Calign:aligning sequences with restricted affine gap penalties

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Calignaligning sequences with restricted affine
gap penalties

• Kun-Mao Chao

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Motivation

• Given a genomic DNA sequence, it is still an open
  problem to determine its coding region, i.e. the
  region consisting of exons and introns.
• The comparison of cDNA and genomic DNA helps the
  understanding of coding region.

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(No Transcript)
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Preliminaries

• InputTwo sequence A(a1a2aM) and B(b1b2.bN),
  where without loss of generality N gt M.
• OutputAn alignment of A and B.
• When aligning a cDNA sequence with a genomic DNA
  sequence, It might be more appropriate to
  penalize each long gap with a constant penalty
• Restricted affine gap penaltieswhen insertion
  gaps are more than l symbols are penalized a lb.

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O(MN) algorithm

• S(i,j) denotes the minimum cost of any alignment
  between a1a2.ai and b1b2....bj
• D(i,j) denotes the minimum cost of any alignment
  between a1a2.ai and b1b2....bj ending with a
  deletion.
• I(i,j) and I(i,j) denote similar with D(i,j).

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O(MN) algorithm(cont.)
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O(MN) algorithm(cont.)
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(0,0)
(0,N)
D(i-1,j)b S(i-1,j)ab
S(i-1,j-1)k(ai,bj)
I(i,j-1) S(i,j-1)alb
D(i,j)
I(i,j)
I(i,j-1)b S(i,j-1)ab
I(i,j)
S(i,j)
(M,N)
(M,0)
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O(NC) algorithm

• Tables D, I, I, S have diagonalwise
  monotonically nondecreasing property.
• Let D(k,c), I(k,c), I(k,c). S(k,c) be the
  largest row I such that DiI,ki) c, I(i,ki)
  c, I(i,ki) c, S(i,ki) c, respectively.

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O(NC) algorithm(cont.)
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O(NC) algorithm(cont.)
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O(NC) algorithm(cont.)

• snake(i,j) max z ai1..aiz bj1..bjz

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K1
k
K-1
D(k1,c-b) S(k1,c-a-b)
I(k-1,c) S(k-1,c-a-lb)
I(k,c)
I(k-1,c-b) S(k-1,c-a-b)
I(k,c)
D(k,c)
S(k,c-r)
i
Snake(I,ki)
S(k,c)