1. Sequence Alignment Tutorial #2.
© Ydo Wexler & Dan Geiger

2. Sequence Comparison Much of bioinformatics involves sequences
DNA sequences
RNA sequences
Protein sequences
We can think of these sequences as strings of letters
DNA & RNA: |alphabet|=4
Protein: |alphabet|=20

3. Global Alignment Input: two sequences over the same alphabet
Output: an alignment of the two sequences
Example:
GCGCATGGATTGAGCGA and TGCGCCATTGATGACCA
A possible alignment:
-GCGC-ATGGATTGAGCGA
TGCGCCATTGAT-GACC-A

4. Global Alignment -GCGC-ATGGATTGAGCGA TGCGCCATTGAT-GACC-A
Example (cont):
-GCGC-ATGGATTGAGCGA
TGCGCCATTGAT-GACC-A
Three elements:
Perfect matches
Mismatches
Insertions & deletions (indel)
Best biological
explanaiton
Biological data
Hypotheses space
Symmetric view of evolution

5. Global Alignment scoring scheme
Score each position independently:
Match: +1
Mismatch: -1
Indel: -2
Score of an alignment is sum of position scores
Example: -GCGC-ATGGATTGAGCGA
TGCGCCATTGAT-GACC-A
Score: (+1x13) + (-1x2) + (-2x4) = 3
------GCGCATGGATTGAGCGA
TGCGCC----ATTGATGACCA--
Score: (+1x5) + (-1x6) + (-2x11) = -23

6. Sequence Alignment Variants
Two basic variants of sequence alignment:
Global alignment (Needelman-Wunsch)
Local alignment (Smith-Waterman)
Today we’ll see :
Overlap alignment
Affine cost for gaps
We’ll use ideas of dynamic programming presented in the lecture

7. Overlap Alignment Consider the following problem:
Find the most significant overlap between two sequences S,T ?
Possible overlap relations: a. b.
Difference from local alignment:
Here we require alignment between the endpoints of the two sequences.

8. Overlap Alignment Formally:
given S[1..n] , T[1..m] find i,j such that:
d=max{D(S[1..i],T[j..m]) , D(S[i..n],T[1..j]) , D(S[1..n],T[i..j]) , D(S[i..j],T[1..m]) }
is maximal.
Solution: Same as Global alignment except we don’t not penalise overhanging ends.

9. Overlap Alignment Initialization: V[i,0]=0 , V[0,j]=0
Recurrence: as in global alignment
Score: maximum value at the bottom line and rightmost line

10. Overlap Alignment (Example)
S = PAWHEAE
T = HEAGAWGHEE
Scoring scheme :
Match: +4
Mismatch: -1
Indel: -5

11. Overlap Alignment (Example)
S = PAWHEAE
T = HEAGAWGHEE
Scoring scheme :
Match: +4
Mismatch: -1
Indel: -5

12. Overlap Alignment (Example)
S = PAWHEAE
T = HEAGAWGHEE
Scoring scheme:
Match: +4
Mismatch: -1
Indel: -5

13. Overlap Alignment (Example)
The best overlap is:
PAWHEAE------
---HEAGAWGHEE
Pay attention!
A different scoring scheme could yield a different result, such as:
---PAW-HEAE
HEAGAWGHEE-
Scoring scheme :
Match: +4
Mismatch: -1
Indel:

14. Affine gap scores
Observation: Insertions and deletions often occur in blocks longer than a single nucleotide.
Consequence:
Current scoring scheme gives a constant penalty per gap unit.
This does not score well the above phenomenon.
Question: How do we modify the scheme to incorporate this?

15. Alignment with affine gap scores
Penalty score for a gap of length g :
d - penalty for introduction of a gap
e - penalty for elongating the gap by one unit.
Typically d > e
Problem:
When aligning S[i] to a gap we do not know whether to penalize by d or e.
Solution: we compute 3 matrices simultaneously
M(i,j) - the score obtained by aligning S[i] to T[j]
IS(i,j) - the score obtained by aligning S[i] to a gap
IT(i,j) - the score obtained by aligning T[j] to a gap

16. Affine gap scores
Initialization: depending on the problem (global, local,…)
Recurrence: uses already known values - M(i’,j’), IS(i’,j’), IT(i’,j’)
M(i-1,j-1)
M(i-1,j)
IS(i-1,j-1)
IS(i-1,j)
IT(i-1,j-1)
IT(i-1,j)
M(i,j-1)
IS(i,j-1)
IT(i,j-1)
We assume that a deletion will not be followed directly by an insertion.
This can be obtained by using

17. Why are two matrices enough?
Affine gap scores
Simplification:
Why are two matrices enough?