---
title: "Transcription factor binding site (TFBS) analysis with the \"TFBSTools\" package"
author: "Ge Tan"
date: "`r doc_date()`"
package: "`r pkg_ver('TFBSTools')`"
abstract: >
  Analysis and manipulation of transcription factor binding sites.
vignette: >
  %\VignetteIndexEntry{Transcription factor binding site (TFBS) analysis with the "TFBSTools" package}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
output: 
  BiocStyle::html_document
bibliography: TFBSTools.bib  
---

```{r, echo = FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
```

```{r code, echo = FALSE}
code <- function(...) {
    cat(paste(..., sep = "\n"))
}

date = "`r doc_date()`"
pkg = "`r pkg_ver('BiocStyle')`"
```

```{r global_options, echo=FALSE}
short=TRUE #if short==TRUE, do not echo code chunks
debug=FALSE
knitr::opts_chunk$set(echo=!short, warning=debug, message=debug, error=FALSE,
               cache.path = "cache/",
               fig.path = "figures/")
```

# Introduction
Eukaryotic regulatory regions are characterized based a set of
discovered transcription factor binding sites (TFBSs),
which can be represented as sequence patterns
with various degree of degeneracy.

This `r Biocpkg("TFBSTools")` package is designed to be a compuational framework
for TFBSs analysis.
Based on the famous perl module TFBS [@lenhard_tfbs:_2002],
we extended the class definitions and enhanced implementations
in an interactive environment.
So far this package contains a set of integrated _R_ _S4_ style classes,
tools, JASPAR database interface functions.
Most approaches can be described in three sequential phases.
First, a pattern is generated for a set of target sequences
known to be bound by a specific transcription factor.
Second, a set of DNA sequences are analyzed to determine
the locations of sequences consistent with the described binding pattern.
Finally, in advanced cases, predictive statistical models of regulatory
regions are constructed based on  mutiple occurrences of the detected
patterns.

Since JASPAR2016, the next generation of
transcription factor binding site, _TFFM_ [@mathelier_next_2013],
was introduced into JASPAR for the first time.
Now `r Biocpkg("TFBSTools")` also supports the manipulation of _TFFM_.
TFFM is based on hidden Markov Model (HMM).
The biggest advantage of TFFM over basic PWM is that
it can model position interdependence within TFBSs and variable motif length.
A novel graphical representation of the TFFM motifs that captures
the position interdependence is also introduced.
For more details regarding TFFM,
please refer to http://cisreg.cmmt.ubc.ca/TFFM/doc/.

`r Biocpkg("TFBSTools")` aims to support all these functionalities
in the environment _R_, except the external motif finding software,
such as _MEME_ [@bailey_fitting_1994].

# _S4_ classes in TFBSTools
The package is built around a number of _S4_ class of
which the `XMatrix`,
`SiteSet` classes are the most important.
The section will briefly explain most of them defined in `r Biocpkg("TFBSTools")`.

## XMatrix and its subclasses
`XMatrix` is a virtual class,
which means no concrete objects can be created directly from it.
The subclass `PFMatrix` is designed to store all the relevant information
for one raw position frequency matrix (PFM).
This object is compatible with one record from JASPAR database.
`PWMatrix` is used to store a position weight matrix (PWM).
Compared with `PFMatrix`, it has one extra slot _pseudocounts_.
`ICMatrix` is used to store a information content matrix (ICM).
Compared with `PWMatrix`, it has one extra slot _schneider_.

The following examples demonstrate the creation of `PFMatrix`,
the conversions between these matrices and some assocated methods defined for these classes.

```{r PFMatrix, echo=TRUE, eval=TRUE}
library(TFBSTools)
## PFMatrix construction; Not all of the slots need to be initialised.
pfm <- PFMatrix(ID="MA0004.1", name="Arnt", 
                matrixClass="Zipper-Type", strand="+",
                bg=c(A=0.25, C=0.25, G=0.25, T=0.25),
                tags=list(family="Helix-Loop-Helix", species="10090",
                          tax_group="vertebrates",medline="7592839", 
                          type="SELEX",ACC="P53762", pazar_tf_id="TF0000003",
                          TFBSshape_ID="11", TFencyclopedia_ID="580"),
                profileMatrix=matrix(c(4L,  19L, 0L,  0L,  0L,  0L,
                                       16L, 0L,  20L, 0L,  0L,  0L,
                                       0L,  1L,  0L,  20L, 0L,  20L,
                                       0L,  0L,  0L,  0L,  20L, 0L),
                                     byrow=TRUE, nrow=4,
                                     dimnames=list(c("A", "C", "G", "T"))
                                     )
                )

pfm

## coerced to matrix
as.matrix(pfm)

## access the slots of pfm
ID(pfm)
name(pfm)
Matrix(pfm)
ncol(pfm)
length(pfm)

## convert a FPM to PWM, ICM
pwm <- toPWM(pfm, type="log2probratio", pseudocounts=0.8,
             bg=c(A=0.25, C=0.25, G=0.25, T=0.25))

icm <- toICM(pfm, pseudocounts=sqrt(rowSums(pfm)[1]), schneider=FALSE,
             bg=c(A=0.25, C=0.25, G=0.25, T=0.25))

## get the reverse complment matrix with all the same information except the strand.
pwmRevComp <- reverseComplement(pwm)
```

## XMatrixList and its subclasses
`XMatrixList` is used to store a set of `XMatrix` objects.
Basically it is a SimpleList for easy manipulation the whole set of
`XMatrix`.
The concrete objects can be `PFMatrix`, `PWMatrix` and
`ICMatrix`.


```{r PFMatrixList, echo=TRUE, eval=TRUE}
pfm2 <- pfm
pfmList <- PFMatrixList(pfm1=pfm, pfm2=pfm2, use.names=TRUE)
pfmList
names(pfmList)
```

## SiteSet, SiteSetList, SitePairSet and SitePairSetList
The `SiteSet` class is a container for storing a set of putative
transcription factor binding sites on a nucleotide sequence
(start, end, strand, score, pattern as a `PWMatrix`, etc.)
from scaning a nucleotide sequence with the corresponding `PWMatrix`.
Similarly, `SiteSetList` stores a set of `SiteSet` objects.

For holding the results returned from a pairwise alignment scaaning,
`SitePairSet` and `SitePairSetList` are provided.

More detailed examples of using these classes will be given in
later Section.

## MotifSet
This `MotifSet` class is used to store the generated motifs from
_de novo_ motif discovery software, such as
_MEME_ [@bailey_fitting_1994].

## TFFM and its subclasses
`TFMM` is a virtual class and two classes
`TFFMFirst` and `TFFMDetail` are derived from this virtual class.
Compared with `PFMatrix` class, `TFFM` has two extra slots
that store the emission distribution parameters and transition probabilities.
`TFFMFirst` class stands for the first-order TFFMs, while
`TFFMDetail` stands for the more detailed and descriptive TFFMs.

Although we provide the constructor functions for `TFFM` class,
the `TFFM` object is usually generated from reading a XML file from
the Python module _TFFM_.

```{r TFFMRead, echo=TRUE, eval=TRUE}
  xmlFirst <- file.path(system.file("extdata", package="TFBSTools"),
                        "tffm_first_order.xml")
  tffmFirst <- readXMLTFFM(xmlFirst, type="First")
  tffm <- getPosProb(tffmFirst)

  xmlDetail <- file.path(system.file("extdata", package="TFBSTools"),
                         "tffm_detailed.xml")
  tffmDetail <- readXMLTFFM(xmlDetail, type="Detail")
  getPosProb(tffmDetail)
```

# Database interfaces for JASPAR2014 database
This section will demonstrate how to operate on the JASPAR 2014 database.
JASPAR is a collection of transcription factor DNA-binding preferences,
modeled as matrices.
These can be converted into PWMs, used for scanning genomic sequences.
JASPAR is the only database with this scope where the data can be used
with no restrictions (open-source).
A `Bioconducto` experiment data package `r Biocexptpkg("JASPAR2014")`
is provided with each release of JASPAR.

## Search JASPAR2014 database
This search function fetches matrix data for all matrices in the database
matching criteria defined by the named arguments
and returns a PFMatrixList object.
For more search criterias,
please see the help page for `getMatrixSet`.

```{r searchDB, echo=TRUE, eval=TRUE}
suppressMessages(library(JASPAR2014))
opts <- list()
opts[["species"]] <- 9606
opts[["name"]] <- "RUNX1"
opts[["type"]] <- "SELEX"
opts[["all_versions"]] <- TRUE
PFMatrixList <- getMatrixSet(JASPAR2014, opts)
PFMatrixList

opts2 <- list()
opts2[["type"]] <- "SELEX"
PFMatrixList2 <- getMatrixSet(JASPAR2014, opts2)
PFMatrixList2
```

## Store, delete and initialize JASPAR2014 database
We also provide some functions to initialize an empty JASPAR2014
style database,
store new `PFMatrix` or `PFMatrixList` into it,
or delete some records based on ID.
The backend of the database is _SQLite_.


```{r operateDb, echo=TRUE, eval=TRUE}
db <- "myMatrixDb.sqlite"
initializeJASPARDB(db, version="2014")
data("MA0043")
storeMatrix(db, MA0043)
deleteMatrixHavingID(db,"MA0043.1")
file.remove(db)
```

# PFM, PWM and ICM methods
This section will give an introduction of matrix operations,
including conversion from PFM to PWM and ICM, profile matrices comparison,
dynamic random profile generation.

## PFM to PWM
The method `toPWM` can convert PFM to PWM [@Wasserman:2004ec].
Optional parameters include _type_, _pseudocounts_, _bg_.
The implementation in this package is a bit different from that in `r Biocpkg("Biostrings")`.

First of all, `toPWM` allows the input matrix to have different column sums,
which means the count matrix can have an unequal number of sequences contributing
to each column. This scenario is rare, but exists in JASPAR SELEX data.

Second, we can specify customized _pseudocounts_.
_pseudocounts_ is necessary for correcting the small number of counts
or eliminating the zero values before log transformation.
In TFBS perl module, the square root of the number of sequences contributing to each column.
However, it has been shown to too harsh [@nishida_pseudocounts_2009].
Hence, a default value of 0.8 is used.
Of course, it can be changed to other customized value or even different values for each column.

```{r PWMmatrixMethods, echo=TRUE, eval=TRUE}
pwm <- toPWM(pfm, pseudocounts=0.8)
pwm
```

## PFM to ICM
The method `toICM` can convert PFM to ICM [@schneider_information_1986].
Besides the similar _pseudocounts_, _bg_,
you can also choose to do the _schneider_ correction.

The information content matrix has a column sum between 0 (no base preference)
and 2 (only 1 base used).
Usually this information is used to plot sequence log.

How a PFM is converted to ICM: we have the PFM matrix $x$,
base backrgound frequency $bg$, $pseudocounts$ for correction.

$$Z[j] = \sum_{i=1}^{4} x[i,j]$$

$$p[i,j] = {(x[i,j] + bg[i] \times pseudocounts[j]) \over (Z[j] + \sum_{i}bg[i] \times pseudocounts[j]}$$

$$D[j] = \log_2{4} + \sum_{i=1}^{4} p[i,j]*\log{p[i,j]}$$

$$ICM[i,j] = p[i,j] \times D[j]$$

```{r ICMmatrixMethods, echo=TRUE, eval=TRUE}
icm <- toICM(pfm, pseudocounts=0.8, schneider=TRUE)
icm
```

To plot the sequence logo, we use the package `r Biocpkg("seqlogo")`.
In sequence logo, each position gives the information content obtained
for each nucleotide.
The higher of the letter corresponding to a nucleotide,
the larger information content and higher probability of getting that nucleotide
at that position.
```{r seqLogo1, echo=TRUE, eval=TRUE, fig.width=6, fig.height=4}
seqLogo(icm)
```

## Align PFM to a custom matrix or IUPAC string
In some cases, it is beneficial to assess similarity of existing profile matrices,
such as JASPAR, to a newly discovered matrix
(as with using BLAST for sequence data comparison when using Genbank).

`r Biocpkg("TFBSTools")` provides tools for comparing pairs of PFMs,
or a PFM with IUPAC string, using a modified Needleman-Wunsch algorithm
[@sandelin_integrated_2003].

```{r PFMSimi, echo=TRUE, eval=TRUE}
## one to one comparison
data(MA0003.2)
data(MA0004.1)
pfmSubject <- MA0003.2
pfmQuery <-  MA0004.1
PFMSimilarity(pfmSubject, pfmQuery)

## one to several comparsion
PFMSimilarity(pfmList, pfmQuery)

## align IUPAC string
IUPACString <- "ACGTMRWSYKVHDBN"
PFMSimilarity(pfmList, IUPACString)
```

## PWM similarity
To measure the similarity of two PWM matrix in three measurements:
_normalised Euclidean distance_, _Pearson correlation_
and _Kullback Leibler divergence_ [@linhart_transcription_2008].
Given two PWMs, $P^1$ and $P^2$, where l is the length.
$P_{i,b}$ is the values in column i with base b.
The normalised Euclidean distance is computed in

$$ D(a,b) = {1 \over {\sqrt{2}l}} \cdot \sum_{i=1}^{l} \sqrt{\sum_{b \in {\{A,C,G,T\}}} (P_{i,b}^1-P_{i,b}^2)^2}$$

This distance is between 0 (perfect identity) and 1 (complete dis-similarity).

The pearson correlation coefficient is computed in

$$ r(P^1, P^2) = {1 \over l} \cdot \sum_{i=1}^l {\sum_{b \in \{A,C,G,T\}} (P_{i,b}^1 - 0.25)(P_{i,b}^2-0.25) \over \sqrt{\sum_{b \in \{A,C,G,T\}} (P_{i,b}^1 - 0.25)^2 \cdot \sum_{b \in \{A,C,G,T\}} (P_{i,b}^2 - 0.25)^2}}$$

The Kullback-Leibler divergence is computed in

$$KL(P^1, P^2) = {1 \over {2l}} \cdot \sum_{i=1}^l \sum_{b \in \{A,C,G,T\}} (P_{i,b}^1\log{ P_{i,b}^1 \over P_{i,b}^2}+ P_{i,b}^2\log{P_{i,b}^2 \over {P_{i,b}^1}})$$


```{r PWMSimilarity, echo=TRUE, eval=TRUE}
data(MA0003.2)
data(MA0004.1)
pwm1 <- toPWM(MA0003.2, type="prob")
pwm2 <- toPWM(MA0004.1, type="prob")
PWMSimilarity(pwm1, pwm2, method="Euclidean")
PWMSimilarity(pwm1, pwm2, method="Pearson")
PWMSimilarity(pwm1, pwm2, method="KL")
```

## Dynamic random profile generation
In this section, we will demonstrate the capability of random profile matrices generation with matrix permutation and probabilitis sampling.
In many computational/simulation studies,
it is particularly desired to have a set of random matrices.
Some cases includes the estimation of distance between putative TFBS
and transcription start site, the evaluation of comparison between matrices [@bryne_jaspar_2008].
These random matrices are expected to have same statistical properties with
the selcted profiles, such as nucleotide content or information content.

The permutation method is relatively easy.
It simply shuffles the columns either constrainted in each matrix, or columns almong all selected matrices.
The probabilistic sampling is more complicated and can be done in two steps:

1. A Dirichlet multinomial mixture model is trained on all available matrices in JASPAR.
2. Random columns are sampled from the posterior distribution of the trained Dirichlet model based on selected profiles.


```{r permuteMatrix, echo=TRUE, eval=TRUE}
## Matrice permutation
permuteMatrix(pfmQuery)
permuteMatrix(pfmList, type="intra")
permuteMatrix(pfmList, type="inter")
```

```{r samplingMatrix, echo=TRUE, eval=FALSE}
## Dirichlet model training
data(MA0003.2)
data(MA0004.1)
pfmList <- PFMatrixList(pfm1=MA0003.2, pfm2=MA0004.1, use.names=TRUE)
dmmParameters <- dmmEM(pfmList, K=6, alg="C")
## Matrice sampling from trained Dirichlet model
pwmSampled <- rPWMDmm(MA0003.2, dmmParameters$alpha0, dmmParameters$pmix,
                      N=1, W=6)
```

# TFFM methods
## The graphical representation of TFFM
Basic PWMs can be graphically represented by the sequence logos shown above.
A novel graphical representation of TFFM is requied for
taking the dinucleotide dependence into account.

For the upper part of the sequence logo,
we represent the nucleotide probabilities
at position $p$ for each possible nucleotide at position $p-1$.
Hence, each column represents a position within a TFBS and
each row the nucleotide probabilities found at that position.
Each row assumes a specific nucleotide has been emitted
by the previous hidden state.
The intersection between a column corresponding to position $p$ and
row corresponding to nucleotide $n$ gives the probabilities of
getting each nucleotide at position $p$ if $n$ has been seen at position $p-1$.
The opacity to represent the sequence logo is proportional to
the probablity of possible row to be used by the TFFM.

```{r TFFMFirstseqLogo, echo=TRUE, eval=TRUE, fig.width=6, fig.height=10}
  ## sequence logo for First-order TFFM
  seqLogo(tffmFirst)
```

```{r TFFMDetailseqLogo, echo=TRUE, eval=TRUE, fig.width=6, fig.height=10}
  ## sequence logo for detailed TFFM
  seqLogo(tffmDetail)
```

# Scan sequence and alignments with PWM pattern
## searchSeq
`searchSeq` scans a nucleotide sequence with the pattern represented in the PWM.
The strand argument controls which strand of the sequence will be searched.
When it is _*_, both strands will be scanned.

A `SiteSet` object will be returned which can be exported into
GFF3 or GFF2 format.
Empirical p-values for the match scores can be calculated by an exact method
from `r CRANpkg("TFMPvalue")` or the distribution of sampled scores.

```{r searchSeq, echo=TRUE, eval=TRUE}
library(Biostrings)
data(MA0003.2)
data(MA0004.1)
pwmList <- PWMatrixList(MA0003.2=toPWM(MA0003.2), MA0004.1=toPWM(MA0004.1),
                        use.names=TRUE)
subject <- DNAString("GAATTCTCTCTTGTTGTAGTCTCTTGACAAAATG")
siteset <- searchSeq(pwm, subject, seqname="seq1", min.score="60%", strand="*")

sitesetList <- searchSeq(pwmList, subject, seqname="seq1",
                         min.score="60%", strand="*")


## generate gff2 or gff3 style output
head(writeGFF3(siteset))
head(writeGFF3(sitesetList))
head(writeGFF2(siteset))

## get the relative scores
relScore(siteset)
relScore(sitesetList)

## calculate the empirical p-values of the scores
pvalues(siteset, type="TFMPvalue")
pvalues(siteset, type="sampling")
```

## searchAln
`searchAln` scans a pairwise alignment with the pattern
represented by the PWM.
It reports only those hits that are present in equivalent positions of both sequences
and exceed a specified threshold score in both,
AND are found in regions of the alignment above the specified.

```{r searchAln, echo=TRUE, eval=TRUE}
library(Biostrings)
data(MA0003.2)
pwm <- toPWM(MA0003.2)
aln1 <- DNAString("ACTTCACCAGCTCCCTGGCGGTAAGTTGATC---AAAGG---AAACGCAAAGTTTTCAAG")
aln2 <- DNAString("GTTTCACTACTTCCTTTCGGGTAAGTAAATATATAAATATATAAAAATATAATTTTCATC")
sitePairSet <- searchAln(pwm, aln1, aln2, seqname1="seq1", seqname2="seq2",
                         min.score="50%", cutoff=0.5,
                         strand="*", type="any")
## generate gff style output
head(writeGFF3(sitePairSet))
head(writeGFF2(sitePairSet))

## search the Axt alignment
library(CNEr)
axtFilesHg19DanRer7 <- file.path(system.file("extdata", package="TFBSTools"),
                                 "hg19.danRer7.net.axt")
axtHg19DanRer7 <- readAxt(axtFilesHg19DanRer7)
sitePairSet <-  searchAln(pwm, axtHg19DanRer7, min.score="80%",
                          windowSize=51L, cutoff=0.7, strand="*",
                          type="any", conservation=NULL, mc.cores=1)
GRangesTFBS <- toGRangesList(sitePairSet, axtHg19DanRer7)
GRangesTFBS$targetTFBS
GRangesTFBS$queryTFBS
```

## searchPairBSgenome
`searchPairBSgenome` is designed to do the genome-wise phylogenetic footprinting.
Given two `BSgenome`, a chain file for liftover from one genome to another,
`searchPairBSgenome` identifies the putative transcription factor binding sites
which are conserved in both genomes.

```{r searchBSgenome, echo=TRUE, eval=FALSE}
library(rtracklayer)
library(JASPAR2014)
library(BSgenome.Hsapiens.UCSC.hg19)
library(BSgenome.Mmusculus.UCSC.mm10)
pfm <- getMatrixByID(JASPAR2014, ID="MA0004.1")
pwm <- toPWM(pfm)
chain <- import.chain("Downloads/hg19ToMm10.over.chain")
sitePairSet <- searchPairBSgenome(pwm, BSgenome.Hsapiens.UCSC.hg19,
                                 BSgenome.Mmusculus.UCSC.mm10,
                                 chr1="chr1", chr2="chr1",
                                 min.score="90%", strand="+", chain=chain)
```

# Use _de novo_ motif discovery software
In this section, we will introduce wrapper functions for external motif discovery programs.
So far, _MEME_ is supported.
## _MEME_
`runMEME` takes a `DNAStringSet` or a set of `characters` as input,
and returns a `MotifSet` object.

```{r MEME-wrapper, echo=TRUE, eval=FALSE}
motifSet <- runMEME(file.path(system.file("extdata",
                                          package="TFBSTools"), "crp0.s"),
                    binary="meme",
                    arguments=list("-nmotifs"=3)
                   )
## Get the sites sequences and surrounding sequences
sitesSeq(motifSet, type="all")
## Get the sites sequences only
sitesSeq(motifSet, type="none")
consensusMatrix(motifSet)
```

# Session info
Here is the output of `sessionInfo()` on the system on which this
document was compiled:

```{r sessionInfo, echo=FALSE}
sessionInfo()
```

# References

[R]: http://r-project.org
[RStudio]: http://www.rstudio.com/
