2.1 Biological background

Transcription factors (TFs) play a crucial role in gene regulation. They function by recognizing and binding to specific DNA stretches that are usually 5-30bp in length which are referred to as transcription factor binding sites (TFBSs). TF-binding acts on the neighboring genes by up- or down-regulating their gene expression levels.

The aim of the motifcounter package is to provide statistical tools for studying putative TFBSs in given DNA sequence, including the presence and location of TFBSs and the enrichment of TFBSs.

2.2 Hallmarks of motifcounter

The main ingredients for an analysis with motifcounter consist of

1. a position frequency matrix (PFM) (also called TF motif)
2. a background model that serves as a reference for the statistical analysis
3. a set of DNA sequences that is subject to the TFBS analysis
4. a false positive probability \(\alpha\) for predicting TFBSs in a random sequence. E.g. \(\alpha=0.001\).

A PFM represents the affinity of a TF to bind a certain DNA segment. A large set of known PFMs can be acquired e.g. from the MotifDb package [@motifdb]. On the other hand, the background model defines the properties of unbound DNA sequences. motifcounter implements the background model as an order-\(d\) Markov model, where \(d\) is prescribed by the user. The advantage of using higher-order background models is that they are able to capture higher-order sequence features which is crucial for studying naturally occurring DNA sequences that are rich in such features (e.g. in CpGs islands).

Using the PFM and the background model, motifcounter computes the motif score for a given DNA sequence, which is defined to be the log-likelihood ratio between the PFM and the background. The motif score represents a measure that indicates whether a certain position in the DNA sequence is bound or unbound by the TF. Intuitively, the higher the score, the more like does the sequence represent a TFBS.

The motif scores are also used to determine motif hits (e.g. putative TFBSs) in the DNA sequence. To this end, motifcounter uses a predetermined score threshold and calls putative TFBSs whenever the observed score at a give position is greater or equal to the score threshold. motifcounter establishes the score threshold automatically based on 1) the score distribution and 2) the user-prescribed false positive level \(\alpha\). To this end, the score distribution is determined by an efficient dynamic programming algorithm for general order-\(d\) background models, similar as described in [@rahmann, @rsat1].

Testing for motif hit enrichment in motifcounter is based on the number of motif hits that are observed in a set of DNA sequences. In order to be able to judge significance of the observed number of hits (e.g. 10 predicted TFBSs in the sequence of length 10kb), the package approximates the distribution of the number of motif hits in random DNA sequences with matched lengths.

Accordingly, motifcounter provides two fast, accurate alternatives for approximating this distribution:

1. A compound Poisson approximation
2. a combinatorial model

Both of those methods support higher-order background models and account for the self-overlapping structure of the motif, which could lead to mutually overlapping motif hits, which
are referred to as clumps [@reinert, @pape]¹. Clumping is characteristic for self-overlapping motifs, including repeat-like motifs or palindromic motifs. motifcounter not only account for overlapping motif hits with respect to a single DNA strand, but also for overlapping reverse complementary hits, if both DNA strands are scanned for motif hits. It is essential to account for clumping, as that influences the distribution of the number of motif hits and thereby the motif hit enrichment test. Ignoring this effect could cause misleading statistical conclusions.

The compound Poisson model in motifcounter is based on an improvement upon [@pape], which was extended to support order-\(d\) background models and uses a refined way to determine the clump size distribution.

On the other hand, the combinatorial model is based on summing over all permutations of placing the \(k\) hits in a finite-length sequence, which employs an efficient dynamic programming algorithm, related to the approach proposed by [@zhang]².

3.1 Preliminary steps

order <- 1
file <- system.file("extdata", "seq.fasta", package = "motifcounter")
seqs <- Biostrings::readDNAStringSet(file)
bg <- readBackground(seqs, order)

3.1.2 Acquire a motif

motifcounter handles motifs in terms of position frequency matrices (PFMs), which are commonly used to represent the binding affinity of transcription factors (TFs).

A convenient source of known motifs is the MotifDb Bioconductor package [@motifdb], which shall be the basis for our tutorial. For example, we retrieve the motif for the human Pou5f1 (or Oct4) transcription factor as follows

# Extract the Oct4 motif from MotifDb
library(MotifDb)
oct4 <- as.list(query(query(query(MotifDb, "hsapiens"), 
                "pou5f1"), "jolma2013"))[[1]]
motif <- oct4

# Visualize the motif using seqLogo
library(seqLogo)
seqLogo(motif)

Hint: motifcounter requires strictly positive entries for a PFM. If this is not the case, the package provides the function normalizeMotif, which adds pseudo-observations and re-normalize the columns:

new_motif <- normalizeMotif(motif)

alpha <- 0.01
motifcounterOptions(alpha)

3.2 Retrieve position- and strand-specific scores and hits

For the following example, we explore the DNA sequences of a set of Oct4-ChIP-seq peaks that were obtained in human hESC by the ENCODE project [@encode2012]. The peak regions were trimmed to 200 bps.

file <- system.file("extdata", "oct4_chipseq.fa", package = "motifcounter")
oct4peaks <- Biostrings::readDNAStringSet(file)

3.2.1 Analysis of individual DNA sequences

The motifcounter package provides functions for exploring position- and strand-specific putative TFBSs in individual DNA sequences. One way to explore a given DNA sequence for TFBSs is by utilizing scoreSequence. This function returns the per position and strand scores for a given Biostring::DNAString-object (left panel below). To put the observed scores into perspective, the right panel shows the theoretical score distribution in random sequences, which is obtained by scoreDist³. Scores at the tail of the distribution occur very rarely by chance. Those are also the ones that give rise to TFBS predictions:

# Determine the per-position and per-strand scores
scores <- scoreSequence(oct4peaks[[1]], motif, bg)

# As a comparison, compute the theoretical score distribution
sd <- scoreDist(motif, bg)

par(mfrow = c(1, 2))
# Plot the observed scores, per position and per strand
plot(1:length(scores$fscores), scores$fscores, type = "l", 
    col = "blue", xlab = "position", ylab = "score", 
    ylim = c(min(sd$score), max(sd$score)), xlim = c(1, 250))
points(scores$rscores, col = "red", type = "l")
legend("topright", c("forw.", "rev."), col = c("blue", "red"), lty = c(1, 1))

# Plot the theoretical score distribution for the comparison
plot(sd$dist, sd$scores, type = "l", xlab = "probability", ylab = "")

To obtain the predicted TFBSs positions and strands, motifcounter provides the function motifHits. This function, applies a score threshold⁴ for calling the motif hits based on the observed scores.

# Call putative TFBSs
mhits <- motifHits(oct4peaks[[1]], motif, bg)

# Inspect the result
fhitpos <- which(mhits$fhits == 1)
rhitpos <- which(mhits$rhits == 1)
fhitpos

## integer(0)

rhitpos

## [1] 94

In the example sequence, we obtain no motif hit on the forward strand and one motif hit on the reverse strand at position 94. The underlying DNA sequence at this hit can be retrieved by

oct4peaks[[1]][rhitpos:(rhitpos + ncol(motif) - 1)]

##   9-letter "DNAString" instance
## seq: ATTTACATA

Next, we illustrate how a relaxed stringency level influences the number of motif hits. Using motifcounterOptions, we prescribe a false positive probability of \(\alpha=0.01\) (the default was \(\alpha=0.001\)). This will increase the tendency of producing motif hits

# Prescribe a new false positive level for calling TFBSs
motifcounterOptions(alpha = 0.01)

# Determine TFBSs
mhits <- motifHits(oct4peaks[[1]], motif, bg)

fhitpos <- which(mhits$fhits == 1)
rhitpos <- which(mhits$rhits == 1)
fhitpos

## [1]  54  87  93 112

rhitpos

## [1]  55  94 111 118

Now we obtain four hits on each strand.

3.2.2 Analysis of a set of DNA sequences

While, scoreSequence and motifHits can be applied to study TFBSs in a single DNA sequence (given by a DNAString-object), one might also be interested in the average score or motif hit profiles across multiple sequences of equal length. This might reveal positional constraints of the motif occurrences with respect to e.g. the TSS, or the summit of ChIP-seq peaks. On the one hand, motifcounter provides the method scoreProfile which can be applied for Biostrings::DNAStringSet-objects.

# Determine the average score profile across all Oct4 binding sites
scores <- scoreProfile(oct4peaks, motif, bg)

plot(1:length(scores$fscores), scores$fscores, type = "l", 
    col = "blue", xlab = "position", ylab = "score")
points(scores$rscores, col = "red", type = "l")
legend("bottomleft", legend = c("forward", "reverse"), 
    col = c("blue", "red"), lty = c(1, 1))

On the other hand, motifHitProfile constructs a similar profile by computing the position and strand specific mean motif hit frequency

motifcounterOptions()  # let's use the default alpha=0.001 again

# Determine the average motif hit profile
mhits <- motifHitProfile(oct4peaks, motif, bg)

plot(1:length(mhits$fhits), mhits$fhits, type = "l", 
    col = "blue", xlab = "position", ylab = "score")
points(mhits$rhits, col = "red", type = "l")
legend("bottomleft", legend = c("forward", "reverse"), 
    col = c("blue", "red"), lty = c(1, 1))

3.3 Test for motif hit enrichment

A central feature of motifcounter represents a sophisticated novel approach for identifying motif hit enrichment in DNA sequences.

To this end, the package contains the method motifEnrichment, which evaluates the P-value associated with the number of motif hits that are found in the observed sequence, compared to the background model.

# Enrichment of Oct4 in Oct4-ChIP-seq peaks
result <- motifEnrichment(oct4peaks[1:10], motif, bg)
result

## $pvalue
## [1] 6.624993e-07
## 
## $fold
## [1] 4.710889

The method returns a list that contains pvalue as well as fold. While, the pvalue represents the probability that more or equally many hits are produced in random DNA sequences, fold represents the fold-enrichment of motif hits relative the expected number of hits in random DNA sequences. That is, it represents a measure of the effect size.