Multiple Sequence Alignment

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Multiple Sequence Alignment

• Dynamic Programming

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Multiple Sequence Alignment

• VTISCTGSSSNIGAG?NHVKWYQQLPG
• VTISCTGTSSNIGS??ITVNWYQQLPG
• LRLSCSSSGFIFSS??YAMYWVRQAPG
• LSLTCTVSGTSFDD??YYSTWVRQPPG
• PEVTCVVVDVSHEDPQVKFNWYVDG??
• ATLVCLISDFYPGA??VTVAWKADS??
• ATLVCLISDFYPGA??VTVAWKADS??
• AALGCLVKDYFPEP??VTVSWNSG-??
• VSLTCLVKGFYPSD??IAVEWESNG-?

• Goal Bring the greatest number of similar
  characters into the same column of the alignment
• Similar to alignment of two sequences.

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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
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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

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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

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Scoring a multiple alignment
A
A
A
A
C
A
A
C
C
C
A
A
C
C
A
Sum of pairs
Star
Tree
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Sum of Pairs
20a - 10ß
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Sum-of-Pairs Scoring Function

• Score of multiple alignment
• ?i ltj score(Si,Sj)
• where score(Si,Sj) score of induced
  pairwise alignment

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Induced Pairwise Alignment

• S1 S - T I S C T G - S - N I
• S2 L - T I C N G S S - N I
• S3 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 I S2 L T I C N G S S
N I
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MSA Dynamic Programming

• The two-sequence alignment algorithm can be
  generalized to any number of sequences.
• E.g., for three sequences X, Y, W
  define Ci,j,k score of optimum alignment
  among X1..i, Y1..j, W1..k
• As for two sequences, divide possible alignments
  into different classes, depending on how they
  end.
• Use to devise recurrence relations for Ci,j,k
• Ci,j,k is the maximum out of all possibilities

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MSA 7 ways alignment can end for 3 sequences
Xi Yj Wk
X1 . . . Xi-1 Xi Y1 . . . Yj-1 Yj W1 . . . Wk-1 Wk
- Yj Wk
Xi - Wk
Xi - -
Xi Yj -
- Yj -
- - Wk
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Dynamic programming for three sequences
Each alignment is a path through the dynamic
programming matrix
S
A
A
N
S
V
S
N
S
Start
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Dynamic Programming for Three Sequences
There are 7 ways to get to Ci,j,k
Ci,j,k
Ci-1,j,k-1
Ci-1,j-1,k-1
Ci-1,j,k-1
Enumerate all possibilities and choose the best
one
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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

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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
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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.

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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
  maximizesstar_score(c) ? sim(Sc, Si) 1 i
  r, i ? cwhere sim(Si, Sj) is the optimal
  score of a pair-wise alignment between Si and Sj

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Algorithm

• Compute sim(Si, Sj) for every pair (i,j)
• Compute star_score(i) for every i
• Choose the index c that minimizes star_score(c)
  and make it the center of the star
• 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.

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Step 4 Detail
Sc A-ACC-TT S2 AGACCGT-
Sc AA--CCTT S1 AATGCC--
Sc A-A--CC-TT S1 A-ATGCC--- S2 AGA--CCGT-