Sequence Alignment III

1. Sequence Alignment III CIS 667 February 10, 2004

2. Extensions to the Basic Algorithm • We have seen that the basic dynamic programming algorithm can be used to solve • Global alignment • Semi-global alignment • Local alignment • We can extend the algorithm to more accurately reflect the cost of gap penalties

3. General Gap Penalty Functions • Gaps are caused by mutations • It is more likely to have a single large gap than several smaller ones • Gap penalties should reflect that • Let w(k) denote a gap penalty function (the cost of a gap of k spaces) • We have been using w(k) = bk - a linear function

4. General Gap Penalty Functions • We can modify the basic algorithm to compute a score with a general gap penalty w (i.e. any function) • The modified algorithm is slower, however - O(n3) • The new algorithm scoring scheme is no longer additive • The space required is also larger

5. Affine Gap Penalty Functions • Can we do better than O(n3) and still have a reasonable function? • Yes. We need to have w(k)  kw(1) • An affine function - w(k) = h + gk with w(0) = 0 and h, g > 0 works • Think of h as the cost of opening a gap and g as the cost of extending a gap • We can develop an algorithm with time complexity O(n2)

6. -12 -16 -9 -16 Gap Penalties - Overview CAGT CCAAGGTTCAGT Imagine we want to align: C-A-G-T----- CCAAGGTTCAGT Bad alignment: --------CAGT CCAAGGTTCAGT Better alignment: Gap cost with linear gap penalty (-2) Gap cost with affine gap penalty (h = -2, k = -1)

7. Multiple Sequence Alignment • Once a protein sequence is newly determined, an important goal is to assign possible functions to it • First search for similar sequences in the DNA and protein sequence databases • If more than one similar sequence is found, the next step is to multiply align all of the sequences

8. Multiple Sequence Alignment • Multiple alignments are key starting point for • Protein secondary structure prediction • Residue accessibility • Function • Also provide the basis for the most sensitive sequence searching algorithms

9. Multiple Sequence Alignment • A multiple sequence alignment is simply an alignment that contains more than two sequences MPQILLL MLR-LL- MK-ILLL MPPVLIL

10. Multiple Sequence Alignment • We must decide how to score a multiple alignment • One possibility is the sum-of-pairs function • Simply add up the pairwise scores of all pairs in a column to get the score of the column • Note that in multiple sequence alignment we may have two spaces in a column - the score of (-,-) then is usually set to 0

11. Multiple Sequence Alignment • A straightforward dynamic programming approach to multiple sequence alignment results in an exponential algorithm • Heuristics can be used to reduce the complexity in most cases

12. Multiple Sequence Alignment • Automatic alignment programs such as CLUSTAL W can be used to produce multiple alignments • The PSI-BLAST program uses multiple sequence alignments to make more sensitive searches of protein sequence databases than is possible with a single sequence

13. PAM Matrices • When comparing protein sequences, we need a more complex scoring scheme • A mismatch with two amino acids with similar biochemical properties should score higher than one with two dissimilar ones • Evolution is more likely to result in a similar amino acid (e.g. same size, both hydrophobic, etc.) replacing another

14. PAM Matrices • PAM - Point Accepted Mutations or Percent of Accepted Mutations • 1-PAM matrix reflects an amount of evolution producing on average one mutation per hundred amino acids • 250-PAM matrix is suitable for comparing sequences that are 250 units of evolution apart • Works well for long, weakly similar sequences • Small values good for short, similar sequences

15. PAM-250 Matrix

16. BLOSUM Matrices • Another widely used set of matrices is BLOSUM - Blocks Substitution Matrix • BLOSUM is often better for highly divergent sequences • PAM better for more highly similar sequences

17. BLAST • BLAST - Basic Local Alignment Search Tool is a family of sequence similarity tools • Can be used to search sequence databases worldwide • Can be run locally, or via web-based interface on a server • Given a query sequence, BLAST returns all matches above a user-defined threshold

18. BLAST • BLAST uses a heuristic technique • Compile list of high-scoring words (use PAM matrix to score words w characters long) • Search for matches in the database (use a hash table to speed up search) - call a match a seed • Extend the seeds in both directions until the score of the extension falls below a limit