University of North Texas
Biocomputing
2
University of North Texas
Biocomputing
2-D vs 3-D Alignment Grid
V
W
2-D edit graph
3-D edit graph
University of North Texas
Biocomputing
Architecture of 3-D Alignment Cell
(i-1,j-1,k-1)
(i,j-1,k-1)
(i,j-1,k)
(i-1,j-1,k)
(i-1,j,k)
(i,j,k)
(i-1,j,k-1)
(i,j,k-1)
University of North Texas
Biocomputing
Multiple Alignment: Dynamic Programming
•
s
i,j,k
= max
•
δ
(
x, y, z
) is an entry in the 3
-D
scoring matrix
s
i-1,j-1,k-1
+
(v
i
, w
j
, u
k
)
s
i-1,j-1,k
+
(v
i
, w
j
, _ )
s
i-1,j,k-1
+
(v
i
, _,
u
k
)
s
i,j-1,k-1
+
(_, w
j
, u
k
)
s
i-1,j,k
+
(v
i
, _ , _)
s
i,j-1,k
+
(_, w
j
, _)
s
i,j,k-1
+
(_, _, u
k
)
cube diagonal:
no indels
face diagonal:
one indel
edge diagonal:
two indels
University of North Texas
Biocomputing
Multiple Alignment: Running Time
•
For 3 sequences of length
n
, the run time is
7
n
3
; O(
n
3
)
•
For
k
sequences, build a
k
-dimensional
Manhattan, with run time (
2
k
-1)(
n
k
); O(
2
k
n
k
)
•
Conclusion: dynamic programming approach
for alignment between two sequences is
easily extended to
k
sequences but it is
impractical due to exponential running time
University of North Texas
Biocomputing
Multiple Alignment Induces Pairwise
Alignments
Every multiple alignment induces pairwise alignments
x:
AC-GCGG-C
y:
AC-GC-GAG
z:
GCCGC-GAG
Induces:
x:
ACGCGG-C;
x:
AC-GCGG-C;
y: