KCF-S: KEGG Chemical Function and Substructure for improved interpretability and prediction in chemical bioinformatics

Background In order to develop hypothesis on unknown metabolic pathways, biochemists frequently rely on literature that uses a free-text format to describe functional groups or substructures. In computational chemistry or cheminformatics, molecules are typically represented by chemical descriptors, i.e., vectors that summarize information on its various properties. However, it is difficult to interpret these chemical descriptors since they are not directly linked to the terminology of functional groups or substructures that the biochemists use. Methods In this study, we used KEGG Chemical Function (KCF) format to computationally describe biochemical substructures in seven attributes that resemble biochemists' way of dealing with substructures. Results We established KCF-S (KCF-and-Substructures) format as an additional structural information of KCF. Applying KCF-S revealed the specific appearance of substructures from various datasets of molecules that describes the characteristics of the respective datasets. Structure-based clustering of molecules using KCF-S resulted the clusters in which molecular weights and structures were less diverse than those obtained by conventional chemical fingerprints. We further applied KCF-S to find the pairs of molecules that are possibly converted to each other in enzymatic reactions, and KCF-S clearly improved predictive performance than that presented previously. Conclusions KCF-S defines biochemical substructures with keeping interpretability, suggesting the potential to apply more studies on chemical bioinformatics. KCF and KCF-S can be automatically converted from Molfile format, enabling to deal with molecules from any data sources.


Background
By analogy with orphan genes in genomic studies [1], metabolites that are not yet known how they are synthesized or degraded are referred to as "orphan metabolites" [2]. In contrast to the increasing number of the successful genome projects, there still remain many orphan metabolites. For example, it is estimated that plants produce over 200,000 secondary metabolites [3] that are not directly involved in the primary metabolism and whose absence is not normally lethal. Kanaya and colleagues have been collecting 50,897 metabolites, and the chemical structures and metabolite-species relationships are publicly available in KNApSAcK database [4]. Some of them are known to function as toxins defending the organisms against pathogens, parasites and predators [5]. The physiological roles of many such metabolites are still unknown; however, some of them are important sources of drugs and industrial materials.
Many studies have been conducted for the experimental identification of the biosynthetic pathways for such orphan metabolites. In many cases when the chemical structure of the final products are apparent, the structures of intermediates and the chemical transformations (enzyme reactions) are hypothesized by the biochemists' expert knowledge based on organic chemistry and biochemistry, and the hypothesis are verified by the experiments such as liquid chromatography / mass spectrometry (LC/MS) and nuclear magnetic resonance (NMR). In order to develop these hypothesis, biochemists frequently rely on literature that uses a free-text format to describe functional groups or substructures. Thus, a direct link between the names and (sub)structures of compounds and the functional groups contained within them is important.
However, the (sub)structures of metabolites in these methods were represented computationally, and it is sometimes difficult to interpret such substructures because they are not designed as similar with the substructures that biochemists usually deal with.
In computational chemistry or cheminformatics, molecules are typically represented by chemical descriptors, i.e., vectors that summarize information on its various properties. One group of such descriptors is called chemical fingerprints, which are bit strings that encode the presence or absence of substructures and various physicochemical properties in a molecule into binary variables. Many fingerprints have been designed for the rapid search of molecules, especially for pharmaceutical purposes, from a large amount of molecules in databases. Representative fingerprints include MACCS fingerprint and PubChem fingerprint, and they can be calculated by many freewares such as Chemistry Development Kit [16]. These fingerprints can be used as an input of various machine learning tasks that include similarity search, classification and regression.
These fingerprints only represent presence or absence of substructures, so the numbers of the substructures are not taken into account. This means that, even if a substrate contains two carboxyl groups and one of them turned into an amide group, these fingerprints only detects the generation of the amide group but do not detect the elimination of a carboxyl group. Moreover, they can not distinguish many functional groups (such as aldehyde R-(C=O)-H and carboxylate R-(C=O)-OH), which are obviously different from the viewpoint of organic reactions because of the difference in reactivities. Therefore, discriminating these two types of carbon when comparing molecules is reasonable. Therefore, a more suitable data representation would be needed for improving the prediction accuracy and interpretability for the de novo metabolic pathway reconstruction.
In this study, we designed KCF-S (KEGG Chemical Function and Substructures), a new chemical data format describing the numbers of different levels of functional groups and substructures that are related to chemical structure conversion in enzyme reactions. This is an extension of the KCF (KEGG Chemical Function) format that we published in 2003 [17]. KCF takes into account physicochemical environmental properties of atoms by assigning well-detailed vertex labels, named as KEGG Atom Types, which distinguish important functional groups such as carboxylate and aldehyde. In KCF-S, substructures are computationally defined using seven attributes: atom, bond, triplet, vicinity, ring, skeleton, and inorganic. These definitions are designed so that many of them can be explained by the words in organic chemistry or biochemistry.
The proposed KCF-S can be used for many applications. As the first application, we used KCF-S for the structurebased clustering of molecules in a large scale database. As the second application, we used KCF-S for the de novo metabolic pathway reconstruction for in the "reaction-filling framework", and showed clearly improved predictive performance compared with the previous method. KCF-S has more potential to apply many other purposes, such as pharmacogenomic analysis and enzyme informatics. pectinolide A, a secondary metabolite taken from plant Hyptis pectinata).

KEGG Chemical Function (KCF) format
KEGG Chemical Function (KCF) format, one of the chemical structure file format, has been defined and published in Hattori et al., 2003 [17], where molecules (chemical compounds) are represented as graphs consisting of atoms as vertices and bonds as edges ( Figure 1). The vertices (atoms) of KCF are labeled by the 68 KEGG Atom types (Table 1), describing the detailed information of atomic properties such as functional groups. The the three-letter labels of the KEGG atoms, such as "C1a" meaning a methyl carbon, represent the hierarchical classification of atom environments. In this study, up to the first, the second, and the third letters of the labels are referred to as the "atom species", the "atom classes", and the "KEGG atoms", respectively. Any organic molecule structure can be converted into KCF, as long as it is described in the Molfile format.

Reactant pairs and compound pairs
A reactant pair is part of a reaction equation, representing a set of substrate and product with conserved chemical moiety [19]. KEGG RPAIR database defines 14,105 reactant pairs as of June 2013. In this study, we used the reactant pairs with "main" types, representing the main flow of atoms, as the positive examples of the de novo metabolic pathway reconstruction.
The possible combinations of compound pairs, other than the ones defined as reactant pairs, are used as negative examples. 6,922 compounds were involved in known reactions, therefore, distinguishing the two distinct directions, i.e., forward and backward, the number of all the compound pairs was 47,907,162.

Conventional chemical fingerprints
We used conventional chemical fingerprints in order to compare the KCF-S descriptors (explained in the Method section) for the interpretability of characterising molecule datasets and for the predictive ability of de novo pathway reconstruction. Chemical fingerprints encode presence or absence (1 or 0) of chemical substructures in molecules, resulting in a high dimensional binary vector. We used the Chemistry Development Kit (CDK) version 1.4.9 [16] to calculate well-known fingerprints, MACCS fingerprint and PubChem fingerprint. Their dimensions are 164, and 879, respectively.

Methods
In this section, we present a novel integer vector representation of chemical compound named "KCF-S descriptor", each element of which corresponds to the number of a substructure included in a chemical compound. We define such substructures on biochemist's notion of substructures of a chemical compound. We also make a brief review of methods for compound clustering and metabolic pathway reconstruction to show the applicability of the KCF-S descriptor in the Results and Discussion section.
Proposed definition of biochemical substructures in KCF-S Every biochemical substructure was computationally represented as a graph object, with non-hydrogen atoms and bonds described as nodes and edges, respectively, as an extension of the method in Kotera et al [2]. They were computationally defined using seven attributes: ATOM, BOND, TRIPLET, VICINITY, RING, SKELE-TON, and INORGANIC. In this study, each substructure was given a label (string of characters) using KEGG Atom Types so that the substructures can be distinguished to each other and be interpreted by the words in organic chemistry or biochemistry. Figure 2 shows example substructures obtained from NADH. In this figure, the graph objects in gray areas represents examples of substructures defined in this study. For example, around the center of Figure 2, there is a substructure labeled as "C1b(O2b)-C1y(O2x)-C1y (O1a)-C1y(O1a)-C1y(N1y+O2x)", which is one of the SKELETON entries extracted from a molecule NADH. This SKELETON entry represents a ribose residue in this molecule. In other words, a ribose residue is an instance of a substructure "C1b(O2b)-C1y(O2x)-C1y (O1a)-C1y(O1a)-C1y(N1y+O2x)", which is a subclass of SKELETON. These "instance_of" and "subclass_of" relationships are described by gray and black arrows in Figure 2, respectively. Note that an atom (or a node) can belong to more than one substructure entries. For example, one of the furanose forms of ribose residues in NADH contains a furan ring (five-membered ring consisting of four carbon and one oxygen atoms) that is a subclass of RING. Similarly, sugar residues (e.g., ribose residue) contain many secondary hydroxyl groups that are represented as a subclass of BOND. In other words, a furanose form of ribose residue has a furan ring, and a sugar residue has secondary hydroxyl groups. This "has_part" relationships are described by dotted arrows in Figure 2. The definitions of the seven attributes of substructures are explained below.
The ATOM attribute in KCF-S An ATOM entry represents KEGG Atom Type (Table 1). In Figure 2, circles represent ATOM entries, corresponding to the nodes that form molecular graphs. For example, "C1y" in Figure 2 is one of such nodes. According to the definition of the KEGG Atom Types, the ATOM entries were classified hierarchically (described by black solid arrows). A KEGG Atom Type (e.g., "C1y") is a subclass of the atom classes represented by the first two letters (termed as KEGG Atom Classes, e.g., "C1"). A KEGG Atom Class (e.g., "C1") is a subclass of the element (e.g. carbon atom), which is a subclass of ATOM entries. In KCF-S, the variable k represents the level of the ATOM attributes: k1, k2 and k3 mean the atom species (or elements), atom classes and atom types, respectively.

The BOND attribute in KCF-S
A BOND entry is defined as a pair of ATOM entries that form a chemical bond in a molecule, corresponding to many named bonds in organic chemistry and biochemistry (e.g., C5a-S2a for carboxylic thioester bond). In Figure 2, the substructure labeled as "C1y-O1a" is shown as an example of a BOND entry, which represents a secondary hydroxyl group on a cyclic structure. In the string that identifies a BOND entry, two ATOM entries were sorted in the alphabetical order, and were connected with a hyphen. This BOND entry was classified according to the hierarchy defined for the ATOM entries; i.e., "C1y-O1a" bond is a subclass of "C1-O1" bond, "C1-O1" bond is a subclass of "C-O" bond, and "C-O" bond is a subclass of a BOND (described by black arrows). Also, a BOND entry has two ATOM entries, and a BOND is part of many other entries (as described by dotted arrows).

The TRIPLET attribute in KCF-S
A TRIPLET entry is defined as a pair of BOND entries that share a central ATOM, which consistis of three ATOMs that are connected sequentially. For example, the triplet "C6a-C1c-N1a", "C6a-C1c-O1a" and "C6a-C5a-O5a" represent the common substructures in alpha-amino acids,    [17], and were used to label the nodes in molecular graphs. KEGG atom label consists of three letters, such as "C1a" meaning a methyl carbon. The first and second letters represent atom species and orbital environments, respectively. The third letter describes the surroundings of a given atom in terms of its bonded neighbors.

Carbon atoms
alpha-hydroxy acids and alpha-oxo acids, respectively. In the string that identifies a TRIPLET entry, the BOND entries were sorted in the alphabetical order of the ATOM entries, three ATOM entries were connected with hyphens so that the central ATOM was placed in the middile. In Figure 2, the triplet "C1y-C1y-O1a" is shown as an example of TRIPLET entries, which represents a larger substructure that contains a secondary hydroxyl group on a cyclic structure. Similary with the BOND entries, the TRIPLET entries were classified according to the hierarchy defined for the ATOM entries. A TRIPLET entry has two BOND entries and three ATOM entries, and TRIPLET is part of many other entries.

The VICINITY attribute in KCF-S
A VICINITY entry is defined as a central atom and the atoms attached to it. Many functional groups correspond to VICINITY entries, e.g., carbamate "C7a(O6a+O7a +N1b)", N-acetyl "C5a(C1a+N1b+O5a)", and phosphate "P1b(O1c+O1c+O1c+O2b)". In Figure 2, the vicinity "C1y(C1y+C1y+O1a)" is shown as an example, which represents an even larger substructure that contains a secondary hydroxyl group on a cyclic structure. In the string that identifies a VICINITY entry, the central ATOM was placed in the head, and the attaching ATOM entries were sorted in the alphabetical order, connected with plus signs, and placed in parentheses. A VICINITY entry consists of at least three BOND entries and at least four ATOM entries.

The RING attribute in KCF-S
A RING entry is defined as a cyclic substructure, containing 3-, 4-, 5-and 6-membered, or larger (up to 12-membered), rings. The strings to identify RING entries were generated in the following way: (i) an atom in the ring was selected as a starter to retrieve ring structures using depth-first search algorithm, (ii) KEGG Atom Types consisting of the ring were connected by hyphens to generate a backbone string, (iii) if there were branch atoms attached to the ring, they were added to the backbone string using parentheses, (iv) the processes (i)-(iii) were repeated for all starting atoms, clockwise and anti-clockwise directions, (v) the obtained strings were sorted in alphabetical order, and (vi) the first string was selected to represent the RING entry.

The SKELETON attribute in KCF-S
A SKELETON entry is defined as a carbon skeleton/ backbone, such as alkyl and aryl groups. The strings to identify SKELETON entries were generated in the following way: (i) a carbon atom in the terminus of the carbon skeleton was selected as a starter to retrieve all carbon chains in the skeleton, (ii) KEGG Atom Types consisting of the chains were connected by hyphens, (iii) if other elements (N, O, S, etc) attach to the chain, they were added to the chain using parentheses, (iv) the longest chain was selected as a seed, and the shorter chains were bundled to generate the string representing the carbon skeleton, (v) the processes (i)-(iv) were repeated for all starting atoms, (vi) the obtained strings were sorted in alphabetical order, and (vii) the first string was selected to represent the SKE-LETON entry.
Some common examples are the N-acetyl group "C1a-

The INORGANIC attribute in KCF-S
An INORGANIC entry is defined as a connected atom groups that consists of elements that are not carbon atoms. The strings to identify INORGANIC entries were generated in the following way: (i) an atom in the terminus of the inorganic component was selected as a starter to retrieve all chains in the inorganic component, (ii) KEGG Atom Types consisting of the chains were connected by hyphens, (iii) if carbon atoms attach to the chain, they were added to the chain using parentheses, (iv) the longest chain was selected as a seed, and the shorter chains were bundled to generate the string representing the inorganic component, (v) the processes (i)-(iv) were repeated for all starting atoms, (vi) the obtained strings were sorted in alphabetical order, and (vii) the first string was selected to represent the INORGANIC entry.

Compound clustering based on the KCF-S descriptors
We perform a hierarchical agglomerative clustering of compounds described by the KCF-S descriptors using a variant of quasi-clique-based clustering (QCC), which was originally developed for clustering of large amount of genes to detect orthologs in KEGG OC [20].
In the original QCC algorithm, each object is represented by a neighbor profile in which each element corresponds to a similarity score with the other objects, and the object-object similarity is evaluated by the inner product of the neighbor profiles. The key parameter of the QCC algorithm is the clique ratio that decides whether or not two clusters should be connected. For example, when the clique ratio is set to 1.0, two clusters should be connected if the similarity scores of all object pairs in the clusters are above the similarity threshold. In this case, this QCC method is equivalent to complete-linkage clustering. When the clique ratio is below 1.0, e.g., 0.7, two clusters should be connected if 70% of the object pairs in the clusters are above the similarity threshold.
In this study, instead of the inner product of the neighbor profiles in the original QCC, we used the weighted Jaccard coefficient of the KCF-S descriptors. We also make a comparison of the clustering result between the KCF-S descriptors and conventional fingerprints (e.g., PubChem/MACCS fingerprints).

Metabolic pathway reconstruction based on the KCF-S descriptors
Our previous study for the de novo metabolic pathway reconstruction [15] predicts a series of reactions of each pair of chemical compounds on a metabolic pathway by solving the following supervised classification problem. Given a collection of n(n−1) compound-compound pairs (C i , C j )(i = 1 , . . . , n, j = 1, . . . , n, i ≠ j), we estimate a linear function f(C, C') that would predict whether or not a chemical compound C is converted to another compound C' in an enzymatic reaction.
Linear models use feature vectors for predictions. Our feature vectors are a generalization of the previous ones [15] from binary vectors to integer vectors. Our KCF-S descriptor represents compounds C and C' as D-dimen- C ) are referred to as common features and differential features, respectively. Using the above operations, we represent any compound-compound pair by two types of feature vectors as follows: The both feature vectors are also generalizations of the previously defined feature vectors [15]. Φ(C, C') and (C, C ) are referred to as "diff-common feature vector" and "diff-only feature vector", respectively. Note that the diff-common and diff-only feature vectors share the differential features, but the diff-common feature vector additionally has the common features. Thus, the both feature vectors are designed to capture substructure changes around the reaction center in the conversion of a chemical compound to another compound. In addition, the diffcommon feature vector is designed to capture core substructures kept in the conversion of a chemical compound to another compound.
Using the feature vectors Φ(C, C') and (C, C ) for compounds C and C', a linear model estimates a linear function f(C, C') = w T Φ(C, C'), where w is a real value vector (weight vector). The reaction between C and C' is predicted by thresholding the value of f(C, C'). The weight vector w is estimated such that it can predict enzymatic-reaction likeness of compound-compound pairs. To estimate the weight vector w, we apply linear support vector machine (SVM) with L 1 -regularization for its high interpretability and high prediction accuracies comparable to SVM with L 2 -regularization. To solve the optimization problem in SVM, we use an efficient optimization algorithm named LIBLINEAR [21], which is available from http://www.csie.ntu.edu.tw/~cjlin/liblinear/. KCF format of molecules have been provided in KEGG as a fundamental chemical structure information since 2003 [17]. The aim of developing another format named KCF-S format is not to replace KCF into KCF-S, but to provide additional information of larger substructures for the correspondence with the names in organic chemistry and biochemistry, and for the application for many analyses such as structure-based clustering of molecules and metabolic pathway reconstruction study. Note that both of KCF and KCF-S formats can be automatically converted from Molfile format. This means that, even though we only used molecules in KEGG and KNAp-SAcK databases in this study, KCF and KCF-S can deal with many other molecules in PubChem [22], ChEBI [23], DrugBank [24], NCI [25] and other databases.

Appearances of substructures in the KEGG and KNApSAcK databases
The three databases collect molecules for different purposes, i.e., KEGG COMPOUND for fundamental biological systems, KEGG DRUG for pharmaceuticals, and KNApSAcK for secondary metabolites. Therefore, even though they share some molecules, their collection of molecules are different from each other. The appearance of substructures made it possible to grasp more detailed characteristics of their databases. Table 2 shows examples of named substructures and appearance in KEGG COMPOUND, KEGG DRUG and KNApSAcK databases. These three databases have been collecting molecules in different purposes, so the appearance of the substructures is naturally different, which is clearly shown in this study. For example, BOND entries include many named bonds such as amide bond "C5a-N1b" and carboxylate ester bond "C7a-O7a". About 13% of molecules (2,192 molecules) in KEGG COMPOUND have amide bonds labeled as "C5a-N1b", and the number of the bond in total was 4,174 (about 1.9 bonds per molecule). About 5% of molecules (2,528 molecules) in KNAp-SAcK have the same bond, and the number of the bond in total was 6,784 (about 2.7 bonds per molecule). This means that, even though KNApSAcK contains about three times more molecules than KEGG COMPOUND, proportion of molecules containing the bonds in KNApSAcK is not as high as that of KEGG COMPOUND, but the average number of the bonds is larger in KNApSAcK.
VICINITY entries define more detailed substructures. For example, the atom class "O1" sufficiently describe a hydroxy group (see Table 1). Among these, the KEGG Atom "O1a" describe a hydroxy group attached to a carbon atom, which is usually referred to as an alcohol group. It is known that primary alcohol group, secondary alcohol group and tertiary alcohol group are different in terms of the reactivity in organic chemistry, and they are distinguished by the BOND entries "C1b-O1a", "C1c-O1a" and "C1d-O1a", respectively. Secondary and tertiary alcohols can be in a ring structure, cyclic secondary alcohol and cyclic tertiary alcohol, and in such cases they are represented as the BOND entries "C1y-O1a" and "C1z-O1a", respectively. The VICINITY entry "C1y(C1y+C1y+O1a)" defines even more detailed subclass of cyclic secondary alcohol, and sugar residues contain many of these entries. Similarly, the BOND entry "C8y-O1a" sufficiently describe a phenolic hydroxy group, and the VICINITY entry "C8y(C8x +C8x+O1a)" defines the phenolic hydroxy group that does not have any substituted groups in the ortho (o-) positions.
RING, SKELETON, and INORGANIC entries captured many substructures that have been defined in literatures in organic chemistry and biochemistry but have not been usually captured by the conventional chemical fingerprints.

Statistics of the substructures in KEGG and KNApSAcK databases
The numbers of KCF Substructures obtained from the KEGG COMPOUND, KEGG DRUG and KNApSAcK databases were summerized in Figure 4. From the three databases, 140,093 substructures were obtained, among  (Figure 4a). Each of the 68 KEGG Atom Types consists of 1-3 characters that hierarchically classify microenvironment of atoms. For example, carbon atoms "C" are classified into alkyl carbon atoms "C1", alkenyl carbon atoms "C2", etc., and alkyl carbon atoms "C1" are further classified into "C1a", "C1b", etc. (see Table 1), which comes up to 98 ATOM entries. All of the three databases use all these ATOM entries.
From the 6567 VICINITY entries obtained in total, only 1,652 (25%) were shared in the all three databases ( Figure  4c). 593 out of 3,822 (16%) and 547 out of 2,886 (19%) were unique in KEGG COMPOUND and KEGG DRUG, respectively, whereas it was found that KNApSAcK database had as many as 2,033 out of 4,905 (41%) unique VICINITY entries.

Characteristic appearance of substructures in respective datasets
We further investigated the characteristic appearance of substructures in respective databases in the following way: the numbers of molecules that do or do not contain the respective substructures are counted in a database and another, and the significantly appearing substructures in the database against those in the other were ranked according to the P-value using Fisher's exact test. The top five characteristic substructures in respective attributes are shown in the Supplementary tables S1-S6 in Additional file 1.
By the comparison of KEGG COMPOUND with KEGG DRUG, it was shown that KEGG COMPOUND has significantly more molecules that contain sugar residues, phosphate groups and adenine residues (Table S1), which reflects that KEGG COMPOUND collects molecules related with fundamental biological systems such as nucleic acids and sugar phosphates.
Comparing KEGG DRUG with KEGG COMPOUND, secondary and tertiary amines, aromatic rings, aryl halides, piperazine rings, ethylenediamine and ethanolamine residues, and sulfur-related inorganic residues were found to be characteristic in KEGG DRUG (Table S2). Similarly, comparison of KNApSAcK with KEGG COM-POUND revealed that carboxylate ester bonds, especially alkyl carboxylate ester bonds, and O-acetyl group was found to be characteristic in KNApSAcK (Table S3). These comparisons reflects the nature of molecules in the respective databases, i.e., DRUG for pharmaceuticals and KNApSAcK for secondary metabolites.
The same analysis can be conducted using any datasets of molecules. In other words, as demonstrated above, the KCF-S enables us to find characteristic substructures in any given datasets of molecules in a way that the obtained substructures are interpretable with the words in biochemistry and organic chemistry.

Structure-based clustering of molecules using KCF-S descriptors
As the first application of KCF-S, we conducted the structure-based clustering of the molecules in the following way; the structures of molecules were represented in the form of the KCF-S descriptors (integer vectors), the similarity between the molecules were defined as a weighted Jaccard coefficient between the two corresponding KCF-S descriptors, and the complete-linkage clustering or the QCC methods were applied with a variety of thresholds. Table 3 shows the comparison of the five completelinkage clusters with weighted Jaccard coefficient >= 0.7 using KCF-S and PubChem/MACCS fingerprints. It appeared that PubChem and MACCS fingerprints tend to generate larger clusters than those by KCF-S. KCF-S generated more numbers of smaller clusters, and the clusters generally consisted of the molecules sharing the same core structures. It was also observed that the clusters obtained by PubChem and MACCS fingerprints do not take into account the number of substituted groups, such that the standard deviation of the molecular weights were generally larger than the clusters obtained by KCF-S descriptor. Many clusters obtained by KCF-S descriptor can be described by the names of compound classes, such as acyl-CoA and disaccharides. In contrast, many clusters obtained by PubChem and MACCS fingerprints were so diverse that we could not find appropriate words to describe the clusters.
We further conducted the QCC clustering of the mixed molecules consisting of KEGG COMPOUND and KNApSAcK, with the weighted Jaccard coefficient >= 0.7 and the clique ratio >= 0.7, and the obtained clusters were plotted onto a scatter diagram ( Figure 5). It was clearly shown that KEGG COMPOUND and KNApSAcK contain different distributions of molecular classes. Two example clusters, glycosylated flavonoids and acyl-CoA molecules were presented as such examples in Figure 5. The former cluster consists of 13 and 228 molecules from KEGG COMPOUND and KNApSAcK, and the latter cluster consists of 144 and 7 molecules from KEGG COMPOUND and KNApSAcK, respectively.

Improved performance in the de novo metabolic pathway reconstruction
As the second application of KCF-S, we tested the proposed descriptors on their abilities to reconstruct metabolic pathways from chemical structures, i.e., to predict the enzymatic-reaction likeness of given compoundcompound pairs from their chemical fingerprint data, following our previous work [15].

Cross-validation experiment to predict enzyme-reaction likeness
We performed the following 5-fold cross-validation. 1) Compound-compound pairs in the gold standard data were split into five subsets of roughly equal sizes. Known reactant pairs were regarded as positive examples, and the other compound-compound pairs as negative examples. 2) Each subset were taken as a test set, and the remaining four subsets as a training set. 3) A predictive model was trained based only on the training set. 4) The prediction scores were computed for compound-compound pairs in the test set. 5) Finally, the prediction accuracy were evaluated over the five folds.
The prediction performance were evaluated by the receiver operating characteristic (ROC) curve, which is a plot of true positives as a function of false positives based on various thresholds, and the precision-recall (PR) curve, which is a plot of precision as a function of recall. The performance were summarized by the area under the ROC curve (AUC) score and the area under the PR curve (AUPR). The parameters involved in the methods were optimized with the AUC score and the AUPR score as the objective functions. Table 4 shows the resulting AUC scores and AUPR scores for five descriptors: KCF-S, PubChem fingerprint, MACCS fingerprint, and KCF. Among the 4 fingerprints, the proposed KCF-S descriptor achieved the highest AUC and AUPR scores. The higher k seems to improve the prediction accuracy to some extent. The KCF-S descriptor outperformed the PubChem fingerprint and the MACCS fingerprint in both AUC and AUPR. This result suggests that the proposed feature vectors are useful.
The AUC score of the diff-common feature vector were slightly higher than those of the diff-only feature vector in L1SVM, while the AUPR score of the diff-common feature vector were much higher than those of the diffonly feature vector in L1SVM. This result implies the importance to take into account not only substructure transformation patterns but also common substructures in the reaction prediction. L1SVM outperformed BASE-LINE, suggesting that supervised learning with the proposed feature vectors is meaningful. #M indicates the numbers of molecules in the clusters. Max MW, Ave MW, and Min MW indicate the molecules with the maximum molecular weight, the molecules with the average molecular weight, and the molecules with the minimum molecular weights, respectively, with the respective molecular weights. SD shows the standard deviation of the obtained clusters. Description after the cluster numbers (#1 -#5) represents the group of molecules, in which "from ... to ..." indicates that the molecular structures in the cluster were so diverse that we could not find appropriate words to describe the clusters.
We conducted further analysis to illustrate how much improvement was achieved by KCF-S compared with KCF. Two types of integer vectors were constructed; the one (ATOM descriptor) only contains the ATOM attributes, the other (BOND descriptor) contains the ATOM and BOND attributes. Both attributes can be obtained by using KCF. As the result of the cross-validation experiments, it was clearly shown that the AUC and AUPR scores by KCF-S descriptors were better than those by ATOM and BOND descriptors (Table 4). Obviously, applying KCF-S

Examples of newly predicted pathways using KNApSAcK
We applied KCF-S 3k 1000 descriptor to conduct de novo metabolic network prediction for all KEGG and KNApSAcK databases. The predicted compound pairs were filtered using the weighted Jaccard coefficient >= 0.9, and the connected subnetworks were extracted from the top 10,000 predicted pairs. We manually examined each of the predicted compound pairs to estimate whether or not the one of the pair can be possibly converted to the other in an enzymatic reactions. Taking the 16th largest subnetwork consisting of 181 compounds (mainly flavonoid glycosides) as an example, among the 16290 pairs theoretically obtained, 831 pairs Figure 6 Example of predicted subnetworks. Nodes (with ID numbers of KEGG COMPOUND or KNApSAcK) represent molecules. Black bold lines indicate the predicted pairs that were considered as positive after manual examination. Black thin lines and gray lines indicate those that were considered suspicious and negative, respectively. (b) An example pair that was considered as positive, representing a cyclization reaction. (c) Another example pair considered as positive, representing a methylation reaction. (d) An example pair that was considered as suspicious, representing a hydroxylation reaction. (e) An example pair that was considered as negative, representing large rearrangement of carbon skeleton that seems impossible to occur.
were predicted, and about 100 were considered as positive as the manual examination. Figure 6 shows the 63th largest subnetwork consisting of 45 compounds (mainly prenyl flavonoids), as another example. Among the 990 theoretically defined pairs, 73 pairs were predicted (Figure 6a), of which 10 pairs were considered as positive, 11 pairs were considered as suspicious, and 52 pairs were considered as negative by manual examination. Among the 10 positive pairs, 9 pairs represented cyclization of prenyl flavonoids to form pyrano flavonoids (e.g., Figure 6b), and 1 pair represented methylation (e.g., Figure 6c). Suspicious pairs include hydroxylation on an aromatic ring (e.g., Figure 6d), and negative pairs include isomerations that seems impossible to occur.

Conclusion
In this study, we introduced a new data structure named KCF-S describing relatively larger biochemical substructures than those defined in KCF format we published in 2003. The main aim of KCF-S is a computationally defined substructures that privides direct links between the names and the substructures in an interpretable way for biochemists. It was shown that the KCF-S helps extract the substructures that are characteristic in any given dataset of molecules. We demonstrated the usefulness of KCF-S for the two applications; structure-based clustering of molecules, and de novo metabolic pathway reconstruction. The clusters of molecules obtained by KCF-S were less diverse than those by PubChem and MACCS fingerprints, and were relatively easy to interpret. The improved predictive performance was also achieved by KCF-S for the de novo pathway reconstruction. We belive that the KCF-S can also be applied for pharmacogenomic analysis and other studies, taking advantage of the interpretability of the defined substructures.

Additional material
Additional file 1: An additional file contains tables S1-S6