Simultaneous Clustering of Multiple Gene Expression and Physical Interaction Datasets
[['Heterogeneous genome-wide datasets provide different views of the biology of a cell , and their rapid accumulation demands integrative approaches that exploit the diversity of views .', 'For instance , data on physical interactions such as interactions between two proteins ( protein-protein ) , or regulatory interactions between a protein and a gene via binding to upstream regions of the gene ( protein-DNA ) inform how various molecules within a cell interact with each other to maintain and regulate the processes of a living cell .', 'On the other hand , data on the abundances or expression of molecules such as proteins or transcripts of genes provide a snapshot of the state of a cell under a particular condition .', 'These two data sources on physical interaction and molecular abundance provide complementary views , as the former captures the wiring diagram or static logic of the cell , and the latter the state of the cell at a timepoint in a condition-dependent , dynamic execution of this logic [1] .', 'Researchers have fruitfully exploited this complementarity by studying the topological patterns of physical interaction among genes with expression profiles that are condition-specific [2] , periodic [3] , or correlated [4]; and similarity of the expression profiles of genes with regulatory , physical , or metabolic interactions among them [5] .', 'Another line of research focuses on integrating the physical and expression datasets to chart out clusters or modules of genes involved in a specific cellular pathway .', 'Methods were developed to search for physically interacting genes that have condition-specific expression ( i . e . , differential expression when comparing two or more conditions , as in “active subnetworks” [6] ) , or correlated expression ( eg . subnetworks in the network of physical interactions that are coherently expressed in a given expression dataset [7]–[9] ) .', 'A challenge in expanding the scope of this research is to enable a flexible integration of any number of heterogeneous networks .', 'The heterogeneity in the connectivity structures or edge density of networks could arise from the different data sources used to construct the networks .', 'For instance , a network of coexpression relations between gene pairs is typically built using expression data of a population of samples ( extracted from genetically varying individuals , or individuals subject to varying conditions/treatments ) .', 'Whereas a network of physical interactions between protein or gene pairs is typically built by testing each interaction in a specific individual or in-vitro condition .', 'Towards addressing this challenge , we propose an efficient solution to a well-defined computational framework for combined analysis of multiple networks , each describing pairwise interactions or coexpression relationships among genes .', 'The problem is to find common clusters of genes supported by all of the networks of interest , using quality measures that are normalized and comparable across heterogeneous networks .', 'Our algorithm solves this problem using techniques that permit certain theoretical guarantees ( approximation guarantees ) on the quality of the output clustering relative to the optimal clustering .', 'That is , we prove these guarantees to show that the clustering found by the algorithm on any set of networks reasonably approximates the optimal clustering , finding which is computationally intractable for large networks .', 'Our approach is hence an advance over earlier approaches that either overlap clusters arising from separate clustering of each graph , or use the clustering structure of one arbitrarily chosen reference graph to explore the preserved clusters in other graphs ( see references in survey [10] ) .', 'JointCluster , an implementation of our algorithm , is more robust than the earlier approaches in recovering clusters implanted in simulated networks with high false positive rates .', 'JointCluster enables integration of multiple expression datasets with one or more physical networks , and hence more flexible than other approaches that integrate a single coexpression or similarity network with a physical network [7]–[9] , or multiple , possibly cross-species , expression datasets without a physical network [11]–[13] .', 'JointCluster seeks clusters preserved in multiple networks so that the genes in such a cluster are more likely to participate in the same biological process .', 'We find such coherent clusters by simultaneously clustering the expression data of several yeast segregants in two growth conditions [14] with a physical network of protein-protein and protein-DNA interactions .', 'In systematic evaluation of clusters detected by different methods , JointCluster shows more consistent enrichment across reference classes reflecting various aspects of yeast biology , or yields clusters with better coverage of the analysed genes .', 'The enriched clusters enable function predictions for uncharacterized genes , and highlight the genetic factors and physical interactions coordinating their transcription across growth conditions .'], ['To integrate the information in multiple physical interaction and gene expression datasets , we first represent each dataset as a network or graph whose nodes are the genes of interest and edges indicate relations between gene pairs such as physical interaction between genes or gene products in physical networks , or transcriptional correlation between genes in coexpression networks .', 'Given multiple graphs defined over the same set of nodes , a simultaneous clustering is a clustering or partition of the nodes such that nodes within each set or cluster in the partition are well connected in each graph , and the total cost of inter-cluster edges ( edges with endpoints in different clusters ) is low .', 'We use a normalized measure to define the connectedness of a cluster in a graph , and take the cost of a set of edges to be the ratio of their weight to the total edge weight in the graph .', 'These normalized measures on clustering quality , described in detail in Methods , enable integration of heterogeneous graphs such as graphs with varying edge densities , and are beneficial over simpler formulations as described in detail in a previous study on clustering a single graph [15] .', 'Our work extends the framework used in the single graph clustering study to jointly cluster multiple graphs , such that the information in all graphs is used throughout the algorithm .', 'The algorithm we designed , JointCluster , simultaneously clusters multiple graphs using techniques that permit theoretical guarantees on the quality of the output clustering relative to the optimal clustering .', 'Since finding the optimal clustering is a computationally hard problem , we prove certain approximation guarantees that show how the cluster connectedness and inter-cluster edge cost measures of the clustering output by our algorithm are reasonably close to that of the optimal clustering ( as formalized in Methods , Theorem 2 ) .', 'The basic algorithm , to which these guarantees apply , works with sparse cuts in graphs .', 'A cut refers to a partition of nodes in a graph into two sets , and is called sparse-enough in a graph if the ratio of edges crossing the cut in the graph to the edges incident at the smaller side of the cut is smaller than a threshold specific to the graph .', 'Graph-specific thresholds enable search for clusters that have varying connectedness in different graphs .', 'The main steps in the basic JointCluster algorithm are: approximate the sparsest cut in each input graph using a spectral method , choose among them any cut that is sparse-enough in the corresponding graph yielding the cut , and recurse on the two node sets of the chosen cut , until well connected node sets with no sparse-enough cuts are obtained .', 'JointCluster implementation employs a novel scaling heuristic to reduce the inter-cluster edge cost even further in practice .', 'Instead of finding sparsest cuts in input graphs separately as in the basic algorithm , the heuristic finds sparsest cuts in mixture graphs that are obtained from adding each input graph to a downscaled sum of the other input graphs .', 'The mixture graph with unit downscaling is the sum graph whose edge weights are the sum of weights of the corresponding edges in all input graphs , and the mixture graphs with very large downscaling approaches the original input graphs .', 'The heuristic starts with mixture graphs with small downscaling to help control inter-cluster edges lost in all graphs .', 'But the resulting clusters are coarse ( eg . clusters well connected in some graphs but split into smaller clusters in the rest are not resolved further ) .', 'The heuristic then refines such coarse clusters at the expense of more inter-cluster edges by increasing the downscaling factor ( see Figure 1 ) .', 'The scaling heuristic works best when combined with a cut selection heuristic: if for a particular downscaling , more than one mixture graph yields a sparse-enough cut , choose among them the cut that is sparse-enough in the most number of input graphs ( breaking ties toward the cut with the least cost of edges crossing the cut in all graphs ) .', 'A rigorous description of the algorithm with heuristics for advancing the downscaling factor and selection of cuts is provided in Methods .', 'Our method runs in an unsupervised fashion since algorithm parameters such as graph-specific thresholds are learnt automatically .', 'The recursive cuts made by our algorithm naturally lead to a hierarchical clustering tree , which is then parsed objectively to produce the final clusters [16] using a modularity score function used in other biological contexts [17] , [18] .', 'The modularity score of a cluster in a graph is the fraction of edges contained within the cluster minus the fraction expected by chance in a randomized graph obtained from degree-preserved shuffling of the edges in the original graph , as described in detail in Supplementary Methods in Text S1 .', 'To aggregate the scores of a cluster across multiple graphs , we take their minimum and use this min-modularity score as the cluster score .', 'The ( min-modularity ) score of a clustering is then the sum of the ( min-modularity ) scores of the constituent clusters .', 'We used simulated datasets to benchmark JointCluster against other alternatives:', '( a ) Tree: Choose one of the input graphs as a reference , cluster this single graph using an efficient spectral clustering method [16] to obtain a clustering tree , and parse this tree into clusters using the min-modularity score computed from all graphs;', '( b ) Coassociation: Cluster each graph separately using the spectral method , combine the resulting clusters from different graphs into a coassociation graph [19] , and cluster this graph using the same method .', 'Tree method resembles the marginal cluster analysis in [20] as it analyses multiple networks using the clustering tree of a single network .', 'The simulated test data was generated as in an earlier study [18] , under the assumption that the true classification of genes into clusters is known .', 'Specifically , one random instance involved generating two test graphs over nodes each , and implanting in each graph the same “true” clustering of equal-sized clusters .', 'A parameter controlled the noise level in the simulated graphs by controlling the average number of inter-cluster edges incident at a node .', 'The average number of total edges incident at a node was set at 16 , so measures the false positive rate in a simulated graph .', 'We used the standard Jaccard index , which ranges from 0 to 1 , to measure the degree of overlap between the true clustering and the clustering detected by the methods .', 'Please see Supplementary Text S1 for more details .', 'Figure 2 A shows the performance of different methods in recovering common clusters in graphs with the same noise level , averaged over random instances of for each value of the noise level parameter .', 'When the noise level is low ( or false positive rate at most 25% ) , the clusters output by all methods are close to the true set of clusters ( a Jaccard index close to ) .', 'But when the noise level is high ( or false positive rate 25%–50% ) , the cluster structure becomes subtler , and JointCluster starts to outperform other methods and achieves the best improvement in Jaccard index over other methods at .', 'Note that values where false positive rates are above 50% do not lead to a meaningful cluster structure , and are only shown for context .', 'Thus , within the setting of this benchmark , JointCluster outperformed the alternatives in recovering clusters , especially ones with a weak presence in multiple graphs .', "To simulate real-world scenarios where the integrated networks could've different reliabilities , we benchmarked the methods on clustering graphs with different noise levels .", 'Instead of varying the common value of the graphs as above , we fixed the noise level of at and varied the of the other graph from 0 to 16 .', 'The relative performance of Tree and Tree methods ( see Figure 2 B ) showed that better clusters were obtained when clustering tree of the graph with the lower noise level was used .', 'JointCluster integrated the information in the two graphs to produce a joint clustering tree , which when parsed yielded better clusters than Coassociation and single tree clusters for a larger range of the parameter values ( see Figure 2 B ) .', 'The empirical evaluation of JointCluster and competing methods was done using large-scale yeast datasets , and described in detail next .', 'Expression of transcripts were measured in segregants derived from a cross between the BY and RM strains of the yeast Saccharomyces cerevisiae ( denoted here as the BxR cross ) , grown under two conditions where glucose or ethanol was the predominant carbon source , by an earlier study [14] .', "From these expression data , we derived glucose and ethanol coexpression networks using all 4 , 482 profiled genes as nodes , and taking the weight of an undirected edge between two genes as the absolute value of the Pearson's correlation coefficient between their expression profiles .", 'The network of physical interactions ( protein-protein indicating physical interaction between proteins and protein-DNA indicating regulatory interaction between a protein and the upstream region of a gene to which it binds ) among the same genes or their protein products , collected from various interaction databases ( eg . BioGRID [21] ) , was obtained from an earlier study [9] .', 'The physical network was treated as an undirected graph after dropping interaction orientations , and contained 41 , 660 non-redundant interactions .', 'We applied JointCluster and other clustering methods to integrate the yeast physical and glucose/ethanol coexpression networks , and assessed the biological significance of the detected clusters using reference sets of genes collected from various published sources .', 'The reference sources fall into five diverse classes: We overlapped the detected clusters with the reference sets in these classes to differentiate clusters arising from spurious associations from those with genes coherently involved in a specific biological process , or coregulated due to the effect of a single gene , TF , or genetic factors .', 'The results are summarized using standard performance measures , sensitivity ( fraction of reference sets significantly enriched for genes of some cluster output by a method ) and specificity ( fraction of clusters significantly enriched for genes of some reference set ) , both reported as percentages for each reference class .', 'The significance cutoff for the enrichment P-value ( denoted hereafter ) is 0 . 005 , after Bonferroni correction for the number of sets tested .', 'The sensitivity measures the “coverage” of different biological processes by the clusters , and the specificity the “accuracy” of the clusters .', 'We compared JointCluster with Coassociation [19] , single graph [16] , and single tree ( Tree ) methods , and when applicable with competing methods , Matisse [9] and Co-clustering [7] , which integrate a single coexpression network with a physical network .', 'All reported results focus only on clusters with at least 10 genes .', 'To provide context , we present results from clustering each network separately using the single graph method ( Glucose/Ethanol/Physical Only ) in Figure 3 A . Physical Only performs better than the other two methods wrt ( with respect to ) GO Process and TF Binding Sites , and Glucose/Ethanol Only fare well wrt eQTL Hotspots .', 'This relative performance is not surprising due to the varying levels of bias in the reference classes , and the different data sources used to construct the networks .', 'Though physical interactions between genes or gene products are known to be predictive of shared GO annotations , certain GO annotations inferred from physical interactions introduce bias .', 'The same ChIP binding data [26] was used to predict TF binding sites and protein-DNA interactions , so validation of clusters derived from the physical network using TF Binding Sites is biased .', 'Finally , the same expression data underlying the coexpression networks was used with the independent genotype data to define the eQTL hotspots [14] .', 'Hence the eQTL Hotspots class does not by itself provide a convincing validation of the coexpression clusters; however it can be used to understand the extent of genetic control of coordinated transcription and to validate clusters derived from networks comprising only physical interactions .', 'The reference classes offering truly independent validation of clusters are TF Perturbations and Compendium of Perturbations , and the three single graph methods perform similarly in these perturbation classes .', 'Integration of the yeast physical network with the glucose/ethanol coexpression networks was done to find sets of genes that clustered reasonably well in all three networks .', 'JointCluster performed a better integration of these networks than Coassociation for all reference classes except eQTL Hotspots ( Figure 3 B ) .', 'The enrichment results of single tree methods in Figure 3 B followed a trend similar to the single graph methods in Figure 3 A , reflecting the bias in the reference classes .', 'In the two truly independent perturbation classes , JointCluster showed better sensitivity than the other methods at comparable or better specificity .', 'In summary , though different single graph and single tree methods were best performers in different reference classes ( from Figures 3 A and 3 B ) , JointCluster was more robust and performed well across all reference classes characterizing diverse cellular processes in yeast ( Figure 3 B , first bar ) .', 'The clusters identified by JointCluster that were consistently enriched for different reference classes are explored in depth next .', 'The clusters in a clustering were ordered by their min-modularity scores , and identified by their rank in this ordering .', 'We highlight the biology and multi-network connectivity of the top-ranked clusters detected by JointCluster in an integrated analysis of the yeast physical and glucose/ethanol coexpression networks .', 'The member genes and enrichment results of all preserved clusters detected by JointCluster are provided as Supplementary Data in Text S1 ( see also Table 1 in Supplementary Text S1 for GO Process enrichment of many top-ranked clusters ) .', 'The preserved cluster with the best min-modularity score , Cluster #1 , comprised genes with a min-modularity score of .', "The respective modularity scores in the physical , glucose , and ethanol networks were , , and , which were significantly higher than the modularity of a random set of genes of the same size in the respective networks ( see Figure 1 in Supplementary Text S1 for the cluster's connectivity in the three networks ) .", 'This cluster was significantly enriched for genes involved in the GO Processes , translation ( 1e-20; see Table 1 in Supplementary Text S1 ) , mitochondrion organization ( 1e-20 ) , mitochondrial translation ( 1 . 8e-17 ) and cellular respiration ( 3 . 1e-8 ) .', 'The enrichments noted for Cluster #1 is consistent with and even extend published results on this dataset .', 'The shift in growth conditions from glucose to ethanol triggers large changes in the transcriptional and metabolic states of yeast [28] , with the primary state being fermentation in glucose and respiration in ethanol .', 'The transcription of functionally related genes , measured across different timepoints during the shift , are highly coordinated [28] .', 'The coregulation of related genes is also evident from the clusters of coexpressed genes found under the glucose condition , using expression profiles of genetically perturbed yeast segregants from the BxR cross [29] .', 'Our results take this evidence a step further , because the coexpression of cluster genes are elucidated by genetic perturbations in both growth conditions ( regardless of the expression level changes of cluster genes between the conditions ) .', 'We also note that the top-ranked cluster is significantly enriched for genes linking to the eQTL hotspot region glu11 in Chromosome 14 [14] ( 4 . 6e-25 ) , which highlights the role of genetic factors in the coregulation of genes involved in ( mitochondrial ) translation and cellular respiration .', 'A different perspective on yeast biology in the glucose medium is offered by Cluster #2 consisting of genes ( with a significant min-modularity score 0 . 00021; see Figure 1 in Supplementary Text S1 ) .', 'This cluster is significantly enriched for ribosome biogenesis ( 2 . 4e-37; see Table 1 in Supplementary Text S1 ) , and related GO Process terms such as ribonucleoprotein complex biogenesis and assembly ( 9 . 4e-37 ) , ribosomal large subunit biogenesis ( 8 . 8e-35 ) , and rRNA processing ( 3 . 8e-33 ) .', 'Genes in this cluster significantly overlap with the perturbation signature of BUD21 , a component of small ribosomal subunit ( SSU ) processosome ( 4 . 1e-15 ) , and with genes whose expression links to genetic variations in the eQTL hotspot region glu12 in Chromosome 15 [14] ( 7 . 9e-16 ) .', 'These results are consistent with the literature on the regulation of yeast growth rate in the glucose or ethanol medium , achieved by coregulation of genes involved in ribosome biogenesis and subsequent protein synthetic processes [28] .', 'To further understand the biological significance of these preserved clusters in physical and coexpression networks , we used the reference yeast protein complexes in MIPS [30] ( comprising literature-based , small-scale complexes of at least five genes , at level at most two in the MIPS hierarchy ) .', 'The enrichment of the joint clusters wrt this MIPS Complex class was % sensitivity and % specificity .', 'Of the clusters not enriched for any MIPS complex , some were significantly enriched for other functionally coherent pathways ( eg . Cluster #13 was enriched for amino acid biosynthetic process; see Table 1 in Supplementary Text S1 ) .', 'So the clusters detected by JointCluster overlapped with several known complexes or other functional pathways .', 'One of the goals of jointly clustering multiple networks is to identify subtle clusters: sets of genes that cluster reasonably well , but not strongly , in all networks .', 'We start with biologically significant clusters i . e . , clusters enriched for some reference set wrt all five reference classes , and test if any such cluster has a weak modularity score in some graph .', 'We identified 5 biologically significant clusters using JointCluster: Clusters #4 , #13 , #15 , #19 , and #28 .', 'Table 2 in Supplementary Text S1 shows the reference sets they were enriched for , and Figure 2 in Supplementary Text S1 the modularity scores of Clusters #4 and #28 .', 'Cluster #28 , the biologically significant cluster with the lowest min-modularity score , had genes and was enriched for the GO Processes , multi-organism process ( 2 . 5e-12 ) and conjugation ( 2e-10 ) .', "This cluster's role in mating was further supported by its significant enrichment for perturbation signatures of STE12 ( 5 . 7e-9 ) and FUS3/KSS1 ( 8 . 1e-21 ) , because Ste12p is a TF regulating the expression of mating genes and is activated by the Fus3p/Kss1p kinases in the well-studied mitogen-activated protein kinase ( MAPK ) cascade [31] .", 'Such a cluster of well-studied genes was recovered just by the single graph method Physical Only , but not by Glucose/Ethanol Only .', 'Here we considered a cluster of genes to be recovered by a method if this cluster is significantly enriched for some cluster found by the given method ( as in reference set enrichment ) .', 'JointCluster was able to detect this cluster due to its high modularity in the physical network combined with its significant , albeit weak , modularity in the coexpression networks ( see Figure 2 in Supplementary Text S1 ) .', 'To explore more subtle clusters , we focused on the clusters identified by JointCluster that were enriched for at least four reference classes , instead of all five required above .', 'Clusters #52 and #54 had the two lowest min-modularity scores among such clusters , and were each recovered just by the Physical Only method , but not by Glucose/Ethanol Only .', 'Cluster #52 comprised of genes had a significant min-modularity score ( see Figure 3 in Supplementary Text S1 ) , and was enriched for the GO Process , ubiquitin-dependent protein catabolic process ( 4 . 4e-23 ) .', 'RPN4 is a TF involved in regulation of the protein catabolic process [32] , and this cluster was significantly enriched for genes in the deletion signature of RPN4 ( 1 . 4e-9 ) and genes with predicted binding sites of RPN4 ( 1 . 8e-23; see Supplementary Data in Text S1 for other enrichments ) .', 'These examples reiterate how a combined analysis of multiple networks by JointCluster detects meaningful clusters that would be missed by separate clustering of the networks .', 'Despite the intense focus on elucidating yeast biology by many researchers , roughly 1 , 000 Open Reading Frames ( ORFs ) are still uncharacterized [33] .', 'Therefore , predicting the function of these ORFs is important to guide future experiments towards strains and perturbations that likely elucidate these ORFs [33] .', 'While there have been many network-based function prediction studies ( see survey [34] ) , our study provides a different perspective by using clusters preserved across multiple coexpression and physical networks .', 'Our prediction strategy , based on a module-assisted guilt-by-association concept [34] , annotates the uncharacterized ORFs in a cluster detected by JointCluster to the GO Process reference set for which this cluster is most significantly enriched .', 'To test the utility of these predictions for a well-studied process in yeast , we focused on clusters enriched for ribosome biogenesis ( Clusters #2 and #22; see Table 1 in Supplementary Text S1 ) .', 'Two ORFs in Cluster #2 , a top-ranked cluster discussed above , were marked as uncharacterized by SGD [35] ( April 2009 version ) : YER067W and YLR455W .', "Our predictions for these ORFs have different types of support: YER067W is significantly correlated with 67 and 33 of the 76 genes in this cluster in glucose/ethanol expression datasets respectively ( Pearson's correlation test , Bonferroni corrected for the cluster size ) , and YLR455W has known protein-protein interactions with five other genes in the cluster , NOC2 , BRX1 , PWP1 , RRS1 , EBP2 , all of which were implicated in ribosome biogenesis .", 'Cluster #22 had 9 uncharacterized ORFs , YIL096C , YOR021C , YIL091C , YBR269C , YCR087C-A , YDL199C , YKL171W , YMR148W , and YOR006C .', 'Two of them ( YIL096C and YOR021C ) have predicted roles in ribosome biogenesis based on function predictions collected from the literature by SGD for some of the uncharacterized ORFs .', 'This lends support to the two predictions and leaves the other novel predictions for further validation .', "All of the uncharacterized ORFs in Cluster #22 except YBR269C were significantly correlated with more than three-fourths of the 35 genes in the cluster in both glucose/ethanol expression datasets ( using the same criteria above based on Pearson's correlation test ) .", 'The predictions here were based on either support from the physical network ( for YLR455W ) or from both coexpression networks ( for the rest ) , and hence illustrates the advantage of using multiple data sources .', 'Of the 990 ORFs classified as uncharacterized by SGD ( April 2009 version ) , 524 overlapped with the genes used to build the yeast networks .', 'We could predict the function for 194 of them , by virtue of their membership in preserved clusters significantly enriched for some GO Process term .', 'Using single graph ( Glucose/Ethanol/Physical Only ) clusters in place of the preserved clusters detected by JointCluster yielded predictions for 143 , 148 and 247 uncharacterized ORFs respectively , reflecting the relative GO Process specificity of these methods ( Figures 3 A and 3 B ) .', 'The relative number of predictions from different methods should be viewed in context of the systematic evaluations above , which showed that whereas Physical Only performed best wrt GO Process , JointCluster produced clusters that were more coherent across all reference classes .', 'The predictions from JointCluster were also complementary to those from Physical Only , with the functions of only uncharacterized ORFs predicted by both methods .', 'The functions predicted using the preserved clusters are available as Supplementary Data in Text S1 , and point to well-studied biological processes that have escaped complete characterization .', 'To compare JointCluster against methods that integrate only a single coexpression network with a physical network , such as Matisse and Co-clustering , we considered joint clustering of a combined glucose+ethanol coexpression network and the physical network .', 'The glucose+ethanol network refers to the single coexpression network built from expression data that is obtained by concatenating the normalized expression profiles of genes under the glucose and ethanol conditions .', 'The results of different methods on this two-network clustering is in Figure 4 A . Since our results focus on clusters with at least 10 genes , we set the minimum cluster size parameter in Matisse to 10 ( from its default 5 ) .', 'All other parameters of Matisse and other competing methods were set at the default values .', 'The default size limit of 100 genes for Matisse clusters was used for JointCluster as well to enable a fair comparison .', "Co-clustering didn't have a parameter to directly limit cluster size .", 'Despite setting its parameter for the number of clusters at 45 to get an expected cluster size of 100 , Co-clustering detected very few ( 26 ) clusters of size at least 10 genes , half of which were large with more than 100 genes ( including one coarse cluster with more than 800 genes ) .', 'So Co-clustering achieves greater specificity than other methods ( Figure 4 A ) at the expense of a coarser clustering comprising few large clusters .', 'JointCluster has sensitivity and specificity that is comparable or slightly lower than Matisse across all reference classes except TF Binding Sites .', 'However , JointCluster produces clusters that cover significantly more genes than Matisse ( 4382 vs 2964 genes respectively; see also Figure 4 A ) .', 'Matisse assumes that the physical network is of better quality , and searches for coexpression clusters that are each connected in the physical network .', 'This connectivity constraint excludes genes whose physical interactions are poorly studied or untested .', 'JointCluster does not use such a constraint when parsing the clustering tree into clusters , and hence identifies clusters supported to varying extents in the two networks , including ones with weak support in the physical network .', 'This could be a huge advantage in organisms such as human and mouse where the knowledge of physical interactions is far less complete than in yeast , especially for interactions that are tissue-specific or condition-specific .', 'The extreme examples among the roughly 1500 genes excluded by Matisse clusters were the physically isolated genes ( i . e . , genes that do n
['Introduction', 'Results', 'Discussion', 'Methods']
['Many genome-wide datasets are routinely generated to study different aspects of biological systems , but integrating them to obtain a coherent view of the underlying biology remains a challenge .', 'We propose simultaneous clustering of multiple networks as a framework to integrate large-scale datasets on the interactions among and activities of cellular components .', 'Specifically , we develop an algorithm JointCluster that finds sets of genes that cluster well in multiple networks of interest , such as coexpression networks summarizing correlations among the expression profiles of genes and physical networks describing protein-protein and protein-DNA interactions among genes or gene-products .', 'Our algorithm provides an efficient solution to a well-defined problem of jointly clustering networks , using techniques that permit certain theoretical guarantees on the quality of the detected clustering relative to the optimal clustering .', 'These guarantees coupled with an effective scaling heuristic and the flexibility to handle multiple heterogeneous networks make our method JointCluster an advance over earlier approaches .', 'Simulation results showed JointCluster to be more robust than alternate methods in recovering clusters implanted in networks with high false positive rates .', 'In systematic evaluation of JointCluster and some earlier approaches for combined analysis of the yeast physical network and two gene expression datasets under glucose and ethanol growth conditions , JointCluster discovers clusters that are more consistently enriched for various reference classes capturing different aspects of yeast biology or yield better coverage of the analysed genes .', 'These robust clusters , which are supported across multiple genomic datasets and diverse reference classes , agree with known biology of yeast under these growth conditions , elucidate the genetic control of coordinated transcription , and enable functional predictions for a number of uncharacterized genes .']
['The generation of high-dimensional datasets in the biological sciences has become routine ( protein interaction , gene expression , and DNA/RNA sequence data , to name a few ) , stretching our ability to derive novel biological insights from them , with even less effort focused on integrating these disparate datasets available in the public domain .', 'Hence a most pressing problem in the life sciences today is the development of algorithms to combine large-scale data on different biological dimensions to maximize our understanding of living systems .', 'We present an algorithm for simultaneously clustering multiple biological networks to identify coherent sets of genes ( clusters ) underlying cellular processes .', 'The algorithm allows theoretical guarantees on the quality of the detected clusters relative to the optimal clusters that are computationally infeasible to find , and could be applied to coexpression , protein interaction , protein-DNA networks , and other network types .', 'When combining multiple physical and gene expression based networks in yeast , the clusters we identify are consistently enriched for reference classes capturing diverse aspects of biology , yield good coverage of the analysed genes , and highlight novel members in well-studied cellular processes .']
['genetics and genomics/bioinformatics', 'computational biology/systems biology', 'computational biology/genomics', 'computational biology/transcriptional regulation']