1. Global, local, repeated and overlaping
Alignment:
Global, local, repeated and overlaping
Jan

2. Global Alignment by the Needleman-Wunsch algorithm
From scoring matrix S
Linear gap penalty F -d
-2d …
-nd -d
F(1,1)
F(2,1)
F(…,1)
F(n,1)
-2d
F(1,2)
F(2,2)
F(…,2)
F(n,2) …
F(1,…)
F(2,…)
F(…,…)
Total score
F(n,…)
-md
F(1,m)
F(2,m)
F(…,m)
F(n,m)
Trace back

3. 2. Local alignment by the Smith-Waterman algorithm
To break uniformative pairwise combinations
From scoring matrix S
Linear gap penalty F …
Total score
F(1,1)
F(2,1)
F(…,1)
F(n,1)
F(1,2)
F(2,2)
F(…,2)
F(n,2) …
F(1,…)
F(2,…)
F(…,…)
max
F(n,…)
F(1,m)
F(2,m)
F(…,m)
F(n,m)
Trace back

4. could be used to search for a repeated domain or motif in a protein
3. Repeated matches
could be used to search for a repeated domain or motif in a protein
care is required in implementation of this algorithm as it is asymmetric in the sense that
x: represents the sequence containing the domain
y: represents the sequence in which we look for repeated matches

5. 3. Repeated matches Traceback from M(n+1,0) records the best alignment
The global alignment contains matched and unmatched regions
Only matches above a threshold, T, are recorded
Scores are computed relative to this threshold
Changing T will thus affect the outcome of the algorithm
If T is too large, some matches will be missed
If T is too small, match regions may be split and too many weak matches may be found
Variation of this algorithm:
WATERMAN-EGGERT ALGORITHM (1987)

6. threshold value 3. Repeated matches (Local alignment) F Total score
F(1,0)
F(2,0)
F(…,0)
F(n,0)
F(n+1,0) …
F(1,1)
F(1,2)
F(1,…)
F(1,m)
F(2,1)
F(2,2)
F(2,…)
F(2,m)
F(…,1)
F(…,2)
F(…,…)
F(…,m)
F(n,1)
F(n,2)
F(n,…)
F(n,m)
Trace back

7. 4. Overlap matches
global alignment strategy which does not penalize overlapping ends
Algorithm is as per global alignment, except at initialization and a slight alteration of traceback
Traceback
starts from the maximum recorded element in the mth row and the nth column
i.e., max{F(n,0), F(n,1),….,F(n,m), F(n-1,m), F(n-2,m),…, F(0,m)}
ends when the 0th row or column is reached.
Hitting the 0th row corresponds to the end of sequence x
Hitting the 0th column corresponds to the end of sequence y

8. ------ threshold value 4. Overlap matches (Global alignment)
(Local alignment) F
F(1,0)
F(2,0)
F(…,0)
F(n,0)
F(0,m+1)
Total score …
F(1,1)
F(1,2)
F(1,…)
F(1,m)
F(1,2)
F(2,2)
F(2,…)
F(2,m)
F(…,1)
F(…,2)
F(…,…)
F(…,m)
F(n,1)
F(n,2)
F(…,m)
F(n,m)
max
Trace back