Kein Folientitel

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DNA, RNA and protein are an alien language ... We
try to cryptographically attack this language ...
we want to decipher both its meaning and its
history
2
Fortunate the genetic code is alphabetic
susceptible to perform string comparisons and
pattern recognition
We do not have to understand the languaje to
identify patterns klaatu barada nikto
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Pairwise Sequence Alignment
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Pairwise Sequence Alignment

• Principles of pairwise sequence comparison
• global / local alignments
• scoring systems
• gap penalties
• Methods of pairwise sequence alignment
• window-based methods
• dynamic programming approaches

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Pairwise Sequence Alignment How to?
A T T C A C A T A T A C A T T A
C G T A C
Sequence 2
Sequence 1
6
Dotplot
A dotplot gives an overview of all possible
alignments
A ? ? ? ? T ? ? ? ?
T ? ? ? ? C ? ? ? A ? ?
? ? C ? ? ? A ? ? ? ?
T ? ? ? ? A ? ? ? ?
T A C A T T A C G T A C
Sequence 2
Sequence 1
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Dotplot
In a dotplot each diagonal corresponds to a
possible (ungapped) alignment
A ? ? ? ? T ? ? ? ?
T ? ? ? ? C ? ? ? A ? ?
? ? C ? ? ? A ? ? ? ?
T ? ? ? ? A ? ? ? ?
T A C A T T A C G T A C
Sequence 2
Sequence 1
T A C A T T A C G T A C A T A C A C T
T A
One possible alignment
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Pairwise Sequence Alignment

• Principles of pairwise sequence comparison
• global / local alignments
• scoring systems
• gap penalties
• Methods of pairwise sequence alignment
• window-based methods
• dynamic programming approaches

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Window-based Approaches

• Word Size
• Window / Stringency

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Word Size Algorithm
T A C G G T A T G A C A G T A T C
Word Size 3
C T A T
? G A
C A T A C G G T A T G
T A C G G T A T G A C A G T A T C
T A C G G T A T G A C A G T A T C
T A C G G T A T G A C A G T A T C
?
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Window / Stringency
Window 5 / Stringency 4
T A C G G T A T G T C A G T A T C
C T A ? T
? G ? A CA
T A C G G T A T G
T A C G G T A T G T C A G T A T C
?
T A C G G T A T G T C A G T A T C
?
T A C G G T A T G T C A G T A T C
?
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Considerations

• The window/stringency method is more sensitive
  than the wordsize
• method (ambiguities are permitted).
• The smaller the window, the larger the weight of
  statistical
• (unspecific) matches.
• With large windows the sensitivity for short
  sequences is reduced.
• Insertions/deletions are not treated explicitly.

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Insertions / Deletions in a Dotplot
T A C T G T C A T T A C T G T T C A T
Sequence 2
Sequence 1
T A C T G - T C A T T A C T G
T T C A T
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Dotplot (Window 130 / Stringency 9)
Hemoglobin?-chain
Output of the programs Compare and DotPlot
Hemoglobin ?-chain
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Dotplot (Window 18 / Stringency 10)
Hemoglobin?-chain
Output of the programs Compare and DotPlot
Hemoglobin ?-chain
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Pairwise Sequence Alignment

• Principles of pairwise sequence comparison
• global / local alignments
• scoring systems
• gap penalties
• Methods of pairwise sequence alignment
• window-based approaches
• dynamic programming approaches
• Needleman and Wunsch
• Smith and Waterman

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Dynamic Programming
Automatic procedure that finds the best
alignment with an optimal score depending on the
chosen parameters.
Recursive solutions. We solve smaller problems
first, and use those solutions to solve larger
problems. Intermediate solutions are stored in a
tabular matrix.
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Basic principles of dynamic programming
- Initialization of alignment matrix the scoring
model - Stepwise calculation of score values
(creation of an alignment path matrix) -
Backtracking (evaluation of the optimal path)
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Initialization of Matrix (BLOSUM 50) A distance
metric
H E A G A W G H E E
P -2 -1 -1 -2 -1 -4 -2 -2 -1 -1 A
-2 -1 5 0 5 -3 0 -2 -1 -1 W -3 -3
-3 -3 -3 15 -3 -3 -3 -3 H 10 0 -2
-2 -2 -3 -2 10 0 0 E 0 6 -1 -3
-1 -3 -3 0 6 6 A -2 -1 5 0 5 -3
0 -2 -1 -1 E 0 6 -1 -3 -1 -3 -3
0 6 6
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Needleman and Wunsch(global alignment)
Sequence 1 H E A G A W G H E E Sequence 2 P A
W H E A E Scoring parameters BLOSUM50
matrix Gap penalty Linear gap penalty of 8
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Creation of an alignment path matrix
IdeaBuild up an optimal alignment using
previous solutions for optimal alignments of
smaller subsequences

• Construct matrix F indexed by i and j (one index
  for each sequence)
• F(i,j) is the score of the best alignment between
  the initial segment x1...i of x up to xi and
  the initial segment y1...j of y up to yj
• Build F(i,j) recursively beginning with F(0,0) 0

- A
E E
H H
G -
W W
A A
G -
A P
E -
H -
Optimal global alignment
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Creation of an alignment path matrix
H E A G A W G H
E E 0 -8 -16 -24 -32 -40 -48
-56 -64 -72 -80 P
-8 -2 -9 -17 -25 -33 -42 -49 -57 -65
-73 A -16 -10 -3 -4 -12 -20 -28 -36
-44 -52 -60 W -24 -18 -11 -6 -7 -15
-5 -13 -21 -29 -37 H -32 -14 -18 -13
-8 -9 -13 -7 -3 -11 -19 E -40 -22
-8 -16 -16 -9 -12 -15 -7 3 -5 A -48
-30 -16 -3 -11 -11 -12 -12 -15 -5
2 E -56 -38 -24 -11 -6 -12 -14 -15
-12 -9 1
HEAGAWGHE-E --P-AW-HEAE
Optimal global alignment
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Creation of an alignment path matrix
F(i, j) F(i-1, j-1) s(xi ,yj) F(i, j)
max F(i, j) F(i-1, j) - d F(i, j) F(i,
j-1) - d
F(i-1, j-1) F(i, j-1) F(i-1,j) F(i, j)
HEAGAWGHE-E --P-AW-HEAE
s(xi ,yj)
-d
-d
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Creation of an alignment path matrix

• If F(i-1,j-1), F(i-1,j) and F(i,j-1) are known we
  can calculate F(i,j)
• Three possibilities
• xi and yj are aligned, F(i,j) F(i-1,j-1)
  s(xi ,yj)
• xi is aligned to a gap, F(i,j) F(i-1,j) - d
• yj is aligned to a gap, F(i,j) F(i,j-1) - d
• The best score up to (i,j) will be the largest of
  the three options

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Creation of an alignment path matrix
H E A G A W G H
E E 0 P A W H E A E
-8 -16 -24 -32 -40 -48 -56 -64 -72 -80
-8 -16 -24 -32 -40 -48 -56
Boundary conditions F(i, 0) -i d
F(j, 0) -j d
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Stepwise calculation of score values
H E A G A W G H
E E 0 -8 -16 -24 -32 -40 -48
-56 -64 -72 -80 P
-8 A -16 W -24 H -32 E -40 A -48
E -56
P-H-2 E-P-1 H-A-2 E-A-1
-2
-9
-10
-3
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Backtracking
H E A G A W G H
E E 0 -8 -16 -24 -32 -40 -48
-56 -64 -72 -80 P
-8 -2 -9 -17 -25 -33 -42 -49 -57 -65
-73 A -16 -10 -3 -4 -12 -20 -28 -36
-44 -52 -60 W -24 -18 -11 -6 -7 -15
-5 -13 -21 -29 -37 H -32 -14 -18 -13
-8 -9 -13 -7 -3 -11 -19 E -40 -22
-8 -16 -16 -9 -12 -15 -7 3 -5 A -48
-30 -16 -3 -11 -11 -12 -12 -15 -5
2 E -56 -38 -24 -11 -6 -12 -14 -15
-12 -9 1
0
-8
-16
-25
-17
-20
-5
-13
-3
3
-5
1
- A
E E
H H
G -
W W
A A
G -
A P
E -
H -
Optimal global alignment
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Smith and Waterman(local alignment)
Two differences 1. 2. An alignment can now
end anywhere in the matrix
0 F(i, j) F(i-1, j-1) s(xi ,yj) F(i,
j) F(i-1, j) - d F(i, j) F(i, j-1) - d
F(i, j) max
Example Sequence 1 H E A G A W G H E E Sequence
2 P A W H E A E Scoring parameters Log-odds
ratiosGap penalty Linear gap penalty of 8
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Smith Waterman alignment
H E A G A W G H
E E 0 0 0 0 0 0 0 0
0 0 0 P 0
0 0 0 0 0 0 0 0 0 0 A
0 0 0 5 0 5 0 0 0 0
0 W 0 0 0 0 2 0 20 12
4 0 0 H 0 10 2 0 0 0 12
18 22 14 6 E 0 2 16 8 0
0 4 10 18 28 20 A 0 0 8
21 13 5 0 4 10 20 27 E 0 0
6 13 18 12 4 0 4 16 26
0
5
20
12
22
28
AA
G-
HH
WW
Optimal local alignment
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Extended Smith Waterman

• To get multiple local alignments
• delete regions around best path
• repeat backtracking

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Extended Smith Waterman
H E A G A W G H
E E 0 0 0 0 0 0 0 0
0 0 0 P 0
0 0 0 0 0 0 0 0 A 0
0 0 5 0 0 0 0 0
0 W 0 0 0 0 2 0
0 0 H 0 10 2 0 0 0 E 0
2 16 8 0 0 A 0 0 8 21
13 5 0 E 0 0 6 13 18 12 4
0
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Extended Smith Waterman
H E A G A W G H
E E 0 0 0 0 0 0 0 0
0 0 0 P 0
0 0 0 0 0 0 0 0 0 A
0 0 0 5 0 0 0 0 0
0 W 0 0 0 0 2 0
0 0 H 0 10 2 0 0 0 E 0
2 16 8 0 0 A 0 0 8 21
13 5 0 E 0 0 6 13 18 12 4
0
0
10
16
21
H H
EE
Second best local alignment
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Further Extensions of Dynamic Programming

• Overlap matches
• Alignment with affine gap scores

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Pairwise Sequence Alignment

• Pairwise sequence comparison
• global / local alignments
• parameters
• scoring systems
• insertions / deletions
• Methods of pairwise sequence alignment
• dotplot
• windows-based methods
• dynamic programming
• algorithm complexity

35
End.of.pa.irwise..sequence
align.ment.cours.e
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Methods of Pairwise Comparison
Progressive Alignment step
Multiple Alignment
1.
Programs perform global alignments

• Needleman Wunsch (Pileup, Tree, Clustal)
• Word Size Method (Clustal)
• X. Huang (MAlign)
• (modified N-W)

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Construction of a Guide Tree
Progressive Alignment step
Multiple Alignment
2.
1 2 3 4 5
Sequence
1 2 3 4 5
Similarity Matrix displays scores of all
sequence pairs.
The similarity matrix is transformed into
a distance matrix . . . . .
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Construction of a Guide Tree
Progressive Alignment step
Multiple Alignment
2.
Guide Tree
1
5
Distance Matrix
2
3
4
Neighbour-Joining Method or UPGMA (unweighted
pair group method of arithmetic averages)
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Multiple Alignment
Progressive Alignment step
Multiple Alignment
3.
Guide Tree
1
5
2
3
2
4
1
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Columns - once aligned - are never changed
Progressive Alignment step
Multiple Alignment
3.
G T C C G - C A G G T T - C G C C - G G
G T C C G - - C A G G T T - C G C - C - G G
T T A C T T C C A G G
T T A C T T C C A G G
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Columns - once aligned - are never changed
Progressive Alignment step
Multiple Alignment
3.
G T C C G - C A G G T T - C G C C - G G
G T C C G - - C A G G T T - C G C - C - G G
T T A C T T C C A G G
T T A C T T C C A G G
. . . . and new gaps are inserted.
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Columns - once aligned - are never changed
Progressive Alignment step
Multiple Alignment
3.
G T C C G - - C A G G T T - C G C - C - G G
G T C C G - - C A G G T T - C G C - C - G G
T T A C T T C C A G G
T T A C T T C C A G G
A T C - T - - C A A T C T G - T C C C T A G
A T C T - - C A A T C T G T C C C T A G
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Sub-sequence alignments
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A K-means like clustering problem
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Clustering resulting model
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Clustering predictions
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Assignments

• Describe a pairwise alignment with a different
  gap penalization.
• Provide an example and perform a multiple global
  alignment. Describe the recipe.
• Provide an example and and perform a multiple
  alignment of subsequences. Describe the recipe.
• Algorithms Order (polynomial, exponential, NP)

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Algorithmic Complexity
How does an algorithms performance in CPU time
and required memory storage scale with the size
of the problem?

• Needleman Wunsch
• Storing (n1)x(m1) numbers
• Each number costs a constant number of
  calculations to compute (three sums and a max)
• Algorithm takes O(nm) memory and O(nm) time
• Since n and m are usually comparable O(n2)