PDB-Explorer: a web-based interactive map of the protein data bank in shape space

Design of the protein shape fingerprint 3DP

In view of a global analysis of the PDB we set out to identify a fingerprint encoding
the 3D-structure of biomacromolecules since it is known to play an important role
in their biological function, their interaction with other molecules, 22]–25] and their evolution 26]–29]. While 3D-SURFER uses a 121-dimensional scalar fingerprint to encode the shape of
the molecular surface of proteins using 3D Zernike descriptors, 13], 14] we searched for a simpler yet more detailed encoding considering not only the shape
of the molecular surface, but also the atom types and the internal structure of the
protein. Inspired by the concept of atom-pair fingerprints proposed by Carhart, 30] Sheridan 31] and Schneider 32] to encode pharmacophores in small organic molecules, we recently reported a detailed
analysis establishing the suitability of atom-pair fingerprints for 3D-shape and pharmacophore
similarity searches in very large databases such as ChEMBL 33] and ZINC 34] using both topological distances read from the 2D-structures 35] and through-space distance read from the 3D-structures 20]. While topological distances cannot be extracted easily from the structures of macromolecules
or even do not exist within non-covalent assemblies, an atom-pair analysis of macromolecules
should be possible using through-space distances which can be directly computed from
the atomic coordinates available in each pdb file. An atom pair 3D-fingerprint, here
called 3DP, was therefore envisioned to encode 3D-structures in the PDB.

The 3DP fingerprint was designed to encode the 3D structure of proteins and other
biomacromolecules in PDB considering the biological assembly as defined by the authors
in each entry. Following our previous approach for small molecules, each atom pair
distance was converted to a Gaussian centered on the atom pair distance with a width
of 18 % of the distance itself, and the Gaussian was sampled at 34 values between
1.45 Å and 342.53 Å covering all atom pair distances present in PDB (Fig. 1a). For each of the 34 values increments were summed across all atom pairs. The 34
resulting sums were normalized to the heavy atom count to the power of 1.5 (HAC
^1.5
) to reduce sensitivity to size (Fig. 1b). The 34 values were computed separately for four different atom categories, using
the corresponding sum of category atoms as HAC for normalization. These four categories
considered as important for macromolecular properties comprised 1) all atoms; 2) positive
charges: lysine and arginine side chains; 3) negative charges: aspartate and glutamate
side chains, phosphate groups; 4) hydrophobic atoms, defined here as carbon atoms
with covalent bonds only to C or H atoms. Due to the smaller number of charged and
hydrophobic atoms compared to all atoms the bit values in the corresponding categories
were on average much smaller and were therefore multiplied by 5 for charged atom categories
and by 2 for the hydrophobic atom category. The final bit values were expressed in
percent and rounded to the integer value. The four combined sets of normalized, rounded
values formed the 136-dimensional 3DP fingerprint.

Fig. 1. 3DP fingerprint design. a 34 sampling values between 1.45 and 400 Å (blue vertical bars) and example Gaussian corresponding to two atom pair distances (red line). b Sampling of bit values of B1–B34 for the atom pairs at 30 and 200 Å from the Gaussian
functions in a. c Average (AV, blue continuous line) and standard deviation (SD, red doted line) of bit values of 3DP for all biological assemblies in the PDB. d Distribution of heavy atom count (HAC) values in the PDB. The analysis is based on
91,223 X-ray structures downloaded from the PDB in September 2014, considering in
each case the biological assembly as defined by the authors

Because most PDB-entries contain thousands of atoms which would require explicit calculation
of many millions of atom pair distances (Fig. 1d), the 3DP calculation was simplified by computing the fingerprint using formal “sum
atoms”. A maximum of 1728 sum atoms (resulting in a maximum of 1.5 million sum atom
pairs) were defined for each PDB-entry by fitting its biological unit into a 12×12×12
grid, using the average coordinates of each atom category within each box as the sum
atom coordinates and the number of category atoms within this box as its relative
weight. 3DP bit values computed with sum atoms were essentially indistinguishable
from those computed with actual atoms.

The 3DP calculation was performed 91,223 X-ray structures downloaded from the PDB
in September 2014 (Additional file 1: Supplement 1), considering in each case the biological assembly as defined by the
authors 36]. The 3DP fingerprint had a high resolution, with 99.99 % of PDB molecules having
unique 3DP fingerprints. The average bit values peaked at 33.76 Å (B20, B122) for
all atoms and hydrophobic atom pairs and at 39.83 Å (B55, B89) for positive and negative
charge atom pairs, while the corresponding standard deviation covered almost the entire
bit value range (Fig. 1c).

3DP encodes protein conformations

The 3DP fingerprint had a remarkable ability to precisely encode the shape of proteins,
as evidenced by investigating the correlation between 3DP similarity and the root
mean square deviation (RMSD) 37], 38] in different conformers of the same molecule, as presented with the following three
test cases. As a first test case a random coil 24-mer peptide was obtained from PDB-entry
4GOF and simulated using the ff99SB force field from the AMBER12 package, 39] with 1 ns simulated annealing followed by 50 ns free simulation in water solvent,
generating a large variety of conformers. The simulation was repeated 50 times, and
in each case the last structure was selected as reference. Its conformer analogs were
defined as all conformers with RMSD lower than 2 Å to that reference, which comprised
up to 136 conformers that were always the last series of frames in the MD run. Retrieval
of these conformers from the 2000 conformers of the corresponding trajectory was then
performed by sorting using the city-block distance CBD
_3DP
as similarity measure. The recovery was excellent, with an area under the curve (AUC)
of 95.85 % for average receiver operator characteristic (ROC) curve, showing that
3DP indeed provided a good encoding of molecular shape in terms of similarity searching
(Fig. 2a). All RMSD analogs were found within CBD
_3DP
??519, while the average distance of these RMSD analogs from the query conformer
was 264 and the largest distance was 2164 (Fig. 2b).

Fig. 2. Retrieval of conformer analogs from the MD trajectory of a 24 residue peptide by 3DP
similarity. a ROC curve for retrieving structures with RMSD??2 Å, relative the last frame in a
50 ns MD simulation taken as reference, by 3DP similarity (blue) and by random selection (red), averaged over 50 different MD simulations. b Recovery of structures with RMSD??2 Å to the reference (blue) and all structures (red) as function of CBD
_3DP
from the reference. The structure alignment and RMSD calculation of all heavy atoms
were carried out with the AMBER12 package. The sequence of the 24-mer peptide is MKKRLAYAIIQFLHDQLRHGGLSS

The correlation between 3DP similarity and RMSD was tested in a second case for a
larger protein by considering ten domain movement frames for glutamine binding protein
(1762 atoms) from the Protein Motion Database 40], 41]. These ten conformers represent different conformations of the binding domain spanning
between open (PDB-entry 1GGG, purple structure in Fig. 3a) 42] and closed state (PDB-entry 1WDN, red structure in Fig. 3a) 43]. A good correlation was observed between 3DP similarity and RMSD (calculated with
all-atom alignment by Maestro 8.5 44]), in particular when considering conformer pairs from one extreme of the movement
range (purple and red lines in Fig. 3b). Representation of the bit value changes showed that 3DP perceived the conformational
change at the level of each of the four different atom type categories (Fig. 3c).

Fig. 3. Correlation between RMSD and CBD
_3DP
in conformers of the glutamine binding protein. a Overlay of 10 structures from domain movement of glutamine binding protein taken
from the Protein Motion Database. The initial structure is PDB-entry 1GGG (purple) and last structure is PDB-entry 1WDN (red). b Correlation between RMSD from all heavy atom alignment and CBD
_3DP
. Each line indicates different reference structure. Purple: 1st (1GGG); Blue: 2nd; Cyan: 3rd; Lime Green: 4th; Green: 5th; Light green: 6th; Yellow: 7th; Yellow orange: 8th; Orange: 9th; Red: 10th (1WDN). c Deviation of bit values to the 5th structure

The sensitivity of 3DP similarity to slight changes in protein conformation was evaluated
in a third test case considering CDK2 (cyclin-dependent kinase 2), an important player
in cell cycle regulation 45]. The activity of CDK2 is induced by conformational changes occurring upon ligand
binding, in particular at the level of the large T-loop 46]. A total of 245 X-ray structures of CDK2 monomers bound with various small molecule
inhibitors are available in the PDB (Additional file 1: Supplement 2). These CDK2 structures are nearly identical in sequence (97 % identity),
but show different conformation at the level of the T-loop due to an induced-fit adaptation
of the protein around the various ligands. Although these 245 CDK2 structures were
almost identical in terms of their global molecular shape, the 3DP analysis readily
distinguished between the different T-loop conformers, with pairwise CBD
_3DP
distances between 75 and 1415 CBD
_3DP
units and maximum population around 300???CBD
_3DP
???500 (Fig. 4a). Three different pairs were analyzed closer in terms of differences in their 3DP
values (Fig. 4b) and their overall structures superimposed by all-atom alignment (Fig. 4c) 47]. In terms of the 3DP values differences were visible in all four atom pair categories.
In terms of the protein structures, the closest pair 3QZH/3ROY at CBD
_3DP
?=?89 and the intermediate pair 3QRT/2C5Y at CBD
_3DP
?=?424 only significantly differed at the level of the T-loop. For the 3QQH/4EZ7 pair
at CBD
_3DP
?=?1021, deviations were not only visible at the level of the T-loop but also in the
?-helix and ?-sheet at the top of the structures. The CDK2 analysis clearly showed
that 3DP was able to perceive small conformational differences residing in a loop
orientation between otherwise highly shape similar proteins.

Fig. 4. 3DP distinguishes between closely related CDK2 T-loop conformers. a Frequency histogram of pairwise CBD
_3DP
values from 245 CDK2 conformations (blue). b Three pairs of CKD2s, 3QZH-3ROY, 3QRT-2C5Y, and 3QQH-4EZ7, were analyzed. They had
CBD
_3DP
values 89 (left red bar in a), 424 (middle red bar in a) and 1021 (right red bar in a) respectively. Differences of bit values are shown for 3QZH-3ROY (blue), 3QRT-2C5Y (red), and 3QQH-4EZ7 (green). c Alignment of 3QZH (blue) and 3ROY (orange); 3QRT (slate blue) and 2C5Y (coral); 3QQH (green) and 4EZ7 (magenta)

3DP analysis of the RSCB protein databank

To facilitate access to PDB-entries a graphical user interface was created based on
an interactive color-coded map representing the 3DP chemical space using the Mapplet
principle previously reported for small molecule databases, by which database entries
are displayed in a visualization window as the mouse cursor moves on the map, and
connects to a fingerprint similarity search window to allow nearest neighbor searches
15]–18]. Although 78 % of the data variability was represented in (PC1, PC2)-plane obtained
by principal component analysis (PCA) of the 3DP dataset, this direct PCA map contained
many scattered pixels with uneven occupancies and was not suitable as an interface
(data not shown). We therefore generated an alternative representation of 3DP by similarity
mapping, which produces more compact and evenly populated maps with a fairly good
rendering for various chemical spaces 18], 48], 49].

To create the similarity map, 3DP similarity values relative to 200 randomly selected
reference molecules from the PDB were calculated, and the (PC1, PC2)-plane obtained
by PCA of the resulting 200-dimensional 3DP-similarity fingerprint was represented.
This (PC1,PC2)-plane, called similarity map, covered 98 % of the similarity fingerprint
data variability and had a compact, comet-like shape without peripheral pixels. Furthermore
the map had a relatively even occupancy of pixels which was highly suitable as a representation
of the PDB in 3DP space (Fig. 5a). PDB-entries were distributed on the map according to their size along the edge
of the comet (Fig. 5b). The position on the map was influenced by the molecular volume occupancy (mvo,
Ã…
³
/atom), a property defined here as the volume of the sphere with a radius corresponding
to the average distance of all atoms to the center of gravity, divided by the total
number of atoms, with the more compact, globular structure present at the comet edge
and less compact structures at the center (Fig. 5c). The map also separated PDB-entries with different fractions of positively charged
atoms, negatively charged atoms, and hydrophobic atoms, whereby the distribution pattern
for the fraction of hydrophobic and positively charged atoms was somewhat similar
(Fig. 5d–f). Color-coding by the normalized principal moments of inertia vector (nPMI1, nPMI2)
distinguishing between rod-like, disc-like and sphere-like shapes, 21] showed that rod-like PDB-entries were located at the comet center, while the more
spherical entries were distributed around the rest of the map (Fig. 5g).

Fig. 5. PDB-maps of 3DP-similarity space color-coded by (a) occupancy, (b) heavy atom count, (c) molecular volume occupancy (mvo), (d) percentage of hydrophobic atoms, (e) percentage of positively charged atoms, (f) percentage of negatively charged atoms. The color-coding is from blue (lowest values) to magenta (highest values). (g) PDB-map color-coded by nPMI values. The rod-like structures are red color; the spherical structures are green color; the disc-like structures are blue color. The maps were computed from 91,223 X-ray structures from the PDB downloaded
in September 2014, considering in each case the biological assembly as defined by
the author

The color-coded similarity maps were combined with the 3DP-similarity search tool
into a web-based application called “PDB-Explorer” for interactive visualization and
3DP-similarity search through the entire PDB (Fig. 6). The website uses the same principles as our previously reported MQN-mapplet, 15]–17] and is based on the open-source project visualizer (http://github.com/NPellet/visualizer) that was already successfully used for another cheminformatic project 50]. The PDB-Explorer consists of a main window to browse through various color-coded
rendering of the 3DP-similarity map. The average PDB molecule in each pixel is shown
in the 3D-viewer of PV, 51] and the “Show Bin” table details the contents of any selected pixel on the map from
which each PDB-entry, shown as ribbon image, can be inspected closer as 3D-model by
opening a secondary JSmol window. The “Locate Molecule” function allows locating any
given PDB-entries on the map and the “Similarity Search” option offers nearest neighbors
of any PDB-entry in the 3DP space within seconds. The application also contains uploading
function to locate and search nearest neighbors of any structure represented as pdb
file. All computations are performed locally by the browser of the user machine. The
color-coded similarity maps and the database for similarity search are updated every
day by adding new entries in the PDB. The detailed PDB-Explorer functions are described
in the HELP page.

Fig. 6. Interface of PDB-Explorer website. Main window: color-coded similarity map of PDB in 3DP-similarity space, with image of the protein
in the pixel marked by the mouse cursor on the map. Upload PDB: place to load a user-defined PDB-file to be shown on the 3DP-similarity map (structure
must contain properly annotated atoms). Average PDB: interactive 3D-view of the molecule corresponding to the most average entry in selected
pixel. Locate Molecule: interface to type PDB entry codes to be shown on the map. Show Bin: full list of all proteins contain in the selected pixel. Similarity Search: window to enter PDB-code and search for nearest neighbours in 3DP-space, and display
of the nearest neighbour list. JSmol: 3D-display of selected entry

Exploring PDB using the PDB-Explorer

The PDB-Explorer allows the rapid analysis and overview of the entire PDB as well
as detailed searches around selected PDB-entries using 3DP similarity as a guiding
principle. Its use is exemplified with three case studies detailed below which further
demonstrate the remarkable ability of 3DP to classify proteins according to their
3D structure.

The case of the conotoxins, a group of 10 to 30 residues neurotoxic peptides containing
multiple intramolecular disulfide bridges and a variety of secondary structures, 52]–54] provides an example of the smallest molecules listed in the PDB. Alpha-conotoxin
PnIA (PDB-entry 1PEN) with 17 residues serves as reference molecule (Fig. 7a). The closest 3DP analog of 1PEN retrieved by 3DP similarity is 1AKG, which belongs
to the similar ?-conotoxin family and is also retrieved as nearest neighbor by BLAST
search with 83 % sequence similarity (Fig. 7b) 55]. By contrast the second analog found by 3DP similarity is a short fibril peptide
complex (Fig. 7c), which has a completely different secondary structure and sequence, but a similar
overall size and shape. The 3rd (Fig. 7d) and 4th analog (Fig. 7e) are both from the enterotoxin family featuring a conotoxin-like shape containing
double disulfide bridges, again without significant sequence similarity to the reference.
Three further conotoxins missed by sequence similarity appear in the 3DP nearest neighbor
search at rank 7 (1NOT, Fig. 7f), rank 9 (1HJE, Fig. 7g) and rank 33 (4TTL, Fig. 7h). In the latter case the bit value profile shows that 4TTL is the only sequence containing
negatively charged residues, while all other cases do not contain any charged residues
(Fig. 7i).

Fig. 7. Analogs of ?-conotoxin 1PEN retrieved by 3DP similarity. a Reference molecule, 1PEN. b–h Structures of selected nearest neighbors and CBD
_3DP
to the reference. i Bit value profiles of conotoxins and analogs

3DP similarity also retrieves shape analogs of molecular assemblies, as exemplified
here with triose phosphate isomerase (TIM), a homodimeric enzyme which contains around
250 amino acids in the monomer 56]. The wild type TIM dimer from yeast (PDB-entry 1YPI) is selected as the reference.
The top 100 neighbors of 1YPI are also protein dimers, with essentially all neighbors
of 1YPI up to CBD
_3DP
?=?800 being TIM enzymes. All TIM structures in PDB (Additional file 1: Supplement 3) in fact occur within a CBD
_3DP
distance of 1200 except 13 TIM enzymes ranked beyond rank 300 (Fig. 8a). The differences in 3DP values are illustrated for the nearest neighbor 4FF7, the
rank 10 analog 8TIM at distance CBD
_3DP
?=?493 representative of the bulk of TIM structures, and 4GNJ found at rank 312 and
CBD
_3DP
?=?1181 representative of the more distant group around CBD
_3DP
?=?1100 (Fig. 8b). The nearest neighbor of 1YPI, 4FF7, is also a yeast TIM with 99 % sequence similarity
and nearly identical structure. PDB-entry 8TIM at rank 10 is a TIM dimer from a different
organism (gallus gallus) with only 52 % of sequence similarity. In both cases the
shape and fold differences to the reference are quite small, and the larger distance
of 8TIM stems from differences in positively charged atoms that are not directly visible
in the protein shape (Fig. 8b/c). The difference in the number and position of charged atoms also explains the further
distance from the reference of 4GNJ, a TIM dimer from leishmania siamensis.

Fig. 8. Similarity search result for triose phosphate isomerase (TIM) dimer, 1YPI. a Frequency histogram of CBD
_3DP
between all of the structures in PDB and 1YPI (blue), and all of the TIM dimers and 1YPI (red). b Deviation of bit values of 4FF7, 8TIM and 4GNJ to the reference 1YPI. c Comparison of the structures of reference 1YPI and rank2, rank10 and rank 321 analogs
retrieved from similarity search. The positively charged atoms are shown as blue spheres and negatively charged atoms are shown as red spheres for 1YPI and 4GNJ

The PDB-Explorer furthermore provides interesting insight at the level of very large
protein assemblies, as exemplified here for the case of a virus capsid. Starting with
the subviral particle of the bursal disease virus capsid (PDB-entry 2GSY) 57] containing 27,120 residues (Fig. 9a), four analogs are readily identified within the distance range CBD
_3DP
??10,000. The nearest neighbor is 3FBM (Fig. 9b) which is a mutant protein of the query 2GSY, 58] and the second and third closest structures 1WCD and 2DF7 are capsids from the same
bursal disease virus (Fig. 9c, d). The fourth analog (PDB-entry 3IDE) is the protein coat of Infectious Pancreatic
Necrosis Virus (IPNV) 59] which has similar spikes and forms a similar icosahedral capsid organization as the
capsid of infectious bursal disease virus (Fig. 9e) 59]. Interestingly the parvovirus capsid protein 1DNV (Fig. 9f), which is very close in size to the reference 2GSY, only appears much further away
in CBD
_3DP
space because its spherical shape does not feature spikes, which significantly impact
its 3DP fingerprint profile (Fig. 9g).

Fig. 9. Similarity search result for virus capsid, 2GSY. a–e The structures of reference and top 4 analogs retrieved from similarity search. f Parvovirus capsid protein, 1DNV. g Bit values of compounds a-f

3DP space automatically clusters proteins from the same superfamily in tight groups
provided that they are in a similar size range. This property is illustrated here
for the recovery of each family from a benchmark dataset of 150 CATH superfamilies,
each containing between 12 and 1533 PDB entries 7], 8], considering proteins in the majority size range (Additional file 1: Supplement 4). The ROC (receiver operator characteristic) curves for recovering
superfamily members from the PDB-entry closest to all same superfamily members in
3DP-space give very high AUC (area under the curve, all above 90 %) and generally
high EF
_0.1%
values (enrichment factor at 0.1 % database coverage in the range 29–1000, Fig. 10a). Most superfamilies also appear as tight groups on the PDB-map (Fig. 10b). The clustering of protein superfamilies in 3DP-space reflects the fact that the
definition of these families considers similarities in folds in addition to function.

Fig. 10. Classification of CATH superfamilies in 3DP-space and comparison of 3DP with structural
alignment tools Fr-TMalign, SPalign and MATT. a AUC and EF
_0.1%
values for ROC curves recovering 150 CATH superfamilies from the entire PDB by 3DP-similarity.
b Locations of 6 CATH superfamilies (1.10.246.10, 2.30.30.40, 2.60.120.20, 3.10.320.10,
3.40.50.200 and 3.40.309.10) on the PDB-map. c Correlation between alignment scores (Fr-TMalign, SPalign, MATT) and CBD
_3DP
obtained from 10 domain movement frames of the glutamine binding protein (Fig. 3). Red square: Fr-TMalign; Blue square: SPalign; Green square: MATT. d Correlation between alignment scores (Fr-TMalign, SPalign, MATT) and CBD
_3DP
for 50 CDK2 and 50 decoys (1225 CDK2 pairs and 2500 CDK2-decoy cross-pairs). Red square: Fr-TMalign; Blue square: SPalign; Green square: MATT; Orange circle: CDK2 proteins. e Example of shape analogs of the CDK2 protein 3PY1 identified by 3DP-similarity or
3D-alignment tools. 1A8E is detected as shape analog of 3PY1 by 3DP similarity, but
not by any of the three alignment tools. 4W9X is similar to 3PY1 in each of the three
alignment tools, but is not a close analog by 3DP similarity

Comparing 3DP with protein structure alignment tools

The performance of 3DP was compared with three protein structure alignment tools,
Fr-TMalign 60], 61], SPalign 62] and MATT 63]. Fr-TMalign is applied to pairwise structure alignment based on fragment similarity,
while SPalign is designed for detecting proteins with similar fold and similar function
of DNA or RNA binding. MATT (Multiple Alignment with Translations and Twists) is a
program to align multiple protein structures allowing certain flexibility between
fragments. These alignment methods are computationally intensive and therefore only
applicable to a limited number of comparisons. They are size independent and focus
on backbone alignment resulting in a focus on secondary structures. On the other hand
3DP is size dependent and considers all protein atoms indiscriminately, resulting
in a sensitivity to the overall shape rather than to secondary structures. Remarkably,
3DP allows an essentially instantaneous comparison with the entire PDB when using
the PDB-Explorer website.

In a first comparative study, all pairwise alignment scores were computed for the
ten domain movement frames for glutamine binding protein and compared with CBD
_3DP
. The data showed that CBD
_3DP
, which performs comparably to overall structure RMSD as dicussed above (Fig. 3), had similar trend but higher sensitivity to conformer differences than Fr-TMalign
or SPalign. MATT was highly sensitive to small conformational changes and classified
all non-identical conformer pairs as low scoring (Fig. 10c).

A further comparison of 3DP with structure alignment tools was carried out for 50
homologous CDK2 proteins (Fig. 4) and 50 non-CDK2 decoy proteins. The 100 structures were in similar size range from
2100–2600 heavy atoms, and decoys consisted of non-homologous proteins with pairwise
sequence identity lower than 30 %. Alignment scores and 3DP distances were computed
for the 1225 CDK2 pairs and the 2500 CDK2-decoy pairs (Fig. 10d). 3DP made a relatively clear cut between CDK2 pairs and CDK2-decoy cross-pairs at
CBD
_3DP
?=?750, with all CDK2 pairs found within the range CBD
_3DP
??1000. However the 3DP comparison recognized some decoys such as 1A8E (serum transferrin)
as CDK2-like due to an overall similar shape, although this decoy had a clearly different
fold as correctly analyzed by each of the three alignment tools (Fig. 10e, left). The three alignment methods correctly assigned a high score to all CDK2 pairs,
but also returned a high core with part of the CDK2-decoys which were not recognized
as CDK2 like by 3DP. For example decoy 4W9X, which is a non-CDK2 kinase, clearly showed
a partly homologous fold to CDK2 leading to a high alignment score, but also showed
substantial differences with the presence of a central helix and an extended terminal
absent from CDK2 which resulted in a relatively high 3DP-distance to CDK2s such as
3PY1 (Fig. 10e, right).