FOCS: a novel method for analyzing enhancer and gene activity patterns infers an extensive enhancer–promoter map

Abstract

Recent sequencing technologies enable joint quantification of promoters and their enhancer regions, allowing inference of enhancer–promoter links. We show that current enhancer–promoter inference methods produce a high rate of false positive links. We introduce FOCS, a new inference method, and by benchmarking against ChIA-PET, HiChIP, and eQTL data show that it results in lower false discovery rates and at the same time higher inference power. By applying FOCS to 2630 samples taken from ENCODE, Roadmap Epigenomics, FANTOM5, and a new compendium of GRO-seq samples, we provide extensive enhancer–promotor maps (http://acgt.cs.tau.ac.il/focs). We illustrate the usability of our maps for deriving biological hypotheses.

Electronic supplementary material

The online version of this article (10.1186/s13059-018-1432-2) contains supplementary material, which is available to authorized users.

Background

Deciphering the regulatory role of the noncoding part of the human genome is a major challenge. With the completion of the sequencing of the genome, efforts have shifted over the past decade towards understanding the epigenome. These efforts aim at understanding regulatory mechanisms outside the protein-coding sequences that allow the production of thousands of different cell types from the same DNA blueprint. Enhancer elements that distally control the activity of target promoters play critical roles in this process. Consequently, large-scale epigenomic projects set out to identify all the cis-regulatory elements that are encoded in the genome. Prominent among them is the ENCODE consortium [1, 2], which applied a variety of epigenomics techniques to a large panel of human cell lines. Profiling epigenetic marks of regulatory activity (including DHS-seq profiling of DNase I hypersensitive sites (DHSs), which is accepted as a common feature of all active elements), ENCODE collectively identified hundreds of thousands of putative regulatory elements in the genome [2]. As ENCODE analyses were mainly applied to cancer cell lines, a follow-up project, the Roadmap Epigenomics, applied similar analyses to a large collection of human primary cells and tissues, in order to establish more physiological maps of common and cell type-specific putative regulatory elements [3]. Given the plethora of candidate enhancer regions called by these projects, the next pressing challenge is to identify which of them is actually functional and map them to the genes they regulate. A naïve approach that is still widely used in genomic studies links enhancers to their nearest genes. Yet, emerging indications suggest that up to 50% of enhancers cross over their most proximal gene and control a more distal one [4]. A common approach that improves this naïve enhancer–promoter (E–P) mapping is based on pairwise correlation between activity patterns of promoters (P) and putative enhancers (E), and identifies E–P pairs, located within a distance limit, that show highly correlated patterns across many samples [2, 3]. However, this approach does not take into account interactions among multiple enhancers that control the same target promoter. Furthermore, Pearson correlation, which is typically applied for this task, is highly sensitive to outliers and thus prone to false positives.

Improved detection of functional enhancers is offered by a recently discovered class of non-coding transcripts, named enhancer RNAs (eRNAs) [5]. eRNAs are mostly transcribed bi-directionally from regions of enhancers that are actively engaged in transcriptional regulation [5] (reviewed in [6, 7]), and, importantly, changes in eRNA expression at specific enhancer regions in response to different stimuli correlate both with changes in the amount of epigenetic marks at these enhancers and with the expression of their target genes [8–11]. Most eRNAs are not polyadenylated and are typically expressed at low levels due to their instability (reviewed in [12]). Therefore, eRNAs are not readily detected by standard RNA-seq protocols, but can be effectively measured by global run-on sequencing (GRO-seq), a technique that measures production rates of all nascent RNAs in a cell [8–10, 13, 14], or by cap-analysis of gene expression (CAGE) followed by sequencing [4, 15, 16]. Utilizing eRNA expression as a mark of enhancer activity, the FANTOM5 consortium recently generated an atlas of predicted enhancers in a large panel of human cancer and primary cell lines and tissues [4]. This study too used pairwise correlation (in this case, calculated between expression levels of an eRNA and a gene whose transcription start site (TSS) is within a distance limit from it) to infer E–P links. Regression analysis was applied to characterize the configuration of promoter regulation by enhancers [4]. However, since all samples were used for training the regression models, this analysis is prone to over-fitting and thus the predictive power of the derived models on new samples is unclear.

Here, we present FOCS (FDR-corrected OLS with Cross-validation and Shrinkage), a novel procedure for inference of E–P links based on correlated activity patterns across many samples from heterogeneous sources. FOCS uses a cross-validation scheme in which regression models are learnt on a training set of samples and then evaluated on left-out samples from other cell types. The models are subjected to a new statistical validation scheme that is tailored for zero-inflated data. Finally, validated models are optimally reduced to derive the most important E–P links. We applied FOCS on massive genomic datasets recorded by ENCODE, Roadmap Epigenomics, and FANTOM5, and on a large compendium of eRNA and gene expression profiles that we compiled from publicly available GRO-seq datasets. We demonstrate that FOCS outperforms extant methods in terms of concordance with E–P interactions identified by ChIA-PET, HiChIP, and eQTL data. Collectively, applying FOCS to these four data resources, we inferred ~ 300,000 cross-validated E–P interactions spanning ~ 16,000 known genes. FOCS and our predicted E–P maps are publicly available at http://acgt.cs.tau.ac.il/focs.

Results

The FOCS procedure for predicting E–P links

We set out to develop an improved statistical framework for prediction of E–P links based on their correlated activity patterns measured over many cell types. As a test case, we first focused on ENCODE’s DHS profiles [2], which constitute 208 samples measured in 106 different cell lines (“Methods”) [2]. This rich resource was previously used to infer E–P links based on pairwise correlation between DHS patterns of promoters and enhancers located within a distance of ±500 kbp. Out of ~ 42 million (M) pairwise comparisons, ~ 1.6 M pairs showed Pearson’s correlation > 0.7 and were regarded as putatively functional E–P links [2]. However, Pearson’s correlation is sensitive to outliers and thus may be prone to high rates of false positive predictions. This is especially exacerbated in cases of sparse data (zero inflation), which are prevalent in enhancer activity patterns, as many of the enhancers are active only in a limited set of conditions. In addition, the combinatorial nature of transcriptional regulation in which a promoter is regulated by multiple enhancers is not considered by such a pairwise approach.

To address these points we developed a novel statistically controlled regression analysis scheme for E–P mapping, which we dubbed FOCS. Specifically, FOCS uses regression analysis to learn predictive models for promoter’s activity from the activity levels of its k closest enhancers, located within a window of ±500 kb around the gene’s TSS. (Throughout our analyses we used k = 10.) Importantly, to avoid over-fitting of the regression models to the training samples, FOCS implements a leave-cell-type-out cross-validation (LCTO CV) procedure, as follows. In a dataset that contains samples from C different cell types, for each promoter FOCS performs C iterations of model learning. In each iteration, all samples belonging to one cell type are left out and the model is trained on the remaining samples. The trained model is then used to predict promoter activity in the left-out samples (Fig. 1).

Fig. 1.

FOCS statistical procedure for inference of E–P links. In a dataset with samples from N different cell types, FOCS starts by performing N cycles of leave-cell-type-out cross-validation (LCTO CV). In cycle j, the set of samples from cell type C_j is left out as a test set, and a regression model is trained, based on the remaining samples, to estimate the level of the promoter P (the independent variable) from the levels of its k closest enhancers (the dependent variables). The model is then used to predict promoter activity in the test set samples. After the N cycles, FOCS tests the agreement between the predicted (P^model) and observed (P^obs) promoter activities using two non-parametric tests. In the binary test, samples are divided into positive (P^obs ≥ 1 RPKM) and negative (P^obs < 1 RPKM) sets, and the ability of the inferred models to separate between the sets is examined using Wilcoxon rank-sum test. In the activity level test, the consistency between predicted and observed activities in the positive set of samples is tested using Spearman correlation. P values are corrected using the BY-FDR procedure, and promoters that passed the validation tests (FDR ≤ 0.1) are considered validated, and full regression models, this time based on all samples, are calculated for them. In the last step, FOCS shrinks each promoter model using elastic net to select its most important enhancers

We implemented and evaluated three alternative regression methods: ordinary least squares (OLS), generalized linear model with the negative binomial distribution (GLM.NB) [17], and zero-inflated negative binomial (ZINB) [18]. GLM.NB accounts for unequal mean-variance relationships within subpopulations of replicates. ZINB is similar to GLM.NB but also accounts for excess of samples with zero entries (“Methods”). For each promoter and regression method, the learning phase yields an activity vector, containing the promoter’s activity in each sample as predicted when it was left out. FOCS applies two non-parametric tests, tailored for zero-inflated data, to evaluate the ability of the inferred models (consisting of the k nearest enhancers) to predict the activity of the target promoter in the left-out samples. The first test is a “binary test” in which samples are divided into two sets, positive and negative, containing the samples in which the promoter was active or not, respectively, based on their measured signal (we used a signal threshold of 1.0 RPKM for this classification). Then, the Wilcoxon signed-rank test is used to compare the predicted promoter activities between these two sets (Fig. 1). The second test is an “activity level test”, which examines the agreement between the predicted and observed promoter’s activities using Spearman’s correlation. In this test, only the positive samples (that is, samples in which the measured promoter signal is ≥ 1.0 RPKM) are considered. Gene models with good predictive power should discriminate well between positive and negative samples (the binary test) and preserve the original activity ranks of the positive samples (the activity level test), and models that pass these tests are regarded as statistically cross-validated. Of note, these two validation tests evaluate each promoter model non-parametrically without assuming any underlying distribution on the data when inferring significance. Next, FOCS corrects the p values obtained by these tests for multiple testing using the Benjamini–Yekutieli (BY) FDR procedure [19] with q-value < 0.1. The BY FDR procedure takes into account possible positive dependencies between tests while the more frequently used Benjamini–Hochberg (BH) FDR procedure [20] assumes the tests are independent.

FOCS results for ENCODE DHS epigenomic data

Applying FOCS to the ENCODE DHS dataset, we only considered promoters and enhancers that were active (that is, with signal > 1.0 RPKM) in at least 30 out of the 208 samples (This preprocessing step filtered out from the analysis 828 genes whose expression was most cell type-specific.) Overall, this dataset contained 92,909 and 408,802 active promoters and enhancers, respectively (“Methods”). We first evaluated the performance of the three alternative regression methods in terms of the number of validated models each of them yielded. We found that the OLS method consistently produced more validated models that passed both the binary and activity level tests (Fig. 2a, b; Additional file 1: Table S1). Using OLS, out of the 92,909 analyzed promoters, 52,658 had models that passed both tests (q-value ≤ 0.1), while for 7007 promoters models passed none of these two tests (Fig. 2c). As expected, promoters with models that passed only the activity level test were active in a very high number of samples while those with models that passed only the binary test were active in a much lower number of samples (Fig. 2d; see Additional file 1: Figure S1 for examples of promoters in different validation categories). To examine the effect of the leave-cell-type-out cross-validation (CV) procedure we compared R² values obtained by OLS models generated without CV to the values obtained when CV was applied (Fig. 2e). The results indicate that without CV, many models are over-fitted to the training samples and have low predictive power on new ones. This problem is more severe in other datasets that we analyzed, as shown in the subsequent section. Fig. 2f shows an example of a promoter model with low predictive power on new samples, and demonstrates the high sensitivity of Pearson’s correlation (or equivalently, of R²) to outliers. Such promoter models do not pass our CV tests and are considered to have low confidence.

Fig. 2.

Performance of three alternative regression methods for inferring E–P models. a Performance of ordinary least squares (OLS), generalized linear model with negative binomial distribution (GLM.NB), and zero-inflated negative binomial (ZINB) regression using the binary test. Point (x,y) on a plot indicates that a fraction x of the models had − log₁₀[q-value] < y computed by Wilcoxon rank sum test. OLS yields a higher fraction of validated models at any q-value cutoff. b Same as a but using the activity level validation test, with p values computed by the Spearman correlation test. Here too, OLS yields a higher fraction of validated models than the other methods. c Number of promoters whose OLS models passed (at q < 0.1) each of the tests (or none). d The distribution of the number of positive samples (samples in which the promoter is active, i.e., has RPKM≥1) for promoters in each category. e Comparison between the R² values with and without cross-validation (CV). Each dot is a promoter model. Blue dots denote models with R² ≥ 0.5 and $R_{\mathit{CV}}^2\ge 0.25$. Red dots denote models with and R² > 0.5 and $R_{\mathit{CV}}^2<0.25$ corresponding to over-fitted models with low predictive power on novel samples. f A promoter whose model as computed without CV has a very high R² (left plot) but when CV is applied a low $R_{\mathit{CV}}^2$ is obtained (right plot). This example demonstrates the sensitivity of R² (and Pearson correlation) to outliers. ρ_s Spearman correlation, Q-value FDR-corrected p value

The configuration of promoter regulation by enhancers

Next, we sought to characterize the configuration of promoter regulation by its enhancers, in terms of the number of regulating enhancers and their relative contribution. For each promoter that passed the validation tests, we now calculated a final model, this time considering all samples (Fig. 1), and estimated the relative contribution of each of its k enhancers to this full model. As in [4], per model, we measured the proportional contribution of each enhancer by calculating the ratio r²/R² where r is the pairwise Pearson correlation between the enhancer and promoter activity patterns and R² is the coefficient of determination of the entire promoter’s model. In the analysis of the ENCODE DHS data, we included in this step the 70,465 promoters that passed the activity level test (or both tests). In agreement with previous observation [4], the closest enhancers make significantly higher contributions than the distal ones (Fig. 3a). However, the proportional contribution quickly reaches a plateau, indicating that, above a certain threshold, distance to promoter is no longer an important factor, and enhancers 6–10 (ordered according to their distance from the promoter) contribute similarly to promoter activity (Fig. 3a). Second, we examined the distribution of R² values of these statistically validated models: 54% of the models (37,716 out of 70,465) had R² ≥ 0.5 (Fig. 3b); 61% of the 52,658 models that passed both tests had R² ≥ 0.5, compared to 32% of the 17,807 models that passed only the activity level test (in contrast, only 13% of 15,437 models that passed only the binary test had R² ≥ 0.5). We note that models that passed the CV tests but have low R² do contain confident and predictive information on E–P links, though the low R² suggests that additional, missing regulatory elements play important roles in the regulation of the target promoter.

Fig. 3.

Configuration of promoter regulation by enhancers. a The proportional contributions of the ten most proximal enhancers (within ±500 kb of the target promoter) to models predicting promoter activity. The x-axis indicates the order of the enhancers by their relative distance from the promoter, with 1 being the closest. b R² values of the models that passed one or both CV tests. c Distribution of the number of enhancers included in the validated, optimally reduced models (i.e., after elastic net shrinkage). Most shrunken models contain one to three enhancers. d Inclusion frequency of enhancers in the shrunken models as a function of their relative proximity to the target promoter

A promoter’s model produced by OLS regression contains all k variables (i.e., enhancers), where each variable is assigned a significance level (p value) reflecting its statistical strength. Next, to focus on the most informative E–P interactions, FOCS seeks the strongest enhancers in each model. To this end, FOCS derives, per promoter, an optimally reduced model by applying model shrinkage (“Methods”). Lasso-based shrinkage was previously used for this task [4]. Here, we chose elastic-net (enet) approach, which combines Lasso and Ridge regularizations, since in cases of highly correlated variables (i.e., the enhancers), Lasso tends to select a single variable while Ridge gives them more equal coefficients (“Methods”). In this analysis too, we included the 70,465 models that passed the activity level test. Figure 3c shows the distribution of the number of enhancers that were included in the enet-reduced models. On average, each promoter was linked to 2.4 enhancers. Inclusion frequency decreased with E–P distance: the most proximal enhancer was included in 63% of the models while the tenth enhancer was included in only 16% of them (Fig. 3d). Here too, the graph reaches a plateau and enhancers 6–10 show very similar inclusion frequencies. Additional file 1: Figure S2A, B show the distribution of the actual E–P distance for the enhancers considered by FOCS and Additional file 1: Figure S2C shows the inclusion frequency as a function of this distance. Regulatory elements located less than 5 kb from their target promoter have markedly higher inclusion frequency. To estimate false positive rate among enhancers included in our final enet-reduced models, we randomly selected 10,000 promoter models from the 70,465 models that passed the CV step, and added to each one of them an additional 11th enhancer randomly selected from a different chromosome. We then applied enet on these 10,000 models. Notably, the random enhancer was retained in only seven out of the 10,000 models, which is significantly lower than the inclusion frequency we observed for any E–P distance bin (Additional file 1: Figure S2C), indicating a low false positive rate also among the long distance E–P links inferred by FOCS.

Comparison of performance of FOCS and extant methods using external validation resources

After optimally reducing the promoter models, FOCS predicted in the ENCODE DHS dataset a total of 167,988 E–P links covering 70,465 promoters and 92,603 distinct enhancers (http://acgt.cs.tau.ac.il/focs/data/encode_interactions.txt). Next, we compared the performance of FOCS and three alternative methods for E–P mapping. (1) Pairwise: pairwise Pearson correlation > 0.7 between E–P pairs located within ±500 kbp, and accounting for multiple testing using BH (FDR < 10⁻⁵; this was the main method used in [4], and also in [2] without multiple testing correction). (2) OLS + LASSO: models are derived by OLS analysis using all samples without CV, selected based on R² ≥ 0.5 and reduced using LASSO shrinkage (“Methods”; this method was also applied in [4]). (3) OLS + enet: same as (2) but with enet shrinkage in place of LASSO. Table 1 summarizes the number of E–P links obtained by each method. FOCS yielded ~ 75% more models than the other methods.

Table 1.

Number of inferred promoter models obtained by four alternative methods on the ENCODE DHS dataset

Method type	Number of promoter models	Number of E–P links	Number of unique enhancers
Pairwise (r ≥ 0.7)+ FDR	39,372	139,170	53,950
OLS-LASSO (R2 ≥ 0.5)a	39,368	122,064	74,104
OLS-enet (R2 ≥ 0.5)a	39,407	150,158	85,926
FOCS	70,465	167,988	92,603

^aThe number of OLS models (R² ≥ 0.5) was 39,892 before LASSO/enet shrinkage. These methods eliminate models in which no enhancer passed the shrinkage

To evaluate the validity of E–P mappings predicted by each method, we used three external omics resources: physical E–P interactions derived from RNAPII ChIA-PET data, physical E–P interactions derived from YY1 HiChIP experiments, and functional E–P links indicated by eQTL analysis (“Methods”). For physical E–P interactions derived from RNAPII ChIA-PET we used data recorded in MCF7, HCT-116, K562, and HelaS3 cell lines (a total of 922,997 interactions). Physical E–P interactions inferred from HiChIP for YY1 (recently suggested to act as a general structural regulator of E–P links) were downloaded from [21] (911,190 interactions, measured in HCT-116, Jurkat, and K562 cell lines). While 3C-based methods are generally not well equipped to identify DNA loops below 25 kb, we intersected our results with the best available loop calls for these data ranges. eQTL data were downloaded from the GTEx project (2,283,827 unique significant eQTL–gene pairs) [22]. We defined a 1-kbp interval for each promoter and enhancer and calculated the fraction of E–P links that were supported by either ChIA-PET, HiChIP, or eQTL data (“Methods”). Notably, FOCS not only yielded many more E–P links (15,000–40,000 more), but also outperformed the alternative methods in terms of the fraction of predictions supported by either RNAPII ChIA-PET (Fig. 4a), YY1 HiChIP (Fig. 4b), or eQTL data (Fig. 4c). Figure 5 shows two FOCS-derived promoter models that are supported by ChIA-PET and eQTLs. Note that for the promoter model of CD4 (Fig. 5b) the $R_{\mathit{CV}}^2$ value was low (~ 0.1) while the Spearman correlation (ρ_s) was 0.53 after CV. This demonstrates that FOCS can capture promoter models that exhibit non-linear relationships between the promoter and enhancer activities.

Fig. 4.

Comparison of the performance of different methods for predicting E–P links using ChIA-PET and eQTL data as external validation. The y-axis shows the total number of predicted E–P links. The x-axis shows the percentage supported by the external source. a Pol-II ChIA-PET. b YY1 HiChIP. c GTEX eQTLs. In c the y-axis shows the total number of predicted E–P links where the promoter is annotated with a known gene. FOCS (green triangle) makes more predictions and also manifests the highest support rate by all methods: RNPII ChIA-PET, 59%; YY1 HiChIP, 37%; and eQTL, 38%. For all methods, the empirical p value by random permutation test was < 0.01 (“Methods”)

Fig. 5.

Examples of FOCS-predicted E–P links supported by ChIA-PET/eQTL data. a, b CD4. c, d ESRP1. TSS location is highlighted in light blue. b, d Heatmaps (log₂[RPKM Signal]) for the activity patterns of CD4/ESRP1 promoters and their ten nearest enhancers. Enhancers included in the shrunken model are denoted by ‘ep’ and those that are not are denoted by ‘e’. For each enhancer, its Pearson and Spearman correlations with the promoter are reported (left and right values in the parentheses). For each model, the $R^2,R_{\mathit{CV}}^2,$ and Spearman correlation after CV (ρ_s) are listed

FOCS performance on additional large-scale datasets

Having demonstrated FOCS proficiency in predicting E–P links on the ENCODE DHS data, we next wished to expand the scope of our E–P mapping. We therefore applied FOCS to three additional large-scale genomic datasets: (1) DHS profiles measured by the Roadmap Epigenomics project, consisting of 350 samples from 73 different cell types and tissues; and (2) FANTOM5 CAGE data that measured expression profiles in 1827 samples from 600 human cell lines and primary cells. The analysis of FANTOM5 data uses eRNA and TSS expression levels for estimating the activity of enhancers and promoters, respectively (“Methods”). (3) A GRO-seq compendium that we compiled. Building on eRNAs as quantitative markers of enhancer activity and the effectiveness of the GRO-seq technique in detecting eRNA expression [23], we compiled a large compendium of eRNA and gene expression profiles from publicly available GRO-seq datasets, spanning a total of 245 samples measured on 23 different human cell lines (“Methods”).

We applied to these datasets the same procedure that we applied above to the ENCODE data. In the analysis of these datasets, OLS yielded more validated models than the other regression methods on the Roadmap Epigenomics and GRO-seq datasets (as was the case in the ENCODE DHS data (Fig. 2a, b)), while GLM.NB and ZINB produced more models on FANTOM5 (Additional file 1: Figure S3A-C and Table S1). The performance of GLM.NB and ZINB on the FANTOM5 dataset is probably due to the high fraction of zero entries in the count matrix of this dataset (~ 54%) compared to ENCODE, Roadmap, and GRO-seq data matrices (8, 4, and 19%, respectively). As OLS performed better on most datasets, all the results reported below are based on OLS. The numbers of promoter models that passed each validation test in each dataset are provided in Additional file 1: Figure S4A–C. The effect of CV is presented in Additional file 1: Figure S5A–C. In these datasets too, many of the models with a high coefficient of determination (R² ≥ 0.5) when trained on all samples had low predictive power on novel samples ($R_{\mathit{CV}}^2<0.25$) (Empirical FDR 16, 20, and 22% in Roadmap, FANTOM5, and GRO-seq, respectively; Additional file 1: Figure S5), demonstrating the utility of CV in alleviating over-fitting and thus reducing false positive models.

We next examined the relative contribution of each of the ten participating enhancers to the validated models, and in these datasets too, the most proximal enhancers had the highest role, but more distal ones made very similar contributions (Additional file 1: Figure S6A). In terms of explained fraction of the observed variability in promoter activity, 41 and 84% of the models that passed both tests in the Roadmap Epigenomics and GRO-seq datasets, respectively, had R² ≥ 0.5, but only 11% of the validated models reached this performance in the FANTOM5 dataset (Additional file 1: Figure S6B), probably due to its exceptionally sparse data matrix. Last, FOCS applied enet model shrinkage to the models that passed the validation tests (the number of validated models and E–P links derived by FOCS on each dataset is summarized in Additional file 1: Table S2). In the optimally reduced models, each promoter was linked, on average, to 3.2, 2.8, and 3.6 enhancers in the Roadmap, FANTOM5, and GRO-seq datasets, respectively (Additional file 1: Figure S7A), and inclusion frequency decreased with E–P distance (Additional file 1: Figures S7B and S8). Finally, benchmarking against RNAPII ChIA-PET, YY1 HiChIP, and eQTL data, for most comparisons, FOCS outperformed the alternative methods for E–P mapping by yielding many more E–P predictions at similar external validation rates (Additional file 1: Figure S9 and Table S3). Collectively, we provide a rich resource of predicted E–P mapping that covers 16,349 known genes, 113,653 promoters, 181,236 enhancers, and 302,050 cross-validated E–P links.

Discussion

In this study we present FOCS, a novel statistical framework for predicting E–P interactions based on activity patterns derived from large-scale omic datasets. Applying FOCS to four different genomic data sources, we derived an extensive resource of statistically cross-validated E–P links. Our E–P mapping resource further illuminates different facets of transcriptional regulation. First, a common naïve practice is to map enhancers to their nearest promoters. In FOCS predicted E–P links, ~ 26% of the enhancers are mapped to a promoter that is not the closest one (Additional file 1: Figure S10). Second, intronic enhancers are very common; 70% of the predicted E–P links involve an intronic enhancer (Additional file 1: Table S2). Third, while in the shrunken models each promoter was linked to, on average, ~ 3 enhancers, many promoters were linked to a single dominant enhancer and some were linked to a very high number of enhancers (8–10).

As an initial step in exploring relationships between the configuration of E–P interactions and gene function, we examined the set of housekeeping genes taken from [24]. These genes are ubiquitously expressed across different cell types, suggesting that they are likely to have a simple regulation logic. Indeed, the promoters of these genes were involved in a significantly lower number of E–P links compared to all other genes (p value < 0.001 in all data types; Additional file 1: Figure S11). To further explore a possible relationship between the breadth of gene expression across tissues and the complexity of transcriptional regulation, we calculated the Shannon entropy for each gene promoter (higher entropy indicates larger expression breadth). Interestingly, we observed a strong negative relationship where promoters with more restricted activity profiles (that is, lower entropy) are associated with a larger number of enhancers (Fig. 6, Additional file 1: Figure S12). As a set, the genes associated with higher numbers of enhancers were enriched for Gene Ontology (GO) categories related to cell adhesion, signal transduction, and differentiation (Additional file 2).

Fig. 6.

Inverse relationship between breadth of promoter activity and complexity of transcriptional regulation. We quantified the breadth of promoter activity over different cell types by Shannon entropy. Promoters were divided into bins according to the number of enhancers included in their optimally reduced models and the distribution of Shannon entropy was calculated for each bin (the number of promoters assigned to each bin is indicated in parentheses). A marked inverse relationship is observed. The results shown here are based on ENCODE DHS data (see Additional file 1: Figure S12 for the same analysis applied to FANTOM5 CAGE data)

We also observed that while the vast majority (~ 90%) of enhancers in FOCS-derived models had positive Pearson and Spearman correlation with the activity pattern of their target promoters, the models also included cases of negative correlation, suggesting that the regulatory element functions as a repressor (Additional file 1: Figure S13). Finally, the activity level test in FOCS, computed using the Spearman correlation, can also account for promoter models where the relationship between the enhancer and promoter activity patterns is not linear, perhaps explaining the R² < 0.5 values observed in the majority of FANTOM5 and Roadmap models (Additional file 1: Figure S6B).

An aspect that we did not consider in our analysis is the constraints imposed on transcriptional regulation by the 3D organization of the genome. Recent findings indicate that most E–P interactions are limited by chromosomal territories called topologically associated domains [25, 26]. Further research is needed to better elucidate this connection between 3D organization and E–P links and to better understand to what extent such constraints are universally or differentially imposed in different cell types.

Biological interpretation of our analysis of DHS data (ENCODE and Roadmap Epigenomics datasets) implicitly assumes that transcription rate at promoters is positively related with promoter DHS signal. We therefore examined DHS–expression correlations in cell lines for which both DHS and RNA-seq data were available in the ENCODE project (17 cell lines in total). In all cases, we observed high Spearman but low Pearson correlations (Additional file 1: Figure S14), indicating a strong monotonic but non-linear relationship.

The leave-cell-type-out scheme applied by FOCS is conservative and ensures that the inferred models have predictive power in diverse cellular contexts. However, it will not infer models for genes whose expression is strictly cell type-specific. Analyzing larger numbers of diverse cell types containing related cell types, we expect a lower chance of missing gene models that are cell type-specific.

While our manuscript was under review another novel method for inference of E–P interactions, called JEME, was introduced [27]. Unlike FOCS, JEME (and the previously published TargetFinder [28]) makes cell type-specific predictions and combines different omic data types within the same model.

Our broad compendium of E–P interactions can greatly assist the functional interpretation of genetic variants that are associated with disease susceptibility, as the majority (~ 90%) of the variants detected by genome-wide association studies are located in noncoding sequences [29]. Similarly, it can help in the interpretation of recurrent noncoding somatic mutations (SMs) in cancer genomes. SM hotspots in regulatory regions are detected at an accelerated pace with the rapid accumulation of whole-genome sequencing (WGS) of tumor samples [30, 31]. Additionally, the predicted E–P links can be integrated into and boost bioinformatics pipelines that seek DNA motifs in regulatory elements that putatively regulate sets of co-expressed genes. Overall, the FOCS method and the compendium we provide hold promise for advancing our understanding of the noncoding regulatory genome.

Conclusions

• FOCS predicts ~ 1.5-fold more E–P links (n = 302,050) compared to the standard pairwise method with Pearson coefficient r > 0.7 (n = 204,276). On average over all datasets, FOCS E–P links show a higher support rate by external validation resources compared to the commonly used pairwise method (r > 0.7). These results demonstrate the improved prediction power and control of false positive E–P links.

• FOCS uses two non-parametric tests to examine the robustness of each promoter model. Using these tests we can correct for multiple promoter models and use them when it is suspected that there is no linear relationship between the E–P activity patterns. Previous methods used the Pearson correlation test (or, equivalently R² values) assuming linearity between enhancer and promoter activity patterns.

• FOCS is capable of detecting repressor–promoter (R-P) links, which result from negative Spearman correlation between R–P activity patterns. R–P links are less known and are also of high interest.

• We provide a new compendium of eRNA and gene expression patterns based on 245 GRO-seq profiles from 23 different cell types. This compendium can be used as a genome-wide resource of enhancer activity in a diverse panel of cell lines.

Methods

ENCODE DHS data preprocessing

DHS peak locations of enhancers and promoters were taken from a master list of 2,890,742 unique, non-overlapping DHS segments [2] (ftp://ftp.ebi.ac.uk/pub/databases/ensembl/encode/integration_data_jan2011/byDataType/openchrom/jan2011/combined_peaks/multi-tissue.master.ntypes.simple.hg19.bed).

We extracted from the master list the set of known (n = 68,762) and novel (n = 44,853) promoter–DHS peaks taken from ftp://ftp.ebi.ac.uk/pub/databases/ensembl/encode/integration_data_jan2011/byDataType/openchrom/jan2011/promoter_predictions.

The remaining (n = 2,777,127) non-promoter–DHS peaks in the master list were considered as putative regulatory elements, collectively referred to here as enhancer elements. To create enhancer/promoter signal matrices, we used the BAM files of 208 UW DNase-seq samples (106 cell types) from the Gene Expression Omnibus (GEO) dataset GSE29692 [2, 29, 32]. The number of reads mapped within each DHS peak was counted using BEDTools utilities [33]. To reduce our FOCS running time we focused only on promoters/enhancers with signal ≥ 1 RPKM in at least 30 samples, resulting in 92,909 promoters and 408,802 putative enhancers.

We defined for each promoter the set of k = 10 candidate enhancers located within a window of 1 Mb (±500 kb upstream/downstream of the promoter’s center position). We mapped promoters to annotated genes using GencodeV10 TSS annotations (ftp://genome.crg.es/pub/Encode/data_analysis/TSS/Gencodev10_TSS_May2012.gff.gz); 54,650 promoters (out of 92,909) were linked to annotated TSSs.

Roadmap epigenomic DHS data preprocessing

DHS peak positions for 474,004 putative enhancer and 33,086 promoter non-overlapping DHS segments [3] were taken from:

• https://personal.broadinstitute.org/meuleman/reg2map/HoneyBadger2-intersect_release/DNase/p10/prom/25/state_calls.RData

• https://personal.broadinstitute.org/meuleman/reg2map/HoneyBadger2-intersect_release/DNase/p10/enh/25/state_calls.RData

To create enhancer/promoter signal matrices, we used the aligned reads (BED files) of 350 UW DNase-seq samples (73 cell types) from GEO dataset GSE18927 [29, 32, 34–36]. The number of reads mapped within each DHS peak was counted using the BEDTools utilities [33]. We focused only on promoters/enhancers with signal ≥ 1 RPKM in at least one sample, resulting in 32,629 promoters and 470,549 putative enhancers.

We defined for each promoter the set of k = 10 candidate enhancers located within a window of ±500 kb. We mapped promoters to annotated genes using GencodeV10 TSS annotations (ftp://genome.crg.es/pub/Encode/data_analysis/TSS/Gencodev10_TSS_May2012.gff.gz) [37]; 17,941 (out of 32,629) promoters were linked to annotated TSSs.

FANTOM5 data preprocessing

Promoter (CAGE tags peak phase 1 and 2) and enhancer (human permissive enhancers phase 1 and 2; n = 65,423) expression matrices (counts and normalized) covering 1827 samples (600 cell types) were downloaded from FANTOM5 DB (http://fantom.gsc.riken.jp/). As in the FANTOM5 paper [4] we focused on promoters with expression ≥ 1 TPM (tags per million) in at least one sample, resulting in 56,290 promoters annotated with 26,489 RefSeq TSSs within ±500 bp. We defined for each promoter the set of k = 10 candidate enhancers located within a window of ±250 kb from the promoter’s TSS. The choice of smaller window here was done for consistency with the FANTOM5 choices.

GRO-seq data preprocessing

We downloaded raw sequence data of 245 GRO-seq samples from the Gene Expression Omnibus (GEO) database (Additional file 3: Table S5). See Additional file 1: Supplemental Methods for further processing details. We defined for each gene the set of k = 10 candidate enhancers located within a window of ±500 kb from its TSS.

FOCS model implementation

The input to FOCS is two activity matrices, one for enhancers (M_e) and the other for promoters (M_p), measured across the same samples. Activity is measured by DHS signal in ENCODE and Roadmap data, and by expression level in FANTOM5 and GRO-seq data. Samples were labeled with a cell-type label out of C cell types. The output of FOCS is predicted E–P links.

First, FOCS builds for each promoter an OLS regression model based on the k enhancers whose center positions are closest to the promoter’s center position (in ENCODE, Roadmap, and FANTOM5) or TSS (in GRO-seq). Formally, let y_p be the promoter p normalized activity pattern (measured in counts per million (CPM); y_p is a row from M_p) and let X_p be the normalized activity matrix of the corresponding k enhancers (CPM; k rows from M_e). We build an OLS linear regression model y_p = X_pβ_p + ε_p, where ε_p is a vector that denotes the errors of the model and β_p is the (k + 1) x 1 vector of coefficients (including the intercept) to be estimated.

Second, FOCS performs leave-cell-type-out cross-validation (LCTO CV) by training the promoter model based on samples from C − 1 cell types and testing the predicted promoter activity of the samples from the left-out cell type. This step is repeated C times. The result is a vector of predicted activity values $y_p^{\mathit{\text{model}}}$ for all samples.

FOCS tests the predicted activity values using two validation tests. (1) The binary test examines whether $y_p^{\mathit{\text{model}}}$ discriminates between the samples in which p was active (observed activity y_p ≥ 1 RPKM) and the samples in which p was inactive (y_p < 1 RPKM). (2) The activity level test calculates, for the active samples, the significance of the Spearman correlation between $y_p^{\mathit{\text{model}}}$ and y_p. Spearman correlation compares the ranks of the original and predicted activities. We obtain two vectors of p values, one for each test, of length n (the number of promoter models).

Third, to correct for multiple testing, FOCS applies on each p value vector the Benjamini–Yekutieli (BY) FDR procedure [19]. Promoter models with q-value ≤0.1 in either both tests or in the activity level test were included in further analyses. In GRO-seq analysis, we also included models that passed only the binary test (m = 2580) since 57% of them had R² ≥ 0.5 (Additional file 1: Figure S6B). For promoters that passed these CV tests final models are trained again using all samples.

FOCS next selects informative enhancers for each final promoter model. The enhancer selection step is described in Additional file 1: Supplemental Methods.

Alternative regression methods

We compared the performance of the OLS method with GLM.NB and ZINB regression methods. We repeated the FOCS steps but in the first step, instead of OLS we applied the GLM.NB or ZINB method (see Additional file 1: Supplemental Methods for details).

FANTOM5 E–P linking using OLS regression was followed by Lasso shrinkage (defined as OLS-LASSO) as described in [4] (see Additional file 1: Supplemental Methods for details).

GO enrichment analysis

GO enrichments were calculated using topGO R package [38] (algorithm = “classic”, statistic = “fisher”, minimum GO set size = 10). We split the genes into target and background sets using their enhancer bin sets. Genes belonging to bins with 1–3/1–4/4–10/5–10 enhancers were considered as the target set and compared to all genes from all bins as the background set. Correction for multiple testing was performed using the BH procedure [20].

External validation of predicted E–P links

We used three external data resources for validating FOCS E–P link predictions: (1) RNAPII ChIA–PET interactions; (2) YY1-HiChIP interactions; and (3) eQTL SNPs.

We downloaded 922,997 ChIA-PET interactions (assayed with RNAPІІ, on four cell lines: MCF7, HCT-116, K562, and HelaS3) from the Chromatin–Chromatin Spatial Interaction (CCSI) database [39] (GEO accession numbers of the original ChIA-PET samples are provided in Additional file 3: Table S6). We used the liftOver tool (from Kent utils package provided by UCSC) to transform the genomic coordinates of the interactions from hg38 to hg19. HiChIP interactions mediated by YY1 TF (HCT116, Jurkat, and K562 cell types) were taken from [21] (GEO accession id GSE99521). As done in [21], we retained 911,190 YY1-HiChIP high-confidence interactions (Origami probability> 0.9). For eQTL SNPs, we used the significant SNP–gene pairs from GTEx analysis V6 and V6p builds; 2,283,827 unique eQTL SNPs covering 44 different tissues were downloaded from the GTEx portal [22].

We used 1-kbp intervals (±500 bp upstream/downstream) for the promoters (relative to the center position in ENCODE/Roadmap/FNATOM5 or to the TSS position in GRO-seq) and the enhancers (±500 bp from the enhancer center). An E–P pair is considered supported by a particular capture interaction if both the promoter and enhancer intervals overlap different anchors of an interaction. An E–P pair is considered supported by an eQTL SNP if the SNP is located within the enhancer’s interval and is associated with the expression of the promoter’s gene. For each predicted E–P pair we checked if the promoter and enhancer intervals are supported by capture interactions and eQTL data. We then measured the fraction of E–P pairs supported by these data resources. See Additional file 1: Supplemental Methods for the significance calculation of the empirical p value.

Statistical tests, visualization, and tools used

All computational analyses and visualizations were done in the R statistical language environment [40]. We used the two-sided Wilcoxon rank-sum test implemented in wilcox.test() function to compute the significance of the binary test. We used the cor.test() function to compute the significance of the Spearman correlation in the activity level test. Spearman/Pearson correlations were computed using the cor() function. To correct for multiple testing we used the p.adjust() function (method = ‘BY’). We used the GenomicRanges package [41] for finding overlaps between genomic positions. We used rtracklayer [42] and GenomicInteractions [43] packages to import/export genomic positions. Counting reads in genomic positions was calculated using BEDTools [33]. OLS models were created using the lm() function in the stat package [40]. GLM.NB models were created using the glm.nb() function in the MASS package [44]. ZINB models were created using the zeroinfl() function in the pscl package [45]. Graphs were made using graphics [40], ggplot2 [46], gplots [47], and the UCSC genome browser (https://genome.ucsc.edu/).

Authors’ contributions

TAH, RE, and RS designed the research. TAH and DA developed the computational method. TAH performed the analyses, parsed the ENCODE, Roadmap, and FANTOM5 data, and assembled the GRO-seq compendium. All authors analyzed the data and wrote the manuscript. All authors read and approved the final manuscript.

Competing interests

The authors declare that they have no competing interests.