Multiple Sequence Alignment

Dynamic Programming

Multiple Sequence Alignment

VTISCTGSSSNIGAGNHVKWYQQLPGVTISCTGTSSNIGSITVNWYQQLPGLRLSCSSSGFIFSSYAMYWVRQAPGLSLTCTVSGTSFDDYYSTWVRQPPGPEVTCVVVDVSHEDPQVKFNWYVDGATLVCLISDFYPGAVTVAWKADSATLVCLISDFYPGAVTVAWKADSAALGCLVKDYFPEPVTVSWNSG-VSLTCLVKGFYPSDIAVEWESNG-

•Goal: Bring the greatest number of similar characters into the same column of the alignment

•Similar to alignment of two sequences.

CLUSTALW MSA

MSA of four oxidoreductase NAD binding domain protein sequences. Red: AVFPMILW. Blue: DE. Magenta: RHK. Green: STYHCNGQ. Grey: all others. Residue ranges are shown after sequence names.

Chenna et al. Nucleic Acids Research, 2003, Vol. 31, No. 13 3497-3500

Multiple Sequence Alignment: Motivation

• Correspondence. Find out which parts “do the same thing”– Similar genes are conserved across widely divergent species,

often performing similar functions

• Structure prediction– Use knowledge of structure of one or more members of a

protein MSA to predict structure of other members – Structure is more conserved than sequence

• Create “profiles” for protein families– Allow us to search for other members of the family

• Genome assembly: Automated reconstruction of “contig” maps of genomic fragments such as ESTs

• MSA is the starting point for phylogenetic analysis

Multiple Sequence Alignment: Approaches

• Optimal Global Alignments -Dynamic programming– Generalization of Needleman-Wunsch– Find alignment that maximizes a score function– Computationally expensive: Time grows as product of

sequence lengths

• Global Progressive Alignments - Match closely-related sequences first using a guide tree

• Global Iterative Alignments - Multiple re-building attempts to find best alignment

• Local alignments– Profiles, Blocks, Patterns

Scoring a multiple alignment

Sum of pairs Star Tree

A

A

C

CA

AA

A

A

A

A

C C

CC

Sum of Pairs

AAAAAAAAAAACACC

A

A

A

AA

10α

A

A

A

CA

+ (6α - 4β)

A

A

C

CA

+ (4α - 6β)

= 20α - 10β

Sum-of-Pairs Scoring Function

Score of multiple alignment

= ∑i <j score(Si,Sj)

where score(Si,Sj) = score of induced pairwise alignment

Induced Pairwise Alignment

S1 S - T I S C T G - S - N IS2 L - T I – C N G S S - N IS3 L R T I S C S G F S Q N I

Induced pairwise alignment of S1, S2:

S1 S T I S C T G - S N IS2 L T I – C N G S S N I

MSA: Dynamic Programming

• The two-sequence alignment algorithm can be generalized to any number of sequences.

• E.g., for three sequences X, Y, W defineC[i,j,k] = score of optimum alignment

among X[1..i], Y[1..j], W[1..k]• As for two sequences, divide possible

alignments into different classes, depending on how they end.– Use to devise recurrence relations for C[i,j,k]– C[i,j,k] is the maximum out of all possibilities

Xi

Yj

Wk

MSA: 7 ways alignment can end for 3 sequences

X1 . . . Xi-1 Xi

Y1 . . . Yj-1 Yj

W1 . . . Wk-1 Wk-Yj

Wk

Xi

-WkXi

Yj

-

--Wk

-Yj

-

Xi

--

Dynamic programming for three sequences

V S N

—

S

S

—

N A —

A S— — —

V S N S

S

N

A

AS

Start

Each alignment is a path through the dynamic programming matrix

For 3 seqs. of length n, time is proportional to n3

Dynamic Programming for Three Sequences

C[i,j,k]

C[i-1,j-1,k-1]

There are 7 ways to get to C[i,j,k]

C[i-1,j,k-1]

C[i-1,j,k-1]

Enumerate all possibilities and choose the best one

Dynamic Programming MSA: General Case

• For k sequences of length n, dynamic programming algorithm does (2k-1) nk

operations – Example: 6 sequences of length 100 require

6.4X1013 calculations• Space for table is nk

• Implementations (e.g., WashU MSA 2.1) use tricks and only search subset of dynamic programming table– Even this is expensive. E.g., Baylor CM Search

launcher limits MSA to 8 sequences of 800 characters and 10 minutes processing time

Problems with SP scoring

• Pair-wise comparisons can over-score evolutionarily distant pairs.

• Reason: For 3 or more sequences, SP scoring does not correspond to any evolutionary tree

But not:

Overcoming problems with SP scoring

• Use weights to incorporate evolution in sum of pairs scoring:– Some pair-wise alignments are more important

than others • E.g., more important to have a good alignment

between mouse and human sequences than mouse and bird

– Assign different weights to different pair-wise alignments.

• Weight decreases with evolutionary distance.

• Use star tree approach – one sequence is assigned as the ancestor and

all others are contrasted it.

Star Alignments

• Construct multiple alignments using pair-wise alignment relative to a fixed sequence

• Out of a set S = {S1, S2, . . . , Sr} of sequences, pick sequence Sc that maximizes

star_score(c) = ∑ {sim(Sc, Si) : 1 ≤ i ≤ r, i ≠ c}

where sim(Si, Sj) is the optimal score of a pair-wise alignment between Si and Sj

Algorithm

1. Compute sim(Si, Sj) for every pair (i,j)2. Compute star_score(i) for every i3. Choose the index c that minimizes

star_score(c) and make it the center of the star

4. Produce a multiple alignment M such that, for every i, the induced pairwise alignment of Sc and Si is the same as the optimum alignment of Sc and Si.

Step 4: Detail

Sc AA--CCTT

S1 AATGCC--

Sc A-ACC-TT

S2 AGACCGT-

Sc A-A--CC-TT

S1 A-ATGCC---

S2 AGA--CCGT-