Contents

1 Overview

The RTN package is designed for the reconstruction of TRNs and analysis of regulons using mutual information (MI) (Fletcher et al. 2013). It is implemented by S4 classes in R (R Core Team 2012) and extends several methods previously validated for assessing regulons, e.g. MRA (Carro et al. 2010), GSEA (Subramanian et al. 2005), and EVSE (Castro et al. 2016). The package tests the association between a given TF and all potential targets using either RNA-Seq or microarray transcriptome data. It is tuned to deal with large gene expression datasets in order to build transcriptional regulatory units that are centered on TFs. RTN allows a user to set the stringency of the analysis in a stepwise process, including a bootstrap routine designed to remove unstable associations. Parallel data processing is available for steps that benefit from high-performance computing.

2 Quick Start

2.1 Transcriptional Network Inference (TNI)

The TNI pipeline starts with the generic function tni.constructor() and creates a TNI-class object, which provides methods for TRN inference from high-throughput gene expression data. The tni.constructor takes in a matrix of normalized gene expression and the corresponding gene and sample annotations, as well as a list of regulators to be evaluated. Here, the gene expression matrix and annotations are available in the tniData dataset, which was extracted, pre-processed and size-reduced from Fletcher et al. (2013) and Curtis et al. (2012). This dataset consists of a list with 3 objects: a named gene expression matrix (tniData$expData), a data frame with gene annotations (tniData$rowAnnotation), and a data frame with sample annotations (tniData$colAnnotation). We will use this dataset to demonstrate the construction of a small TRN that has only 5 regulons. In general, though, we recommend building regulons for all TFs annotated for a given species; please see the case study sections for additional recommendations.

The tni.constructor method will check the consistency of all the given arguments. The TNI pipeline is then executed in three steps: (i) compute MI between a regulator and all potential targets, removing non-significant associations by permutation analysis; (ii) remove unstable interactions by bootstrapping; and (iii) apply the ARACNe algorithm. Additional comments are provided throughout the examples.

library(RTN)
data(tniData)
# Input 1: 'expData', a named gene expression matrix (genes on rows, samples on cols); 
# Input 2: 'regulatoryElements', a vector listing genes regarded as TFs
# Input 3: 'rowAnnotation', an optional data frame with gene annotation
# Input 4: 'colAnnotation', an optional data frame with sample annotation
tfs <- c("FOXM1","E2F2","E2F3","RUNX2","PTTG1")
rtni <- tni.constructor(expData = tniData$expData, 
                        regulatoryElements = tfs, 
                        rowAnnotation = tniData$rowAnnotation, 
                        colAnnotation = tniData$colAnnotation)
# p.s. alternatively, 'expData' can be a 'SummarizedExperiment' object

Then the tni.permutation() function takes the pre-processed TNI-class object and returns a TRN inferred by permutation analysis (with corrections for multiple hypothesis testing).

# Please set nPermutations >= 1000
rtni <- tni.permutation(rtni, nPermutations = 100)

Unstable interactions are subsequently removed by bootstrap analysis using the tni.bootstrap() function, which creates a consensus bootstrap network, referred here as refnet (reference network).

rtni <- tni.bootstrap(rtni)

At this stage each target in the TRN may be linked to multiple TFs. Because regulation can occur by both direct (TF-target) and indirect interactions (TF-TF-target), the pipeline next applies the ARACNe algorithm (Margolin, Nemenman, et al. 2006) to remove the weakest interaction in any triplet formed by two TFs and a common target gene, preserving the dominant TF-target pair (Meyer, Lafitte, and Bontempi 2008). The ARACNe algorithm uses the data processing inequality (DPI) theorem to enrich the regulons with direct TF-target interactions, creating a DPI-filtered TRN, referred here as tnet (transcriptional network). For additional details, please refer to Margolin, Wang, et al. (2006) and Fletcher et al. (2013). Briefly, consider three random variables, X, Y and Z that form a network triplet, with X interacting with Z only through Y (i.e., the interaction network is X->Y->Z), and no alternative path exists between X and Z). The DPI theorem states that the information transferred between Y and Z is always larger than the information transferred between X and Z. Based on this assumption, the ARACNe algorithm scans all triplets formed by two regulators and one target and removes the edge with the smallest MI value of each triplet, which is regarded as a redundant association.

rtni <- tni.dpi.filter(rtni)

For a summary of the resulting regulatory network we recommend using the tni.regulon.summary() function. From the summary below, we can see the number of regulons, the number of inferred targets and the regulon size distribution.

tni.regulon.summary(rtni)
## Regulatory network comprised of 5 regulons.
## -- DPI-filtered network:
## regulatoryElements            Targets              Edges 
##                  5               1218               1385 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##      78     238     349     277     357     363
## -- Reference network:
## regulatoryElements            Targets              Edges 
##                  5               1218               2629 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##      78     504     621     526     677     749 
## ---

The tni.regulon.summary() function also lets us get detailed information about a specific regulon, including the number of positive and negative targets. Please use this information as an initial guide in assessing the set of regulons. Usually small regulons (<15 targets) are not useful for most downstream methods, and highly unbalanced regulons (e.g. those with only positive targets) provide unstable activity readouts.

tni.regulon.summary(rtni, regulatoryElements = "FOXM1")
## The FOXM1 regulon has 238 targets, it's a large and balanced regulon.
## -- DPI filtered network targets:
##    Total Positive Negative 
##      238      134      104
## -- Reference network targets:
##    Total Positive Negative 
##      621      370      251
## -- Regulators with mutual information:
## E2F2, E2F3, PTTG1
## 
## ---

All results available in the TNI-class object can be retrieved using the tni.get() accessory function. For example, setting what = 'regulons.and.mode' will return a list with regulons, including the weight assigned for each interaction.

regulons <- tni.get(rtni, what = "regulons.and.mode", idkey = "SYMBOL")
head(regulons$FOXM1)
##   C1orf106        HBB       MAPT       HBA2    ZNF385B       FOSB 
##  0.1321503 -0.1378999 -0.2063462 -0.1029147 -0.1092636 -0.1271561

The absolute value of a weight represents the MI value, while the sign (+/-) indicates the predicted mode of action based on the Pearson’s correlation between the regulator and its targets. We can also retrieve the inferred regulons into an igraph-class object (Csardi 2019) using the tni.graph() function, which sets some basic graph attributes for visualization in the RedeR R package (Castro et al. 2012).

g <- tni.graph(rtni, regulatoryElements = c("FOXM1","E2F2","PTTG1"))

The next chunk shows how to plot the igraph-class object using RedeR (Figure 1).

library(RedeR)
rdp <- RedPort()
calld(rdp)
addGraph(rdp, g, layout=NULL)
addLegend.color(rdp, g, type="edge")
addLegend.shape(rdp, g)
relax(rdp, ps = TRUE)

title Figure 1. Graph representation of three regulons inferred by the RTN package.

2.2 Transcriptional Network Analysis (TNA)

In the previous section we outlined the TNI pipeline, which calculates a TRN and makes information available on its regulons. Here, we describe the TNA pipeline, which provides methods for doing enrichment analysis over a list of regulons. The TNA pipeline starts with the function tni2tna.preprocess(), converting the TNI-class into a TNA-class object. Then regulons will be tested for association with a given gene expression signature, provided here in the tnaData dataset. Note that the dataset in this vignette should be used for demonstration purposes only. It consists of a list with 3 objects: a named numeric vector with log2 fold changes from a differential gene expression analysis, called here a ‘phenotype’ (tnaData$phenotype), a character vector listing the differentially expressed genes (tnaData$hits), and a data frame with gene annotations mapped to the phenotype (tnaData$phenoIDs).

# Input 1: 'object', a TNI object with regulons
# Input 2: 'phenotype', a named numeric vector, usually log2 differential expression levels
# Input 3: 'hits', a character vector, usually a set of differentially expressed genes
# Input 4: 'phenoIDs', an optional data frame with gene anottation mapped to the phenotype
data(tnaData)
rtna <- tni2tna.preprocess(object = rtni, 
                           phenotype = tnaData$phenotype, 
                           hits = tnaData$hits, 
                           phenoIDs = tnaData$phenoIDs)

The tna.mra() function takes the TNA-class object and runs the Master Regulator Analysis (MRA) (Carro et al. 2010) over a list of regulons (with corrections for multiple hypothesis testing). The MRA assesses the overlap between each regulon and the genes listed in the hits argument.

# Run the MRA method
rtna <- tna.mra(rtna)

All results available in the TNA-class object can be retrieved using the tna.get() accessory function; setting what = 'mra' will return a data frame listing the total number of genes in the TRN (Universe.Size), the number of targets in each regulon (Regulon.Size), the number of genes listed in the hits argument (Total.Hits), the expected overlap between a given regulon and the ‘hits’ (Expected.Hits), the observed overlap between a given regulon and the ‘hits’ (Observed.Hits), the statistical significance of the observed overlap assessed by the phyper() function (Pvalue), and the adjusted P-value (Adjusted.Pvalue).

# Get MRA results;
#..setting 'ntop = -1' will return all results, regardless of a threshold
mra <- tna.get(rtna, what="mra", ntop = -1)
head(mra)
##      Regulon Universe.Size Regulon.Size Total.Hits Expected.Hits Observed.Hits
## 1870    E2F2          5304          349        660         43.43            87
## 2305   FOXM1          5304          238        660         29.62            61
## 9232   PTTG1          5304          363        660         45.17            74
## 1871    E2F3          5304          357        660         44.42            61
## 860    RUNX2          5304           78        660          9.71             6
##       Pvalue Adjusted.Pvalue
## 1870 2.5e-11         1.3e-10
## 2305 1.0e-08         2.6e-08
## 9232 6.0e-06         1.0e-05
## 1871 5.0e-03         6.3e-03
## 860  9.4e-01         9.4e-01

As a complementary approach, the tna.gsea1() function runs the one-tailed gene set enrichment analysis (GSEA-1T) to find regulons associated with a particular ‘response’, which is represented by a ranked list of genes generated from a differential gene expression signature (i.e. the ‘phenotype’ included in the TNI-to-TNA preprocessing step). Here the regulon’s target genes are considered a gene set, which is evaluated against the phenotype. The GSEA-1T uses a rank-based scoring metric in order to test the association between the gene set and the phenotype (Subramanian et al. 2005).

# Run the GSEA method
# Please set nPermutations >= 1000
rtna <- tna.gsea1(rtna, nPermutations=100)

Setting what = 'gsea1' in the tna.get() accessory function will retrive a data frame listing the GSEA statistics, and the corresponding GSEA plots can be generated using the tna.plot.gsea1() function (Figure 2).

# Get GSEA results
gsea1 <- tna.get(rtna, what="gsea1", ntop = -1)
head(gsea1)
##      Regulon Regulon.Size Observed.Score     Pvalue Adjusted.Pvalue
## 1870    E2F2          349           0.68 4.2409e-26      1.5769e-25
## 9232   PTTG1          362           0.65 6.3075e-26      1.5769e-25
## 2305   FOXM1          238           0.68 1.9083e-22      3.1806e-22
## 1871    E2F3          357           0.59 2.6079e-18      3.2598e-18
## 860    RUNX2           78           0.45 1.6832e-01      1.6832e-01
# Plot GSEA results
tna.plot.gsea1(rtna, labPheno="abs(log2 fold changes)", ntop = -1)

title Figure 2. GSEA analysis showing genes in each regulon (vertical bars) ranked by differential gene expression analysis (phenotype). This toy example illustrates the output from the TNA pipeline evaluated by the tna.gsea1() function.

The GSEA-1T, however, does not indicate the direction of the association. Next the TNA pipeline uses the two-tailed GSEA (GSEA-2T) approach to test whether the regulon is positively or negatively associated with the phenotype. The tna.gsea2() function separates the regulon into positive and negative targets (based on Pearson’s correlation between the TF and its targets), and then assesses the distribution of the targets across the ranked list of genes.

# Run the GSEA-2T method
# Please set nPermutations >= 1000
rtna <- tna.gsea2(rtna, nPermutations = 100)

Setting what = 'gsea2' in the tna.get() accessory function will retrieve a data frame listing the GSEA-2T statistics, and the corresponding GSEA plots can be generated using the tna.plot.gsea2() function.

# Get GSEA-2T results
gsea2 <- tna.get(rtna, what = "gsea2", ntop = -1)
head(gsea2$differential)
##      Regulon Regulon.Size Observed.Score     Pvalue Adjusted.Pvalue
## 9232   PTTG1          362           1.09 0.00064381       0.0032191
## 860    RUNX2           78           1.21 0.02970300       0.0742570
## 2305   FOXM1          238           0.44 0.18812000       0.2475200
## 1870    E2F2          349           0.35 0.24752000       0.2475200
## 1871    E2F3          357           0.06 0.24752000       0.2475200

In GSEA-2T (Figure 3), a regulon’s positive and negative targets are each considered as separate pos and neg gene sets, which are then evaluated against the phenotype. For each gene set (pos and neg) a walk down the ranked list is performed, stepwise. When a gene in the gene set is found, its position is marked in the ranked list. A running sum, shown as the pink and blue (pos and neg gene sets, respectively) lines, increases when the gene at that position belongs to the gene set and decreases when it doesn’t. The maximum distance of each running sum from the x-axis represents the enrichment score. GSEA-2T produces two per-phenotype enrichment scores (ES), whose difference (dES = ESpos - ESneg) represents the regulon activity. The goal is to assess whether the target genes are overrepresented among the genes that are more positively or negatively differentially expressed. A large positive dES indicates an induced (activated) regulon, while a large negative dES indicates a repressed regulon. Please refer to Campbell et al. (2016) and Campbell et al. (2018) for cases illustrating the use of this approach; an extension of the GSEA-2T to single samples was implemented by Castro et al. (2016) and Groeneveld et al. (2019).

# Plot GSEA-2T results
tna.plot.gsea2(rtna, labPheno="log2 fold changes", tfs="PTTG1")

title Figure 3. Two-tailed GSEA analysis showing regulon’s positive or negative targets (red/blue vertical bars) ranked by differential gene expression analysis (phenotype). This toy example illustrates the output from the TNA pipeline evaluated by the tna.gsea2() function (Campbell et al. (2016) and Campbell et al. (2018) provide examples on how to interpret results from this method).

3 TCGA-BRCA case study

3.1 Context

Here we show how to prepare input data for the RTN package using publicly available mRNA-seq data, and clinical/molecular data for the TCGA-BRCA cohort. We show how to download harmonized GRCh38/hg38 data from the Genomic Data Commons (GDC) using the TCGAbiolinks package (Colaprico et al. 2016). The preprocessing will generate a SummarizedExperiment object that contains gene expression data, which we will then use to compute BRCA-specific regulons.

3.2 Package and data requirements

Please ensure you have installed all libraries before proceeding.

library(RTN)
library(TCGAbiolinks)
library(SummarizedExperiment)
library(TxDb.Hsapiens.UCSC.hg38.knownGene)
library(snow)

3.3 Data preprocessing

We’ll use the Bioconductor package TCGAbiolinks to query and download from the GDC. We want the GRCh38/hg38 harmonized, normalized RNA-seq data for the TCGA-BRCA cohort. TCGAbiolinks will create a directory called GDCdata in your working directory and will save into it the files downloaded from the GDC. The files for each patient will be downloaded in a separate file, and we will use a subset of 500 cases for demonstration purposes only. As a large number of mRNA-seq text files will be downloaded, totaling >140 MB, the download can take a while. Then, the GDCprepare() function will compile the files into an R object of class RangedSummarizedExperiment. The RangedSummarizedExperiment has 6 slots. The most important are rowRanges (gene annotation), colData (sample annotation), and assays, which contains the gene expression matrix.

# Set GDCquery for the TCGA-BRCA cohort
# Gene expression data will be aligned against hg38
query <- GDCquery(project = "TCGA-BRCA",
                  data.category = "Transcriptome Profiling",
                  data.type = "Gene Expression Quantification", 
                  workflow.type = "HTSeq - FPKM-UQ",
                  sample.type = c("Primary solid Tumor"))

# Get a subset for demonstration (n = 500 cases)
cases <- getResults(query, cols = "cases")
cases <- sample(cases, size = 500)
query <- GDCquery(project = "TCGA-BRCA",
                  data.category = "Transcriptome Profiling",
                  data.type = "Gene Expression Quantification", 
                  workflow.type = "HTSeq - FPKM-UQ",
                  sample.type = c("Primary solid Tumor"),
                  barcode = cases)
GDCdownload(query)
tcgaBRCA_mRNA_data <- GDCprepare(query)

The object downloaded from the GDC contains gene-level expression data that include both coding and noncoding genes (e.g. lncRNAs). We will filter these, retaining only genes annotated in the UCSC hg38 gene list (~30,000 genes).

# Subset by known gene locations
geneRanges <- genes(TxDb.Hsapiens.UCSC.hg38.knownGene)
tcgaBRCA_mRNA_data <- subsetByOverlaps(tcgaBRCA_mRNA_data, geneRanges)
nrow(rowData(tcgaBRCA_mRNA_data))
## [1] ~30,000

Finally, we’ll simplify names in the cohort annotation for better summarizations in the subsequent RTN functions. When this step has been run, the tcgaBRCA_mRNA_data object is ready for the TNI pipeline. Please ensure that you save the tcgaBRCA_mRNA_data object in an appropriated folder.

# Change column names in gene annotation for better summarizations
colnames(rowData(tcgaBRCA_mRNA_data)) <- c("ENSEMBL", "SYMBOL", "OG_ENSEMBL")
# Save the preprocessed data for subsequent analyses
save(tcgaBRCA_mRNA_data, file = "tcgaBRCA_mRNA_data_preprocessed.RData")

3.4 Inferring the transcriptional regulatory network

Next we will generate regulons for the TCGA-BRCA cohort, following the steps described in the Quick Start section. For the regulon reconstruction, we will use a comprehensive list of regulators available in the tfsData dataset, comprising 1612 TFs compiled from Lambert et al. (2018). This pipeline should be used on data sets containing at least 100 transcriptome profiles. This represents an empirical lower bound for the ARACNe algorithm (Margolin, Wang, et al. 2006).

# Load TF annotation
data("tfsData")
# Check TF annotation:
# Intersect TFs from Lambert et al. (2018) with gene annotation 
# from the TCGA-BRCA cohort
geneannot <- rowData(tcgaBRCA_mRNA_data)
regulatoryElements <- intersect(tfsData$Lambert2018$SYMBOL, geneannot$SYMBOL)
# Run the TNI constructor
rtni_tcgaBRCA <- tni.constructor(expData = tcgaBRCA_mRNA_data, 
                                 regulatoryElements = regulatoryElements)

We can offer some general practical guidance. To compute a large regulatory network we recommend using a multithreaded mode with the snow package. As minimum computational resources, we suggest a processor with >= 4 cores and RAM >= 8 GB per core (you should adjust specific routines to suit your available resources). The makeCluster() function will set the number of nodes to create on the local machine, making a cluster object available for the TNI-class methods. For example, it should take ~3h to reconstruct 1600 regulons from a gene expression matrix with ~30,000 genes and 500 samples when running on a 2.9 GHz Core i9-8950H workstation with 32GB DDR4 RAM. Please note that running large datasets in parallel can consume all the system memory. We recommend monitoring the parallelization to avoid working too close to the memory ceiling; the parChunks argument available in the tni.permutation() and tni.bootstrap() functions can be used to adjust the job size sent for parallelization. Finally, for RNA-seq data we recommend using the non-parametric estimator of mutual information (default option of the tni.permutation() function).

# Compute the reference regulatory network by permutation and bootstrap analyses.
# Please set 'spec' according to your available hardware
options(cluster=snow::makeCluster(spec=4, "SOCK"))
rtni_tcgaBRCA <- tni.permutation(rtni_tcgaBRCA, pValueCutoff = 1e-7)
rtni_tcgaBRCA <- tni.bootstrap(rtni_tcgaBRCA)
stopCluster(getOption("cluster"))

Next we run the ARACNe algorithm with eps = 0, which sets the tolerance for removing the edge with the smallest weight in each triplet. For example, the XY edge in the XYZ triplet is removed if its weight is below YZ - eps and XZ - eps (see comments in section 2.1 and the aracne() function documentation). Empirically, values between 0 (no tolerance) and 0.15 should be used (Margolin, Wang, et al. 2006). As a less arbitrary approach we suggest setting eps = NA, which will estimate the threshold from the null distribution computed in the permutation and bootstrap steps.

# Compute the DPI-filtered regulatory network
rtni_tcgaBRCA <- tni.dpi.filter(rtni_tcgaBRCA, eps = 0)
# Save the TNI object for subsequent analyses
save(rtni_tcgaBRCA, file="rtni_tcgaBRCA.RData")

The choice of pValueCutoff threshold will depend on the desired tradeoff between false positives and false negatives. A sensible pValueCutoff threshold can be selected a priori by dividing the desired expected number of false positives by the number of tested TF-target interactions (Margolin, Wang, et al. 2006). For example, in this example we tested about 5e+7 TF-target interactions (i.e. ~1,600 TFs vs. ~30,000 genes); therefore a pValueCutoff threshold of 1e-7 should result in about 5 false positives.

Note that some level of missing annotation is expected, as not all gene symbols listed in the regulatoryElements might be available in the TCGA-BRCA preprocessed data. Also, data that are inconsistent with the calculation may be removed in the tni.constructor preprocess. For example, if a gene’s expression does not vary across a cohort, it is not possible to associate this gene’s expression with the expression of other genes in the cohort. As an extreme case, genes that exhibit no variability (e.g. that are not expressed in all samples) are excluded from the analysis. For a summary of the resulting regulatory network we recommend using the tni.regulon.summary() function (see the Quick Start section).

Note also that the MI metric is based on a gene’s expression varying across a cohort. Large cohorts of tumour samples typically contain multiple molecular subtypes, and typically provide good expression variability for building regulons. In contrast, sample sets that are more homogeneous may be more challenging to explore with regulons, and this may be the case with sets of normal, non-cancerous samples. We do not recommend computing regulons for sample sets of low expression variability.

3.5 How to select the significance level when inferring regulons from different cohorts

An important challenge in comparing regulatory information for different cohorts is to generate regulons under similar statistical conditions in each cohort. For example, say cohort A has gene expression data for 300 samples and B for 100 samples. In each cohort, we’d infer regulons with RTN by running four sequential steps: tni.constructor() to check the input data; tni.permutation(), where we’d set a pValueCutoff for the mutual information (MI) between expression profiles for pairs of genes; tni.bootstrap(), which assesses the stability of MI; and finally tni.dpi.filter(), which enhances direct regulator-target interactions.

If we set a permutation pValueCutoff = 1e-5 to infer regulons for A, what should be our choice of pValueCutoff for B? The issue here is that the p-value is an inverse function of the sample size; that is, for a smaller cohort we should use a larger (less stringent) p-value. Ideally, sample size for a second cohort should be determined a priori, but this is seldom an option, as regulons are typically reconstructed from large retrospective cohort studies.

For RTN regulons, the ‘effect size’ is the MI value between a regulator and a potential target gene, and our null hypothesis is that the expression profiles for a regulator and a potential target gene have a statistically non-significant relationship; so, for this regulator, the transcriptional network should not retain this target gene. In general, and in RTN’s MI permutation calculations, the p-value threshold controls the rate of Type I errors (i.e. when we reject a true null hypothesis, creating a false positive result), but it also affects the rate of Type II errors (when we fail to reject a false null hypothesis, creating a false negative result) (Miller 2019). Type I and Type II error rates are denoted by α and β, respectively, and the power of a statistical test is defined as 1 - β. Decreasing α increases β and vice-versa (Mudge et al. 2012). Because α determines the power to detect a given effect size, the choice of a pValueCutoff makes implicit decisions about β; that is, about the true regulatory interactions that RTN will likely consider non-significant, and so will reject. When it comes to assessing the regulatory commonalities between regulons reconstructed from two different cohorts (e.g. A and B), failing to detect a real effect only in A should be considered as serious an error as falsely detecting a non-existent effect only in B. To minimize the risk of such problems we suggest adjusting α by looking at the tradeoff between Type I and Type II errors. Mudge et al. (2012) developed R code to calculate optimal α levels for correlations; we adapted this code by implementing the tni.alpha.adjust() function to assist choosing the pValueCutoff when analyzing datasets with different numbers of samples.

# For example, to estimate 'alphaB' for 'nB', given 'nA', 'alphaA', and 'betaA'
alphaB <- tni.alpha.adjust(nB = 100, nA = 300, alphaA = 1e-5, betaA = 0.2)
alphaB
# [1] 0.029

For the second cohort B, we suggest using a value close to alphaB for the pValueCutoff in the tni.permutation() function (and for cohort A, alphaA), in order that RTN will return regulon results that have been generated with similar tradeoffs between Type I and Type II errors for both cohorts.

4 METABRIC case study

4.1 Context

Fletcher et al. (2013) reconstructed regulons for 809 transcription factors (TFs) using microarray transcriptomic data from the METABRIC breast cancer cohort (Curtis et al. 2012). Castro et al. (2016) found that 36 of these TF regulons were associated with genetic risk of breast cancer. The risk TFs were in two distinct clusters. The “cluster 1” risk TFs were associated with estrogen receptor-positive (ER+) breast cancer risk, and included ESR1, FOXA1, and GATA3, whereas the “cluster 2” risk TFs were associated with estrogen receptor-negative (ER-), basal-like breast cancer. Our goal here is to demonstrate how to generate regulon activity profiles for individual tumour samples, using the regulons reconstructed by Fletcher et al. (2013) for the 36 risk TFs.

4.2 Package and data requirements

Please ensure you have installed all libraries before proceeding. The Fletcher2013b data package is available from the R/Bioconductor repository. Installing and then loading this package will make available all data required for this case study. The rtni1st dataset is a pre-processed TNI-class object that includes the regulons reconstructed by Fletcher et al. (2013) and a gene expression matrix for the METABRIC cohort 1 (n=997 primary tumors).

library(RTN)
library(Fletcher2013b)
library(pheatmap)
# Load 'rtni1st' data object, which includes regulons and expression profiles
data("rtni1st")
# A list of transcription factors of interest (here 36 risk-associated TFs)
risk.tfs <- c("AFF3", "AR", "ARNT2", "BRD8", "CBFB", "CEBPB", "E2F2", "E2F3", "ENO1", "ESR1", "FOSL1", "FOXA1", "GATA3", "GATAD2A", "LZTFL1", "MTA2", "MYB", "MZF1", "NFIB", "PPARD", "RARA", "RB1", "RUNX3", "SNAPC2", "SOX10", "SPDEF", "TBX19", "TCEAL1", "TRIM29", "XBP1", "YBX1", "YPEL3", "ZNF24", "ZNF434", "ZNF552", "ZNF587")

4.3 Regulon activity profiles

Regulon activity profiles (RAPs) characterize regulatory program similarities and differences between samples in a cohort. In order to assess a large number of samples, we implemented a function that computes the two-tailed GSEA for an entire cohort (additional details are provided in Groeneveld et al. (2019)). Briefly, for each regulon, the tni.gsea2() function estimates a regulon activity score for each sample available in the TNI-class object. For each gene in a sample, a differential gene expression is calculated from its expression in the sample relative to its average expression in the cohort; the genes are then ordered as a ranked list representing a differential gene expression signature in that sample, which is used to run the GSEA-2T as explained in tna.gsea2 method (see section 2.2).

# Compute regulon activity for individual samples
rtni1st <- tni.gsea2(rtni1st, regulatoryElements = risk.tfs)
metabric_regact <- tni.get(rtni1st, what = "regulonActivity")

The tni.gsea2 returns a list with the calculated enrichment scores: ESpos, ESneg and dES, which represents the regulon activity of individual samples. Next, the pheatmap package is used to generate a heatmap showing RAPs along with some sample attributes (Figure 4).

# Get sample attributes from the 'rtni1st' dataset
metabric_annot <- tni.get(rtni1st, "colAnnotation")
# Get ER+/- and PAM50 attributes for pheatmap
attribs <- c("LumA","LumB","Basal","Her2","Normal","ER+","ER-")
metabric_annot <- metabric_annot[,attribs]
# Plot regulon activity profiles
pheatmap(t(metabric_regact$dif), 
         main="METABRIC cohort 1 (n=977 samples)",
         annotation_col = metabric_annot, 
         show_colnames = FALSE, annotation_legend = FALSE, 
         clustering_method = "ward.D2", fontsize_row = 6,
         clustering_distance_rows = "correlation",
         clustering_distance_cols = "correlation")

title Figure 4. Regulon activity profiles of individual tumour samples from the METABRIC cohort 1 (for an example where this approach has been used, please see Figures 4A and 5A from Robertson et al. (2017)).

5 Assessing samples with regulons calculated from a different cohort

You may want to assess transcriptome data for a set of samples from cohort B against regulons that you have previously calculated for cohort A. For example, cohort A may be large enough to support inferring regulons, while cohort B may be too small for these calculations. Alternatively, you may wish to compare regulon results between two cohorts (see Figures 4 and 5).

The tni.replace.samples() function is the entry point for assessing new samples with previously calculated regulons. This function will require an existing TNI-class object from cohort A, whose gene expression matrix and sample annotation will be replaced by cohort B. The tni.replace.samples will check all the given arguments, particularly the consistency of gene annotations between the two datasets. Next we show how to generate RAPs for TCGA-BRCA samples using the regulons reconstructed for METABRIC cohort 1 by Fletcher et al. (2013).

# Replace samples
rtni1st_tcgasamples <- tni.replace.samples(rtni1st, tcgaBRCA_mRNA_data)
# Compute regulon activity for the new samples
rtni1st_tcgasamples <- tni.gsea2(rtni1st_tcgasamples, regulatoryElements = risk.tfs)
tcga_regact <- tni.get(rtni1st_tcgasamples, what = "regulonActivity")
# Get sample attributes from the 'rtni1st_tcgasamples' dataset
tcga_annot <- tni.get(rtni1st_tcgasamples, "colAnnotation")
# Adjust PAM50 attributes for pheatmap
tcga_annot <- within(tcga_annot,{
  'LumA' = ifelse(subtype_BRCA_Subtype_PAM50%in%c("LumA"),1,0)
  'LumB' = ifelse(subtype_BRCA_Subtype_PAM50%in%c("LumB"),1,0)
  'Basal' = ifelse(subtype_BRCA_Subtype_PAM50%in%"Basal",1,0)
  'Her2' = ifelse(subtype_BRCA_Subtype_PAM50%in%c("Her2"),1,0)
  'Normal' = ifelse(subtype_BRCA_Subtype_PAM50%in%c("Normal"),1,0)
})
attribs <- c("LumA","LumB","Basal","Her2","Normal")
tcga_annot <- tcga_annot[,attribs]
# Plot regulon activity profiles
pheatmap(t(tcga_regact$dif), 
         main="TCGA-BRCA cohort subset (n=500 samples)",
         annotation_col = tcga_annot, 
         show_colnames = FALSE, annotation_legend = FALSE, 
         clustering_method = "ward.D2", fontsize_row = 6,
         clustering_distance_rows = "correlation",
         clustering_distance_cols = "correlation")

title Figure 5. Regulon activity profiles of individual tumour samples for a subset (n=500) of the TCGA-BRCA cohort using regulons reconstructed by Fletcher et al. (2013) (for an example where this approach has been used, please see Figure S7A-F from Corces et al. (2018)).

The unsupervised hierarchical clustering in Figure 5 is obtained using RAPs from 500 samples of the TCGA-BRCA cohort for the set of 36 regulons calculated from the METABRIC cohort 1. Despite the different cohorts, and different technologies used to quantify gene expression on these cohorts (TCGA used RNA-seq, while METABRIC used microarrays), the luminal, basal and Her2 covariate tracks indicate that the RAPs in Figures 4 and 5 return similar clustering structure.

6 Citation

The RTN, RTNsurvival and RTNduals packages provide methods that were implemented by the authors and contributors. When using these packages in publications, please cite the appropriate papers that introduced the methods and analysis pipelines.

When using the TNI and TNA analysis pipelines:

When using the GSEA-2T method to estimate regulon activity:

When using RAPs to characterize regulatory similarities and differences between samples in a cohort:

When using the EVSE method to explore regulators of genetic risk:

When using the conditional mutual information analysis pipeline to explore modulators of transcription factors:

When using the survival analysis pipeline to integrate RAPs with clinical variables:

When using the dual-regulon analysis pipeline to search for co-regulatory associations between pairs of regulators:

7 Session information

## R version 4.3.0 RC (2023-04-13 r84269)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 22.04.2 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.17-bioc/R/lib/libRblas.so 
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB              LC_COLLATE=C              
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## time zone: America/New_York
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] RTN_2.24.0       BiocStyle_2.28.0
## 
## loaded via a namespace (and not attached):
##  [1] tidyselect_1.2.0            viridisLite_0.4.1          
##  [3] dplyr_1.1.2                 mixtools_2.0.0             
##  [5] bitops_1.0-7                fastmap_1.1.1              
##  [7] lazyeval_0.2.2              RCurl_1.98-1.12            
##  [9] digest_0.6.31               lifecycle_1.0.3            
## [11] survival_3.5-5              magrittr_2.0.3             
## [13] kernlab_0.9-32              compiler_4.3.0             
## [15] rlang_1.1.0                 sass_0.4.5                 
## [17] tools_4.3.0                 igraph_1.4.2               
## [19] utf8_1.2.3                  yaml_2.3.7                 
## [21] data.table_1.14.8           knitr_1.42                 
## [23] htmlwidgets_1.6.2           DelayedArray_0.26.0        
## [25] RColorBrewer_1.1-3          abind_1.4-5                
## [27] KernSmooth_2.23-20          purrr_1.0.1                
## [29] viper_1.34.0                BiocGenerics_0.46.0        
## [31] grid_4.3.0                  stats4_4.3.0               
## [33] fansi_1.0.4                 e1071_1.7-13               
## [35] colorspace_2.1-0            ggplot2_3.4.2              
## [37] scales_1.2.1                MASS_7.3-59                
## [39] SummarizedExperiment_1.30.0 cli_3.6.1                  
## [41] rmarkdown_2.21              generics_0.1.3             
## [43] httr_1.4.5                  cachem_1.0.7               
## [45] proxy_0.4-27                zlibbioc_1.46.0            
## [47] splines_4.3.0               parallel_4.3.0             
## [49] BiocManager_1.30.20         XVector_0.40.0             
## [51] matrixStats_0.63.0          vctrs_0.6.2                
## [53] Matrix_1.5-4                jsonlite_1.8.4             
## [55] carData_3.0-5               pwr_1.3-0                  
## [57] bookdown_0.33               car_3.1-2                  
## [59] IRanges_2.34.0              S4Vectors_0.38.0           
## [61] minet_3.58.0                limma_3.56.0               
## [63] plotly_4.10.1               tidyr_1.3.0                
## [65] jquerylib_0.1.4             snow_0.4-4                 
## [67] glue_1.6.2                  gtable_0.3.3               
## [69] GenomeInfoDb_1.36.0         GenomicRanges_1.52.0       
## [71] munsell_0.5.0               tibble_3.2.1               
## [73] pillar_1.9.0                htmltools_0.5.5            
## [75] GenomeInfoDbData_1.2.10     R6_2.5.1                   
## [77] evaluate_0.20               lattice_0.21-8             
## [79] Biobase_2.60.0              segmented_1.6-4            
## [81] pheatmap_1.0.12             RedeR_2.4.0                
## [83] bslib_0.4.2                 class_7.3-21               
## [85] nlme_3.1-162                xfun_0.39                  
## [87] MatrixGenerics_1.12.0       pkgconfig_2.0.3

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