CSCI 490 Bioinformatics Multiple Sequence Alignment Multiple - - PowerPoint PPT Presentation

CSCI 490 Bioinformatics

Multiple Sequence Alignment

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?

Scoring Function: Sum Of Pairs

Definition: Induced pairwise alignment A pairwise alignment induced by the multiple

alignment

Example:

x: ACGCGGC y: ACGCGAG z: GCCGCGAG

Induces:

x: ACGCGG-C; x: AC-GCGG-C; y: AC-GCGAG y: ACGC-GAC; z: GCCGC-GAG; z: GCCGCGAG

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)

Example:

x: AC-GCGG-C y: AC-GC-GAG z: GCCGC-GAG A C G T

• A

1 -1 -1 -1 -1 C

• 1

1 -1 -1 -1 G

• 1 -1

1 -1 -1 T

• 1 -1 -1

1 -1

• 1 -1 -1 -1

(A,A) + (A,G) x 2 = -1 (G,G) x 3 = 3 (-,A) x 2 + (A,A) = -1 Total score = (-1) + 3 + (-2) + 3 + 3 + (-2) + 3 + (-1) + (-1) = 5

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?

Compatible pairwise alignments

AAAATTTT TTTTGGGG AAAAGGGG AAAATTTT----

• ---TTTTGGGG

AAAATTTT---- AAAA----GGGG

• ---TTTTGGGG

AAAA----GGGG

AAAATTTT----

• ---TTTTGGGG

AAAA----GGGG

Incompatible pairwise alignments

AAAATTTT TTTTGGGG GGGGAAAA AAAATTTT----

• ---TTTTGGGG
• ---AAAATTTT

GGGGAAAA---- TTTTGGGG----

• ---GGGGAAAA

?

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))

• Example: in 3D (three sequences):
• 23 – 1 = 7 neighbors/cell

F(i-1,j-1,k-1) + S(xi, yj, zk), F(i-1,j-1,k ) + S(xi, yj, -), F(i-1,j ,k-1) + S(xi, -, zk), F(i,j,k) = max F(i ,j-1,k-1) + S(-, yj, zk), F(i-1,j ,k ) + S(xi, -, -), F(i ,j-1,k ) + S(-, yj, -), F(i ,j ,k-1) + S(-, -, zk)

Multidimensional Dynamic Programming (MDP)

(i,j,k) (i,j,k-1) (i-1,j,k-1) (i-1,j-1,k-1) (i-1,j-1,k) (i,j-1,k) (i-1,j,k) (i,j-1,k-1)

Multidimensional Dynamic Programming (MDP)

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

Faster MDP

• Carrillo & Lipman, 1988

– Branch and bound – Other heuristics

• Implemented in a tool called MSA
• Practical for about 6 sequences of length

about 200-300.

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 – For any partial path, if Scurrent + Sperspective < lower- bound, can give up that path – Guarantees optimality

Score of the alignment between k and l induced by m

Optimal msa

Score of optimal alignment between k and l

Progressive Alignment

• Multiple Alignment is NP-hard
• Most used heuristic: Progressive Alignment

Algorithm:

1. Align two of the sequences xi, xj 2. Fix that alignment 3. Align a third sequence xk to the alignment xi,xj 4. Repeat until all sequences are aligned

Running Time: O(NL2)

Each alignment takes O(L2) Repeat N times

Progressive Alignment

• 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)

x w y z

Progressive Alignment: CLUSTALW

CLUSTALW: most popular multiple protein alignment Algorithm:

1. Find all dij: alignment dist (xi, xj)

• High alignment score => short distance

2. Construct a tree (similar to hierarchical clustering.) 3. Align nodes in order of decreasing similarity

+ a large number of heuristics

CLUSTALW example

• S1 ALSK
• S2 TNSD
• S3 NASK
• S4 NTSD

CLUSTALW example

• S1 ALSK
• S2 TNSD
• S3 NASK
• S4 NTSD

s1 s2 s3 s4 s1 9 4 7 s2 8 3 s3 7 s4 Distance matrix

CLUSTALW example

• S1 ALSK
• S2 TNSD
• S3 NASK
• S4 NTSD

s1 s2 s3 s4 s1 9 4 7 s2 8 3 s3 7 s4 s1 s3 s2 s4

CLUSTALW example

• S1 ALSK
• S2 TNSD
• S3 NASK
• S4 NTSD

s1 s2 s3 s4 s1 9 4 7 s2 8 3 s3 7 s4 s1 s3 s2 s4

• ALSK

NA-SK

CLUSTALW example

• S1 ALSK
• S2 TNSD
• S3 NASK
• S4 NTSD

s1 s2 s3 s4 s1 9 4 7 s2 8 3 s3 7 s4 s1 s3 s2 s4

• ALSK

NA-SK

• TNSD

NT-SD

CLUSTALW example

• S1 ALSK
• S2 TNSD
• S3 NASK
• S4 NTSD

s1 s2 s3 s4 s1 9 4 7 s2 8 3 s3 7 s4 s1 s3 s2 s4

• ALSK

NA-SK

• TNSD

NT-SD

• ALSK
• TNSD

NA-SK NT-SD

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

Iterative Refinement

Frozen! Now clear: correct y should be GA-CTT

Iterative Refinement

Algorithm (Barton-Stenberg):

• 1. Align most similar xi, xj
• 2. Align xk most similar to (xixj)
• 3. Repeat 2 until (x1…xN) are aligned
• 4. For j = 1 to N,

Remove xj, and realign to x1…xj-1xj+1…xN

• 5. Repeat 4 until convergence

Progressive alignment

Iterative Refinement (cont’d)

For each sequence y

• 1. Remove y
• 2. Realign y

(while rest fixed)

x y z x,z fixed projection allow y to vary

Iterative Refinement

Example: align (x,y), (z,w), (xy, zw):

x: GAAGTTA y: GAC-TTA z: GAACTGA w: GTACTGA

After realigning y:

x: GAAGTTA y: G-ACTTA + 3 matches z: GAACTGA w: GTACTGA

Iterative Refinement

• Example not handled well:

x: GAAGTTA y1: GAC-TTA y2: GAC-TTA y3: GAC-TTA z: GAACTGA w: GTACTGA

Realigning any single yi changes nothing

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

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)

– “local”

• PROBCONS (Do, 2004)

– Probabilistic consistency-based – Best accuracy on benchmarks

• ProDA (Phuong, 2006)

– Allow repeated and shuffled regions

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 – Consistency-based

Heuristic