423f11-lec4-gaps

# 423f11-lec4-gaps - Gap Penalties CMSC 423 General Gap...

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Unformatted text preview: Gap Penalties CMSC 423 General Gap Penalties • Now, the cost of a run of k gaps is gap × k • It might be more realistic to support general gap penalty, so that the score of a run of k gaps is gap ( k ) < gap × k . • Then, the optimization will prefer to group gaps together. AAAGAATTCA A-A-A-T-CA AAAGAATTCA AAA----TCA vs. These have the same score, but the second one is often more plausible. A single insertion of “GAAT” into the Frst string could change it into the second. General Gap Penalties AAAGAATTCA A-A-A-T-CA AAAGAATTCA AAA----TCA vs. Previous DP no longer works with general gap penalties because the score of the last character depends on details of the previous alignment: AAAGAAC AAA---- AAAGAATC AAA----- vs. Instead, we need to “know” how long a Fnal run of gaps is in order to give a score to the last subproblem. Three Matrices We now keep 3 different matrices: M[i,j] = score of best alignment of x[1..i] and y[1..j] ending with a character- character match or mismatch . X[i,j] = score of best alignment of x[1..i] and y[1..j] ending with a space in X . Y[i,j] = score of best alignment of x[1..i] and y[1..j] ending with a space in Y . M [ i,j ] = match( i,j ) + max > < > : M [ i- 1 ,j- 1] X [ i- 1 ,j- 1] Y [ i- 1 ,j- 1] X [ i,j ] = max ( M [ i,j- k ]- gap( k ) for 1 k j Y [ i,j- k ]- gap( k ) for 1 k j Y [ i,j ] = max ( M [ i- k,j ]- gap( k ) for 1 k i X [ i- k,j ]- gap( k ) for 1 k i The M Matrix M [ i,j ] = match( i,j ) + max > < > : M [ i- 1 ,j- 1] X [ i- 1 ,j- 1] Y [ i- 1 ,j- 1] We now keep 3 different matrices: M[i,j] = score of best alignment of x[1..i] and y[1..j] ending with a character- character match or mismatch ....
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423f11-lec4-gaps - Gap Penalties CMSC 423 General Gap...

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