Reciprocal-space Refinement Research Articles

Toward Real Real-Space Refinement of Atomic Models.

High-quality atomic models providing structural information are the results of their refinement versus diffraction data (reciprocal-space refinement), or versus experimental or experimentally based maps (real-space refinement). A proper real-space refinement can be achieved by comparing such a map with a map calculated from the atomic model. Similar to density distributions, the maps of a limited and even inhomogeneous resolution can also be calculated as sums of terms, known as atomic images, which are three-dimensional peaky functions surrounded by Fourier ripples. These atomic images and, consequently, the maps for the respective models, can be expressed analytically as functions of coordinates, atomic displacement parameters, and the local resolution. This work discusses the practical feasibility of such calculation for the real-space refinement of macromolecular atomic models.

Reciprocal-space refinement and map calculation for cryo-EM single-particle structures

Reciprocal-space refinement and map calculation for cryo-EM single-particle structures

Tools for macromolecular 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.

Improved low-resolution crystallographic refinement with Phenix and Rosetta

Refinement of macromolecular structures against low-resolution crystallographic data is limited by the ability of current methods to arrive at a high-quality structure with realistic geometry. We have developed a new method for crystallographic refinement which combines the Rosetta sampling methodology and all atom energy function with likelihood-based reciprocal space refinement in Phenix, and find, on a test set of difficult low-resolution refinement cases, that models refined with the new method have significantly improved model geometry, and in most cases, lower free R factors and RMS deviation to the final model. Integration of the software packages additionally makes advanced sampling methods used in structure prediction and design available for crystallographic refinement and model-building, and also provides a strategy for improving the Rosetta force field for better agreement with experimental data.

Improved crystallographic models through iterated local density-guided model deformation and reciprocal-space refinement.

An approach is presented for addressing the challenge of model rebuilding after molecular replacement in cases where the placed template is very different from the structure to be determined. The approach takes advantage of the observation that a template and target structure may have local structures that can be superimposed much more closely than can their complete structures. A density-guided procedure for deformation of a properly placed template is introduced. A shift in the coordinates of each residue in the structure is calculated based on optimizing the match of model density within a 6 Å radius of the center of that residue with a prime-and-switch electron-density map. The shifts are smoothed and applied to the atoms in each residue, leading to local deformation of the template that improves the match of map and model. The model is then refined to improve the geometry and the fit of model to the structure-factor data. A new map is then calculated and the process is repeated until convergence. The procedure can extend the routine applicability of automated molecular replacement, model building and refinement to search models with over 2 Å r.m.s.d. representing 65-100% of the structure.

Crystal Structure of C5b-6 Suggests Structural Basis for Priming Assembly of the Membrane Attack Complex

The complement membrane attack complex (MAC) forms transmembrane pores in pathogen membranes. The first step in MAC assembly is cleavage of C5 to generate metastable C5b, which forms a stable complex with C6, termed C5b-6. C5b-6 initiates pore formation via the sequential recruitment of homologous proteins: C7, C8, and 12-18 copies of C9, each of which comprises a central MAC-perforin domain flanked by auxiliary domains. We recently proposed a model of pore assembly, in which the auxiliary domains play key roles, both in stabilizing the closed conformation of the protomers and in driving the sequential opening of the MAC-perforin β-sheet of each new recruit to the growing pore. Here, we describe an atomic model of C5b-6 at 4.2 Å resolution. We show that C5b provides four interfaces for the auxiliary domains of C6. The largest interface is created by the insertion of an interdomain linker from C6 into a hydrophobic groove created by a major reorganization of the α-helical domain of C5b. In combination with the rigid body docking of N-terminal elements of both proteins, C5b becomes locked into a stable conformation. Both C6 auxiliary domains flanking the linker pack tightly against C5b. The net effect is to induce the clockwise rigid body rotation of four auxiliary domains, as well as the opening/twisting of the central β-sheet of C6, in the directions predicted by our model to activate or prime C6 for the subsequent steps in MAC assembly. The complex also suggests novel small molecule strategies for modulating pathological MAC assembly.

Performance of phased rotation, conformation and translation function: accurate protein model building with tripeptidic and tetrapeptidic fragments

The automatic building of protein structures with tripeptidic and tetrapeptidic fragments was investigated. The oligopeptidic conformers were positioned in the electron-density map by a phased rotation, conformation and translation function and refined by a real-space refinement. The number of successfully located fragments lay within the interval 75-95% depending on the resolution and phase quality. The overlaps of partially located fragments were analyzed. The correctly positioned fragments were connected into chains. Chains formed in this way were extended directly into the electron density and a sequence was assigned. In the initial stage of the model building the number of located fragments was between 60% and 95%, but this number could be increased by several cycles of reciprocal-space refinement and automatic model rebuilding. A nearly complete structure can be obtained on the condition that the resolution is reasonable. Computer graphics will only be needed for a final check and small corrections.

Multiple Conformers in Active Site of Human Dihydrofolate Reductase F31R/Q35E Double Mutant Suggest Structural Basis for Methotrexate Resistance

Methotrexate is a slow, tight-binding, competitive inhibitor of human dihydrofolate reductase (hDHFR), an enzyme that provides key metabolites for nucleotide biosynthesis. In an effort to better characterize ligand binding in drug resistance, we have previously engineered hDHFR variant F31R/Q35E. This variant displays a >650-fold decrease in methotrexate affinity, while maintaining catalytic activity comparable to the native enzyme. To elucidate the molecular basis of decreased methotrexate affinity in the doubly substituted variant, we determined kinetic and inhibitory parameters for the simple variants F31R and Q35E. This demonstrated that the important decrease of methotrexate affinity in variant F31R/Q35E is a result of synergistic effects of the combined substitutions. To better understand the structural cause of this synergy, we obtained the crystal structure of hDHFR variant F31R/Q35E complexed with methotrexate at 1.7-A resolution. The mutated residue Arg-31 was observed in multiple conformers. In addition, seven native active-site residues were observed in more than one conformation, which is not characteristic of the wild-type enzyme. This suggests that increased residue disorder underlies the observed methotrexate resistance. We observe a considerable loss of van der Waals and polar contacts with the p-aminobenzoic acid and glutamate moieties. The multiple conformers of Arg-31 further suggest that the amino acid substitutions may decrease the isomerization step required for tight binding of methotrexate. Molecular docking with folate corroborates this hypothesis.

Уточнение макромолекулярных структур без стереохимических ограничений как метод выявления альтернативных конформаций

Уточнение макромолекулярных структур без стереохимических ограничений как метод выявления альтернативных конформаций

Simulated-annealing real-space refinement as a tool in model building.

Methods have been developed that further automate the building of macromolecular structures into electron-density maps. The software supports molecular-dynamics real-space refinement of an atomic model to local regions of a map within the context of a popular molecular-modeling program, O [Jones et al. (1991), Acta Cryst. A47, 110-119]. It is implemented as a module to the CNS refinement package [Brünger et al. (1998), Acta Cryst. D54, 905-921], controlled by a graphical user interface and commands executed directly through the molecular-graphics package. The method is illustrated with examples of the building and rebuilding of protein and nucleic acid models in which laborious manual adjustments are avoided. The resulting models show improved convergence during subsequent reciprocal-space refinement. The novel feature of the RSRef2000 software is the combination of simulated-annealing optimization with local real-space refinement, allowing several local minima to be explored quickly and automatically within the context of interactive model building.

Critical initial real-space refinement in the structure determination of arginine kinase.

Arginine kinase (AK), a homologue of creatine kinase, catalyses the reversible transfer of a phosphoryl group between a guanidino phosphate and ADP. The family of phosphagen kinases eluded structure determination for over 25 years until an inactive form creatine kinase (CK) structure was determined [Fritz-Wolf et al. (1996). Nature (London), 381, 341-345]. The structure determination of the active-form transition-state complex was non-trivial, owing to the distant relatedness and domain reorientation of AK compared with CK. Phases from a molecular-replacement solution of the large domain, supplemented by single isomorphous replacement and inter-crystal averaging, did not reveal interpretable electron density for the small domain. Reciprocal-space refinement of the initial model (Rfree = 0.54) by any of the commonly used methods, including post facto application of maximum-likelihood methods, led to overfitting without significant improvement of the partial initial model. By contrast, in the local real-space refinements which proved successful, the interdependence of atoms is limited to immediate neighbors, and atomic positions are not influenced by errors or omissions in remote parts of the structure. Modest improvement was possible without overfitting, and this was critical to the calculation of improved phases. Phases were refined and extended from 4.0 to 2.5 A resolution by Fourier inversion of omit maps, combination with isomorphous replacement phases and averaging between crystal forms, after several batches of real- and reciprocal-space atomic refinement. The final structure refinement, against a 1.86 A cryo data set yielded a high-quality model with R = 0.196 and Rfree = 0.224.

Potential use of real-space refinement in protein structure determination.

Through testing refinement protocols using free R-factor estimates of model quality, it is shown that real-space refinement can be a useful addition to conventional reciprocal-space refinement, even for protein structures with poor electron-density maps derived from multiple isomorphous replacement. By alternating real- and reciprocal-space refinements, starting with an experimental map, then calculating 2F(o) - F(c) maps, it is demonstrated with the structure of HMG-CoA reductase, that quick automatic refinement can yield a model with a free R factor 1.5% better than exhaustive reciprocal-space refinement, and within 1% of a model that was interactively rebuilt and refined repeatedly.

Refined X-ray crystal structures of the reactive site modified ovomucoid inhibitor third domains from silver pheasant (OMSVP3 ∗) and from Japanese quail (OMJPQ3 ∗)

Tetragonal and triclinic crystals of two ovomucoid inhibitor third domains from silver pheasant and Japanese quail, modified at their reactive site bonds Met18Glu19 (OMSVP3 ∗) and Lys18Asp19 (OMJPQ3 ∗), respectively, were obtained. Their molecular and crystal structures were solved using X-ray data to 2.5 Å and 1.55 Å by means of Patterson search methods using truncated models of the intact (virgin) inhibitors as search models. Both structures were crystallographically refined to R-values of 0.185 and 0.192, respectively, applying an energy restraint reciprocal space refinement procedure. Both modified inhibitors show large deviations from the intact derivatives only in the proteinase binding loops (Pro14 to Arg21) and in the amino-terminal segments (Leul to Val6). In the modified inhibitors the residues immediately adjacent to the cleavage site (in particular P2, P1, P1′) are mobile and able to adapt to varying crystal environments. The charged end-groups i.e. Met18 COO − and Glu19 NH 3 + in OMSVP3 ∗, and Lys18 COO − and Aspl9 NH 3 + in OMJPQ3 ∗, do not form ion pairs with one another. The hydrogen bond connecting the side-chains of Thr17 and Glu19 (i.e. residues on either side of the scissile peptide bond) in OMSVP3 is broken in the modified form, and the hydrogen-bond interactions observed in the intact molecules between the Asn33 side-chain and the carbonyl groups of loop residues P2 and P1′ are absent or weak in the modified inhibitors. The reactive site cleavage, however, has little effect on specific interactions within the protein scaffold such as the side-chain hydrogen bond between Asp27 and Tyr31 or the side-chain stacking of Tyr20 and Pro22. The conformational differences in the amino-terminal segment Leul to Val6 are explained by their ability to move freely, either to associate with segments of symmetry-related molecules under formation of a four-stranded β-barrel (OMSVP3 ∗ and OMJPQ3) or to bind to surrounding molecules. Together with the results given in the accompanying paper, these findings probably explain why K hyd of small protein inhibitors of serine proteinases is generally found to be so small.

2.5 Å structure of aspartate carbamoyltransferase complexed with the bisubstrate analog N-(phosphonacetyl)- l-aspartate

In an X-ray diffraction study using the method of multiple isomorphous replacement, the structure of aspartate Carbamoyltransferase (EC 2.1.3.2) complexed with the bisubstrate analog N-(phosphonacetyl)- l-aspartate (PALA) ‡ has been solved to 2.5 Å. Ten rounds of model building and 123 cycles of restrained reciprocal space refinement have resulted in a model containing 94.4% of the theoretical atoms of the protein-inhibitor complex with an R-factor of 0.231. The fit of the model to the density is excellent, except for occasional side-chains and two sections of the regulatory chains that may be disordered. The electron density for the PALA molecule is readily identifiable for both catalytic (c) chains of the asymmetric unit and bonding interactions with several important residues including Ser52, Arg54, Thr55, Ser80, Lys84, Arg105, His134, Arg165, Arg229 and Gln231 are apparent. The carboxylate groups of the PALA molecule are in a nearly cis conformation. Gross quaternary changes between the T and R forms are noted and in agreement with earlier work from this laboratory. Namely, in the new structure the catalytic trimers move apart by 12 Å along the 3-fold axis of the enzyme and relocate by 10 ° relative to each other, adopting a more eclipsed position. The regulatory (r) chains in the new structure reorient about their 2-fold axis by 15 °. Large tertiary changes that include domain migration and rearrangement are also present between these two forms. In the R form both domains of the catalytic chain relocate closer to each other in order to bind to the inhibitor. The polar domain seems to bind primarily to the carbamoyl phosphate moiety of PALA, and the equatorial domain binds primarily to the l-aspartate moiety. Other changes in tertiary structure bring the 80s loop (from an adjacent catalytic chain) and the 240s loop into a position to interact with the PALA molecule. Changes have been searched for in all interface regions of the enzyme. While the C1–C4 § § Capital letters, C and R, followed by a number, e.g. C1, R2, refer to a particular chain in a particular location of the dodecamer as specified in Fig. I. Lowercase letters, c and r, in Figures and text refer to catalytic and regulatory chains as a type classification only and do not refer to a particular chain in the enzyme. Lowercase letters are frequently used in combinations with subscripts to create combinations such as: regulatory dimers, r 2: catalytic trimers, c 3 etc. and C1–R4 regions have been completely altered, most of the other interchain interfaces are similar in the T and R forms. The intrachain interfaces, between domains of the same catalytic chains, have undergone some reorganization as these domains move closer to each other when the inhibitor is bound. This new structure allows a reinterpretation of genetic and chemical modification studies done to date. As such, the roles of Ser52, Lys84 and His134 are supported. Other residues implicated in similar studies such as Cys47, Tyr165, Lys232 and Tyr240 are too far from the inhibitor to have a direct interaction. Finally, on the basis of the above results, a preliminary model for the homotropic transition is offered. In it, the change to the R-form is triggered by the binding of l-aspartate to the equatorial domain of a catalytic chain in which carbamoyl phosphate is bound to its site in the polar domain. Each C1–C4 group within the enzyme appears to be able to adopt its more active form somewhat independently, but the reorientation of the regulatory dimers that accompanies the homotropic transition serves to facilitate a T to R state transition in the other C1–C4 units. During the change from the T to R states most contact areas between r c pairs and between r r pairs are preserved. This is consistent with the suggestion that c-r-r-c is a functionally important unit. In addition, direct communication between C1–C4 is also consistent with the new structure.

REFINEMENT OF THE CRYSTAL STRUCTURE OF INSULIN AT 1.2 RESOLUTION

The crystal structure of 2 Zn porcine insulin has been refined at 1.2 resolution. The reciprocal space refinement was restrained by the incorporation of extensive chemical observations into the least squares equations. In addition to the non-hydrogen atoms, hydrogen atoms of protein, water molecules and the bulk solvent have been determined and refined. After two cycles of anisotropic refinement of non-hydrogen atoms of insulin, the final agreement factor was 0.128 for 20,005 reflexions (F_o1σ(F_o)) in a spacing 1.2 and the root mean squares deviation from ideal covalent bond lengths was 0.021. On the electron density maps, the appearances of weight and shape of non-hydrogen atoms were very clear and reasonable. The anisotropic appearances of sulphur atoms could be seen clearly. After anisotropic refinement, the situation fit to the electron density was improved distinctly.

The molecular structure of d(ICpCpGpG), a fragment of right-handed double helical A-DNA.

The DNA tetramer d(ICpCpGpG) or ICCGG crystallizes as a double-stranded 4-base pair (bp) segment of an A helix. Two such tetramer helices are packed together in the crystal with local helix axes nearly coincident, simulating an 8-bp helix, and four such octamers make up the tetragonal unit cell. Restrained energy and reciprocal space refinement has led to an R factor of 20.5% at 2.1 A resolution. The ICCGG helix has a twist corresponding to 10.7 bp per turn, a 19 degree base tilt and a 2.3 A rise per base pair along the helix axis. The mean propeller twist of 18 degree is comparable with, and has the same rotational sense as that observed in the B-DNA dodecamer CGCGAATTCGCG at similarly high alcohol concentration. Backbone phosphate groups in A-DNA are extensively hydrated, including a network across the opening of the major groove, whereas base edge N and O groups in major and minor grooves are less hydrated than in B-DNA. The minor groove spine of hydration observed in B-DNA is totally absent. These observations of relative hydration confirm and extend the model for the B- to A- helix transition proposed earlier on the basis of the B helix structure.

Conformation change of cytochrome c: I. Ferrocytochrome c structure refined at 1·5 Å resolution

Tuna ferrocytochrome c has been crystallographically refined at a resolution of 1.5 Å using the Diamond real-space method followed by Jack-Levitt restrained energy and reciprocal space refinement, monitoring progress continuously with superimposed Fourier and difference Fourier maps: The final R factor for cytochrome plus 53 solvent molecules, using 13,840 reflections with intensities greater than 2 σ, is 17·3%. The overall structure remains as described earlier (Takano et al., 1977), but structural details have been clarified to the point where meaningful comparison can be made with the oxidized molecule (following paper). Main and side-chain flexibility as judged by isotropic temperature parameters correlate with position in the molecule, with greatest flexibility at external chain loops. The haem group is held tightly in place by its attachments and neighbours, and is deformed slightly into a saddle shape. The iron does not deviate significantly from the best mean plane of the haem, and bond lengths to ligands are as expected from model compounds. A water molecule buried in the haem crevice is bonded to Asn52, Tyr67 and Thr78, the latter two being bonded also to Met80 and the outer haem propionate. It is proposed that this buried water molecule is involved in the reduction of ferricytochrome c by chromous ion, and the reactions of Tyr67 with KI 3 and tetranitromethane. Two other buried water molecules occur beneath the 20's loop at the right, and within the 40's loop at the bottom. Reasonable if tentative functional assignments can be made for all 24 of the evolutionarily invariant residues in the cytochrome molecule.

Conformation change of cytochrome c: II. Ferricytochrome c refinement at 1·8 Å and comparison with the ferrocytochrome structure

Tuna ferricytochrome c has been crystallographically refined at a resolution of 1·8 Å using Diamond real-space methods followed by Jack Levitt restrained energy and reciprocal space refinement, with Fourier and difference Fourier map monitoring. The final R factor for two independent cytochromes plus 49 solvent molecules, using 16,831 reflections to 1.8 Å is 20·8%. The structure is essentially the same as described at 2.0 Å (Swanson et al., 1977), but the increased accuracy now permits detailed comparison with the reduced cytochrome c molecule (preceding paper). Twelve water molecules are found in identical positions in both oxidized molecules and also in the reduced. Three of these are buried: one between Asn52, Tyr67 and Thr78 to the lower left of the haem, a second inside the 20s loop, and a third below the buried haem propionate. The first of these three buried water molecules is involved in a concerted shift of side-chains and even main-chain at the bottom of the molecule, that accompanies the change in redox state of the haem. The shift of this water molecule and a slight outward movement of the haem both give the haem a more hydrophilic environment in ferricytochrome c. This same buried water molecule may be involved in the alkaline conformation transition that ferricytochrome c undergoes at pH 9·4, assisting in the replacement of Met80 by a different low-spin ligand. The absence of such transition in ferrocytochrome c until pH 12 is reached may be ascribed to the shift in water position observed in the reduced state. The water molecule buried in the 20s loop, in turn, may be involved in the acid transformation that ferricytochrome c undergoes at pH 2·5. The conformations observed by X-rays for both ferricytochrome c and ferrocytochrome c appear to be post-transfer states, i.e. states that are most compatible with the particular redox state of the haem, rather than being poised to give up or receive electrons. These conformations have been interpreted as being effects of changes in haem redox state rather than causes, but if binding to another macromolecule were to induce either conformation, then transfer of an electron might thereby be facilitated.