionary entry contains information about the atom types, their connectivity and all the appropriate restraints. Torsion angles are not usually restrained, but they do have optimum values. In the special case of flexible five- and six-membered rings, including pentose and hexose sugars, the ring pucker is defined by combinations of torsion angles and the pucker affects the position of substituents.
doi:10.1107/S090744490604604X
PMCID: PMC2483478  PMID: 17164527
stereochemistry; restraints; bond lengths; bond angles; protein structure; crystallographic refinement
16.  Low-resolution refinement tools in REFMAC5 
Low-resolution refinement tools implemented in REFMAC5 are described, including the use of external structural restraints, helical restraints and regularized anisotropic map sharpening.
Two aspects of low-resolution macromolecular crystal structure analysis are considered: (i) the use of reference structures and structural units for provision of structural prior information and (ii) map sharpening in the presence of noise and the effects of Fourier series termination. The generation of interatomic distance restraints by ProSMART and their subsequent application in REFMAC5 is described. It is shown that the use of such external structural information can enhance the reliability of derived atomic models and stabilize refinement. The problem of map sharpening is considered as an inverse deblurring problem and is solved using Tikhonov regularizers. It is demonstrated that this type of map sharpening can automatically produce a map with more structural features whilst maintaining connectivity. Tests show that both of these directions are promising, although more work needs to be performed in order to further exploit structural information and to address the problem of reliable electron-density calculation.
doi:10.1107/S090744491105606X
PMCID: PMC3322599  PMID: 22505260
low-resolution refinement; REFMAC5
17.  Exploiting structure similarity in refinement: automated NCS and target-structure restraints in BUSTER  
Local structural similarity restraints (LSSR) provide a novel method for exploiting NCS or structural similarity to an external target structure. Two examples are given where BUSTER re-refinement of PDB entries with LSSR produces marked improvements, enabling further structural features to be modelled.
Maximum-likelihood X-ray macromolecular structure refinement in BUSTER has been extended with restraints facilitating the exploitation of structural similarity. The similarity can be between two or more chains within the structure being refined, thus favouring NCS, or to a distinct ‘target’ structure that remains fixed during refinement. The local structural similarity restraints (LSSR) approach considers all distances less than 5.5 Å between pairs of atoms in the chain to be restrained. For each, the difference from the distance between the corresponding atoms in the related chain is found. LSSR applies a restraint penalty on each difference. A functional form that reaches a plateau for large differences is used to avoid the restraints distorting parts of the structure that are not similar. Because LSSR are local, there is no need to separate out domains. Some restraint pruning is still necessary, but this has been automated. LSSR have been available to academic users of BUSTER since 2009 with the easy-to-use -autoncs and -­target target.pdb options. The use of LSSR is illustrated in the re-refinement of PDB entries 5rnt, where -target enables the correct ligand-binding structure to be found, and 1osg, where -autoncs contributes to the location of an additional copy of the cyclic peptide ligand.
doi:10.1107/S0907444911056058
PMCID: PMC3322596  PMID: 22505257
BUSTER; NCS restraints; target-structure restraints; local structural similarity restraints
18.  YUP.SCX: Coaxing Atomic Models into Medium Resolution Electron Density Maps 
Journal of structural biology  2008;163(2):163-174.
The structures of large macromolecular complexes in different functional states can be determined by cryo-electron microscopy, which yields electron density maps of low to intermediate resolutions. The maps can be combined with high-resolution atomic structures of components of the complex, to produce a model for the complex that is more accurate than the formal resolution of the map. To this end, methods have been developed to dock atomic models into density maps rigidly or flexibly, and to refine a docked model so as to optimize the fit of the atomic model into the map. We have developed a new refinement method called YUP.SCX. The electron density map is converted into a component of the potential energy function to which terms for stereochemical restraints and volume exclusion are added. The potential energy function is then minimized (using simulated annealing) to yield a stereochemically-restrained atomic structure that fits into the electron density map optimally. We used this procedure to construct an atomic model of the 70S ribosome in the pre-accommodation state. Although some atoms are displaced by as much as 33 Å, they divide themselves into nearly rigid fragments along natural boundaries with smooth transitions between the fragments.
doi:10.1016/j.jsb.2008.05.001
PMCID: PMC2702770  PMID: 18572416
Electron microscopy; simulated annealing; structural refinement
19.  A conformation-dependent stereochemical library improves crystallographic refinement even at atomic resolution 
A script was created to allow SHELXL to use the new CDL v.1.2 stereochemical library which defines the target values for main-chain bond lengths and angles as a function of the residue’s ϕ/ψ angles. Test refinements using this script show that the refinement behavior of structures at resolutions even better than 1 Å is substantially enhanced by the use of the new conformation-dependent ideal geometry paradigm.
To utilize a new conformation-dependent backbone-geometry library (CDL) in protein refinements at atomic resolution, a script was written that creates a restraint file for the SHELXL refinement program. It was found that the use of this library allows models to be created that have a substantially better fit to main-chain bond angles and lengths without degrading their fit to the X-ray data even at resolutions near 1 Å. For models at much higher resolution (∼0.7 Å), the refined model for parts adopting single well occupied positions is largely independent of the restraints used, but these structures still showed much smaller r.m.s.d. residuals when assessed with the CDL. Examination of the refinement tests across a wide resolution range from 2.4 to 0.65 Å revealed consistent behavior supporting the use of the CDL as a next-generation restraint library to improve refinement. CDL restraints can be generated using the service at http://pgd.science.oregonstate.edu/cdl_shelxl/.
doi:10.1107/S090744491102292X
PMCID: PMC3144852  PMID: 21795811
stereochemical libraries; refinement; conformation-dependent library
20.  TagDock: An efficient rigid body docking algorithm for oligomeric protein complex model construction and experiment planning 
Biochemistry  2013;52(33):5577-5584.
We report here new computational tools and strategies to efficiently generate three-dimensional models for oligomeric biomolecular complexes in cases where there is limited experimental restraint data to guide the docking calculations. Our computational tools are designed to rapidly and exhaustively enumerate all geometrically possible docking poses for an oligomeric complex, rather than generate detailed, atomic-resolution models. Experimental data, such as inter-atomic distance measurements, are then used to select and refine docking poses that are consistent with the experimental restraints. Our computational toolkit is designed for use with sparse datasets to generate intermediate-resolution docking models, and utilizes distance difference matrix analysis to identify further restraint measurements that will provide maximum additional structural refinement. Thus, these tools can be used to help plan optimal residue positions for probe incorporation in labor-intensive biophysical experiments such as chemical crosslinking, EPR, or FRET spectroscopy studies. We present benchmark results for docking the collection of all 176 heterodimer protein complexes from the ZDOCK database, as well as a protein homodimer with recently collected experimental distance restraints, to illustrate the toolkit’s capabilities and performance, and to demonstrate how distance difference matrix analysis can automatically identify and prioritize additional restraint measurements that allow us to rapidly optimize docking poses.
doi:10.1021/bi400158k
PMCID: PMC3804560  PMID: 23875708
21.  Protein Structure Refinement of CASP Target Proteins Using GNEIMO Torsional Dynamics Method 
A longstanding challenge in using computational methods for protein structure prediction is the refinement of low-resolution structural models derived from comparative modeling methods into highly accurate atomistic models useful for detailed structural studies. Previously, we have developed and demonstrated the utility of the internal coordinate molecular dynamics (MD) technique, generalized Newton–Euler inverse mass operator (GNEIMO), for refinement of small proteins. Using GNEIMO, the high-frequency degrees of freedom are frozen and the protein is modeled as a collection of rigid clusters connected by torsional hinges. This physical model allows larger integration time steps and focuses the conformational search in the low frequency torsional degrees of freedom. Here, we have applied GNEIMO with temperature replica exchange to refine low-resolution protein models of 30 proteins taken from the continuous assessment of structure prediction (CASP) competition. We have shown that GNEIMO torsional MD method leads to refinement of up to 1.3 Å in the root-mean-square deviation in coordinates for 30 CASP target proteins without using any experimental data as restraints in performing the GNEIMO simulations. This is in contrast with the unconstrained all-atom Cartesian MD method performed under the same conditions, where refinement requires the use of restraints during the simulations.
doi:10.1021/ci400484c
PMCID: PMC3985798  PMID: 24397429
22.  The X-ray Crystal Structure of Glutathionylcobalamin Revealed 
Inorganic chemistry  2010;49(21):9921-9927.
The first evidence of a complex between glutathione and cobalamin, glutathionylcobalamin (GSCbl), was presented by Wagner and Bernhauer more than 40 years ago (Ann N Y Acad Sci, 1964, 112, 580). More recently, NMR and EXAFS solution studies by Brown et al (Biochemistry, 1993, 32, 8421) and Scheuring et al. (Biochemistry, 1994, 33, 6310), respectively, provided evidence that the glutathionyl moiety in GSCbl is bound to the cobalt center via a Co-S bond. Despite continued efforts, the structural analysis of glutathionylcobalamin in the solid state has remained elusive. Here we report the first atomic resolution crystal structure of GSCbl, refined to a crystallographic R-factor of 0.0683. The glutathione moiety is bound to the cobalt center through the sulfur atom as expected, with a Co-S bond distance of 2.295(1) A. This distance agrees with the distance obtained from the EXAFS analysis of GSCbl (2.280(5) Å). However, the bond to the axial α-5,6-dimethylbenzimidazole base (DMB), 2.074(3) Å, is significantly shorter than that determined from the EXAFS measurements (Co-N3B = 2.15(3) Å). The corrin fold angle is 24.7°, the highest ever reported for a cobalamin structure, and points in the direction of the β-face of the corrin, towards the glutathione (GS−). The GS− ligand has been modeled in two conformations, each featuring distinct hydrogen bonding interactions. In both conformations, the α-carboxylate group of the GS− ligand interacts with the generally rigid side chain a of the cobalamin molecule, resulting in two distinct conformations. A comparison with the structure of other thiolatocobalamins revealed high similarity in the positions of the atoms in the cysteinyl moiety, the fold of the corrin rings, and the Co-S bond distances.
doi:10.1021/ic101173b
PMCID: PMC2964671  PMID: 20863098
Glutathionylcobalamin; glutathione; thiolatocobalamin; Co-S bond; X-ray structure; synchrotron diffraction
23.  Atomic Resolution Structure of a Protein Prepared by Non-Enzymatic His-Tag Removal. Crystallographic and NMR Study of GmSPI-2 Inhibitor 
PLoS ONE  2014;9(9):e106936.
Purification of suitable quantity of homogenous protein is very often the bottleneck in protein structural studies. Overexpression of a desired gene and attachment of enzymatically cleavable affinity tags to the protein of interest made a breakthrough in this field. Here we describe the structure of Galleria mellonella silk proteinase inhibitor 2 (GmSPI-2) determined both by X-ray diffraction and NMR spectroscopy methods. GmSPI-2 was purified using a new method consisting in non-enzymatic His-tag removal based on a highly specific peptide bond cleavage reaction assisted by Ni(II) ions. The X-ray crystal structure of GmSPI-2 was refined against diffraction data extending to 0.98 Å resolution measured at 100 K using synchrotron radiation. Anisotropic refinement with the removal of stereochemical restraints for the well-ordered parts of the structure converged with R factor of 10.57% and Rfree of 12.91%. The 3D structure of GmSPI-2 protein in solution was solved on the basis of 503 distance constraints, 10 hydrogen bonds and 26 torsion angle restraints. It exhibits good geometry and side-chain packing parameters. The models of the protein structure obtained by X-ray diffraction and NMR spectroscopy are very similar to each other and reveal the same β2αβ fold characteristic for Kazal-family serine proteinase inhibitors.
doi:10.1371/journal.pone.0106936
PMCID: PMC4169406  PMID: 25233114
24.  HAAD: A Quick Algorithm for Accurate Prediction of Hydrogen Atoms in Protein Structures 
PLoS ONE  2009;4(8):e6701.
Hydrogen constitutes nearly half of all atoms in proteins and their positions are essential for analyzing hydrogen-bonding interactions and refining atomic-level structures. However, most protein structures determined by experiments or computer prediction lack hydrogen coordinates. We present a new algorithm, HAAD, to predict the positions of hydrogen atoms based on the positions of heavy atoms. The algorithm is built on the basic rules of orbital hybridization followed by the optimization of steric repulsion and electrostatic interactions. We tested the algorithm using three independent data sets: ultra-high-resolution X-ray structures, structures determined by neutron diffraction, and NOE proton-proton distances. Compared with the widely used programs CHARMM and REDUCE, HAAD has a significantly higher accuracy, with the average RMSD of the predicted hydrogen atoms to the X-ray and neutron diffraction structures decreased by 26% and 11%, respectively. Furthermore, hydrogen atoms placed by HAAD have more matches with the NOE restraints and fewer clashes with heavy atoms. The average CPU cost by HAAD is 18 and 8 times lower than that of CHARMM and REDUCE, respectively. The significant advantage of HAAD in both the accuracy and the speed of the hydrogen additions should make HAAD a useful tool for the detailed study of protein structure and function. Both an executable and the source code of HAAD are freely available at http://zhang.bioinformatics.ku.edu/HAAD.
doi:10.1371/journal.pone.0006701
PMCID: PMC2724740  PMID: 19693270
25.  X-ray refinement significantly underestimates the level of microscopic heterogeneity in biomolecular crystals 
Nature Communications  2014;5:3220.
Biomolecular X-ray structures typically provide a static, time- and ensemble-averaged view of molecular ensembles in crystals. In the absence of rigid-body motions and lattice defects, B-factors are thought to accurately reflect the structural heterogeneity of such ensembles. In order to study the effects of averaging on B-factors, we employ molecular dynamics simulations to controllably manipulate microscopic heterogeneity of a crystal containing 216 copies of villin headpiece. Using average structure factors derived from simulation, we analyse how well this heterogeneity is captured by high-resolution molecular-replacement-based model refinement. We find that both isotropic and anisotropic refined B-factors often significantly deviate from their actual values known from simulation: even at high 1.0 Å resolution and Rfree of 5.9%, B-factors of some well-resolved atoms underestimate their actual values even sixfold. Our results suggest that conformational averaging and inadequate treatment of correlated motion considerably influence estimation of microscopic heterogeneity via B-factors, and invite caution in their interpretation.
The structural heterogeneity of a biomolecular crystal structure is typically captured using atomic B-factors, determined during structure refinement. Here, the authors use molecular dynamics to show that this strategy is flawed, and that crystallographic B-factors underestimate structural heterogeneity.
doi:10.1038/ncomms4220
PMCID: PMC3926004  PMID: 24504120

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