drug discovery and development 
 has become increasingly challenging 
 in recent years , evidenced by the estimated cost of around $ 1.8 billion 
 for the development of a novel molecular entity with suitable pharmacological 
 properties .
this cost increase partly 
 originates from the failure of many drug candidates in phase ii or 
 iii clinical trials due to their toxicity or lack of efficacy .
the efficiency of drug discovery and development 
 might be improved by adopting a systemic approach that takes into 
 consideration the interaction of existing drugs and candidate compounds 
 with the entire network of target proteins and other biomolecules 
 in a cell .
indeed , the  one gene , 
 one drug , one disease  paradigm is widely recognized to fail 
 in describing experimental observations .
many drugs act on multiple targets , and many targets are themselves 
 involved in multiple pathways .
for example , -lactam antibiotics 
 and most antipsychotic drugs exert their effect through interactions 
 with multiple proteins .
biological networks are highly 
 robust to single - gene knockouts , as recently shown for yeast where 
 80% of the gene knockouts did not affect cell survival .
similarly , 81% of the 1500 genes knocked out 
 in mice did not cause embryonic lethality , further corroborating the 
 robustness of biological networks against single target perturbagens .
these results suggest that quantitative systems 
 pharmacology strategies that take account of target ( and drug ) promiscuities 
 can present attractive alternative routes to drug discovery .
recent years have seen many network - based models adopted to reduce 
 the complexity of , and efficiently explore , drug  target interaction 
 systems . in particular , the development of computational methods 
 that can efficiently assess potential new interactions became an important 
 goal . in this regard , the important role that machine learning approaches 
 such as active learning ( al ) can play has been recently been highlighted .
computational approaches used to predict unknown 
 drug  target interactions can be divided into roughly four categories : 
 chemical - similarity - based methods , target - similarity - based 
 methods , integrative ( both target- and chemical - similarity - based ) 
 methods , and holistic approaches .
the first two posit that if two entities are chemically or structurally 
 similar they will share interactions .
the integrative approaches combine 
 the chemical- and target - similarity methods . while the intuition behind 
 these approaches is very reasonable
, their performance has been observed 
 to be tied to the underlying similarity computation method .
we also 
 note that the utility of different methods may depend on the size 
 of the data set being analyzed , e.g. , computing chemical 
chemical 
 and target  target similarity matrices can be problematic for 
 large databases like stitch ( that contains 
 information on the interactions between more than 2.6 million proteins 
 and 300  000 chemicals ) .
to overcome these limitations , holistic 
 methods have been introduced , which utilize a number of different 
 data sources such as gene expression perturbation or high - throughput screening . in this study
, we propose a novel approach by using a collaborative 
 filtering algorithm to predict interactions without reliance on chemical / target 
 similarity or external data collection .
we validate the utility of 
 probabilistic matrix factorization ( pmf ) for predicting unknown drug 
the method is shown to group drugs according to their therapeutic 
 effects , irrespective of their three - dimensional ( 3d ) shape similarity . 

benchmarking computations show that the method outperforms recent 
 methods when applied 
 to large data sets of protein  drug associations , such as those 
 of enzyme and ion channel  drug pairs ; whereas the performance 
 falls short of these methods with decreasing size of the examined 
 data set ( e.g. , gpcr- and nuclear receptor - drug data sets ) .
the ability 
 of the method to efficiently analyze and make inferences from large data sets of protein  drug interactions suggests 
 that , with growing sizes of those data sets , the utility ( and accuracy ) 
 of the method will further improve .
application of the same 
 benchmarking procedure to drugbank confirms 
 its ability to disclose hidden data : 
 88 out of the top 100 predictions ( or 587 out of 1000 ) are found to 
 hit known ( but hidden ) interactions , when only 30% of the entire data 
 is used for training .
finally , when the method is trained on the entire 
 data set of drug  target interactions compiled in drugbank , 
 de novo predictions for drug repurposing can be made along with the 
 corresponding confidence levels .
top de novo predictions include many 
 drugs indicated for neurodegenerative diseases or neurobiological 
 disorders , including drug  target pairs apparently supported 
 by previous experiments ( not reported in drugbank ) , e.g. , ergotamine  serotonin 
 receptor 1a ( 5ht1a ) , amoxapine-5-ht2a , and verapamil  calmodulin . in conclusion
, the newly introduced computational 
 method provides an efficient approach for identifying potential drug 
target 
 association between chemicals and targets and formulating new hypotheses 
 for repurposable drugs or side effects , thus complementing those deduced 
 from chemical  chemical or target  target similarities .
the drug  target 
 interaction network is a bipartite graph with two types of nodes : 
 drugs and targets ( supporting information figure s1 ) .
target interaction identification problem 
 is to determine the missing edges that are likely to exist given all 
 nodes and some of the edges in the network .
we used drugbank ( version 
 of september 20 , 2011 ) as the database .
all drugs annotated therein as approved , along with their annotated 
 targets , are included in our data set ( i.e. , we excluded compounds 
 annotated as withdrawn or nutraceutical ) , resulting in n = 1413 drugs and m = 1050 targets with 4731 interactions 
 among them .
the interaction network displays small - world characteristics : 
 many nodes have low degree and a few , very high degree , as illustrated 
 in panels b and c of supporting information figure s1 , in line with previous studies on drug  target networks . on average , there are 3.35 interactions per 
 drug , and 4.50 interactions per target .
pmf is a member of the collaborative 
 filtering family of machine 
 learning algorithms that decomposes the connectivity matrix , rnm , of 
 a bipartite graph of n drugs and m targets as a product of two matrices of latent variables ( lvs).rnm is defined as1the 
 matrix rnm is modeled as the product of two matrices und and vdm , that 
 express each drug / target in terms of d lvs .
our objective 
 is to find the best approximation for lvs , while 
 avoiding overfitting .
the predicted rnm is then expressed as2where u and v are composed of n rows ui and m columns vj , respectively , each being d - dimensional .
the pmf adopts a probabilistic linear model 
 with gaussian noise to model the interaction .
therefore , the conditional 
 probability over observed interactions is represented as3where f(x| ,  ) is the gaussianly distributed probability 
 density function for x , with mean  and variance 
  , and iij is the 
 indicator function equal to 1 if the entry rij is known and 0 otherwise .
therefore , p(r|u , v ,  ) gives us a probabilistic representation of the connectivity 
 matrix , r. using zero - mean , 
 spherical gaussian priors on lvs , we can write45which leads to the log - likelihood 
 of u and v given by6here c is a term that does 
 not depend on lvs ; the first term on the right - hand side is the squared 
 error function to be minimized ; and the two summations over the square 
 magnitudes of ui and vj are regularization terms that 
 favor simpler solutions and penalize overfitting .
the above log - likelihood 
 directly follows from the bayes rule where r stands 
 for data , and u and v represent the model 
 ( see the supporting information for details ) . 
 to learn an optimal model means to find the u and v matrices , or the d - dimensional lv vectors , ui ( 1  i 
n ) and vj ( 1  j  m ) , that maximize the log - likelihood function .
the pmf method 
 yields the optimal ui and vj vectors corresponding to each 
 drug , di , and each target tj , respectively .
the basic 
 idea is that the model is forced toward making a  no - interaction  
 prediction by the regularization 
, there is a penalty associated 
 with any nonzero value in the lv matrices .
however , there is also 
 a penalty for failing to capture known interactions  i.e . , if 
 the dot product of the lv vectors corresponding to an interacting 
 drug  target pair is close to zero
therefore the learning of 
 a model means to optimally balance out two objectives : developing 
 a sufficiently complex model to describe the known interactions , but 
 not overly complex to end up in overfitting . in this study , we use 
 gradient descent for optimization .
the adoption of higher d values usually yields more accurate results , although 
 beyond a certain limit the increase in complexity and decrease in 
 efficiency may not warrant the marginal improvement , if any , in prediction 
 accuracy .
the method is highly efficient : a 50-dimensional 
 model is trained on the entire drugbank in approximately 2 s using 
 a 2.00 ghz amd opteron processor .
moreover , the computing time to 
 learn a pmf model scales linearly with the number of interactions , 
 and as such , the method can be advantageously used for much larger 
 data sets .
the al strategy adopted in the present study 
 is , in part , motivated by the success reported by warmuth et al . who demonstrated that hit maximization is a 
 viable al strategy applicable to predicting drug  target interactions . 

our method differs in that we aim at capturing the interactions 
 between all drugs and targets , as opposed to predicting activity against 
 a single target .
the procedure is the following : we begin with 
 the set of n drugs and m targets , 
 and known associations , schematically shown in figure 1 by black connectors .
for 
 each candidate interaction , say the possible interaction between di and tj , we compute the model s estimate , f(rij|uitvj ,  ) ( eq 3 ) .
the dot product uivj serves as a weight ij for the edge / connector between di and tj .
clearly , ij , or the likelihood 
 of association between di and tj , is high when ui and vj have both large values of the same sign at the same 
 dimension(s ) .
for example , a relatively large weight may originate 
 from the second component of both ui and vj , which means 
 that the predicted association is mainly due to latent variable 2 . 

we evaluated the statistical weights ij(di , tj ) for the n  m pairs of drug targets for two purposes : ( i ) benchmarking the methodology 
 via an iterative al scheme and ( ii ) making de novo predictions . in 
 the former case
, the method is benchmarked by hiding 70% of known 
 interactions and examining whether the top - ranking prediction is a 
  hit 
, i.e. , whether it corresponds to a known ( but 
 hidden ) interaction .
the outcome from this test is fed back to the 
 model , to repeat the calculation for the next prediction .
therefore , 
 the al model is updated at each iteration using the newly acquired 
hit  
 or  miss  data until a predetermined number ( m ) of predictions are made .
the passive learner ( pl ) makes 
 the m predictions simultaneously without updating 
 its model .
the known interactions between drugs and targets ( indicated 
 by the black lines ) are used to learn the lv vectors 
 ( shown adjacent to each node ) that describe each drug and target . 

the dot product uivj of the lvs for each pair 
 of drug di and target tj defines the predicted statistical 
 weight ij of corresponding connection . 

all drugbank 
 data were used 
 as input . de novo predictions also lend themselves to an al scheme 
 provided that the top - ranking prediction is experimentally tested 
 and then the new hit or miss data are incorporated in the model to 
 perform a new prediction , and so on , until the experimentation budget 
 is exhausted .
to assess whether the lvs provide us with a pharmacologically meaningful 
 metric , we examined the clustering of drugs in the d - dimensional space of the latent vectors .
the clustering was performed 
 for d = 30the value that gave the lowest 
 akaike information criterion , using as 
 basis the drug 
drug distance l1(di , dj ) = k|uik  ujk| where uik designates the kth component of ui , and 
 the summation is performed over d components .
inasmuch as our method evaluates drugs based on their interaction 
 profiles with targets , which in turn refer to specific therapeutic 
 or phenotypic actions , the similarity of a pair of drugs should be 
 high when their therapeutic effects are comparable and vice versa . 

thus , the method will tend to cluster drugs that exhibit similar patterns 
 of interactions ( with target proteins ) , which we term as functionally 
 similar drugs .
the heat map in figure 2a displays the resulting 
 organization of drugs in 30 clusters ( indicated by different colors 
 and indices along the axes ) . supporting information table 1 lists the dominant therapeutic action associated with each 
 cluster .
the dark blocks along the diagonal show that most clusters include 
 highly similar members , except for two ( clusters 29 and 30 ) , which apparently combine the outliers .
comparison 
 of pairwise similarities of drugs , based on their ( a ) 
 therapeutic targets compiled in drugbank and ( b ) 3d structure .
( a ) 
 30 clusters of drugs ( color - coded along the axes ; see supporting information table s1 for their dominant 
 therapeutic indication ) deduced from the pmf of 1413 approved drugs 
 and corresponding 1050 targets compiled in drugbank . by definition , 

drugs belonging to a given cluster share similar interaction patterns 
 with respect to targets .
( b ) 3d similarities , with the drugs being 
 ordered as in panel a. dark regions indicate high 
 similarity based on lvs ( panel a ) or 3d similarities ( panel b ) .
comparison 
 of the panels shows that close proximity in lv space ( which indicates 
 functional similarity ) does not necessarily imply 3d - structure similarity . 

lv distances were distributed in the range [ 0 , 1 ] ; with the distribution 
 of values also skewed in different ways . to render the two sets comparable , 
 we performed rank normalization on both the lv similarities and 3d 
 similarities .
selected boxes are enlarged in figures 3 ( white ) and 4 ( yellow ) , and supporting information figure s2 ( green ) .
given that ( promiscuous ) proteins present more than one site 
 for 
 ligand - binding , different functionalities may be modulated by chemical - structurally 
 different drugs , depending on the binding site on the target ( e.g. , 
 catalysis , substrate recognition , or allosteric signaling ) .
furthermore , 
 a shared phenotype may arise from the targeting of different proteins 
 along a given pathway . in order to make a better assessment of the 
 properties of drugs grouped in those clusters
high similarities would suggest that they 
 bind similar epitopes , if not similar ( or identical ) structural domains 
 or proteins .
if , on the contrary , they are structurally dissimilar , 
 this might indicate a different site on the same protein , a different 
 target on the same pathway , or other indirect effect due to drug 
the extent of 3d structure similarity 
 between pairs of drugs was 
 computed using the openeye scientific software ( http://www.eyesopen.com/ ) .
3d similarity was reported to be a better predictor than 2d methods 
 for off - target interactions and to perform equally well in on - target 
 interactions , although 3d methods may 
 suffer from more noise due to the conformational flexibility of the 
 small molecule .
we generated for each drug all possible stereoisomers 
 using openeye flipper and up to 200 conformers 
 per stereoisomer using openeye omega .
all combinations of conformers accessible to the examined pair of 
 drugs were examined using openeye shape toolkit ; and the best matching pair was adopted to assign a 3d similarity 
 score .
this computationally expensive task led to the heat map presented 
 in panel b of figure 2 . the drugs
( along the 
 axes ) are ordered as in panel a to enable visual comparison .
the comparison of figure 2 shows that some 
 clusters of functionally similar drugs ( panel a ) also exhibit some 
 3d similarities ( panel b ) , whereas others display little structural 
 similarity .
we examined more closely the individual clusters to see 
 if shared therapeutic functions were captured even when 3d similarities 
 were absent .
this cluster essentially consists 
 of antianxiety drugs , the majority of which are both functionally 
 ( panel b ) and structurally ( panel c ) similar .
however , the cluster 
 also includes a structurally dissimilar drug , ethchlorvynol ( panel 
 a ) , which shares the same type of phenotypic action ( as a sedative ) 
 as the majority of the cluster membership ( mostly targeting gaba receptors ) . 

the present approach thus detects chemically or structurally distinctive 
 drugs that share common activities , which would have been missed by 
 methods based on ligand fingerprint similarities .
closer examination of the similarities 
 between the members of cluster 14 in figure 2 ( enclosed in white boxes in figure 2 , enlarged in panels b and c here ) shows that the cluster 
 contains a series of antianxiety drugs
. a few members of this cluster 
 ( indicated by orange boxes along the abscissa of panels b and c ) are 
 displayed in panel a , to illustrate their shared structural features , 
 also indicated by panel c that reflects their 3d similarities
. the 
 same cluster however contains ethchlorvynol , also used as a sedative , 
 which would have been missed if we had used exclusively used 3d similarity 
 to identify functionally similar drugs .
another interesting observation concerns the cross - correlations 
 between different clusters ( i.e. , the off - diagonal regions of the 
 heat maps ) .
lvs are able to capture the commonality 
 between the clusters 11 and 14 as 
 may be seen by the strong signal ( dark region ) at the off - diagonal 
 region enlarged in figure 4b .
the 3d similarity , 
 on the other hand , can not recognize the functional similarity and 
 potential interference / side effects between these drugs in these two 
 clusters ( figure 4c ) . see supporting information figure s2 , which illustrates the same 
 behavior for another cluster , whose members are mostly antineoplastic 
 agents , albeit with various 3d structures .
the lvs thus provide information 
 on drug groups that potentially share pathways or exhibit similar 
 activity patterns despite their distinct physicochemical properties .
strong 
 cross - correlations between different clusters of drugs , 
 consistent with their similar therapeutic functions .
cluster 11 , color - coded cyan , is essentially composed 
 of hypnotics and sedatives .
target interaction 
 network , as shown in panel a , consistent with their similar actions . 

the lv - derived heat maps capture the functional similarity between 
 these two clusters ( as indicated by strong signals , or the dark region , in panel b ) ; the maps based on 3d similarity 
 ( panel c ) do not . in panel
cytoscape is used for visualization . to evaluate the 
 performance of the method in comparison to previous work
, we considered 
 three important studies in this area , one recently published by gonen and two by yamanishi et al .
gonen used a kernel - based matrix factorization ( kbmf ) with chemical 
 and genomic similarities to predict multiple targets .
, on the other hand , integrated chemical , genomic , and pharmacological 
 data to map all drugs and targets to the same unified feature space 
 where each protein  compound pair closer than a predefined threshold 
 was predicted to interact .
our approach differs from both studies , 
 in that pmf assumes an independent lv for each row and column with 
 gaussian priors ; whereas kbmf employs lvs spanning all rows and columns 
 with gaussian process priors , and yamanishi et al .
project drugs and 
 targets into a pharmacological space based on the eigenvalue decomposition 
 of the graph - based similarity matrix .
the benchmarking procedure 
 that we adopted is a 5-fold cross - validation of drugs on four target 
 classes : enzymes , ion channels , g - protein coupled receptors ( gpcrs ) , 
 and nuclear receptors . in order to achieve comparable results
, we 
 used the same protocol as that adopted earlier , i.e. , we divided our 
 data set into five subsets ; each was used as a test set , and the others , 
 as training sets . due to the randomness involved in the selection 
 of subsets
, we repeated the cross - validation experiments 100 times 
 with randomly selected subsets and evaluated the average auc ( area 
 under the receiver operating curve ) for each subset .
the first four 
 rows in table 1 compare the results ( columns 
 610 ) for the four classes , and the fifth row lists the average 
 performances weighted by the size of the interaction space .
our method 
 performs best when applied to large data sets ( e.g. , enzymes and ion 
 channels ) ; whereas gonen s performs best in the case of gpcrs , 
 and yamanishi et al . exhibits the highest 
 performance for nuclear receptors , where the present method yields 
 a relatively low ( 0.642 ) auc value .
examination of the statistical 
 significance of our results ( supporting information figure s3a ) indicates that the mean auc values obtained for all 
 four sets are highly robust .
their covariances vary from 2% ( enzymes 
 and ion channels ) to 11% ( nuclear receptors ) . finally , the application 
 of the same benchmarking protocol to drugbank yielded an accuracy 
 rate of 79.4  0.01% ( table 1 , last row , 
 and figure s3 ) , supporting the utility of the method when applied 
 to large data sets .
the last 
 four columns present the 
 comparison with the results of yamanishi and gonen for the same data set .
weighted - average mean and covariances , 
 evaluated using the number of interactions as weights . in principle , it might be intrinsically 
 harder to make accurate 
 predictions for larger data sets as the size of the potential interaction 
 space n  m grows quadratically 
 when the number of drugs and targets grow linearly , particularly if 
 the number of known interactions is small .
the occupancy of the n  m interaction matrix is only 1.5% 
 in the enzyme class , which could make it difficult to learn an informative 
 model . the present pmf technique , however , successfully learned an 
 informative model and handled the complexity of interactions in this 
 space of interactions , apparently due to the availability of a sufficiently 
 large ( absolute ) number of known interactions ( supporting information figure s3b ) .
the ion channel 
 drug class has the second largest number of known 
 interactions among the four .
although the size of interaction space 
 is 1 order of magnitude smaller than the enzyme class , there are 776 
 known interactions leading to a percent occupancy of 5.37% of all 
 possible ion channel - drug associations .
the success of our method 
 in this case may be attributed to both the relatively large number 
 of known interactions and the rich annotation of that class of interactions .
the two other classes , gpcrs and nuclear receptors , are significantly 
 smaller in terms of their interaction space and/or occupancy of that 
 space .
a method that relies solely on connectivity , like ours , 
 can not presumably formulate an informative model when the set of  edges  
 to construct the network connectivity matrix is incomplete .
in those 
 cases , the data that come from other sources , e.g. chemical similarity 
 and genomic patterns , amend this lack of information .
consequently , 
 methods that incorporate such features outperform 
 ours . to further examine the effect of scarcity of known interactions 
 on the performance of the present method
panels a  d show the performance on ion channels , 
 enzymes , gpcrs , and nuclear receptors , respectively .
these results 
 show that the performance depends on the fraction of known interactions . 
 to put the results into perspective , we indicated by a vertical dashed 
 line in each panel the fraction of data ( 80% ) used in previous studies for training purposes .
consistent with the above findings , ion channels 
 yield the best result : previous auc values ( of 0.799 ; table 1 ) are matched with about 
 only 35% of the data . in the enzyme group ,
( auc of 0.845 ) with 
 roughly 70% of the data used for training .
gpcrs and nuclear receptors 
 yield auc values lower than those previously attained , irrespective of the fraction of hidden interactions . in summary , 

the method is particularly suitable for screening and 
 inferring repurposable drugs or potential side effects from large 
 data sets where computational assessment of structure similarity kernels 
 become prohibitively expensive . in cases where the data set of known 
 interactions is too small , on the other hand ,
2d or 3d similarity 
 metrics provide more accurate assessments . as a more stringent test ,
3318 ( 70% ) of the known 
 4731 interactions in drugbank were randomly hidden , reducing the average 
 number of interactions per drug from 3.35 to 1 .
interaction matrix was then used to predict the hidden interactions , 
 one at a time ( rank - ordered by statistical weights ij(di , tj ) ) as described 
 in materials and methods .
the outcome was 
 checked in a simulated experiment to assess whether the predicted 
 interaction is a true positive ( tp ) or a false positive ( fp ) . if the 
 prediction is an existing , but hidden , interaction ,
the result is 
 considered a tp ( or hit ) , otherwise a fp ( or miss ) .
then the model 
 is updated in line with our al scheme , and this loop is repeated until 
 the completion of m = 1000 predictions . at that point , 
 the simulation is halted and the overall performance of the model , 
 or the hit ratio , is evaluated . note that this method gives us a lower 
 bound for hit ratio because the predictions are labeled as hits only 
 if they are annotated in drugbank , although they can be true but not 
 yet observed experimentally or annotated in drugbank .
the figure displays 
 the number of hits as a function of the number of predictions , obtained 
 with three approaches : active learning ( dark blue curves ) , passive learning ( dark red curves ) , and 
 random ( green ) . the approach is able to achieve , 
 on average , 587 hits out of 1000 predictions via al , 407 hits , via 
 pl ; and the corresponding variances ( indicated by the dashed curves ) 
 are 35 and 46 , respectively . compared to the random probability of 
 2.23 hits per 1000 predictions ,
the al improvement 
 over random was reported to be up to 3.19-fold in a previous svm - based 
 study for predicting the activity of 1316 drugs against a single target .
closer examination of the results 
 from the top 100 predictions ( enlarged in the inset ) further shows 
 that hit ratios of 88.0  4.7% and 82.2  6.4% are obtained 
 by the respective al and pl protocols .
the results are obtained with d = 50 , which yields optimal results , as can be seen from supporting information figures s5 and 6 display the dependence of the results on d , in support of the choice of d = 50 .
target 
 interactions . the number of drug  target interactions per drug 
 was reduced from 3.35 ( average ) to 1 by hiding 70% of known interactions , 
 selected randomly .
simulations were repeated n = 
 96 times for each of the 1 < m < 1000 predictions 
 ( abscissa ) and the number of hits ( correctly identified hidden interactions ) 
 is plotted for each run , along the ordinate .
the dark blue 
 and dark red solid curves refer to the average performance 
 obtained by active learning and passive learning protocols , respectively , 
 using d = 50 ,  = 3 ,  = 0.01 , and  
 = 0.9 in the adopted pmf algorithm .
dashed curves show the corresponding 
 variances ( by one standard deviation ) above and below the mean value . 

the green curves ( practically overlapping with the 
 abscissa ) refer to results from random predictions .
al reaches an accuracy rate 
 ( hit ratio ) of 88.0  4.7% and 58.7  3.5% in the respective 
 cases of m = 100 and 1000 predictions .
improvement in prediction accuracy by al over random ( a ) 
 and over 
 pl ( b ) , as a function of the latent space dimensionality .
fold improvement 
 is based on hit ratios obtained at the end of 1000 predictions , using 
 same parameters as figure 5 .
the al performance 
 levels off at about d = 50 in panel a. the last bar 
 in each panel refers to the work of warmuth et al .
first , a hit ratio 
 of 88% is attainable in the top 100 predictions ( and 59% in top 1000 ) 
 upon adopting a pmf - based al strategy for identifying hidden / unknown 
 interactions in a sparse ( 0.32% occupancy ) data set of about 1.5 million 
 potential interactions .
second , the al method outperforms random by 
 2 orders of magnitude and pl by a ratio of 1.5 approximately , in support 
 of al strategy for predicting new interactions .
we used our method to predict new ( potential ) 
 drug  target interactions after training our model on the latest 
 available version of drugbank ( september 10 , 2013 ) comprised of 5041 
 interactions between 1502 approved drugs and 1138 targets .
the highest 
 confidence pairs obtained for twenty distinct drugs are presented 
 in table 2 .
the pairs therein were observed 
 to lie frequently among the top - ranking 10 pairs ( in the space of n  m = 1.7  10 potential 
 interactions ) , deduced from 10 independent runs initiated 
 with different random numbers .
abbreviations : 
 gaba -aminobutyric - acid 
 receptor ; 5-ht 5-hydroxytryptamine ( or serotonin ) receptor ; net norepinephrine 
 ( or noradrenaline ) transporter ; adra1a adrenoreceptor 1 a ; 
 dat dopamine transporter .
the cases listed as  indirect  
 refer to interactions of the drugs with different subtypes of the 
 identified target .
orphenadrine 
 inhibits norepinephrine 
 reuptake thus potentiating the effect of norepinephrine there are 
 several drugs acting as norepinephrine - dopamine reuptake inhibitors , 
 and ophenadrine might exhibit the same behavior .
we note that the list of de novo 
 predictions in table 2 is dominated by drugs 
 used for neurological or 
 psychiatric disorders , consistent with the known pharmacological promiscuity 
 of this of drugs .
the last column in table 2 lists the experimental support from the literature , if any , for 
 the possible interaction of the drug 
target pair in each row . 
 among pairs supported by previous experiments , we note ergotamine  serotonin 
 receptor 1a ( 5ht1a ) , amoxapine-5-ht2a , verapamil  calmodulin , paliperidone-5-htc , meperidine  sodium channels , and cinnarizine  calmodulin .
we also note that chronic treatment with paroxetine 
 has been recently reported to increase the mrna levels of histamine 
 receptor h1 , indicating an association between paroxetine 
 and histamine receptor h1 .
although paroxetine 
 is a potent serotonin reuptake inhibitor , its weight gain side effect 
 has been attributed to its medication action on histamine receptors .
many others ( indicated as  indirect  ) 
 are interactions 
 known to occur either with subtypes of the listed targets or proteins 
 implicated in the same phenotype ( e.g. , citalopram induces norepinephrine 
 receptor hypoactivity , which may relate 
 to norepinephrine transport by net ) . yet , the validity of these predictions 
 need to be established by experiments . here , for exploratory purposes , 
 we examined the potential binding pose and energetics of verapamil  calmodulin . 

its 
 interaction with calmodulin is supported by the fluorescence experiments and by the inhibition of calmodulin - stimulated 
 ( ca + mg ) atpase activity .
we used as template the protein databank ( pdb ) structure of the cocrystal between calmodulin 
 and trifluoperazine ( pdb identifier 1ctr ) and examined 
 the binding affinity of verapamil relative to that of trifluoperazine , 
 using the module smina , based on autodock 
 vina .
the software yielded an attractive 
 energy of 4.8 kcal / mol for trifluoperazine binding to calmodulin , 
 which after energy minimization , becomes 6.8 kcal / mol .
docking 
 of verapamil to the same location and energy minimization led to 5.8 
 kcal / mol ( figure 7 ) . while docking software 
 with fixed target often fails to provide a quantitative assessment 
 of binding affinity , and more elaborate simulation methods
have been 
 developed for druggability assessment ( see , e.g. , our recent work ) , these results support , qualitatively , the 
 shape complementarity between calmodulin and verapamil , as well as 
 their favorable electrostatic interaction . establishment of this and 
 other predicted interactions , however , awaits experimental verifications 
 by essays designed to test the specific drug  target interactions .
the molecular surfaces of both the drug and calmodulin are colored 
 by electrostatic potential ( a and b ) and a close - up view is shown 
 in panel c. calmodulin surface , especially at the ligand - binding cleft , 
 is negatively ( partial ) charged , favorably interacting with the verapamil 
 surface that has partial positive charge . note the shape between the 
 verapamil and calmodulin .
over the last couple 
 of years , there have been a number of computational 
 studies performed to identify targets of existing drugs and drug candidates 
 other than those originally known / proposed to be targeted .
a pioneering 
 study is that of roth , shoichet , and co - workers based on compound chemical similarities .
dudley et al . focused on 
 inverse correlations between gene expression profiles in the presence 
 of a drug and in a disease state .
yamanishi 
 and his colleagues represented drugs and targets in an integrated 
  pharmacological space  .
we proposed a pmf - based al methodology that 
 can be advantageously used for large data sets .
the applicability 
 of the method to large data sets is worth further 
 attention , given that we will increasingly have access to bigger data 
 ( e.g. , stitch database ) , which will be 
 exploited for repurposable drug identification .
the software developed 
 here , made accessible in http://www.csb.pitt.edu/faculty/bahar/files/ , is readily scalable . for very large data sets , which typically 
 have more known interactions , the pmf is able to construct a better 
 model using the plethora of available data ; whereas when the number 
 of known interactions is limited , the use of chemical and genomic 
 kernels allows kbmf to outperform pmf .
the application of kbmf to 
 large data sets may , however , become challenging , for example , stitch 
 contains on the order of 10 proteins and 10 compounds , implying that 10 sequence and 10 chemical similarity comparisons are needed to make predictions . 
 however , the pmf method is independent of chemical , structural or 
 other similarity metrics , and its computation time scales linearly 
 with the number of known interactions ; and it proves to perform well 
 on large data sets .
the data sets reporting drug  target interactions 
 are constantly improving in quality and quantity and , therefore , expected 
 to give even better results when analyzed by an efficient tool .
finally , 
 the extension of the method to analyzing big data ( with millions of 
 nodes ) is foreseeable in the near future .
the recently introduced 
 graphchi tool can be used for optimized 
 and parallelized model learning for further performance improvements .
the fact that the pmf is independent of 2d/3d shape comparison 
 methods commonly employed in drug 
target pair inferences implies 
 that the derived lvs capture similarities based on the interaction 
 patterns of drugs at the cellular level , even if their molecular structures 
 are dissimilar ( see figures 2 and 3 ) . as such , the method may be advantageously used 
 for lead hopping , thus complementing those ( e.g. , svm classification 
 algorithms ) used in conjunction with 2d or 3d pharmacophoric fingerprints 
 ( see the work of saeh et al . ) .
inasmuch 
 as the currently proposed method does not require structural data 
 for proteins but knowledge of drug  target interactions , it 
 can be advantageously applied to membrane proteins ( major drug targets ) 
 for which structural data still remain sparse .
it can also be used 
 to make predictions across major drug or target classification boundaries . 

one implication is that the de novo predictions are not restricted 
 to major drug or target classification boundaries .
a major utility 
 of the developed tool is the ability to deliver 
 testable hypotheses with regard to repurposable drugs , thus significantly 
 reducing the search space for identifying potent applications of existing 
 drugs ( that proved to meet admet requirements ) .
the number of experiments 
 that can be efficiently conducted is usually limited , e.g. of the 
 order of 10 if not 10 for high - confidence 
 assays as opposed to the complete space of 1.5 million combinations 
 for the data set used in this study .
the fact that the top - ranking 
 predictions exhibit a hit ratio of 59% ( for the top 1000 predictions ; 
 or 88% for top 100 predictions ) suggest that de novo predictions made 
 by the presently introduced method of approach applied to increasingly 
 large data sets are likely to provide useful guidance for experimentally 
 testing , streamlining or prioritizing existing or investigational 
 drugs or new compounds .
another important byproduct is the probabilistic 
 assessments on potential side effects , a topic that will become increasingly 
 important with advances in personalized medicine .
 quantitative analysis of known drug  
 target 
 interactions 
 emerged in recent years as a useful approach for drug repurposing 
 and assessing side effects . in the present study , 
 we present a method 
 that uses probabilistic matrix factorization ( pmf ) for this purpose , 
 which is particularly useful for analyzing large interaction networks . 
 
 drugbank drugs clustered based on pmf latent variables show phenotypic 
 similarity even in the absence of 3d shape similarity . 
 benchmarking 
 computations show that the method outperforms those recently introduced 
 provided that the input data set of known interactions is sufficiently 
 large  which is the case for enzymes and ion channels , but not 
 for g - protein coupled receptors ( gpcrs ) and nuclear receptors . 
 runs 
 performed on drugbank after hiding 70% of known interactions show 
 that , on average , 88 of the top 100 predictions hit the hidden interactions . 
 
 de novo predictions permit us to identify new potential interactions . 
 
 drug  target pairs implicated in neurobiological disorders are 
 overrepresented among de novo predictions . 
Introduction
Materials and Methods
Results and Discussion
Concluding Remarks