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Added pretty-printing to motif matrices
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mdehoon committed Dec 27, 2012
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11 changes: 11 additions & 0 deletions Bio/Motif/_Motif.py
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Expand Up @@ -26,6 +26,17 @@ def __init__(self, alphabet, values):
self.alphabet = alphabet self.alphabet = alphabet
self.__letters = sorted(self.alphabet.letters) self.__letters = sorted(self.alphabet.letters)


def __str__(self):
words = ["%6d" % i for i in range(self.length)]
line = " " + " ".join(words)
lines = [line]
for letter in self.__letters:
words = ["%6.2f" % value for value in self[letter]]
line = "%c: " % letter + " ".join(words)
lines.append(line)
text = "\n".join(lines) + "\n"
return text

def __getitem__(self, key): def __getitem__(self, key):
if isinstance(key, tuple): if isinstance(key, tuple):
if len(key)==2: if len(key)==2:
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136 changes: 100 additions & 36 deletions Doc/Tutorial.tex
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Expand Up @@ -10789,15 +10789,39 @@ \section{Motif objects}
\begin{verbatim} \begin{verbatim}
>>> m = Motif.Motif(instances=instances) >>> m = Motif.Motif(instances=instances)
\end{verbatim} \end{verbatim}
All instances should have the same sequence length. The length of the motif Printing out the Motif object shows the instances from which it was constructed:
is then defined as this sequence length: %cont-doctest
\begin{verbatim}
>>> print m
TACAA
TACGC
TACAC
TACCC
AACCC
AATGC
AATGC
<BLANKLINE>
\end{verbatim}
The length of the motif defined as the sequence length, which should be the same for all instances:
%cont-doctest %cont-doctest
\begin{verbatim} \begin{verbatim}
>>> len(m) >>> len(m)
5 5
\end{verbatim} \end{verbatim}
The Motif object has an attribute \verb+.counts+ containing the counts of each The Motif object has an attribute \verb+.counts+ containing the counts of each
nucleotide at each position. You can access the counts as a dictionary: nucleotide at each position. Printing this counts matrix shows it in an easily readable format:
%cont-doctest
\begin{verbatim}
>>> print m.counts
0 1 2 3 4
A: 3.00 7.00 0.00 2.00 1.00
C: 0.00 0.00 5.00 2.00 6.00
G: 0.00 0.00 0.00 3.00 0.00
T: 4.00 0.00 2.00 0.00 0.00
<BLANKLINE>
\end{verbatim}

You can access these counts as a dictionary:
%cont-doctest %cont-doctest
\begin{verbatim} \begin{verbatim}
>>> m.counts['A'] >>> m.counts['A']
Expand All @@ -10814,11 +10838,11 @@ \section{Motif objects}
>>> m.counts['T',3] >>> m.counts['T',3]
0 0
\end{verbatim} \end{verbatim}
Column-like access works like this: You can also directly access columns of the counts matrix
%Don't doctest this as dictionary order is platform dependent: %Don't doctest this as dictionary order is platform dependent:
\begin{verbatim} \begin{verbatim}
>>> m.counts[:,3] >>> m.counts[:,3]
{'A': 3, 'C': 0, 'G': 4, 'T': 0} {'A': 2, 'C': 2, 'T': 0, 'G': 3}
\end{verbatim} \end{verbatim}
Instead of the nucleotide itself, you can also use the index of the nucleotide 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 the sorted letters in the alphabet of the motif:
Expand Down Expand Up @@ -10861,21 +10885,22 @@ \section{Motif objects}
Here, W and R follow the IUPAC nucleotide ambiguity codes: W is either A or T, and V is A, C, or G \cite{cornish1985}. The degenerate consensus sequence is constructed followed the rules specified by Cavener \cite{cavener1987}. Here, W and R follow the IUPAC nucleotide ambiguity codes: W is either A or T, and V is A, C, or G \cite{cornish1985}. The degenerate consensus sequence is constructed followed the rules specified by Cavener \cite{cavener1987}.


We can also get the reverse complement of a motif: We can also get the reverse complement of a motif:
%>>> m.reverse_complement()
%<Bio.Motif.Motif.Motif object at 0xb39890>
%cont-doctest %cont-doctest
\begin{verbatim} \begin{verbatim}
>>> m.reverse_complement().consensus >>> r = m.reverse_complement()
>>> r.consensus
Seq('GCGTA', IUPACUnambiguousDNA()) Seq('GCGTA', IUPACUnambiguousDNA())
>>> for i in m.reverse_complement().instances: >>> r.degenerate_consensus
... print i Seq('GBGTW', IUPACAmbiguousDNA())
>>> print r
TTGTA TTGTA
GCGTA GCGTA
GTGTA GTGTA
GGGTA GGGTA
GGGTT GGGTT
GCATT GCATT
GCATT GCATT
<BLANKLINE>
\end{verbatim} \end{verbatim}


The reverse complement and the degenerate consensus sequence are The reverse complement and the degenerate consensus sequence are
Expand Down Expand Up @@ -11000,11 +11025,25 @@ \section{Position-Weight Matrices}
%cont-doctest %cont-doctest
\begin{verbatim} \begin{verbatim}
>>> pwm = m.counts.normalize(pseudocounts=0.5) >>> pwm = m.counts.normalize(pseudocounts=0.5)
>>> print pwm
0 1 2 3 4
A: 0.39 0.83 0.06 0.28 0.17
C: 0.06 0.06 0.61 0.28 0.72
G: 0.06 0.06 0.06 0.39 0.06
T: 0.50 0.06 0.28 0.06 0.06
<BLANKLINE>
\end{verbatim} \end{verbatim}
Alternatively, \verb+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: Alternatively, \verb+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:
%cont-doctest %cont-doctest
\begin{verbatim} \begin{verbatim}
>>> pwm = m.counts.normalize(pseudocounts={'A':0.6, 'C': 0.4, 'G': 0.4, 'T': 0.6}) >>> pwm = m.counts.normalize(pseudocounts={'A':0.6, 'C': 0.4, 'G': 0.4, 'T': 0.6})
>>> print pwm
0 1 2 3 4
A: 0.40 0.84 0.07 0.29 0.18
C: 0.04 0.04 0.60 0.27 0.71
G: 0.04 0.04 0.04 0.38 0.04
T: 0.51 0.07 0.29 0.07 0.07
<BLANKLINE>
\end{verbatim} \end{verbatim}
The position-weight matrix has its own methods to calculate the consensus, anticonsensus, and degenerate consensus sequences: The position-weight matrix has its own methods to calculate the consensus, anticonsensus, and degenerate consensus sequences:
%cont-doctest %cont-doctest
Expand All @@ -11022,7 +11061,18 @@ \section{Position-Weight Matrices}
>>> m.degenerate_consensus >>> m.degenerate_consensus
Seq('WACVC', IUPACAmbiguousDNA()) Seq('WACVC', IUPACAmbiguousDNA())
\end{verbatim} \end{verbatim}
The reverse complement of the position-weight matrix can be calculated directly from the \verb+pwm+. The reverse complement of the position-weight matrix can be calculated directly from the \verb+pwm+:
%cont-doctest
\begin{verbatim}
>>> rpwm = pwm.reverse_complement()
>>> print rpwm
0 1 2 3 4
A: 0.07 0.07 0.29 0.07 0.51
C: 0.04 0.38 0.04 0.04 0.04
G: 0.71 0.27 0.60 0.04 0.04
T: 0.18 0.29 0.07 0.84 0.40
<BLANKLINE>
\end{verbatim}


\section{Position-Specific Scoring Matrices} \section{Position-Specific Scoring Matrices}


Expand All @@ -11031,34 +11081,46 @@ \section{Position-Specific Scoring Matrices}
odds of a particular symbol to be coming from a motif against the odds of a particular symbol to be coming from a motif against the
background. We can use the \verb|.log_odds()| method on the position-weight background. We can use the \verb|.log_odds()| method on the position-weight
matrix: matrix:

%cont-doctest
\begin{verbatim} \begin{verbatim}
>>> pwm.log_odds() >>> pssm = pwm.log_odds()
{'A': [0.6780719051126378, 1.7560744171139109, -1.9068905956085187, 0.2085866218114176, -0.4918530963296747], 'C': [-2.4918530963296748, -2.4918530963296748, 1.2630344058337941, 0.09310940439148147, 1.5081469036703254], 'T': [1.031708859727338, -1.9068905956085187, 0.2085866218114176, -1.9068905956085187, -1.9068905956085187], 'G': [-2.4918530963296748, -2.4918530963296748, -2.4918530963296748, 0.5956097449206647, -2.4918530963296748]} >>> print pssm
0 1 2 3 4
A: 0.68 1.76 -1.91 0.21 -0.49
C: -2.49 -2.49 1.26 0.09 1.51
G: -2.49 -2.49 -2.49 0.60 -2.49
T: 1.03 -1.91 0.21 -1.91 -1.91
<BLANKLINE>
\end{verbatim} \end{verbatim}
Here we can see positive values for symbols more frequent in the motif 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 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. $0.0$ means that it's equally likely to see a symbol in the
background and in the motif (e.g. `T' in the second-last position). background and in the motif.


This assumes that A, C, G, and T are equally likely in the background. To 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 calculate the position-specific scoring matrix against a background with
unequal probabilities for A, C, G, T, use the \verb+background+ argument. unequal probabilities for A, C, G, T, use the \verb+background+ argument.
For example, against a background with a 40\% GC content, use For example, against a background with a 40\% GC content, use
%cont-doctest
\begin{verbatim} \begin{verbatim}
>>> pwm.log_odds(background={'A':0.3,'C':0.2,'G':0.2,'T':0.3}) >>> pssm = pwm.log_odds(background={'A':0.3,'C':0.2,'G':0.2,'T':0.3})
{'A': [0.415037499278844, 1.493040011280117, -2.169925001442312, -0.054447784022376135, -0.7548875021634684], 'C': [-2.1699250014423126, -2.1699250014423126, 1.5849625007211563, 0.4150374992788437, 1.8300749985576878], 'T': [0.7686744538935444, -2.169925001442312, -0.054447784022376135, -2.169925001442312, -2.169925001442312], 'G': [-2.1699250014423126, -2.1699250014423126, -2.1699250014423126, 0.9175378398080271, -2.1699250014423126]} >>> print pssm
0 1 2 3 4
A: 0.42 1.49 -2.17 -0.05 -0.75
C: -2.17 -2.17 1.58 0.42 1.83
G: -2.17 -2.17 -2.17 0.92 -2.17
T: 0.77 -2.17 -0.05 -2.17 -2.17
<BLANKLINE>
\end{verbatim} \end{verbatim}


The maximum and minimum score obtainable from the PSSM are stores in the The maximum and minimum score obtainable from the PSSM are stored in the
\verb+.max+ and \verb+.min+ properties: \verb+.max+ and \verb+.min+ properties:
%cont-doctest %cont-doctest
\begin{verbatim} \begin{verbatim}
>>> pssm = pwm.log_odds()
>>> print "%4.2f" % pssm.max >>> print "%4.2f" % pssm.max
6.15 6.59
>>> print "%4.2f" % pssm.min >>> print "%4.2f" % pssm.min
-11.87 -10.85
\end{verbatim} \end{verbatim}


Similarly, the mean and standard deviation of the PSSM scores are stored in Similarly, the mean and standard deviation of the PSSM scores are stored in
Expand All @@ -11068,14 +11130,17 @@ \section{Position-Specific Scoring Matrices}
>>> mean = pssm.mean >>> mean = pssm.mean
>>> std = pssm.std >>> std = pssm.std
>>> print "mean = %0.2f, standard deviation = %0.2f" % (mean, std) >>> print "mean = %0.2f, standard deviation = %0.2f" % (mean, std)
mean = 3.22, standard deviation = 2.49 mean = 3.21, standard deviation = 2.59
\end{verbatim} \end{verbatim}
The mean is particularly important, as its value is equal to the The mean is particularly important, as its value is equal to the
Kullback-Leibler divergence or relative entropy, and is a measure for 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 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 the base-2 logarithm is used in the calculation of the log-odds scores, the
information content has units of bits. information content has units of bits.


The \verb+.reverse_complement+, \verb+.consensus+, \verb+.anticonsensus+, and
\verb+.degenerate_consensus+ methods can be applied directly to PSSM objects.

\section{Searching for instances} \section{Searching for instances}
\label{sec:search} \label{sec:search}


Expand All @@ -11092,7 +11157,7 @@ \section{Searching for instances}
%cont-doctest %cont-doctest
\begin{verbatim} \begin{verbatim}
>>> for pos,seq in m.search_instances(test_seq): >>> for pos,seq in m.search_instances(test_seq):
... print pos,seq.tostring() ... print pos, seq
... ...
0 TACAC 0 TACAC
10 TACAA 10 TACAA
Expand All @@ -11101,8 +11166,8 @@ \section{Searching for instances}
We can do the same with the reverse complement (to find instances on the complementary strand): We can do the same with the reverse complement (to find instances on the complementary strand):
%cont-doctest %cont-doctest
\begin{verbatim} \begin{verbatim}
>>> for pos,seq in m.reverse_complement().search_instances(test_seq): >>> for pos,seq in r.search_instances(test_seq):
... print pos,seq.tostring() ... print pos, seq
... ...
6 GCATT 6 GCATT
20 GCATT 20 GCATT
Expand All @@ -11111,14 +11176,13 @@ \section{Searching for instances}
It's just as easy to look for positions, giving rise to high log-odds scores against our motif: It's just as easy to look for positions, giving rise to high log-odds scores against our motif:
%cont-doctest %cont-doctest
\begin{verbatim} \begin{verbatim}
>>> pssm = pwm.log_odds()
>>> for position, score in pssm.search(test_seq, threshold=4.0): >>> for position, score in pssm.search(test_seq, threshold=4.0):
... print "Position %i gives score %0.2f" % (position, score) ... print "Position %i gives score %0.2f" % (position, score)
... ...
Position 0 gives score 5.77 Position 0 gives score 5.62
Position -20 gives score 4.75 Position -20 gives score 4.60
Position 13 gives score 5.30 Position 13 gives score 5.74
Position -6 gives score 4.75 Position -6 gives score 4.60
\end{verbatim} \end{verbatim}
The negative positions refer to instances of the motif found on the The negative positions refer to instances of the motif found on the
reverse strand of the test sequence, and follow the Python convention reverse strand of the test sequence, and follow the Python convention
Expand All @@ -11136,12 +11200,12 @@ \section{Searching for instances}
%Don't use a doc test for this as the spacing can differ %Don't use a doc test for this as the spacing can differ
\begin{verbatim} \begin{verbatim}
>>> pssm.calculate(test_seq) >>> pssm.calculate(test_seq)
array([ 5.76755142, -5.53445292, -3.87148786, 0.49856207, array([ 5.62230396, -5.6796999 , -3.43177247, 0.93827754,
-7.2893405 , -1.89541376, -10.70437813, -2.92593575, -6.84962511, -2.04066086, -10.84962463, -3.65614533,
0.69650143, -3.18081594, 3.76755118, -2.0039382 , -0.03370807, -3.91102552, 3.03734159, -2.14918518,
-1.04141295, 5.29843712, -0.94949049, -4.0039382 , -0.6016975 , 5.7381525 , -0.50977498, -3.56422281,
-9.17386341, -0.53891265, -0.45645046, -2.24905086, -8.73414803, -0.09919716, -0.6016975 , -2.39429784,
-10.70437813, -2.92593575], dtype=float32) -10.84962463, -3.65614533], dtype=float32)
\end{verbatim} \end{verbatim}
In general, this is the fastest way to calculate PSSM scores. In general, this is the fastest way to calculate PSSM scores.


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