Pealkiri

1
Position Weight Matrices for Representing Signals
in Sequences
Triinu Tasa, Koke 04.02.05
2
Definitions

• Sequence, string ordered arrangement of letters
  'A', 'C', 'G', 'T'
• Pattern simplified regular expression, alphabet
  'A', 'C', 'G', 'T', '.', where '.' - wild-card
  of length 1 ('A', 'C', 'G' or 'T')

Triinu Tasa, Koke 04.02.05
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What is a weight matrix?
What is a weight matrix?

• GATGAG
• GATGAT
• TGATAT
• GATGAT
• or
• GTAGTAGTAGT

Triinu Tasa, Koke 04.02.05
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What is a weight matrix?
Better
GATGAG GATGAT TGATAT

• Alignment matrix C
• A 0 2 1 0 3 0
• C 0 0 0 0 0 0
• G 2 1 0 2 0 1
• T 1 0 2 1 0 2
• Frequency matrix F
• A 0 0.7 0.3 0 1 0
• C 0 0 0 0 0 0
• G 0.7 0.3 0 0.7 0 0.3
• T 0.3 0 0.7 0.3 0 0.7

Triinu Tasa, Koke 04.02.05
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Or weight matrix W
What is a weight matrix?

• where
• N number of sequences used
• - a priori probability of letter i

Triinu Tasa, Koke 04.02.05
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Importance matrix I
What is a weight matrix?

• I(i, j)

A 0 1.4 0.3 0 3 0 C 0 0 0 0 0 0 G 1.4 0.3 0 1.4
0 0.3 T 0.3 0 1.4 0.3 0 1.4
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Applications
Applications - Clustering

• Pattern clustering
• 1. G.GATGAG.T 62/75 139/49
  223/26 R17.3026 BP1.12008e-37
• 2. G.GATGAG 89/110 145/60
  244/50 R10.436 BP1.61764e-34
• 3. GATGAG.T 124/148 152/70
  272/78 R7.36961 BP2.79148e-33
• 4. TG.AAA.TTT 132/145 153/61
  279/84 R6.84578 BP1.83509e-32
• 5. AAAATTTT 200/231 163/77
  2137/154 R4.69239 BP1.19109e-30
• 6. TGAAAA.TTT 104/114 145/53
  259/61 R7.78277 BP3.86086e-29
• 7. AAA.TTTT 343/537 179/145
  2264/392 R3.05349 BP5.66833e-29
• 8. G.AAA.TTTT 135/156 151/62
  284/94 R6.19534 BP5.69933e-29
• 9. TG.GATGAG 49/57 130/35
  219/22 R16.1117 BP9.35765e-28
• 10. TG.AAA.TTTT 86/91 140/43
  246/48 R8.87311
  BP1.1124e-27
• ...

Triinu Tasa, Koke 04.02.05
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G.GATGAG.T
Applications - Clustering

• GAGATGAGAT
• GTGATGAGAT
• GAGATGAGGT
• ...
• A -6.9 0.98 -6.9 1.38 -6.9 -6.9 1.38 -6.9 0.98 -6.
  9
• C -6.9 -6.9 -6.9 -6.9 -6.9 -6.9 -6.9 -6.9 -6.9 -6.
  9
• G 1.38 -6.9 1.38 -6.9 -6.9 1.38 -6.9 1.38 0.29 -6.
  9
• T -6.9 0.29 -6.9 -6.9 1.38 -6.9 -6.9 -6.9 -6.9 1.3
  8

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Compare matrices with each other using the
dynamic programming approach
Applications - Clustering

• where
• A, B matrices
• i, j - columns
• If D(m,n) gt threshold gt matrices are different

Triinu Tasa, Koke 04.02.05
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Applications - Clustering

• G.GATGAG.T TG.AAA.TTT AAAATTTT
• G.GATGAG TGAAAA.TTT AAA.TTTT
• GATGAG.T TG.AAA.TTTT
• We want to represent the clusters by
• logos
• We need to align the patterns first position
  the similar parts of the patterns above each
  other
• G.GATGAG.T
• G.GATGAG--
• --GATGAG.T
• or the logo will look like this

Triinu Tasa, Koke 04.02.05
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Multiple Alignment
Applications Multiple alignment

• Importance matrix I represents the aligned
  patterns.
• Example
• G.GATGAG.T
• GATGAG.T
• G.GATGAG
• 1. Insert the first pattern into I ('.' gives
  0.25 to each)
• A 0 0.25 0 1 0 0 1 0 0.25 0
• C 0 0.25 0 0 0 0 0 0 0.25 0
• G 1 0.25 1 0 0 1 0 1 0.25 0
• T 0 0.25 0 0 1 0 0 0 0.25 1
• 2. Align the second pattern with I using a
  dynamic programming approach

Triinu Tasa, Koke 04.02.05
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Applications Multiple alignment

• Dynamic programming matrix
• G . G A T G
  A G . T
• G 0.00 0.10 0.01 0.10 0.00 0.00
  0.10 0.00 0.10 0.01 0.00
• A 0.00 0.00 0.11 0.00 0.20 0.00
  0.00 0.20 0.00 0.11 0.00
• T 0.00 0.00 0.01 0.00 0.00 0.30
  0.00 0.00 0.00 0.01 0.21
• G 0.00 0.10 0.01 0.11 0.00 0.00
  0.40 0.00 0.10 0.01 0.00
• A 0.00 0.00 0.11 0.00 0.21 0.00
  0.00 0.50 0.00 0.11 0.00
• G 0.00 0.10 0.01 0.21 0.00 0.00
  0.10 0.00 0.60 0.01 0.00
• . 0.00 0.00 0.10 0.01 0.21 0.00
  0.00 0.10 0.00 0.60 0.01
• T 0.00 0.00 0.01 0.00 0.00 0.31
  0.00 0.00 0.00 0.01 0.70
• G.GATGAG.T
• --GATGAG.T

Triinu Tasa, Koke 04.02.05
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Applications Multiple alignment

• 3. Add the pattern '--GATGAG.T' to I, if
  necessary add columns to the matrix.
• 4. Repeat the procedure for every pattern.
• Output
• G.GATGAG.T
• G.GATGAG--
• --GATGAG.T
• Why importance matrix?

Triinu Tasa, Koke 04.02.05
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Applications Multiple alignment

• Example
• Pattern GATG
• So far aligned
• GATGATGTA-
• - - - GATGTGG
• We want w(G, 4) gt w(G, 1) gt w(G, 9)
• Solution importance matrix

Triinu Tasa, Koke 04.02.05
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Applications Weight matrix matching

• Weight Matrix Matching
• Purpose find the sequences that the weight
  matrix describes best in a given text file
• ...CATAGGAAATTCCACCTCTTTGGCTTTGCCCAGTCTTCCCTTGAGGA
  TGCCTACGTTC...
• 1. Calculate the score for each position
• 2. if score gt threshold gt signal
• Problem finding a good threshold
• Threshold 99.5 quantile

Triinu Tasa, Koke 04.02.05
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Questions?
Triinu Tasa, Koke 04.02.05