Sequence Alignment

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Sequence Alignment
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Motivation Types

• Two sequences of same length, some characters are
  different (Database search)
• Aagtacggaga
• aagcaccgaga
• Two seq are of different length, possible gaps in
  one of them (Database search)
• Aaccaccgaga
• Aa-caccgaga

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Motivation Types

• Match longest prefix of one with the suffix of
  the other (fragment assembly)
• Aaacgtcgata
• gatacgatg
• Local alignment longest substring matching over
  two sequences (homolog search)
• Gatacgatgctagtttacg
• agagcgatgcataattcgaatga

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Motivation Types

• Multiple sequence alignment
• (page 71) (Comparative studies of sequences)

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Formalizing sequence comparison

• Either a character matches with the corresponding
  character in an an alignment (1),
• Or, it does not (-1),
• Or, a gap needs to be inserted (-2)

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Global Alignment

• Smith-Waterman (1981) Dynamic programming
  algorithm
• Scoring matrix for alignment (p 31)
• Initializing boundaries of the scoring matrix for
  gaps in front of either string
• Meaning of an entry to the matrix
• Corner element is the final score

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Global Alignment

• Three alternatives in each iteration
• Ordering of calculation row or column-wise
• The algorithm (p 52)
• Recursive recovery process from corner element
  (constant m and n, the string lengths)
• Variable len returned by the algorithm
• Convention for tie braking

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Local alignment

• Alignment will stop anywhere
• So, the min score is zero, even on boundaries
• Best local alignment is where the score is max in
  the matrix
• Recovery starts from that max value, stops at a
  zero value

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Semi-global (as-required alignment) alignment

• Four alternatives penalty-less gaps in front of
  string s, in front of t, at the back of s, back
  of t)
• Prefix-suffix matching by playing with
  alternatives
• E.g., suffix of s with prefix of t gaps at the
  back of s but in the front of t

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Semi-global alignment

• Example p 56
• Gaps in front zeros in row or column
  representing the string
• Gaps at the back recovery starts from the max of
  row or column representing the string
• Above may be combined as required
• Exercise how to combine for matching suffix of s
  with prefix of t

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Generalized gap penalty

• Multiple gaps with the same penalty as that of
  one or by some formula w(k)
• Each block matching gaps is to be considered as
  one unit (like a char)
• Boundary (first row and col) initialization with
  w(k)

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Generalized gap penalty

• Three matrices interplaying
• one for character matching with p(I,j)
• One for gaps in s
• One for gaps in t
• Formula on p 63

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Affine gap penalty

• Generalized gap penalty, with
• W(k) h gk, first gap costs more hg
• Formula changes slightly with known w(k)
• block gap-matrices compares only previous
  elements complexity reduces

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Multiple sequence alignment

• Function for each column character or gap for
  each sequence
• Combinatorics 2k 1, for k sequences (-1 for
  not putting gaps in all columns)
• But . . .

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Multiple sequence alignment

• Order of arguments for the function should not
  matter f(I,-,v) f(I,v,-)
• Score pairwise on a column
• Combinatorics (k choose 2)
• For k10, 2k-1 1111, kC245
• We need gap to gap scoring now

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Multiple sequence alignment

• Total score can be measured either way
• Sum over all columns, Or,
• Sum over all pairs of sequences
• If p(-, -) 0, then both the scoring above is
  same

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Multiple sequence alignment

• Consider 3 sequence alignment s1, s2, and s3
• (I, j, k)-th entry of the scoring matrix is for
  aligning s11..I, s21..j, s31..k
• 3D matrix (n x m x l) dimension, for s1n,
  s2m, s3l

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Multiple sequence alignment

• Each entry in scoring matrix will be at a corner
  of a 3D box
• Optimal score is calculated over all other 7
  corners (max)
• AI-1, j,k, AI, j-1, k, AI,j, k-1,
• AI-1, j-1, k, AI-1, j, k-1, AI, j-1, k-1,
• AI-1, j-1, k-1
• Vector(I,j,k) - bit-vector
• In each case sum-of-pair scores are to be added
  for the column EXAMPLE
• Initialization (-4)I 1ltIltn, for two gaps
  against substrings of s1, likewise for s2 and s3

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Multiple sequence alignment

• For k sequences, k-dimensional matrix
• Each entry is a calculation over 2k 1 other
  corners of the box
• Formula page 72

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Alignment improvements

• Alignment could be from the back also
• SI1..n, tj1..m
• Front and back alignment could be combined to
  cut alignment compute the two matrices, add
  them, align according to the added matrix

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Alignment improvements

• When the length of two sequences are comparable
  and expectation is to have good global alignment
• Retrieval is mostly along the diagonal
• Computation can focus around a strip (fixed (k)
  number) around diagonal k-band
• More efficient
• Usage of relevant cells only

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Multiple sequence alignment Star alignment

• One sequence at center all others are pairwise
  aligned against it
• Which sequence to put at the center?
• Try each
• create a 2D similarity matrix for all pairs,
  pick up the best (least of summed) row page 79

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Multiple sequence alignment Tree alignment

• A spanning tree out of the sequences nodes are
  sequences
• Each edge labels the similarity between pair of
  nodes
• Total tree cost, or aggregate over edges should
  be max
• Star is a special tree

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PAM matrix for matching residues
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BLAST search engine