Source of the materials: Biopython cookbook (adapted) Status: Draft
This chapter gives an overview of the functionality of the Bio.motifs
package included in Biopython. It is intended for people who are
involved in the analysis of sequence motifs, so I’ll assume that you are
familiar with basic notions of motif analysis. In case something is
unclear, please look at Section [sec:links] for some relevant links.
Most of this chapter describes the new Bio.motifs
package included in
Biopython 1.61 onwards, which is replacing the older Bio.Motif
package
introduced with Biopython 1.50, which was in turn based on two older
former Biopython modules, Bio.AlignAce
and Bio.MEME
. It provides
most of their functionality with a unified motif object implementation.
Speaking of other libraries, if you are reading this you might be interested in TAMO, another python library designed to deal with sequence motifs. It supports more de-novo motif finders, but it is not a part of Biopython and has some restrictions on commercial use.
Since we are interested in motif analysis, we need to take a look at
Motif
objects in the first place. For that we need to import the
Bio.motifs library:
In [1]:
from Bio import motifs
and we can start creating our first motif objects. We can either create
a Motif
object from a list of instances of the motif, or we can obtain
a Motif
object by parsing a file from a motif database or motif
finding software.
Suppose we have these instances of a DNA motif:
In [2]:
from Bio.Seq import Seq
instances = [Seq("TACAA"),
Seq("TACGC"),
Seq("TACAC"),
Seq("TACCC"),
Seq("AACCC"),
Seq("AATGC"),
Seq("AATGC")]
then we can create a Motif object as follows:
In [3]:
m = motifs.create(instances)
The instances are saved in an attribute m.instances
, which is
essentially a Python list with some added functionality, as described
below. Printing out the Motif object shows the instances from which it
was constructed:
In [4]:
print(m)
The length of the motif is defined as the sequence length, which should be the same for all instances:
In [5]:
len(m)
Out[5]:
The Motif object has an attribute .counts
containing the counts of
each nucleotide at each position. Printing this counts matrix shows it
in an easily readable format:
In [6]:
print(m.counts)
You can access these counts as a dictionary:
In [ ]:
m.counts['A']
but you can also think of it as a 2D array with the nucleotide as the first dimension and the position as the second dimension:
In [7]:
m.counts['T', 0]
Out[7]:
In [8]:
m.counts['T', 2]
Out[8]:
In [9]:
m.counts['T', 3]
Out[9]:
You can also directly access columns of the counts matrix
In [ ]:
m.counts[:, 3]
Instead of the nucleotide itself, you can also use the index of the nucleotide in the sorted letters in the alphabet of the motif:
In [ ]:
m.alphabet
In [ ]:
m.alphabet.letters
In [ ]:
sorted(m.alphabet.letters)
In [ ]:
m.counts['A',:]
In [ ]:
m.counts[0,:]
The motif has an associated consensus sequence, defined as the sequence
of letters along the positions of the motif for which the largest value
in the corresponding columns of the .counts
matrix is obtained:
In [ ]:
m.consensus
as well as an anticonsensus sequence, corresponding to the smallest
values in the columns of the .counts
matrix:
In [ ]:
m.anticonsensus
You can also ask for a degenerate consensus sequence, in which ambiguous nucleotides are used for positions where there are multiple nucleotides with high counts:
In [ ]:
m.degenerate_consensus
Here, W and R follow the IUPAC nucleotide ambiguity codes: W is either A or T, and V is A, C, or G @cornish1985. The degenerate consensus sequence is constructed following the rules specified by Cavener @cavener1987.
We can also get the reverse complement of a motif:
In [ ]:
r = m.reverse_complement()
r.consensus
In [ ]:
r.degenerate_consensus
In [ ]:
print(r)
The reverse complement and the degenerate consensus sequence are only defined for DNA motifs.
If we have internet access, we can create a weblogo:
In [ ]:
m.weblogo("mymotif.png")
We should get our logo saved as a PNG in the specified file.
Creating motifs from instances by hand is a bit boring, so it’s useful to have some I/O functions for reading and writing motifs. There are not any really well established standards for storing motifs, but there are a couple of formats that are more used than others.
One of the most popular motif databases is
JASPAR. In addition to the motif sequence
information, the JASPAR database stores a lot of meta-information for
each motif. The module Bio.motifs
contains a specialized class
jaspar.Motif
in which this meta-information is represented as
attributes:
matrix_id
- the unique JASPAR motif ID, e.g. ’MA0004.1’
name
- the name of the TF, e.g. ’Arnt’
collection
- the JASPAR collection to which the motif
belongs, e.g. ’CORE’
tf_class
- the structual class of this TF, e.g. ’Zipper-Type’
tf_family
- the family to which this TF belongs, e.g.
’Helix-Loop-Helix’
species
- the species to which this TF belongs, may have multiple
values, these are specified as taxonomy IDs, e.g. 10090
tax_group
- the taxonomic supergroup to which this motif
belongs, e.g. ’vertebrates’
acc
- the accession number of the TF protein, e.g. ’P53762’
data_type
- the type of data used to construct this motif, e.g.
’SELEX’
medline
- the Pubmed ID of literature supporting this motif, may
be multiple values, e.g. 7592839
pazar_id
- external reference to the TF in the
PAZAR database, e.g. ’TF0000003’
comment
- free form text containing notes about the construction
of the motif
The jaspar.Motif
class inherits from the generic Motif
class and
therefore provides all the facilities of any of the motif formats —
reading motifs, writing motifs, scanning sequences for motif instances
etc.
JASPAR stores motifs in several different ways including three different flat file formats and as an SQL database. All of these formats facilitate the construction of a counts matrix. However, the amount of meta information described above that is available varies with the format.
sites
format {#the-jaspar-sites-format .unnumbered}The first of the three flat file formats contains a list of instances.
As an example, these are the beginning and ending lines of the JASPAR
Arnt.sites
file showing known binding sites of the mouse
helix-loop-helix transcription factor Arnt.
>MA0004 ARNT 1
CACGTGatgtcctc
>MA0004 ARNT 2
CACGTGggaggtac
>MA0004 ARNT 3
CACGTGccgcgcgc
...
>MA0004 ARNT 18
AACGTGacagccctcc
>MA0004 ARNT 19
AACGTGcacatcgtcc
>MA0004 ARNT 20
aggaatCGCGTGc
The parts of the sequence in capital letters are the motif instances that were found to align to each other.
We can create a Motif
object from these instances as follows:
In [ ]:
from Bio import motifs
with open("Arnt.sites") as handle:
arnt = motifs.read(handle, "sites")
The instances from which this motif was created is stored in the
.instances
property:
In [ ]:
print(arnt.instances[:3])
In [ ]:
for instance in arnt.instances:
print(instance)
The counts matrix of this motif is automatically calculated from the instances:
In [ ]:
print(arnt.counts)
This format does not store any meta information.
pfm
format {#the-jaspar-pfm-format .unnumbered}JASPAR also makes motifs available directly as a count matrix, without
the instances from which it was created. This pfm
format only stores
the counts matrix for a single motif. For example, this is the JASPAR
file SRF.pfm
containing the counts matrix for the human SRF
transcription factor:
2 9 0 1 32 3 46 1 43 15 2 2
1 33 45 45 1 1 0 0 0 1 0 1
39 2 1 0 0 0 0 0 0 0 44 43
4 2 0 0 13 42 0 45 3 30 0 0
We can create a motif for this count matrix as follows:
In [ ]:
with open("SRF.pfm") as handle:
srf = motifs.read(handle, "pfm")
In [ ]:
print(srf.counts)
As this motif was created from the counts matrix directly, it has no instances associated with it:
In [ ]:
print(srf.instances)
We can now ask for the consensus sequence of these two motifs:
In [ ]:
print(arnt.counts.consensus)
In [ ]:
print(srf.counts.consensus)
As with the instances file, no meta information is stored in this format.
jaspar
{#the-jaspar-format-jaspar .unnumbered}The jaspar
file format allows multiple motifs to be specified in a
single file. In this format each of the motif records consist of a
header line followed by four lines defining the counts matrix. The
header line begins with a >
character (similar to the Fasta file
format) and is followed by the unique JASPAR matrix ID and the TF name.
The following example shows a jaspar
formatted file containing the
three motifs Arnt, RUNX1 and MEF2A:
>MA0004.1 Arnt
A [ 4 19 0 0 0 0 ]
C [16 0 20 0 0 0 ]
G [ 0 1 0 20 0 20 ]
T [ 0 0 0 0 20 0 ]
>MA0002.1 RUNX1
A [10 12 4 1 2 2 0 0 0 8 13 ]
C [ 2 2 7 1 0 8 0 0 1 2 2 ]
G [ 3 1 1 0 23 0 26 26 0 0 4 ]
T [11 11 14 24 1 16 0 0 25 16 7 ]
>MA0052.1 MEF2A
A [ 1 0 57 2 9 6 37 2 56 6 ]
C [50 0 1 1 0 0 0 0 0 0 ]
G [ 0 0 0 0 0 0 0 0 2 50 ]
T [ 7 58 0 55 49 52 21 56 0 2 ]
The motifs are read as follows:
In [ ]:
fh = open("jaspar_motifs.txt")
for m in motifs.parse(fh, "jaspar"))
print(m)
Note that printing a JASPAR motif yields both the counts data and the available meta-information.
In addition to parsing these flat file formats, we can also retrieve
motifs from a JASPAR SQL database. Unlike the flat file formats, a
JASPAR database allows storing of all possible meta information defined
in the JASPAR Motif
class. It is beyond the scope of this document to
describe how to set up a JASPAR database (please see the main
JASPAR website). Motifs are read from a
JASPAR database using the Bio.motifs.jaspar.db
module. First connect
to the JASPAR database using the JASPAR5 class which models the the
latest JASPAR schema:
In [ ]:
from Bio.motifs.jaspar.db import JASPAR5
In [ ]:
JASPAR_DB_HOST = <hostname>
JASPAR_DB_NAME = <db_name>
JASPAR_DB_USER = <user>
JASPAR_DB_PASS = <passord>
In [ ]:
jdb = JASPAR5(
host=JASPAR_DB_HOST,
name=JASPAR_DB_NAME,
user=JASPAR_DB_USER,
password=JASPAR_DB_PASS
)
Now we can fetch a single motif by its unique JASPAR ID with the
fetch_motif_by_id
method. Note that a JASPAR ID conists of a base ID
and a version number seperated by a decimal point, e.g. ’MA0004.1’. The
fetch_motif_by_id
method allows you to use either the fully specified
ID or just the base ID. If only the base ID is provided, the latest
version of the motif is returned.
In [ ]:
arnt = jdb.fetch_motif_by_id("MA0004")
Printing the motif reveals that the JASPAR SQL database stores much more meta-information than the flat files:
In [ ]:
print(arnt)
We can also fetch motifs by name. The name must be an exact match
(partial matches or database wildcards are not currently supported).
Note that as the name is not guaranteed to be unique, the
fetch_motifs_by_name
method actually returns a list.
In [ ]:
motifs = jdb.fetch_motifs_by_name("Arnt")
print(motifs[0])
The fetch_motifs
method allows you to fetch motifs which match a
specified set of criteria. These criteria include any of the above
described meta information as well as certain matrix properties such as
the minimum information content (min_ic
in the example below), the
minimum length of the matrix or the minimum number of sites used to
construct the matrix. Only motifs which pass ALL the specified criteria
are returned. Note that selection criteria which correspond to meta
information which allow for multiple values may be specified as either a
single value or a list of values, e.g. tax_group
and tf_family
in
the example below.
In [ ]:
motifs = jdb.fetch_motifs(
collection = 'CORE',
tax_group = ['vertebrates', 'insects'],
tf_class = 'Winged Helix-Turn-Helix',
tf_family = ['Forkhead', 'Ets'],
min_ic = 12
)
for motif in motifs:
pass # do something with the motif
An important thing to note is that the JASPAR Motif
class was designed
to be compatible with the popular Perl TFBS
modules. Therefore some specifics about the
choice of defaults for background and pseudocounts as well as how
information content is computed and sequences searched for instances is
based on this compatibility criteria. These choices are noted in the
specific subsections below.
**Choice of background:**\
The Perl TFBS
modules appear to allow a choice of custom
background probabilities (although the documentation states that
uniform background is assumed). However the default is to use a
uniform background. Therefore it is recommended that you use a
uniform background for computing the position-specific scoring
matrix (PSSM). This is the default when using the Biopython
motifs
module.
**Choice of pseudocounts:**\
By default, the Perl TFBS
modules use a pseudocount equal to
$\sqrt{N} * \textrm{bg}[\textrm{nucleotide}]$, where $N$ represents
the total number of sequences used to construct the matrix. To apply
this same pseudocount formula, set the motif pseudocounts
attribute using the jaspar.calculate\_pseudcounts()
function:
In [ ]:
motif.pseudocounts = motifs.jaspar.calculate_pseudocounts(motif)
Note that it is possible for the counts matrix to have an unequal
number of sequences making up the columns. The pseudocount
computation uses the average number of sequences making up
the matrix. However, when `normalize` is called on the counts
matrix, each count value in a column is divided by the total number
of sequences making up that specific column, not by the average
number of sequences. This differs from the Perl `TFBS` modules
because the normalization is not done as a separate step and so the
average number of sequences is used throughout the computation of
the pssm. Therefore, for matrices with unequal column counts, the
PSSM computed by the `motifs` module will differ somewhat from the
pssm computed by the Perl `TFBS` modules.
**Computation of matrix information content:**\
The information content (IC) or specificity of a matrix is computed
using the mean
method of the
PositionSpecificScoringMatrix
class. However of note, in the Perl
TFBS
modules the default behaviour is to compute the IC without
first applying pseudocounts, even though by default the PSSMs are
computed using pseudocounts as described above.
**Searching for instances:**\
Searching for instances with the Perl TFBS
motifs was usually
performed using a relative score threshold, i.e. a score in the
range 0 to 1. In order to compute the absolute PSSM score
corresponding to a relative score one can use the equation:
In [ ]:
abs_score = (pssm.max - pssm.min) * rel_score + pssm.min
To convert the absolute score of an instance back to a relative
score, one can use the equation:
In [ ]:
rel_score = (abs_score - pssm.min) / (pssm.max - pssm.min)
For example, using the Arnt motif before, let’s search a sequence
with a relative score threshold of 0.8.
In [ ]:
test_seq=Seq("TAAGCGTGCACGCGCAACACGTGCATTA", unambiguous_dna)
arnt.pseudocounts = motifs.jaspar.calculate_pseudocounts(arnt)
pssm = arnt.pssm
max_score = pssm.max
min_score = pssm.min
abs_score_threshold = (max_score - min_score) * 0.8 + min_score
for position, score in pssm.search(test_seq,
In [ ]:
rel_score = (score - min_score) / (max_score - min_score)
print("Position %d: score = %5.3f, rel. score = %5.3f" % (
MEME @bailey1994 is a tool for discovering motifs in a group of related DNA or protein sequences. It takes as input a group of DNA or protein sequences and outputs as many motifs as requested. Therefore, in contrast to JASPAR files, MEME output files typically contain multiple motifs. This is an example.
At the top of an output file generated by MEME shows some background information about the MEME and the version of MEME used:
********************************************************************************
MEME - Motif discovery tool
********************************************************************************
MEME version 3.0 (Release date: 2004/08/18 09:07:01)
...
Further down, the input set of training sequences is recapitulated:
********************************************************************************
TRAINING SET
********************************************************************************
DATAFILE= INO_up800.s
ALPHABET= ACGT
Sequence name Weight Length Sequence name Weight Length
------------- ------ ------ ------------- ------ ------
CHO1 1.0000 800 CHO2 1.0000 800
FAS1 1.0000 800 FAS2 1.0000 800
ACC1 1.0000 800 INO1 1.0000 800
OPI3 1.0000 800
********************************************************************************
and the exact command line that was used:
********************************************************************************
COMMAND LINE SUMMARY
********************************************************************************
This information can also be useful in the event you wish to report a
problem with the MEME software.
command: meme -mod oops -dna -revcomp -nmotifs 2 -bfile yeast.nc.6.freq INO_up800.s
...
Next is detailed information on each motif that was found:
********************************************************************************
MOTIF 1 width = 12 sites = 7 llr = 95 E-value = 2.0e-001
********************************************************************************
--------------------------------------------------------------------------------
Motif 1 Description
--------------------------------------------------------------------------------
Simplified A :::9:a::::3:
pos.-specific C ::a:9:11691a
probability G ::::1::94:4:
matrix T aa:1::9::11:
To parse this file (stored as meme.dna.oops.txt
), use
In [ ]:
handle = open("meme.dna.oops.txt")
record = motifs.parse(handle, "meme")
handle.close()
The motifs.parse
command reads the complete file directly, so you can
close the file after calling motifs.parse
. The header information is
stored in attributes:
In [ ]:
record.version
In [ ]:
record.datafile
In [ ]:
record.command
In [ ]:
record.alphabet
In [ ]:
record.sequences
The record is an object of the Bio.motifs.meme.Record
class. The class
inherits from list, and you can think of record
as a list of Motif
objects:
In [ ]:
len(record)
In [ ]:
motif = record[0]
print(motif.consensus)
In [ ]:
print(motif.degenerate_consensus)
In addition to these generic motif attributes, each motif also stores its specific information as calculated by MEME. For example,
In [ ]:
motif.num_occurrences
In [ ]:
motif.length
In [ ]:
evalue = motif.evalue
print("%3.1g" % evalue)
In [ ]:
motif.name
In addition to using an index into the record, as we did above, you can also find it by its name:
In [ ]:
motif = record['Motif 1']
Each motif has an attribute .instances
with the sequence instances in
which the motif was found, providing some information on each instance:
In [ ]:
len(motif.instances)
In [ ]:
motif.instances[0]
In [ ]:
motif.instances[0].motif_name
In [ ]:
motif.instances[0].sequence_name
In [ ]:
motif.instances[0].start
In [ ]:
motif.instances[0].strand
In [ ]:
motif.instances[0].length
In [ ]:
pvalue = motif.instances[0].pvalue
print("%5.3g" % pvalue)
TRANSFAC is a manually curated database of transcription factors, together with their genomic binding sites and DNA binding profiles @matys2003. While the file format used in the TRANSFAC database is nowadays also used by others, we will refer to it as the TRANSFAC file format.
A minimal file in the TRANSFAC format looks as follows:
ID motif1
P0 A C G T
01 1 2 2 0 S
02 2 1 2 0 R
03 3 0 1 1 A
04 0 5 0 0 C
05 5 0 0 0 A
06 0 0 4 1 G
07 0 1 4 0 G
08 0 0 0 5 T
09 0 0 5 0 G
10 0 1 2 2 K
11 0 2 0 3 Y
12 1 0 3 1 G
//
This file shows the frequency matrix of motif motif1
of 12
nucleotides. In general, one file in the TRANSFAC format can contain
multiple motifs. For example, this is the contents of the example
TRANSFAC file transfac.dat
:
VV EXAMPLE January 15, 2013
XX
//
ID motif1
P0 A C G T
01 1 2 2 0 S
02 2 1 2 0 R
03 3 0 1 1 A
...
11 0 2 0 3 Y
12 1 0 3 1 G
//
ID motif2
P0 A C G T
01 2 1 2 0 R
02 1 2 2 0 S
...
09 0 0 0 5 T
10 0 2 0 3 Y
//
To parse a TRANSFAC file, use
In [ ]:
handle = open("transfac.dat")
record = motifs.parse(handle, "TRANSFAC")
handle.close()
The overall version number, if available, is stored as record.version
:
In [ ]:
record.version
Each motif in record
is in instance of the Bio.motifs.transfac.Motif
class, which inherits both from the Bio.motifs.Motif
class and from a
Python dictionary. The dictionary uses the two-letter keys to store any
additional information about the motif:
In [ ]:
motif = record[0]
motif.degenerate_consensus # Using the Bio.motifs.Motif method
In [ ]:
motif['ID'] # Using motif as a dictionary
TRANSFAC files are typically much more elaborate than this example, containing lots of additional information about the motif. Table [table:transfaccodes] lists the two-letter field codes that are commonly found in TRANSFAC files:
[table:transfaccodes]
AC
Accession number
AS
Accession numbers, secondary
BA
Statistical basis
BF
Binding factors
BS
Factor binding sites underlying the matrix
CC
Comments
CO
Copyright notice
DE
Short factor description
DR
External databases
DT
Date created/updated
HC
Subfamilies
HP
Superfamilies
ID
Identifier
NA
Name of the binding factor
OC
Taxonomic classification
OS
Species/Taxon
OV
Older version
PV
Preferred version
TY
Type
XX
Empty line; these are not stored in the Record.
: Fields commonly found in TRANSFAC files
Each motif also has an attribute .references
containing the references
associated with the motif, using these two-letter keys:
RN
Reference number
RA
Reference authors
RL
Reference data
RT
Reference title
RX
PubMed ID
: Fields used to store references in TRANSFAC files
Printing the motifs writes them out in their native TRANSFAC format:
In [ ]:
print(record)
You can export the motifs in the TRANSFAC format by capturing this output in a string and saving it in a file:
In [ ]:
text = str(record)
handle = open("mytransfacfile.dat", 'w')
handle.write(text)
handle.close()
In [ ]:
print(arnt.format("pfm"))
Similarly, we can use format
to write the motif in the JASPAR jaspar
format:
In [ ]:
print(arnt.format("jaspar"))
To write the motif in a TRANSFAC-like matrix format, use
In [ ]:
print(m.format("transfac"))
To write out multiple motifs, you can use motifs.write
. This function
can be used regardless of whether the motifs originated from a TRANSFAC
file. For example,
In [ ]:
two_motifs = [arnt, srf]
print(motifs.write(two_motifs, 'transfac'))
Or, to write multiple motifs in the jaspar
format:
In [ ]:
two_motifs = [arnt, mef2a]
print(motifs.write(two_motifs, "jaspar"))
The .counts
attribute of a Motif object shows how often each
nucleotide appeared at each position along the alignment. We can
normalize this matrix by dividing by the number of instances in the
alignment, resulting in the probability of each nucleotide at each
position along the alignment. We refer to these probabilities as the
position-weight matrix. However, beware that in the literature this term
may also be used to refer to the position-specific scoring matrix, which
we discuss below.
Usually, pseudocounts are added to each position before normalizing.
This avoids overfitting of the position-weight matrix to the limited
number of motif instances in the alignment, and can also prevent
probabilities from becoming zero. To add a fixed pseudocount to all
nucleotides at all positions, specify a number for the pseudocounts
argument:
In [ ]:
pwm = m.counts.normalize(pseudocounts=0.5)
print(pwm)
Alternatively, pseudocounts
can be a dictionary specifying the
pseudocounts for each nucleotide. For example, as the GC content of the
human genome is about 40%, you may want to choose the pseudocounts
accordingly:
In [ ]:
pwm = m.counts.normalize(pseudocounts={'A':0.6, 'C': 0.4, 'G': 0.4, 'T': 0.6})
print(pwm)
The position-weight matrix has its own methods to calculate the consensus, anticonsensus, and degenerate consensus sequences:
In [ ]:
pwm.consensus
In [ ]:
pwm.anticonsensus
In [ ]:
pwm.degenerate_consensus
Note that due to the pseudocounts, the degenerate consensus sequence calculated from the position-weight matrix is slightly different from the degenerate consensus sequence calculated from the instances in the motif:
In [ ]:
m.degenerate_consensus
The reverse complement of the position-weight matrix can be calculated
directly from the pwm
:
In [ ]:
rpwm = pwm.reverse_complement()
print(rpwm)
Using the background distribution and PWM with pseudo-counts added, it’s
easy to compute the log-odds ratios, telling us what are the log odds of
a particular symbol to be coming from a motif against the background. We
can use the .log_odds()
method on the position-weight matrix:
In [ ]:
pssm = pwm.log_odds()
print(pssm)
Here we can see positive values for symbols more frequent in the motif than in the background and negative for symbols more frequent in the background. $0.0$ means that it’s equally likely to see a symbol in the background and in the motif.
This assumes that A, C, G, and T are equally likely in the background.
To calculate the position-specific scoring matrix against a background
with unequal probabilities for A, C, G, T, use the background
argument. For example, against a background with a 40% GC content, use
In [ ]:
background = {'A':0.3,'C':0.2,'G':0.2,'T':0.3}
pssm = pwm.log_odds(background)
print(pssm)
The maximum and minimum score obtainable from the PSSM are stored in the
.max
and .min
properties:
In [ ]:
print("%4.2f" % pssm.max)
In [ ]:
print("%4.2f" % pssm.min)
The mean and standard deviation of the PSSM scores with respect to a
specific background are calculated by the .mean
and .std
methods.
In [ ]:
mean = pssm.mean(background)
std = pssm.std(background)
print("mean = %0.2f, standard deviation = %0.2f" % (mean, std))
A uniform background is used if background
is not specified. The mean
is particularly important, as its value is equal to the Kullback-Leibler
divergence or relative entropy, and is a measure for the information
content of the motif compared to the background. As in Biopython the
base-2 logarithm is used in the calculation of the log-odds scores, the
information content has units of bits.
The .reverse_complement
, .consensus
, .anticonsensus
, and
.degenerate_consensus
methods can be applied directly to PSSM objects.
The most frequent use for a motif is to find its instances in some sequence. For the sake of this section, we will use an artificial sequence like this:
In [ ]:
test_seq=Seq("TACACTGCATTACAACCCAAGCATTA", m.alphabet)
len(test_seq)
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for pos, seq in m.instances.search(test_seq):
print("%i %s" % (pos, seq))
We can do the same with the reverse complement (to find instances on the complementary strand):
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for pos, seq in r.instances.search(test_seq):
print("%i %s" % (pos, seq))
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for position, score in pssm.search(test_seq, threshold=3.0):
print("Position %d: score = %5.3f" % (position, score))
The negative positions refer to instances of the motif found on the
reverse strand of the test sequence, and follow the Python convention on
negative indices. Therefore, the instance of the motif at pos
is
located at test_seq[pos:pos+len(m)]
both for positive and for negative
values of pos
.
You may notice the threshold parameter, here set arbitrarily to $3.0$. This is in $log_2$, so we are now looking only for words, which are eight times more likely to occur under the motif model than in the background. The default threshold is $0.0$, which selects everything that looks more like the motif than the background.
You can also calculate the scores at all positions along the sequence:
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pssm.calculate(test_seq)
In general, this is the fastest way to calculate PSSM scores. The scores
returned by pssm.calculate
are for the forward strand only. To obtain
the scores on the reverse strand, you can take the reverse complement of
the PSSM:
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rpssm = pssm.reverse_complement()
rpssm.calculate(test_seq)
If you want to use a less arbitrary way of selecting thresholds, you can explore the distribution of PSSM scores. Since the space for a score distribution grows exponentially with motif length, we are using an approximation with a given precision to keep computation cost manageable:
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distribution = pssm.distribution(background=background, precision=10**4)
The distribution
object can be used to determine a number of different
thresholds. We can specify the requested false-positive rate
(probability of “finding” a motif instance in background generated
sequence):
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threshold = distribution.threshold_fpr(0.01)
print("%5.3f" % threshold)
or the false-negative rate (probability of “not finding” an instance generated from the motif):
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threshold = distribution.threshold_fnr(0.1)
print("%5.3f" % threshold)
or a threshold (approximately) satisfying some relation between the false-positive rate and the false-negative rate ($\frac{\textrm{fnr}}{\textrm{fpr}}\simeq t$):
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threshold = distribution.threshold_balanced(1000)
print("%5.3f" % threshold)
or a threshold satisfying (roughly) the equality between the false-positive rate and the $-log$ of the information content (as used in patser software by Hertz and Stormo):
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threshold = distribution.threshold_patser()
print("%5.3f" % threshold)
For example, in case of our motif, you can get the threshold giving you exactly the same results (for this sequence) as searching for instances with balanced threshold with rate of $1000$.
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threshold = distribution.threshold_fpr(0.01)
print("%5.3f" % threshold)
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for position, score in pssm.search(test_seq, threshold=threshold):
print("Position %d: score = %5.3f" % (position, score))
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from Bio import motifs
with open("Arnt.sites") as handle:
motif = motifs.read(handle, 'sites')
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print(motif.counts)
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print(motif.pwm)
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print(motif.pssm)
The negative infinities appear here because the corresponding entry in the frequency matrix is 0, and we are using zero pseudocounts by default:
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for letter in "ACGT":
print("%s: %4.2f" % (letter, motif.pseudocounts[letter]))
If you change the .pseudocounts
attribute, the position-frequency
matrix and the position-specific scoring matrix are recalculated
automatically:
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motif.pseudocounts = 3.0
for letter in "ACGT":
print("%s: %4.2f" % (letter, motif.pseudocounts[letter]))
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print(motif.pwm)
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print(motif.pssm)
You can also set the .pseudocounts
to a dictionary over the four
nucleotides if you want to use different pseudocounts for them. Setting
motif.pseudocounts
to None
resets it to its default value of zero.
The position-specific scoring matrix depends on the background distribution, which is uniform by default:
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for letter in "ACGT":
print("%s: %4.2f" % (letter, motif.background[letter]))
Again, if you modify the background distribution, the position-specific scoring matrix is recalculated:
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motif.background = {'A': 0.2, 'C': 0.3, 'G': 0.3, 'T': 0.2}
print(motif.pssm)
Setting motif.background
to None
resets it to a uniform
distribution:
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motif.background = None
for letter in "ACGT":
print("%s: %4.2f" % (letter, motif.background[letter]))
If you set motif.background
equal to a single value, it will be
interpreted as the GC content:
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motif.background = 0.8
for letter in "ACGT":
print("%s: %4.2f" % (letter, motif.background[letter]))
Note that you can now calculate the mean of the PSSM scores over the background against which it was computed:
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print("%f" % motif.pssm.mean(motif.background))
as well as its standard deviation:
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print("%f" % motif.pssm.std(motif.background))
and its distribution:
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distribution = motif.pssm.distribution(background=motif.background)
threshold = distribution.threshold_fpr(0.01)
print("%f" % threshold)
Note that the position-weight matrix and the position-specific scoring
matrix are recalculated each time you call motif.pwm
or motif.pssm
,
respectively. If speed is an issue and you want to use the PWM or PSSM
repeatedly, you can save them as a variable, as in
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pssm = motif.pssm
Once we have more than one motif, we might want to compare them.
Before we start comparing motifs, I should point out that motif boundaries are usually quite arbitrary. This means we often need to compare motifs of different lengths, so comparison needs to involve some kind of alignment. This means we have to take into account two things:
alignment of motifs
some function to compare aligned motifs
To align the motifs, we use ungapped alignment of PSSMs and substitute zeros for any missing columns at the beginning and end of the matrices. This means that effectively we are using the background distribution for columns missing from the PSSM. The distance function then returns the minimal distance between motifs, as well as the corresponding offset in their alignment.
To give an example, let us first load another motif, which is similar to
our test motif m
:
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with open("REB1.pfm") as handle:
m_reb1 = motifs.read(handle, "pfm")
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m_reb1.consensus
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print(m_reb1.counts)
To make the motifs comparable, we choose the same values for the
pseudocounts and the background distribution as our motif m
:
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m_reb1.pseudocounts = {'A':0.6, 'C': 0.4, 'G': 0.4, 'T': 0.6}
m_reb1.background = {'A':0.3,'C':0.2,'G':0.2,'T':0.3}
pssm_reb1 = m_reb1.pssm
print(pssm_reb1)
We’ll compare these motifs using the Pearson correlation. Since we want it to resemble a distance measure, we actually take $1-r$, where $r$ is the Pearson correlation coefficient (PCC):
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distance, offset = pssm.dist_pearson(pssm_reb1)
print("distance = %5.3g" % distance)
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print(offset)
This means that the best PCC between motif m
and m_reb1
is obtained
with the following alignment:
m: bbTACGCbb
m_reb1: GTTACCCGG
where b
stands for background distribution. The PCC itself is roughly
$1-0.239=0.761$.
Currently, Biopython has only limited support for de novo motif finding. Namely, we support running and parsing of AlignAce and MEME. Since the number of motif finding tools is growing rapidly, contributions of new parsers are welcome.
Let’s assume, you have run MEME on sequences of your choice with your
favorite parameters and saved the output in the file meme.out
. You can
retrieve the motifs reported by MEME by running the following piece of
code:
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from Bio import motifs
with open("meme.out") as handle:
motifsM = motifs.parse(handle, "meme")
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motifsM
Besides the most wanted list of motifs, the result object contains more useful information, accessible through properties with self-explanatory names:
.alphabet
.datafile
.sequence_names
.version
.command
The motifs returned by the MEME Parser can be treated exactly like regular Motif objects (with instances), they also provide some extra functionality, by adding additional information about the instances.
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motifsM[0].consensus
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motifsM[0].instances[0].sequence_name
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motifsM[0].instances[0].start
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motifsM[0].instances[0].strand
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motifsM[0].instances[0].pvalue
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from Bio import motifs
with open("alignace.out") as handle:
motifsA = motifs.parse(handle, "alignace")
Again, your motifs behave as they should:
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motifsA[0].consensus
In fact you can even see, that AlignAce found a very similar motif as MEME. It is just a longer version of a reverse complement of the MEME motif:
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motifsM[0].reverse_complement().consensus
If you have AlignAce installed on the same machine, you can also run it directly from Biopython. A short example of how this can be done is shown below (other parameters can be specified as keyword parameters):
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command="/opt/bin/AlignACE"
input_file="test.fa"
from Bio.motifs.applications import AlignAceCommandline
cmd = AlignAceCommandline(cmd=command, input=input_file, gcback=0.6, numcols=10)
stdout, stderr= cmd()
Since AlignAce prints all of its output to standard output, you can get to your motifs by parsing the first part of the result:
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motifs = motifs.parse(stdout, "alignace")