Density-modification Procedures Research Articles

A new density-modification procedure extending the application of the recent |ρ|-based phasing algorithm to larger crystal structures.

The incorporation of the new peakness-enhancing fast Fourier transform compatible ipp procedure (ipp = inner-pixel preservation) into the recently published SM algorithm based on |ρ| [Rius (2020). Acta Cryst A76, 489-493] improves its phasing efficiency for larger crystal structures with atomic resolution data. Its effectiveness is clearly demonstrated via a collection of test crystal structures (taken from the Protein Data Bank) either starting from random phase values or by using the randomly shifted modulus function (a Patterson-type synthesis) as initial ρ estimate. It has been found that in the presence of medium scatterers (e.g. S or Cl atoms) crystal structures with 1500 × c atoms in the unit cell (c = number of centerings) can be routinely solved. In the presence of strong scatterers like Fe, Cu or Zn atoms this number increases to around 5000 × c atoms. The implementation of this strengthened SM algorithm is simple, since it only includes a few easy-to-adjust parameters.

Using a partial atomic model from medium-resolution cryo-EM to solve a large crystal structure.

Medium-resolution cryo-electron microscopy maps, in particular when they include a significant number of α-helices, may allow the building of partial models that are useful for molecular-replacement searches in large crystallographic structures when the structures of homologs are not available and experimental phasing has failed. Here, as an example, the solution of the structure of a bacteriophage portal using a partial 30% model built into a 7.8 Å resolution cryo-EM map is shown. Inspection of the self-rotation function allowed the correct oligomerization state to be determined, and density-modification procedures using rotation matrices and a mask based on the cryo-EM structure were critical for solving the structure. A workflow is described that may be applicable to similar cases and this strategy is compared with direct use of the cryo-EM map for molecular replacement.

Improvement of cryo-EM maps by density modification.

A density modification procedure for improving maps from single-particle electron cryo-microscopy is presented. The theoretical basis of the method is identical to that of maximum-likelihood density modification, previously used to improve maps from macromolecular X-ray crystallography. Key differences from applications in crystallography are that the errors in Fourier coefficients are largely in the phases in crystallography but in both phases and amplitudes in electron cryo-microscopy, and that half-maps with independent errors are available in electron cryo-microscopy. These differences lead to a distinct approach for combination of information from starting maps with information obtained in the density modification process. The density modification procedure was applied to a set of 104 datasets and improved map-model correlation and increased the visibility of details in many of the maps. The procedure requires two unmasked half-maps and a sequence file or other source of information on the volume of the macromolecule that has been imaged.

Building the atomic model of a boreal lake virus of unknown fold in a 3.9 Å cryo-EM map.

We report here the protocol adopted to build the atomic model of the newly discovered virus FLiP (Flavobacterium infecting, lipid-containing phage) into 3.9 Å cryo-electron microscopy (cryo-EM) maps. In particular, this report discusses the combination of density modification procedures, automatic model building and bioinformatics tools applied to guide the tracing of the major capsid protein (MCP) of this virus. The protocol outlined here may serve as a reference for future structural determination by cryo-EM of viruses lacking detectable structural homologues.

Molecular symmetry-constrained systematic search approach to structure solution of the coiled-coil SRGAP2 F-BARx domain.

SRGAP2 (Slit-Robo GTPase-activating protein 2) is a cytoplasmic protein found to be involved in neuronal branching, restriction of neuronal migration and restriction of the length and density of dendritic postsynaptic spines. The extended F-BAR (F-BARx) domain of SRGAP2 generates membrane protrusions when expressed in COS-7 cells, while most F-BARs induce the opposite effect: membrane invaginations. As a first step to understand this discrepancy, the F-BARx domain of SRGAP2 was isolated and crystallized after co-expression with the carboxy domains of the protein. Diffraction data were collected from two significantly non-isomorphous crystals in the same monoclinic C2 space group. A correct molecular-replacment solution was obtained by applying a molecular symmetry-constrained systematic search approach that took advantage of the conserved biological symmetry of the F-BAR domains. It is shown that similar approaches can solve other F-BAR structures that were previously determined by experimental phasing. Diffraction data were reprocessed with a high-resolution cutoff of 2.2 Å, chosen using less strict statistical criteria. This has improved the outcome of multi-crystal averaging and other density-modification procedures.

Introduction to phasing.

When collecting X-ray diffraction data from a crystal, we measure the intensities of the diffracted waves scattered from a series of planes that we can imagine slicing through the crystal in all directions. From these intensities we derive the amplitudes of the scattered waves, but in the experiment we lose the phase information; that is, how we offset these waves when we add them together to reconstruct an image of our molecule. This is generally known as the 'phase problem'. We can only derive the phases from some knowledge of the molecular structure. In small-molecule crystallography, some basic assumptions about atomicity give rise to relationships between the amplitudes from which phase information can be extracted. In protein crystallography, these ab initio methods can only be used in the rare cases in which there are data to at least 1.2 A resolution. For the majority of cases in protein crystallography phases are derived either by using the atomic coordinates of a structurally similar protein (molecular replacement) or by finding the positions of heavy atoms that are intrinsic to the protein or that have been added (methods such as MIR, MIRAS, SIR, SIRAS, MAD, SAD or combinations of these). The pioneering work of Perutz, Kendrew, Blow, Crick and others developed the methods of isomorphous replacement: adding electron-dense atoms to the protein without disturbing the protein structure. Nowadays, methods from small-molecule crystallography can be used to find the heavy-atom substructure and the phases for the whole protein can be bootstrapped from this prior knowledge. More recently, improved X-ray sources, detectors and software have led to the routine use of anomalous scattering to obtain phase information from either incorporated selenium or intrinsic sulfurs. In the best cases, only a single set of X-ray data (SAD) is required to provide the positions of the anomalous scatters, which together with density-modification procedures can reveal the structure of the complete protein.

ACORN2: new developments of theACORNconcept

The density-modification procedures incorporated in ACORN, available in the CCP4 package, have proved to be very successful in solving and refining high-resolution crystal structures from very poor starting sets. These can be calculated from a correctly positioned initial fragment containing between 1 and 8% of the scattering power of the total structure. Improvements of ACORN, reported here and incorporated in the program ACORN2, have lowered the size of the fragment required and examples are given of structures solved with only 0.25% of the scattering power in the fragment, which may be a single atom. Applications of ACORN2 to structures with space group P1 have shown the remarkable property that when the starting point is a pair of equal atoms, or even a single atom placed at the origin, the refinement process breaks the centric nature of the initial phases and converges to phases corresponding to one of the two possible enantiomorphs. Examples are given of the application of ACORN2 to the solution and/or refinement of a number of known trial structures and to the refinement of structures when phases are available either from MAD or from a molecular-replacement model.

An extremely SAD case: structure of a putative redox-enzyme maturation protein fromArchaeoglobus fulgidusat 3.4 Å resolution

This paper describes the crystal structure of AF0173, a putative redox-enzyme maturation protein (REMP) from Archaeoglobus fulgidus. The REMPs serve as chaperones in the maturation of extracytoplasmic oxidoreductases in archaea and bacteria. The all-helical subunits of AF0173 form a dimer arising from the interaction of residues located in a funnel-shaped cavity on one subunit surface with an uncut expression tag from the other subunit. This cavity is likely to represent a binding site for the twin-arginine motif that interacts with REMPs. The conservation of the overall fold in AF0173 and bacterial REMPs as well as the presence of conserved residues in their putative binding sites indicates that REMPs act in a similar manner in archaea and bacteria despite their limited sequence similarity. A model of the binding of the twin-arginine motif by AF0173 is suggested. The solution of the AF0173 structure by the single anomalous dispersion method represents an extreme case of SAD structure determination: low resolution (3.4 A), the absence of NCS and the presence of only two anomalously scattering atoms in the asymmetric unit. An unusually high solvent content (73%) turned out to be important for the success of the density-modification procedures.

ACORN: a review

The ACORN system was originally developed as a means of ab initio solution of protein structures when atomic resolution data were available. The first step is to obtain a starting set of phases, which must be at least slightly better than random. These may be calculated from a fragment of the structure, which can be anything from a single metal atom to a complete molecular-replacement model. A number of standard procedures are available in ACORN to orientate and position such a fragment. The fragment provides initial phases that give the first of a series of maps that are iteratively refined by a dynamic density-modification (DDM) process. Another FFT-based procedure is Sayre-equation refinement (SER), which modifies phases better to satisfy the Sayre equation. With good-quality atomic resolution data, the final outcome of applying DDM and SER is a map similar in appearance to that found from a refined structure, which is readily interpreted by automated procedures. Further development of ACORN now enables structures to be solved with less than atomic resolution data. A critical part of this development is the artificial extension of the data from the observed limit to 1 A resolution. These extended reflections are allocated unit normalized structure amplitudes and then treated in a similar way to observed reflections except that they are down-weighted in the calculation of maps. ACORN maps, especially at low resolution, tend to show C atoms less well, in particular C(alpha) atoms which fall within the first diffraction minimum of their three neighbours. Two new density-modification procedures (DDM1 and DDM2) and a density-enhancement procedure (ENH) have been devised to counter this problem. It is demonstrated that high-quality maps showing individual atoms can be produced with the new ACORN. ACORN has also been demonstrated to be very effective in refining phase sets derived from physical processes such as those using anomalous scattering or isomorphous derivative data. Future work will be directed towards applying ACORN to resolutions down to 2 A.

A modifiedACORNto solve protein structures at resolutions of 1.7 Å or better

ACORN has previously been shown to provide an efficient density-modification procedure for the solution of protein structures using diffraction data to better than 1.3 A. The initial phase set could be obtained from a variety of sources such as the position of a heavy atom, a set of scatterers such as S that had been positioned from anomalous dispersion measurements, a fragment or a very low homology model placed from a molecular-replacement search. Several structures solved using the early version of ACORN have been reported in the literature. Here, the effect of applying the original ACORN procedures at lower resolution is reported and new procedures that yield good-quality maps with data sets of resolution down to 1.7 A are described. These new procedures involve the artificial extension of data to atomic resolution and new density-modification processes that develop density at atomic positions that was previously suppressed. The test calculations were aimed firstly towards a proof of principle using a small fragment of a known structure to demonstrate that the procedure could generate correct density and a derived model in initially empty regions of the cell. Further tests addressed the use of more realistic starting models.

Abinitiostructure solution of nucleic acids and proteins by direct methods: reciprocal-space and real-space approach

Anab initiomethod for solving macromolecular structures is described. The heavy atom(s) or some disulfide bridge in the structure are located from the phase sets selected on the basis of a figure of merit of a reciprocal-space-based multiple-solution direct method. Subsequent weighted Fourier recycling reveals recognizable structures for two nucleic acids where data resolution is 1.3 Å or better. With lower than 1.3 Å data resolution or sulfur as the heaviest atom in the structure, the phase refinement has been carried out using the density modification procedure (PERP) operating in direct space. The resulting electron density map can readily be interpreted. The methodology has been illustrated with six known nucleic acids and proteins crystallizing in different space groups. It has proved to be fast, simple to use and a very effective tool for solving macromolecular structures with data resolution up to 1.7 Å.

The Crystal Structure of the Herpes Simplex Virus 1 ssDNA-binding Protein Suggests the Structural Basis for Flexible, Cooperative Single-stranded DNA Binding

All organisms including animal viruses use specific proteins to bind single-stranded DNA rapidly in a non-sequence-specific, flexible, and cooperative manner during the DNA replication process. The crystal structure of a 60-residue C-terminal deletion construct of ICP8, the major single-stranded DNA-binding protein from herpes simplex virus-1, was determined at 3.0 A resolution. The structure reveals a novel fold, consisting of a large N-terminal domain (residues 9-1038) and a small C-terminal domain (residues 1049-1129). On the basis of the structure and the nearest neighbor interactions in the crystal, we have presented a model describing the site of single-stranded DNA binding and explaining the basis for cooperative binding. This model agrees with the beaded morphology observed in electron micrographs.

Three-beam interference is a sensitive measure of the efficacy of macromolecular refinement techniques.

Triplet phases recorded from insulin crystals were used to measure the improvement of phases during model refinement and to quantify the contribution made by each step in the refinement. Conventional amplitude data were recorded to 1.5 A resolution from rhombohedral pig insulin crystals using 1.54 A Cu Kalpha radiation. An initial atomic model and starting phases were obtained from a published structure and the atomic model was refined against the amplitude data using CNS. The refined phases were compared with 800 triplet phases that were measured from similar crystals using a three-beam interference technique and 1.1 A wavelength synchrotron radiation. The solvent region was improved further using a novel density-modification procedure. Calculated triplet phases were obtained from the model after each step in the refinement and were compared with the recorded triplet phases. The average difference between the recorded triplet phases and the calculated triplet phases was used as an unbiased measure of the correctness of the model at each stage in the refinement. The average individual phase error was estimated from discrepancies from triplet phases after each refinement step. Conventional atomic refinement of an approximate starting model reduced the average individual phase error from 21.6 to 14.7 degrees. Improvement of the solvent region, including the difference-map flattening procedure, reduced the individual phase error by a further 2.6 degrees. Modeling the discrete disorder of four amino acids accounted for an additional 0.5 degrees improvement and the final individual phase error was 11.6 degrees.

Ab initio structure determination of cytochrome c6 by combined reciprocal space-real space approach

Abstract The direct method program SAYTAN has been applied successfully to redetermine the structure of cytochrome c6, a heme-containing redox protein with 89 amino acids, a Fe atom and 151 solvent water molecules in the asymmetric unit and data to 1.1 Å resolution. The crystal system is rhombohedral with space group R3, cell parameters a = b = c = 40.43(10) Å, α = β = γ = 80.25(5)°. Starting with initially random phases, useful phase sets could be obtained from multiple trials of direct methods based on reciprocal space. The E-map corresponding to the phase set with the lowest mean phase error, 45.4°, showed a distorted octahedral coordination around the Fe site. The phase estimates from the metal atom and a few neighbouring atoms in the initial E-map have been improved by density modification procedure (PERP) operating in direct space. The resulting electron density map can be interpreted readily by an automated procedure to build up the protein structure.

General concepts underlying ACORN, a computer program for the solution of protein structures

ACORN has been shown to be a successful program for the solution of small and medium-size protein structures, when data at atomic resolution or better are available. At the heart of ACORN lies a density modification method called DDM (Dynamic Density Modification). DDM operates on any density map containing a minimum of information. Its action is to progressively enhance positive features of the map and to reduce, at the same time, undesired noise and bias towards very small values. This is indeed a feature claimed by other density modification procedures. The effectiveness of the procedure arises from the fact that the shape of DDM's modification curve is one of a restricted class of functions, whose properties will be described. The importance of a proper weighting scheme will also be considered. Tests on a few structures will help to clarify the theoretical concepts involved as well as to make clear the potential applications and limits of the program.

A direct-methodab initiophasing of a protein, cupredoxin amicyanin, at 1.31 Å resolution

The direct-methods program MULTAN88 has been applied successfully to redetermine the structure of a protein, cupredoxin amicyanin, containing 808 non-H atom sites, one Cu atom and 132 ordered water molecules in the asymmetric unit using data at 1.31 A resolution. Starting with initially random phases, useful phase sets selected by figures of merit could be obtained from multiple trials. The E maps corresponding to the best eight phase sets in order of combined figures of merit (CFOM2) revealed a distorted tetrahedral geometry around the Cu site. The phase estimates from the metal and a few neighbouring atoms in the initial E map corresponding to the set with the highest CFOM2 could be improved by the density-modification procedure PERP and led to an interpretable electron-density map.

An improved phase-extension procedure for isomorphous replacement phases.

A new phase-extension procedure has been applied to isomorphous replacement data and shown to yield improved phases and maps compared with standard solvent flattening operating on a full set of centroid phases. In this procedure, a starting subset of core phases is selected based on the sharpness of the phase-probability curves. Phase extension using solvent flattening as the density-modification procedure is then carried out, gradually adding additional phases. In tests with known protein structures, the mean phase errors for the output expanded phase sets were reduced by 3-9 degrees and the corresponding map correlation coefficients were increased by 0.05-0.18 relative to phase sets from standard solvent-flattening procedures. With SIR data, the lowest final mean phase errors were approximately 58 degrees and the corresponding map correlation coefficients were in the range 0.53-0.68.

Evaluation of phase accuracy via topological and geometrical analysis of electron-density maps.

An empirical function is developed to measure the protein-like character of electron-density maps. The function is based upon a systematic analysis of numerous local and global map properties or descriptors. Local descriptors measure the occurrence throughout the unit cell of unique patterns on various defined templates, while global descriptors enumerate topological characteristics that define the connectivity and complexity of electron-density isosurfaces. We examine how these quantitative descriptors vary as error is introduced into the phase sets used to generate maps. Informative descriptors are combined in an optimal fashion to arrive at a predictive function. When the topological and geometrical analysis is applied to protein maps generated from phase sets with varying amounts of error, the function is able to estimate changes in average phase error with an accuracy of better than 10 degrees. Additionally, when used to monitor maps generated with experimental phases from different heavy-atom models, the analysis clearly distinguishes between the correct heavy-atom substructure solution and incorrect heavy-atom solutions. The function is also evaluated as a tool to monitor changes in map quality and phase error before and after density-modification procedures.

Density constraints and low-resolution phasing.

Direct phasing needs additional information of a non-specific kind in order to select the correct phase set from all possible ones. This paper analyses the use of constraints which can be formulated in terms of electron-density values. One- and multi-dimensional histograms and connectivity properties are implemented as such constraints in density-modification procedures. These approaches usually cannot unambiguously select the best solution from a set of alternative phase variants. Nevertheless, they do allow the rejection of wrong solutions and the use of cluster analysis and averaging on the remaining variants provide a good starting point for further phase-refinement procedures.

A two-dimensional histogram-matching method for protein phase refinement and extension.

A new method has been developed for protein phase improvement using the joint distribution of the electron density and its gradient (two-dimensional histogram) as a constraint in a density-modification procedure. Matching the two-dimensional (2D) histogram of a given map to that of an ideal 2D histogram was achieved through alternating applications of one-dimensional (1D) histogram matching on electron density and on density gradient. The 2D histogram-matching method was compared with the 1D density histogram-matching method for phase refinement and extension starting from either medium-resolution or high-resolution data on three different types of phases. These included phase refinement and extension using MIR phases of T(6) insulin and phases with randomly generated errors. The test results demonstrated significant improvement of the phases and the overall map quality using the 2D histogram-matching method compared with the 1D density histogram-matching method in each of the three test cases.