We applied a previously described network-modeling procedure 18 to integrate three complementary sources of gene-regulatory information in yeast: 5,558 promoter-binding interactions for 106 transcription factors measured using chromatin immunoprecipitation followed by microarray chip hybridization (ChIP-chip) 3; the set of all 15,116 pairwise protein-protein interactions recorded in the Database of Interacting Proteins as of April 2004 19; and a panel of mRNA expression profiles for 273 individual gene-deletion experiments 20. Software for performing the network-modeling procedure is available as a plug-in to the Cytoscape package 2122 on our supplementary website 23.

For each gene-deletion experiment, the modeling procedure identified the most probable paths of protein-protein and promoter-binding interactions that connect the deleted gene (the perturbation) to genes that were differentially expressed in response to the deletion (the effects of perturbation). Thus, a path represented one possible physical explanation by which a deleted gene regulates a second gene downstream. From the expression data, each interaction on a path was annotated with its probable direction of information flow and its probable regulatory effect as an inducer or repressor.

For example, the model in Figure 1a (top center) includes a path from GLN3 through GCN4 to a block of downstream affected genes. This model integrates evidence that: Gln3p binds the promoter of GCN4 with high significance in a ChIP-chip assay 3 (p ≤ 8 × 10^-4); Gcn4p binds the promoters of many genes in the ChIP-chip assay (RIB5, YJL200C, and others in the downstream block); and a significant number of genes in the block are upregulated in a gln3Δ knockout but downregulated in a gcn4Δ knockout 20. Together, this evidence confirms Gcn4p as an activator of downstream genes 24 and leads to a (novel) annotation that Gln3p is likely to regulate GCN4 via transcriptional repression.

In total, the modeling process generated 4,836 paths, each explaining expression changes for a particular gene in one or more knockout experiments. Of the 965 interactions covered by paths, 194 had regulatory effects that were uniquely determined by the data, while regulatory effects of the remaining 771 interactions were ambiguous. For example, Figure 1b includes ambiguous interaction paths through SWI4, SOK2, and MSN4, explaining the observation that many genes for which the promoters are bound by Msn4p are upregulated in a swi4Δ knockout. This observation can be explained by several alternative annotations: one scenario is that SWI4 activates SOK2 and SOK2 represses MSN4 (Figure 1b), whereas another is that SWI4 represses SOK2 and SOK2 activates MSN4 (Figure 1c). These regulatory annotations could be uniquely determined by measuring the expression changes of genes downstream of MSN4 in the model in response to a sok2Δ deletion and an msn4Δ deletion (see below).

Paths with ambiguous interactions were partitioned into 37 independent network models (numbered 1-37), where each model contained a distinct region of the physical network (see Materials and methods and Additional data file 1). The remaining non-ambiguous paths were grouped into a single model (Model 0). As shown in Table 1, 21 of the models (55%) contained pathways that are well documented in the literature or are significantly enriched for genes belonging to specific Munich Information Center for Protein Sequences (MIPS) 25 functional categories. Of 132 protein-DNA interactions incorporated into Model 0, we found that 50 had been confirmed in classical (low-throughput) assays as reported in the Proteome BioKnowledge Library 26. Moreover, the inferred regulatory roles (induction or repression) for 48 out of 50 of these interactions agreed with their experimentally determined roles (96%, binomial p-value < 1.22 × 10^-7). Wiring diagrams for Models 0 and 1 are given in Figure 1; diagrams for all other regulatory network models are provided in Additional data file 1 and at 23.

As shown in Figure 2, we implemented an information-theoretic approach to discriminate between ambiguous model annotations using the fewest additional gene-expression experiments. All non-lethal single-gene knockout experiments were ranked by their projected information content based on the inferred models (see Materials and methods). Table 2 reports the list of top-ranking experiments. This list coincides roughly with biological intuition, in the sense that informative target genes typically encode proteins that are network 'hubs', each having a large number of regulatory interactions with downstream genes in the models. However, as discussed later, knocking out hubs only is not as effective as using the information-theoretic criteria.

Among the highest-priority experiments, Model 1 (Figure 1b) was the most often targeted, containing three of the top 10 highest-scoring genetic perturbations: sok2Δ, yap6Δ, and msn4Δ. A fourth perturbation to Model 1, hap4Δ, was also highly ranked (rank 34). Therefore, Model 1 was chosen for further experimentation.

Knockout strains corresponding to the high-ranking perturbations sok2Δ, yap6Δ, hap4Δ, and msn4Δ were grown in quadruplicate under conditions identical to those for the initial 273 knockouts by Hughes et al. 20. Gene-expression profiles were obtained for each knockout culture versus wild type using yeast genome microarrays. We sought to test the three regulatory cascades leading from SWI4 to SOK2 to either MSN4, HAP4, or YAP6 (Figure 1b). To verify these cascades independently of the model, we analyzed the expression patterns of gene sets known to be directly regulated by MSN4, HAP4, or YAP6 (obtained from the Proteome BioKnowledge Library 26; see Additional data file 1). To normalize between our microarray procedures and those of Hughes et al., we also repeated the original swi4Δ expression profile, and filtered the above sets to select only those genes with expression changes that were reproducible (that is, same direction of change) between the Hughes et al. swi4Δ profile and our new profile. Expression changes were reproducible for 28 of 42 Msn4p-regulated genes, 11 of 29 Hap4p-regulated genes, and 64 of 119 Yap6p-regulated genes. Expression similarity among the genes in each filtered set was captured formally in a measure called 'coherence'; details of the computation of expression coherence and the selection of the gene sets are described further in Materials and methods and 23.

As shown in Figure 3a, the gene set downstream of MSN4 showed coherent upregulation in the swi4Δ (p ≤ 10^-4) and sok2Δ (p ≤ 10^-4) knockouts, but downregulation in the msn4Δ (p ≤ 8 × 10^-4) knockout. This result supports the existence of a regulatory cascade leading from SWI4 to SOK2 to MSN4. Furthermore, in the context of the present regulatory cascade, MSN4 appears to be an inducer as its downstream gene set was downregulated in the msn4Δ experiment. In contrast, SOK2 appears to be a repressor of MSN4 as a sok2Δ deletion experiment upregulates the same set of genes. Finally, SWI4 appears to be an inducer of SOK2 as the swi4Δ knockout has the same effect as sok2Δ (that is, upregulation).

Results were qualitatively similar for the HAP4 pathway (Figure 3b). The gene set downstream of HAP4 was upregulated in the swi4Δ (p ≤ 10^-2) and sok2Δ (p ≤ 9 × 10^-4) knockouts but downregulated in hap4Δ (p ≤ 10^-4). These results suggest that swi4Δ, sok2Δ, and hap4Δ deletions affect the set of genes immediately downstream of HAP4, supporting the SWI4-SOK2-HAP4 regulatory pathway hypothesis. In contrast to the MSN4 and HAP4 pathways, the gene set downstream of YAP6 had insignificant responses to all follow-up knockout experiments (Figure 3c). Thus, the existence of the SWI4-SOK2-YAP6 regulatory pathway was not supported by our validation experiments.

We used our modeling procedure to construct a new physical network model using the original 273 knockout gene-expression experiments of Hughes et al. combined with the new sok2Δ, hap4Δ, msn4Δ, and yap6Δ profiles. Overall, 60 protein-DNA interactions were disambiguated by our data: 50 interactions were resolved as definite inducers or repressors, whereas ten interactions were removed from the model because the expression of downstream genes did not change as a result of the knockout. In the updated Model 1, MSN4 and HAP4 were unambiguously annotated as inducers of downstream genes, SOK2 was annotated as a repressor of MSN4 and HAP4, and SWI4 was annotated as an inducer of SOK2 (Figure 3e). These results agree with our previous manually derived annotations (see 'Model validation' above).

We quantified the efficiency of our information-based approach by comparing it to two other methods of prioritizing gene knockout experiments: prioritizing hubs and prioritizing genes randomly. First, we generated a 'reference' model by fixing each ambiguous interaction in Models 1-37 to be an inducer or repressor. Assignments were chosen arbitrarily from the set of annotations that were consistent with the original knockout data. Next, we used each method (information, hub, or random) to iteratively 'learn' these assignments. In each iteration, we selected the highest-priority knockout experiment, simulated the resulting expression changes (up/down) using the reference model, updated the inferred model, and recorded the number of ambiguous interactions that were resolved. This iterative learning procedure was repeated 100 times.

As shown in Figure 4, the mutual information criterion significantly outperformed hub-based and random selection. The learning curves also provide an estimate of the number of additional experiments needed to reduce model ambiguity below a given level. For example, using the information-based score, ten knockout experiments are needed to reduce the number of ambiguous interactions by 50%. In contrast, over 25 experiments are needed according to the hub-based method. Figure 4 suggests that performing 40 additional experiments selected using the information-based score will clarify the regulatory roles of about 70% of the ambiguous interactions. The learning rate of the final 30% becomes very slow because these interactions are isolated in the physical network, unconnected to others, and thus require separate knockouts to decipher each of them.

Physical mechanisms of transcriptional regulation were modeled using an approach described previously 18. Briefly, we postulated that the regulatory effects of deleting a gene are propagated along paths of physical interactions (protein-protein and protein-DNA). We formalized the properties of these paths and interactions using a factor graph 32 and found the most probable set of paths using the max-product algorithm 32. The resulting set of paths was partitioned into independent network models, also as described previously 18. The raw data used in the modeling procedure included 5,558 promoter-binding interactions (at p-value < 0.001) for 106 transcription factors 3, the set of all 15,166 pairwise protein-protein interactions recorded in the Database of Interacting Proteins as of April 2004 19, and mRNA expression profiles for 273 individual gene deletion experiments 20. Expression changes with a p-value < 0.02 were considered significant.

We calculated the expected information gain for each of the 4,756 possible non-lethal single-gene deletion experiments that were not included in the set of 273 deletions used to generate our network models. Intuitively, information gain measures (the logarithm of) the number of ambiguous annotations in the model that are likely to be determined after generating a yeast-genome expression profile in response to a particular gene deletion under consideration. Each gene-deletion experiment predicts a distinct expression profile given a particular configuration of model annotations. Experiments with high information gain are those for which the predicted expression profiles are highly variable over the set of possible annotations. In these cases, only one (or at most a few) of the predicted profiles will match the true observed profile, efficiently constraining the space of possible model annotations.

The information gain discussed above arises from the expected value of information calculations in statistical decision theory 12. Here we describe the score more directly in terms of reduction of model entropy. The entropy of a set of ambiguous model annotations is given by:

The expected information gain is the difference between the entropies before and after a hypothetical experiment:

where Y^e denotes the vector of predicted expression changes for each gene in the model under experiment e. The conditional entropy H(M|Y^e) requires us to consider all possible models and corresponding outcomes resulting from experiment e. Direct enumeration of all values of M and Y^e is impractical; instead, we make several simplifying approximations as described at 23.

Expression profiling experiments were based on the wild-type diploid BY4743 and homozygous gene knockout strains derived from this parent 33 (Invitrogen), with cultures grown identically to those of Hughes et al. 20. Labeled cDNA from each gene knockout strain was co-hybridized versus wild type cDNA in quadruplicate two-color microarray hybridizations. Total RNA was isolated by hot acid phenol extraction, purified to mRNA (Ambion PolyAPure kits), and labeled with Cy3 or Cy5 by direct incorporation (Amersham CyScribe First-Strand cDNA Labeling Kit). DNA microarrays were spotted from the Yeast Genome Oligo Set v1.1 (Qiagen) on Corning UltraGAPS slides using an OmniGrid 100 robot (Genomic Solutions). Lyophilized Cy3- and Cy5-labeled samples were resuspended in 50 μl buffer (5× SSC, 0.1% SDS, 1× Denhardt's solution, 25% formamide) and co-hybridized at 42°C beneath a coverslip for 15 h. Arrays were imaged at 10 μm resolution using a ScanArray Lite instrument (PerkinElmer). Raw quantitated background intensities were smoothed using a 7 × 7 median filter, separately for the Cy3 and Cy5 channels, and data were corrected for cyanine-dye dependent bias using a Qspline normalization 34. The VERA/SAM package 34 was used to assign a log-likelihood statistic λ with each gene, indicating its significance of differential expression in each experiment. Microarray expression data are deposited in the ArrayExpress database 35 under accession numbers A-MEXP-217 (Arrays) and E-MEXP-351 (Experiments).

The expression coherence of a set of genes measures whether the expression levels of these genes behave similarly in a particular experiment. Each gene i in gene-deletion experiment e has an expression ratio r_ie (versus wild type) and associated p-value p_ie of differential expression. First, we filter out insignificant expression changes with a p-value > 0.5. Then, we use the inverse Gaussian cumulative distribution function, Φ^-1, to convert each remaining p-value into a z-score 3637:

z_ie = Φ^-1 (1 - p_ie)

Next, we compute a 'signed z-score' by multiplying z by +1 if the expression level is increasing and by -1 if it is decreasing. The average signed z-score for a gene subset of size N is computed as:

Gene sets with expression changes that are significant and in the same direction result in large Z-values. A distribution of Z values obtained from random gene sets of size N was used to determine a p-value for each expression coherence score.