1. Lecture 8: Multiple Sequence Alignment
CS 5263 Bioinformatics
Lecture 8: Multiple Sequence Alignment

2. Roadmap
Homework?
Review of last lecture
Multiple sequence alignment

3. Homework #1: dsDNA => mRNA => protein Coding strand
Template strand
The genetic code
mRNA
Template strand
mRNA
protein

4. Problem #2
For two strings of lengths m and n, the number of alignment is equal to the number of paths from (0, 0) to (m, n)
How many ways we can get to (i, j) depend on how many ways we can get to its preceding neighbors

5. Problem #3 Similar to problem #2
But there are some limitations on certain paths
(i-1, j-1)→(i-1, j)→(i, j) is illegal
So is (i-1, j-1)→(i, j-1)→(i, j)
How many ways to get to (i-1, j) without using (i-1, j-1)→(i-1, j)?
How many ways to get to (i, j-1) without using (i-1, j-1)→(i, j-1)?

6. Problem #4 Implementation is easy
Histogram: how you bin it may affect your results
bin for each discrete value you observed in your scores
Scores related to base frequency?
Scores differ between global and local alignments?
Score distribution?

7. BLAST Main idea: Construct a dictionary of all the words in the query
Alignment initiated between words of alignment score  T
Alignment:
Ungapped extensions until score below statistical threshold
Output:
All local alignments with score > statistical threshold ……
query ……
scan DB
query

8. BLAST
A C G A A G T A A G G T C C A G T
Example:
k = 4, T = 4
The matching word GGTC initiates an alignment
Extension to the left and right with no gaps until alignment falls < 50%
Output:
GTAAGGTCC
GTTAGGTCC
C C C T T C C T G G A T T G C G A

9. Gapped BLAST Added features: Pairs of words can initiate alignment
A C G A A G T A A G G T C C A G T
Added features:
Pairs of words can initiate alignment
Extensions with gaps in a band around anchor
Output:
GTAAGGTCCAGT
GTTAGGTC-AGT
C T G A T C C T G G A T T G C G A

10. Advantages Disadvantages Fast!!!!
A few minute to search a database of 1011 bases
Disadvantages
Sensitivity may be low
Often misses weak homologies

11. New improvement Make it even faster Make it more sensitive
But even less sensitive
Mainly for aligning very similar sequences or really long sequences
E.g. whole genome vs whole genome
Make it more sensitive
PSI-BLAST: iteratively add more homologous sequences
PatternHunter: discontinuous seeds

12. Things we’ve covered so far
Global alignment
Needleman-Wunsch and variants
Improvement on space and time
Local Alignment
Smith-Waterman
Heuristic algorithms
BLAST families
Statistics for sequence alignment
Extreme value distribution

13. Commonality They all deal with aligning two sequences
Pair-wise sequence alignment

14. Today Aligning multiple sequences all together
Multiple sequence alignment

16. Motivation
A faint similarity between two sequences becomes very significant if present in many
Protein domains
Motifs responsible for gene regulation

17. 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 global map is maximum
Pairwise alignment: a hypothesis on the evolutionary relationship between the letters of two sequences
Same for a multiple alignment!

18. Scoring Function Ideally:
Find alignment that maximizes probability that sequences evolved from common ancestor x y ? z
Phylogenetic tree
or evolution tree w v

19. Scoring Function (cont’d)
Unfortunately: too many parameters
Compromises:
Ignore phylogenetic tree
Compute from pair-wise scores
Based on sum of all pair-wise scores
Based on scores with a consensus sequence

20. 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

21. 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

22. Sum Of Pairs (cont’d)
The sum-of-pairs 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)

23. 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
(C,C) x 3 = 3
(-,A) x 2 + (A,A) = -1
Total score = (-1) (-2) (-2) (-1) + (-1) = 5

24. 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

25. 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)

26. Multiple Sequence Alignments
Algorithms

27. 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))

28. 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)

29. 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)

30. Faster MDP Carrillo & Lipman, 1988
Branch and bound
Other heuristics
Practical for about 6 sequences of length about

31. 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

32. 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)

33. 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
(Neighbor-joining hierarchical clustering. Will discuss in future)
Align nodes in order of decreasing similarity
+ a large number of heuristics

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

35. 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

36. 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

37. 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

38. 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

39. CLUSTALW example S1 ALSK S2 TNSD S3 NASK S4 NTSD -ALSK -TNSD NA-SK
Question: how do you align two alignments?
S1 ALSK
S2 TNSD
S3 NASK
S4 NTSD
-ALSK
NA-SK
-ALSK
-TNSD
NA-SK
NT-SD
-TNSD
NT-SD s1 s1 s2 s3 s4 9 4 7 8 3 s3 s2 s4

40. Aligning two alignments
You can treat each column in an alignment as a single letter
Remember in the case of gene finder, we aligned three nucleic acids at a time
How do we score it?
Naïve: compute Sum of Pair
Better: only compute the cross terms
We already have (K, K) and (D, D)
Need to add 2x(K, D)
-ALSK
NA-SK
-TNSD
NT-SD

41. CLUSTALW & the CINEMA viewer

42. 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

43. 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
Note: Guaranteed to converge
Running time: O(kNL2), k: number of iterations

44. 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

45. 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

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

47. 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)

48. 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.

49. Other approaches Profile Hidden Markov Models
Statistical learning methods
Will discuss in future

50. Multiple alignment tools
Clustal W (Thompson, 1994)
Most popular
PRRP (Gotoh, 1993)
HMMT (Eddy, 1995)
DIALIGN (Morgenstern, 1998)
T-Coffee (Notredame, 2000)
MUSCLE (Edgar, 2004)
Align-m (Walle, 2004)
PROBCONS (Do, 2004)

51. In summary Multiple alignment algorithms: MDP (too slow)
B&B doesn’t solve the problem entirely
Progressive alignment: clustalW
Iterative refinement
Restricted MDP