We have focused on the yeast Saccharomyces cerevisiae, for which a wealth of functional genomics data is available. We compiled a library of ~750 expression patterns from various sources, and combined it with the genome-wide promoter occupancies in mid-log phase and rich medium for 113 TFs as measured by Lee et al. 4. It was determined that 37 transcription factor occupancy patterns out of the full set of 113 are significant predictors of mRNA expression for one or more experiments in our library (see Methods). Note that the library of expression data we used obviously does not cover all possible experimental conditions and our method is therefore likely to underestimate the number of transcription factors that are present in the nucleus under the conditions used by Lee et al. 4. For each of the 37 factors selected for further analysis, a transcription factor activity profile (TFAP) was computed ("Step 1" in Fig. 1a) and the TF-target coupling strength was determined ("Step 2" in Fig. 1a). The number of genes in each group (B-, B+/C+, and B+/C-) is listed in Table 1 for the 37 transcription factors analyzed. On average 58% of significantly bound genes are classified as significantly coupling genes. Activity profiles and B+/C+ target predictions for all 37 factors are available on the website supporting this paper.

Several analyses were performed to validate our results. First, we established that B+/C+ genes are significantly enriched for specific Gene Ontology (GO) categories (hypergeometric distribution; 5% false discovery rate) 20. This result is not surprising, as we would already expect the set B+ of ChIP positives per se to be enriched for roughly the same functional categories. By contrast, for almost all TFs analyzed we found no significant enrichment for any GO category in the set of non-coupling (B+/C-) genes (Fig. 2, see supplementary website for details). This result is very significant because it suggests that our criterion for distinguishing functional from non-functional TF targets based on regulatory coupling is accurate: There seems to have been no evolutionary pressure on the set of B+/C- genes.

Next, we analyzed the expression response to transcription factor deletion for the B+/C+ and B+/C- genes. The mean and the standard deviation of the gene expression log-ratio between mutant and wild type as obtained in Hughes et al. were calculated for all genes in the genome, as well as for the B+/C+ and B+/C- groups 21. A sample t-test was performed to determine the significance of the change in expression. The B+/C+ genes show a significant change in mRNA expression for the 7 transcription factors for which deletion and ChIP data are both available. By contrast, the response of the B+/C- genes is insignificant for most transcription factors (Table 2).

In a third analysis to validate our results, we tested for over-representation of 4 different cell cycle related DNA consensus motifs (MCB, SCB, Swi5p and SFF) in the upstream regions of 7 cell cycle related TFs (Ace2, Fkh2, Mbp1, Mcm1, Ndd1, Swi4 and Swi5). The binomial distribution was used to score motif enrichment in the B+/C+ and B+/C- gene sets for each of the transcription factors. We found certain DNA motifs to be significantly over-represented in B+/C+ genes for one or more TFs, but dramatically less so in B+/C- genes (Table 3). Finally, we defined B+/C+ groups using duplicate ChIP experiments for 7 cell cycle regulators performed by Simon et al. and found the overlap with the B+/C+ genes for the data of Lee et al. to be 85% on average 422.

Taken together, the results mentioned above convincingly demonstrate that the use of a coupling factor threshold as a novel additional criterion leads to significantly improved specificity in the prediction of functional TF targets. The biological implications of our analysis are highlighted in the case of divergently transcribed genes that share a common promoter region, represented as a single microarray probe. There are 1592 such probes out of the total 4532 probes in the ChIP experiments of Lee et al. 4. When the ChIP data indicate that a TF binds to the intergenic region, nothing can be said about whether it regulates one of the genes or both based on that information alone. By contrast, our regulatory coupling analysis naturally allows us to distinguish between these different scenarios and make precise statements about which genes are controlled by each of the factors that occupy the promoter region (see Fig. 3). Both uni- and bi-directional control by TFs is observed. Indeed, we found the functional annotation of the protein encoded by the coupled targets to be consistent with what was known about the function of the bound TF in most cases analyzed 20.

Since TF occupancy data from ChIP experiments can be used to separate direct from indirect targets among the genes that respond to TF deletion, combining ChIP data with deletion data can potentially achieve the same goal as our more sophisticated analysis. Keeping Occam's Razor in mind, it is therefore important to investigate to what extent mRNA expression log-ratios from a TF deletion mutant vs. wild type experiment can replace our regulatory coupling strength on the vertical axis in Fig. 1b. We defined sets B+/D+ and B+/D- for each of the seven TFs for which data are available in Hughes et al., the D+ genes being those that show a response to the TF deletion at P < 10^-2, using the P-value provided by those authors 21. In the regulatory coupling analysis described above, we found no significant enrichment for specific GO categories in the group B+/C- of genes that are bound but not coupled. In the present case however, similar levels of enrichment for GO categories are found for B+/D+ and B+/D- genes (Table 4). This result indicates that a substantial fraction of the functional direct targets of a typical transcription factor is being missed even if one combines transcription factor deletion data with ChIP data. A plausible explanation for this lack of sensitivity is that each TF deletion experiment, by definition, is performed under a single condition in which not all possible co-factors of the deleted TF may be present. By using a large and heterogeneous library of experimental conditions as input, our method samples most or all co-factor combinations that occur as the context for control by each TF, naturally taking into account the combinatorial nature of transcriptional control.

A library of 751 genomewide mRNA expression patterns (transcriptomes) was compiled from a variety of sources (see supplementary data for complete references). ChIP data for 113 transcription factors was downloaded from the website accompanying Lee et al. 4. We used the P-values provided by these authors to determine which genes were significantly bound by each given factor at a confidence level of P < 10^-3. All microarray data used in our analysis was represented as log-ratio base two.

For each separate transcriptome t, we used the following multivariate regression model to infer transcription factor activities for each microarray experiment:

Here E_gt represents the mRNA expression log-ratio of gene g in experiment t, while B_fg represents the ChIP log-ratio for transcription factor f and the promoter region of gene g. The intercept F_0t represents a baseline expression level, while the regression coefficients F_ft can be interpreted as inferred transcription factor activities. Starting with the full set of 113 transcription factors, we used backward selection to eliminate uninformative transcription factors from our model: First, for each microarray experiment a P-value corresponding to each regression coefficient was determined, based on an F-test 26. The transcription factors were then sorted based on the smallest P-value among all 751 experiments. In an iterative procedure, the transcription factor with the most insignificant P-value was removed until all factors were significant at a P-value of 0.005/751. Since this analysis in itself is novel and useful, we have made an online ChIP regression tool available at http://bussemaker.bio.columbia.edu/tools/.

For each pair-wise combination of a gene g (represented by its mRNA expression profile E_gt) and a transcription factor f (represented by the inferred activity profile F_ft), a regulatory coupling factor was calculated, equal to the Pearson correlation between E_gt and F_ft:

For each value of r, an associated P-value was computed by performing a t-test on t = r[(G-2)/(1-r²)]^1/2. To account for the parallel testing of many TF-target pairs, but at the same time avoid the overly conservative Bonferroni correction, we set a threshold for t by requiring a false discovery rate of 5% 27. The end result of this procedure is a list of genes that are significantly coupled to a transcription factor. Strictly speaking, to avoid circularity, the coupling of each gene should be evaluated based on a TFAP derived from expression data for all but that gene. However, as the TFAP is derived from the expression profile of all genes bound by the TF, the effect of leaving out one gene is relatively insignificant in practice. Moreover, repeating this procedure for every gene in the genome would be computationally unfeasible.

Based on the regulatory coupling analysis described above, the genes bound a given transcription factor (B+) were sorted in two classes, B+/C+ (bound and coupled) and B+/C- (bound but not coupled). These two sets were used as input for further analysis. The cumulative hypergeometric distribution was used to determine whether a set of genes is enriched for one or more Gene Ontology categories 20. The Bonferroni correction was applied to all P-values to deal with the parallel testing of GO categories. The organism-independent ontology and the gene-association table (version May 2003) for S. cerevisiae were downloaded from http://www.geneontology.org.

Expression data for mutant vs. wild-type comparison for the transcription factors Dig1, Gcn4, Hir2, Mbp1, Swi4, Swi5, and Yap1 were obtained from Hughes et al. 21. To test whether a given subset of genes responded to TF deletion, a sample t-test was performed, comparing the average expression log-ratio in the subset with the genome-wide distribution of expression changes. To guarantee that this analysis was fair, the respective TF deletion experiments were excluded from the library used to calculate the coupling factors that define the C+ and C- groups.

Four different DNA motifs found as top-scoring motifs by REDUCE and also reported in Spellman et al. were tested for over-representation in the set of B+/C+ and B+/C- genes, respectively, for the 7 cell-cycle related transcription factors within the set of 37 factors analyzed by us 1628. These motifs are: ACGCGT (MCB), CGCGAAA (SCB), AACCAGC (Swi5p) and GTAAACA (SFF). Motifs were counted in non-coding regions up to 600 bp upstream from the ORF start position, and expected counts were based on upstream regions of all genes. No overlapping matches were counted. The cumulative binomial distribution was used to assign a P-value to the enrichment for these motifs.