the online version of this article ( doi:10.1186/s13321 - 015 - 0089-z ) contains supplementary material , which is available to authorized users .
recent work has demonstrated the power of network - based approaches in drug discovery [ 13 ] .
we have shown previously that a large semantic network of drug  target interactions provides a powerful framework for predicting new associations   and that an algorithm that predict drug - target associations by using this network performs surprisingly well , even without training datasets or incorporating target preference . in this work ,
we apply a random walk - based link prediction algorithm based on chen et al .   to a more extensive drug 
we combine three networks  drug  drug , target  target , and drug  target  to construct a heterogeneous network of drugs and targets .
the links between drugs are obtained by quantifying molecular similarity with chemical fingerprints and examining the shared targets .
the links between targets are obtained by calculating sequence similarity between proteins and again examining the shared drugs .
random walk is a useful mathematical framework that provides a systematic way to measure importance of nodes in a network .
pagerank , developed for ranking web pages , measures page clicks of hypothetical web surfers who randomly click hyperlinks in the network of webpages . since it is possible for the surfer to be trapped in a dead - end webpage that does not have any outgoing link , at each time step the surfer may jump to a random webpage with a probability c. interestingly , this formulation also provides a simple way to define a random walk - based  distance  from a node a ( or a set of nodes ) to every other node , namely by allowing the random walkers to jump only to the source node a ( or the source set of nodes ) and restart from there . as a result , it is more likely to find the random walker at the vicinity of the source node than at a distant part of the network , and thus we are able to estimate the relevance ( closeness ) of each node with respect to the source node .
the prediction method applies this idea to identify drugs and targets that are relevant to a set given set of drugs and targets .
consider an undirected , unweighted network g  =  ( v , e ) , where v is the set of nodes and e is the set of links .
for each pair of nodes \documentclass[12pt]{minimal } 
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				 \begin{document}$$ a , b \in v $ $ \end{document}a , bv we can assign a proximity score by executing the following procedure : ( 1 ) we start a random walker from a. ( 2 ) at each time step , with the probability 1    c , the walker walks to one of the neighbors , b , according to the transition probability matrix wab  =  sab / ka , where sab is the adjacency matrix of the network and ( sab equals 1 if node a and b are connected , 0 otherwise ) ka denotes the degree of a. ( 3 ) with the probability c , the walker goes back to a. ( 4 ) after many time steps the probability of finding the random walker at node x converges to the steady - state probability , which is our proximity score sax .
this approach allows us to generate candidate targets for a given drug even if the drug does not have any known targets .
if there is a missing interaction between drug d and target t , we expect that d is more likely to interact with other targets that are similar to t , and drugs that are similar to d are more likely to interact with t. therefore , we expect to see many indirect paths that connect d and t. these indirect paths are likely to be captured by the random walkers .
we apply the rwr algorithm to a drug  target network and use an external dataset extracted from chembl 15 ( 544 drugs and 467 proteins ) at bioactivity cutoff points of 10 and 1  m to quantitatively evaluate the performance and robustness of the approach .
we compile a set of approved drugs from drugbank database ( version 3.0 ) , consisting of 727 compounds and 3519 protein targets ( additional file 1 ) . to construct the network between drugs ,
we incorporate two types of similarity measures : chemical ( structural ) similarity and target similarity .
we calculate chemical similarity between drugs by using the jaccard index ( tanimoto coefficient ) between their chemical fingerprints .
the jaccard index is defined as the size of the intersection of two sets divided by the size of the union of the sets , ranging between 0 and 1 . for binary vectors like chemical fingerprints ,
it is defined as c/(a  +  b    c ) where c is the number of bits in common , a is the number of bits in one of the fingerprints , and b is the number of bits in the other fingerprint .
we use four types of chemical features namely , mdl maccs166 keys ( fragmental descriptors ) , ecfp6 fingerprints ( extended connectivity fingerprint path 6 ) , 2d pharmacophore fingerprints ( phfp4 )   and rocs program which uses tanimoto combo similarity  which combines shape and color measures of a compound , we calculate them with rocs program .
ecfp ( extended connectivity fingerprint ) encodes information on atom - centered fragments that is derived from the variant of the morgan algorithm .
ecfps are generated using the neighborhood of each non - hydrogen atom into multiple circular layers up to a given diameter .
these atom - centric substructural features are then mapped into integer codes using a hashing procedure , which constitute the extended - connectivity fingerprint .
ecfp can , for instance , represent a very large number of features ( over 4 billion ) , do not rely on predefined dictionary of features , can represent stereochemical information , and can be interpreted as the presence of particular substructures .
pharmacophore fingerprints consist of pairs , triplets , or quartets of molecular features and the corresponding bond distances among them .
we use phfp_4 ( quartets which includes number of bonds in the shortest path between the features ) fingerprints for the calculation .
the feature vectors of quartets involve four pharmacophoric features , six euclidean distances separating those features , and an indication of chirality . for 3d alignment and similarity
we used rocs 3.2 , which is a shape - similarity method based on the tanimoto - like overlap of volumes .
the alignment was developed using the combo score , which combines the tanimoto shape score with the color score that added the score for the appropriate overlap of groups with similar properties ( donor , acceptor , hydrophobe , cation , anion , and ring ) [ http://docs.eyesopen.com/rocs/shape_theory.html ] defined by smarts .
conformers for the data set is created using omega , about 250 conformers with rmsd threshold of 0.6 is generated .
rocs score performed in color optimization mode where it optimizes the molecular overlay to maximize both the shape overlap and the color overlap obtained by aligning groups with the same properties that are contained in the color force field file .
this overlay is then subsequently scored using the sum of shape tanimoto for the overlay and the color score called tanimoto combo score .
we use cs to refer the n by n chemical compounds similarity matrix . for the 727 drugs we used different chemical descriptors to calculate the tanimoto similarity distribution to create a view of 

1 shows that for four fingerprints ( 166 maccs keys , phfp4 , 3d rocs , and ecfp6 ) , 0.56% had a similarity above 0.7 for the maccs keys , 0.31% had similarity above 0.4 for phfp4 , 0.88% had similarity above 1.2 tanimoto combo score for rocs , 0.24% had similarity above 0.3 for ecfp6 .
the mean similarity is 0.346 , 0.019 , 0.742 , and 0.063 for maccs , phfp4 , rocs , ecfp6 fingerprints , respectively .
this indicates how diverse chemical structures are in the drug dataset ( additional file 2).fig . 
1plots showing the compounds similarity distributions according to the four types of chemical fingerprints . a rocs similarity , b phfp4 similarity , c maccs similarity , d ecfp similarity .
plots showing the compounds similarity distributions according to the four types of chemical fingerprints . a rocs similarity ,
we extracted 3,519 target proteins across all available species and their sequences from the drugbank database .
as proteins in other species may provide useful information in our network - based approach , we keep all the proteins regardless of species . note
we calculate the sequence similarity matrix ts by using the r biostrings package and the normalization procedure proposed by bleakley and yamanishi : 1\documentclass[12pt]{minimal } 
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				 \begin{document}$$ t_{s } = \frac{{sw\left ( { g , g^ { ' } } \right)}}{{\sqrt { sw\left ( { g , g } \right ) } \sqrt { sw\left ( { g^ { ' } , g^ { ' } } \right ) } } } , $ $ \end{document}ts = swg , gswg , gswg,g,where sw (  ,  ) means the original smith  waterman similarity score .
we construct a drug - target relationship matrix a whose element a(i , j ) is 1 if drug i interacts with target j , otherwise 0 . the matrix is sparse ; the total number of connections among the drugs and targets is only 2,557 , with 687 drugs having at least one known target and with 628 proteins having at least one drug .
2a ) that affect nervous systems mostly psychoanaleptics and psycholeptics have the largest number of interactions . as most drugs are metabolized by cytochrome p450 , which serves as an important protein target and enzyme for the drugs , the interaction between important enzymes cyp3a4 , cyp2d6 and cyp3a5 are not considered on the drug target interaction matrix except for the drug paliperidone , which has interactions to all the three cytochromes targets mentioned above.fig .  2 
 a drugs with the most target associations and b targets with the most drug associations . 
 a drugs with the most target associations and b targets with the most drug associations .
the top frequent targets are muscarinic receptor ( acm1 ) , adrenoreceptor alpha 1a ( ada1a ) , histamine receptors ( 5ht2a ) , and dopamine receptors ( drd2 ) . in addition to the drug  drug similarity matrix cs ( based on chemical similarity ) and target  target similarity matrix ts ( based on sequence similarity ) , we introduce additional measure of drug  drug and target  target similarities based on the network structure .
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				 \begin{document}$$ c_{s}^{n } $ $ \end{document}csn is a drug  drug similarity matrix based on the number of shared targets between drugs ; \documentclass[12pt]{minimal } 
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				 \begin{document}$$ t_{s}^{n } $ $ \end{document}tsn is a target  target similarity matrix based on the shared drugs .
the similarity between two drugs di and dj is quantified by jaccard coefficient , which is defined by:2\documentclass[12pt]{minimal } 
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				 \begin{document}$$ c_{s}^{n } ( d_{i } , d_{j } ) = \frac{{m_{l } ( i , j)}}{{m_{l } \left ( { i , i } \right ) + m_{l } \left ( { j , j } \right ) - m_{l } ( i , j ) } } , $ $ \end{document}csn(di , dj)=ml(i , j)mli , i+mlj , j - ml(i , j),where ml is the inner product of the drug  target interaction matrix .
we define the final drug  drug similarity matrix sd by taking a linear combination of the chemical similarity matrix ( cs ) and target sharing similarity matrix ( \documentclass[12pt]{minimal } 
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				 \begin{document}$$ c_{s}^{n } $ $ \end{document}csn ) .
similarly , the final target  target similarity matrix st is calculated using the sequence similarity matrix ( ts ) and drug sharing similarity matrix \documentclass[12pt]{minimal } 
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				 \begin{document}$$ ( t_{s}^{n } ) $ $ \end{document}(tsn).3\documentclass[12pt]{minimal } 
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				 \begin{document}$$ { s_{d } = \ , w_{d } c_{s } + \ , \left ( { 1 - w_{d } } \right)c_{s}^{n } } $ $ \end{document}sd = wdcs+1-wdcsn4\documentclass[12pt]{minimal } 
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				 \begin{document}$$ s_{t } = \ , w_{t } t_{s } + \ , \left ( { 1 - w_{t } } \right)t_{s}^{n } $ $ \end{document}st = wtts+1-wttsn we combined drug 
drug , drug  target , and target  target networks into a undirected heterogeneous network .
many nodes have connections to both drugs and targets and we call them bridge nodes . at a bridge node , a random walker may jump to a node with the other type or to a node with the same type .
for instance , if a random walker is at a drug node , it can jump to one of the connected target nodes with the probability  , or jump to connected drug nodes with the probability 1    . we call the parameter  the jumping probability .
if  is 0 , a random walker will explore only one type of networks .
most importantly , the probability p(i ) is the probability of finding the random walker at node i in the steady state .
it gives a measure of probability of source and target node ( proximity ) between node i and the source nodes where the random walks restarts .
the transition matrix is represented by,\documentclass[12pt]{minimal } 
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				 \begin{document}$$ w = \left [ { \begin{array}{*{20}c } { w_{tt } } & { w_{td } } \\ { w_{td } } & { w_{dd } } \\ \end{array } } \right ] $ $ \end{document}w = wttwtdwtdwddhere wtt is the target to target transition matrix , wdd is the drug to drug transition matrix , wdt is drug to target transition matrix and wtd is target to drug transition matrix .
the calculation of each of the transition matrix in discussed in chen et al . .
( 5 ) given below5\documentclass[12pt]{minimal } 
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				 \begin{document}$$ p_{t + 1 } = \ , \left ( { 1 - c } \right)w^{t } p_{t } + \ , cp_{0 } $ $ \end{document}pt+1=1-cwtpt+cp0pt is a vector in which ith elements holds the probability of finding the random walker at node i at time step t. initial probability vector p0 controls the restart probability c.6\documentclass[12pt]{minimal } 
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				 \begin{document}$$ p_{0 } = \left [ { \begin{array}{*{20}c } { ( 1 - \eta ) u_{0 } } \\ { \eta v_{0 } } \\ \end{array } } \right]\left ( { \text{initial probability matrix } } \right ) $ $ \end{document}p0=(1-)u0v0initial probability matrixu0 and v0 be the initial probability vectors for target network and drug network , respectively .
parameter  controls the importance of two kinds of seed nodes , i.e. drug node and target node .
we tested the importance parameter \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta $ $ \end{document} for different values ranging from 0 to 1 .
after a number of iteration steps , the pt converges to a steady - state probability vector p , where \documentclass[12pt]{minimal } 
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				 \begin{document}$$ p_{\infty } = \left [ { \begin{array}{*{20}c } { u_{\infty } } \\ { v_{\infty } } \\
\end{array } } \right ] $ $ \end{document}p=uv. in practice , we consider pt  =  p if the change between pt and pt  +  1 ( measure by the frobenius norm ) is less than 10 . for finding novel targets for a given drug
, we set the drug and the targets that are directly connected to the drug as our seed nodes .
we set t2 , t3 , and d3 as the source nodes , namely u0  =   and v0  =   the stationary probability p represents the expected relevance of each drugs and targets regarding the source node set t2 , t3 and d3 . for instance , if the value for t1 is the largest among t1 , t4 and t5 , then we expect that t1 is most likely to interact with d3 .
we compile a set of approved drugs from drugbank database ( version 3.0 ) , consisting of 727 compounds and 3519 protein targets ( additional file 1 ) . to construct the network between drugs ,
we incorporate two types of similarity measures : chemical ( structural ) similarity and target similarity .
we calculate chemical similarity between drugs by using the jaccard index ( tanimoto coefficient ) between their chemical fingerprints .
the jaccard index is defined as the size of the intersection of two sets divided by the size of the union of the sets , ranging between 0 and 1 . for binary vectors like chemical fingerprints , it is defined as c/(a  +  b    c ) where c is the number of bits in common , a is the number of bits in one of the fingerprints , and b is the number of bits in the other fingerprint .
we use four types of chemical features namely , mdl maccs166 keys ( fragmental descriptors ) , ecfp6 fingerprints ( extended connectivity fingerprint path 6 ) , 2d pharmacophore fingerprints ( phfp4 )   and rocs program which uses tanimoto combo similarity  which combines shape and color measures of a compound , we calculate them with rocs program .
ecfp ( extended connectivity fingerprint ) encodes information on atom - centered fragments that is derived from the variant of the morgan algorithm .
ecfps are generated using the neighborhood of each non - hydrogen atom into multiple circular layers up to a given diameter .
these atom - centric substructural features are then mapped into integer codes using a hashing procedure , which constitute the extended - connectivity fingerprint .
ecfp can , for instance , represent a very large number of features ( over 4 billion ) , do not rely on predefined dictionary of features , can represent stereochemical information , and can be interpreted as the presence of particular substructures .
pharmacophore fingerprints consist of pairs , triplets , or quartets of molecular features and the corresponding bond distances among them .
we use phfp_4 ( quartets which includes number of bonds in the shortest path between the features ) fingerprints for the calculation .
the feature vectors of quartets involve four pharmacophoric features , six euclidean distances separating those features , and an indication of chirality . for 3d alignment and similarity
we used rocs 3.2 , which is a shape - similarity method based on the tanimoto - like overlap of volumes .
the alignment was developed using the combo score , which combines the tanimoto shape score with the color score that added the score for the appropriate overlap of groups with similar properties ( donor , acceptor , hydrophobe , cation , anion , and ring ) [ http://docs.eyesopen.com/rocs/shape_theory.html ] defined by smarts .
conformers for the data set is created using omega , about 250 conformers with rmsd threshold of 0.6 is generated .
rocs score performed in color optimization mode where it optimizes the molecular overlay to maximize both the shape overlap and the color overlap obtained by aligning groups with the same properties that are contained in the color force field file .
this overlay is then subsequently scored using the sum of shape tanimoto for the overlay and the color score called tanimoto combo score .
we use cs to refer the n by n chemical compounds similarity matrix . for the 727 drugs we used different chemical descriptors to calculate the tanimoto similarity distribution to create a view of 

1 shows that for four fingerprints ( 166 maccs keys , phfp4 , 3d rocs , and ecfp6 ) , 0.56% had a similarity above 0.7 for the maccs keys , 0.31% had similarity above 0.4 for phfp4 , 0.88% had similarity above 1.2 tanimoto combo score for rocs , 0.24% had similarity above 0.3 for ecfp6 .
the mean similarity is 0.346 , 0.019 , 0.742 , and 0.063 for maccs , phfp4 , rocs , ecfp6 fingerprints , respectively .
this indicates how diverse chemical structures are in the drug dataset ( additional file 2).fig . 
1plots showing the compounds similarity distributions according to the four types of chemical fingerprints . a rocs similarity , b phfp4 similarity , c maccs similarity , d ecfp similarity .
plots showing the compounds similarity distributions according to the four types of chemical fingerprints . a rocs similarity , b phfp4 similarity , c maccs similarity , d ecfp similarity .
we extracted 3,519 target proteins across all available species and their sequences from the drugbank database .
as proteins in other species may provide useful information in our network - based approach , we keep all the proteins regardless of species . note
we calculate the sequence similarity matrix ts by using the r biostrings package and the normalization procedure proposed by bleakley and yamanishi : 1\documentclass[12pt]{minimal } 
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				 \begin{document}$$ t_{s } = \frac{{sw\left ( { g , g^ { ' } } \right)}}{{\sqrt { sw\left ( { g , g } \right ) } \sqrt { sw\left ( { g^ { ' } , g^ { ' } } \right ) } } } , $ $ \end{document}ts = swg , gswg , gswg,g,where sw (  ,  ) means the original smith  waterman similarity score .
we construct a drug - target relationship matrix a whose element a(i , j ) is 1 if drug i interacts with target j , otherwise 0 .
the matrix is sparse ; the total number of connections among the drugs and targets is only 2,557 , with 687 drugs having at least one known target and with 628 proteins having at least one drug .
2a ) that affect nervous systems mostly psychoanaleptics and psycholeptics have the largest number of interactions . as most drugs are metabolized by cytochrome p450 , which serves as an important protein target and enzyme for the drugs , the interaction between important enzymes cyp3a4 , cyp2d6 and cyp3a5 are not considered on the drug target interaction matrix except for the drug paliperidone , which has interactions to all the three cytochromes targets mentioned above.fig .  2 
 a drugs with the most target associations and b targets with the most drug associations . 
 a drugs with the most target associations and b targets with the most drug associations .
the top frequent targets are muscarinic receptor ( acm1 ) , adrenoreceptor alpha 1a ( ada1a ) , histamine receptors ( 5ht2a ) , and dopamine receptors ( drd2 ) .
in addition to the drug  drug similarity matrix cs ( based on chemical similarity ) and target  target similarity matrix ts ( based on sequence similarity ) , we introduce additional measure of drug  drug and target  target similarities based on the network structure .
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				 \begin{document}$$ c_{s}^{n } $ $ \end{document}csn is a drug  drug similarity matrix based on the number of shared targets between drugs ; \documentclass[12pt]{minimal } 
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				 \begin{document}$$ t_{s}^{n } $ $ \end{document}tsn is a target  target similarity matrix based on the shared drugs .
the similarity between two drugs di and dj is quantified by jaccard coefficient , which is defined by:2\documentclass[12pt]{minimal } 
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				 \begin{document}$$ c_{s}^{n } ( d_{i } , d_{j } ) = \frac{{m_{l } ( i , j)}}{{m_{l } \left ( { i , i } \right ) + m_{l } \left ( { j , j } \right ) - m_{l } ( i , j ) } } , $ $ \end{document}csn(di , dj)=ml(i , j)mli , i+mlj , j - ml(i , j),where ml is the inner product of the drug  target interaction matrix .
we define the final drug  drug similarity matrix sd by taking a linear combination of the chemical similarity matrix ( cs ) and target sharing similarity matrix ( \documentclass[12pt]{minimal } 
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				 \begin{document}$$ c_{s}^{n } $ $ \end{document}csn ) .
similarly , the final target  target similarity matrix st is calculated using the sequence similarity matrix ( ts ) and drug sharing similarity matrix \documentclass[12pt]{minimal } 
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				 \begin{document}$$ { s_{d } = \ , w_{d } c_{s } + \ , \left ( { 1 - w_{d } } \right)c_{s}^{n } } $ $ \end{document}sd = wdcs+1-wdcsn4\documentclass[12pt]{minimal } 
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				 \begin{document}$$ s_{t } = \ , w_{t } t_{s } + \ , \left ( { 1 - w_{t } } \right)t_{s}^{n } $ $ \end{document}st = wtts+1-wttsn
we compile a set of approved drugs from drugbank database ( version 3.0 ) , consisting of 727 compounds and 3519 protein targets ( additional file 1 ) . to construct the network between drugs ,
we incorporate two types of similarity measures : chemical ( structural ) similarity and target similarity .
we calculate chemical similarity between drugs by using the jaccard index ( tanimoto coefficient ) between their chemical fingerprints .
the jaccard index is defined as the size of the intersection of two sets divided by the size of the union of the sets , ranging between 0 and 1 . for binary vectors like chemical fingerprints , it is defined as c/(a  +  b    c ) where c is the number of bits in common , a is the number of bits in one of the fingerprints , and b is the number of bits in the other fingerprint .
we use four types of chemical features namely , mdl maccs166 keys ( fragmental descriptors ) , ecfp6 fingerprints ( extended connectivity fingerprint path 6 ) , 2d pharmacophore fingerprints ( phfp4 )   and rocs program which uses tanimoto combo similarity  which combines shape and color measures of a compound , we calculate them with rocs program .
ecfp ( extended connectivity fingerprint ) encodes information on atom - centered fragments that is derived from the variant of the morgan algorithm .
ecfps are generated using the neighborhood of each non - hydrogen atom into multiple circular layers up to a given diameter .
these atom - centric substructural features are then mapped into integer codes using a hashing procedure , which constitute the extended - connectivity fingerprint .
ecfp can , for instance , represent a very large number of features ( over 4 billion ) , do not rely on predefined dictionary of features , can represent stereochemical information , and can be interpreted as the presence of particular substructures .
pharmacophore fingerprints consist of pairs , triplets , or quartets of molecular features and the corresponding bond distances among them .
we use phfp_4 ( quartets which includes number of bonds in the shortest path between the features ) fingerprints for the calculation .
the feature vectors of quartets involve four pharmacophoric features , six euclidean distances separating those features , and an indication of chirality . for 3d alignment and similarity
we used rocs 3.2 , which is a shape - similarity method based on the tanimoto - like overlap of volumes .
the alignment was developed using the combo score , which combines the tanimoto shape score with the color score that added the score for the appropriate overlap of groups with similar properties ( donor , acceptor , hydrophobe , cation , anion , and ring ) [ http://docs.eyesopen.com/rocs/shape_theory.html ] defined by smarts .
conformers for the data set is created using omega , about 250 conformers with rmsd threshold of 0.6 is generated .
rocs score performed in color optimization mode where it optimizes the molecular overlay to maximize both the shape overlap and the color overlap obtained by aligning groups with the same properties that are contained in the color force field file .
this overlay is then subsequently scored using the sum of shape tanimoto for the overlay and the color score called tanimoto combo score .
we use cs to refer the n by n chemical compounds similarity matrix . for the 727 drugs we used different chemical descriptors to calculate the tanimoto similarity distribution to create a view of 

1 shows that for four fingerprints ( 166 maccs keys , phfp4 , 3d rocs , and ecfp6 ) , 0.56% had a similarity above 0.7 for the maccs keys , 0.31% had similarity above 0.4 for phfp4 , 0.88% had similarity above 1.2 tanimoto combo score for rocs , 0.24% had similarity above 0.3 for ecfp6 .
the mean similarity is 0.346 , 0.019 , 0.742 , and 0.063 for maccs , phfp4 , rocs , ecfp6 fingerprints , respectively .
this indicates how diverse chemical structures are in the drug dataset ( additional file 2).fig . 
1plots showing the compounds similarity distributions according to the four types of chemical fingerprints . a rocs similarity , b phfp4 similarity , c maccs similarity , d ecfp similarity .
plots showing the compounds similarity distributions according to the four types of chemical fingerprints . a rocs similarity , b phfp4 similarity , c maccs similarity , d ecfp similarity .
we extracted 3,519 target proteins across all available species and their sequences from the drugbank database .
as proteins in other species may provide useful information in our network - based approach , we keep all the proteins regardless of species .
we calculate the sequence similarity matrix ts by using the r biostrings package and the normalization procedure proposed by bleakley and yamanishi : 1\documentclass[12pt]{minimal } 
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				 \begin{document}$$ t_{s } = \frac{{sw\left ( { g , g^ { ' } } \right)}}{{\sqrt { sw\left ( { g , g } \right ) } \sqrt { sw\left ( { g^ { ' } , g^ { ' } } \right ) } } } , $ $ \end{document}ts = swg , gswg , gswg,g,where sw (  ,  ) means the original smith  waterman similarity score .
we construct a drug - target relationship matrix a whose element a(i , j ) is 1 if drug i interacts with target j , otherwise 0 .
the matrix is sparse ; the total number of connections among the drugs and targets is only 2,557 , with 687 drugs having at least one known target and with 628 proteins having at least one drug .
2a ) that affect nervous systems mostly psychoanaleptics and psycholeptics have the largest number of interactions . as most drugs are metabolized by cytochrome p450 , which serves as an important protein target and enzyme for the drugs , the interaction between important enzymes cyp3a4 , cyp2d6 and cyp3a5 are not considered on the drug target interaction matrix except for the drug paliperidone , which has interactions to all the three cytochromes targets mentioned above.fig .  2 
 a drugs with the most target associations and b targets with the most drug associations . 
 a drugs with the most target associations and b targets with the most drug associations .
the top frequent targets are muscarinic receptor ( acm1 ) , adrenoreceptor alpha 1a ( ada1a ) , histamine receptors ( 5ht2a ) , and dopamine receptors ( drd2 ) . in addition to the drug  drug similarity matrix cs ( based on chemical similarity ) and target  target similarity matrix ts ( based on sequence similarity ) , we introduce additional measure of drug  drug and target  target similarities based on the network structure .
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				 \begin{document}$$ c_{s}^{n } $ $ \end{document}csn is a drug  drug similarity matrix based on the number of shared targets between drugs ; \documentclass[12pt]{minimal } 
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				 \begin{document}$$ t_{s}^{n } $ $ \end{document}tsn is a target  target similarity matrix based on the shared drugs .
the similarity between two drugs di and dj is quantified by jaccard coefficient , which is defined by:2\documentclass[12pt]{minimal } 
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				 \begin{document}$$ c_{s}^{n } ( d_{i } , d_{j } ) = \frac{{m_{l } ( i , j)}}{{m_{l } \left ( { i , i } \right ) + m_{l } \left ( { j , j } \right ) - m_{l } ( i , j ) } } , $ $ \end{document}csn(di , dj)=ml(i , j)mli , i+mlj , j - ml(i , j),where ml is the inner product of the drug  target interaction matrix .
we define the final drug  drug similarity matrix sd by taking a linear combination of the chemical similarity matrix ( cs ) and target sharing similarity matrix ( \documentclass[12pt]{minimal } 
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				 \begin{document}$$ c_{s}^{n } $ $ \end{document}csn ) .
similarly , the final target  target similarity matrix st is calculated using the sequence similarity matrix ( ts ) and drug sharing similarity matrix \documentclass[12pt]{minimal } 
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				 \begin{document}$$ ( t_{s}^{n } ) $ $ \end{document}(tsn).3\documentclass[12pt]{minimal } 
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				 \begin{document}$$ { s_{d } = \ , w_{d } c_{s } + \ , \left ( { 1 - w_{d } } \right)c_{s}^{n } } $ $ \end{document}sd = wdcs+1-wdcsn4\documentclass[12pt]{minimal } 
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				 \begin{document}$$ s_{t } = \ , w_{t } t_{s } + \ , \left ( { 1 - w_{t } } \right)t_{s}^{n } $ $ \end{document}st = wtts+1-wttsn
many nodes have connections to both drugs and targets and we call them bridge nodes . at a bridge node , a random walker may jump to a node with the other type or to a node with the same type .
for instance , if a random walker is at a drug node , it can jump to one of the connected target nodes with the probability  , or jump to connected drug nodes with the probability 1    . we call the parameter  the jumping probability .
if  is 0 , a random walker will explore only one type of networks .
most importantly , the probability p(i ) is the probability of finding the random walker at node i in the steady state .
it gives a measure of probability of source and target node ( proximity ) between node i and the source nodes where the random walks restarts .
the transition matrix is represented by,\documentclass[12pt]{minimal } 
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				 \begin{document}$$ w = \left [ { \begin{array}{*{20}c } { w_{tt } } & { w_{td } } \\ { w_{td } } & { w_{dd } } \\ \end{array } } \right ] $ $ \end{document}w = wttwtdwtdwddhere wtt is the target to target transition matrix , wdd is the drug to drug transition matrix , wdt is drug to target transition matrix and wtd is target to drug transition matrix .
the calculation of each of the transition matrix in discussed in chen et al . .
( 5 ) given below5\documentclass[12pt]{minimal } 
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				 \begin{document}$$ p_{t + 1 } = \ , \left ( { 1 - c } \right)w^{t } p_{t } + \ , cp_{0 } $ $ \end{document}pt+1=1-cwtpt+cp0pt is a vector in which ith elements holds the probability of finding the random walker at node i at time step t. initial probability vector p0 controls the restart probability c.6\documentclass[12pt]{minimal } 
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				 \begin{document}$$ p_{0 } = \left [ { \begin{array}{*{20}c } { ( 1 - \eta ) u_{0 } } \\ { \eta v_{0 } } \\
\end{array } } \right]\left ( { \text{initial probability matrix } } \right ) $ $ \end{document}p0=(1-)u0v0initial probability matrixu0 and v0 be the initial probability vectors for target network and drug network , respectively .
parameter  controls the importance of two kinds of seed nodes , i.e. drug node and target node .
we tested the importance parameter \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta $ $ \end{document} for different values ranging from 0 to 1 .
after a number of iteration steps , the pt converges to a steady - state probability vector p , where \documentclass[12pt]{minimal } 
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				 \begin{document}$$ p_{\infty } = \left [ { \begin{array}{*{20}c } { u_{\infty } } \\ { v_{\infty } } \\
\end{array } } \right ] $ $ \end{document}p=uv. in practice , we consider pt  =  p if the change between pt and pt  +  1 ( measure by the frobenius norm ) is less than 10 . for finding novel targets for a given drug
, we set the drug and the targets that are directly connected to the drug as our seed nodes .
we set t2 , t3 , and d3 as the source nodes , namely u0  =   and v0  =   the stationary probability p represents the expected relevance of each drugs and targets regarding the source node set t2 , t3 and d3 . for instance , if the value for t1 is the largest among t1 , t4 and t5 , then we expect that t1 is most likely to interact with d3 .
we evaluated our approach using a perturbed network where we have removed some links to measure how well our approach re - identifies those removed links .
there are five parameter to explore : the restart probability c , the jumping probability  , the relative importance  , which controls the relative importance between two types of seeds , wd and wt that weigh the drug and target similarity matrices and network based similarity measure of the drugs and proteins , respectively . among these five parameters , we have tested  because , to our knowledge , the restart probability c , jumping probability  , and wd and wt are not likely to affect the results in a significant way .
first , it is known that in most cases the choice of restart probability c does not affect performance of pagerank algorithm and other pagerank - based algorithms .
for instance , the results of pagerank are highly insensitive to the choice of restart probability [ 14 , 15 ] .
it has been shown that the prediction results from rwr are also robust [ 7 , 1416 ] .
because of these evidences , we here simply adopt the previously used value of 0.3 .
second , the robustness of  ( jumping probability ) has already been discussed [ 1517 ] . it has been shown that the weight parameters wd and wt are robust among the prediction results . in our drug target network 684 ( 94% ) drugs have at least one target .
we prepare a test network of 684 drugs where we remove one links from 684 drugs with a total of 684 drug 
the links include drugs which has only one target in order to see if the method able to predict single known interaction .
we divide the number of actual targets that are in the top n lists by the number of tests ( 684 ) and call the fraction as 
recoveredfraction. we also used a random set to calculate the statistics with same parameters and found that the results are way better than random set .
we tested our results with different values of wd and wt ranging from 0 to 1 and found that at extreme point like 0 and 1 the performances drops radically but the performance gets best on values of wd and wt of 0.5 given in additional file 3 : sheet 3 .
we test different values of \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta $ $ \end{document} for the four different chemical fingerprints to identify the optimal value of \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta $ $ \end{document} and the right of chemical features .
we observed that the prediction performance becomes optimal when \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta $ $ \end{document} is small but not 0 .
we found optimal performance at \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta = 0.0 1 $ $ \end{document}=0.01 .
for all the other values of \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta \left ( { 0 .
9 } \right ) $ $ \end{document}0.1 - 0.9 the prediction rate for all fingerprints is equal .
we find nearly 28% of the true interactions out of 684 can be retrieved at the top 10 rank positions and more than 38% of the interactions can be retrieved at the top 50 rank positions .
we also prepare 10 test networks of drugs that have more than two targets links , where we randomly remove 1001,000 links . using the 10 test networks we predicted the removed links .
we repeat this process , from preparing a test network to calculating the recovered fraction , 50 times to obtain the 
average recovered fraction. from table  1 we can see that if we remove 100 links it gave us the best prediction rates and as we increase the number of removed links to 1,000 the prediction rates falls . from table  2
shows the recovered fraction rates for top 10 , 25 , 50 , 100 , 200 , 500 , 1,000 retrieved targets we also find almost 32% of the true interactions can be retrieved at the top 10 rank positions for each of the test networks and more than 75% of the true interactions can be retrieved at the top 50 rank positions .
this indicates that the method performs well if we remove links from drugs which are having at least two or more known interactions , since it uses the given interaction information in the network .
we also measured the area under accumulation curve , area under roc curve auc ( top 10% ) , bedroc and enrichment factor given in table  1 .
the area under the receiver operating characteristic ( roc ) curve ( auc ) is widely used to evaluate the performance of the ranking method .
the advantage of using auc is , the value ranges from 0 to 1 with 0.5 corresponding to randomness .
another key criterion for measuring the success of ranking prediction is the enrichment of annotated associations among top ranking associations .
the higher the percentage of annotated associations among the top ranking associations , the better the performance of the prediction .
the enrichment criterion is evaluated by enrichment factor ( ef ) [ 16 , 17 ] .
ef reflects the capability of a screening application to detect true links ( true positives ) compared to random selection .
thus , its value should always be greater than 1 and the higher it is , the better the enrichment performance . when we are predicting links it should rank true links in the top - ranking list .
metric likes roc not sensitive to early recognition for example considering cases like where ( 1 ) true links are retrieved at beginning of a rank ordered list , ( 2 ) where true links are randomly distributed and ( 3 ) where true links , which are retrieved in the middle of the rank , ordered list . in all of the above cases roc is 0.5 but in terms of early recognition we see that case ( 1 ) is better than ( 2 ) and ( 3 ) . to overcome these limitations methods such as rie and bedroc
, one can test whether the method is able to rank true links early or not.table  1shows the recovered fraction values for top 10 , 25 , 50 , 100 , 200 , 500 and 1,000 ranks with the number of links removednumber of links removedauacaucbedrocefauc ( top 10%)1000.9470.9910.8339.230.8672000.9380.9950.8279.1000.8573000.9300.9950.8188.950.8454000.9200.9910.8058.790.8305000.9160.9970.8018.710.8246000.9080.9950.7898.560.8127000.8990.9810.7808.420.8028000.8850.9970.7618.200.7839000.8690.9550.7417.910.7651,0000.8540.9560.7157.620.741table  2shows the recovered fraction values for top 10 , 25 , 50 , 100 , 200 , 500 and 1,000 ranks with the number of links removed # of links removedtop 10 ( % ) top 25 ( % ) top 50 ( % ) top 100 ( % ) top 200 ( % ) top 500 ( % ) top 1,000 ( % ) 10032.2478.2487.7690.7491.9293.2293.8820031.9277.9587.2689.8691.1592.3793.1230032.1478.3186.8289.4890.6891.8092.6340032.0477.485.3488.0789.2490.3391.4550032.6277.3985.0487.5688.7089.9591.160032.5376.2183.6886.2387.5488.8690.1670032.575.6482.6985.1886.5787.8989.3380033.0674.1380.8883.4584.8686.3587.9790033.5872.1478.4981.0482.7784.5786.381,00033.7169.8176.00878.3180.2282.1284.42 shows the recovered fraction values for top 10 , 25 , 50 , 100 , 200 , 500 and 1,000 ranks with the number of links removed shows the recovered fraction values for top 10 , 25 , 50 , 100 , 200 , 500 and 1,000 ranks with the number of links removed we found that the performance of the algorithm for ranking the targets by different chemical features is approximately same which indicates using this approach a user can identify protein targets with any one set of chemical features .
we used public 166 maccs keys , ecfp6 , phfp4 and 3d rocs to perform the analysis and it is surprising that the commercial programs feature performance is same as the 166 public maccs keys . as a baseline ,
we randomized the interactions and similarity matrices and performed rwr and found the random set prediction rate was way below our original prediction rate as given in additional file 3 : sheet 1 .
in addition to the internal evaluation using link perturbation approach , we evaluate the performance of our method using an external dataset , namely chembl version 15 database . from chembl 15 data we extract all the drugs and targets that have activity values not more than 1  m ( additional file 3 : sheet 4 ) and 10  m ( additional file 3 : sheet 4 ) with units ic50 , ki , kd , ec50 , ac50 , lc50 , and gi50 .
our training model is based on drugbank and uniprot database so we mapped the drugs and targets chembl ids with the drugbank ids and uniprot ids .
we used pubchem mapping tool ( http://pubchem.ncbi.nlm.nih.gov/idexchange/ ) to map chembl ids to drugbank ids and the uniprot mapping tool ( http://www.uniprot.org/?tab=mapping ) to map target chembl ids to uniprot ids .
it gives us 544 drugs and 467 protein targets , with 3,463 and 564 drug target interactions those are below 10 and 1  m , respectively .
naturally , there are lots of interactions that are present in both drugbank and chembl .
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				 \begin{document}$$ \eta $ $ \end{document} at different values on chembl 1  m set and 10  m having which have more than 0 , 1 and 2 target relations .
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				 \begin{document}$$ \eta $ $ \end{document} ( eta ) values for chembl datat at 1 and 10  m cutoff with different fingerprints respectively.fig . 
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				 \begin{document}$$ \eta $ $ \end{document} ( eta ) values for chembl datat at 1  m cutoff .
the recovered fraction is calculated by the number of targets retrieved at different rank positions over total number true interactions .
a maccs , b phfp4 , c rocs , d ecfp4.fig .  4showing the recovered fractions against the rank with different \documentclass[12pt]{minimal } 
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the recovered fraction is calculated by the number of targets retrieved at different rank positions over total number true interactions .
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				 \begin{document}$$ \eta $ $ \end{document} ( eta ) values for chembl datat at 1  m cutoff .
the recovered fraction is calculated by the number of targets retrieved at different rank positions over total number true interactions .
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				 \begin{document}$$ \eta $ $ \end{document} ( eta ) values for chembl data at 10  m cutoff .
the recovered fraction is calculated by the number of targets retrieved at different rank positions over total number true interactions .
a maccs , b phfp4 , c rocs , d ecfp4 . from tables  3 and 4
we observe that rwr performance is better for 1  m target than 10  m because at 10  m we have lots off targets from different classes and as a result of that the prediction rate falls .
for chembl 1  m dataset , drugs having more than 0 , 1 and 2 targets we achieve bedroc score of 0.433 , 0.553 and 0.611 , respectively , which is much better than a random set of interactions . to test whether random walk performs better than just a simple sequence similarity search we took the approved drugs and it s known targets from the chembl 10  m dataset and performed sequence similarity based sech against 3,519 targets and ranked them . we found rwr performance is way better in ranking targets than performing simple sequence based search .
this is the first time that the random walk - based method is evaluated using a binding assay dataset ( cf . [ 3 , 5]).table  3shows the types of data we used the drug target interaction having more than 1 and 2 drug interactions , area under the accumulated curve ( auac ) , area under the roc curve ( auc ) , bedroc and , enrichment factor ( ef ) and auc top 10%data typesnumber of targetsauac ( % ) auc ( % ) bedrocefauc ( top 10%)chembl 1 m ( rwr)>00.7090.9950.4335.0580.455chembl 1 m ( seq)>00.6700.6700.3964.480.414chembl 1 m ( random rwr)>00.4940.4930.0751.0900.079chembl 10 m ( rwr)>00.5960.8370.3233.8650.351chembl 10 m ( seq)>00.5180.5180.2372.6410.2555chembl 10 m ( random rwr)>00.3940.3640.0360.9540.029chembl 1 m ( rwr)>10.7840.7840.5536.2860.569chembl 1 m ( seq)>10.6520.6510.3904.5070.412chembl 1 m ( random rwr)>10.4830.4830.0811.2900.083chembl 10 m ( rwr)>10.6130.610.3534.0910.378chembl 10 m ( seq)>10.5510.5520.2793.0840.300chembl 10 m ( random rwr)>10.5140.5140.0751.2440.088chembl 1 m ( rwr)>20.8230.8240.6116.8660.631chembl 1 m ( seq)>20.7010.7050.5135.1090.469chembl 1 m>20.5330.5330.06711.4650.065chembl 10 m ( rwr)>20.6320.6330.3994.5690.422chembl 10 m ( seq)>20.5690.5690.2983.030.315chembl 10 m ( random rwr)>20.5210.5210.2621.950.125table  4shows the types of data we used the drug target interaction having more than 1 and 2 drug interactions and sensitivity ( hit rate ) at top 10 , 25 , 50 , 100 and 200 predicted targetsdata typesnumber of targetstop 10 ( % ) top 25 ( % ) top 50 ( % ) top 100 ( % ) top 200 ( % ) chembl 1  m ( rwr)>00.1440.3420.4700.5320.607chembl 1  m ( seq)>00.1640.3150.3940.4200.430chembl 1  m ( random rwr)>00.0020.0130.0180.0360.021chembl 10  m ( rwr)>00.110.2470.3240.3860.409chembl 10  m ( seq)>00.1220.1830.2340.2490.254chembl 10  m ( random rwr)>00.0140.0230.0350.0480.079chembl 1  m ( rwr)>10.2740.4770.5500.5800.614chembl 1  m ( seq)>10.1890.3500.4280.4720.513chembl 1  m ( random rwr)>10.0070.0230.0380.0760.091chembl 10  m ( rwr)>10.2200.2770.3480.4170.446chembl 10  m ( seq)>10.130.2120.2760.2960.302chembl 10  m ( random rwr)>10.0140.0230.0350.0480.079chembl 1  m ( rwr)>20.2710.5180.5980.6340.677chembl 1  m ( seq)>20.190.3930.530.560.598chembl 1  m>20.0060.0180.0340.0550.08chembl 10  m ( rwr)>20.2330.2970.3530.42990.472chembl 10  m ( seq)>20.130.220.2950.3160.324chembl 10  m ( random rwr)>20.0120.0280.0400.0570.093 shows the types of data we used the drug target interaction having more than 1 and 2 drug interactions , area under the accumulated curve ( auac ) , area under the roc curve ( auc ) , bedroc and , enrichment factor ( ef ) and auc top 10% shows the types of data we used the drug target interaction having more than 1 and 2 drug interactions and sensitivity ( hit rate ) at top 10 , 25 , 50 , 100 and 200 predicted targets here , as a case study we investigate the target profiles of the popular top selling drugs in 2012 .
first , we consider \documentclass[12pt]{minimal } 
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				 \begin{document}$$ u_{\infty } , $ $ \end{document}u , the steady - state probability vector for the targets in our framework , as  target profile of a drug .
we find that some targets are associated with many drugs ( see table  5 ) .
for instance , adrenoceptor alpha 1a appears in 60% of drug s top 10 target association lists ; serotonin receptor 5ht2a appear in 43% ; and adrenoceptor alpha 1b in 35% .
most drugs shown on the table  5 mostly belong to the rhodopsin class of gpcr s . in additional file 4 ,
5 shows a bipartite network of 110 drugs with top 10 predicted targets for each drug.table  5the top 10 associated targets of 110 drugs with true percentage of associated target before prediction and predicted percentage of associationtargetspercentage of drugs associated with the targets based on drugbank and chembl ( % ) percentage of drug associations appearing in top-10 target list in our prediction ( % ) 
 ada1a 
 7.2760 
 5ht2a 
 4.5443.63 
 ada1b 
 7.2735.45 
 5ht1a 
 4.5433.63 
 adrb1 
 5.4531.81 
 5ht1b 
 5.4530.90 
 5ht2c 
 3.6330 
 acm2 
 9.0926.36 
 5ht3a 
 4.5425.45 

the size and label of the target nodes is proportional to the degree of the nodes .
the top 10 associated targets of 110 drugs with true percentage of associated target before prediction and predicted percentage of association shows the network of the top 10 predicted targets of 110 drugs .
the size and label of the target nodes is proportional to the degree of the nodes .
we took some random drugs and tried to find known binding associations to protein targets .
we searched three databases chembl , pdsp , and pubchem   using the binding coefficients like ic50 and ki .
further investigation may have significant values on understanding side effects of existing drugs as well as repurposing them.table  6drug target interactions with association values from different databasesproteindrugsourceactivity tpeactivity m 
 5ht2a 
 carvedilolpubchem aid 625192ic500.41 
 5ht2a 
 desloratadinepubchem aid 625192ic500.033 
 kcnh2 
 lidocainechemblic50263.02 
 adrb1 
 salmetorolchemblic500.501 

5ht1a 
 amphetaminepdsp databaseki6.6 
 hdac2 
 atorvastatinchemblic5022.5 
 ada1a 
 duloxentinepdspki10 
 acm1 
 montelukastpubchem aid 625153ic508.045 
 sc6a4 
 quetiapinepdspki10 drug target interactions with association values from different databases finally , let us summarize the contributions of this paper .
first , we offer a general approach that takes the whole drug target network into account without separating protein categories , in contrast to the previous study .
the number of interactions between drugs and targets is 2,557 , which makes 684 drugs to have at least one known target and 457 drugs to have two or more interactions .
the proteins in the dataset are grouped under 15 different categories according to chembl target classifications ( https://www.ebi.ac.uk/chembl/target/browser ) . out of 3,519 proteins , 1,386 proteins
the number of drugs that have at least two interactions with proteins that are categorized is 412 . among these 412 drugs ,
the number of drugs that have interactions with proteins from multiple groups is 169 . in other words
, we estimate that about 40% of drugs have interactions across multiple groups according chembl dataset .
therefore , it is more reasonable to consider all proteins together , rather than running the prediction model separately for each category .
second , we further investigate the methodology by presenting a benchmark of a parameter  in conjunction with the four chemical fingerprint types : maccs 166 keys , ecfp6 fingerprints , phfp4 fingerprints , and rocs . in the previous study
, the parameter space of  is not explored below 0.1 , but we find that we can improve the performance by decreasing eta below 0.1 .
we also find that the performance is robust under the choice of chemical fingerprinting method , particularly when  is around the optimum ( ~0.01 ) .
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				 \begin{document}$$ \eta $ $ \end{document} eta means the walk in the target network is much more important than the walk on the drug  drug network . in a sense
we evaluated our approach using a perturbed network where we have removed some links to measure how well our approach re - identifies those removed links .
there are five parameter to explore : the restart probability c , the jumping probability  , the relative importance  , which controls the relative importance between two types of seeds , wd and wt that weigh the drug and target similarity matrices and network based similarity measure of the drugs and proteins , respectively . among these five parameters , we have tested  because , to our knowledge , the restart probability c , jumping probability  , and wd and wt are not likely to affect the results in a significant way .
first , it is known that in most cases the choice of restart probability c does not affect performance of pagerank algorithm and other pagerank - based algorithms .
for instance , the results of pagerank are highly insensitive to the choice of restart probability [ 14 , 15 ] .
it has been shown that the prediction results from rwr are also robust [ 7 , 1416 ] .
because of these evidences , we here simply adopt the previously used value of 0.3 .
second , the robustness of  ( jumping probability ) has already been discussed [ 1517 ] . it has been shown that the weight parameters wd and wt are robust among the prediction results . in our drug target network 684 ( 94% ) drugs have at least one target .
we prepare a test network of 684 drugs where we remove one links from 684 drugs with a total of 684 drug 
the links include drugs which has only one target in order to see if the method able to predict single known interaction .
we divide the number of actual targets that are in the top n lists by the number of tests ( 684 ) and call the fraction as 
recoveredfraction. we also used a random set to calculate the statistics with same parameters and found that the results are way better than random set .
we tested our results with different values of wd and wt ranging from 0 to 1 and found that at extreme point like 0 and 1 the performances drops radically but the performance gets best on values of wd and wt of 0.5 given in additional file 3 : sheet 3 .
we test different values of \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta $ $ \end{document} for the four different chemical fingerprints to identify the optimal value of \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta $ $ \end{document} and the right of chemical features .
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				 \begin{document}$$ \eta $ $ \end{document} is small but not 0 .
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for all the other values of \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta \left ( { 0 .
9 } \right ) $ $ \end{document}0.1 - 0.9 the prediction rate for all fingerprints is equal .
we find nearly 28% of the true interactions out of 684 can be retrieved at the top 10 rank positions and more than 38% of the interactions can be retrieved at the top 50 rank positions .
we also prepare 10 test networks of drugs that have more than two targets links , where we randomly remove 1001,000 links . using the 10 test networks we predicted the removed links .
we repeat this process , from preparing a test network to calculating the recovered fraction , 50 times to obtain the 
average recovered fraction. from table  1 we can see that if we remove 100 links it gave us the best prediction rates and as we increase the number of removed links to 1,000 the prediction rates falls . from table  2
shows the recovered fraction rates for top 10 , 25 , 50 , 100 , 200 , 500 , 1,000 retrieved targets we also find almost 32% of the true interactions can be retrieved at the top 10 rank positions for each of the test networks and more than 75% of the true interactions can be retrieved at the top 50 rank positions .
this indicates that the method performs well if we remove links from drugs which are having at least two or more known interactions , since it uses the given interaction information in the network .
we also measured the area under accumulation curve , area under roc curve auc ( top 10% ) , bedroc and enrichment factor given in table  1 .
the area under the receiver operating characteristic ( roc ) curve ( auc ) is widely used to evaluate the performance of the ranking method .
the advantage of using auc is , the value ranges from 0 to 1 with 0.5 corresponding to randomness .
another key criterion for measuring the success of ranking prediction is the enrichment of annotated associations among top ranking associations .
the higher the percentage of annotated associations among the top ranking associations , the better the performance of the prediction .
the enrichment criterion is evaluated by enrichment factor ( ef ) [ 16 , 17 ] .
ef reflects the capability of a screening application to detect true links ( true positives ) compared to random selection .
thus , its value should always be greater than 1 and the higher it is , the better the enrichment performance . when we are predicting links it should rank true links in the top - ranking list .
metric likes roc not sensitive to early recognition for example considering cases like where ( 1 ) true links are retrieved at beginning of a rank ordered list , ( 2 ) where true links are randomly distributed and ( 3 ) where true links , which are retrieved in the middle of the rank , ordered list . in all of the above cases roc is 0.5 but in terms of early recognition we see that case ( 1 ) is better than ( 2 ) and ( 3 ) . to overcome these limitations methods such as rie and bedroc
, one can test whether the method is able to rank true links early or not.table  1shows the recovered fraction values for top 10 , 25 , 50 , 100 , 200 , 500 and 1,000 ranks with the number of links removednumber of links removedauacaucbedrocefauc ( top 10%)1000.9470.9910.8339.230.8672000.9380.9950.8279.1000.8573000.9300.9950.8188.950.8454000.9200.9910.8058.790.8305000.9160.9970.8018.710.8246000.9080.9950.7898.560.8127000.8990.9810.7808.420.8028000.8850.9970.7618.200.7839000.8690.9550.7417.910.7651,0000.8540.9560.7157.620.741table  2shows the recovered fraction values for top 10 , 25 , 50 , 100 , 200 , 500 and 1,000 ranks with the number of links removed # of links removedtop 10 ( % ) top 25 ( % ) top 50 ( % ) top 100 ( % ) top 200 ( % ) top 500 ( % ) top 1,000 ( % ) 10032.2478.2487.7690.7491.9293.2293.8820031.9277.9587.2689.8691.1592.3793.1230032.1478.3186.8289.4890.6891.8092.6340032.0477.485.3488.0789.2490.3391.4550032.6277.3985.0487.5688.7089.9591.160032.5376.2183.6886.2387.5488.8690.1670032.575.6482.6985.1886.5787.8989.3380033.0674.1380.8883.4584.8686.3587.9790033.5872.1478.4981.0482.7784.5786.381,00033.7169.8176.00878.3180.2282.1284.42 shows the recovered fraction values for top 10 , 25 , 50 , 100 , 200 , 500 and 1,000 ranks with the number of links removed shows the recovered fraction values for top 10 , 25 , 50 , 100 , 200 , 500 and 1,000 ranks with the number of links removed we found that the performance of the algorithm for ranking the targets by different chemical features is approximately same which indicates using this approach a user can identify protein targets with any one set of chemical features .
we used public 166 maccs keys , ecfp6 , phfp4 and 3d rocs to perform the analysis and it is surprising that the commercial programs feature performance is same as the 166 public maccs keys . as a baseline ,
we randomized the interactions and similarity matrices and performed rwr and found the random set prediction rate was way below our original prediction rate as given in additional file 3 : sheet 1 .
in addition to the internal evaluation using link perturbation approach , we evaluate the performance of our method using an external dataset , namely chembl version 15 database . from chembl 15 data we extract all the drugs and targets that have activity values not more than 1  m ( additional file 3 : sheet 4 ) and 10  m ( additional file 3 : sheet 4 ) with units ic50 , ki , kd , ec50 , ac50 , lc50 , and gi50 .
our training model is based on drugbank and uniprot database so we mapped the drugs and targets chembl ids with the drugbank ids and uniprot ids .
we used pubchem mapping tool ( http://pubchem.ncbi.nlm.nih.gov/idexchange/ ) to map chembl ids to drugbank ids and the uniprot mapping tool ( http://www.uniprot.org/?tab=mapping ) to map target chembl ids to uniprot ids .
it gives us 544 drugs and 467 protein targets , with 3,463 and 564 drug target interactions those are below 10 and 1  m , respectively . naturally , there are lots of interactions that are present in both drugbank and chembl .
we tested performance of parameter \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta $ $ \end{document} at different values on chembl 1  m set and 10  m having which have more than 0 , 1 and 2 target relations .
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				 \begin{document}$$ \eta $ $ \end{document} ( eta ) values for chembl datat at 1 and 10  m cutoff with different fingerprints respectively.fig . 
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				 \begin{document}$$ \eta $ $ \end{document} ( eta ) values for chembl datat at 1  m cutoff .
the recovered fraction is calculated by the number of targets retrieved at different rank positions over total number true interactions .
a maccs , b phfp4 , c rocs , d ecfp4.fig .  4showing the recovered fractions against the rank with different \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta $ $ \end{document} ( eta ) values for chembl data at 10  m cutoff .
the recovered fraction is calculated by the number of targets retrieved at different rank positions over total number true interactions .
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				 \begin{document}$$ \eta $ $ \end{document} ( eta ) values for chembl datat at 1  m cutoff .
the recovered fraction is calculated by the number of targets retrieved at different rank positions over total number true interactions .
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				 \begin{document}$$ \eta $ $ \end{document} ( eta ) values for chembl data at 10  m cutoff .
the recovered fraction is calculated by the number of targets retrieved at different rank positions over total number true interactions .
a maccs , b phfp4 , c rocs , d ecfp4 . from tables  3 and 4
we observe that rwr performance is better for 1  m target than 10  m because at 10  m we have lots off targets from different classes and as a result of that the prediction rate falls .
for chembl 1  m dataset , drugs having more than 0 , 1 and 2 targets we achieve bedroc score of 0.433 , 0.553 and 0.611 , respectively , which is much better than a random set of interactions . to test whether random walk performs better than just a simple sequence similarity search we took the approved drugs and it s known targets from the chembl 10  m dataset and performed sequence similarity based sech against 3,519 targets and ranked them .
we found rwr performance is way better in ranking targets than performing simple sequence based search .
this is the first time that the random walk - based method is evaluated using a binding assay dataset ( cf . [ 3 , 5]).table  3shows the types of data we used the drug target interaction having more than 1 and 2 drug interactions , area under the accumulated curve ( auac ) , area under the roc curve ( auc ) , bedroc and , enrichment factor ( ef ) and auc top 10%data typesnumber of targetsauac ( % ) auc ( % ) bedrocefauc ( top 10%)chembl 1 m ( rwr)>00.7090.9950.4335.0580.455chembl 1 m ( seq)>00.6700.6700.3964.480.414chembl 1 m ( random rwr)>00.4940.4930.0751.0900.079chembl 10 m ( rwr)>00.5960.8370.3233.8650.351chembl 10 m ( seq)>00.5180.5180.2372.6410.2555chembl 10 m ( random rwr)>00.3940.3640.0360.9540.029chembl 1 m ( rwr)>10.7840.7840.5536.2860.569chembl 1 m ( seq)>10.6520.6510.3904.5070.412chembl 1 m ( random rwr)>10.4830.4830.0811.2900.083chembl 10 m ( rwr)>10.6130.610.3534.0910.378chembl 10 m ( seq)>10.5510.5520.2793.0840.300chembl 10 m ( random rwr)>10.5140.5140.0751.2440.088chembl 1 m ( rwr)>20.8230.8240.6116.8660.631chembl 1 m ( seq)>20.7010.7050.5135.1090.469chembl 1 m>20.5330.5330.06711.4650.065chembl 10 m ( rwr)>20.6320.6330.3994.5690.422chembl 10 m ( seq)>20.5690.5690.2983.030.315chembl 10 m ( random rwr)>20.5210.5210.2621.950.125table  4shows the types of data we used the drug target interaction having more than 1 and 2 drug interactions and sensitivity ( hit rate ) at top 10 , 25 , 50 , 100 and 200 predicted targetsdata typesnumber of targetstop 10 ( % ) top 25 ( % ) top 50 ( % ) top 100 ( % ) top 200 ( % ) chembl 1  m ( rwr)>00.1440.3420.4700.5320.607chembl 1  m ( seq)>00.1640.3150.3940.4200.430chembl 1  m ( random rwr)>00.0020.0130.0180.0360.021chembl 10  m ( rwr)>00.110.2470.3240.3860.409chembl 10  m ( seq)>00.1220.1830.2340.2490.254chembl 10  m ( random rwr)>00.0140.0230.0350.0480.079chembl 1  m ( rwr)>10.2740.4770.5500.5800.614chembl 1  m ( seq)>10.1890.3500.4280.4720.513chembl 1  m ( random rwr)>10.0070.0230.0380.0760.091chembl 10  m ( rwr)>10.2200.2770.3480.4170.446chembl 10  m ( seq)>10.130.2120.2760.2960.302chembl 10  m ( random rwr)>10.0140.0230.0350.0480.079chembl 1  m ( rwr)>20.2710.5180.5980.6340.677chembl 1  m ( seq)>20.190.3930.530.560.598chembl 1  m>20.0060.0180.0340.0550.08chembl 10  m ( rwr)>20.2330.2970.3530.42990.472chembl 10  m ( seq)>20.130.220.2950.3160.324chembl 10  m ( random rwr)>20.0120.0280.0400.0570.093 shows the types of data we used the drug target interaction having more than 1 and 2 drug interactions , area under the accumulated curve ( auac ) , area under the roc curve ( auc ) , bedroc and , enrichment factor ( ef ) and auc top 10% shows the types of data we used the drug target interaction having more than 1 and 2 drug interactions and sensitivity ( hit rate ) at top 10 , 25 , 50 , 100 and 200 predicted targets
here , as a case study we investigate the target profiles of the popular top selling drugs in 2012 .
first , we consider \documentclass[12pt]{minimal } 
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				 \begin{document}$$ u_{\infty } , $ $ \end{document}u , the steady - state probability vector for the targets in our framework , as  target profile of a drug .
we find that some targets are associated with many drugs ( see table  5 ) .
for instance , adrenoceptor alpha 1a appears in 60% of drug s top 10 target association lists ; serotonin receptor 5ht2a appear in 43% ; and adrenoceptor alpha 1b in 35% .
most drugs shown on the table  5 mostly belong to the rhodopsin class of gpcr s . in additional file 4 ,
5 shows a bipartite network of 110 drugs with top 10 predicted targets for each drug.table  5the top 10 associated targets of 110 drugs with true percentage of associated target before prediction and predicted percentage of associationtargetspercentage of drugs associated with the targets based on drugbank and chembl ( % ) percentage of drug associations appearing in top-10 target list in our prediction ( % ) 
 ada1a 
 7.2760 
 5ht2a 
 4.5443.63 
 ada1b 
 7.2735.45 
 5ht1a 
 4.5433.63 
 adrb1 
 5.4531.81 
 5ht1b 
 5.4530.90 

5ht2c 
 3.6330 
 acm2 
 9.0926.36 
 5ht3a 
 4.5425.45 
 5ht1d 
 5.4523.63 
 acm3 
 9.0921.81 
 5ht7r 
 4.5418.18fig . 
the size and label of the target nodes is proportional to the degree of the nodes .
the top 10 associated targets of 110 drugs with true percentage of associated target before prediction and predicted percentage of association shows the network of the top 10 predicted targets of 110 drugs .
the size and label of the target nodes is proportional to the degree of the nodes .
we took some random drugs and tried to find known binding associations to protein targets .
we searched three databases chembl , pdsp , and pubchem   using the binding coefficients like ic50 and ki .
further investigation may have significant values on understanding side effects of existing drugs as well as repurposing them.table  6drug target interactions with association values from different databasesproteindrugsourceactivity tpeactivity m 
 5ht2a 
 carvedilolpubchem aid 625192ic500.41 
 5ht2a 
 desloratadinepubchem aid
625192ic500.033 
 kcnh2 
 lidocainechemblic50263.02 
 adrb1 
 salmetorolchemblic500.501 
 5ht1a 
 amphetaminepdsp databaseki6.6 
 hdac2 
 atorvastatinchemblic5022.5 
 ada1a 
 duloxentinepdspki10 
 acm1 
 montelukastpubchem aid 625153ic508.045 
 sc6a4 
 quetiapinepdspki10 drug target interactions with association values from different databases finally , let us summarize the contributions of this paper .
first , we offer a general approach that takes the whole drug target network into account without separating protein categories , in contrast to the previous study .
the number of interactions between drugs and targets is 2,557 , which makes 684 drugs to have at least one known target and 457 drugs to have two or more interactions .
the proteins in the dataset are grouped under 15 different categories according to chembl target classifications ( https://www.ebi.ac.uk/chembl/target/browser ) . out of 3,519 proteins , 1,386 proteins
the number of drugs that have at least two interactions with proteins that are categorized is 412 . among these 412 drugs ,
the number of drugs that have interactions with proteins from multiple groups is 169 . in other words
, we estimate that about 40% of drugs have interactions across multiple groups according chembl dataset .
therefore , it is more reasonable to consider all proteins together , rather than running the prediction model separately for each category .
second , we further investigate the methodology by presenting a benchmark of a parameter  in conjunction with the four chemical fingerprint types : maccs 166 keys , ecfp6 fingerprints , phfp4 fingerprints , and rocs . in the previous study
, the parameter space of  is not explored below 0.1 , but we find that we can improve the performance by decreasing eta below 0.1 .
we also find that the performance is robust under the choice of chemical fingerprinting method , particularly when  is around the optimum ( ~0.01 ) .
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				 \begin{document}$$ \eta $ $ \end{document} eta means the walk in the target network is much more important than the walk on the drug  drug network . in a sense
we have demonstrated that rwr approach provides a powerful way of predicting of drug  target interactions .
first , it provides a natural way to integrate multiple types of information such as drug  drug similarity , target  target similarity , and existing drug  target interactions into a coherent framework .
second , in contrast to other approaches like short - path - based methods , the random walk framework incorporates the network structure around a single or multiple points of interests extensively , taking into account not only the closeness of targets , but also the multitude of the paths to the targets .
these properties allow us to predict novel targets even for the drugs that have no known target , by connecting such drugs to the network through the drug  drug similarity .
still , the performance of rwr could be further improved by incorporating more known drug  target interactions .
we have studied the performance of the method under the variations of  parameter and the choice of fingerprints methods , showing that while training the model one can use any of the chemical features as similarity matrix with parameter \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \eta = 0.0 1 $ $ \end{document}=0.01 to obtain the predicted results , without significantly affecting the outcomes .
additional file 1:binary drug target matrix consisting of 727 drugs and 3,519 proteins.additional file 2:four drug  drug similarity matrices.additional file 3:predictions results.additional file 4:110 drugs predicted results with 3,519 targets .
we thank jeremy yang university of new mexico for sharing the code to do nn rocs and also helped in creating the chembl subset of compounds in the study .
we thank jaehong shin , ying ding and other members of the cheminformatics group at indiana university for discussion and comments .
 backgroundpredicting novel drug  target associations is important not only for developing new drugs , but also for furthering biological knowledge by understanding how drugs work and their modes of action . as more data about drugs , targets , and their interactions becomes available , 
 computational approaches have become an indispensible part of drug target association discovery . in this paper 
 we apply random walk with restart ( rwr ) method to a heterogeneous network of drugs and targets compiled from drugbank database and investigate the performance of the method under parameter variation and choice of chemical fingerprint methods.resultswe show that choice of chemical fingerprint does not affect the performance of the method when the parameters are tuned to optimal values . 
 we use a subset of the chembl15 dataset that contains 2,763 associations between 544 drugs and 467 target proteins to evaluate our method , and we extracted datasets of bioactivity 1 and 10  m activity cutoff . for 1  
 m bioactivity cutoff , we find that our method can correctly predict nearly 47 , 55 , 60% of the given drug  
 target interactions in the test dataset having more than 0 , 1 , 2 drug target relations for chembl 1  m dataset in top 50 rank positions . for 10  m bioactivity cutoff 
 , we find that our method can correctly predict nearly 32.4 , 34.8 , 35.3% of the given drug  
 target interactions in the test dataset having more than 0 , 1 , 2 drug target relations for chembl 1  m dataset in top 50 rank positions . 
 we further examine the associations between 110 popular top selling drugs in 2012 and 3,519 targets and find the top ten targets for each drug.conclusionswe demonstrate the effectiveness and promise of the approach  
 rwr on heterogeneous networks using chemical features  for identifying novel drug target interactions and investigate the performance.electronic supplementary materialthe online version of this article ( doi:10.1186/s13321 - 015 - 0089-z ) contains supplementary material , which is available to authorized users . 