some drug pairs elicit 
 a phenotype that is significantly greater 
 than expected , a phenomenon called drug synergy . synergistic drug combinations are of high medical interest , 
 because they allow increased efficacy at lower dosage . as the number of possible drug combinations is astronomical , 
 prediction methods can help expedite the search for synergistic drug 
 combinations . several studies have been successful in predicting drug 
 synergy ; however , these methods often require costly ( chemogenomic 
 profiling , microarray analysis , binding assays ) , 
 subjective ( drug targets , drug indications , drug side effects ) , or incomplete ( genetic interactions , protein interactions ) input data sets . there have been many 
 studies aimed at predicting biological activities 
 of chemicals often via application of quantitative 
 structure  activity relationship modeling . toward this goal , is perhaps the most well - known guide to identifying chemicals with 
 desirable pharmacokinetic properties . according to this rule , drug - like molecules have characteristic 
 physicochemical properties : molecular weight less than 500 da , octanol - partition 
 coefficient ( logp ) less than 5 , h - bond donors less than 5 , and h - bond 
 acceptors less than 10 . since its inception 
 in the 1990s , the application of this rule and its extensions have 
 been widely used to narrow investigational focus on compounds . a particularly attractive feature of the lipinski s 
 rule 
 is that the relevant physicochemical properties are simple and readily 
 obtained . the molecular structure information on a drug readily yields 
 its molecular weight , h - bond donor and h - bond acceptor values . the 
 determination of the logp of a compound requires only simple experimental 
 measurement of the relative solubility of a compound in octanol versus 
 water . a high logp indicates a preference 
 toward hydrophobic interactions , which is interpreted as lipophilicity . for example , 
 the structure - derived estimate termed xlogp3 is almost perfectly correlated 
 with experimentally determined logp values . xlogp3 values for compounds are publicly available in the pubchem 
 database . while the relationship 
 between physicochemical properties and drug - likeness 
 has been extensively studied , it has not yet been explored to predict 
 drug interactions . here we analyzed 
 two drug interaction networks , one experimentally generated for yeast 
 ( 31 nodes , 165 edges ) and one literature - curated for humans ( 428 nodes , 
 919 edges ) . we observed that in both yeast and human , combinations 
 of lipophilic compounds frequently result in synergistic drug interactions . these results uncover a novel phenomenon that may explain a large 
 proportion of synergistic drug interactions . we analyzed experimental 
 data measuring synergy of antifungal ( antimycotic ) 
 compounds for 175 drug pairs ( supplementary table 
 1 ) among 33 drugs ( supplementary table 
 2 ) . the drugs and pairs in this 
 screen were selected on the basis of antifungal activity , having known 
 targets , and in some cases based on the presence of genetic interactions 
 among drug targets . they were not selected on the basis of physicochemical 
 properties . for each of these drugs , we extracted the four physicochemical 
 properties associated with lipinski s rule of five from pubchem . these properties were ( 1 ) molecular weight ( mw ) , ( 2 ) lipophilicity 
 ( xlogp3 ) , ( 3 ) h - bond donor ( h - don ) , and 
 ( 4 ) h - bond acceptor ( h - acc ) . lithium and cisplatin did not have reported 
 xlogp3 scores and were not considered further , bringing the total 
 number of tested drug pairs to 165 . among the remaining 31 drugs , 
 we observed a large range for each of these properties : mw ranged 
 from 421101 da ; xlogp3 from 6.68.5 ; h - don 
 from 014 ; and h - acc from 118 . as there are ( 31/2 ) 
 = 465 possible pairings of 31 drugs , 165 tests represent 35% of the 
 drug pair space . for example , 
 45% of the entire data set involved 6 drugs that had each been tested 
 against more than 20 drugs . of these for each of the 31 drugs , we computed  synergicity  
 defined by the fraction of tested partners exhibiting synergy . drug 
 synergicities covered a wide - range between 0 and 60% , in accordance 
 with previous observations that some drugs are more likely to exhibit 
 drug synergy . next , we compared the synergicity 
 of drugs with their mw , xlogp3 , 
 h - don , and h - acc values ( supplementary figure 
 1 ) . we found a significant correlation between synergicity 
 and xlogp3 ( spearman r = 0.51 , p = 3.6  10 ; figure 1 left ) . this relationship is strengthened among drugs that are tested 
 against more than five partners ( spearman r = 0.68 , p = 3.7  10 ) . this observation 
 suggested that drugs that have a higher lipophilicity are more likely 
 to show synergy . in contrast , mw , h - don , and h - acc did not show any 
 significant correlation with synergicity for either the entire drug 
 set or among drugs that are tested against more than five partners . ( left ) 
 each circle represents one drug and the size of each circle corresponds 
 to the number of drug synergy tests . the x - axis corresponds 
 to the ratio of synergies the drug exhibited among all drugs it was 
 tested against ( synergicity ) . the y - axis corresponds 
 to the lipophilicity ( xlogp3 ) of each drug . there is a significant 
 positive correlation between synergicity and lipophilicity ( spearman r = 0.51 , p = 0.0036 . ) . ( right ) histograms 
 of xlogp3 distribution for nonsynergistic ( black histogram ) and synergistic 
 ( red histogram ) partner drugs of two heavily tested drugs with a high 
 synergicity ( pentamidine and terbinafine ) . both drugs exhibited significantly 
 more synergy with lipophilic drugs ( pentamidine p = 6.5  10 , terbinafine p = 9.1  10 , mann we more closely examined six drugs ( benomyl , latrunculin 
 b , pentamidine , staurosporine , tacrolimus , terbinafine ) that had been 
 tested against more than 20 partners for drug synergy . pentamidine 
 exhibited a synergistic interaction with 12 drugs among 24 tests , 
 making its synergicity 50% ( figure 1 left , 
 lower blue disc ) . we found that the 12 drugs that exhibit synergy 
 with pentamidine have significantly higher xlogp3 values than the 
 12 drugs that did not exhibit synergy with pentamidine ( figure 1 middle ) ( p = 6.5  10 , mann  whitney u - test ) . when we compared the 
 xlogp3 values of compounds positive or negative for synergy with terbinafine 
 ( 15 and 11 cases , respectively ) , the same trend was observed ( figure 1 right ) ( p = 9.1  10 , mann latrunculin b and staurosporine 
 also showed this trend ; however , their p - values ( p = 0.03 , p = 0.02 , respectively ) fell 
 short of significance after bonferroni correction for six drugs . we hypothesized that the relationship between drug lipophilicity 
 and drug synergicity is not a simple result of one of the partner 
 drug s lipophilicity , but depends on the lipophilicity of both 
 drugs in a drug pair . yeast antifungal synergy 
 network  to visualize both synergy and the lipophilicity of 
 each drug ( figure 2 ) . this network showed clearly 
 that synergistic edges are more common among pairs of lipophilic drugs . each node represents one of 
 31 tested chemicals with antifungal effect on s. cerevisiae growth . the 48 red edges represent synergistic interactions and 117 
 black edges represent tested drug interactions with no synergy . visual 
 inspection of the network suggests a greater tendency for pairs of 
 lipophilic compounds to have synergistic interactions . to explore this trend in greater detail , we binned 
 drug pairs in 
 two dimensions according to the xlogp3 of each drug and calculated 
 the prevalence of synergy within each bin . the resulting two - variable 
 probability mass function ( pmf ) , shown in figure 3 top , shows clearly that synergistic drug pairs are almost 
 exclusively among lipophilic ( xlogp3 > 0 ) drugs . an equivalent 
 pmf 
 was generated for the prevalence of nonsynergy ( figure 3 , middle ) , showing that lack of synergy is more widely distributed 
 among drugs with both low and high lipophilicity . ( top and middle ) the probability mass functions of synergistic or 
 nonsynergistic edges are shown as a function of the xlogp3 of the 
 drugs in a pair . visual analysis suggests that synergistic interactions 
 are mostly among antifungals with xlogp3 > 1 , while nonsynergistic 
 interactions are more distributed . ( bottom ) the difference of the 
 top and middle probability mass functions is shown . red or black - shaded 
 regions represent the drug xlogp3 pairs with proportion of synergy 
 or nonsynergy , respectively . the difference matrix suggests that antifungal 
 pairs where both drugs have xlogp3 > 1 are more likely to be synergistic . examining the difference between 
 the synergy and no - synergy pmf s 
 ( figure 2 bottom ) , we observed a clear pattern 
 that when two drugs each have xlogp3 values higher than 1 , they are 
 more likely to be synergistic . results 
 in a statistically significant enrichment ( p = 5.7 
  10 , fisher s exact test ) and fails 
 to capture only six of 48 synergistic drug pairs . moreover , we found 
 that a generalized simple rule that states :  if two drugs both 
 have lipophilicity higher than a threshold xlogp3 , they will be synergistic  
 results in a classification accuracy with area under the roc curve 
 ( au - roc ) value of 0.74 and area under the precision - recall curve ( au - pr ) 
 value of 0.54 ( supplementary figure 2 ) . these observations strongly suggest that combinations of lipophilic 
 antifungal compounds frequently exhibit synergistic toxicity to yeast . we note that there are many examples of lipophilic drug combinations 
 that do not exhibit synergy . in other words , although the predictions 
 are highly sensitive , they are not perfectly specific . next , 
 we carried out 5-fold cross validation ( 5-fold cv ) to assess 
 generalization performance of synergy predictions based on lipophilicity 
 ( see methods ) . in terms of a graph representation , drug synergy is a commutative edge property , while drug pair lipophilicity 
 is a noncommutative property of two nodes . because lipophilicity is 
 not a commutative feature , we considered all 330 ordered drug pairs . we then explored whether a decision tree model that uses only drug 
 lipophilicity information could predict synergy in a 5-fold cv setting . ( training set ) and predicted 
 synergy for the remaining 20% ( test set ) . we ensured that the two 
 instances of the same drug pair are in the same fold to avoid a setting 
 where the same drug pair appears both in training and test set . we 
 repeated this 5-fold cv analysis 10 times and calculated average performance 
 statistics . we found a striking performance with au - roc of 0.80 and 
 au - pr of 0.63 . these values are both better than the predictive performance 
 of the  generalized simple rule  that we investigated 
 in the above analysis . to assess the predictive performance 
 of the decision tree model , we repeated our analysis with randomized 
 drug synergy networks . we randomized the network in two ways : ( i ) 
 permute the synergy / no synergy labels of the drug pairs ( edge randomization ) ; 
 ( ii ) permute the xlogp3 values of the drugs ( node randomization ) ( see 
 figure 4 top ) . since some drugs 
 have high synergicity , we expected that the decision tree model trained 
 with node randomized data will still have some predictive value , since 
 the model is likely to learn that if a certain drug is frequently 
 found in synergistic interactions in 80% of the data set , it will 
 probably show synergy in the remaining 20% as well . we created 1000 
 random networks for each type of randomization and performed 5-fold 
 cv analysis 10 times for each network . each node represents one drug ; red or black edges represent 
 synergistic or nonsynergistic interactions , respectively . in the edge - shuffled 
 network , known edges are shuffled , which can lead to swapping of synergistic / nonsynergistic 
 edges , hence disrupting network topology . in the node - shuffled network , 
 nodes are swapped ; this leads to loss of lipophilicity information 
 for drugs , but preserves the network topology . ( bottom ) area under 
 the roc curve ( au - roc ) and area under the precision - recall curve ( au - pr ) 
 for a 5-fold cross validation for a decision tree model that used 
 real network is given as black bars . distribution of the au - roc and 
 au - pr curves in a 5-fold cv for 1000 edge - shuffled ( blue ) or node - shuffled 
 ( green ) networks . while the node - shuffled networks have predictive 
 power better than edge - shuffled networks , predictive power of the 
 real network is higher than node - shuffled networks in all 1000 randomizations . finally , we compared the performance 
 of the model learned from 
 the real network to the performance of the models learned from random 
 networks . expectedly , models trained with edge - randomized 
 networks had poor predictive value for synergy , while models trained 
 with node - randomized networks performed better . we found that the 
 predictive performance of the original model ( both au - roc and au - pr ) 
 is higher than the predictive performance of all the models learned 
 from 1000 random networks . therefore , the predictive performance of 
 decision trees is significantly better when the real network is used 
 as opposed to node - shuffled networks ( p - value < 
 0.001 ) . because the only difference between node - shuffled networks 
 and the real network is the lipophilicity of drugs , hence we searched drugbank for adverse drug interactions 
 that are reported to increase toxicity in humans ( see methods ) , yielding 1038  synergistic human toxicity 
 drug pairs  ( supplementary table 3 ) . we were able to extract the xlogp3 value for both members of 919 
 synergistic human toxicity drug pairs , involving a total of 428 drugs 
 ( supplementary table 4 ) . synergistic human toxicity network  combining drug 
 lipophilicity and synergistic toxicity ( supplementary 
 figure 3 ) . one important limitation of this network is that 
 it only contains synergistic edges , in contrast to the yeast antifungal 
 synergy network , which harbored both synergistic and nonsynergistic 
 edges . by necessity however , because we were unable 
 to define a simple  synergicity  for drugs and compare 
 with lipophilicity , we compared the lipophilicity of each node with 
 its degree ( number of synergistic partners ) . we observed a small , 
 but significant correlation ( spearman r = 0.22 , p = 3.5  10 ) . although it is formally 
 possible that this correlation is the result of investigational bias 
 ( e.g. , if lipophilic compounds have been more extensively studied 
 for toxic interactions ) , we know of no such bias . thus , we interpret 
 the correlation between lipophilicity and adverse toxic interactions 
 as support for the idea that drug lipophilicity can predict synergistic 
 toxicity in humans . three drugs in the synergistic human toxicity 
 network ( trospium , trimethobenzamide , triprolidine ) have increased 
 toxicity in combination with more than 60 drugs . for each of these 
 drugs , we compared the xlogp3 values of drugs that result in increased 
 toxicity with the rest of the drugs , similar to the analysis presented 
 in figure 2 ( figure 5 ) . we found that all three drugs show increased toxicity with lipophilic 
 drugs ( trospium p = 2.3  10 , trimethobenzamide p = 2.9  10 , triprolidine p = 1.2  10 , mann next , we compared the xlogp3 probability 
 distributions for drug pairs with increased toxicity with the negative 
 set ( figure 6 ) , analogous to the analysis presented 
 in figure 3 . we observed a striking similarity 
 with the pattern we observed for yeast : combinations of drugs with 
 xlogp3 higher than 1 had a tendency to show increased toxicity ( fisher s 
 exact test , p = 5.2  10 ) . histograms are shown for three drugs that were 
 reported to result in increased toxicity when combined pairwise with 
 more than 60 drugs . xlogp3 distribution of drugs that are reported 
 or not to increase pairwise toxicity are shown as magenta or black 
 histograms , respectively . trospium , trimethobenzamide , and triprolidine 
 are reported to exhibit pairwise toxicity significantly more with 
 lipophilic drugs ( trospium p = 2.3  10 , trimethobenzamide p = 2.9  
 10 , triprolidine p = 1.2  
 10 , mann combinations of lipophilic drugs are more likely to be 
 reported 
 as increased toxic interactions in human . ( top and middle ) the probability 
 mass function of increased or unknown toxicity edges are shown as 
 a function of drug xlogp3 . ( bottom ) the difference of the top and 
 middle probability mass functions is shown . magenta or black - shaded 
 regions represent the drug pair xlogp3 regions with increased toxicity 
 or not , respectively . the difference matrix suggests that drug pairs 
 where both drugs have xlogp3 > 1 are more likely to have increased 
 toxicity . as a final check for the correspondence 
 between drug lipophilicity 
 and synergistic toxicity of a drug combination , we performed 5-fold 
 cross - validation using decision tree models based on only drug lipophilicity . 
 in the synergistic human toxicity network , only 1% of the possible 
 edges have reported increased toxicity in combination , with remaining 
 99% being unobserved . using all the unobserved edges as the negative 
 set would result in an extremely unbalanced data , which in turn would 
 complicate the learning by the decision tree model . instead , for each 
 positive edge in our data set , we sampled three edges ( similar to 
 the ratio of positive / negative edges in the yeast antifungal synergy 
 network ) from the unobserved edges and defined these edges as negative . fitting the decision tree model with this data , we were able to achieve 
 an au - roc of 0.72 and au - pr of 0.48 . similar to the analysis for the 
 yeast network , we constructed 1000 random interaction networks by 
 shuffling edges or nodes and conducted 5-fold cross - validation . we 
 observed that edge - shuffled networks have no predictive value as au - roc 
 values were approximately 0.5 , but node shuffled networks had some 
 predictive value , which is expected since some drugs are reported 
 to show increased toxicity more frequently . however , the decision 
 tree model that used the real data had a higher au - roc in all 1000 
 randomizations ( p < 0.001 ) and higher au - pr value 
 in all but 6 randomizations ( p = 0.006 ) ( supplementary figure 4 ) . since the only difference 
 between node - shuffled networks and the real network is the lipophilicity 
 of drugs , we conclude that drug lipophilicity is a predictor of synergistic 
 human toxicity of a drug combination . here 
 we showed that combinations of lipophilic drugs often result 
 in an increased phenotypic effect , as observed for antifungal synergy 
 against yeast and reported adverse toxic drug interactions in humans . knowledge of the lipophilicity of any compound is readily available , 
 so that this phenomenon represents a powerful and cost - free method 
 to prioritize potentially synergistic compound pairs . this property 
 sets our methodology apart from previous synergy prediction methods , 
 which require various costly data types often not available for most 
 compounds . it has 
 been previously established that lipophilic drugs are promiscuous , 
 with many cellular targets . it has also 
 been suggested that lipophilic drugs generally enter the cell via 
 passive diffusion across the cell membrane rather than through protein 
 transporters . given these properties , 
 it is important to consider the enhanced efficacy we observe between 
 lipophilic drug combinations in the context of previously proposed 
 drug synergy models . according to the parallel pathway inhibition model 
 for drug synergy , two drugs will be synergistic for a phenotype if 
 they inhibit two parallel pathways that are required for that phenotype 
 ( e.g. , growth ) . this model uses the relationship 
 between the cellular effects of individual drugs to predict 
 drug synergy . as lipophilic drugs are more likely to have multiple 
 targets ( polypharmacology ) , they are likely to alter many pathways 
 to varying degrees . as the number of inhibited pathways increases , 
 the probability to inhibit a parallel pathway would be expected to 
 increase , correspondingly increasing the synergicity of lipophilic 
 compounds . according to the bioavailability model for drug synergy , 
 two drugs 
 will be synergistic if one of the drugs increases the other s 
 availability to its cellular targets . bioavailability 
 can be enhanced by the alteration of drug transporters , modification 
 of drug metabolism , or via permeabilization of the cell membrane . it has been previously observed that compounds that disrupt membrane 
 integrity are often promiscuously synergistic . in accordance with the bioavailability model , 
 the presence of a lipophilic compound may disrupt the integrity of 
 the cell membrane , hence enhancing the access of the other drug to 
 its targets (  synergistic membrane diffusion  ) . another 
 possible hypothesis is a  synergistic detergent effect  
 of drugs , whereby two drugs disrupt the integrity of the membrane 
 more effectively in combination . while outside the scope of this study , 
 these hypotheses can be evaluated by molecular dynamics studies and 
 experiments with artificial membranes . comparison of drug pairs differing 
 in synergy , but similar in lipophilicity may provide starting points 
 for future mechanistic analyses . better understanding of the 
 mechanism of the relationship between 
 lipophilicity and drug synergy could inform the treatment of diseases 
 that require administration of multiple drugs , such as hiv and cancer . for example , highly lipophilic adjuvants are known to increase drug 
 potency as with the chemotherapeutic cisplatin . however , our finding that combinations of lipophilic compounds 
 often result in antifungal synergy may have immediate medical implications 
 for treatment of infectious disease . for example , pentamidine is one 
 of the few treatment options for sulfa - resistant pneumocystis 
 jirovecii , an opportunistic yeast infection . in our 
 analysis , we found that pentamidine has a tendency to show antifungal 
 synergy with lipophilic compounds , which suggests that lipophilic 
 drugs should be prioritized for clinical trials of combinations involving 
 pentamidine . in clinical scenarios where treatment side effects may 
 outweigh therapeutic benefits , the potential for enhanced toxicity 
 in the patient this data set is comprised 
 of an experimental screen of 165 drug pairs , of which 48 were found 
 to be synergistic ( supplementary table 1 ) . experimental variability was estimated 
 by 25 experiments testing the  combination  of a drug 
 with itself . s. cerevisiae cells were 
 grown for 24 h in an 8  8 grid of drug combinations , where the 
 concentration of each drug was linearly increased along each axis . the lowest concentration for each drug was set at 0 and the highest 
 concentration was chosen to be close to the minimum inhibitory concentration . 
 thus , for each drug pair , cell growth was measured under 64 different 
 conditions : 49 different concentration combinations of the two drugs , 
 7 single - drug concentrations for each drug , and 1 condition with no 
 drug . for each condition , a detailed time course of growth was obtained , 
 with time points every 15 min for 24 h. using this growth data , significant 
 synergy was assessed according to the loewe additivity model , where 
 combinations of synergistic drug pairs are significantly more efficacious 
 than the combination of a drug with itself . to assess confidence of 
 growth measurements under individual drugs and drug combinations , 
 25 self  self combinations  ( combinations of 
 a drug with itself ) were examined . the replicates had a very high 
 correlation , indicating the reproducibility of growth measurements 
 ( r = 0.98 , p < 10 ) . this data set comprises 
 of 1038 drug pairs that are reported in drugbank.ca to have increased 
 toxicity when combined ( supplementary table 3 ) . of these 1038 , 919 pairs among 428 compounds involved 2 drugs 
 with known molecular weight and xlogp3 . all drug interaction section 
 data derived from drugbank was manually identified as toxicity - related 
 or not , in duplicate by independent curators , until a consensus was 
 reached . we 
 used matlab s classificationtree method to train decision trees , 
 using default parameters : minimum node size of 10 and gini s 
 diversity index criterion when choosing a split . we tried pruning 
 the tree within the 5-fold cv framework by determining the optimal 
 pruning level by nested cross validation . for each training set ( i.e. , defined by 5-fold cv ) , we used matlab s cvloss method ( with 
 parameters subtrees = all , treesize = min ) that considers 
 10-fold cross - validation performance to determine the optimal pruning 
 level for the fitted decision tree , and predicted the held out interaction 
 after pruning the tree . however , predictions of pruned tree resulted 
 in decreased performance for both yeast and human data .
physicochemical 
 properties of compounds have been instrumental 
 in selecting lead compounds with increased drug - likeness . 
 however , 
 the relationship between physicochemical properties of constituent 
 drugs and the tendency to exhibit drug interaction has not been systematically 
 studied . 
 we assembled physicochemical descriptors for a set of antifungal 
 compounds (  drugs  ) previously examined for interaction . 
 analyzing the relationship between molecular weight , lipophilicity , 
 h - bond donor , and h - bond acceptor values for drugs and their propensity 
 to show pairwise antifungal drug synergy , we found that combinations 
 of two lipophilic drugs had a greater tendency to show drug synergy . 
 we developed a more refined decision tree model that successfully 
 predicted drug synergy in stringent cross - validation tests based on 
 only lipophilicity of drugs . 
 our predictions achieved a precision 
 of 63% and allowed successful prediction for 58% of synergistic drug 
 pairs , suggesting that this phenomenon can extend our understanding 
 for a substantial fraction of synergistic drug interactions . 
 we also 
 generated and analyzed a large - scale synergistic human toxicity network , 
 in which we observed that combinations of lipophilic compounds show 
 a tendency for increased toxicity . 
 thus , lipophilicity , a simple and 
 easily determined molecular descriptor , is a powerful predictor of 
 drug synergy . 
 it is well established that lipophilic compounds ( i ) 
 are promiscuous , having many targets in the cell , and ( ii ) often penetrate 
 into the cell via the cellular membrane by passive diffusion . 
 we discuss 
 the positive relationship between drug lipophilicity and drug synergy 
 in the context of potential drug synergy mechanisms .