Pairwise Sequence Alignment

1
Pair-wise Sequence Alignment

• What happened to the sequences of similar genes?
• random mutation
• deletion, insertion

• What is pair-wise sequence alignment?

Seq. 1 515 EVIRMQDNNPFSFQSDVYSYG EVI
P DVSY Seq. 2 451 EVI---EHKPYNHKADVFS
YA

• Why pair-wise alignment?

• Homology vs. similarity

2
Some concepts

• Gaps

• Gap penalty

• Optimal alignment

• Global alignment

• Local alignment

• Substitution matrix

3
Dotplot

• A simplified representation

• What dotplot shows

• What dotplot does not show

4
Sequence Alignment

• Total number of possible alignments for length n
• 22n / sqrt(2?n)

• Dynamic programming
• a method for some optimization problems
• determine a scoring scheme
• best solution based on a scoring scheme

• Needleman-Wunsch - global

5

• Questions
• How does it work?
• How to come up with a DP approach
• to an exponential problem?
• How to implement a DP approach?

6
Dynamic Programming Algorithm

• Break a problem into subproblems
• Solve each subproblem separately

F(i-1,j-1) s(xi, yj)
F(i,j-1) g
F(i,j) max
F(i-1,j) g
F(i,j) The max score for aligning 1st i
symbols of sequence 1 with 1st j symbols of
sequence 2
s(xi, yj) substitution score for aligning xi
with yj
g gap penalty
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Example
Match 1 Mismatch 0 Gap -1
ACAGTAG
ACTCG

• Initialization
• matrix filling (scoring)
• Trace back

8
Group Discussion 9/23/08 Due in class

• Fill up the table in the previous example
• What is the optimal alignment in this example?

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j 0, 1, 2, 3, 4, 5, 6, 7
A C A G T A G
i0
A
i1
C
i2
T
i3
C
i4
G
i5
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Local Alignment Smith- Waterman

• Biological significance

0
F(i-1,j-1) s(xi, yj)
F(i,j) max
F(i,j-1) g
F(i-1,j) g

• O(n2) time

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Local Alignment
A A C C T A T A G C T
G
C
G
A
T
A
T
A
AACCTATAGCT GCGATATA
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Issues in alignment

• Different ways to fill the table

• Multiple optimal alignments

• s(xi, yj) from substitution matrix

• gap penalty
• linear w(k) gk

h gk, k1
Affine w(k)
0, k0
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Gap models

• New gap vs. gap extension

• A gap of length k vs. k gaps of length 1

• 1 insersion / deletion event vs. k events

• gap penalty
• linear w(k) gk

h gk, k1
Affine w(k)
0, k0
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Affine Gap Penalty

• ? Wrong with the F(i,j) formula if AGP is used

• Aligning 1st i symbols of x with 1st j symbols of
  y

M( i, j ) best score when xi aligned with yj Ix
(i, j) best score when xi aligned with a
gap Iy (i, j) best score when yj aligned with
a gap

• Three matrices

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DP for global alignment for AGP
M(i-1, j-1) s(xi, yj) Ix (i-1, j-1) s(xi,
yj) ly (i-1, j-1) s(xi, yj)
M (i, j) max
M(i-1, j) h g Iy(i-1, j) h g lx (i-1, j)
g
Ix (i, j) max
M(i, j-1) h g Ix(i, j-1) h g ly (i, j-1)
g
Iy (i, j) max
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DP for global alignment using AGP

• Initialization
• M(0, 0) 0
• Ix(i, 0) hgi
• ly(0, j) hgj
• all other cases -?

• Start at the largest element in the three
  matrices
• M(m, n), Ix(m, n), ly(m, n)

• Traceback to (0,0)

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DP for local alignment for AGP
M(i-1, j-1) s(xi, yj) Ix (i-1, j-1) s(xi,
yj) ly (i-1, j-1) s(xi, yj) 0
M (i, j) max
M(i-1, j) h g Iy(i-1, j) h g //
ignored lx (i-1, j) g
Ix (i, j) max
M(i, j-1) h g Ix(i, j-1) h g //
ignored ly (i, j-1) g
Iy (i, j) max
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DP for Local Alignment for AGP

• Initialization
• M(0, 0) 0
• Ix(i, 0) 0
• ly(0, j) 0
• all other cases -?

• Start at the largest M(i, j), Ix(i, j), ly(i, j)

• Traceback till M(i, j) 0

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Database searching methods

• Ideas Regions that are similar likely to share
  short identical subsequences

• Quick search for the regions, then check
  carefully locally

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FASTA related methods

• Heuristic approximation

1. Quick initial guess common subsequences

• Word, word size (2,6), sensitivity vs. speed

• What are the words in the query also in target

• Pre-computed table that stores locations of words
  hashing

• An example

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FASTA related methods
2. Find the region with high population of common
words

• Process diagonals, rescore, join regions, using
  gaps

3. Local alignment (DP) in the region identified

• Use Smith-Waterman method
• in a band, 32 aa wide around the best score

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Limitation of FASTA

• Speed vs. sensitivity

• Identical words

• Can miss biologically significant similarity
• some proteins do not share identical a.a.
• initial step
• Different codons encodes same protein

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BLAST

• Previous 2 kinds approaches

• Theoretically sound
• search for common subsequences

• 1. Word list
• Incorporate similarity measurement for words
• PAM120
• e.g. ACDE

• Scan for word occurrences
• hash table
• Finite state machine

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BLAST

• 2. Extend words to HSP (locally optimal pairs)
• Find additional words within threshold
• Merge within distance A

3. Select significant HSPs, use DP in banded
region
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Multiple Sequence Alignment

• Motivation

• What is MSA?

• How do we extend knowledge of pair-wise alignment?

• An example AGAC, AC, AG

AGAC --AC
AGAC AG--
AC AG
AG--
Some possibilities
--AC
AGAC

• Fix pair-wise alignment and then add?
• Evaluate all the possible alignment of N
  sequences?

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Scoring MSA

• Sum of pairs (SP) scoring methods

Given a alignment of N sequences, each of which
has length L, in the LxN alignment
Pair-wise sum for each column, then sum all
columns

• Example
• (c(match)1, c(mismatch)-1, c(gap)-2,
  c(gap,gap) 0
• SP4SP(I,-,I,V) -21-1-2-2-1-7
• SP SP1 SP2 SP8

AQPILLLV ALR-LL- AK-ILLL- CPPVLILV

• SP tends to overweight a single mutation

SP(A,A,A,C) 0, SP(A,A,A,A) 6
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Extension of DP for N sequences

• Extend F(i,j) for N dimensions

• DP of N dimensions using SP
• Time in the order of (LN)(2N-1)N2 O((2L)NN2)

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STAR method

• DP provide optimal solution but costly

• Heuristic methods STAR, CLUSTALW,
• Progressive alignment

• STAR
• - pair-wise
• - build similarity matrix
• - find a star sequence
• - use star to align other sequence
• - once gap, all time gap

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STAR method

• Example

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CLUSTAL family

• What are the disadvantages of STAR method?

• Build Similarity tree clustering
• Alignment starts at most similar sequences

• Pair-wise alignment -- distance matrix
• Fast approximate approach or DP

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CLUSTALW
2. Construct similarity tree, the guide tree
UPGMA (un-weighted pair-group method using
arithmetic average)
3. Progressive alignment

• Start with most similar sequences
• Align group with group using pair-wise alignment
• e.g.