Motif Finding

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Motif Finding
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Motif Finding

• Can be used identify
• Promoters
• Transcription Factor Binding Sites
• Problem The identification of a motif without
  any prior knowledge of how the motif looks
• If you do not know what the motif looks like, or
  where it is located, you need an algorithm that
  given a set of sequences, it can find short
  substrings that occurs more often than random.
• Methods
• Position Weight Matrices
• Maximization Expectation
• Gibbs Sampling
• Phylogenetic Footprinting

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An Example

• 7 32-nucleotide DNA sequences, generated randomly

CTGCGGTACCCCAAAGTTTCTGTCTTACTAAC TGGTCCCAGGACTCATG
CGTAGGCTAAGAGTT GTGTAATGGTCAACGTGTCCCGCCAAACATTA A
ATGTCTCACTGGTGCCATTAATTATAGAATG TTTAACCGATATGAAATA
GGCCTGGCCACATT GCCGTACCGACACACATTCTTTGGCATCCCTA TA
GGTCTCGCTCGGCTGGTCGAATGGTCCGAG
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An Example

• Insert a pattern, PATGCAACT of length l8 at
  random positions in each sequence

CTGCGGTACATGCAACTCCCAAAGTTTCTGTCTTACTAAC TGGTCCCAG
GACTCATGCATGCAACTGTAGGCTAAGAGTT GTATGCAACTGTAATGGT
CAACGTGTCCCGCCAAACATTA AATGTCATGCAACTTCACTGGTGCCAT
TAATTATAGAATG TTTAACCGATATGAAATAGGCCTGGCCATGCAACTA
CATT GCCGTACCGACACACATTCTTTGGATGCAACTCATCCCTA TAGG
TCTCGCTATGCAACTCGGCTGGTCGAATGGTCCGAG
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Problem

• If you dont know what the pattern is, or where
  it has been inserted, can you find the pattern?

CTGCGGTACATGCAACTCCCAAAGTTTCTGTCTTACTAAC TGGTCCCAG
GACTCATGCATGCAACTGTAGGCTAAGAGTT GTATGCAACTGTAATGGT
CAACGTGTCCCGCCAAACATTA AATGTCATGCAACTTCACTGGTGCCAT
TAATTATAGAATG TTTAACCGATATGAAATAGGCCTGGCCATGCAACTA
CATT GCCGTACCGACACACATTCTTTGGATGCAACTCATCCCTA TAGG
TCTCGCTATGCAACTCGGCTGGTCGAATGGTCCGAG
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Solution

• Count the number of times each l-mer occurs in
  the sequences.
• (328)7 280 total nucleotides
• The probability of finding any 8-mer is less than
  280/480.004
• After counting all 8-mers, 1 appears many more
  times. This overrepresented 8-mer is the pattern
  P we are trying to find. Use EMBOSSwordcount.

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Problem 2

• Suppose we allow for mutations at some positions
  (try to use EMBOSSwordcount)

CTGCGGTACATcCAgCTCCCAAAGTTTCTGTCTTACTAAC TGGTCCCAG
GACTCATGCggGCAACTGTAGGCTAAGAGTT GTATGgAtCTGTAATGGT
CAACGTGTCCCGCCAAACATTA AATGTCAaGCAACcTCACTGGTGCCAT
TAATTATAGAATG TTTAACCGATATGAAATAGGCCTGGCCtTGgAACTA
CATT GCCGTACCGACACACATTCTTTGGATGCcAtTCATCCCTA TAGG
TCTCGCTATGgcACTCGGCTGGTCGAATGGTCCGAG
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Solution

• Use a profile matrix to allow for variations in
  the pattern
• The length (number of columns) of the matrix is
  the length of the profile, l.
• The rows of the matrix correspond to the number
  of possible bases/residues.

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Solution

• Given a set of t sequences, construct a 4 x l
  matrix, and align the sequences in all possible
  positions.
• For each possible starting position for all the
  sequences
• Count the number of times each nucleotide appears
  in each position.
• The score of the resulting alignment is the
  maximum score of each nucleotide in each
  position.
• The alignment with the greatest score corresponds
  to the motif.

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Example
CTGCGGTACATcCAgCTCCCAAAGTTTCTGTCTTACTAAC TGGTCCCAG
GACTCATGCggGCAACTGTAGGCTAAGAGTT GTATGgAtCTGTAATGGT
CAACGTGTCCCGCCAAACATTA AATGTCAaGCAACcTCACTGGTGCCAT
TAATTATAGAATG TTTAACCGATATGAAATAGGCCTGGCCtTGgAACTA
CATT GCCGTACCGACACACATTCTTTGGATGCcAtTCATCCCTA TAGG
TCTCGCTATGgcACTCGGCTGGTCGAATGGTCCGAG

• Construct a PWM for the alignment in bold

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Example
CTGCGGTACATcCAgCTCCCAAAGTTTCTGTCTTACTAAC TGGTCCCAG
GACTCATGCggGCAACTGTAGGCTAAGAGTT GTATGgAtCTGTAATGGT
CAACGTGTCCCGCCAAACATTA AATGTCAaGCAACcTCACTGGTGCCAT
TAATTATAGAATG TTTAACCGATATGAAATAGGCCTGGCCtTGgAACTA
CATT GCCGTACCGACACACATTCTTTGGATGCcAtTCATCCCTA TAGG
TCTCGCTATGgcACTCGGCTGGTCGAATGGTCCGAG

• Construct a PWM for the alignment in bold

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Example

• Score the alignment by taking the maximum score
  in each column

• Score 25
• Consensus Sequence TTGGTCCA

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Example
CTGCGGTACATcCAgCTCCCAAAGTTTCTGTC
TTACTAAC TGGTCCCAGGACTCATGCggGCAACTGTAGGC
TAAGAGTT
GTATGgAtCTGTAATGGTCAACGTGTCCCGCCAAACATTA
AATGTCAaGCAACcTCACTGGTGCCATTAATTATAGAA
TG TTTAACCGATATGAAATAGGCCTGGCCtTGgAACTACATT
GCCGTACCGACACACATTCTTTGGATGCcAtTCATCCCTA
TAGGTCTCGCTATGgcACTCGGCTGGTCGAATGGTCCGAG

• Construct a PWM for the alignment in bold

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Example
CTGCGGTACATcCAgCTCCCAAAGTTTCTGTC
TTACTAAC TGGTCCCAGGACTCATGCggGCAACTGTAGGC
TAAGAGTT
GTATGgAtCTGTAATGGTCAACGTGTCCCGCCAAACATTA
AATGTCAaGCAACcTCACTGGTGCCATTAATTATAGAA
TG TTTAACCGATATGAAATAGGCCTGGCCtTGgAACTACATT
GCCGTACCGACACACATTCTTTGGATGCcAtTCATCCCTA
TAGGTCTCGCTATGgcACTCGGCTGGTCGAATGGTCCGAG

• Construct a PWM for the alignment in bold

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Example

• Score the alignment by taking the maximum score
  in each column

• Score 42
• Consensus Sequence ATGCAACT

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Formally Stated

• Given
• Set of t DNA sequences, each with n nucleotides
• Select one position in each of the t sequences
  forming an array of starting positions
  s(s1,s2,,st) where 1ltsiltn-l1
• How many starting positions are these in each
  sequence?
• How many combinations of starting positions are
  there in all?

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Scoring

• Let P(s) profile matrix corresponding to
  starting positions s.
• Mp(s)(j) largest count in column j of P(s).
• Mp(last example)(1) 5
• Mp(last example)(3) 6
• Score

This score is based on absolute frequencies. A
statistically based score would be
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Representing patterns Matrices
CTTGGTGACGTG GTGAGTGACGTC CGGGTTGACGCA CCTACTTACGT
A TATGGTGACGTC TCGGATGACGAT TAGGATGACGTC CCTGGTGAC
GCC CGCGGTGACGTA GCCGTTGACGCC CGCGATGACGCA CCTGTTG
ACGTG TTGCATGACGTC GTTGGTGACGTG GAGGATGACGTT GGTCG
TGACGTA
Given N sequence fragments of fixed length, one
can assemble a position frequency matrix (number
of times a particular nucleotide appears at a
given position)
A 0 3 0 2 5 0 0 16 0 0 1 5 C 7
5 3 3 1 0 0 0 16 0 5 6 G 5 4 6 11
7 0 15 0 0 16 0 3 T 4 4 7 0 3 16
1 0 0 0 10 2
Position frequency matrix (PFM) (aka raw count
matrix or conservation and substitution matrix)
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More on scores
Using pseudocounts (N 16)
Converting a PFM into a PWM
A 0 3 0 2 5 0 0 16 0 0 1 5 C 7
5 3 3 1 0 0 0 16 0 5 6 G 5 4 6 11
7 0 15 0 0 16 0 3 T 4 4 7 0 3 16
1 0 0 0 10 2
For each matrix element do
A -2 0 -2 -0.415 0.585 -2 -2
2.088 -2 -2 -1 0.585 C 1 0.585
0 0 -1 -2 -2 -2 2.088 -2
0.585 0.807 G 0.585 0.322 0.807 1.585
1 -2 2 -2 -2 2.088 -2 0 T
0.319 0.322 1 -2 0 2.088 -1
-2 -2 -2 1.459 -0.415
n(b,i) raw count (PFM matrix element) of
nucleotide b in column i N number of
sequences used to create PFM ( column sum)
- pseudocounts (correction for small sample
size) p(b) - background frequency of nucleotide
b
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Detecting binding sites using a PWM
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Problems with Matrices

• Large search space gives larger portion of false
  positives
• There are (n-l1)t sets of starting points for t
  sequences of length n, when looking for a motif
  of length l.
• This grows exponentially with the number of
  sequences.

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• Phylogenetic footprinting

Using cross-species conservation of regulatory
elements to improve binding site prediction
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Phylogenetic-Footprinting

• A method of identifying conserved motifs in a set
  of orthologous sequences from multiple species
  using the notion that
• Selective pressure causes functional elements to
  evolve at a slower rate than nonfunctional
  sequences
• Identifies the best conserved motifs in those
  regions
• Guaranteed to report all sets of motifs with the
  lowest parsimony scores.

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Parsimony Score

• Hamming distance (Parsimony Score)
• Number of changes applied to a sequence to obtain
  another sequence
• If vATTGTC and wACTCTC, then d(v,w) 2

v ATTGTC x x w ACTCTC
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Substring Parsimony Problem

• Given
• n orthologous sequences S1, S2, S3, , Sn
• T phylogenetic tree relating sequences
• k length of motif
• d maximum parsimony score
• Problem
• Find set of k-mers, one from each input sequence
  with parsimony score lt d with respect to T
• Parameters
• k and d can be specified by the user

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Terminology
Leaf Nodes
Internal Nodes
Chicken Human Mouse
v
C(v)Human, Mouse
C(v)?
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DP Solution

• Proceeds from the leaves of T up to its root
• At each node u of T, compute a table W(u)
  containing 4k entries, one for each possible
  k-mer
• For a string s of length k,
• Wus the best parsimony score that can be
  achieved for the subtree rooted at u

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DP Solution

• C(u) set of children of u
• d(s,t) Hamming distance between sequences s and
  t
• ? A,C,G,T
• Tables W can now be computed
• 0 if u is a leaf and s is a substring of Su
• ? if u is a leaf and s is not a substring of Su
• if u is not a leaf

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An Exact Algorithm
Wu s best parsimony score for subtree rooted
at node u, if u is labeled with string s.
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Small Example
ATGC... (Chicken) ACGT... (Human) ACGG... (Mouse)
Size of motif sought k 2
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Problems with Phylogenetic-Footprinting

• Divergence of organisms being compared needs to
  be sufficient to allow for sequence divergence
• Comparing non-mammalian organisms to mammalian
  organisms can limit types of functional elements
  being found (primate specific, mammalian
  specific, etc)
• Requires several different organisms