Sequence Alignment - III

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Sequence Alignment - III

• Chitta Baral

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Scoring Model

• When comparing sequences
• Looking for evidence that they have diverged from
  a common ancestor by a process of mutation and
  selection
• Basic mutational processes
• Substitutions
• insertions deletions (together referred to as
  gaps)
• Total Score
• sum for each aligned pair terms for each gap
• Corresponds to logarithm of the related
  likelihood that the sequences are related,
  compared to being unrelated.
• Identities and conservative substitutions to be
  more likely (than by chance) contribute positive
  score terms
• Non-conservative changes are observed to be less
  frequently in real alignments than we expect by
  chance contribute negative score terms
• Additive scoring scheme Based on assumption that
  mutations at different sites in a sequence to
  have occurred independently
• Reasonable for DNA and protein sequences
• Inaccurate for structural RNAs

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Substitution Matrices

• Notation pair of sequence x1..n and y1..m
• Let xi be the ith symbol in x
• And yj be the jth symbol in y
• Let pxiyi probability that xi and yi are
  related
• Let qxi probbaility that we have xi by chance
• Frequency of occurrence of xi
• Score log P(x and y supposing they are
  related)/ P (x and y supposing they are
  unrelated)
• P(x and y supposing they are related) px1y1
  px2y2
• P(x and y supposing they are unrelated)
• 
  qx1q x2 X qy1qy2
• Odds ratio (px1y1/qx1qy1) X (px2y2/qx2qy2) X
• Log-odds ratio s(x1,y1) s(x2, y2)
• Where s(a,b) log (pab/qaqb)
• The s(a,b) table is known as the score matrix or
  substitution matrix

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Gap Penalties

• Also based on a probabilistic model of alignment
• Less widely recognized than the probabilistic
  basis of substitution matrices
• Gap of length g due to insertion of a1ag
• p(gap because of mutation) f(g) (qa1qag)
• p(having a1ag by chance) qa1qag
• Ratio f(g)
• Log of ratio log (f(g))
• Geometric distribution f(g) ke-xg
• Suppose f(g) e-gd then log of ratio -gd
  linear score
• Suppose f(g) ke-ge then log of ratio -ge
  log k
• -ge e (log k - e) - (e - log k) (g
  1) e
• - d (g-1) e where d e log k
  affine score

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Repeated matches

• A big string x1..n and smaller string y1..m
• Asymmetric looking for multiple matches of y in
  x.
• As we do the matching and fill the table, we need
  to decide when to stop going further in y, and
  start over from the beginning of y.
• F(i,0) Assuming xi is in an unmatched region,
  what is the best total score so far.
• F(i,j), j gt 1 Assuming xi is in a matched
  region and the last matching ends at xi and yj,
  the best total score so far.
• F(0,0) 0.
• F(i,i) maximum of F(i,0) F(i-1,j-1)
  s(xi,yj) F(i-1,j)-d F(i,j-1) d
• F(i,0) corresponds to start over option (but now
  we store the total score so far)
• F(i,0) maximum of
• F(i-1,0)
• F(i-1, j) T j 1, , m
• T is a threshold and we are only interested in
  matches scoring higher than the threshold.
  (Important because there are always short local
  alignments with small positive scores even
  between entirely unrelated sequences.)

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Illustration of repeated matches
H E A G A W G H E E
0 0 0 0 1 1 1 1 1 3 9 ?9
P 0 0 0 0 1 1 1 1 1 3 9
A 0 0 0 5 1 6 1 1 1 3 9
W 0 0 0 0 2 1 21 13 5 3 9
H 0 10 2 0 1 1 13 19 23 15 9
E 0 2 16 8 1 1 5 11 19 29 21
A 0 0 8 21 13 6 1 5 11 21 28
E 0 0 6 13 18 12 4 1 5 17 27
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Next

• Alignment with affine gap scores.
• Heuristic based approach.