The basic and intuitive idea of the DDM-MDS approach is illustrated in Figure 1. Assuming the availability of two sets of promoters of differentially regulated genes, it can be expected that their responsiveness to a given stimulus can be explained by TFBSs shared by both sets of promoters, though this may not explain the direction of the response. Next to this common set of TFBSs, every set of promoters might bear one or more TFBSs that are more characteristic of the promoters of the up-regulated or of the down-regulated group of genes, and might explain, at least partially, the observed differential behavior. These 'differential' TFBSs can be found using the following procedure. First, every promoter of each set is used as input for the Match™ program 11, or any other similar program, which will predict TFBSs on it using a precompiled library of positional weight matrices (PWMs). The results, being the number of predicted TFBSs per PWM per promoter (further referred to as counts), are collected in the form of a matrix in which each row corresponds to a promoter sequence while the columns correspond to the used PWM. The columns are further referred to as PWM-vectors, characterizing a PWM by its number of predicted TFBSs per promoter. (Figure 1a). Our choice for using the total number of predicted TFBSs per PWM per promoter is motivated by the observation of Papatsenko et al. 12 that regulatory regions of Drosophila melanogaster contain multiple copies of robust motifs as well as weaker copies. In general, it is reasonable to assume that the presence of multiple binding sites for a transcription factor plays an important role. As our method considers both overrepresentation and association, considering multiple matches per promoter may help discover putative functional TFBSs by overrepresentation. Two TFBSs are considered correlated if their corresponding columns in the matrix are similar. Similarity between the columns can be measured using a distance function. With this approach, distance matrices summarizing all TFBS associations are constructed for the TFBSs in both sets of promoters (Figure 1b). Finally, by calculating the DDM (Figure 1c) and performing MDS on this matrix to visualize its content in two dimensions, we can distinguish TFBSs that do not contribute to the observed differential gene expression, as they will be mapped near the origin of the DDM-MDS plot, from 'deviating' TFBSs that are likely responsible for the observed differential gene expression (Figure 1d). As the MDS procedure will plot TFBSs that are strongly associated closer together than less associated ones, it highlights most of the otherwise often fuzzy interactions between TFBSs in the promoter datasets.

The rationale behind this procedure is based on association and individual overrepresentation (of one condition compared to the other). Important modules in one condition but not the other will be characterized by the overrepresentation of their consisting TFBSs and will be associated. This results in low DD values for two associated TFBSs, whereas the DD value for a TFBS that is overrepresented and common TFBSs will be high. Whether the TFBSs (and module) is typical for either the first or the second set of promoters can be derived from the sign of the column value sum of the original DDM.

The plot for an artificial example is shown in Figure S1 (in Additional data file 1). In a background of counts for all PWMs for two sets of randomly created promoters, two mutually exclusive modules of three TFBSs were inserted into the first set and one module of three TFBSs was inserted into the second set. The modules appear clearly separated from the irrelevant TFBSs.

Using the DDM-MDS protocol, we calculate the distance between the origin of the DDM-MDS plot and each mapped TFBS. A P value is associated with this distance using the following procedure. We constructed 10,000 sets of two groups of randomly selected promoter sequences from the human genome; the sizes of the groups and lengths of constituting promoter sequences reflected the dataset under study. The DDM-MDS procedure was applied to the random sets. The distances obtained with each PWM in the null model follow a gamma distribution, the shape of which depends upon the PWM used. As an example, the distances obtained with the V$CEBPB_01 PWM and the V$E2F1_Q3 PWM using the null model are given in Figures S2 and S3 (in Additional data file 2), respectively. Fitting of the distance distribution was performed using the 'fitdistr' command of the R package 'MASS' 13 and the goodness-of-fit were evaluated using the Kolmogorov-Smirnov test. Finally, since one P value is calculated for each PWM, a correction for multiple testing becomes necessary. We employ the concept of false discovery rates (FDRs), which allows us to adjust the size of our result set as a function of the number of false discoveries we allow. Although the significance calculation of the MDS-distance is done per PWM, there is apparently a close correlation between the increase in distance from the origin of the DDM-MDS plot to the mapped TFBS and the statistical significance of the observation.

Typical DDM-MDS plots using 800 base-pair (bp) upstream promoter sequences can be found in Figures 2 and 3. Every dot corresponds to one PWM from the TRANSFAC 8.4 Professional Motif library. The parameters for Match to obtain the number of predicted TFBSs per PWM were set to 0.9 for core similarity and 0.75 for matrix similarity. These are relatively relaxed threshold values that reduce false negatives while increasing false positives. This should be viewed in the context of our interest in the logical relationships between the matched sites.

Examples of logical relationships are: AND logic, multiple required binding sites; OR logic, a set of motifs any of which satisfies a binding site; and NOT logic, a binding site that should not be present 14. The prediction of TFBSs is the first step in our approach, and it is crucial that the logical relationships between TFBSs are not lost from the beginning. For instance, if the threshold value is set very high to minimize the number of false positives, a maximum of false negatives having a count of zero will be recorded in the input matrices. This would break the AND logical aspects eventually being present between high scoring binding sites and those that score moderately, falling below the threshold score used. The increase in false positive predictions is not a big problem because they participate in random associations in both sets of promoters; as a result, their PWM will be mapped around the origin in the DDM-MDS plot. This is illustrated in the artificial example shown in Figure S1 (Additional data file 1) as the orange cloud of irrelevant PWMs mapped around the origin.

For the biological datasets, most of the PWMs were mapped around the origin, indicating that they are irrelevant for the observed differential expression. The further away a PWM is located from the origin, the stronger the individual overrepresentation of the corresponding TFBSs in one group of promoters compared to the other. The greater the degree of association of TFBSs, the more closely their PWMs will be plotted together. The color of the dot indicates whether the TFBSs corresponding to the PWM are overrepresented in promoters of up-regulated genes (red, positive sum of DD values) or down-regulated genes (green, negative sum of DD values). We also considered the presence of repetitive elements. These elements may contain potential transcriptional regulating signals and, therefore, may be relevant to transcriptional regulation. We therefore ran the DDM-MDS analysis with both masked and unmasked promoter sequences. The results are shown in Figures S4 and S5 (in Additional data file 3). In these particular cases, the effects of masking repeat sequences are only marginal, indicating that repetitive elements are not involved in regulating the observed differential gene expression. With respect to the chosen length of the promoters of 800 bp, most known TFBSs in TRANSFAC have preferred locations between -300 and +50 bp relative to the transcription start site (TSS) 15. This implies that the basal promoter and nearby upstream regulatory elements are found in this region, which is in agreement with the findings of a previous study 16. That study, using a luciferase-based transfection assay in four human cultured cell types, found that 91% of 152 DNA fragments containing regions -550 to +50 relative to the TSS were transcriptionally active. Including an excessive amount of irrelevant sequence would add noise to our approach, and 800 bp upstream of the TSS may provide a reasonable balance between signal and noise in most of the cases. In order to evaluate the effect of taking longer upstream promoter sequences, we compared the results of the DDM-MDS analyses obtained with the 800 bp and 1,500 bp upstream promoter regions of the E2F (Figure S7) and p53 (Figure S8) datasets (see Additional data file 6). The overall pictures remain similar: the main TFBSs appear in positions relatively conserved with respect to the origin of the plot and to each other.

Vernell et al. 17 identified 97 genes as physiological targets of the p16^INK4A-pRB-E2F pathway. Of these, a set of 74 genes is repressed by pRB and p16, but induced by E2F. Another set of 23 genes is induced by pRB and p16, but repressed by E2F. The promoters of the genes that were annotated as known target genes in the published dataset were compiled in a dataset of 18 promoters of genes that are up-regulated by E2F and down-regulated by pRB and p16, and another dataset of 17 promoters of genes that are down-regulated by E2F and up-regulated by pRB and p16.

Figure 2 shows the DDM-MDS plot of the TFBS associations found in this dataset, and Tables 1 and 2 list the highest scoring PWMs whose predicted TFBSs are associated with the promoters of up- and down-regulated target genes, respectively. Associated with up-regulation (red) we find binding sites for E2F, ZF5, AP-2alpha and AP-2gamma. Associated with down-regulation we find binding sites for several CEBPs, STATs, HNFs and AP3.

Using DNA microarrays, Kannan et al. 18 selected 38 and 24 primary targets that were, respectively, up- and down-regulated upon activation of the temperature-sensitive murine p53 in a human lung cancer cell line. Promoter sequences of genes that could be unambiguously identified were collected and used in this analysis. This yielded a dataset of 17 promoters of genes that are up-regulated by p53 and 14 promoters of genes that are down-regulated by p53.

The results of the DDM-MDS analysis are shown in Figure 3. In the set of promoters of up-regulated genes, we find binding sites for several CEBPs, HNFs and STATs, while in the set of promoters of down-regulated genes we observe binding sites for E2F, ZF5 AP-2alpha and AP-2gamma. Table 3 (promoters of up-regulated target genes) and Table 4 (promoters of down-regulated target genes) show the lists of the PWMs with the strongest associations with the observed expression.

Coller et al. 19 identified by oligonucleotide microarray analysis a set of genes that were either consistently induced or consistently repressed upon activation of c-MYC in primary human fibroblasts. The 800 bp human genomic sequences upstream of the genes listed in this dataset were collected. This yielded 28 promoters of genes that were up-regulated and 8 promoters that were down-regulated upon c-MYC activation.

Supplemental Figure S6 (in Additional data file 4) shows the result of the DDM-MDS procedure. Associated with up-regulation we find binding sites for MYC, STAT3, MZF-1 and ARNT. Associated with down-regulation, binding sites for STATx, CdxA and Sp1 are found. The PWMs whose TFBSs show the strongest associations with the observed expression are shown in Tables S1 and S2 (in Additional data file 4).

When we compare the TFBSs associated with differential up-regulation of E2F target genes (Table 1) with those associated with differential down-regulation of p53 target genes (Table 4), we find binding sites for AP-2alpha, AP-2gamma, CHCH, pRb:E2F-1:DP-1, E2F-1:DP-1, E2F-1, c-Myc:Max, Sp1 and ZF5 in both sets of promoters. An overlapping subset of TFBSs is also found when comparing the TFBSs associated with differential down-regulation of E2F target genes (Table 2) with those associated with differential up-regulation of p53 target genes (Table 3). This subset comprises binding sites for AP-3, C/EBPalpha, C/EBPbeta, IRF, STAT4 and STAT6.

The inverse relationships between the two datasets became clearer when we looked at the DDM-MDS plots for these datasets, as shown in Figures 2 and 3. As the MDS procedure plots strongly associated TFBSs closer together than less associated ones, the fuzzy interactions between TFBSs in the datasets are visualized as recognizable patterns. For both datasets, two clusters of TFBS associations emerge: one corresponds to up-regulated gene-TFBS associations (more red) and another to down-regulated gene-TFBS associations (more green). While the positions of the common aforementioned TFBSs in each cluster are relatively conserved, the main difference between them in the two clusters of each dataset is their inverse color. TFBSs characteristic of up-regulation in the E2F dataset are characteristic of down-regulation in the p53 dataset, and vice versa.

We compared our DDM-based method to several methods that claim to be able to find the TFBSs or CRMs responsible for the difference in the response to a stimulus. Since the results of the comparisons are not useful due to the largely disappointing results of the other methods, notes and data about the considered and executed methods can be found in the Additional data files.

In short, LogicMotif 20 and CMA 21 effectively produced some results, but they turned out to be of limited use. These results are given in Tables S3 and S4 (in Additional data file 5), respectively. CREME 22 did not find any module. The output of POCO 23, consisting of five lists of short sequences representing overrepresented TFBSs, is not directly comparable with the output of our approach because our approach takes into account the associations between TFBSs and works only with TFBSs for known transcription factors. CLOVER 24, another program that seeks only for individually overrepresented TFBSs in a promoter set, but in a quite original way, was also compared to our method.

The datasets of the promoters were constructed by extracting nucleotide sequences spanning positions -800 to +0, and -1,500 to +0 relative to the TSS, as reported in the NCBI reference sequences (RefSeq) record of their genes from the May 2004 (hg17) GenBank™ freeze, using the UCSC genome annotation database 49. RefSeq provides standards for genomes, proteins and transcripts resulting from either manual curation or computational gene predictions on pre-assembled contigs 50. In cases where genes had a RefSeq status of at most 'predicted', an additional verification of the TSS was performed using DBTSS (the DataBase of Transcriptional Start Sites) 51.

Upstream promoter sequences (number = n) are used as input for the Match™ program 11, which predicts TFBSs on these sequences making use of a precompiled library containing p PWMs. The information of the annotated output is then collected in the form of a data matrix (N) in which the n rows correspond to the promoter instances and the p columns to the PWMs (and hence their corresponding TFBSs). N_ij is the number of times a TFBS for PWM j was predicted in promoter sequence i.

Match distributed with the TRANSFAC Professional version 8.4 database 52 (Biobase Biological Databases) was used to identify putative transcription factor binding sites within each upstream sequence. As a precompiled library of motif matrices, we used the subset of 512 vertebrate motifs from the TRANSFAC Professional version 8.4 database. Before performing the matrix search, the repetitive elements in the promoter sequences can be optionally masked using 'CENSOR', a program that makes use of 'Repbase Update', a database of eukaryotic repetitive elements, to identify and eliminate repetitive elements from DNA sequences 5354.

The overall strategy is shown in Figure S9 (in Additional data file 7). Given an n_A × p data matrix A, we are interested in the distances between the p PWM-vectors that characterize this particular set of n_A promoter sequences. D^A is the p × p distance matrix containing the distances D^A_ij between PWM-vectors i and j (i and j in [1, p]) from matrix A, normalized for the number n_A of promoters in A (using function f):

D i j A = | A , i − A , j | f ( n A ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWGebWaa0baaSqaaiaadMgacaWGQbaabaGaamyqaaaakiabg2da9maalaaabaGaaiiFaiaadgeadaWgaaWcbaGaaiilaiaadMgaaeqaaOGaeyOeI0IaamyqamaaBaaaleaacaGGSaGaamOAaaqabaGccaGG8baabaGaamOzaiaacIcacaWGUbWaaSbaaSqaaiaadgeaaeqaaOGaaiykaaaaaaa@443B@

where A,_i and A,_j are columns i and j of matrix A, the PWM-vectors i and j. We exclusively used the Euclidean distance as a distance measure between PWM-vectors, hence the function f(x) equals x MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaadaGcaaqaaiaadIhaaSqabaaaaa@3445@.

Given another n_B × p data matrix B, the elements DijA−B MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWGebWaa0baaSqaaiaadMgacaWGQbaabaGaamyqaiabgkHiTiaadkeaaaaaaa@387A@ of the distance difference matrix D^{A - B} are:

D i j A − B = D i j A − D i j B MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWGebWaa0baaSqaaiaadMgacaWGQbaabaGaamyqaiabgkHiTiaadkeaaaGccqGH9aqpcaWGebWaa0baaSqaaiaadMgacaWGQbaabaGaamyqaaaakiabgkHiTiaadseadaqhaaWcbaGaamyAaiaadQgaaeaacaWGcbaaaaaa@41B4@

Based on the notion that two PWMs are correlated on the TFBS level if their corresponding PWM-vectors in either D^A or D^B are similar, it is clear that D^A and D^B contain information about all the associations that exist between the different PWMs in the sets of promoter sequences.

MDS 55 is a method for mapping a set of N objects to N points in k-space such that a given set of target distances or dissimilarities are approximated as well as possible. The procedure finds two-dimensional coordinates of the PWMs by approximating the distance difference values of the DDM on a two-dimensional scale. In the DDM-MDS plot the distance to the origin is used as a relevance measure for each PWM, and the distances between the 'PWM dots' on the plot tell us which TFBSs co-occur on the same promoters. Hence, MDS helps us to determine which PWMs behave the most differently in the two compared promoter sets with respect to all other PWMs. MDS was performed using the cmdscale command in R 13. This function corresponds to an implementation of classical MDS (CMDS), also known as principal coordinates analysis (PCO) or metric MDS. CMDS calculates an eigenanalysis of the DDM to maximize variability along axes. The largest variability is captured by the first two eigenvalues, which enables us to provide a global view of the importance and interactions of the TFBSs in a two-dimensional plot.

Our aim is to identify the TFBS associations responsible for the observed differential gene expression. First, using the DDM-MDS protocol, we calculate the distance between the origin of the MDS plot and the mapped TFBS. This distance quantifies the degree to which this TFBS participates differently in associations with other TFBSs. In the second step, a P value is estimated for this distance. To this end, we define the null hypothesis that the TFBSs do not participate in associations with other TFBSs. This requires specification of a probabilistic model that will be used to estimate the probability that this model generates a distance at least as large as the observed distance. Randomness can be implemented in the null model either by applying shuffling algorithms on the promoter sequences themselves, or by taking randomly chosen fragments or promoter sequences of the organism's genome. In the present study, we opted for the latter because it may reflect a more biologically adequate null model that takes into account global promoter sequence parameters much more so than randomly generated sequences. Since all TFBSs have their particular behavior and are described by positional weight matrices of different quality, we expect differences in random distance distributions for each TFBS. Hence, the DDM-MDS procedure was applied to 10,000 random sets and the resultant distances from each mapped TFBS to the origin of the DDM-MDS plot were obtained. Subsequently, the P value of a real distance was calculated from the fraction of the corresponding 'background distances' exceeding this real distance.

To adjust for the multiple testing problem in our analysis, we adopted the concept of the FDR introduced by Benjamini and Hochberg 56. FDR is defined as the fraction of significant results that are likely due to chance. FDR can be estimated, when calling all P values less than or equal to some threshold t significant (0 < t ≤ 1), by TΦ_t/n_t, where T is the number of TFBS, Φ_t the expected proportion of false positive errors at the specified significance level, and n_t the number of significant tests at that level. Storey and Tibshirani 57 provide an automated way of estimating Φ_t from the observed P values. We used the implementation of their approach in the R package 'GeneTS' 58.

The tool can be accessed at our web server 59. The user can submit data or try the datasets described in this paper. Three matrix sets can be used to characterize the promoter regions of interest: TRANSFAC8.4 52, JASPAR CORE, or JASPAR phyloFACTS 60. This generates the DDM-MDS plot and a set of two tables comprising the most significant transcription factors that explain the differences in the datasets.