# Introduction to the motifcounter package In motifcounter: R package for analysing TFBSs in DNA sequences

library(knitr)
knit_hooks$set(plot = function(x, options) { paste('<figure><img src="', opts_knit$get('base.url'), paste(x, collapse = '.'),
'"><figcaption>', options$fig.cap, '</figcaption></figure>', sep = '') }) library(motifcounter) library(MotifDb) library(seqLogo) opts_chunk$set(fig.path="fig/")


This software package grew out of the work that I did to obtain my PhD. If it is of help for your analysis, please cite

@Manual{,
title = {motifcounter: R package for analysing TFBSs in DNA sequences},
author = {Wolfgang Kopp},
year = {2017},
doi = {10.18129/B9.bioc.motifcounter}
}


Details about the compound Poisson model are available under

@article{improvedcompound,
title={An improved compound Poisson model for the number of motif hits in DNA sequences},
author={Kopp, Wolfgang and Vingron, Martin},
journal={Bioinformatics},
pages={btx539},
year={2017},
publisher={Oxford University Press}
}


# Usage examples

# Estimate a background model on a set of sequences

# Normalize a given PFM
new_motif <- normalizeMotif(motif)

# Evaluate the scores along a given sequence
scores <- scoreSequence(sequence, motif, bg)

# Evaluate the motif hits along a given sequence
hits <- motifHits(sequence, motif, bg)

# Evaluate the average score profile
average_scores <- scoreProfile(sequences, motif, bg)

# Evaluate the average motif hit profile
average_hits <- motifHitProfile(sequences, motif, bg)

# Compute the motif hit enrichment
enrichment_result <- motifEnrichment(sequences, motif, bg)


# Introduction

## 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.

## 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 (e.g. 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. Details of the algorithm are described our paper (see above).

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 and accurate alternatives for approximating this distribution:

1. A compound Poisson approximation (see Kopp and Vingron (2017) Bioinformatics.)
2. A combinatorial model (manuskript in preparation)

Both of these methods support higher-order background models and account for the self-overlapping structure of the motif. For example, a repeat-like word, e.g. 'AAAA', likely gives rise to a string of mutually overlapping hits which
are referred to as clumps [@reinert, @pape]^[ By contrast, a simple binomial approximation [@rsat1,@rahmann] does not account for self-overlapping matches.]. 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.

# Getting started

## Preliminary steps

### Acquire a background model

The background model is used to specify the properties of unbound DNA sequences. That is, it plays a role as a reference for identifying putative TFBSs as well as for judging motif hit enrichment.

motifcounter offers the opportunity to use order-$d$ Markov model with user-defined $d$. The background model is estimated on a set of user-provided DNA sequences which are supplied as DNAStringSet-objects from the Biostrings Bioconductor package.

The following code fragment illustrates how an order-$1$ background model is estimated from a given set of DNA sequences:

order <- 1
file <- system.file("extdata", "seq.fasta", package = "motifcounter")

**Hint:** Ideally, the DNA sequence for estimating the background model should be representative (or even the same) as the sequences that are latter analysed (e.g. for motif hit enrichment).

Hint: For the purpose of motif enrichment testing, we recommend to use orders $d=1$ or $d=2$. Using a background with very high order $d$ might be very costly to compute and, more importantly, due to its increased flexibility, might capture relevant TFBS signals. In that case, enriched motifs might not be recovered.

### 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: wzxhzdk:12

### Optional settings

By default, motifcounter identifies TFBS with a the false positive probability of $\alpha=0.001$. The user might want to change the stringency level of $\alpha$, which is facilitated by motifcounterOptions:

alpha <- 0.01
motifcounterOptions(alpha)


For other options consult ?motifcounterOptions.

## 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 centered around the midpoint.

file <- system.file("extdata", "oct4_chipseq.fa", package = "motifcounter")


### 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 scoreDist^[The score distribution is computed using an efficient dynamic programming algorithm.]. 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$scores, type = "l", xlab = "probability", ylab = "")  To obtain the predicted TFBSs positions and strands, motifcounter provides the function motifHits. This function calls motif hits if the observed score exceeds a pre-determined score threshold^[The threshold is determined for a user-defined false positive level$\alpha$(e.g.$\alpha=0.001$) based on the theoretical score distribution.]. # Call putative TFBSs mhits <- motifHits(oct4peaks[[1]], motif, bg) # Inspect the result fhitpos <- which(mhits$fhits == 1)
rhitpos <- which(mhits$rhits == 1) fhitpos rhitpos  In the example sequence, we obtain no motif hit on the forward strand and one motif hit on the reverse strand at position 94. The underlying DNA sequence at this hit can be retrieved by oct4peaks[[1]][rhitpos:(rhitpos + ncol(motif) - 1)]  Next, we illustrate how a relaxed stringency level influences the number of motif hits. Using motifcounterOptions, we prescribe a false positive probability of$\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$rhits == 1) fhitpos rhitpos  Now we obtain four hits on each strand. ### Analysis of a set of DNA sequences While, scoreSequence and motifHits can be applied to study TFBSs in a single DNA sequence (given by a DNAString-object), one might also be interested in the average score or motif hit profiles across multiple sequences of equal length. This might reveal positional constraints of the motif occurrences with respect to e.g. the TSS, or the summit of ChIP-seq peaks. On the one hand, motifcounter provides the method scoreProfile which can be applied for Biostrings::DNAStringSet-objects. # Determine the average score profile across all Oct4 binding sites scores <- scoreProfile(oct4peaks, motif, bg) plot(1:length(scores$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")

# Session Info

sessionInfo()


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motifcounter documentation built on Nov. 8, 2020, 5:44 p.m.