Interactive comparison and remediation of collections of macromolecular structures

Abstract

Often similar structures need to be compared to reveal local differences throughout the entire model or between related copies within the model. Therefore, a program to compare multiple structures and enable correction any differences not supported by the density map was written within the Phenix framework (Adams et al., Acta Cryst 2010; D66:213–221). This program, called Structure Comparison, can also be used for structures with multiple copies of the same protein chain in the asymmetric unit, that is, as a result of non‐crystallographic symmetry (NCS). Structure Comparison was designed to interface with Coot(Emsley et al., Acta Cryst 2010; D66:486–501) and PyMOL(DeLano, PyMOL 0.99; 2002) to facilitate comparison of large numbers of related structures. Structure Comparison analyzes collections of protein structures using several metrics, such as the rotamer conformation of equivalent residues, displays the results in tabular form and allows superimposed protein chains and density maps to be quickly inspected and edited (via the tools in Coot) for consistency, completeness and correctness.

Introduction

It is desirable that atomic models of different crystal structures of a protein vary only in regions where genuine heterogeneity occurs (due to ligand binding, crystal packing, conformational changes, etc.), while excluding differences due to resolution, map quality or refinement methods. For models determined at low resolution, the internal consistency of related structures can be enforced during refinement by restraining the refinement model to a reference structure, which is implemented in various forms in phenix.refine1 Refmac,2, 3 CNS,4, 5 and Buster‐TNT.6 Similar methods are also used to enforce non‐crystallographic symmetry between multiple copies of a macromolecule in the crystallographic asymmetric unit.7 However, none of these approaches provides a robust solution to the problems of distinguishing between real and artificial structural heterogeneity or of evaluating the likelihood that a validation outlier is an intrinsic feature of the macromolecule instead of an error.

Here, we describe the program “Structure Comparison” which addresses these issues by simultaneous validation and conformational analysis of multiple closely related structures. The goal is to make the entire collection of structures as correct, complete and consistent as possible. Inconsistencies should be confined to instances supported by experimental data, for example, density. We have used the Phenix Structure Comparison program to analyze several sets of published structures and show that it facilitates rapid correction of spurious deviations between otherwise similar models.

Program Description

Implementation and general use

The program is written in Python with C++ extensions and is distributed as part of the Phenix software.8 All user interactions are through a graphical user interface (GUI). Required inputs are a collection of two or more related protein chains. Separate files and NCS‐related copies in a single file are permitted. Optionally, a sequence file is used to extract the chains of interest defaulting to the first chain found in the first model if omitted. The user may optionally supply diffraction data used for the calculation of 2mF _obs–DF _model and mF _obs–DF _model difference maps, or pre‐calculated map coefficients in MTZ format.

A reference structure to use for global superposition of chains may be provided, defaulting to the first structure in the input list if omitted. If the reference structure has multiple chains, the first chain is selected for finding NCS copies in all input models, but a user provided chain ID will override this selection. Similarly, if a sequence file is provided, the index of the sequence in the file can be chosen. This is useful when a model contains more than one type of chain. The chosen sequence is then used to find all copies of that chain in all model files. The default for sequence identity between models or chains, 80%, can be adjusted, as can the number of processes used for performing calculations.

An important choice is whether to superpose the structures on a reference structure. If superposition is enabled, all similar chains (including NCS copies) and their density maps are superposed onto the reference. The results of the comparison are the same, but the visual display will show all chains superposed onto the reference structure. The superposition is performed using phenix.superpose_pdbs with the main chain C_α atoms selected for the matching algorithm. If map coefficients or diffraction data are provided, the resulting maps are superposed using phenix.superpose_maps.

Automatic file loading

Automatic file detection functionality is available in the Structure Comparison GUI. The “Add directory” option will search in the chosen directory for model and data/map file pairs. The “Add directory tree” option searches for file pairs by walking a directory tree and choosing a single pair from each directory. mmCIF format files have precedence over Protein Data Bank (PDB)9 format files.

The program begins by extracting near‐identical chains, based on comparison to the reference sequence, and performing optional superposition. Diffraction data, if supplied, are used to calculate maps. All tasks can be executed in parallel with the program typically taking only a few minutes to run on a multiprocessor computer. Depending on whether the structures are superposed or not, coordinate files for the individual chains can be saved. The results of the structure comparison are displayed in a new set of tabs within the program window, starting with a summary of the extracted chains and their basic properties. Additional tabs, described in section 2.4, include side‐chain rotamer, Ramachandran, ligand, secondary structure, missing atoms, water cluster, cis‐peptide, histidine protonation, and B‐factors or atomic displacement parameters (ADP) analyses. Optionally, a HTML report can be created which contains tabular summaries of each of these analyses, the list of structures compared and their one‐letter amino acid sequences.

Alignment and superposition of structures and maps

Although the program is designed to analyze structures with homogeneous residue numbering, it is also capable of handling variable insertions/deletions (and, potentially, close homologues). The default mode of operation assumes that the sequences are essentially identical, except for point mutations, and treats residue numbers as transferrable between structures. Where this is not applicable, the program may instead align the sequences of all chains under comparison to a common reference sequence using the open‐source program MUSCLE.10

The individual chains may remain in their original positions or are superposed on to a reference model. This allows all chains to be viewed in a common frame of reference regardless of crystal form, or location in the asymmetric unit if NCS is present. Density maps, if calculated, will be simultaneously transformed to follow their associated models by interpolation onto a pseudo‐P1 grid in the new orientation and saved in CCP4 map format. These routines are also available in the program phenix.superpose_maps.

The main limitation of the superposition procedure is the transformation of molecules away from their original context, such as crystal packing and ligands, although these effects are somewhat mitigated by the transformation of density with the models. The transformation matrices are automatically saved so that the original placement in the unit cell can be recovered using the Coot Control Window (see below). The models may therefore be edited in Coot 11 to improve agreement between equivalent residues and the full structures can be afterwards regenerated.

Extraction of features and presentation of results

The program is primarily designed to display all matching residues with heterogeneous properties; however, this may be overridden by a user‐defined atom selection. Each of the reports discussed below is presented in a tab on the results page and can be viewed interactively within a Coot window. If no differences were found for a particular analysis, the corresponding result tab will not appear. For example, if there are no missing atoms or residues in the input models, the “missing atoms” tab will not be shown. Figure 1 shows a typical Structure Comparison session with the results tab for rotamers and a Coot window displaying the models selected by the Coot Control Window. In this example session, Coot is showing a portion of the models that were selected in the Structure Comparison results tab (note that density maps are not being displayed in this view).

Figure 1.

Typical Structure Comparison session showing the results tab for the rotamer angles and a Coot window displaying the models selected by the Coot Control Window (center bottom).

For each type of analysis, the structure comparison results are presented and discussed using specific examples. These models were taken directly from the PDB and used without any refinement. The groupings of PDB codes are listed below. The PDB and ligand codes are written following the convention outlined in the editor's notes in the Computation Crystallography Newsletter.12

• Five high resolution (0.75 Å–0.87 Å) structures of bovine trypsin (BT) which resulted from a study investigating the reproducibility of protein models from different crystals obtained under similar conditions.13

• Two high resolution models of PfluDING at pH 4.5 (0.98 Å, PDB code 4F1U) and pH 8.5 (0.88 Å, PDB code 4F1V), obtained from two different crystals and refined independently.14

• A lower resolution model (PDB code: 1Z3Z, resolution 2.9 Å) and a higher resolution model (PDB code: 1ZoD, resolution 1.8 Å) of the protein dialkylglycine decarboxylase.15

• Four human factor Xa protein with different bound inhibitors: 3ENS (resolution: 2.3 Å, inhibitor: ENS16), 3HPT (resolution: 2.2 Å, inhibitor: YET17), 3K9X (resolution: 1.9 Å, inhibitor MBM18) and 3SW2 (resolution: 2.4 Å, inhibitor: Fi119). The latter contains only one copy of the biological unit (two protein chains) while the other structures contain two copies.

• Several models of a human heart fatty acid‐binding protein (H‐FABP): two determined at high resolution (3WVM: 0.88 Å resolution, 4TJZ: 0.87 Å resolution) and one model determined via serial femtosecond crystallography (3WXQ).

• A model of cobalamin‐dependent methionine synthase with two NCS related chains (3BoF) solved at 1.7 Å.20

A description of each of the possible results tabs follows. By default, the program runs all property analyses, but the user can limit those performed.

Summary

Each chain matching the reference occupies a row in the summary table, which lists the filename, chain ID, number of residues, and atoms, percentage identity to the reference and the mean isotropic Atomic Displacement Parameter of the chain (water molecules and ligands are not taken into account). If the chains were superposed, the root‐mean‐square deviation (RMSD) values of the C_α atoms are displayed as well.

Figure 2(A) shows the summary results tab for five BT structures. The leftmost column lists the filenames of the models, followed by the chain identifier. The third and fourth columns show the number of atoms and residues, respectively in the protein chains. The number of atoms is similar for the five BT models (the only difference arises from the number of water molecules) and the number of residues is the same (223 in all cases). The fifth column indicates the sequence identity in percent, which is 100%, as no mutations or other modifications are present. The sixth column lists the mean ADPs, which are between 8.2 and 8.6 Ų, except for model 4i8H, which has an even lower value of 7.6 Ų. It can be noted that the diffraction data for 4i8H have also the highest resolution (0.75 Å). The seventh column summarizes the RMSD between model 4i8G and the other models (the value for 4i8G is therefore blank). The RMSD varies between 0.105 and 0.078 Å, indicating that the BT models superpose very well.

Figure 2.

Summary results tab (A) and ligand summary results tab (B) for five BT models.

At the bottom of the results summary tab are the controls for Coot 11 and PyMOL.21 Furthermore, the button “Export as HTML” enables saving all result tables in HTML format.

Ligand summary

If ligands are present, the ligand summary tab appears and lists basic information for each ligand, that is, chain ID, 3‐letter code, residue number, number of atoms and mean isotropic ADP. Columns are sortable for ease of determining the most interesting comparisons.

Figure 2(B) shows the ligand summary tab for five models of BT, which each contain the inhibitor benzamidine (BEN), a glycerol molecule (GOL) and two sulfate ions.

Side‐chain rotamers

Side‐chains are compared to the Rotamer Library22, 23 using the program phenix.rotalyze. By default, any set of equivalent residues for which multiple rotamer classes are identified, plus any outliers, will be displayed in the results table. The color‐coding of the cells allows quick identification of areas of interest. Outliers are colored red whilst cells without sufficient information, such as in the case of missing or incomplete residues, are shaded grey and otherwise left blank. If more than 50% of side‐chains for a common residue share a single rotamer class, the cell is highlighted in green, while minority conformations are highlighted in orange. Side‐chains adopting multiple conformations are shaded blue (with white font). A similar color code is used for most other result tabs (red for outliers, blue for multiple conformations, grey for missing residues etc.).

Recently, rotamer validation was extended to include the concept of favored and allowed rotamers.23 The cutoff values are based on the probability of the set of side‐chain dihedrals in a protein model. Less than 0.3% probability is considered an outlier while a probability of greater than 2% is considered favorable. The values of the side‐chain dihedral angles determine the rotamer class, with rotamer IDs taken from Lovell et al.22 The allowed designation for a rotamer indicates that the side‐chain is on the edge of the specific rotamer space. These are shown with the use of italic font in the appropriate grid cell.

Therefore, there are seven possible categorizations of a residue in the rotamer tab. It can be the majority consensus, either favored or allowed; in the minority group, favored or allowed; alternative location; outlier; or not included in the evaluation.

Differences in side‐chain rotamers can be a sensitive indicator of functionally relevant changes in the protein structure. They can also be due to poor density in mobile portions of the protein.

Figure 3 shows the rotamer table for the factor Xa proteins. The rotamer table consists of two sections. The upper section contains the data for each chain that has non‐uniform results or outliers. Because the rotamer table is the most information rich, an overview table is included in the lower section to summarize the results and to act as a legend for the cell colors. The leftmost column lists the rotamer discrepancies for residue Gln20, which is present in chain B and D of each of the models with the exception of 3SW2 that only has one copy of the two protein chains in the biological unit. The side‐chain of the latter is incomplete—truncated at C_γ as shown in Figure 4 (yellow)—and the cell is therefore highlighted in grey. In the 3ENS model, chain B, Gln20 is an outlier and highlighted in red. In the overview section, there is a row that contains the number of outliers (if present). A similar scheme follows for all the other six categories available in the side‐chain rotamer tables. Looking at the seven overlaying instances of Gln20 in Figure 4 shows that this outlier (red) is very similar to the majority of the other rotamers.

Figure 3.

Rotamer results table for the factor Xa group of proteins.

Figure 4.

Gln20 in all models and chains (seven instances) of the factor Xa group of proteins as well as 2mF _obs–DF _model density map from 3HPT:B at 1.5σ contour level.

The majority of the Gln20 rotamers are in the mt0 conformation and the cells are therefore highlighted green. Note that two of the instances of mt0 are written in italics which indicates that these two residues, 3ENS:D and 3HPT:D, are in the allowed region of the mt0 rotamer space while the other two are in the favored region. This disparity is also shown in the overview table. The instance of Gln20 in 3HPT:B is in a different rotamer state (green), which is supported by the density (Fig. 4). It is shown as the minority result.

Figure 5 (left) shows a close‐up of the rotamer results table for Arg143, for which only one rotamer, 3K9X:D, differs from the other rotamers. Arg143 and the mF _obs–DF _model and 2mF _obs–DF _model density maps from 3K9X:D are shown in Figure 5 (right). Clearly, the rotamer does not fit the density, as there is a negative peak at the N and C atoms of the guanidine group of the side‐chain and a positive peak for the correct rotamer, mtt180, matching the other instances.

Figure 5.

Left: Close‐up of the rotamer results table for Arg143 in the factor Xa group of proteins. Right: Arg143 in all models and chains of the factor Xa group of proteins as well as mF _obs–DF _model (positive: green, negative: red) and 2mF _obs–DF _model density maps from 3K9X:D at 1.5σ and ±3σ contour level, respectively. It can be noted that the side‐chain is incomplete for 3HPT:D (lightgreen).

Models 3ENS, 3HPT, and 3K9X are crystallized in space group P2₁ while 3SW2 is in P2₁2₁2₁. The rotamer designation for Gln26 in all chains of the former is tt0 while it is mt‐10 for the latter. An investigation of the crystal contacts shows that Glu26 in 3SW2 is within 2.9 Å of a symmetry related residue while in the other models the distance between Gln26 and any symmetry related residue exceeds 9 Å. Furthermore, the instance of Glu26 in 3SW2 is rotated towards the symmetry copy of Asn160 in chain A to form a hydrogen bond with the side chain nitrogen atom.

Gln30 exemplifies another interesting application of the rotamer analysis. All of the instances of residue Gln30 are in the tp40 conformation except 3HPT:D, which is tp‐100. These conformations are approximately 180 degrees apart and examination of the superposed side‐chains shows that the conformations can be rationalized by an NQH flip24 of the side chain oxygen and nitrogen atoms.

Ramachandran angles

Ramachandran angles are calculated using phenix.ramalyze, which uses the same structure database as the rotamer distributions.25 The probability cutoffs for “favored” and “allowed” angles are identical to those used in Molprobity. By default, any set of equivalent residues for which multiple Ramachandran angles are identified, plus any outliers, will be displayed. The cells of the results table display the ϕ/ψ angles for each residue. Outliers are highlighted in red, while favored and allowed angles are shaded in green and orange, respectively. Alternative conformations are shaded in blue.

The Ramachandran angles describe the rotation of the protein chain. Differences can therefore indicate real changes in the local fold or possible fitting errors. Residues with different assignments in different models, that is, flagged as an outlier in one model while having a favored angle in another model, require special attention.

Figure 6(A) shows a part of the Ramachandran analysis results table for the two models of dialkylglycine decarboxylase. There are two outliers, Asp6 in model 1ZoD and Ala55 in model 1Z3Z. Model 1ZoD was determined at 1.8 Å resolution, which might justify the conformation of the Asp6 main‐chain. However, model 1Z3Z was determined at 2.9 Å resolution, it is therefore less likely that the X‐ray data definitively supports the outlier for residue Ala55. Also, the same residue adopts a favored conformation in model 1ZoD, which suggests that the Ala55 main‐chain of model 1Z3Z should not be modeled as an outlier.

Figure 6.

(A) Results table from the Ramachandran angle analysis and (B) Secondary structure results tab for models of 1ZoD and 1Z3Z of dialkylglycine decarboxylase.

Secondary structure

Secondary structure annotation can be performed with different procedures, including CaBLAM,26 which uses pseudo‐torsion and other angles along the protein main chain to classify secondary structure, or ksDSSP (the default), an open‐source implementation of the original DSSP algorithm.27 Any set of matching residues with more than one type of secondary structure assignment, for example, a residue labeled as helix in one chain and without secondary structure assignment in another, will be reported in the results table. Color‐coding is based on the secondary structure annotation: α‐helices are green, 3₁₀‐helices are blue, β‐sheets are orange, non‐secondary structure residues are white and missing residues are grey.

Differences in secondary structure annotation can highlight structural changes between models, such as those induced by ligand binding.28, 29 However, they can also occur if there are relatively small conformational differences between models, such as at the extremities of helices and strands or in short loops.30

Figure 6(B) shows an example for the secondary structure results tab after comparing a lower resolution model and a higher resolution model of the protein dialkylglycine decarboxylase. Different secondary structure annotations are found for 12 residues (His16, Thr172, Tyr173, Arg174, Tyr185, Leu186, Ala257, Cys258, Gln259, Arg260, Asp261, and Gly403). Five of them are at helix termini (His16, Tyr185 and Leu186, Asp261) or at the extremity of a beta‐sheet (Gly403). Residues 172–174 in 1ZoD were apparently mis‐assigned as 3₁₀‐helix by the annotation algorithm. Visual inspection shows that the main chain adopts a loop in this region. Finally, residues 257–260 adopt an imperfect helical conformation, which leads to assignment of type alpha or 3₁₀ in 1Z3Z and 1ZoD, respectively. The different assignments are most likely due to small conformational differences between 1Z3Z and 1ZoD in this area. This shows the necessity to visually inspect the results from secondary structure differences to identify areas of genuine variations.

Omega angles

Cis‐peptides and nonplanar omega angles are calculated using phenix.omegalyze. If the omega angle (ω) is within 30° of 180° or 0°, the peptide is deemed as a trans‐ or as a cis‐peptide, respectively. All other ω are denoted as twisted. Residues with cis peptides or twisted ω are displayed using blue and orange, respectively.

The ω peptide angle is overwhelmingly trans in proteins. The occurrence of a cis‐peptide is likely to be conserved between structures of the same protein. This is not the case for Glu559 of the PDB entry 3BoF, which is twisted in chain A and trans in chain B. Visual inspection of the residue in Coot shows that the density for this residue, the penultimate residue in each chain, is poor compared to the rest of the model.

Interestingly, the pair of twisted peptides, Ser412, have a large amount of difference density. Refining these residues to the trans conformation, a feature available in phenix.refine using the apply_cis_trans_specification parameter, results in a better fit to density and a reduction in the overall angle rmsd from 1.01° to 0.92°.

Missing atoms

If atoms or entire residues are missing in one chain while present in at least one other chain, they will be listed in the results table. Residues missing side‐chain or backbone atoms are shaded orange and red, respectively, and the names of the missing atoms are shown in the cell. If the entire residue is missing, the cell is colored blue while matching complete residues are highlighted in green.

Entire residues are sometimes not modeled when there is no clear density to support their location, such as at chain termini and in loops. Similarly, it may occur that side‐chain atoms cannot be placed¹ which happens typically for residues with long side‐chains located at the protein surface (for example, Lys or Glu). However, it is also possible that atoms are misplaced unintentionally during file conversions, manual inspection or switching between different programs. To address these issues, the “missing atoms” tab gives a concise summary of missing atoms and residues for all input models. It should be noted that the analysis is based on the input models or the input sequence. Furthermore, at present hydrogen atoms are omitted from the missing atom analysis.

Figure 7(A) shows the missing atoms results table for two models of the protein PfluDING. Residues Glu1372, Ala1373, and Ala1374 are missing in model 4F1V. They are located at the C‐terminal and there is no clear electron density to support their location, which explains why they were not modeled. Furthermore, Leu1370 lacks the atoms N, CA, CB, CG, CD1, and CD2 of the B‐conformation (i.e., the C, O, and HA atoms of conformation B are present). It can be noted that both of the neighboring residues of Leu1370 adopt an alternative conformation. It is likely that the missing atoms of the B conformation of Leu1370 were part of a double conformation, which was not entirely deleted (as the C, O, and HA atoms remained) during manual model building.

Figure 7.

(A) Results from the missing atom analysis for two PfluDING models. The cell width can be expanded to show all missing atom names, such as in the case of Leu1370. (B) Results from the histidine protonation analysis for two PfluDING models.

Histidine protonation

Histidine residues have three different protonation states: either one or both of the ND1 and NE2 nitrogen atoms of the imidazole can be protonated. The results table displays different protonation states of histidine, if hydrogen atoms are present in at least one of the input models. Hydrogen atoms are only seen experimentally at very high resolution (better than 1 Å) but it is possible to infer the position of the histidine hydrogen atoms from their parent heavy atoms. Hydrogen atoms are therefore routinely added to lower resolution models to improve refinement and the analysis of geometry clashes. However, when the electron density of the H atoms is not visible, it often cannot reliably be deduced from the analysis of suitable H‐bond donors or acceptors in the vicinity. Automatic procedures might therefore produce inconsistent models.

Figure 7(B) shows the results table for the comparison for two models of the protein PfluDING that contains two histidine residues. The comparison shows that the ND1 atoms of His57 and His317 are protonated in model 4F1U, while the NE2 atoms are protonated in model 4F1V. It seems likely that NE2 should be protonated in both structures, as there are unfavorable interactions with an asparagine NH2 head group if ND2 is protonated.

Water molecules

Differences in solvation site between models are of interest, as they may reflect genuine changes in structure or could be a result of misidentification of water and/or ion atoms.

In a model file, water molecules can be either associated with a macromolecular chain (this assignment is currently performed upon deposition of a model to the wwPDB11) or they may be placed in a separate chain (this is common practice in model building and refinement programs). The latter kind of model is analyzed using a simple procedure to assign water molecules to protein chains. Water molecules (and ions and ligands) are associated with a protein chain if they are located within 3.5 Å distance of one or more protein atoms. Once a molecule has been assigned to a chain, it cannot be moved to another protein chain. This procedure—if necessary—is carried out automatically by the Structure Comparison tool prior to the water cluster analysis (see Methods). The analysis results in a list of clusters containing up to N water molecules, where N is the number of superposed chains. Any cluster with less than N water molecules is displayed in the results table. Clusters with heterogeneous compositions of water and ions are particularly interesting and are reported at the beginning of the table. Cells representing a water molecule are highlighted in green and marked with the corresponding residue name used for water in the model (such as “HOH”), while the cell of the chain with no corresponding water is white and otherwise left blank. Cells containing ions are highlighted in orange.

Figure 8 shows the water results table for the factor Xa structures, with the sodium locations in the two left columns. Note that the column header of the second column shows a symbol, r0.8, that indicates the approximate radius of the cluster rounded up to the nearest tenth of an  Ångström. The number 303 is the residue ID of the water molecule in the reference structure.

Figure 8.

Water analysis results table for the factor Xa group of proteins. Note that the sodium locations are in the two left columns.

Figure 9 shows the sodium ions in all models of factor Xa group. Models 3HPT and 3K9X have the same arrangement of sodium ions and water molecules [see Fig. 9(A)]. Model 3ENS contains a sodium ion near the water locations of the first two models and there is a positive density peak near the sodium locations of models 3HPT and 3K9X [Fig. 9(B)], strongly suggesting that it actually occupies the center position and not the modeled one. In 3WS2, the sodium is at the same position as in the first two models but is missing the two water molecules for which positive density peaks appear in the difference map [Fig. 9(C)].

Figure 9.

Sodium ions (violet spheres) in all structures of the factor Xa group; (A) Models 3HPT and 3K9X; (B) Model 3ENS; (C) Model 3WS2. The mF _ob– DF _model (green) and 2mF _obs–DF _model electron density maps are contoured at 3σ and 2σ, respectively, except in the case of 3SW2:B, where the contours are 4σ and 1.5σ. Water molecules are displayed as red spheres.

The results from the water analysis can also be used to investigate the possibility of a side‐chain rotamer misfit into a water site or even the unnecessary use of alternative locations for a side‐chain when the solvent model should in fact be updated.

Ligands

Many proteins are co‐crystallized with ligands or molecules from the crystallization agent or buffer solutions. The development of new small molecule therapeutics often relies on the detailed analysis of ligand/macromolecule complexes and their associated densities. The differences between complexes can be particularly important for proposing changes to the small molecules to improve their efficacy or specificity. With the Structure Comparison tool, all ligands and small molecules can be localized to compare the molecule's position and orientation as well as any conformational changes in the protein.

For each ligand, the center of mass is calculated and a cluster analysis (similar to the method employed for water molecules, see Methods) is carried out. The results table lists all ligand clusters, making it possible to easily see which ligands are located at similar positions.

Figure 10 shows the four ligands (nine instances) from the factor Xa structures. The Fi1 ligand in 3WS2 has the largest difference in chemical structure from the others but has a convincing fit to its density. As with the water location table, a radius is provided in the table based on the center of mass of each of the ligands to give a measure of the superposition.

Figure 10.

Superposition of the four ligands (nine instances) from the factor Xa group. Yellow: FI1 in 3SW2 chain B; Red: ENS in 3ENS chain B; Pink: ENS in 3ENS chain D; Dark green: YET in 3HPT chain B; Light green: YET in 3HPT chain D; Dark blue: MBM in 3K9X chain B; Light blue: MBM in 3K9X chain D.

Atomic displacement parameters

Isotropic ADPs are extracted from each structure. The per‐residue ADP averages for all atoms, main‐chain atoms only and side‐chain atoms are calculated. Because the ADPs for different structures may be on significantly different scales depending on resolution or crystal form, the ratio of the local average to the mean for the entire chain is also calculated, providing a normalized plot. The plot can be saved as an image and the values can be saved to a CSV file. The plot also displays points along the bottom corresponding to the residues appearing in the Ramachandran and rotamer tabs so that the relationship between high ADP values and validation outliers or modeling mismatches can be explored.

The ADP of an atom or a group of atoms represents, in part, small‐scale static and dynamic disorder (as opposed to occupancies that represent the same but large‐scale). Differences in ADP can be therefore indicative of different mobility, or local order in the structure. However, higher ADPs can also reflect model errors, as they typically increase when there is no strong density to support the modeled position.

Figure 11(A) shows the ADP profile (normalized by chain) for three models of heart fatty acid‐binding protein (H‐FABP). Overall, the profiles look very similar, but there are two residues where the ADPs differ significantly: Met1 in 3WXQ and Asp110 in 3WVM. Figure 11(B) shows a superposition of all three H‐FABP models, as well as density maps for 3WVM in the vicinity of Asp110. The OD2 atom of the Asp110 side‐chain is not optimally placed, as it is covered with negative difference density. The orientation of the Asp 110 side‐chain is most likely similar to that in model 4TJZ (cyan), as suggested by a positive difference density peak and a 2mF _obs–DF _model peak in the vicinity of the OD1 and OD2 atoms of Asp110 in 4TJZ. Furthermore, the side‐chain rotamer is flagged as an outlier for Asp110 in 3WVM. Along with the density and the rotamer angle, the high ADP of this residue compared to the other models is highly suggestive of a sub‐optimal orientation of Asp110. Similarly, inspection of the electron density maps near Met1 suggests that its orientation in 3WXQ can be optimized (not shown). Also, the Ramachandran angle of Met1 is in the outlier region, which further implies that its initial orientation can be improved. The ADP profile can therefore help to identify regions, which should be inspected.

Figure 11.

(A) ADP profile of three H‐FABP models, as it is represented in the ADP results tab; 3WVM: blue, 3WXQ: orange and 4TJZ: green. The red diamonds and blue triangles designate residues with rotamer and Ramachandran differences, respectively. (B) Asp110 in three H‐FABP models, 3WVM: color by atom, 3WXQ: violet and 4TJZ: cyan, and electron density maps for 3WVM. The positive (green) and negative (red) mF _obs–DF _model maps are contoured at ±2.5σ. The 2mF _obs–DF _model electron density is represented in blue at 1.5 σ contour level.

Interaction with graphics programs

A key component of the Phenix GUI is the ability to control a Coot or PyMOL session through Python extensions to these programs.31 After the initial calculations are complete, all models and maps are loaded into one or both viewers. Double‐clicking on any non‐empty cell in the result tables immediately centers the view(s) on the appropriate residue. It should be noted that clicking on an empty cell (often designated by “—”) will not change the view.

Control panels within Phenix toggle the visibility of individual objects and enable additional actions such as recovery of edited models from Coot in their original orientations or display of all divergent residues for a specific analysis in PyMOL.

The PyMOL Control Window has an additional pull‐down choice that will select and highlight only those residues listed in the corresponding tab. This can be very helpful in viewing only the ligands and producing publication ready images.

Methods

Water clustering

A clustering algorithm is applied to find regions that have localized water molecules. Distance criteria are used to assign the water molecules to clusters that represent a preserved water location. The clustering scheme is based on an hierarchical algorithm32 with the addition of a termination criterion. The algorithm begins with each water molecule forming a cluster of one molecule. Looping over the list of distances between clusters (initially water molecules) from shortest to longest, it is determined if there is no water molecule from a different chain in the neighboring cluster, that is, the intersection of the sets of chain ID from each cluster is empty. If so, the two clusters are merged into a single cluster. This cluster will consist of, at most, a water molecule from each chain. This could be termed a trans‐chain droplet.

If there is a water molecule from the same chain in a neighbouring cluster, both clusters are “frozen” so that no more water molecules can be added to either. The cluster cannot expand because there is a water molecule in the same real space that should belong to another cluster.

The result is a list of clusters containing between one and the number of superposed chains water molecules. If the cluster has a water molecule from each chain, it is preserved. However, if there are fewer water molecules in a cluster than the number of chains, the non‐uniformity requires attention.

The clustering algorithm is not unique to water molecules. Ions can be included in the analysis and the resulting clusters may therefore contain both water molecules and ions (but only either a water molecule or ion from each chain). Depending on the circumstances, mixed ion/water clusters can represent either badly placed ions, badly placed water molecules or a physically meaningful change in the environment between models.

Because the clustering algorithm is based on a single point in space, it can be also applied to small molecules and ligands by using the center of mass of each entity.

Map superposition

In the Structure Comparison program, the models are superposed using the phenix.superpose_pdbs tool. The rotation and translation operators obtained by least squares fitting of equivalent coordinates are saved and used in the map superpose step. An orthogonal box around the reference molecule is determined and both the molecule and corresponding map are shifted into that box. The rotation‐translation operations are applied to the map corresponding to the moving model. Both reference and moving maps are defined on a regular grid. However, applying the rotation and translation to the moving map does not guarantee an exact superposition of grid nodes so tricubic interpolation is used to calculate the map values on the transformed map grid. The command line utility to superpose models and maps is phenix.superpose_maps.

Conclusion

The comparison of similar models or NCS copies of chains can provide valuable information to improve model building and perform validation. Differences between models require in many cases some deeper consideration. They can highlight genuine heterogeneity originating from different crystal contexts (such as the rotamer change of Glu26 in 3SW2 to form a hydrogen‐bond with a symmetry‐related residue due to crystal packing) or conformational changes, which happen, that is, upon ligand binding.

On the other hand, differences can be also due to errors in model building (such as Arg143 in the factor Xa group that has a consensus for rotamer mtt180 and also the density to support it), or highlight areas that cannot be clearly modeled, that is, when the experimental data does not provide any clear evidence for a particular conformation.33 It can be noted that there is often more than one indicator of a problem such as in the example discussing the ADPs, where problematic residues are also flagged as rotamer or Ramachandran outliers.

With the advent of cryo‐EM structures, it is envisage that this tool will be expanded to cover the comparison of structures and maps directly. Also, the neutron refinement structures can be included with the development of a deuterium aware missing atoms module.

In several examples used here, refining with a modern refinement program can correct a number of the problems but there are often differences that need further attention.

Download instructions: Structure Comparison is available from the Phenix release version 1.12.

A tutorial video, explaining how to use Structure Comparison and discussing results using example data, is available on the Phenix Tutorials YouTube Channel (www.youtube.com/c/phenixtutorials).