This article has Open Peer Review reports available.
ProtNN: fast and accurate protein 3D-structure classification in structural and topological space
- Wajdi Dhifli^{1} and
- Abdoulaye Baniré Diallo^{1}Email authorView ORCID ID profile
Received: 23 March 2016
Accepted: 22 August 2016
Published: 23 September 2016
Abstract
Background
Studying the functions and structures of proteins is important for understanding the molecular mechanisms of life. The number of publicly available protein structures has increasingly become extremely large. Still, the classification of a protein structure remains a difficult, costly, and time consuming task. The difficulties are often due to the essential role of spatial and topological structures in the classification of protein structures.
Results
We propose ProtNN, a novel classification approach for protein 3D-structures. Given an unannotated query protein structure and a set of annotated proteins, ProtNN assigns to the query protein the class with the highest number of votes across the k nearest neighbor reference proteins, where k is a user-defined parameter. The search of the nearest neighbor annotated structures is based on a protein-graph representation model and pairwise similarities between vector embedding of the query and the reference protein structures in structural and topological spaces.
Conclusions
We demonstrate through an extensive experimental evaluation that ProtNN is able to accurately classify several datasets in an extremely fast runtime compared to state-of-the-art approaches. We further show that ProtNN is able to scale up to a whole PDB dataset in a single-process mode with no parallelization, with a gain of thousands order of magnitude in runtime compared to state-of-the-art approaches.
Keywords
Introduction
Proteins are ubiquitous in the living cells. They play key roles in the functional and evolutionary machinery of species. Studying protein functions and structures is paramount for understanding the molecular mechanisms of life. High-throughput technologies are yielding millions of protein-encoding sequences that currently lack any functional characterization [1–3]. The number of proteins in the Protein Data Bank (PDB) [4] has more than tripled over the last decade. Alternative databases such as SCOP [5] and CATH [6] are undergoing the same trend. However, the classification of protein structures remains a difficult, costly, and time consuming task. Manual protein classification methods are no longer able to follow the rapid increase of data. Accurate computational and machine learning tools present an efficient alternative that could offer considerable boosting to meet the increasing load of data.
Proteins are composed of complex three-dimensional folding of long chains of amino acids. This spatial structure is an essential component in protein functionality and is thus subject to evolutionary pressures to optimize the inter-residue contacts that support it [7]. Existing computational methods for protein classification try to simulate biological phenomena that define the structure and function of a protein. The most conventional technique is to perform a similarity search between an unknown protein and a reference database of annotated proteins. The query protein is assigned with the same class of the most similar (based on the sequence or the structure) reference protein. There exists several classification methods based on the protein sequence (e.g. Blast [8], ProtFun [9], SVM-Prot [10, 11] …); or on the protein structure (e.g. Combinatorial Extension [12], Sheba [13], FatCat [14], Fragbag [15], …). These methods rely on the assumption that proteins sharing the most common sites are more likely to belong to the same class. This classification strategy is based on the hypothesis that structurally similar proteins could share a common ancestor [16]. Another popular approach for protein functional classification is to look for relevant subsequences or substructures (also so-called motifs) among known proteins, then use them as features to classify unknown proteins. Such motifs could be discriminative [17], representative [18], cohesive [7], etc. Each of the mentioned protein classification approaches suffers different drawbacks. Sequence (and subsequences)-based classification do not incorporate spatial information of amino acids that are not contiguous in the primary structure but interconnected in 3D space. This makes them less efficient in the classification of structurally similar proteins with low sequence similarity (remote homologues). Both structure and substructure-based classification techniques do incorporate spatial information which makes them more efficient than sequence-based classification. However, such consideration makes these methods subject to the “no free lunch” principle [19], where the gain in accuracy comes with an offset of computational cost. Hence, it is essential to find an efficient way to incorporate 3D-structure information with low computational complexity.
In this paper, we present PROTNN, a novel approach for protein 3D-structure classification. PROTNN incorporates protein 3D-structure information via the combination of a rich set of structural and topological descriptors. This guarantees an informative multi-view representation of the structure that considers spatial information through different dimensions. Such a representation transforms the complex protein 3D-structure into an attribute-vector of fixed size which guarantees the computational efficiency. For classification, PROTNN assigns to a query protein the class having the highest number of votes across the set of its k most similar reference proteins, where k is a user-defined parameter. Experimental evaluation shows that PROTNN is able to accurately classify different benchmark datasets with a gain of up to 47x of computational cost compared to gold standard approaches from the literature such as Combinatorial Extension [12] and FatCat [14]. We further show that PROTNN is able to scale up to a PDB-wide dataset in a single-process mode with no parallelization, where it outperformed state-of-the-art approaches with thousands order of magnitude in runtime on classifying a 3D-structure against the entire PDB.
Methods
Graph representation of protein 3D-structures
- -
Covalent bonds between atoms sharing pairs of valence electrons,
- -
Ionic bonds of electrostatic attractions between oppositely charged components,
- -
Hydrogen bonds between two partially negatively charged atoms sharing a partially positively charged hydrogen,
- -
Hydrophobic interactions where hydrophobic amino acids in the protein closely associate their side chains together,
- -
Van der Waals forces which represent transient and weak electrical attraction of one atom for another when electrons are fluctuating.
Structural and topological embedding of protein graphs
Graph embedding
Graph-based representations are broadly used in multiple application fields including bioinformatics [16, 18, 21]. However, they suffer major drawbacks with regards to processing tools and runtime. Graph embedding into vector spaces is a very popular technique to overcome both drawbacks [21]. It aims at providing a feature vector representation for every graph, allowing to bridge the gap between the representational power of graphs, the rich set of algorithms that are available for feature-vector representations, and the need for rapid processing algorithms to handle the massively available biological data. In PROTNN, each protein 3D-structure is represented by a graph according to Eq. 1. Then, each graph is embedded into a vector of structural and topological features under the assumption that structurally similar graphs should give similar structural and topological feature-vectors. In such manner, PROTNN guarantees accuracy and computational efficiency.
Structural and topological attributes
- A1-
Number of nodes: The total number of nodes of the graph, |V|.
- A2-
Number of edges: The total number of edges of the graph, |E|.
- A3-
Average degree: The degree of a node u, denoted deg(u), is the number of its adjacent nodes. The average degree of a graph G is the average of all deg(u), ∀u∈G. Formally: \( deg(G) = \frac {1}{\mid V\mid } \sum ^{\mid V\mid }_{i=1} deg(u_{i})\).
- A4-
Density: The density of a graph G=(V,E) measures how many edges are in E compared to the number of maximum possible edges between the nodes in V. Formally: \( den(G) = \frac {2 \mid E\mid }{(\mid V\mid \ast (\mid V\mid -1))}\).
- A5-
Average clustering coefficient: The clustering coefficient of a node u, denoted c(u), measures how complete the neighborhood of u is, \(c(u)= \frac {2 e_{u}}{k_{u} (k_{u} - 1)}\) where k_{ u } is the number of neighbors of u and e_{ u } is the number of connected pairs of neighbors. The average clustering coefficient of a graph G, is given as the average value over all of its nodes. Formally: \(C(G)= \frac {1}{\mid V\mid } \sum _{i=1}^{\mid V\mid } c(u_{i})\).
- A6-
Average effective eccentricity: For a node u, the effective eccentricity represents the maximum length of the shortest paths between u and every other node v in G, e(u)=max{d(u,v):v∈V,u≠v}, where d(u,v) is the length of the shortest path from u to v. The average effective eccentricity is defined as \(Ae(G)= \frac {1}{\mid V\mid }\sum _{i=1}^{\mid V\mid } e(u_{i})\).
- A7-
Effective diameter: It represents the maximum value of effective eccentricity over all nodes in the graph G, i.e., diam(G)=max{e(u)∣u∈V} where e(u) represents the effective eccentricity of u as defined above.
- A8-
Effective radius: It represents the minimum value of effective eccentricity over all nodes of G, rad(G)=min{e(u)∣u∈V}.
- A9-
Closeness centrality: The closeness centrality measures how fast information spreads from a given node to other reachable nodes in the graph. For a node u, it represents the reciprocal of the average shortest path length between u and every other reachable node in the graph G, \(C_{c}(u) = \frac {{\mid V\mid }-1}{\sum _{v\in \lbrace V\setminus u\rbrace } d(u,v)}\) where d(u,v) is the length of the shortest path between the nodes u and v. For G, we consider the average value of closeness centrality of all its nodes, \(C_{c}(G) = \frac {1}{\mid V\mid } \sum _{i=1}^{\mid V\mid } C_{c}(u_{i})\).
- A10-
Percentage of central nodes: It is the ratio of the number of central nodes from the number of nodes in the graph. A node u is central if the value of its eccentricity is equal to the effective radius of the graph, e(u)=rad(G).
- A11-
Percentage of end points: It represents the ratio of the number of nodes with deg(u)=1 from the total number of nodes of G.
- A12-
Number of distinct eigenvalues: A scalar \(\leftthreetimes \) is called an eigenvalues of a squared matrix M if there exists an eigenvectorx such that \(Mx = \leftthreetimes x\). The adjacency matrix A of G has a set of eigenvalues. We count the number of distinct eigenvalues of A.
- A13-
Spectral radius: Let \(\leftthreetimes _{1}, \leftthreetimes _{2},..., \leftthreetimes _{m}\) be the set of eigenvalues of the adjacency matrix A of G. The spectral radius of G, denoted ρ(G), represents the largest magnitude eigenvalue, i.e., \(\rho (G) = max(\mid \leftthreetimes _{i}\mid)\) where i∈{1,..,m}.
- A14-
Second largest eigenvalue: The value of the second largest eigenvalue.
- A15-
Energy: The energy of an adjacency matrix A of a graph G is defined as the squared sum of the eigenvalues of A. Formally: \(E(G) = \sum ^{m}_{i=1}{\leftthreetimes _{i}^{2}}\).
- A16-
Neighborhood impurity: For a node u having a label L(u) and a neighborhood N(u), it is defined as ImpNeigh(u)=∣L(v):v∈N(u),L(u)≠L(v)∣. The neighborhood impurity of G is the average ImpNeigh over all nodes.
- A17-
Link impurity: An edge {u,v} is considered to be impure if L(u)≠L(v). The link impurity of a graph G with |E| edges is defined as: \(\frac {\mid \{u,v\}\in E: L(u)\neq L(v)\mid }{\mid E\mid }\).
- A18-
Label entropy: It measures the uncertainty of labels. For a graph G of k labels, it is defined as \(E(G)= -\sum _{i=1}^{k} p(l_{i})\textit {log }p(l_{i})\), where l_{ i } is the i^{ t h } label.
Complexity
The computational complexity of the structural and topological attributes differ from one attribute to another. Some of the attributes are very easy to compute like the number of nodes and the number of edges which are respectively computed in \(\mathcal {O}(n)\) and \(\mathcal {O}(e)\) where n is the number of nodes and e is that of edges in the graph. The density of the graph can directly computed from the number of nodes and that of edges. The average degree can be computed in \(\mathcal {O}(n+e)\). Some other attributes are more complex to compute and thus require higher computational runtime. The average clustering coefficient can be computed in the \(\mathcal {O}(n^{2})\). The average effective eccentricity, the effective diameter, the effective radius, the closeness centrality, and the percentage of end points are all computed based on the set of shortest paths between all pairs of nodes of the graph. For each node, the shortest path can be computed in \(\mathcal {O}(n+e)\) and thus in \(\mathcal {O}(n^{2}+ne)\) for all nodes of the graph. The percentage of end points can directly be computed in \(\mathcal {O}(n+e)\). The number of distinct eigenvalues, the spectral radius, the second largest eigenvalue, and the energy are all computed based on the eigenvalue decomposition of the graph which is upper bounded by \(\mathcal {O}(n^{3})\) in the worst case. However, for sparse graphs it can be computed in less time. The computation of the neighborhood impurity is upper bounded by \(\mathcal {O}(nk)\), where k is the largest node degree in the graph. The link impurity and label entropy can respectively be computed in \(\mathcal {O}(n+e)\) and \(\mathcal {O}(n)\).
PROTNN: nearest neighbor protein functional classification
We propose PROTNN, a protein structure classification approach based on the principal of the k-nearest neighbor algorithm [28]. The general classification pipeline of PROTNN can be described as follows: first a preprocessing is performed on the reference protein database Ω in which a graph model G_{ P } is created for each reference protein P, ∀P∈Ω, according to Eq. 1. A structural and topological description vector V_{ P } is created for each graph model G_{ P }, by computing the corresponding values of each of the structural and topological attributes described in Section “Structural and topological attributes”. The resulting matrix \(M_{\Omega } = \bigcup V_{P}\), ∀P∈Ω, represents the preprocessed reference database that is used for prediction in PROTNN. In order to guarantee an equal participation of all used attributes in the classification, a min-max normalization (\(x_{normalized} = \frac {x - min}{max-min}\), where x is an attribute value, min and max are the minimum and maximum values for the attribute vector) is applied on each attribute of M_{ Ω } independently such that no attribute will dominate in the prediction. It is also worth mentioning that for real world applications M_{ Ω } is computed once, and it can be incrementally updated with other attributes as well as newly added protein 3D-structures with no need to recompute the attributes for the entire set. This guarantees a high flexibility and easy extension of PROTNN in real world application.
The prediction step in PROTNN is described in Algorithm 1. In prediction, a query protein 3D-structure Q with an unknown function, is first transformed into its corresponding graph model G_{ Q }. The structural and topological attributes are computed for G_{ Q } forming its query description vector V_{ Q }. The query protein Q is scanned against the entire reference database Ω, where the distance between V_{ Q } and each of the reference vectors ∀V_{ P }∈M_{ Ω } is computed and stored in Vdist_{ Q }, with respect to a distance measure. The k most similar reference proteins NN\(_{Q}^{k}\) are selected, and the query protein Q is predicted to belong to the class with the highest number of votes across the set of NN\(_{Q}^{k}\) reference proteins, where k is user-defined.
Datasets
Benchmark datasets
Characteristics of the experimental datasets
Dataset | SCOP ID | Family name | Pos. | Neg. | Avg. ∣V∣ | Avg. ∣E∣ | Max. ∣V∣ | Max. ∣E∣ |
---|---|---|---|---|---|---|---|---|
DS1 | 48623 | Vertebrate phospholipase A2 | 29 | 29 | 160 | 628 | 451 | 1812 |
DS2 | 52592 | G-proteins | 33 | 33 | 246 | 971 | 897 | 3544 |
DS3 | 48942 | C1-set domains | 38 | 38 | 238 | 928 | 768 | 2962 |
DS4 | 56437 | C-type lectin domains | 38 | 38 | 185 | 719 | 775 | 3016 |
DS5 | 56251 | Proteasome subunits | 35 | 35 | 231 | 929 | 897 | 3544 |
DS6 | 88854 | Protein kinases, catalyc subunits | 41 | 41 | 275 | 1077 | 775 | 3016 |
Vertebrate phospholipase A2:
Phospholipase A2 are enzymes from the class of hydrolase, which release the fatty acid from the hydroxyl of the carbon 2 of glycerol to give a phosphoglyceride lysophospholipid. They are located in most mammalian tissues.
G-proteins:
G-proteins are also known as guanine nucleotide-binding proteins. These proteins are mainly involved in transmitting chemical signals originating from outside a cell into the inside of it. G-proteins are able to activate a cascade of further signaling events resulting a change in cell functions. They regulate metabolic enzymes, ion channels, transporter, and other parts of the cell machinery, controlling transcription, motility, contractility, and secretion, which in turn regulate diverse systemic functions such as embryonic development, learning and memory, and homeostasis.
C1-set domains:
The C1-set domains are immunoglobulin-like domains, similar in structure and sequence. They resemble the antibody constant domains. They are mostly found in molecules involved in the immune system, in the major histocompatibility complex class I and II complex molecules, and in various T-cell receptors.
C-type lectin domains:
Lectins occur in plants, animals, bacteria and viruses. The C-type (Calcium-dependent) lectins are a family of lectins which share structural homology in their high-affinity carbohydrate-recognition domains. This dataset involves groups of proteins playing diverse functions including cell-cell adhesion, immune response to pathogens and apoptosis.
Proteasome subunits:
Proteasomes are critical protein complexes that primarily function to breakdown unneeded or damaged proteins. They are located in the nucleus and cytoplasm. The proteasome recycles damaged and misfolded proteins as well as degrades short-lived regulatory proteins. As such, it is a critical regulator of many cellular processes, including the cell cycle, DNA repair, signal transduction, and the immune response.
Protein kinases, catalyc subunits:
Protein kinases, catalytic subunit play a role in various cellular processes, including division, proliferation, apoptosis, and differentiation. They are mainly proteins that modify other ones by chemically adding phosphate groups to them. This usually results in a functional change of the target protein by changing enzyme activity, cellular location, or association with other proteins. The catalytic subunits of protein kinases are highly conserved, and several structures have been solved, leading to large screens to develop kinase-specific inhibitors for the treatments of a number of diseases.
The protein data bank
In order to assess the scalability of PROTNN to large scale real-world applications, we evaluate the runtime of our approach on the entire Protein Data Bank (PDB) [4] which contains the list of all known protein 3D-structures. We use 94126 structures representing all the available protein 3D-structures in the PDB by the end of July 2014.
Protocol and settings
Experiments were conducted on a CentOS Linux workstation with an Intel core-i7 CPU at 3.40 GHz, and 16.00 GB of RAM. All the experiments are performed in a single process mode with no parallelization. To transform protein into graph, we used a δ value of 7Å. The evaluation measure is the classification accuracy, and the evaluation technique is Leave-One-Out (LOO) where each dataset is used to create N classification scenarios, where N is the number of proteins in the dataset. In each scenario, a reference protein is used as a query instance and the rest of the dataset is used as reference. The aim is to correctly predict the class of the query protein. The classification accuracy for each dataset is averaged over results of all the N evaluations.
Results and discussion
PROTNN classification results
Results using different distance measures
Overall, varying the distance measure did not significantly affect the classification accuracy of PROTNN on the six datasets. Indeed, the standard deviation of the classification accuracy of PROTNN with each distance measure did not exceed 4 % on the six datasets. A ranking based on the average classification accuracy over the six datasets suggests the following descending order: (1) Manhattan, (2) Braycurtis, (3) std-Euclidean, (4) Canberra, (5) Cosine, (6) Euclidean - Minkowski, (8) Correlation, (9) Chebyshev.
Results using different numbers of nearest neighbors
Analysis of the used attributes
Empirical ranking of the structural and topological attributes
Data | Attributes | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 | A11 | A12 | A13 | A14 | A15 | A16 | A17 | A18 | |
DS1 | 0 | 2 | 1 | 6 | 2 | 1 | 5 | 9 | 10 | 1 | 2 | 8 | 6 | 13 | 16 | 17 | 12 | 17 |
DS2 | 8 | 12 | 15 | 16 | 18 | 4 | 9 | 16 | 23 | 17 | 9 | 21 | 11 | 14 | 25 | 17 | 23 | 9 |
DS3 | 8 | 13 | 2 | 6 | 17 | 10 | 16 | 11 | 11 | 4 | 8 | 18 | 21 | 2 | 21 | 23 | 9 | 18 |
DS4 | 4 | 7 | 21 | 17 | 20 | 6 | 11 | 17 | 16 | 7 | 2 | 14 | 21 | 22 | 20 | 21 | 24 | 17 |
DS5 | 12 | 12 | 8 | 10 | 12 | 5 | 7 | 7 | 17 | 17 | 7 | 23 | 23 | 9 | 20 | 9 | 19 | 18 |
DS6 | 5 | 11 | 9 | 8 | 11 | 6 | 14 | 14 | 13 | 6 | 1 | 17 | 14 | 18 | 24 | 10 | 17 | 13 |
Total | 37 | 57 | 56 | 63 | 80 | 32 | 62 | 74 | 90 | 52 | 29 | 101 | 96 | 78 | 126 | 97 | 104 | 92 |
Score | 0.25 | 0.38 | 0.37 | 0.42 | 0.53 | 0.21 | 0.41 | 0.49 | 0.6 | 0.35 | 0.19 | 0.67 | 0.64 | 0.52 | 0.84 | 0.65 | 0.69 | 0.61 |
Rank | 16 | 13 | 14 | 11 | 8 | 17 | 12 | 10 | 7 | 15 | 18 | 3 | 5 | 9 | 1 | 4 | 2 | 6 |
It is clear that the best subset of attributes is dataset dependent. The five most informative attributes are respectively: A15 (energy), A17 (link impurity), A12 (number of distinct eigenvalues), A16 (neighborhood impurity), and A13 (spectral radius). All spectral attributes showed to be very informative. Indeed, three of them (A15, A12, and A13) ranked in the top-five, and A14 (second largest eigenvalue) ranked in the top-ten (9^{ th }) with a score of 0.52 meaning that for more than half of all the experiments, all spectral attributes were selected in the optimal subset of attributes. Unsurprisingly, A11 (percentage of end points) ranked last with a very low score. This is because proteins are dense molecules and thus very few nodes of their respective graphs will be end points (extremity amino acids in the primary structure with no spatial links). Label attributes also showed to be very informative. Indeed, A17, A16, and A18 (label entropy) ranked respectively 2 ^{ n d }, 4^{ th }, and 6^{ th } with scores of more than 0.61. This is due to the importance of the distribution of the types of amino acids and their interactions. Both have to follow a certain harmony in order to produce a particular structural form (for instance an α-helix or a β-sheet) and to exert a specific function. A9 (closeness centrality), A5 (average clustering coefficient) and A8 (effective radius) ranked in the top-ten with scores of more than 0.5 (A8 scored 0.49 ≃ 0.5). However, all A1 (number of nodes), A2 (number of edges), A3 (average degree), A4 (density), A6 (average effective eccentricity), A7 (effective diameter), and A10 (percentage of central nodes) scored less than 0.5. This is because each one of them is represented by one of the top-ten attributes and thus presents a redundant information. A6 and A9 are both expressed based on all shortest paths of the graph. Both A7 and A8 are expressed based on A6. A10 is expressed based on A8 and thus on A6 too. A1, A2, A3, and A4 are all highly correlated to A5.
Analysis of the used classifier
Accuracy comparison of PROTNN and PROTSVM
Dataset | Classification approach | ||
---|---|---|---|
ProtNN | ProtSVM(linear) | ProtSVM(rbf) | |
DS1 | 0.97 | 0.88 | 0.83 |
DS2 | 0.8 | 0.68 | 0.56 |
DS3 | 0.96 | 0.87 | 0.78 |
DS4 | 0.97 | 0.80 | 0.82 |
DS5 | 0.9 | 0.79 | 0.73 |
DS6 | 0.96 | 0.84 | 0.72 |
Avg. accuracy^{1} | 0.93 ±0.06 | 0.81 ±0.07 | 0.74 ±0.1 |
Comparison with other classification techniques
Accuracy comparison of PROTNN with other classification techniques
Dataset | Classification approach | ||||||||
---|---|---|---|---|---|---|---|---|---|
Blast | Sheba | FatCat | CE | LPGBCMP | D&D | GAIA | ProtNN | ProtNN* | |
DS1 | 0.88 | 0.81 | 1 | 0.45 | 0.88 | 0.93 | 1 | 0.97 | 0.97 |
DS2 | 0.82 | 0.86 | 0.89 | 0.49 | 0.73 | 0.76 | 0.66 | 0.8 | 0.89 |
DS3 | 0.9 | 0.95 | 0.84 | 0.59 | 0.90 | 0.96 | 0.89 | 0.96 | 0.97 |
DS4 | 0.76 | 0.92 | 1 | 0.46 | 0.9 | 0.93 | 0.89 | 0.97 | 0.97 |
DS5 | 0.86 | 0.99 | 0.94 | 0.76 | 0.87 | 0.89 | 0.72 | 0.9 | 0.94 |
DS6 | 0.78 | 1 | 0.94 | 0.81 | 0.91 | 0.95 | 0.87 | 0.96 | 0.96 |
Avg. accuracy^{1} | 0.83 ±0.05 | 0.92 ±0.07 | 0.94 ±0.06 | 0.59 ±0.15 | 0.86 ±0.06 | 0.9 ±0.07 | 0.84 ±0.12 | 0.93 ±0.06 | 0.95 ±0.03 |
Avg. distances^{2} | 0.14 ±0.07 | 0.05 ±0.07 | 0.04 ±0.05 | 0.38 ±0.15 | 0.11 ±0.03 | 0.7 ±0.04 | 0.14 ±0.09 | 0.05 ±0.03 | 0.02 ±0.01 |
Rank | 8 | 4 | 2 | 9 | 6 | 5 | 7 | 3 | 1 |
The alignment-based approaches FatCat and Sheba outperformed CE, Blast, and all the subgraph-based approaches. Indeed, FatCat scored best with three of the first four datasets and Sheba scored best with the two last datasets. Except CE, all the other approaches scored on average better than Blast. This shows that the spatial information constitutes an important asset for protein classification by emphasizing structural properties that the primary sequence alone do not provide. For the subgraph-based approaches, D&D scored better than LPGBCMP and GAIA on all cases except with DS1 where GAIA scored best. On average, PROTNN* ranked first with the smallest distance between its results and the best obtained accuracies with each dataset. This is because PROTNN considers both structural information, and hidden topological properties that are omitted by the other approaches. However, all the top four classification methods, namely PROTNN*, FatCat, PROTNN (without parameter optimization) and Sheba, have shown close and very competitive classification results.
In order to make the classification evaluation more challenging we construct a seventh dataset out of the previous six benchmark datasets. This dataset contains seven classes that represent the six positive classes as well as a seventh class that contains all the negative instances from the six benchmark datasets. The fusion of all the negatives into a single large class makes the dataset imbalanced with 29, 33, 38, 38, 35 and 41 instances respectively for the six first classes and 214 instances for the seventh class. This makes the classification even more challenging. We evaluate the classification performance of our approach (namely PROTNN and PROTNN*) compared to FatCat and CE which are the structural alignment approaches used in the PDB website^{1}. The classification results on this dataset were 0.53, 0.84, 0.88 and 0.95 respectively for CE, PROTNN, PROTNN* and FatCat. Although FatCat showed a better performance than our approach on this dataset, overall all the approaches did not show a large variation compared to the results on the six first datasets. By counting these results with those on Table 4, both PROTNN* and FatCat have equivalent average classification accuracy of respectively 0.94 ±0.03 and 0.94 ±0.07 on all the datasets, while CE and PROTNN respectively scored 0.58 ±0.15 and 0.91 ±0.07.
Scalability and runtime analysis
Scalability to a PDB-wide classification
Runtime results of PROTNN, FatCat and CE on the entire Protein Data Bank
Task | Total runtime^{1} | Runtime^{1}/protein |
---|---|---|
Building graph models | 23h:9m:57s | 0.9s |
Computation of attributes | 5d:8h:12m:29s | 4.9s |
Classification | 2h:55m:15s | 0.1s |
ProtNN (all) | 6d:10h:17m:41s | 5.9s |
FatCat | Forever^{2} | 1d:18h:31m:35s^{3} |
CE | Forever^{2} | 1d:8h:37m:34s^{3} |
Conclusion
In this paper, we proposed PROTNN, a new fast and accurate approach for protein 3D-structure classification. We defined a graph transformation and embedding model that incorporates explicit as well as hidden structural and topological properties of the 3D-structure of proteins. We successfully implemented the proposed model and we experimentally demonstrated that it allows to classify protein 3D-structures efficiently. Empirical results of our experiments showed that considering structural information constitutes a major asset for an accurate classification of proteins. They also showed that the alignment-based classification as well as subgraph-based classification present very competitive approaches. Yet, as the number of pairwise comparisons between proteins grows tremendously with the size of dataset, enormous computational costs would be the results of more detailed models. Here, we highlight that PROTNN could accurately classify multiple benchmark datasets from the literature with very low computational costs. With all large-scale studies, it is an asset that PROTNN scales up to a PDB-wide dataset in a single-process mode with no parallelization, where it outperformed state-of-the-art approaches with thousands order of magnitude in runtime on classifying a 3D-structure against the entire PDB. In future works, we aim to study and integrate more attributes in our model in order to further enhance the accuracy of our classification system.
Endnote
Declarations
Acknowledgements
Not applicable.
Funding
This study is funded by the Natural Science and Engineering Research Council through a discovery grant to ABD.
Availability of data and material
The datasets supporting the conclusions of this article are included within the article (and its Additional file ??).
Authors’ contributions
WD conceived and developed the approach, WD and ABD designed the experiments, WD performed the experiments. WD and ABD interpreted the results and wrote the paper. All authors read and approved the final manuscript.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Ethics approval and consent to participate
Not applicable.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
References
- Brenner SE, Levitt M. Expectations from structural genomics. Protein Sci. 2000; 9:197–200.View ArticlePubMedPubMed CentralGoogle Scholar
- Lee D, Redfern O, Orengo C. Predicting protein function from sequence and structure. Nat Rev Mol Cell Biol. 2007; 8:995–1005.View ArticlePubMedGoogle Scholar
- Molloy K, Van MJ, Barbara D, Shehu A. Exploring representations of protein structure for automated remote homology detection and mapping of protein structure space. BMC Bioinformatics. 2014; 15(8):1–14.Google Scholar
- Berman HM, Westbrook JD, Feng Z, Gilliland G, Bhat TN, Weissig H, Shindyalov IN, Bourne PE. The protein data bank. Nucleic Acids Res. 2000; 28(1):235–42.View ArticlePubMedPubMed CentralGoogle Scholar
- Andreeva A, Howorth D, Chandonia JM, Brenner SE, Hubbard TJP, Chothia C, Murzin AG. Data growth and its impact on the scop database: new developments. Nucleic Acids Res. 2008; 36(1):419–25.Google Scholar
- Sillitoe I, Lewis TE, Cuff AL, Das S, Ashford P, Dawson NL, Furnham N, Laskowski RA, Lee D, Lees JG, Lehtinen S, Studer RA, Thornton JM, Orengo CA. CATH: comprehensive structural and functional annotations for genome sequences. Nucleic Acids Res. 2015; 43(Database-Issue):376–81.View ArticleGoogle Scholar
- Meysman P, Zhou C, Cule B, Goethals B, Laukens K. Mining the entire protein databank for frequent spatially cohesive amino acid patterns. BioData Mining. 2015; 8:4.View ArticlePubMedPubMed CentralGoogle Scholar
- Altschul S, Gish W, Miller W, Myers E, Lipman D. Basic local alignment search tool. J Mol Biol. 1990; 215:403–10.View ArticlePubMedGoogle Scholar
- Jensen LJ, Gupta R, Stærfeldt HH, Brunak S. Prediction of human protein function according to gene ontology categories. Bioinformatics. 2003; 19(5):635–42.View ArticlePubMedGoogle Scholar
- Cai CZ, Han LY, Ji ZL, Chen X, Chen YZ. Svm-prot: web-based support vector machine software for functional classification of a protein from its primary sequence. Nucleic Acids Res. 2003; 31(13):3692–7.View ArticlePubMedPubMed CentralGoogle Scholar
- Jaramillo-Garzón JA, Gallardo-Chacón JJ, Castellanos-Domínguez CG, Perera-Lluna A. Predictability of gene ontology slim-terms from primary structure information in embryophyta plant proteins. BMC Bioinformatics. 2013; 14(1):1–11.View ArticleGoogle Scholar
- Shindyalov IN, Bourne PE. Protein structure alignment by incremental combinatorial extension of the optimum path. Protein Eng. 1998; 11(9):739–47.View ArticlePubMedGoogle Scholar
- Jung J, Lee B. Protein structure alignment using environmental profiles. Protein Eng. 2000; 13:535–43.View ArticlePubMedGoogle Scholar
- Ye Y, Godzik A. Flexible structure alignment by chaining aligned fragment pairs allowing twists. Bioinformatics. 2003; 19:246–55.Google Scholar
- Budowski-Tal I, Nov Y, Kolodny R. Fragbag, an accurate representation of protein structure, retrieves structural neighbors from the entire pdb quickly and accurately. Proc Nat Acad Sci. 2010; 107(8):3481–6.View ArticlePubMedPubMed CentralGoogle Scholar
- Borgwardt KM, Ong CS, Schönauer S, Vishwanathan SVN, Smola AJ, Kriegel H. Protein function prediction via graph kernels. In: Proceedings Thirteenth International Conference on Intelligent Systems for Molecular Biology 2005, Detroit, MI, USA, 25–29 June 2005. p. 47–56.Google Scholar
- Zhu Y, Yu JX, Cheng H, Qin L. Graph classification: a diversified discriminative feature selection approach. In: 21st ACM International Conference on Information and Knowledge Management. New York, NY, USA: ACM: 2012. p. 205–14.Google Scholar
- Dhifli W, Saidi R, Mephu Nguifo E. Smoothing 3D protein structure motifs through graph mining and amino-acids similarities. J Comput Biol. 2014; 21(2):162–72.View ArticlePubMedGoogle Scholar
- Wolpert D, Macready WG. No free lunch theorems for optimization. IEEE Trans Evol Comput. 1997; 1(1):67–82.View ArticleGoogle Scholar
- Huan J, Bandyopadhyay D, Wang W, Snoeyink J, Prins J, Tropsha A. Comparing graph representations of protein structure for mining family-specific residue-based packing motifs. J Comput Biol. 2005; 12(6):657–71.View ArticlePubMedGoogle Scholar
- Gibert J, Valveny E, Bunke H. Graph of words embedding for molecular structure-activity relationship analysis. In: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer: 2010. p. 30–7.Google Scholar
- Watts DJ, Strogatz SH. Collective dynamics of ‘small-world’ networks. Nature. 1998; 393:440–2.View ArticlePubMedGoogle Scholar
- Reka Albert HJ, Barabasi AL. Internet: Diameter of the world-wide web. Nature. 1999; 401:130–1.View ArticleGoogle Scholar
- Luo B, Wilson RC, Hancock ER. Spectral embedding of graphs. Pattern Recognit. 2003; 36(10):2213–30.View ArticleGoogle Scholar
- Leskovec J, Kleinberg J, Faloutsos C. Graphs over time: densification laws, shrinking diameters and possible explanations. In: Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining. New York, NY, USA: ACM: 2005. p. 177–87.Google Scholar
- Li G, Semerci M, Yener B, Zaki MJ. Graph classification via topological and label attributes. In: 9th Workshop on Mining and Learning with Graphs (with SIGKDD). MLG’11. San Diego: ACM: 2011.Google Scholar
- Li G, Semerci M, Yener B, Zaki MJ. Effective graph classification based on topological and label attributes. Stat Anal Data Mining. 2012; 5(4):265–83.View ArticleGoogle Scholar
- Mitchell TM. Machine Learning, 1st ed. New York, NY, USA: McGraw-Hill, Inc; 1997.Google Scholar
- Jin N, Young C, Wang W. Graph classification based on pattern co-occurrence. In: ACM International Conference on Information and Knowledge Management: 2009. p. 573–82.Google Scholar
- Jin N, Young C, Wang W. GAIA: graph classification using evolutionary computation. In: Proceedings of the 2010 ACM SIGMOD International Conference on Management of Data. New York, NY, USA: ACM: 2010. p. 879–90.Google Scholar
- Fei H, Huan J. Boosting with structure information in the functional space: an application to graph classification. In: ACM Knowledge Discovery and Data Mining Conference (KDD): 2010. p. 643–52.Google Scholar
- Sergio J, Rojas G, Blanco-Silva FJ, Christensen EA. Learning SciPy for Numerical and Scientific Computing - Second Edition. Community experience distilled. Birmingham, UK: Packt Publishing; 2015.Google Scholar
- Guyon I, Weston J, Barnhill S, Vapnik V. Gene selection for cancer classification using support vector machines. Mach Learn. 2002; 46(1–3):389–422.View ArticleGoogle Scholar
- Vapnik V, Cortes C. Support-vector networks. Machine Learn. 1995; 20:273–97.Google Scholar
- Yan X, Cheng H, Han J, Yu PS. Mining significant graph patterns by leap search. In: Proceedings of the ACM SIGMOD International Conference on Management of Data. SIGMOD. New York, NY, USA: ACM: 2008. p. 433–44.Google Scholar
- Saigo H, Krämer N, Tsuda K. Partial least squares regression for graph mining. In: ACM Knowledge Discovery and Data Mining Conference (KDD): 2008. p. 578–86.Google Scholar
- Ranu S, Singh AK. Graphsig: A scalable approach to mining significant subgraphs in large graph databases. In: IEEE 25th International Conference on Data Engineering: 2009. p. 844–55.Google Scholar