1. Multiple Sequence Alignment
CS 5263 & CS 4593 Bioinformatics
Multiple Sequence Alignment

2. Multiple Sequence Alignment
Motivation:
A faint similarity between two sequences becomes very significant if present in many sequences
Definition
Given N sequences x1, x2,…, xN: Insert gaps (-) in each sequence xi, such that
All sequences have the same length L
Score of the alignment is maximum
Two issues
How to score an alignment?
How to find a (nearly) optimal alignment?

3. Scoring function - first assumption
Columns are independent
Similar in pair-wise alignment
Therefore, the score of an alignment is the sum of all columns
Need to decide how to score a single column

4. Scoring function (cont’d)
Ideally:
An n-dimensional matrix, where n is the number of sequences
E.g. (A, C, C, G, -) for aligning 5 sequences
Total number of parameters: (k+1)n, where k is the alphabet size
Direct estimation of such scores is difficult
Too many parameters to estimate
Even more difficult if need to
consider phylogenetic relationships x y
Phylogenetic tree
or evolution tree ? z w v

5. Scoring Function (cont’d)
Compromises:
Compute from pair-wise scores
Option 1: Based on sum of all pair-wise scores
Option 2: Based on scores with a consensus sequence
Other options
Consider tree topology explicitly
Information-theory based score
Difficult to optimize

6. Scoring Function: Sum Of Pairs
Definition: Induced pairwise alignment
A pairwise alignment induced by the multiple alignment
Example:
x: AC-GCGG-C
y: AC-GC-GAG
z: GCCGC-GAG
Induces:
x: ACGCGG-C; x: AC-GCGG-C; y: AC-GCGAG
y: ACGC-GAC; z: GCCGC-GAG; z: GCCGCGAG - - - -

7. Sum Of Pairs (cont’d)
The sum-of-pairs (SP) score of an alignment is the sum of the scores of all induced pairwise alignments
S(m) = k<l s(mk, ml)
s(mk, ml): score of induced alignment (k,l)

8. Example: x: AC-GCGG-C y: AC-GC-GAG z: GCCGC-GAG A C G T - 1 -1
(A,A) + (A,G) x 2 = -1
(G,G) x 3 = 3
(-,A) x 2 + (A,A) = -1
Total score = (-1) (-2) (-2) (-1) + (-1) = 5

9. Sum Of Pairs (cont’d) Drawback: no evolutionary characterization
Every sequence derived from all others
Heuristic way to incorporate evolution tree
Weighted Sum of Pairs:
S(m) = k<l wkl s(mk, ml)
wkl: weight decreasing with distance
Human
Mouse
Duck
Chicken

10. Consensus score -AGGCTATCACCTGACCTCCAGGCCGA--TGCCC---
TAG-CTATCAC--GACCGC--GGTCGATTTGCCCGAC
CAG-CTATCAC--GACCGC----TCGATTTGCTCGAC
CAG-CTATCAC--GACCGC--GGTCGATTTGCCCGAC
Consensus sequence:
Find optimal consensus string m* to maximize
S(m) = i s(m*, mi)
s(mk, ml): score of pairwise alignment (k,l)

11. Multiple Sequence Alignments Algorithms
Can also be global or local
We only talk about global for now
A simple method
Do pairwise alignment between all pairs
Combine the pairwise alignments into a single multiple alignment
Is this going to work?

12. Compatible pairwise alignments
AAAATTTT
AAAATTTT----
----TTTTGGGG
AAAATTTT----
AAAA----GGGG
AAAATTTT----
----TTTTGGGG
AAAA----GGGG
TTTTGGGG
AAAAGGGG
----TTTTGGGG
AAAA----GGGG

13. Incompatible pairwise alignments
AAAATTTT
AAAATTTT----
----TTTTGGGG
----AAAATTTT
GGGGAAAA---- ?
TTTTGGGG
GGGGAAAA
TTTTGGGG----
----GGGGAAAA

14. Multidimensional Dynamic Programming (MDP)
Generalization of Needleman-Wunsh:
Find the longest path in a high-dimensional cube
As opposed to a two-dimensional grid
Uses a N-dimensional matrix
As apposed to a two-dimensional array
Entry F(i1, …, ik) represents score of optimal alignment for s1[1..i1], … sk[1..ik]
F(i1,i2,…,iN) = max(all neighbors of a cell) (F(nbr)+S(current))

15. Multidimensional Dynamic Programming (MDP)
Example: in 3D (three sequences):
23 – 1 = 7 neighbors/cell
(i-1,j-1,k-1)
(i-1,j,k-1)
(i-1,j-1,k)
(i-1,j,k)
F(i-1,j-1,k-1) + S(xi, xj, xk),
F(i-1,j-1,k ) + S(xi, xj, -),
F(i-1,j ,k-1) + S(xi, -, xk),
F(i,j,k) = max F(i ,j-1,k-1) + S(-, xj, xk),
F(i-1,j ,k ) + S(xi, -, -),
F(i ,j-1,k ) + S(-, xj, -),
F(i ,j ,k-1) + S(-, -, xk)
(i,j-1,k-1)
(i,j,k-1)
(i,j-1,k)
(i,j,k)

16. Multidimensional Dynamic Programming (MDP)
Running Time:
Size of matrix: LN;
Where L = length of each sequence
N = number of sequences
Neighbors/cell: 2N – 1
Therefore………………………… O(2N LN)

17. Faster MDP Carrillo & Lipman, 1988 Implemented in a tool called MSA
Branch and bound
Other heuristics
Implemented in a tool called MSA
Practical for about 6 sequences of length about

18. Faster MDP
Basic idea: bounds of the optimal score of a multiple alignment can be pre-computed
Upper-bound: sum of optimal pair-wise alignment scores, i.e.
S(m) = k<l s(mk, ml)  k<l s(k, l)
lower-bounded: score computed by any approximate algorithm (such as the ones we’ll talk next)
For any partial path, if Scurrent + Sperspective < lower-bound, can give up that path
Guarantees optimality
Optimal msa
Score of the alignment between k and l induced by m
Score of optimal alignment between k and l

19. Progressive Alignment
Multiple Alignment is NP-hard
Most used heuristic: Progressive Alignment
Algorithm:
Align two of the sequences xi, xj
Fix that alignment
Align a third sequence xk to the alignment xi,xj
Repeat until all sequences are aligned
Running Time: O(NL2)
Each alignment takes O(L2)
Repeat N times

20. Progressive Alignmentx y z w
When evolutionary tree is known:
Align closest first, in the order of the tree
Example:
Order of alignments: 1. (x,y)
2. (z,w)
3. (xy, zw)

21. Progressive Alignment: CLUSTALW
CLUSTALW: most popular multiple protein alignment
Algorithm:
Find all dij: alignment dist (xi, xj)
High alignment score => short distance
Construct a tree
(similar to hierarchical clustering. Will discuss in future)
Align nodes in order of decreasing similarity
+ a large number of heuristics

22. CLUSTALW example
S1 ALSK
S2 TNSD
S3 NASK
S4 NTSD

23. CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD s1 s2 s3 s4 9 4 7 8 39 4 7 8 3
Distance matrix

24. CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD s1 s1 s2 s3 s4 9 4 79 4 7 8 3 s3 s2 s4

25. CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD s1 s1 s2 s3 s4 9 4 79 4 7 8 3 s3 s2 s4

26. CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD s1 s1 s2 s3 s4 9 4 79 4 7 8 3 s3 s2 s4

27. CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD -ALSK -TNSD NA-SK9 4 7 8 3 s3 s2 s4

28. Iterative Refinement Problems with progressive alignment:
Depend on pair-wise alignments
If sequences are very distantly related, much higher likelihood of errors
Initial alignments are “frozen” even when new evidence comes
Example:
x: GAAGTT
y: GAC-TT
z: GAACTG
w: GTACTG
Frozen!
Now clear: correct y should be GA-CTT

29. Iterative Refinement Algorithm (Barton-Stenberg):
Align most similar xi, xj
Align xk most similar to (xixj)
Repeat 2 until (x1…xN) are aligned
For j = 1 to N,
Remove xj, and realign to x1…xj-1xj+1…xN
Repeat 4 until convergence
Progressive alignment

30. Iterative Refinement (cont’d)
For each sequence y
Remove y
Realign y
(while rest fixed) z x
allow y to vary y
x,z fixed projection
Note: Guaranteed to converge (why?)
Running time: O(kNL2), k: number of iterations

31. Iterative Refinement Example: align (x,y), (z,w), (xy, zw):
x: GAAGTTA
y: GAC-TTA
z: GAACTGA
w: GTACTGA
After realigning y:
y: G-ACTTA + 3 matches

32. Iterative Refinement Example not handled well: x: GAAGTTA y1: GAC-TTA
z: GAACTGA
w: GTACTGA
Realigning any single yi changes nothing

33. Restricted MDP Similar to bounded DP in pair-wise alignment
Construct progressive multiple alignment m
Run MDP, restricted to radius R from m z x y
Running Time: O(2N RN-1 L)

34. Restricted MDP Within radius 1 of the optimal
x: GAAGTTA
y1: GAC-TTA
y2: GAC-TTA
y3: GAC-TTA
z: GAACTGA
w: GTACTGA
Within radius 1 of the optimal
 Restricted MDP will fix it.

35. Other approaches Statistical learning methods
Profile Hidden Markov Models
Consistency-based methods
Still rely on pairwise alignment
But consider a third seq when aligning two seqs
If block A in seq x aligns to block B in seq y, and both aligns to block C in seq z, we have higher confidence to say that the alignment between A-B is reliable
Essentially: change scoring system according to consistency
Then apply DP as in other approaches
Pioneered by a tool called T-Coffee

36. Multiple alignment tools
Clustal W (Thompson, 1994)
Most popular
T-Coffee (Notredame, 2000)
Another popular tool
Consistency-based
Slower than clustalW, but generally more accurate for more distantly related sequences
MUSCLE (Edgar, 2004)
Iterative refinement
More efficient than most others
DIALIGN (Morgenstern, 1998, 1999, 2005)
“local”
Align-m (Walle, 2004)
PROBCONS (Do, 2004)
Probabilistic consistency-based
Best accuracy on benchmarks
ProDA (Phuong, 2006)
Allow repeated and shuffled regions

37. In summary Multiple alignment scoring functions
Sum of pairs
Other funcs exist, but less used
Multiple alignment algorithms:
MDP
Optimal
too slow
Branch & Bound doesn’t solve the problem entirely
Progressive alignment: clustalW
Iterative refinement
Restricted MDP
Consistency-based
Heuristic