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hw2solutions

hw2solutions - BCB 567/CprE 548 Bioinformatics I Fall 2007...

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BCB 567/CprE 548 Bioinformatics I Fall 2007 Homework 2 Solutions 1. Consider the cells in which we look for the best alignment score as sets labeled M . For global alignment, we look only at the lower right cell: M g = { S [ i, j ] | i = n AND j = m } . For semi- global alignment, we look at the entire last row and column: M s = { S [ i, j ] | i = n OR j = m } . For local alignment we consider the entire table: M l = { S [ i, j ] } . We see that M g M s M l . Because A B Max ( A ) MAX ( B ), we conclude global semiglobal local. One final consideration is that, for any cell, the score in the local alignment table are greater than or equal to the score in the semiglobal alignment table, which is in turn greater than or equal to the score in the global alignment table. This is because in each case, additional negative values are replaced with zeros when filling out the table. Thus the difference in scores between the tables reinforce the relationships indicated above. 2. The best scoring path traveling outside of the the k-band will have exactly two gaps of total length 2 k and n - k matches. The first gap is used to travel outside the k-band, while the second is used to travel back to main diagonal. The total score of this path is 2 g + 2 kh + ( n - k ) α . 3. Initialize the first row and first column of the table with zeros. When filling in the a cell in the first t rows or first t columns of the table, use the equation for local alignment: S [ i, j ] = S [ i - 1 , j - 1] + δ ( i - 1 , j - 1) S [

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hw2solutions - BCB 567/CprE 548 Bioinformatics I Fall 2007...

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