# 1 Motivation and Necessity

Genetic variants associated with diseases often affect non-coding regions, thus likely having a regulatory role. To understand the effects of genetic variants in these regulatory regions, identifying genes that are modulated by specific regulatory elements (REs) is crucial. The effect of gene regulatory elements, such as enhancers, is often cell-type specific, likely because the combinations of transcription factors (TFs) that are regulating a given enhancer have cell-type specific activity. This TF activity can be quantified with existing tools such as diffTF and captures differences in binding of a TF in open chromatin regions. Collectively, this forms a enhancer-mediated gene regulatory network (eGRN) with cell-type and data-specific TF-RE and RE-gene links. Here, we reconstruct such a eGRN using bulk RNA-seq and open chromatin (e.g., using ATAC-seq or ChIP-seq for open chromatin marks) and optionally TF activity data. Our network contains different types of links, connecting TFs to regulatory elements, the latter of which is connected to genes in the vicinity or within the same chromatin domain (TAD). We use a statistical framework to assign empirical FDRs and weights to all links using a permutation-based approach.

In summary, we present a framework to reconstruct predictive enhancer-mediated regulatory network models that are based on integrating of expression and chromatin accessibility/activity pattern across individuals, and provide a comprehensive resource of cell-type specific gene regulatory networks for particular cell types.

# 2 Installation

## 2.1GRaNIE package and required dependency packages

GRaNIE is available on Bioconductor. The package and installation instructions can be found here and are very simple.

The basic installation installs all required packages but not necessarily those that are listed under Suggests unless you installed the package with BiocManager::install("GRaNIE", dependencies = TRUE).

Note that from the additional packages, only some of the genome annotation packages are actually also required, which of them, however, depends on your genome assembly version (see below).

Overall, we tried to minimize the installation burden and only require packages if they are absolutely necessary for the main workflow. If you want to pre-install also all optional packages, please consider the following options:

1. Use BiocManager::install("GRaNIE", dependencies = TRUE) which however installs all annotation packages for all supported genomes, which may take a longer time due to the overall download size of multiple Gb.
2. Install only the required annotation packages, along with all other optional packages. You may use the following for it:
• Genome annotation packages (only one of the four is optionally needed for some functions, see section below, which of them depends on your genome assembly version):

• hg38: BiocManager::install(c("org.Hs.eg.db", "BSgenome.Hsapiens.UCSC.hg38", "TxDb.Hsapiens.UCSC.hg38.knownGene"))
• hg19: BiocManager::install(c("org.Hs.eg.db", "BSgenome.Hsapiens.UCSC.hg19", "TxDb.Hsapiens.UCSC.hg19.knownGene"))
• mm10: BiocManager::install(c("org.Mm.eg.db", "BSgenome.Mmusculus.UCSC.mm10", "TxDb.Mmusculus.UCSC.mm10.knownGene"))
• mm9 BiocManager::install(c("org.Mm.eg.db", "BSgenome.Mmusculus.UCSC.mm9", "TxDb.Mmusculus.UCSC.mm9.knownGene"))
• For all other optional packages: BiocManager::install(c("IHW", "robust", "csaw", "variancePartition", "topGO", "ReactomePA", "DOSE", "clusterProfiler", "BiocFileCache", "BiocParallel"))

## 2.3 Detailed information about the scope of the optional packages

GRaNIE has a number of packages that enhance the functionality for particular cases, may be required depending on certain parameters, only when using a particular functionality or that generally speed-up the computation. In detail, the following packages are currently optional and may be needed context-specifically:

• Genome assembly and annotation packages (only one of the four is optionally needed, which of them depends on your genome assembly version)

• all of the following packages are ONLY needed for either additional peak annotation in combination with ChIPseeker (see below) or if the chosen peak normalization method is GC based: EDASeq_GC_peaks, gcqn_peaks
• org.Hs.eg.db: Needed only when genome assembly version is hg19 or hg38
• org.Mm.eg.db: Needed only when genome assembly version is mm9 or mm10
• BSgenome.Hsapiens.UCSC.hg19, TxDb.Hsapiens.UCSC.hg19.knownGene: Needed only when genome assembly version is hg19
• BSgenome.Hsapiens.UCSC.hg38, TxDb.Hsapiens.UCSC.hg38.knownGene: Needed only when genome assembly version is hg38
• BSgenome.Mmusculus.UCSC.mm10, TxDb.Mmusculus.UCSC.mm10.knownGene: Needed only when genome assembly version is mm10
• BSgenome.Mmusculus.UCSC.mm9, TxDb.Mmusculus.UCSC.mm9.knownGene: Needed only when genome assembly version is mm9
• ChIPseeker: Not needed strictly speaking, but used only for the function addData() to provide additional peak annotation, fully optional otherwise.
• Additional statistical packages and for enhanced functionality
• IHW: Needed only for the function filterGRNAndConnectGenes for p-value adjustment of the raw peak-gene p-values when using the IHW framework (parameter peak_gene.fdr.method)
• robust: Needed only when setting addRobustRegression = TRUE in the functions addConnections_peak_gene() and add_TF_gene_correlation() for enabling robust regression (an experimental, largely undocumented feature so far).
• csaw: Needed only for a cyclic LOESS normalization, which is the default normalization currently for adding TF activity data via addData_TFActivity()
• variancePartition: Needed only for the function add_featureVariation to quantify multiple sources of biological and technical variation for features (TFs, peaks, and genes)
• Enrichment-associated packages
• topGO, ReactomePA, DOSE, clusterProfiler: Needed only for all enrichment functions for GO, Reactome, DO, and KEGG respectively
• Computational efficacy
• BiocFileCache: Needed only for loadExampleObject(), in cases when this function is executed multiple times, caching is considerably faster than re-downloading the file anew every time the function is executed.
• BiocParallel: Only used but highly recommended in the functions addConnections_peak_gene(), add_TF_gene_correlation(), and overlapPeaksAndTFBS() to speed-up computation when requesting multiple cores.

# 4 Input

In our GRaNIE approach, we integrate multiple data modalities. Here, we describe them in detail and their required format.

## 4.1 Open chromatin and RNA-seq data

Open chromatin data may come from ATAC-seq, DNAse-seq or ChIP-seq data for particular histone modifications that associate with open chromatin such as histone acetylation (e.g., H3K27ac). They all capture open chromatin either directly or indirectly, and while we primarily tested and used ATAC-seq while developing the package, the others should also be applicable for our framework. From here on, we will refer to these regions simply as peaks.

For RNA-seq, the data represent expression counts per gene across samples.

Here is a quick graphical representation which format is required to be compatible with our framework:

• columns are samples, rows are peaks / genes
• column names are required while row names are ignored
• except for one ID columns, all other columns must be numeric and represent counts per sample
• ID column:
• The name of the ID column can be anything and can be specific later in the pipeline. For peaks, we usually use peakID while for RNA-seq, we use EnsemblID
• for peaks, the required format is “chr:start-end”, with chr denoting the chromosome, followed by :, and then start, -, and end for the peak start and end, respectively. Coordinates are assumed to be zero-based exclusive, the standard for BED files, see here or here for more information. In short, the first base in a chromosome is numbered 0, and the last base is not included in the feature. For example, a peak with the coordinates chr1:100-150 starts at position 100 (or the 101th base of the chromosome, as counting starts with 0), spans 50 bp and ends at 149 (and NOT 150).
• counts should be raw if possible (that is, integers), but we also support pre-normalized data. See here for more information.
• peak and RNA-seq data may contain a distinct set of samples, with some samples overlapping but others not. This is no issue and as long as some samples are found in both of them, the GRaNIE pipeline can work with it. Note that only the shared samples between both data modalities are kept, however, so make sure that the sample names match between them and share as many samples as possible. See the methods part for guidelines on how many samples we recommend.

Note that peaks must not overlap. If they do, an informative error message is thrown and the user is requested to modify the peak input data so that no overlaps exist among all peaks. This can be done by either merging overlapping peaks or deleting those that overlap with other peaks based on other criteria such as peak signal, by keeping only the strongest peak, for example.

For guidelines on how many peaks are necessary or recommended, see the section below.

## 4.2 TF and TFBS data

TF and TFBS data is mandatory as input. Specifically, the package requires a bed file per TF with TF binding sites (TFBS). TFBS can either be in-silico predicted, or experimentally verified, as long as genome-wide TFBS can be used. For convenience and orientation, we provide TFBS predictions for HOCOMOCO-based TF motifs that were used with PWMScan for hg19, hg38 and mm10. Check the workflow vignette for an example.

However, you may also use your own TFBS data, and we provide full flexibility in doing so. Only some manual preparation is necessary. Briefly, if you decide to use your own TFBS data, you have to prepare the following:

• a folder that contains one TFBS file per TF in bed or bed.gz format, 6 columns
• file names must be {TF}{suffix}.{fileEnding}, where {TF} specifies the name of the TF, {suffix} an optional and arbitrary string (we use _TFBS, for example), and {fileEnding} the file type (supported are bed and bed.gz).
• the folder must also contain a so-called translation table that must be called translationTable.csv. This file must have the following structure: 3 columns (tab-separated), called SYMBOL, ENSEMBL, and HOCOID. The first column denotes a symbol or shortcut for the TF that is used throughout the pipeline (e.g., AHR), the second the ENSEMBL ID (without the dot suffix; e.g., ENSG00000106546) and the third column the prefix of how the file is called with the TFBS (e.g., AHR.0.B if the file for AHR is called AHR.0.B_TFBS.bed.gz).
• we provide example files for all supported genome assemblies (hg19, hg38 and mm10) that are fully compatible with GRaNIE as separate downloads. For more information, check here.

For more methodological details, details on how to construct these files, their exact format etc we refer to diffTF paper and website for details.

## 4.3 Sample metadata (optional but highly recommended)

Providing sample metadata is optional, but highly recommended - if available, the sample metadata is integrated into the PCA plots to understand where the variation in the data comes from and whether any of the metadata (e.g., age, sex, sequencing batch) is associated with the PCs from a PC, indicating a batch effect that needs to be addressed before running the GRaNIE pipeline.

The integration of sample metadata can be achieved in the addData() function (click the link for more information).

## 4.4 Hi-C data (optional)

Integration of Hi-C data is optional and serves as alternative to identifying peak-gene pairs to test for correlation based on a predefined and fixed neighborhood size (see Methods).

If Hi-C data are available, the pipeline expects a BED file format with at least 3 columns: chromosome name, start, and end. An ID column is optional and assumed to be in the 4th column, all additional columns are ignored.

For more details, see the R help (?addConnections_peak_gene) and the Methods.

## 4.5 SNP data (optional, coming soon)

We also plan to integrate SNP data soon, stay tuned!

# 5 Methodological Details and Basic Mode of Action

In this section, we give methodological details and guidelines.

## 5.1 Data normalization

An important consideration is data normalization for RNA and open chromatin data. We currently support six choices of normalization of either peak or RNA-Seq data: limma_quantile, DESeq2_sizeFactors, limma_cyclicloess, limma_scale, csaw_cyclicLoess_orig, csaw_TMM plus none to skip normalization altogether. For peaks, two additional GC-based normalization schemes are offered: EDASeq_GC_peaks and gcqn_peaks. We refer to the R help for more details (?addData). The default for RNA-Seq is a quantile normalization, while for the open chromatin peak data, it is DESeq2_sizeFactora (i.e., a “regular” DESeq2 size factor normalization). Importantly, DESeq2_sizeFactora requires raw data, while limma_quantile does not necessarily. We nevertheless recommend raw data as input, although it is also possible to provide pre-normalized data as input and then topping this up with another normalization method or none.

While we recommend raw counts for both peaks and RNA-Seq as input and offer several normalization choices in the pipeline, it is also possible to provide pre-normalized data. Note that the normalization method may have a large influence on the resulting eGRN network, so make sure the choice of normalization is reasonable. For more details, see the next sections.

## 5.2 Permutations

We integrate a permutation-based approach into our framework for assessing the quality and abundance of both TF-enhancer and enhancer-gene links. That is, data are permuted in addition to the real data for comparison. Specifically, we permute the samples labels for the RNA-seq data and run the whole pipeline for both permuted and non-permuted data. This allows to compare the connectivity for the real and random eGRNs.

Internally, we label the permuted data with a “1”, while the non-permuted data is labeled as “0” in the GRN object. For example, GRN@connections$TF_peaks[["0"]] stores the original, non-permuted connections, while GRN@connections$TF_peaks[["1"]] stores those based on permuted data.

All output files should either contain the permuted label to designate that permuted data have been used to generate the plot, while the original, non-permuted version is labeled as original.

## 5.3 TF-peak connections

Generally speaking, TF-peak connections are found by correlating a suitable measure related to TFs with peak accessibility, and then identifying statistically significant links. By default, TF expression is used as TF measure, but we also implemented an additional measure for establishing these links based on a measure called TF activity (see below). For more details on how we establish TF-peak links, please check the Supplement of the corresponding publication. See References for links.

### 5.3.1 TF Activity connections

As explained above, TF-peak connections are found by correlation TF expression with peak accessibility. In addition to expression, we also offer to identify statistically significant TF-peak links based on TF Activity. The concept of TF Activity is described in more detail in our diffTF paper. In short, we define TF motif activity, or TF activity for short, as the effect of a TF on the state of chromatin as measured by chromatin accessibility or active chromatin marks (i.e., ATAC-seq, DNase sequencing [DNase-seq], or histone H3 lysine 27 acetylation [H3K27ac] ChIP-seq). A TF Activity score is therefore needed for each TF and each sample.

TF Activity information can either be calculated within the GRaNIE framework using a simplified and empirical approach) or it can be calculated outside of our framework using designated methods and then imported into our framework. We now describe these two choices in more detail.

#### 5.3.1.1 Calculating TF Activity

In our GRaNIE approach, we empirically estimate TF Activity for each TF with the following approach:

• normalize the raw peak counts by one of the supported normalization methods (see below)
• from the TF-peak accessibility matrix as calculated before, identify the subset of peaks with a TFBS overlap for the particular TF based on the user-provided TFBS data
• scaling and centering of the normalized accessibility scores per row (i.e., peak) so that row means are close to 0 for each peak
• the column means (i.e., sample means) from the scaled and centered counts are then taken as approximation for the TF Activity

By default, we currently offer the four different types of normalizing the raw data for calculating TF Activity. Options 2 to 4 are described in more detail in the section Data normalization above, while option 1 is currently only available for TF Activity and therefore explained below (this may change in the future):

1. Cyclic LOESS normalization (default)
Local regression (LOESS) is a commonly used approach for fitting flexible non-linear functions, which involves computing many local linear regression fits and combining them. Briefly, a normalization factor is derived per gene and sample using the normOffsets function of the csaw package in R as opposed to using one size factor for each sample only as with the regular size factor normalization in DeSeq. For each sample, a LOWESS (Locally Weighted Scatterplot Smoothing) curve is fitted to the log-counts against the log-average count. The fitted value for each bin pair is used as the generalized linear model offset for that sample. The use of the average count provides more stability than the average log-count when low counts are present. For more details, see the csaw package in R and the normOffsets methods therein.
2. Standard size factor normalization from DeSeq
3. Quantile normalization
4. No normalization

#### 5.3.1.2 Importing TF Activity

Soon, it will also be possible to import TF Activity data into our framework as opposed to calculating it using the procedure as described above. This feature is currently in development and will be available soon.

#### 5.3.1.3 Adding TF Activity TF-peak connections

Once TF Activity data is available, finding TF-peak links and assessing their significance is then done in complete analogy as for the TF expression data - just the input data is different (TF Activity as opposed to TF expression). The so-called connection type - expression or TF Activity, is stored in the GRN object and output tables and therefore allows to tailor and filter the resulting network accordingly. All output PDFs also contain the information whether a TF-peak link has been established via the TF expression or TF Activity.

## 5.4 Peak-gene associations

We offer two options of where in the gene the overlap with the extended peak may occur: at the 5’ end of the gene (the default) or anywhere in the gene. For more information see the R help (?addConnections_peak_gene and the parameter overlapTypeGene in particular)

We offer two options to decide which peak-gene pairs to test for correlation: in absence of additional topologically associating domain (TADs) data from Hi-C or similar approaches, the pipeline used a local neighborhood-based approach with a custom neighborhood size (default: 250 kb up- and downstream of the peak) to select peak-gene pairs to test. In the presence of TAD data, all peak-gene pairs within a TAD are tested, while peaks located outside of any TAD domain are ignored. The user has furthermore the choice to specify whether overlapping TADs should be merged or not.

This section will be completed soon. We are working on it.

## 5.6 Constructing the eGRN network

After a filtered set of TF-peak-gene links (i.e., a full eGRN) has been build with filterGRNAndConnectGenes(), the actual graph must be constructed using the function build_eGRN_graph based on the filtered eGRN.

Importantly, two types of networks are constructed:

1. TF-peak-gene network: The networks is tripartite and contains TF, peak, and gene nodes. For example, if a TF links to multiple peaks, all of which may link to the same target gene, these will be represented by separate and different edges in the network.
2. TF-gene network: The networks is bipartite and contains only TF and gene, but not peak nodes. Thus, if a TF links to multiple peaks in the underlying set of filtered connections, all of which may link to the same target gene, these will be represented as only one edge in the network after removing duplicate links.

For subsequent functions, either of the two networks is used, and the user can choose which type of network to use if both are possible (such as for visualizeGRN).

For more information, see the R help (?build_eGRN_graph).

## 5.7 Enrichment analyses

After the graph has been built, three types of enrichment analysis are available within the GRaNIE framework:

1. Enrichment based on the full network
2. Enrichment based on communities
3. Enrichment based on TF regulons

All enrichment functions here use the TF-gene graph in the GRN object.

This section will be completed soon. We are working on it.

## 5.8 Network visualization

We also provide a function to visualize a filtered eGRN network! It is very easy to invoke, but provides many options to customize the output and the way the graph is drawn. We recommend to explore the options in the R help (?visualizeGRN).

This section will be completed soon. We are working on it.

# 6 Guidelines, Recommendations, Limitations, Scope

In this section, we provide a few guidelines and recommendations that may be helpful for your analysis.

## 6.1 Package scope

In this section, we want explicitly mention the designated scope of the GRaNIE package, its limitations and additional / companion packages that may be used subsequently or beforehand.

This section will be completed soon. We are working on it.

## 6.2 Transcription factor binding sites (TFBS)

TFBS are a crucial input for any GRaNIE analysis. Our GRaNIE approach is very agnostic as to how these files are generated - as long as one BED file per TF is provided with TFBS positions, the TF can be integrated.As explained above, we usually work with TFBS as predicted by PWMScan based on HOCOMOCO TF motifs, while in-silico predicted TFBS are by no means a requirement of the pipeline. Instead, JASPAR TFBS or TFBS from any other database can also be used. The total number of TF and TFBS per TF seems more relevant here, due to the way we integrate TFBS: We create a binary 0/1 overlap matrix for each peak and TF, with 0 indicating that no TFBS for a particular TF overlaps with a particular peak, while 1 indicates that at least 1 TFBS from the TFBS input data does indeed overlap with the particular peak by at least 1 bp. Thus, having more TFBS in general also increases the number of 1s and therefore the foreground of the TF (see the diagnostic plots) while it makes the foreground also more noisy if the TFBS list contains too many false positives. As always in biology, this is a trade-off.

## 6.3 Peaks

The number of peaks that is provided as input matters greatly for the resulting eGRN and its connectivity. From our experience, this number should be in a reasonable range so that there is enough data and TFBS overlap to build a eGRN, but also not too many so that the whole pipeline runs unnecessarily long. We have good experience with the number of peaks ranging between 50,000 and 200,000, although these are not hard thresholds but rather recommendations.

With respect to the recommended width of the peaks, we usually use peaks that have a width of a couple of hundred base pairs until a few kb, while the default is to filter peaks if they are wider than 10,000 bp (parameter maxSize_peaks in the function filterData()). Remember: peaks are used to overlap them with TFBS, so if a particular peak is too narrow, the likelihood of not overlapping with any (predicted) TFBS from any TF increases, and such a peak is subsequently essentially ignored.

## 6.4 RNA-Seq

The following list is subject to change and provides some rough guidelines for the RNA-Seq data:

1. We recommend using raw counts if possible, and checking carefully in a PCA whether any batch effects are visible (provide and check with metadata such as age or gender - the more, the better).
2. Genes with very small counts across samples are advised to be removed by running the function filterData(), see the argument minNormalizedMeanRNA for more information. You may want to check beforehand how many gens have a row mean of >1. This number is usually in the tens of thousands.
3. At the moment, we did not properly test our framework for single-cell RNA-Seq data, and therefore cannot provide support for it. Thus, use regular bulk data until we advanced with the single-cell applicability. However, you may read the SCENIC+ paper (see the References).

## 6.5 Peak-gene p-values accuracy and violations

This section will be completed soon. We are working on it.

# 7 Output

Here, we describe the various output files that are produced by the pipeline. They are described in the order they are produced in the pipeline.

## 7.1 GRN object

Our pipeline works and output a so-called GRN object. The goal is simple: All information is stored in it, and by keeping everything within one object and sharing it with others, they have all the necessary data and information to run the GRN workflow. A consistent and simple workflow logic makes it easy and intuitive to work with it, similar to other packages such as DESeq2.

Technically speaking, it is an S4 object of class GRN. As you can see from the workflow vignette, almost all GRaNIE functions return a GRN object (with the notable exception of get functions - i.e., all functions that start with get). Except initializeGRN(), which creates an empty GRN object, they also all require a GRN object as first argument, which makes is easy and intuitive to work with.

GRN objects contain all data and results necessary for the various functions the package provides, and various extractor functions allow to extract information out of an GRN object such as the various get functions. In addition, printing a GRN object results in an object summary that is printed (try it out and just type GRN in the console if your GRN object is called like this!). In the future, we aim to add more convenience functions. If you have specific ideas, please let us know.

The slots of a GRN object are described in the R help, see GRN-class for details. While we work on general extractor functions for the various slots for optimal user experience, we currently suggest to also access and explore the data directly with the @ operator until we finalized it. For example, for a GRN object called GRN, GRN@config accesses the configuration slot that contains all parameters and object metadata, and slotNames(GRN) prints all available slots of the object.

## 7.2 PCA plots and results

The pipeline outputs PCA plots for both peaks and RNA as well as original (i..e, the counts the user provided as input) and normalized (i.e., the counts after normalizing them if any normalization method has been provided) data. Thus, in total, 4 different PCA plots are produced, 2 per data modality (peaks and RNA) and 2 per data type (original and normalized counts).

Each PDF consists of three parts: PCA results based on the top 500, top 1000 and top 5000 features (see page headers). For each part, different plot types are available and briefly explained in the following:

1. Multi-density plot across all samples (1 page)
1. Screeplot (1 page)
1. PCA plots with different metadata being colored (5 or more pages, depending on available metadata)

Currently, the actual PCA result data are not stored in the GRN object, but we may change this. We will update the Vignette once this is done and mention it in the Changelog.

## 7.3 TF-peak diagnostic plots

TF-peak diagnostic plots are available for each TF, and they currently look as follows:

The TF name is indicated in the title, and each page shows two plots. In each plot, the TF-peak FDR for each correlation bin (ranging from -1 to 1 in bins of size 0.05) is shown. The only difference between the two plots is the directionality upon which the FDR is empirically derived from: the upper plot is for the positive and the lower plot for the negative direction. Each plot is also colored by the number of distinct TF-peak connections that fall into the particular bin. Mostly, correlation bins with smaller absolute correlation values have higher frequencies (i.e., more TF-peak links fall into them) while correlation bins with more extreme correlation values are less frequent. In the end, for the resulting network, the directionality can be ignored and only those TF-peak links are kept with small FDRs, irrespective of the directionality.

## 7.4 Activator-repressor classification diagnostic plots and results

The pipeline produces 3 different plot types related to the activator-repressor (AR) classification that can optionally be run as part of the GRaNIE workflow. For each of the 3 types, plots are produced for both the original, non-permuted (labeled as original) as well as the permuted (labeled as permuted) data.

The AR classification is run for the RNA expression data (labeled as expression) and can additionally also be run for TF activity data (labeled as TFActivity, see the function addConnections_TF_peak() and its parameter options).

In the following, the 3 plot types are briefly explained:

1. Summary heatmaps (files starting with TF_classification_summaryHeatmap): This is described in detail in the diffTF documentation.

We explain and summarize this type of plot in the Workflow Vignette. Please check there for details.

2. Classification stringency summary plots (files starting with TF_classification_stringencyThresholds): This is described in detail in the diffTF documentation.

3. Density plots per TF (files starting with TF_classification_densityPlotsForegroundBackground): Density plots for each TF, with one TF per page. The plot shows the foreground (red, labeled as Motif) and background (gray, labeled as Non-motif) densities of the correlation coefficient (either Pearson or Spearman, see x-axis label) from peaks with (foreground) or without (background) a (predicted) TFBS in the peak for the particular TF. The numbers in the parenthesis summarize the underlying total number of peaks.

It is also possible to extract the results from the AR classification out of a GRN object. Currently, this can only be done manually, extractor functions are in the works that will further enhance the user experience. The results are stored in the slot GRN@data$TFs$classification[[permIndex]] [[connectionType]]$TF.classification. Here, permIndex refers to the original, non-permuted (“0”) or permuted (“1”) data, while connectionType here is either expression or TFActivity, depending on whether the pipeline has also be run for TF Activity in addition to expression (see function addConnections_TF_peak()). Thus, typically, the results for the original data are stored in GRN@data$TFs$classification[["0"]] [["expression"]]$TF.classification. If intermediate results from the classification have not been deleted (the default is to delete them as they can occupy a large amount of memory in the object, see the parameters of AR_classification_wrapper for details), they can be accessed similarly within GRN@data$TFs$classification[[permIndex]] [[connectionType]]: TF_cor_median_foreground, TF_cor_median_background, TF_peak_cor_foreground, TF_peak_cor_background, and act.rep.thres.l.

## 7.5 Peak-gene diagnostic plots

We provide a number of diagnostic plots for the peak-gene links that are imperative for understanding the biological system and GRN. In what follows, we describe them briefly, along with some notes on expected patterns, implications etc. Note that this section is subject to continuous change.

We currently offer a summary QC figure for the peak-gene connections that looks as follows:

As you can see, the Figure is divided into two rows: the upper row focuses on the peak-gene raw p-value of the correlation results, while the lower row focuses on the peak-gene correlation coefficient. The left side visualizes the data of the corresponding metrics via density plots, while the right side bins the metrics and visualizes them with barplots for highlighting differences between real and permuted data as well as negatively and positively correlated peak-gene links (denoted as r+ and r-, respectively).

We now describe these plots in more detail.

### 7.5.1 Correlation raw p-value distribution

First and most importantly, we focus on the distribution of the raw p-values from the correlation tests (peak accessibility vs gene expression) of all peak-gene links. We can investigate these from multiple perspectives.

Let’s start with a density plot. The upper left plot shows the raw p-value density for the particular gene type as indicated in the title (here: all gene types), stratified on two levels:

1. Random (permuted, left) and non-random (real, right) connections
2. Connections that have a negative (r-, gray) and positive (r+, black) correlation coefficient, respectively

Generally speaking, we consider both the random connections as well as r- connections as background.

What we would like to see is:

• random connections show little to no signal, with a flat curve along the x-axis, with little to no difference between r+ and r- connections
• for the real connections and r+ links, a strong peak at small p-values, and a (marginally) flat distribution for higher ones (similar to a well-calibrated raw p-value distribution for any hypothesis test such as differential expression). For r- links, the peak at small p-values should be much smaller and ideally the curve is completely flat. However, from the datasets we examined, this is rarely the case.

If any of these quality controls is not met, it may indicate an issue with data normalization, the underlying biology and what the GRN represents, or an issue with data size or covariates influencing the results.

To quantify the difference between r+ and r- links within each connection type (random vs real), we can also plot the results in form of ratios rather than densities for either the r+ / r- or the real / permuted dimension. These plots are shown in the upper right panel of the summary plot.

For the r+ / r- dimension and permuted data, the ratios should be close to 1 across all p-value bins, while for the real data, a high ratio is typically seen for small p-values. In general, the difference between the permuted and real bar should be large for small p-values and close to 1 for larger ones.

For the real / permuted dimension, what we want to see is again a high ratio for small p-value bins for the r+ links, indicating that when comparing permuted vs real, there are many more small p-value links in real data as compared to permuted. This usually does not hold true for the r- links, though, as can be seen also from the plot: the gray bars are smaller and closer to 1 across the whole binned p-value range.

Lastly, we can also stratify the raw p-value distribution for r+ and r- peak-gene connections according to different biological properties such as the peak-gene distance and others (see below). Here, we focus solely on the real data and additionally stratify the p-value distributions of peak-gene links by their genomic distance (measured as the distance of the middle of the peak to the TSS of the gene, in base pairs). For this, we bin the peak-gene distance equally into 10 bins, which results in the bins containing a non-equal number of data points but genomic distance is increased uniformly from bin to bin:

We generally (hope to) see that for smaller peak-gene distances (in particular those that overlap, i.e., the peak and the gene are in direct vicinity or even overlapping), the difference between r+ and r- links is bigger as for more distant links. We also include the random links, for which no difference between r+ and r- links is visible, as expected for a well-calibrated background.

Let’s plot the same, but stratified by peak-gene distance and r+ / r- within each plot instead:

### 7.5.2 Correlation coefficient distribution

So far, we analyzed the raw p-value distribution in detail. Let’s focus now on the distribution of the correlation coefficient per se.

Here, we can also include the random links for comparison. We see that the distribution of the correlation coefficient is also slightly different across bins, and most extreme for links with a small genomic distance (darker colored lines).

## 7.6 Connection summary plots

We currently offer two different connection summary PDFs, both of which are produced from the function plot_stats_connectionSummary(). Both PDFs shows the number of connections for each node type (TF, peak, and gene), while in the boxplots, peaks are further differentiated into TF-peak and peak-gene entities. They also iterate over various parameters and plot one plot per page and parameter combination, as indicated in the title:

1. allowMissingTFs: TRUE or FALSE (i.e., allow TFs to be missing when summarizing the eGRN network. If set to TRUE, a valid connection may consist of just peak to gene, with no TF being connected to the peak. For more details, see the R help for plot_stats_connectionSummary)
2. allowMissingGenes: TRUE or FALSE (i.e., allow genes to be missing when summarizing the eGRN network. If set to TRUE, a valid connection may consist of just TF to peak, with no gene being connected to the peak. For more details, see the R help for plot_stats_connectionSummary)
3. TF_peak.connectionType. Either expression or TFActivity to denote which connection type the summary is based on.

Both plot types compare the connectivity for the real and permuted data (denoted as Network type in the boxplot PDF), which allows a better judgment of the connectivity from the real data.

An example page for the summary heatmap looks like this:

Here, two heatmaps are shown, one for real (top) and one for permuted (bottom) network. Each of them shows for different combinations of TF-peak and peak-gene FDRs (0.01 to 0.2) the number of unique node types for the given FDR combination (here: TFs).

Second, a multi-page summary PDF for the connections in form of a boxplot, as exemplified with the following Figure:

## 7.7 Output tables

During a typical GRaNIE analysis, all results are automatically stored in GRN object that is used as input. The only exception is the function getGRNConnections() that can be used to extract the resulting eGRN network from a GRN object and returns a separate data frame and NOT a GRN object. For more information, see the corresponding R help ( ?getGRNConnections).

# 8 Memory footprint and execution time, feasibility with large datasets

In this section, we will give an overview over CPU and memory requirements when running or planning an analysis with GRaNIE.

Both CPU time and memory footprint primarily depend on similar factors, namely the number of

1. TFs
2. peaks
3. samples

While the number of TFs is typically similar across analyses when the default database is used (HOCOMOCO + PWMScan), the number of peaks and samples may vary greatly across analyses.

For optimized CPU times, make sure to have the package BiocParallel installed, which is not automatically installed with GRANIE, even though it should be already installed for most Bioconductor installations as it is one of the core packages.

## 8.1 CPU time

A typical analysis runs within an hour or two on a standard machine with 2 to 4 cores or so. CPU time non-surprisingly depends primarily on the number of used cores for those functions that support multiple cores and that are time-consuming in nature.

## 8.2 Memory footprint

The maximum memory footprint can be a few GB in R. We recommend not using more than 100,000 to 200,000 or so peaks as the memory footprint as well as running time may otherwise increase notably.

Given that our approach is a correlation-based one, it seems preferable to maximize the number of samples while retaining only peaks that carry a biological signal that is differing among samples.

The size of the GRN object is typically in the range of a few hundred MB, but can exceed 1 GB for large datasets. If you have troubles with big datasets, let us know! We always look for ways to further optimize the memory footprint.