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1.  Indexing amyloid peptide diffraction from serial femtosecond crystallography: new algorithms for sparse patterns 
Special methods are required to interpret sparse diffraction patterns collected from peptide crystals at X-ray free-electron lasers. Bragg spots can be indexed from composite-image powder rings, with crystal orientations then deduced from a very limited number of spot positions.
Still diffraction patterns from peptide nanocrystals with small unit cells are challenging to index using conventional methods owing to the limited number of spots and the lack of crystal orientation information for individual images. New indexing algorithms have been developed as part of the Computational Crystallography Toolbox (cctbx) to overcome these challenges. Accurate unit-cell information derived from an aggregate data set from thousands of diffraction patterns can be used to determine a crystal orientation matrix for individual images with as few as five reflections. These algorithms are potentially applicable not only to amyloid peptides but also to any set of diffraction patterns with sparse properties, such as low-resolution virus structures or high-throughput screening of still images captured by raster-scanning at synchrotron sources. As a proof of concept for this technique, successful integration of X-ray free-electron laser (XFEL) data to 2.5 Å resolution for the amyloid segment GNNQQNY from the Sup35 yeast prion is presented.
doi:10.1107/S1399004714026145
PMCID: PMC4321489  PMID: 25664747
XFEL; Sup35 yeast prion; indexing methods; crystallography
2.  Improved crystal orientation and physical properties from single-shot XFEL stills 
X-ray free-electron laser crystallography relies on the collection of still-shot diffraction patterns. New methods are developed for optimal modeling of the crystals’ orientations and mosaic block properties.
X-ray diffraction patterns from still crystals are inherently difficult to process because the crystal orientation is not uniquely determined by measuring the Bragg spot positions. Only one of the three rotational degrees of freedom is directly coupled to spot positions; the other two rotations move Bragg spots in and out of the reflecting condition but do not change the direction of the diffracted rays. This hinders the ability to recover accurate structure factors from experiments that are dependent on single-shot exposures, such as femtosecond diffract-and-destroy protocols at X-ray free-electron lasers (XFELs). Here, additional methods are introduced to optimally model the diffraction. The best orientation is obtained by requiring, for the brightest observed spots, that each reciprocal-lattice point be placed into the exact reflecting condition implied by Bragg’s law with a minimal rotation. This approach reduces the experimental uncertainties in noisy XFEL data, improving the crystallographic R factors and sharpening anomalous differences that are near the level of the noise.
doi:10.1107/S1399004714024134
PMCID: PMC4257623  PMID: 25478847
X-ray free-electron lasers; single-shot exposures
3.  Metrics for comparison of crystallographic maps 
Rank scaling of Fourier syntheses leads to new tools for the comparison of crystallographic contour maps. The new metrics are in better agreement with a visual map analysis than the conventional map correlation coefficient.
Numerical comparison of crystallographic contour maps is used extensively in structure solution and model refinement, analysis and validation. However, traditional metrics such as the map correlation coefficient (map CC, real-space CC or RSCC) sometimes contradict the results of visual assessment of the corresponding maps. This article explains such apparent contradictions and suggests new metrics and tools to compare crystallographic contour maps. The key to the new methods is rank scaling of the Fourier syntheses. The new metrics are complementary to the usual map CC and can be more helpful in map comparison, in particular when only some of their aspects, such as regions of high density, are of interest.
doi:10.1107/S1399004714016289
PMCID: PMC4188004  PMID: 25286844
Fourier syntheses; crystallographic contour maps; map comparison; sigma scale; rank scaling; correlation coefficients
4.  Flexible torsion-angle noncrystallographic symmetry restraints for improved macromolecular structure refinement 
Flexible torsion angle-based NCS restraints have been implemented in phenix.refine, allowing improved model refinement at all resolutions. Rotamer correction and rotamer consistency checks between NCS-related amino-acid side chains further improve the final model quality.
One of the great challenges in refining macromolecular crystal structures is a low data-to-parameter ratio. Historically, knowledge from chemistry has been used to help to improve this ratio. When a macromolecule crystallizes with more than one copy in the asymmetric unit, the noncrystallographic symmetry relationships can be exploited to provide additional restraints when refining the working model. However, although globally similar, NCS-related chains often have local differences. To allow for local differences between NCS-related molecules, flexible torsion-based NCS restraints have been introduced, coupled with intelligent rotamer handling for protein chains, and are available in phenix.refine for refinement of models at all resolutions.
doi:10.1107/S1399004714003277
PMCID: PMC4014122  PMID: 24816103
macromolecular crystallography; noncrystallographic symmetry; NCS; refinement; automation
5.  Automated identification of elemental ions in macromolecular crystal structures 
The solvent-picking procedure in phenix.refine has been extended and combined with Phaser anomalous substructure completion and analysis of coordination geometry to identify and place elemental ions.
Many macromolecular model-building and refinement programs can automatically place solvent atoms in electron density at moderate-to-high resolution. This process frequently builds water molecules in place of elemental ions, the identification of which must be performed manually. The solvent-picking algorithms in phenix.refine have been extended to build common ions based on an analysis of the chemical environment as well as physical properties such as occupancy, B factor and anomalous scattering. The method is most effective for heavier elements such as calcium and zinc, for which a majority of sites can be placed with few false positives in a diverse test set of structures. At atomic resolution, it is observed that it can also be possible to identify tightly bound sodium and magnesium ions. A number of challenges that contribute to the difficulty of completely automating the process of structure completion are discussed.
doi:10.1107/S1399004714001308
PMCID: PMC3975891  PMID: 24699654
refinement; ions; PHENIX
6.  Ligand placement based on prior structures: the guided ligand-replacement method 
A new module, Guided Ligand Replacement (GLR), has been developed in Phenix to increase the ease and success rate of ligand placement when prior protein-ligand complexes are available.
The process of iterative structure-based drug design involves the X-ray crystal structure determination of upwards of 100 ligands with the same general scaffold (i.e. chemotype) complexed with very similar, if not identical, protein targets. In conjunction with insights from computational models and assays, this collection of crystal structures is analyzed to improve potency, to achieve better selectivity and to reduce liabilities such as absorption, distribution, metabolism, excretion and toxicology. Current methods for modeling ligands into electron-density maps typically do not utilize information on how similar ligands bound in related structures. Even if the electron density is of sufficient quality and resolution to allow de novo placement, the process can take considerable time as the size, complexity and torsional degrees of freedom of the ligands increase. A new module, Guided Ligand Replacement (GLR), was developed in Phenix to increase the ease and success rate of ligand placement when prior protein–ligand complexes are available. At the heart of GLR is an algorithm based on graph theory that associates atoms in the target ligand with analogous atoms in the reference ligand. Based on this correspondence, a set of coordinates is generated for the target ligand. GLR is especially useful in two situations: (i) modeling a series of large, flexible, complicated or macrocyclic ligands in successive structures and (ii) modeling ligands as part of a refinement pipeline that can automatically select a reference structure. Even in those cases for which no reference structure is available, if there are multiple copies of the bound ligand per asymmetric unit GLR offers an efficient way to complete the model after the first ligand has been placed. In all of these applications, GLR leverages prior knowledge from earlier structures to facilitate ligand placement in the current structure.
doi:10.1107/S1399004713030071
PMCID: PMC3919265  PMID: 24419386
ligand placement; guided ligand-replacement method; GLR
7.  Automating crystallographic structure solution and refinement of protein–ligand complexes 
A software system for automated protein–ligand crystallography has been implemented in the Phenix suite. This significantly reduces the manual effort required in high-throughput crystallographic studies.
High-throughput drug-discovery and mechanistic studies often require the determination of multiple related crystal structures that only differ in the bound ligands, point mutations in the protein sequence and minor conformational changes. If performed manually, solution and refinement requires extensive repetition of the same tasks for each structure. To accelerate this process and minimize manual effort, a pipeline encompassing all stages of ligand building and refinement, starting from integrated and scaled diffraction intensities, has been implemented in Phenix. The resulting system is able to successfully solve and refine large collections of structures in parallel without extensive user intervention prior to the final stages of model completion and validation.
doi:10.1107/S139900471302748X
PMCID: PMC3919266  PMID: 24419387
protein–ligand complexes; automation; crystallographic structure solution and refinement
8.  Nanoflow electrospinning serial femtosecond crystallography 
A low flow rate liquid microjet method for delivery of hydrated protein crystals to X-ray lasers is presented. Linac Coherent Light Source data demonstrates serial femtosecond protein crystallography with micrograms, a reduction of sample consumption by orders of magnitude.
An electrospun liquid microjet has been developed that delivers protein microcrystal suspensions at flow rates of 0.14–3.1 µl min−1 to perform serial femtosecond crystallography (SFX) studies with X-ray lasers. Thermolysin microcrystals flowed at 0.17 µl min−1 and diffracted to beyond 4 Å resolution, producing 14 000 indexable diffraction patterns, or four per second, from 140 µg of protein. Nanoflow electrospinning extends SFX to biological samples that necessitate minimal sample consumption.
doi:10.1107/S0907444912038152
PMCID: PMC3478121  PMID: 23090408
serial femtosecond crystallography; nanoflow electrospinning
9.  Model morphing and sequence assignment after molecular replacement 
A procedure for model building is described that combines morphing a model to match a density map, trimming the morphed model and aligning the model to a sequence.
A procedure termed ‘morphing’ for improving a model after it has been placed in the crystallographic cell by molecular replacement has recently been developed. Morphing consists of applying a smooth deformation to a model to make it match an electron-density map more closely. Morphing does not change the identities of the residues in the chain, only their coordinates. Consequently, if the true structure differs from the working model by containing different residues, these differences cannot be corrected by morphing. Here, a procedure that helps to address this limitation is described. The goal of the procedure is to obtain a relatively complete model that has accurate main-chain atomic positions and residues that are correctly assigned to the sequence. Residues in a morphed model that do not match the electron-density map are removed. Each segment of the resulting trimmed morphed model is then assigned to the sequence of the molecule using information about the connectivity of the chains from the working model and from connections that can be identified from the electron-density map. The procedure was tested by application to a recently determined structure at a resolution of 3.2 Å and was found to increase the number of correctly identified residues in this structure from the 88 obtained using phenix.resolve sequence assignment alone (Terwilliger, 2003 ▶) to 247 of a possible 359. Additionally, the procedure was tested by application to a series of templates with sequence identities to a target structure ranging between 7 and 36%. The mean fraction of correctly identified residues in these cases was increased from 33% using phenix.resolve sequence assignment to 47% using the current procedure. The procedure is simple to apply and is available in the Phenix software package.
doi:10.1107/S0907444913017770
PMCID: PMC3817698  PMID: 24189236
morphing; model building; sequence assignment; model–map correlation; loop-building
10.  Phaser.MRage: automated molecular replacement 
The functionality of the molecular-replacement pipeline phaser.MRage is introduced and illustrated with examples.
Phaser.MRage is a molecular-replacement automation framework that implements a full model-generation workflow and provides several layers of model exploration to the user. It is designed to handle a large number of models and can distribute calculations efficiently onto parallel hardware. In addition, phaser.MRage can identify correct solutions and use this information to accelerate the search. Firstly, it can quickly score all alternative models of a component once a correct solution has been found. Secondly, it can perform extensive analysis of identified solutions to find protein assemblies and can employ assembled models for subsequent searches. Thirdly, it is able to use a priori assembly information (derived from, for example, homologues) to speculatively place and score molecules, thereby customizing the search procedure to a certain class of protein molecule (for example, antibodies) and incorporating additional biological information into molecular replacement.
doi:10.1107/S0907444913022750
PMCID: PMC3817702  PMID: 24189240
molecular replacement; pipeline; automation; phaser.MRage
11.  Structure of FabH and factors affecting the distribution of branched fatty acids in Micrococcus luteus  
In an effort to better understand the control of the formation of branched fatty acids in Micrococcus luteus, the structure of β-ketoacyl-ACP synthase III, which catalyzes the initial step of fatty-acid biosynthesis, has been determined.
Micrococcus luteus is a Gram-positive bacterium that produces iso- and anteiso-branched alkenes by the head-to-­head condensation of fatty-acid thioesters [coenzyme A (CoA) or acyl carrier protein (ACP)]; this activity is of interest for the production of advanced biofuels. In an effort to better understand the control of the formation of branched fatty acids in M. luteus, the structure of FabH (MlFabH) was determined. FabH, or β-ketoacyl-ACP synthase III, catalyzes the initial step of fatty-acid biosynthesis: the condensation of malonyl-ACP with an acyl-CoA. Analysis of the MlFabH structure provides insights into its substrate selectivity with regard to length and branching of the acyl-CoA. The most structurally divergent region of FabH is the L9 loop region located at the dimer interface, which is involved in the formation of the acyl-binding channel and thus limits the substrate-channel size. The residue Phe336, which is positioned near the catalytic triad, appears to play a major role in branched-substrate selectivity. In addition to structural studies of MlFabH, transcriptional studies of M. luteus were also performed, focusing on the increase in the ratio of anteiso:iso-branched alkenes that was observed during the transition from early to late stationary phase. Gene-expression microarray analysis identified two genes involved in leucine and isoleucine metabolism that may explain this transition.
doi:10.1107/S0907444912028351
PMCID: PMC3447401  PMID: 22993086
biofuels; β-ketoacyl-ACP synthase III; iso- and anteiso-branched alkenes; microarray
12.  Intensity statistics in the presence of translational noncrystallographic symmetry 
The statistical effects of translational noncrystallographic symmetry can be characterized by maximizing parameters describing the noncrystallographic symmetry in a likelihood function, thereby unmasking the competing statistical effects of twinning.
In the case of translational noncrystallographic symmetry (tNCS), two or more copies of a component in the asymmetric unit of the crystal are present in a similar orientation. This causes systematic modulations of the reflection intensities in the diffraction pattern, leading to problems with structure determination and refinement methods that assume, either implicitly or explicitly, that the distribution of intensities is a function only of resolution. To characterize the statistical effects of tNCS accurately, it is necessary to determine the translation relating the copies, any small rotational differences in their orientations, and the size of random coordinate differences caused by conformational differences. An algorithm to estimate these parameters and refine their values against a likelihood function is presented, and it is shown that by accounting for the statistical effects of tNCS it is possible to unmask the competing statistical effects of twinning and tNCS and to more robustly assess the crystal for the presence of twinning.
doi:10.1107/S0907444912045374
PMCID: PMC3565438  PMID: 23385454
translational noncrystallographic symmetry; intensity statistics; twinning; maximum likelihood
13.  Improved crystallographic models through iterated local density-guided model deformation and reciprocal-space refinement 
A density-based procedure is described for improving a homology model that is locally accurate but differs globally. The model is deformed to match the map and refined, yielding an improved starting point for density modification and further model-building.
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.
doi:10.1107/S0907444912015636
PMCID: PMC3388814  PMID: 22751672
molecular replacement; automation; macromolecular crystallography; structure similarity; modeling; Phenix; morphing
14.  Towards automated crystallographic structure refinement with phenix.refine  
phenix.refine is a program within the PHENIX package that supports crystallographic structure refinement against experimental data with a wide range of upper resolution limits using a large repertoire of model parameterizations. This paper presents an overview of the major phenix.refine features, with extensive literature references for readers interested in more detailed discussions of the methods.
phenix.refine is a program within the PHENIX package that supports crystallographic structure refinement against experimental data with a wide range of upper resolution limits using a large repertoire of model parameterizations. It has several automation features and is also highly flexible. Several hundred parameters enable extensive customizations for complex use cases. Multiple user-defined refinement strategies can be applied to specific parts of the model in a single refinement run. An intuitive graphical user interface is available to guide novice users and to assist advanced users in managing refinement projects. X-ray or neutron diffraction data can be used separately or jointly in refinement. phenix.refine is tightly integrated into the PHENIX suite, where it serves as a critical component in automated model building, final structure refinement, structure validation and deposition to the wwPDB. This paper presents an overview of the major phenix.refine features, with extensive literature references for readers interested in more detailed discussions of the methods.
doi:10.1107/S0907444912001308
PMCID: PMC3322595  PMID: 22505256
structure refinement; PHENIX; joint X-ray/neutron refinement; maximum likelihood; TLS; simulated annealing; subatomic resolution; real-space refinement; twinning; NCS
15.  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
16.  Application of DEN refinement and automated model building to a difficult case of molecular-replacement phasing: the structure of a putative succinyl-diaminopimelate desuccinylase from Corynebacterium glutamicum  
DEN refinement and automated model building with AutoBuild were used to determine the structure of a putative succinyl-diaminopimelate desuccinylase from C. glutamicum. This difficult case of molecular-replacement phasing shows that the synergism between DEN refinement and AutoBuild outperforms standard refinement protocols.
Phasing by molecular replacement remains difficult for targets that are far from the search model or in situations where the crystal diffracts only weakly or to low resolution. Here, the process of determining and refining the structure of Cgl1109, a putative succinyl-diaminopimelate desuccinylase from Corynebacterium glutamicum, at ∼3 Å resolution is described using a combination of homology modeling with MODELLER, molecular-replacement phasing with Phaser, deformable elastic network (DEN) refinement and automated model building using AutoBuild in a semi-automated fashion, followed by final refinement cycles with phenix.refine and Coot. This difficult molecular-replacement case illustrates the power of including DEN restraints derived from a starting model to guide the movements of the model during refinement. The resulting improved model phases provide better starting points for automated model building and produce more significant difference peaks in anomalous difference Fourier maps to locate anomalous scatterers than does standard refinement. This example also illustrates a current limitation of automated procedures that require manual adjustment of local sequence misalignments between the homology model and the target sequence.
doi:10.1107/S090744491104978X
PMCID: PMC3322598  PMID: 22505259
reciprocal-space refinement; DEN refinement; real-space refinement; automated model building; succinyl-diaminopimelate desuccinylase
17.  Joint X-ray and neutron refinement with phenix.refine  
The implementation of crystallographic structure-refinement procedures that include both X-ray and neutron data (separate or jointly) in the PHENIX system is described.
Approximately 85% of the structures deposited in the Protein Data Bank have been solved using X-ray crystallography, making it the leading method for three-dimensional structure determination of macromolecules. One of the limitations of the method is that the typical data quality (resolution) does not allow the direct determination of H-atom positions. Most hydrogen positions can be inferred from the positions of other atoms and therefore can be readily included into the structure model as a priori knowledge. However, this may not be the case in biologically active sites of macromolecules, where the presence and position of hydrogen is crucial to the enzymatic mechanism. This makes the application of neutron crystallo­graphy in biology particularly important, as H atoms can be clearly located in experimental neutron scattering density maps. Without exception, when a neutron structure is determined the corresponding X-ray structure is also known, making it possible to derive the complete structure using both data sets. Here, the implementation of crystallographic structure-refinement procedures that include both X-ray and neutron data (separate or jointly) in the PHENIX system is described.
doi:10.1107/S0907444910026582
PMCID: PMC2967420  PMID: 21041930
structure refinement; neutrons; joint X-ray and neutron refinement; PHENIX
18.  electronic Ligand Builder and Optimization Workbench (eLBOW): a tool for ligand coordinate and restraint generation 
A new software system for automated ligand coordinate and restraint generation is presented.
The electronic Ligand Builder and Optimization Workbench (eLBOW) is a program module of the PHENIX suite of computational crystallographic software. It is designed to be a flexible procedure that uses simple and fast quantum-chemical techniques to provide chemically accurate information for novel and known ligands alike. A variety of input formats and options allow the attainment of a number of diverse goals including geometry optimization and generation of restraints.
doi:10.1107/S0907444909029436
PMCID: PMC2748967  PMID: 19770504
ligands; coordinates; restraints; Python; object-oriented programming
19.  Structure of endoglucanase Cel9A from the thermoacidophilic Alicyclobacillus acidocaldarius  
Here, the crystal structure of an endoglucanase, Cel9A, from Alicyclobacillus acidocaldarius (Aa_Cel9A) is reported which displays a modular architecture composed of an N-terminal Ig-like domain connected to the catalytic domain. This paper describes the overall structure and the detailed contacts between the two modules.
The production of biofuels using biomass is an alternative route to support the growing global demand for energy and to also reduce the environmental problems caused by the burning of fossil fuels. Cellulases are likely to play an important role in the degradation of biomass and the production of sugars for subsequent fermentation to fuel. Here, the crystal structure of an endoglucanase, Cel9A, from Alicyclobacillus acidocaldarius (Aa_Cel9A) is reported which displays a modular architecture composed of an N-terminal Ig-like domain connected to the catalytic domain. This paper describes the overall structure and the detailed contacts between the two modules. Analysis suggests that the inter­action involving the residues Gln13 (from the Ig-­like module) and Phe439 (from the catalytic module) is important in maintaining the correct conformation of the catalytic module required for protein activity. Moreover, the Aa_Cel9A structure shows three metal-binding sites that are associated with the thermostability and/or substrate affinity of the enzyme.
doi:10.1107/S0907444909012773
PMCID: PMC2714717  PMID: 19622857
endoglucanases; thermoacidophiles; cellulases; biofuels
20.  PHENIX: a comprehensive Python-based system for macromolecular structure solution 
The PHENIX software for macromolecular structure determination is described.
Macromolecular X-ray crystallography is routinely applied to understand biological processes at a molecular level. How­ever, significant time and effort are still required to solve and complete many of these structures because of the need for manual interpretation of complex numerical data using many software packages and the repeated use of interactive three-dimensional graphics. PHENIX has been developed to provide a comprehensive system for macromolecular crystallo­graphic structure solution with an emphasis on the automation of all procedures. This has relied on the development of algorithms that minimize or eliminate subjective input, the development of algorithms that automate procedures that are traditionally performed by hand and, finally, the development of a framework that allows a tight integration between the algorithms.
doi:10.1107/S0907444909052925
PMCID: PMC2815670  PMID: 20124702
PHENIX; Python; macromolecular crystallography; algorithms
21.  On the use of logarithmic scales for analysis of diffraction data 
Conventional and free R factors and their difference, as well as the ratio of the number of measured reflections to the number of atoms in the crystal, were studied as functions of the resolution at which the structures were reported. When the resolution was taken uniformly on a logarithmic scale, the most frequent values of these functions were quasi-linear over a large resolution range.
Predictions of the possible model parameterization and of the values of model characteristics such as R factors are important for macromolecular refinement and validation protocols. One of the key parameters defining these and other values is the resolution of the experimentally measured diffraction data. The higher the resolution, the larger the number of diffraction data N ref, the larger its ratio to the number N at of non-H atoms, the more parameters per atom can be used for modelling and the more precise and detailed a model can be obtained. The ratio N ref/N at was calculated for models deposited in the Protein Data Bank as a function of the resolution at which the structures were reported. The most frequent values for this distribution depend essentially linearly on resolution when the latter is expressed on a uniform logarithmic scale. This defines simple analytic formulae for the typical Matthews coefficient and for the typically allowed number of parameters per atom for crystals diffracting to a given resolution. This simple dependence makes it possible in many cases to estimate the expected resolution of the experimental data for a crystal with a given Matthews coefficient. When expressed using the same logarithmic scale, the most frequent values for R and R free factors and for their difference are also essentially linear across a large resolution range. The minimal R-factor values are practically constant at resolutions better than 3 Å, below which they begin to grow sharply. This simple dependence on the resolution allows the prediction of expected R-factor values for unknown structures and may be used to guide model refinement and validation.
doi:10.1107/S0907444909039638
PMCID: PMC2789003  PMID: 19966414
resolution; logarithmic scale; R factor; data-to-parameter ratio
22.  Averaged kick maps: less noise, more signal…and probably less bias 
Averaged kick maps are the sum of a series of individual kick maps, where each map is calculated from atomic coordinates modified by random shifts. These maps offer the possibility of an improved and less model-biased map interpretation.
Use of reliable density maps is crucial for rapid and successful crystal structure determination. Here, the averaged kick (AK) map approach is investigated, its application is generalized and it is compared with other map-calculation methods. AK maps are the sum of a series of kick maps, where each kick map is calculated from atomic coordinates modified by random shifts. As such, they are a numerical analogue of maximum-likelihood maps. AK maps can be unweighted or maximum-likelihood (σA) weighted. Analysis shows that they are comparable and correspond better to the final model than σA and simulated-annealing maps. The AK maps were challenged by a difficult structure-validation case, in which they were able to clarify the problematic region in the density without the need for model rebuilding. The conclusion is that AK maps can be useful throughout the entire progress of crystal structure determination, offering the possibility of improved map interpretation.
doi:10.1107/S0907444909021933
PMCID: PMC2733881  PMID: 19690370
kick maps; OMIT maps; density-map calculation; model bias; maximum likelihood
23.  Decision-making in structure solution using Bayesian estimates of map quality: the PHENIX AutoSol wizard 
Ten measures of experimental electron-density-map quality are examined and the skewness of electron density is found to be the best indicator of actual map quality. A Bayesian approach to estimating map quality is developed and used in the PHENIX AutoSol wizard to make decisions during automated structure solution.
Estimates of the quality of experimental maps are important in many stages of structure determination of macromolecules. Map quality is defined here as the correlation between a map and the corresponding map obtained using phases from the final refined model. Here, ten different measures of experimental map quality were examined using a set of 1359 maps calculated by re-analysis of 246 solved MAD, SAD and MIR data sets. A simple Bayesian approach to estimation of map quality from one or more measures is presented. It was found that a Bayesian estimator based on the skewness of the density values in an electron-density map is the most accurate of the ten individual Bayesian estimators of map quality examined, with a correlation between estimated and actual map quality of 0.90. A combination of the skewness of electron density with the local correlation of r.m.s. density gives a further improvement in estimating map quality, with an overall correlation coefficient of 0.92. The PHENIX AutoSol wizard carries out automated structure solution based on any combination of SAD, MAD, SIR or MIR data sets. The wizard is based on tools from the PHENIX package and uses the Bayesian estimates of map quality described here to choose the highest quality solutions after experimental phasing.
doi:10.1107/S0907444909012098
PMCID: PMC2685735  PMID: 19465773
structure solution; scoring; Protein Data Bank; phasing; decision-making; PHENIX; experimental electron-density maps
24.  Generalized X-ray and neutron crystallographic analysis: more accurate and complete structures for biological macromolecules 
X-ray and neutron crystallographic data have been combined in a joint structure-refinement procedure that has been developed using recent advances in modern computational methodologies, including cross-validated maximum-likelihood target functions with gradient-based optimization and simulated annealing.
X-ray and neutron crystallographic techniques provide complementary information on the structure and function of biological macromolecules. X-ray and neutron (XN) crystallo­graphic data have been combined in a joint structure-refinement procedure that has been developed using recent advances in modern computational methodologies, including cross-validated maximum-likelihood target functions with gradient-based optimization and simulated annealing. The XN approach for complete (including hydrogen) macromolecular structure analysis provides more accurate and complete structures, as demonstrated for diisopropyl fluorophosphatase, photoactive yellow protein and human aldose reductase. Furthermore, this method has several practical advantages, including the easier determination of the orientation of water molecules, hydroxyl groups and some amino-acid side chains.
doi:10.1107/S0907444909011548
PMCID: PMC2685734  PMID: 19465771
joint X-ray and neutron crystallography; structure refinement
25.  Crystallographic model quality at a glance 
The representation of crystallographic model characteristics in the form of a polygon allows the quick comparison of a model with a set of previously solved structures.
A crystallographic macromolecular model is typically characterized by a list of quality criteria, such as R factors, deviations from ideal stereochemistry and average B factors, which are usually provided as tables in publications or in structural databases. In order to facilitate a quick model-quality evaluation, a graphical representation is proposed. Each key parameter such as R factor or bond-length deviation from ‘ideal values’ is shown graphically as a point on a ‘ruler’. These rulers are plotted as a set of lines with the same origin, forming a hub and spokes. Different parts of the rulers are coloured differently to reflect the frequency (red for a low frequency, blue for a high frequency) with which the corresponding values are observed in a reference set of structures determined previously. The points for a given model marked on these lines are connected to form a polygon. A polygon that is strongly compressed or dilated along some axes reveals unusually low or high values of the corresponding characteristics. Polygon vertices in ‘red zones’ indicate parameters which lie outside typical values.
doi:10.1107/S0907444908044296
PMCID: PMC2651759  PMID: 19237753
model quality; PDB; validation; refinement; PHENIX

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