BCB 567/CprE 548 Bioinformatics I
Fall 2007
Homework 2 Solutions
1. Consider the cells in which we look for the best alignment score as sets labeled
M
. For global
alignment, we look only at the lower right cell:
M
g
=
{
S
[
i, j
]

i
=
n
AND
j
=
m
}
. For semi
global alignment, we look at the entire last row and column:
M
s
=
{
S
[
i, j
]

i
=
n
OR
j
=
m
}
.
For local alignment we consider the entire table:
M
l
=
{
S
[
i, j
]
}
. We see that
M
g
⊂
M
s
⊂
M
l
.
Because
A
⊂
B
→
Max
(
A
)
≤
MAX
(
B
), we conclude global
≤
semiglobal
≤
local.
One final consideration is that, for any cell, the score in the local alignment table are greater
than or equal to the score in the semiglobal alignment table, which is in turn greater than
or equal to the score in the global alignment table. This is because in each case, additional
negative values are replaced with zeros when filling out the table.
Thus the difference in
scores between the tables reinforce the relationships indicated above.
2. The best scoring path traveling outside of the the kband will have exactly two gaps of
total length 2
k
and
n

k
matches.
The first gap is used to travel outside the kband,
while the second is used to travel back to main diagonal.
The total score of this path is
2
g
+ 2
kh
+ (
n

k
)
α
.
3. Initialize the first row and first column of the table with zeros. When filling in the a cell in
the first
t
rows or first
t
columns of the table, use the equation for local alignment:
S
[
i, j
] =
S
[
i

1
, j

1] +
δ
(
i

1
, j

1)
S
[
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 Fall '06
 OLIVEREULENSTEIN
 The Table, Column, Equals sign, The Score, Row, SCORE Association

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