Multiple Sequence Alignment

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Multiple Sequence Alignment

• Creating optimal alignment of many sequences
• VTISCTGSSSNIGAG-NHVKWYQQLPG VTISCTGTSSNIGS--ITVN
  WYQQLPG LRLSCSSSGFIFSS--YAMYWVRQAPG
  LSLTCTVSGTSFDD--YYSTWVRQPPG PEVTCVVVDVSHEDPQVKFN
  WYVDG-- ATLVCLISDFYPGA--VTVAWKADS--AALGCLVKDYFPE
  P--VTVSWNSG--- VSLTCLVKGFYPSD--IAVEWESNG--
• Why do multiple alignments?
• Finding motifs or conserved domains
• First step in doing phylogenetic analysis
• Prediction of secondary structure of proteins
• Alignment of a family of sequences may provide
  more information than a pair-wise alignment of
  any two of those sequences

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Pairwise vs Multiple

• Pairwise
• Used to identify previously unknown biological
  relationship based on sequence similarity
• Multiple
• Inverse of pairwise
• Based on known biological relationships between
  sequences, identify unknown conserved subpatterns

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Multiple Sequence Alignment

• For pair-wise alignment
• Dynamic Programming
• Heuristic
• Whats the difference?
• Which one makes sense to model after?

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Approximation Methods

• Progressive
• Iterative
• Locally Conserved Pattern
• Statistical and Probabilistic

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Progressive Global Alignment

• Uses dynamic programming

• of sequences is small for reason of DP
• For pair-wise
• Assume 2 protein sequences of length 300
• of comparisons?
• For multiple
• Assume 3 sequences of length 300
• of comparisons?
• Assume 4 sequences,
• of comparisons?

3002 9x104
3003 2.7x107
3004 8.1x109
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Scoring a Multiple Alignment

• Let
• A be a finite alphabet
• for DNA, A A, C, G, T
• for AA, A set of all 20 amino acids
• A A U -
• a1,,ak be k sequences over A
• Assume each string contains n characters

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Scoring a Multiple Alignment

• Alignment of ak sequences is a dimensional
  matrix, M
• Each element of M is a member of A
• Each row i contains characters of ai (and a
  possible gap -)
• Every column contains at least one symbol from A

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Scoring a Multiple Alignment - Sum of Pairs

• A12 Alignment score of sequence 1 and sequence
  2
• A13 Alignment score of sequence 1 and sequence
  3
• A23 Alignment score of sequence 2 and sequence
  3
• OAij Optimal alignment score of sequence i and
  j
• Alignment Divergence eij Aij OA(ij)
• Degree of Divergence d ?e
• The larger eij the more divergent the msa from
  the pair-wise alignment gt smaller contribution
  to the MSA
• Closely related sequences will have low
  divergence
• Distantly related sequences will have high
  divergence

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Progressive Alignment

• ClustalW
• Uses a heuristic alignment approach
• Build a multiple alignment progressively by a
  series of pair-wise alignments
• Align most closely related sequences gradually
  adding in more distant ones
• Known as a greedy algorithm

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Problems with Progressive Alignment

• Local Minimum
• Dependence of final MSA on initial pair-wise
  alignments (incorrect branching order in initial
  tree)
• Highly divergent sequences (lt30 identity) causes
  progressive approach to be much less reliable
• Parameter Choice
• Choice of suitable scoring matrices and gap
  penalties (different matrices are optimal at
  different evolutionary distances)
• Range of gap penalties, will find correct or best
  possible solution, can be very broad of highly
  similar sequences

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ClustalW

• Basic Algorithm
• Align all pairs of sequences to calculate
  distance matrix
• Calculate guide tree from distance matrix
• Progressively align sequences according to
  branching order in guide tree

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Distance Matrix / Pairwise Alignments

• Fast Approximate Method
• Heuristic
• Scores calculated as
• of k-tuples matches between two sequences
  (gap penalty of gaps)
• k1,2 for aa, 2-4 for dna
• Slow Accurate Method
• Dynamic Programming
• Score
• 1 (( of identities / length of sequences) /
  100))

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Guide Tree

• ClustalW initially used UPGMA
• Unweighted Pair Group Method by Arithmetic Mean
• Simplest method of tree construction
• Assumes equal rates of mutation along the
  branches
• UPGMA Algorithm
• Definition Node in a tree is called an
  Operational Taxonomic Unit (OTU)
• From distance matrix, cluster pair of OTUs with
  smallest distance, and calculate new distance
• Repeat previous step until clusters converge

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Guide Tree - UPGMA

• Cluster pair with smallest distance
• Recalculate distance matrix

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Guide Tree - UPGMA

• Calculate new distance using composite OTU(A,B)
• Distance between a simple OTU and a composite OTU
  is the average of the distances between the
  simple OTU and the constituent simple OTUs of the
  composite OTU
• dist (A,B),C (dist A,C dist B,C) / 2 (4
  4) / 2 4dist (A,B),D (dist A,D dist B,D) /
  2 (6 6) / 2 6dist (A,B),E (dist A,E
  dist B,E) / 2 (6 6) / 2 6 dist (A,B),F
  (dist A,F dist B,F) / 2 (8 8) / 2 8

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Guide Tree - UPGMA

• Calculate new distance using composite OTU(A,B)
• Distance between a simple OTU and a composite OTU
  is the average of the distances between the
  simple OTU and the constituent simple OTUs of the
  composite OTU

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Guide Tree - UPGMA

• Second Iteration

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Guide Tree - UPGMA

• Third Iteration

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Guide Tree - UPGMA

• Fourth Iteration

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Guide Tree - UPGMA

• Fifth Iteration

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Guide Tree

• ClustalW uses Neighbor-Joining
• Assumes unequal rates of mutation along each
  branch
• Produces tree with branch lengths proportional to
  estimated divergence along each branch
• Neighbor-Joining Algorithm
• Find pairs of OTUs that minimize total branch
  length at each stage of clustering starting with
  a starlike tree (Minimum-Evolution Tree).

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Guide Tree - Neighbor-Joining

• Start with a star tree with N nodes
• Combine the pair with the smallest branch lengths
• Continue until all N-3 interior branches are
  found
• Dij distance between OTUs i and j

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Definitions

• Lab branch lengths between nodes a and b
• Sum of branch lengths

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Definitions

• Assuming 1 2 are any pair of (closest)
  neighbors
• Any pair of OTUs can take the position of 1
  2, N(N-1)/2 waysof choosing pairs
• Choose the pair that gives the smallest branch
  lengths

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Definitions

• Branch lengtbetween XY is now
• Removing XY givestwo star-like trees

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Definitions

• Sum of branch lengths
• If 12 are closestneighbors, join themto make
  new OTU and recalculate distance

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Definitions

• To find the tree branch lengths when 3 nodes left

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Guide Tree - Neighbor-Joining

• Calculate each branch length

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Guide Tree - Neighbor-Joining

• Calculate each branch length

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Guide Tree - Neighbor-Joining

• Calculate each branch length

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Guide Tree - Neighbor-Joining

• Calculate each branch length

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Guide Tree - Neighbor-Joining

• Recalculate distances
• Recalculate sum of branch lengths

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Guide Tree - Neighbor-Joining

• Start next iteration, nodes 5 6

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Guide Tree - Neighbor-Joining
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Guide Tree - Neighbor-Joining

• Next Iteration (1-2) 3

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Guide Tree - Neighbor-Joining
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Guide Tree - Neighbor-Joining
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Progressive Alignment

• Use a series of pairwise alignments to align
  larger and larger groups of sequences, following
  the branching order in the guide tree
• Align the most closely related sequence then add
  the next more closely related sequence,
  iteratively
• Full DP algorithm is used by aligning two
  existing alignments or sequences
• Gaps in present/older alignments remain fixed