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

4. Alignments -GCGC-ATGGATTGAGCGA TGCGCCATTGAT-GACC-A Three elements:
Perfect matches
Mismatches
Insertions & deletions (indel)

5. Simple Scoring Rule Score each position independently: Match: +1
Mismatch : -1
Indel -2
Score of an alignment is sum of position scores

6. Example Example: -GCGC-ATGGATTGAGCGA TGCGCCATTGAT-GACC-A
Score: (+1x13) + (-1x2) + (-2x4) = 3
------GCGCATGGATTGAGCGA
TGCGCC----ATTGATGACCA--
Score: (+1x5) + (-1x6) + (-2x11) = -23

7. Variants of Sequence Alignment
We have seen two basic variants of sequence alignment:
Global alignment (Needelman-Wunsch)
Local alignment (Smith-Waterman)
This tutorial we will pose and solve two problems :
Finding the best overlap alignment
Using an affine cost for gaps
The solution is based on the ideas of dynamic programming presented in the lecture

8. Question I: Overlap Alignment
Consider the following question:
Can we find the most significant overlap between two sequences s,t ?
Possible overlap relations: a. b.
The difference between this problem and local alignment studied in class is that here we require alignment between the endpoints of the two sequences.

9. Question I: Overlap Alignment
Formally, given s[1..n] and 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 that the dynamic programming should not penalise overhanging ends.

10. Overlap Alignment
Initialization: V[i,0]=0 , V[0,j]=0

11. Overlap Alignment Example
s = PAWHEAE
t = HEAGAWGHEE
Scoring system:
Match: +4
Mismatch: -1
Indel: -5

12. 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 in the matrix

13. Overlap Alignment Example
s = PAWHEAE
t = HEAGAWGHEE
Scoring system:
Match: +4
Mismatch: -1
Indel: -5

14. Overlap Alignment Example
s = PAWHEAE
t = HEAGAWGHEE
Scoring system:
Match: +4
Mismatch: -1
Indel: -5

15. Overlap Alignment Example
The best overlap is:
PAWHEAE------
---HEAGAWGHEE
Pay attention! A different scoring system could yield a different result, such as:
---PAW-HEAE
HEAGAWGHEE-

16. Question II: Alignment with affine gap scores
Observation: Insertions and deletions often occur in blocks longer than a single nucleotide.
Consequence: Standard scoring of alignment studied in lecture, which give a constant penalty d per gap unit , does not score well this phenomenon; Hence, a better gap score model is needed.
Question: Can you think of an appropriate change to the scoring system for gaps?

17. Alignment with affine gap scores
Define the penalty score for a gap of length g to be
d is the penalty for the introduction of a gap, while e is the penalty for elongating the gap by one.
Denote:
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
We assume that a deletion will not be followed directly by an insertion.
This can be obtained by using

18. Alignment with affine gap scores
Recurrence takes advantage of the 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) *

19. Alignment with affine gap scores
And to put it in a familiar form