Scribe: S. Oak

Today's Handouts and Announcements

• Searching Protein Sequence Libraries: Comparison of the Sensitivity and Selectivity of the Smith - Waterman and FASTA Algorithms

 - William R. Pearson.
 
• An O(ND) Difference Algorithm and its Variations

 - Eugene W. Myers.

Today's Topics

• Similarity of 2 sequences gives a measure of how similar the sequences are.
• Alignment of 2 sequences is a way of placing one sequence above the other inorder to make clear the correspondence between similar characters or substrings from the substrings.
• Methods for comparing sequences:

Global comparison in which we are interested in alignments involving the entire sequences.

Local comparison in which we are interested in alignments involving the substrings of the sequences.

There is also a third type of comparison in which we are interested in aligning the prefixes and sufixes of the given sequences, which is   called the semi global comparison.

• All the problems can be solved by dynamic programming.
• The basic algorithm computes the scores for every gap, match and mismatch in the given sequences and then add up the column scores.
• The scoring system is such that matches are rewarded (positive score) and mismatches and spaces are penalised (negative score).
• Dynamic programming results in a (m+1)(n+1) matrix

where m = total number of bases in seq 1 ;
    and n =  total number of bases in seq 2.
• Each cell in the matrix, cell(i,j) corresponds to matching prefix of seq 1 of length i with prefix of seq 2 of length j.
• Scoring for Global Alignment:
• The score a[i,j] in cell[i,j]  = max (
                                                             a[i,j-1] - 2       -- gap
                                                             a[i-1,j] -2       -- gap
                                                             a[i-1, j-1] - 1  -- mismatch
                                                             a[i-1,j-1] + 1  --  match
                                                             )
• Asymtotic Time complexity = mn
• Asymtotic Space complexity = mn
• Scoring for Local Alignment:
• The score a[i,j] in cell[i,j]  = max (
                                                             a[i,j-1] - 2       -- gap
                                                             a[i-1,j] -2       -- gap
                                                             a[i-1, j-1] - 1  -- mismatch
                                                             a[i-1,j-1] + 1  --  match
                                                             0
                                                            )
• Asymtotic Time complexity = mn
• Asymtotic Space complexity = mn
• Space saving can be accomplished by Divide and conquer technique.
• Gap penalty Functions considers that with mutations involved the occurrence of a gap with 'k' spaces is more probable than the occurence of 'k' isolated spaces.
• We use the same dynamic programming algo. but adding a third dimension for each cell that maintains the length of gaps leading to that particular cell.
• Asymtotic Time complexity = (m+n)mn
• Asymtotic Space complexity = (m+n)mn

Today's Sources

• Setubal and Meidanis:Chapter 3.(pages 47 - 65)
• Salzberg, Searls, and Kasif: Not Used.