We constructed an integrated S. cerevisiae network by combining five types of biological interaction. Nodes in the network represent genes or proteins, and differently colored links represent different biological interaction types. These include: 3,060 SSL interactions derived from synthetic genetic array (SGA) analysis 4; 40,438 protein sequence homology relationships from a genome-wide BLAST search 12; 57,367 correlated mRNA expression relationships derived from microarray data 13; 49,537 stable protein interactions defined by shared membership in a protein complex 141516; and 4,357 transcriptional regulatory interactions from a genome-wide chromatin immuno-precipitation (ChIP) study 7. This collection of data resulted in a single integrated network involving 5,831 nodes and 154,759 links in total (for a full list see Additional data file 1).

Networks of protein-protein and synthetic genetic interaction have been reported to be scale-free and 'small-world' 41718. Being a small-world network implies neighborhood clustering, where neighbors of a given node tend to interact with one another, resulting in an abundance of three-node interconnection patterns – that is, 'triangles'. In addition, relationships such as sequence homology and correlated expression are often transitive (that is, if gene A is homologous to gene B, and gene B is homologous to gene C, then gene A is often homologous to gene C). Thus, a triangle motif for each of these component subnetworks is expected. In order to find additional motifs involving multiple interaction types, we looked for frequently occurring patterns of interconnection in the integrated network, assessing their significance by comparing the observed network with appropriately randomized networks.

We first exhaustively tested all three-node interconnection patterns defined by a single type of link between each pair of nodes (there are 50 such patterns; for a full list see Additional data file 2). Shown in Figure 1 is a list of enriched three-node network motifs, each describing a significantly (p < 0.001) enriched topological relationship among biological interactions of varying types in the integrated S. cerevisiae network. We found that most motifs can be explained in terms of higher-order structures, or network themes, which are representative of the underlying biological phenomena. We classified these motifs into seven sets (Figure 1a–g) according to the themes discussed below. There are five additional motifs that we could not classify into themes (Figure 1h). These are addressed further in the Discussion.

The first motif set contains the transcriptional feed-forward motif (Figure 1a), which has been characterized in several earlier studies of single-color networks of transcriptional regulation 56711. Because transcriptional regulation links often overlap co-expression links, we added to this set another motif composed of two genes with correlated expression that are also indirectly connected by transcriptional regulatory links through an intermediate gene. We noticed that gene triads matching the feed-forward motif in the S. cerevisiae network often overlap with one another to form large clusters, as in the E. coli and C. elegans transcriptional regulatory networks 61011. For example, Swi4 and its transcriptional activator Mcm1 together regulate a number of cell-cycle-related genes (Figure 1a) 192021. Most gene triads matching the feed-forward motif belong to such clusters, leading us to note a 'feed-forward' theme – a pair of transcription factors, one regulating the other, and both regulating a common set of target genes that are often involved in the same biological process.

The next set contains 'co-pointing' motifs, in which a target gene is regulated by two transcription factors that interact physically or share sequence homology (Figure 1b). These co-pointing motifs reflect the fact that two transcription factors regulating the same target gene are often derived from the same ancestral gene, or function as a protein complex. We found that these motifs also overlap extensively, forming a co-pointing theme, in which multiple transcription factors, connected to one another by physical interaction or sequence homology, regulate a common set of target genes. Figure 1b shows one such example, where Hap2, Hap3, Hap4 and Hap5 form the CCAAT-binding factor complex 22 which regulates common target genes, many of which are involved in carbohydrate metabolism 23.

A third set of motifs contains two targets of the same transcription factor bridged by a link of correlated expression, protein-protein interaction, or sequence homology (Figure 1c). These motifs indicate that transcriptional co-regulation is often accompanied by co-expression, membership in the same protein complex, or descent from a common ancestor 324, and suggest a 'regulonic complex' theme in which co-regulated proteins are often components of a complex or related by gene duplication and divergence. Illustrating this theme, six members of the histone octamer, Hhf1, Hhf2, Hht1, Hht2, Hta1 and Htb1 are all regulated by Hir1 and Hir2, histone transcriptional co-repressors that are required for periodic repression of the histone genes (Figure 1c) 25.

The fourth motif set consists of four three-node motifs each containing protein-protein interactions or correlated expression links (Figure 1d). Protein-protein interaction is known to correlate positively with co-expression 12, and proteins corresponding to these motifs often reside in the same complex. Thus, motifs within this set are likely to be signatures of a 'protein complex' theme. One of the many examples is the ATP synthase complex 2627, whose members are linked extensively to one another by protein-protein interaction and correlated expression (Figure 1d).

The fifth motif set contains three-node motifs linked by SSL interaction or by sequence homology (Figure 1e). In the SSL network, neighbors of the same gene often interact with one another 4. This translates into a triangle motif of three SSL links. Furthermore, homology relationships are often transitive (that is, if gene A is homologous to gene B, and gene B is homologous to gene C, then gene A is often homologous to gene C). These phenomena, combined with the fact that genes sharing sequence homology have an increased tendency to show SSL interaction, suggest an underlying theme of the neighborhood clustering in the integrated SSL/homology network: SSL or homology neighbors of one node tend to be linked to one another by SSL interaction or sequence homology. This theme is exemplified by Myo2 and a number of genes connected to Myo2 by SSL interaction or sequence homology (Figure 1e) 42829.

The sixth motif set describes network motifs containing two nodes linked either by SSL interaction or by sequence homology, with a third node connected to each of them through protein-protein interaction or through correlated expression (Figure 1f). All three proteins (a, b and c, as in the schematic diagram in Figure 1f) may be members of the same complex, with either b or c being sufficient to support the essential function of the complex. Proteins b and c may either reside in the complex at the same time, or be mutually exclusive (that is, competing for the same docking position in the complex). This can be generalized to a network theme of a protein complex with partially redundant or compensatory members. As one instance of this theme, both Ssn8 and Cdc73 associate with the RNA polymerase II complex 3031, and only one of them is required for viability (Figure 1f) 4.

We found the seventh motif set particularly interesting. Motifs in this set contain two nodes linked by protein-protein interaction or correlated expression, with a third node connected to both either by SSL interaction or by sequence homology (Figure 1g). Considering previously observed correlations between protein-protein interaction and co-expression 12 and between SSL interaction and sequence homology 4, these motifs indicate that members of a given protein complex or biological process often have common synthetic genetic interaction partner(s) (Figure 1g). For instance, four out of the five Gim complex proteins 32 exhibit synthetic lethality with Sec72 (Figure 1g) 4. A 'compensatory protein and complex/process' theme, in which a protein and a distinct protein complex or biological process have compensatory function, results in synthetic sickness or lethality between the protein and any member of the complex/process essential to the function of that complex/process. It is also possible for the single protein to be part of another complex/process, so that these motifs may in turn be signatures of a larger 'compensatory complexes/processes' theme, which we examine further below.

In addition to the motif sets described above, there are five motifs that we did not categorize (Figure 1h). These are especially interesting, as they may represent unknown biological phenomena (described further in the Discussion).

There are over 5,000 different connected four-node interconnection patterns with each pair of nodes bridged by at most one link type. Here, we have focused on a subset of four-node patterns of particular interest. Recalling the 'compensatory protein and complex/process' theme (Figure 1g), in which a protein has compensatory function with other proteins in a complex or a process, we wondered whether there also exists a network theme corresponding to a pair of complexes/processes with compensatory function (connected to each other by many links of SSL interaction or sequence homology). We searched for all four-node interconnection patterns that would fit this 'compensatory complexes/processes' theme (there are a total of 66 such patterns – for a full list see Additional data file 3). Each pattern is composed of two pairs of nodes such that a protein-protein interaction or correlated expression link exists within each pair and SSL or sequence homology links extend between the two pairs (Figure 2). Using one thousand randomized networks to assess significance, 48 out of the 66 patterns corresponding to this theme were found to be network motifs defined by significant enrichment (p < 0.001) in the real network (see Figure 2 for a few examples and Additional data file 3 for a full list). This supports our hypothesis that compensatory pairs of complexes or processes are a theme in the integrated S. cerevisiae network. The endoplasmic reticulum (ER) protein-translocation subcomplex 33 and the Gim complex 32, connected by many SSL interactions 4, together illustrate this theme. This example also encompasses the 'compensatory protein and complex/process' theme depicted in Figure 1g, wherein multiple SSL or homology links connect Sec72 and the Gim complex.

In order to identify additional pairs of protein complexes with overlapping or compensatory function, we rendered a map of the network in terms of the 'compensatory complexes' theme. This map can also serve as a guide to 'redundant systems' within the integrated S. cerevisiae network, wherein two complexes provide the organism with robustness with respect to random mutation when each complex acts as a 'failsafe mechanism' for the other. To generate a thematic map of compensatory complexes, we searched for pairs of protein complexes with many inter-complex SSL interactions. For this purpose, we only considered links of protein-protein interaction and SSL interaction and reduced the original network to one in which nodes are complexes and links are SSL interactions (with multiple links allowed between a pair of 'collapsed' nodes). For each pair of protein complexes, we calculated the number of links between them and assessed the significance of enrichment (see the Materials and methods section for details). Among the 72 complexes examined (for a list of complexes see Additional data file 1), we found 21 pairs of complexes (involving 26 complexes; listed in Additional data file 4) showing significant enrichment (p ≤ 0.05) for inter-complex SSL interactions. These compensatory complexes can be visualized as a thematic map in which each node represents a protein complex and each link bridges a pair of complexes connected by a significant number of SSL interactions (Figure 3).

Other themes depicted in Figure 1 that might be usefully exploited to generate a simplified thematic map include the 'regulonic complex' theme (Figure 1c), wherein one transcription factor (TF) regulates multiple members of a given protein complex. Such a phenomenon has been observed previously 34. Here, we provide an automated procedure for drawing the map in terms of this network theme. To this end, we examined all possible pairings of a transcription factor with a particular protein complex (together, a 'TF-complex pair'). We reduced the integrated network of stable protein-protein interactions and transcriptional regulations to one in which nodes are either transcription factors or complexes and links indicate transcriptional regulation (with multiple links allowed between a pair of nodes). For each TF-complex pair, we calculated the number of links between them, and assessed the significance according to the probability of obtaining at least the observed number of links if each transcription factor were to choose its regulatory targets randomly. A total of 91 TF-complex pairs showed significant enrichment (p ≤ 0.05) for transcriptional regulation links. These significant TF-complex relationships can also be viewed as a network whose nodes are transcription factors or complexes and whose links represent TF-complex pairs with significantly enriched transcriptional regulation (Figure 4a). Judging from experimental evidence, many of the links connect transcription factors and protein complexes involved in the same biological process, and complexes of related function are often connected to the same transcription factor (Figure 4b).

Synthetic genetic interactions between 132 query genes and about 5,000 array genes were obtained from a recent large-scale SGA analysis in S. cerevisiae 4. Genome-wide BLAST 12 was performed using all yeast protein sequences. Pairs of proteins with E values of less than 10^-3 were considered homologous. Pearson correlation coefficients were calculated for all pairs of yeast proteins based on the Rosetta compendium microarray dataset 13. Protein pairs with correlation coefficients larger than 0.6 were regarded as having correlated expression. Protein complexes were obtained from the MIPS 14 database and two large-scale affinity purification studies 1516. All pairs of proteins residing in the same complex were treated as having stable protein-protein interactions. Transcriptional regulation was inferred from the genome-wide ChIP studies of 106 yeast transcription factors 7. If transcription factor A binds to the promoter region of gene B with a p value of less than 0.001, then a directed transcriptional regulatory link is assigned from A to B.

We enumerated all connected three-node subgraphs in the network as previously described 5. For each interconnection pattern defined by one link between each pair of nodes, we recorded the number of subgraphs matching this pattern in the real network as well as in all randomized networks. A subgraph is considered a 'match' to the pattern if the subgraph can be transformed to the pattern by any combination of node identity permutations or link removals. The p value for the enrichment of an interconnection pattern is defined by the fraction of randomized networks having at least the number of matching subgraphs as the real network.

Different types of interactions in the integrated network were randomized independently, and then overlaid to generate a randomized multi-color network. For each interaction type, we applied a previously described method 60 to sample from an ensemble of random networks with the property that the expected degree of each node is the same as its degree in the real network. Such a method uniformly samples networks with the same degree sequence. The fugacities – parameters controlling the expected degree for each node 60 – were obtained using the multidimensional Newton-Raphson method.

Links in the network of transcription regulation are directional, originating from the transcriptional regulator and ending at the target gene. We distinguished two types of degree for each node – the in-degree (the number of links that end at the node) and the out-degree (the number of links that originate from the node). We then sampled from an ensemble of random networks 60 such that the expected in-degree and out-degree of each node in the ensemble are the same as the corresponding in-degree and out-degree, respectively, in the real network. Such a randomization procedure preserved the directionality of the transcriptional regulatory links.

Nodes in the SSL network can be divided into three mutually-exclusive categories – genes that were used as both query and array genes in the SGA analysis (denoted as 'query/array' genes), genes that were used only as query genes (denoted as 'query-only' genes), and genes that were used only as array genes (denoted as 'array-only' genes) 4. Since an SSL link can only exist between a query gene (that is, either a 'query/array' gene or a 'query-only' gene) and an array gene (that is, either a 'query/array' gene or an 'array-only' gene) 4, we decomposed the SSL network into three sub-networks – a 'query/array↔query/array' sub-network containing only links between 'query/array' genes, a 'query-only↔query/array' sub-network containing only links between 'query-only' genes and 'query/array' genes, and a 'query↔array-only' sub-network containing only links between 'query' genes (that is, either 'query/array' or 'query-only' genes) and 'array-only' genes. When randomizing each of the three sub-networks, only links between the specified gene groups were allowed (for example, in the 'query↔array-only' sub-network, only links between 'query' genes and 'array-only' genes were allowed in the randomized network). A randomized SSL network was then generated by overlaying three such random sub-networks, one from each type. The above procedure preserved the inspection bias of the SGA method, and prohibited any link that could never be observed based on the experiment design.

To generate a thematic map of compensatory complexes, the integrated protein network containing SSL interaction links from the SGA analysis 4 and stable protein-protein interaction links from the MIPS complex catalog 14 was transformed to a network of protein complexes by merging multiple nodes belonging to the same protein complex into a single node. Nodes that do not belong to any known protein complex were removed, along with their associated SSL links. A few mistakes in the MIPS complex catalog were corrected, and some redundantly listed complexes were merged (for the final list of complexes see Additional data file 1). This generated a multi-graph in which multiple links are allowed between two nodes. For each pair of complexes, we recorded the number of links between them, and calculated the probability of obtaining an equal or greater number of links if each protein were to choose its SSL interaction partners randomly from all eligible proteins. Here two proteins are eligible interaction partners for each other if the pair has been tested by the SGA method 4 and both have at least one observed SSL partner in the transformed network. The nature of the SSL network, introduced from the SGA experiments, complicates the analysis, because interactions were tested only between 'query' genes and each of the 5,000 or so 'array' genes 4. For each complex, therefore, some links originate with a query gene in the complex and end with a query gene outside the complex, some links connect a query gene within the complex and a non-query gene outside the complex, while others link a non-query gene within the complex and a query gene outside the complex. Hence, each complex has three different degree types, and the total number of links between two complexes follows a distribution corresponding to the sum of three hypergeometric distributions. The p values were calculated based on this composite distribution. A pair of complexes is connected in the map if the p value is less than 0.05 and there are two or more inter-complex SSL links.

The integrated protein network containing directed transcriptional regulation links from the genome-wide ChIP study (with a p value threshold of 0.005) 7, and stable protein-protein interaction links from the MIPS complex catalog was transformed to a network of transcription factors and protein complexes by collapsing nodes belonging to the same protein complex into a single node. Pairs of complexes that overlap by more than 50% were merged. This generates a multigraph in which multiple links are allowed between two nodes. For each TF-complex pair, we recorded the number of links between them, and calculated the probability of obtaining at least the same number of links if each node chose its interaction partners randomly. We calculated p values according to the cumulative hypergeometric distribution. A TF-complex pair is connected in the map if the p value is less than 0.05 and there are two or more regulatory links between the TF and the complex.