Smith-Waterman Alignment
Using Mismatch and Gap
Penalties
To accompany “Sequence Similarity
and Database Searching”
Smith-Waterman Alignment
• Assume we want to align the following
Query:
Database:
D E V D V E F D
D V V E D F D
Smith-Waterman Alignment
• Recall the recursive scoring function
si-1,j-1
Max
s
i-x,j-1 + gx-1
Sij = sij + Max
Max si-1,j-y + gy-1
g = gap penalty
S = alignment score
s = match/mismatch score
Smith-Waterman Alignment
• Assume the following scoring matrix
D
E
F
V
gap
D
2
-1
-1
-1
-1
E
-1
2
-1
-1
-1
F
-1
-1
2
-1
-1
V
-1
-1
-1
2
-1
gap
-2
-2
-2
-2
0
One Possible Alignment
D
V
V
E
D
V
D
D
E
V
D
V
E
F
D
D E V - D V E F D
D V V E D V - - D
Another Possible Alignment
D
V
V
E
D
V
D
D
E
V
D
V
E
F
D
D E V - D V E F D
D V V E D V - - D
D E V D V E - F D
D - V - V E D V D
A Third Alignment
D
V
V
E
D
V
D
D
E
V
D
V
E
F
D
D E V - D V E F D
D V V E D V - - D
D E V D V E - F D
D - V - V E D V D
D E V D V E F - D
D - V - V E D V D
Scoring Stage
D
V
V
E
D
V
D
0
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
-12
-12
-14
-14
D
-2
+2
-4
-3
-6
-5
-4
-7
-10
-6
-12
-11
-14
-10
-16
-2
-4
+2
0
0
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
E
-4
-3
0
+1
-2
-1
-4
0
-6
-5
-8
-7
-10
-9
-12
V
-4 -6 -6
-6 -5 -8
0 -2 -2
-2 +2 -4
+1 -1 +2
-1 +3 0
-1 -3 +3
-3 -2 +1
0 -2 +1
-2 -1 -1
-2 -4 -1
-4 0 -3
-4 -6 0
-6 -5 -2
-6 -8 -2
D
V
-8 -8 -10
-4 -10 -9
-4 -4 -6
-3 -6 -2
0
0 -2
+1 -2 +2
+1 +1 -1
+2 -1 0
-1 +2 0
+3 0 +1
-3 +3 +1
-2 +1 +5
-2 +1 -1
+2 -1 0
-4 +2 0
-10
-12
-6
-8
-2
-4
+2
0
0
-2
+1
-1
+5
+3
0
E
-12
-11
-8
-7
-4
-3
0
+4
-2
-1
-1
0
+3
+4
-2
-12
-14
-8
-10
-4
-6
0
-2
+4
+2
+2
0
+3
+1
+4
F
-14
-13
-10
-9
-6
-5
-2
-1
+2
+3
0
+1
+1
+2
+2
-14
-16
-10
-12
-6
-8
-2
-4
+2
0
+3
+1
+1
-1
+2
D
-16
-12
-12
-11
-8
-7
-4
-3
0
+4
+1
+2
-1
+3
0
-16
-18
-12
-14
-8
-10
-4
-6
0
-2
+4
+2
+2
0
3
Traceback Stage
D
V
V
E
D
V
D
0
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
-12
-12
-14
-14
D
-2
+2
-4
-3
-6
-5
-4
-7
-10
-6
-12
-11
-14
-10
-16
-2
-4
+2
0
0
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
E
-4
-3
0
+1
-2
-1
-4
0
-6
-5
-8
-7
-10
-9
-12
V
-4 -6 -6
-6 -5 -8
0 -2 -2
-2 +2 -4
+1 -1 +2
-1 +3 0
-1 -3 +3
-3 -2 +1
0 -2 +1
-2 -1 -1
-2 -4 -1
-4 0 -3
-4 -6 0
-6 -5 -2
-6 -8 -2
D
V
-8 -8 -10
-4 -10 -9
-4 -4 -6
-3 -6 -2
0
0 -2
+1 -2 +2
+1 +1 -1
+2 -1 0
-1 +2 0
+3 0 +1
-3 +3 +1
-2 +1 +5
-2 +1 -1
+2 -1 0
-4 +2 0
-10
-12
-6
-8
-2
-4
+2
0
0
-2
+1
-1
+5
+3
0
E
-12
-11
-8
-7
-4
-3
0
+4
-2
-1
-1
0
+3
+4
-2
-12
-14
-8
-10
-4
-6
0
-2
+4
+2
+2
0
+3
+1
+4
F
-14
-13
-10
-9
-6
-5
-2
-1
+2
+3
0
+1
+1
+2
+2
-14
-16
-10
-12
-6
-8
-2
-4
+2
0
+3
+1
+1
-1
+2
D
-16
-12
-12
-11
-8
-7
-4
-3
0
+4
+1
+2
-1
+3
0
-16
-18
-12
-14
-8
-10
-4
-6
0
-2
+4
+2
+2
0
3
Traceback Results
DEV-DVEFN
| | || |
DVVEDV--N
2-1+2-2+2+2-2-2+2 = 3
DEVDVE-FN
| | || |
D-V-VEDVN
2-2+2-2+2+2-2-1+2 = 3
DEVDVEF-N
| | || |
D-V-VEDVN
2-2+2-2+2+2-1-2+2 = 3
Smith-Waterman Problem #1
• Align the following 2 sequences
K N M K K L L K K N L Q
K N L K L K N L N Q
• Match = 5, Mismatch = -4,
• Open Gap = 0, Extend Gap = -7
Answer
K
N
L
K
L
K
N
L
N
Q
0
0
0
0
0
0
0
0
0
0
0
K N
0 0
5 0
0 10
0 3
5 0
0 1
5 0
0 10
0 3
0 5
0 0
M K
0 0
0 5
3 0
6 0
0 11
0 4
0 5
3 0
6 0
0 2
1 3
K L L K
0 0 0 0
5 0 0 5
1 1 0 0
0 6 6 0
5 0 2 11
7 10 5 4
9 3 6 10
2 5 0 3
0 7 10 3
0 0 3 6
0 0 0 0
K N L Q
0 0 0 0
5 0 0 0
1 10 3 0
0 3 15 8
5 0 8 11
7 1 5 4
9 3 0 1
6 14 7 0
0 7 19 12
0 5 12 15
2 0 5 17
Answer
K N M K K L L K - K N L - Q
|
| |
| | |
|
K N L K L K N L N Q
17+19+14+9+4+11+6+1+5 = 86
Thanks to...
• Dr. Duane Szafron (University of
Alberta) for sharing his ideas on how
to visualize and animate sequence
alignment