BACKGROUND
by analogy with orphan genes in genomic studies  <cit> , metabolites that are not yet known how they are synthesized or degraded are referred to as "orphan metabolites"  <cit> .
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  <dig>  secondary metabolites  <cit>  that are not directly involved in the primary metabolism and whose absence is not normally lethal.
kanaya and colleagues have been collecting  <dig>  metabolites, and the chemical structures and metabolite-species relationships are publicly available in knapsack database  <cit> .
some of them are known to function as toxins defending the organisms against pathogens, parasites and predators  <cit> .
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  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  and nuclear magnetic resonance .
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 structures of compounds and the functional groups contained within them is important.
some computational studies conduct de novo metabolic pathway reconstruction, i.e., automated generation of hypothetical metabolic pathway  <cit> .
among them, a group of methods deal with the problem of "enzymatic-reaction likeness", i.e., whether or not a compound-compound pair is possibly converted to each other by enzymatic reactions  <cit> .
however, the 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  <cit> .
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 -h and carboxylate r--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 , 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  format that we published in  <dig>  <cit> .
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 structure-based 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.
data
kegg and knapsack as chemical structure databases
we obtained chemical structure of molecules in kegg  <cit>  and knapsack  <cit>  databases in the molfile format.
kyoto encyclopedia of genes and genomes  is a database resource for understanding high-level functions and utilities of the biological system, which contains a variety of sub-databases such as kegg compound and kegg drug.
kegg compound collects small molecules and other chemical substances  that are relevant to biological systems.
each kegg compound entry is identified by the id number consisting of the letter "c" and the five digit numerals .
kegg drug is a comprehensive drug information resource for approved drugs in japan, usa, and europe unified based on the chemical structures and/or the chemical components , and associated with target, metabolizing enzyme, and other molecular interaction network information.
each kegg drug entry is identified by the id number consisting of the letter "d" and the five digit numerals .
knapsack database  is a comprehensive species-metabolite relationship database that contains  <dig>  metabolites and  <dig>  metabolite-species relationships .
each knapsack entry is identified by id consisting of the letter "c" and the eight digit numerals .
kegg chemical function  format
kegg chemical function  format, one of the chemical structure file format, has been defined and published in hattori et al.,  <dig>  <cit> , where molecules  are represented as graphs consisting of atoms as vertices and bonds as edges .
the vertices  of kcf are labeled by the  <dig> kegg atom types , 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.
kegg atom types were defined in  <dig>  <cit> , 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.
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  <cit> .
kegg rpair database defines  <dig>  reactant pairs as of june  <dig>  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.
<dig>  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  <dig> , <dig>
conventional chemical fingerprints
we used conventional chemical fingerprints in order to compare the kcf-s descriptors  for the interpretability of characterising molecule datasets and for the predictive ability of de novo pathway reconstruction.
chemical fingerprints encode presence or absence  of chemical substructures in molecules, resulting in a high dimensional binary vector.
we used the chemistry development kit  version  <dig> .
<dig>  <cit>  to calculate well-known fingerprints, maccs fingerprint and pubchem fingerprint.
their dimensions are  <dig>  and  <dig>  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  <cit> .
they were computationally defined using seven attributes: atom, bond, triplet, vicinity, ring, skeleton, and inorganic.
in this study, each substructure was given a label  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.
the atom attribute in kcf-s
an atom entry represents kegg atom type .
in figure  <dig>  circles represent atom entries, corresponding to the nodes that form molecular graphs.
for example, "c1y" in figure  <dig> is one of such nodes.
according to the definition of the kegg atom types, the atom entries were classified hierarchically .
a kegg atom type  is a subclass of the atom classes represented by the first two letters .
a kegg atom class  is a subclass of the element , which is a subclass of atom entries.
in kcf-s, the variable k represents the level of the atom attributes: k <dig>  k <dig> and k <dig> mean the atom species , 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 .
in figure  <dig>  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 .
also, a bond entry has two atom entries, and a bond is part of many other entries .
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, 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  <dig>  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", n-acetyl "c5a", and phosphate "p1b".
in figure  <dig>  the vicinity "c1y" 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 , rings.
the strings to identify ring entries were generated in the following way:  an atom in the ring was selected as a starter to retrieve ring structures using depth-first search algorithm,  kegg atom types consisting of the ring were connected by hyphens to generate a backbone string,  if there were branch atoms attached to the ring, they were added to the backbone string using parentheses,  the processes - were repeated for all starting atoms, clockwise and anti-clockwise directions,  the obtained strings were sorted in alphabetical order, and  the first string was selected to represent the ring entry.
some common examples are the phenyl ring "c8x-c8x-c8x-c8x-c8x-c8y", imidazole ring "c8x-c8y-n5x-c8x-n4x" and pyrrole ring "c8x-c8x-c8y-c8x-n4x".
pyranose sugar ring was represented as "c1y-c1y-c1y-c1y-c1y-o2x".
ring also deals with condensed rings.
for example, adenine in nadh was represented as a 9-membered condensed ring "c8x-n4y-c8y-n5x-c8x-n5x-c8y-c8y-n5x", consisting of a 5-membered ring "c8x-n4y-c8y-c8y-n5x" and a 6-membered ring "c8x-n5x-c8y-c8y-c8y-n5x".
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:  a carbon atom in the terminus of the carbon skeleton was selected as a starter to retrieve all carbon chains in the skeleton,  kegg atom types consisting of the chains were connected by hyphens,  if other elements  attach to the chain, they were added to the chain using parentheses,  the longest chain was selected as a seed, and the shorter chains were bundled to generate the string representing the carbon skeleton,  the processes - were repeated for all starting atoms,  the obtained strings were sorted in alphabetical order, and
the first string was selected to represent the skeleton entry.
some common examples are the n-acetyl group "c1a-c5a", o-acetyl group "c1a-c7a", and hexopyranose sugar ring o-glycoside "c1b-c1y-c1y-c1y-c1y-c1y".
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:  an atom in the terminus of the inorganic component was selected as a starter to retrieve all chains in the inorganic component,  kegg atom types consisting of the chains were connected by hyphens,  if carbon atoms attach to the chain, they were added to the chain using parentheses,  the longest chain was selected as a seed, and the shorter chains were bundled to generate the string representing the inorganic component,  the processes - were repeated for all starting atoms,  the obtained strings were sorted in alphabetical order, and  the first string was selected to represent the inorganic entry.
some common examples are primary alcohol phosphate ester "o1c-p1b)-o1c", and sulfonate "o1d-s4a-o1d".
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 , which was originally developed for clustering of large amount of genes to detect orthologs in kegg oc  <cit> .
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  <dig> , 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  <dig> , e.g.,  <dig> , 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 .
metabolic pathway reconstruction based on the kcf-s descriptors
our previous study for the de novo metabolic pathway reconstruction  <cit>  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 compound-compound pairs , we estimate a linear function f 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  <cit>  from binary vectors to integer vectors.
our kcf-s descriptor represents compounds c and c' as d-dimensional integer vectors as Φ = t and Φc′=c′ <dig> c′ <dig> ...,c′dt, respectively, where ck, ck′∈ℤ,k=  <dig> …,d.
let min be a function that returns ck if ck≤ck′ and otherwise returns ck′, and let max be a function that returns ck if ck≤ck′ and otherwise returns ck′.
we define two operations for the descriptors as follows:
)=,min,...,min)
and
⊖Φ) =, max,.
.
.
,max).
the both operations are generalizations of the previously defined operations  <cit>  from binary vectors to integer vectors.
∧ Φ) captures common kcf-s features between Φ and Φ, while  captures kcf-s features present in Φ and absent in Φ.
∧ Φ) and  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:
Φ=,Φc⊖Φ,Φ⊖Φ)t
and
Φ¯=,Φ⊖Φ)t.
the both feature vectors are also generalizations of the previously defined feature vectors  <cit> .
Φ and Φ¯ 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 diff-common feature vector is designed to capture core substructures kept in the conversion of a chemical compound to another compound.
using the feature vectors Φ and Φ¯ for compounds c and c', a linear model estimates a linear function f = wtΦ, where w is a real value vector .
the reaction between c and c' is predicted by thresholding the value of f. 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  with l1-regularization for its high interpretability and high prediction accuracies comparable to svm with l2-regularization.
to solve the optimization problem in svm, we use an efficient optimization algorithm named liblinear  <cit> , which is available from http://www.csie.ntu.edu.tw/~cjlin/liblinear/.
RESULTS
kcf-s  format
kcf format of molecules have been provided in kegg as a fundamental chemical structure information since  <dig>  <cit> .
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 knapsack databases in this study, kcf and kcf-s can deal with many other molecules in pubchem  <cit> , chebi  <cit> , drugbank  <cit> , nci  <cit>  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.
examples of named substructures
#s represents the numbers of kcf-substructures, and #c represent the numbers of compounds containing the kcf-substructures.
note that the annotations are not necessary-and-sufficient definitions.
for example, "n1b-n1b" bond is a hydrazine bond, but there are some other types of hydrazine bonds; e.g., "n1b-n1c" is a hydrazine bond with three substituted groups, and "n1x-n1x" is a hydrazine bond in a ring structure.
in contrast, about 14%  molecules in compound have "c7a-o7a" carboxylate ester bond, whereas about 26%  molecules in knapsack have the same bond.
in addition to essential amino acids, there are many other alpha-amino acids.
the triplet attribute grasps the substructure that defines alpha-amino acids "c6a-c1c-n1a", which resulted in finding  <dig>  molecules in compound,  <dig>  molecules in drug, and  <dig>  molecules in knapsack.
vicinity entries define more detailed substructures.
for example, the atom class "o1" sufficiently describe a hydroxy group .
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" 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" defines the phenolic hydroxy group that does not have any substituted groups in the ortho  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.
for example, an ring entry "c8x-n4y-c8y-n5x-c8x-n5x-c8y-c8y-n5x" represented an adenine ring that is attached with a carbon atom in a ring structure .
this adenine ring and the imidazole ring "c8x-n4y-c8y-c8y-n5x" are examples of the ring entries that are frequently found in compound but not in drug and knapsack databases.
in contrast, piperazine ring "c1x-c1x-n1y-c1x-c1x-n1y" is an example ring entry that are frequently found only in drug database.
many sugar rings were found in ring entries, including a pyranose sugar ring "c1y-c1y-c1y-c1y-c1y-o2x".
sugar residues were also found in skeleton entries, such as a ribofuranose "c1b-c1y-c1y-c1y-c1y" that is attached to an aromatic nitrogenous ring such as nucleic bases.
skeleton entries captured many named amino acid residues such as leucine residue" c1a-c1c-c1b-c1c-c5a".
inorganic entries contained orthophosphate, pyrophosphate, sulfate, sulfite, nitro, etc, and the variations and the positions of substituted groups were discriminated, such as primary alcohol orthophosphate "o1c-p1b)-o1c", cyclic secondary alcohol orthophosphate "o1c-p1b)-o1c" and cyclic orthophosphate "o1c-p1b))-o1c".
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  <dig>  from the three databases,  <dig>  substructures were obtained, among which only  <dig>   appeared in all of the three databases.
among the  <dig>  substructures from kegg compound,  <dig>  substructures  were unique .
similarly, among the  <dig>  and  <dig>  substructures from kegg drug and knapsack databases,  <dig>   and  <dig>   substructues were unique, respectively .
each of the  <dig> kegg atom types consists of 1- <dig> 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.
, which comes up to  <dig> atom entries.
all of the three databases use all these atom entries.
from the three databases,  <dig> bond entries were obtained, among which  <dig>  appeared in all of the three databases .
among the  <dig> bond entries from kegg compound,  <dig> substructures  were unique .
similarly, among the  <dig> and  <dig> bond entries from kegg drug and knapsack databases,  <dig>  and  <dig>  substructues were unique, respectively.
<dig> triplet entries were obtained in total from the three databases, among which  <dig>  were shared .
unique triplet entries in kegg compound, kegg drug and knapsack databases were  <dig> out of  <dig>  ,  <dig> out of  <dig>   and  <dig> out of  <dig>  , respectively.
from the  <dig> vicinity entries obtained in total, only  <dig>   were shared in the all three databases .
<dig> out of  <dig>   and  <dig> out of  <dig>   were unique in kegg compound and kegg drug, respectively, whereas it was found that knapsack database had as many as  <dig>  out of  <dig>   unique vicinity entries.
the proportion of the shared entries were even fewer in inorganic, ring and skeleton entries, which were  <dig> out of  <dig>  ,  <dig>  out of  <dig>  , and  <dig>  out of  <dig>  , respectively .
the numbers of unique entries in kegg compound were generally small;  <dig>  out of  <dig> inorganic entries,  <dig>   out of  <dig>  ring entries, and  <dig>   out of  <dig>  skeleton entries.
those in kegg drug were larger;  <dig>  out of  <dig> inorganic entries,  <dig>   out of  <dig>  ring entries, and  <dig>   out of  <dig>  skeleton entries.
knapsack generally had even more entries;  <dig>  out of  <dig> inorganic entries,  <dig>   out of  <dig>  ring entries, and  <dig>   out of  <dig>  skeleton 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-s <dig> in additional file  <dig>
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 , 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 .
similarly, comparison of knapsack with kegg compound revealed that carboxylate ester bonds, especially alkyl carboxylate ester bonds, and o-acetyl group was found to be characteristic in knapsack .
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 , 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.
#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  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 further conducted the qcc clustering of the mixed molecules consisting of kegg compound and knapsack, with the weighted jaccard coefficient >=  <dig>  and the clique ratio >=  <dig> , and the obtained clusters were plotted onto a scatter diagram .
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  <dig>  the former cluster consists of  <dig> and  <dig> molecules from kegg compound and knapsack, and the latter cluster consists of  <dig> and  <dig> 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 compound-compound pairs from their chemical fingerprint data, following our previous work  <cit> .
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  curve, which is a plot of true positives as a function of false positives based on various thresholds, and the precision-recall  curve, which is a plot of precision as a function of recall.
the performance were summarized by the area under the roc curve  score and the area under the pr curve .
the parameters involved in the methods were optimized with the auc score and the aupr score as the objective functions.
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 diff-only 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 baseline, suggesting that supervised learning with the proposed feature vectors is meaningful.
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  only contains the atom attributes, the other  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 .
obviously, applying kcf-s needs more computational time and memory than kcf.
for example, cross-validation experiment needed about  <dig> seconds and  <dig> mb memory when using bond descriptor, whereas about  <dig>  seconds and  <dig> mb memory when using kcf-s descriptor.
examples of newly predicted pathways using knapsack
we applied kcf-s 3k  <dig> 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 >=  <dig> , and the connected subnetworks were extracted from the top  <dig>  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  <dig> compounds  as an example, among the  <dig> pairs theoretically obtained,  <dig> pairs were predicted, and about  <dig> were considered as positive as the manual examination.
CONCLUSIONS
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  <dig>  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.
competing interests
the authors declare that they have no competing interests.
authors' contributions
mko conceived of the study, designed the algorithm and drafted the manuscript.
yt and yy implemented the algorithms, tested the performance and drafted the manuscript.
ym conducted the structure-based clustering of molecules and interpreting the results.
tt helped the manual inspection of the output and interpret the results.
mka and sg developed the original kcf format, and helped draft the manuscript.
all authors read and approved the final manuscript.
supplementary material
additional file 1
an additional file contains tables s1-s6
click here for file
acknowledgements
computational resources were provided by the bioinformatics center, institute for chemical research and the super computer laboratory, kyoto university.
funding from the ministry of education, culture, sports, science and technology of japan, the japan science and technology agency, and the japan society for the promotion of science; mext/jsps kakenhi .
this work was also supported by the program to disseminate tenure tracking system, mext, japan, and kyushu university interdisciplinary programs in education and projects in research development.
declarations
the publication cost for this work was supported by mext kakenhi  <dig>
this article has been published as part of bmc systems biology volume  <dig> supplement  <dig>  2013: selected articles from the 24th international conference on genome informatics .
the full contents of the supplement are available online at http://www.biomedcentral.com/bmcsystbiol/supplements/7/s <dig>

 by analogy with orphan genes in genomic studies, metabolites that are not yet known how they are synthesized or degraded are referred to as "orphan metabolites". 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 secondary metabolites that are not directly involved in the primary metabolism and whose absence is not normally lethal. kanaya and colleagues have been collecting metabolites, and the chemical structures and metabolite-species relationships are publicly available in knapsack database. some of them are known to function as toxins defending the organisms against pathogens, parasites and predators. 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 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 and nuclear magnetic resonance. 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 structures of compounds and the functional groups contained within them is important. some computational studies conduct de novo metabolic pathway reconstruction, i.e., automated generation of hypothetical metabolic pathway. among them, a group of methods deal with the problem of "enzymatic-reaction likeness", i.e., whether or not a compound-compound pair is possibly converted to each other by enzymatic reactions. however, the 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. 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 -h and carboxylate r--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, 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 format that we published in. 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 structure-based 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. data kegg and knapsack as chemical structure databases we obtained chemical structure of molecules in kegg and knapsack databases in the molfile format. kyoto encyclopedia of genes and genomes is a database resource for understanding high-level functions and utilities of the biological system, which contains a variety of sub-databases such as kegg compound and kegg drug. kegg compound collects small molecules and other chemical substances that are relevant to biological systems. each kegg compound entry is identified by the id number consisting of the letter "c" and the five digit numerals. kegg drug is a comprehensive drug information resource for approved drugs in japan, usa, and europe unified based on the chemical structures and/or the chemical components, and associated with target, metabolizing enzyme, and other molecular interaction network information. each kegg drug entry is identified by the id number consisting of the letter "d" and the five digit numerals. knapsack database is a comprehensive species-metabolite relationship database that contains metabolites and metabolite-species relationships. each knapsack entry is identified by id consisting of the letter "c" and the eight digit numerals. kegg chemical function format kegg chemical function format, one of the chemical structure file format, has been defined and published in hattori et al.,, where molecules are represented as graphs consisting of atoms as vertices and bonds as edges. the vertices of kcf are labeled by the kegg atom types, 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. kegg atom types were defined in, 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. 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. kegg rpair database defines reactant pairs as of june 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. 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, conventional chemical fingerprints we used conventional chemical fingerprints in order to compare the kcf-s descriptors for the interpretability of characterising molecule datasets and for the predictive ability of de novo pathway reconstruction. chemical fingerprints encode presence or absence of chemical substructures in molecules, resulting in a high dimensional binary vector. we used the chemistry development kit version. to calculate well-known fingerprints, maccs fingerprint and pubchem fingerprint. their dimensions are and 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. they were computationally defined using seven attributes: atom, bond, triplet, vicinity, ring, skeleton, and inorganic. in this study, each substructure was given a label 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. the atom attribute in kcf-s an atom entry represents kegg atom type. in figure circles represent atom entries, corresponding to the nodes that form molecular graphs. for example, "c1y" in figure is one of such nodes. according to the definition of the kegg atom types, the atom entries were classified hierarchically. a kegg atom type is a subclass of the atom classes represented by the first two letters. a kegg atom class is a subclass of the element, which is a subclass of atom entries. in kcf-s, the variable k represents the level of the atom attributes: k k and k mean the atom species, 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. in figure 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. also, a bond entry has two atom entries, and a bond is part of many other entries. 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, 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 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", n-acetyl "c5a", and phosphate "p1b". in figure the vicinity "c1y" 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, rings. the strings to identify ring entries were generated in the following way: an atom in the ring was selected as a starter to retrieve ring structures using depth-first search algorithm, kegg atom types consisting of the ring were connected by hyphens to generate a backbone string, if there were branch atoms attached to the ring, they were added to the backbone string using parentheses, the processes - were repeated for all starting atoms, clockwise and anti-clockwise directions, the obtained strings were sorted in alphabetical order, and the first string was selected to represent the ring entry. some common examples are the phenyl ring "c8x-c8x-c8x-c8x-c8x-c8y", imidazole ring "c8x-c8y-n5x-c8x-n4x" and pyrrole ring "c8x-c8x-c8y-c8x-n4x". pyranose sugar ring was represented as "c1y-c1y-c1y-c1y-c1y-o2x". ring also deals with condensed rings. for example, adenine in nadh was represented as a 9-membered condensed ring "c8x-n4y-c8y-n5x-c8x-n5x-c8y-c8y-n5x", consisting of a 5-membered ring "c8x-n4y-c8y-c8y-n5x" and a 6-membered ring "c8x-n5x-c8y-c8y-c8y-n5x". 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: a carbon atom in the terminus of the carbon skeleton was selected as a starter to retrieve all carbon chains in the skeleton, kegg atom types consisting of the chains were connected by hyphens, if other elements attach to the chain, they were added to the chain using parentheses, the longest chain was selected as a seed, and the shorter chains were bundled to generate the string representing the carbon skeleton, the processes - were repeated for all starting atoms, the obtained strings were sorted in alphabetical order, and the first string was selected to represent the skeleton entry. some common examples are the n-acetyl group "c1a-c5a", o-acetyl group "c1a-c7a", and hexopyranose sugar ring o-glycoside "c1b-c1y-c1y-c1y-c1y-c1y". 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: an atom in the terminus of the inorganic component was selected as a starter to retrieve all chains in the inorganic component, kegg atom types consisting of the chains were connected by hyphens, if carbon atoms attach to the chain, they were added to the chain using parentheses, the longest chain was selected as a seed, and the shorter chains were bundled to generate the string representing the inorganic component, the processes - were repeated for all starting atoms, the obtained strings were sorted in alphabetical order, and the first string was selected to represent the inorganic entry. some common examples are primary alcohol phosphate ester "o1c-p1b)-o1c", and sulfonate "o1d-s4a-o1d". 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, which was originally developed for clustering of large amount of genes to detect orthologs in kegg oc. 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, 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, e.g.,, 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. metabolic pathway reconstruction based on the kcf-s descriptors our previous study for the de novo metabolic pathway reconstruction 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 compound-compound pairs, we estimate a linear function f 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 from binary vectors to integer vectors. our kcf-s descriptor represents compounds c and c' as d-dimensional integer vectors as Φ = t and Φc′=c′ c′...,c′dt, respectively, where ck, ck′∈ℤ,k=  …,d. let min be a function that returns ck if ck≤ck′ and otherwise returns ck′, and let max be a function that returns ck if ck≤ck′ and otherwise returns ck′. we define two operations for the descriptors as follows: )=,min,...,min) and ⊖Φ) =, max,.. .,max). the both operations are generalizations of the previously defined operations from binary vectors to integer vectors. ∧ Φ) captures common kcf-s features between Φ and Φ, while captures kcf-s features present in Φ and absent in Φ. ∧ Φ) and 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: Φ=,Φc⊖Φ,Φ⊖Φ)t and Φ¯=,Φ⊖Φ)t. the both feature vectors are also generalizations of the previously defined feature vectors. Φ and Φ¯ 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 diff-common feature vector is designed to capture core substructures kept in the conversion of a chemical compound to another compound. using the feature vectors Φ and Φ¯ for compounds c and c', a linear model estimates a linear function f = wtΦ, where w is a real value vector. the reaction between c and c' is predicted by thresholding the value of f. 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 with l1-regularization for its high interpretability and high prediction accuracies comparable to svm with l2-regularization. to solve the optimization problem in svm, we use an efficient optimization algorithm named liblinear, which is available from http://www.csie.ntu.edu.tw/~cjlin/liblinear/.  kcf-s format kcf format of molecules have been provided in kegg as a fundamental chemical structure information since. 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 knapsack databases in this study, kcf and kcf-s can deal with many other molecules in pubchem, chebi, drugbank, nci 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. examples of named substructures #s represents the numbers of kcf-substructures, and #c represent the numbers of compounds containing the kcf-substructures. note that the annotations are not necessary-and-sufficient definitions. for example, "n1b-n1b" bond is a hydrazine bond, but there are some other types of hydrazine bonds; e.g., "n1b-n1c" is a hydrazine bond with three substituted groups, and "n1x-n1x" is a hydrazine bond in a ring structure. in contrast, about 14% molecules in compound have "c7a-o7a" carboxylate ester bond, whereas about 26% molecules in knapsack have the same bond. in addition to essential amino acids, there are many other alpha-amino acids. the triplet attribute grasps the substructure that defines alpha-amino acids "c6a-c1c-n1a", which resulted in finding molecules in compound, molecules in drug, and molecules in knapsack. vicinity entries define more detailed substructures. for example, the atom class "o1" sufficiently describe a hydroxy group. 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" 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" defines the phenolic hydroxy group that does not have any substituted groups in the ortho 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. for example, an ring entry "c8x-n4y-c8y-n5x-c8x-n5x-c8y-c8y-n5x" represented an adenine ring that is attached with a carbon atom in a ring structure. this adenine ring and the imidazole ring "c8x-n4y-c8y-c8y-n5x" are examples of the ring entries that are frequently found in compound but not in drug and knapsack databases. in contrast, piperazine ring "c1x-c1x-n1y-c1x-c1x-n1y" is an example ring entry that are frequently found only in drug database. many sugar rings were found in ring entries, including a pyranose sugar ring "c1y-c1y-c1y-c1y-c1y-o2x". sugar residues were also found in skeleton entries, such as a ribofuranose "c1b-c1y-c1y-c1y-c1y" that is attached to an aromatic nitrogenous ring such as nucleic bases. skeleton entries captured many named amino acid residues such as leucine residue" c1a-c1c-c1b-c1c-c5a". inorganic entries contained orthophosphate, pyrophosphate, sulfate, sulfite, nitro, etc, and the variations and the positions of substituted groups were discriminated, such as primary alcohol orthophosphate "o1c-p1b)-o1c", cyclic secondary alcohol orthophosphate "o1c-p1b)-o1c" and cyclic orthophosphate "o1c-p1b))-o1c". 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 from the three databases, substructures were obtained, among which only appeared in all of the three databases. among the substructures from kegg compound, substructures were unique. similarly, among the and substructures from kegg drug and knapsack databases, and substructues were unique, respectively. each of the kegg atom types consists of 1- 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., which comes up to atom entries. all of the three databases use all these atom entries. from the three databases, bond entries were obtained, among which appeared in all of the three databases. among the bond entries from kegg compound, substructures were unique. similarly, among the and bond entries from kegg drug and knapsack databases, and substructues were unique, respectively. triplet entries were obtained in total from the three databases, among which were shared. unique triplet entries in kegg compound, kegg drug and knapsack databases were out of, out of and out of, respectively. from the vicinity entries obtained in total, only were shared in the all three databases. out of and out of were unique in kegg compound and kegg drug, respectively, whereas it was found that knapsack database had as many as out of unique vicinity entries. the proportion of the shared entries were even fewer in inorganic, ring and skeleton entries, which were out of, out of, and out of, respectively. the numbers of unique entries in kegg compound were generally small; out of inorganic entries, out of ring entries, and out of skeleton entries. those in kegg drug were larger; out of inorganic entries, out of ring entries, and out of skeleton entries. knapsack generally had even more entries; out of inorganic entries, out of ring entries, and out of skeleton 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-s in additional file 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, 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. similarly, comparison of knapsack with kegg compound revealed that carboxylate ester bonds, especially alkyl carboxylate ester bonds, and o-acetyl group was found to be characteristic in knapsack. 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, 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. #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 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 further conducted the qcc clustering of the mixed molecules consisting of kegg compound and knapsack, with the weighted jaccard coefficient >= and the clique ratio >=, and the obtained clusters were plotted onto a scatter diagram. 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 the former cluster consists of and molecules from kegg compound and knapsack, and the latter cluster consists of and 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 compound-compound pairs from their chemical fingerprint data, following our previous work. 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 curve, which is a plot of true positives as a function of false positives based on various thresholds, and the precision-recall curve, which is a plot of precision as a function of recall. the performance were summarized by the area under the roc curve score and the area under the pr curve. the parameters involved in the methods were optimized with the auc score and the aupr score as the objective functions. 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 diff-only 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 baseline, suggesting that supervised learning with the proposed feature vectors is meaningful. 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 only contains the atom attributes, the other 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. obviously, applying kcf-s needs more computational time and memory than kcf. for example, cross-validation experiment needed about seconds and mb memory when using bond descriptor, whereas about seconds and mb memory when using kcf-s descriptor. examples of newly predicted pathways using knapsack we applied kcf-s 3k 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 >=, and the connected subnetworks were extracted from the top 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 compounds as an example, among the pairs theoretically obtained, pairs were predicted, and about were considered as positive as the manual examination.  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 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. competing interests the authors declare that they have no competing interests. authors' contributions mko conceived of the study, designed the algorithm and drafted the manuscript. yt and yy implemented the algorithms, tested the performance and drafted the manuscript. ym conducted the structure-based clustering of molecules and interpreting the results. tt helped the manual inspection of the output and interpret the results. mka and sg developed the original kcf format, and helped draft the manuscript. all authors read and approved the final manuscript. supplementary material additional file 1 an additional file contains tables s1-s6 click here for file acknowledgements computational resources were provided by the bioinformatics center, institute for chemical research and the super computer laboratory, kyoto university. funding from the ministry of education, culture, sports, science and technology of japan, the japan science and technology agency, and the japan society for the promotion of science; mext/jsps kakenhi. this work was also supported by the program to disseminate tenure tracking system, mext, japan, and kyushu university interdisciplinary programs in education and projects in research development. declarations the publication cost for this work was supported by mext kakenhi this article has been published as part of bmc systems biology volume supplement 2013: selected articles from the 24th international conference on genome informatics. the full contents of the supplement are available online at http://www.biomedcentral.com/bmcsystbiol/supplements/7/s 
in computational chemistry or cheminformatics, molecules are typically represented by chemical descriptors, i.e., vectors that summarize information on its various properties. kcf and kcf-s can be automatically converted from molfile format, enabling to deal with molecules from any data sources. 16- december 24th international conference on genome informatics singapore, singapore 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. 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. 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. 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 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 format to computationally describe biochemical substructures in seven attributes that resemble biochemists' way of dealing with substructures.  we established kcf-s 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.  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. 16- december 24th international conference on genome informatics singapore, singapore 