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lect3 Blast Local Alignment and other flavors

# An Introduction to Bioinformatics Algorithms (Computational Molecular Biology)

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Fa05 CSE 182 L3: Blast: Local Alignment and other flavors

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Fa05 CSE 182 An Example Align s=TCAT with t=TGCAA Match Score = 1 Mismatch score = -1, Indel Score = -1 Score A1?, Score A2?  T C A T - T G C A A T C A T T G C A A A1 A2
Fa05 CSE 182 Sequence Alignment Recall: Instead of computing the optimum alignment, we are  computing the score of the optimum alignment Let S[i,j] denote the score of the optimum alignment of the prefix  s[1..i] and t [1..j]

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Fa05 CSE 182 An O(nm) algorithm for score computation The iteration ensures that all values on the right are computed in earlier steps. S [ i , j ] = max S [ i - 1, j - 1]+ C ( s i , t j ) S [ i - 1, j ]+ C ( s i ,- ) S [ i , j - 1]+ C (- , t j ) For i = 1 to n For j = 1 to m
Fa05 CSE 182 Base case (Initialization) S [0,0] = 0 S [ i ,0] = C ( s i ,- ) + S [ i - 1,0] " i S [0, j ] = C (- , s j ) + S [0, j - 1] " j

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Fa05 CSE 182 A tableaux approach s n 1 i 1 j n Μ S[i,j-1] S[i,j] S[i-1,j] S[i-1,j-1] t Cell (i,j) contains the score S[i,j]. Each cell only looks at 3  neighboring cells S [ i , j ] = max S [ i - 1, j - 1]+ C ( s i , t j ) S [ i - 1, j ]+ C ( s i ,- ) S [ i , j - 1]+ C (- , t j )
Fa05 CSE 182 0 -1 -2 -3 -4 -5 -1 1 0 -1 -2 -3 -2 0 0 1 0 -1 -3 -1 -1 0 2 1 -4 -2 -2 -1 1 1 T G C A A T C A T Alignment Table

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Fa05 CSE 182 1 1 -1 -2 -2 -4 1 2 0 -1 -1 -3 -1 0 1 0 0 -2 -3 -2 -1 0 1 -1 -5 -4 -3 -2 -1 0 T G C A A T C A T Alignment Table S[4,5] = 1 is the score of an  optimum alignment Therefore, A2 is an optimum  alignment We know how to obtain the  optimum Score. How do we get  the best alignment?
Fa05 CSE 182 Computing Optimum Alignment At each cell, we have 3 choices We maintain additional information to record the choice at each step. For i = 1 to n For j = 1 to m S [ i , j ] = max S [ i - 1, j - 1]+ C ( s i , t j ) S [ i - 1, j ]+ C ( s i ,- ) S [ i , j - 1]+ C (- , t j ) If (S[i,j]= S[i-1,j-1] + C(s i ,t j )) M[i,j] = If (S[i,j]= S[i-1,j] + C(s i ,-)) M[i,j] = If (S[i,j]= S[i,j-1] + C(-,t j ) ) M[i,j] = j-1 i-1 j i

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Fa05 CSE 182 T G C A A T C A T 1 1 -1 -2 -2 -4 1 2 0 -1 -1 -3 -1 0 1 0 0 -2 -3 -2 -1 0 1 -1 -5 -4 -3 -2 -1 0 Computing Optimal Alignments
Fa05 CSE 182 Retrieving Opt.Alignment 1 1 -1 -2 -2 -4 1 2 0 -1 -1 -3 -1 0 1 0 0 -2 -3 -2 -1 0 1 -1 -5 -4 -3 -2 -1 0 T G C A A T C A T M[4,5]=     Implies that S[4,5]=S[3,4]+C( A,T )                   or A T M[3,4]= Implies that S[3,4]=S[2,3] +C( A,A ) or A T A A 1 2 3 4 5 1 3 2 4

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Fa05 CSE 182 Retrieving Opt.Alignment 1 1 -1 -2 -2 -4 1 2 0 -1 -1 -3 -1 0 1 0 0 -2 -3 -2 -1 0 1 -1 -5 -4 -3 -2 -1 0 T G C A A T C A T M[2,3]=     Implies that S[2,3]=S[1,2]+C( C,C )                   or A T M[1,2]= Implies that S[1,2]=S[1,1] +C (-,G ) or A T A A A A C C C C - G T T 1 2 3 4 5 1 3 2 4
Fa05 CSE 182 Algorithm to retrieve optimal alignment RetrieveAl(i,j) if (M[i,j] == `\’)  return (RetrieveAl (i-1,j-1) .         )   else if (M[i,j] == `|’)  return (RetrieveAl (i-1,j) .         ) s i t j s i - - t j else if (M[i,j] == `--’) else if (M[i,j] == `--’)                   return (RetrieveAl (i,j-1) .            ) return (RetrieveAl (i,j-1) .            )

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Fa05 CSE 182 Summary
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lect3 Blast Local Alignment and other flavors - L3 Blast...

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