Sequence Alignment

Assignment Read Lesk, Problem: Given two sequences R and S of length n, how many alignments of R and S are possible? If you don’t find an exact answer, how tight of a Big-O bound can you derive? (optional)

The ‘bio’ statement of the problem Given two or more sequences: Measure their similarity Establish a correspondence Find conserved and varied locations Infer evolutionary relationships

The ‘cs’ statement Given two or more sequences: Establish an optimal residue-residue correspondence

Definition of alignment An alignment is a set of correspondences between pairs of residues which preserves their order. Example: a b c d e – a – c d e f Note: gaps are permitted in both sequences

Definition of ‘optimal’ Requires a scoring system May include positive and negative value Best (highest scoring) of all possible values Question: given two sequences of length n, how many alignments are possible?

Dot plots W H I R L I N G W H I I I R L I G I I I G

Dot plots W H I R L I N G W H I I I R L I G I I I G

Dotplots and alignments Dotplots are visual representations of similarity Any path from upper left to lower right, using only S, E and SE moves, is an alignment

Edit distance The minimal number of edit operations (insert/delete, change) to transform one sequence to another Operations can be weighted: –Indels by length –Transformations by type

A weighted scheme Transitions (a g, c t) are more common than transversions a t g c a c g t

Gap penalties For DNA alignment, CLUSTAL-W uses: –+1 for a match –0 for a mismatch –10 for gap initiation –0.1 for gap extension

Dynamic programming Gives global optimum Takes 0(nm) time Doesn’t distinguish among equal-scoring alignments

Variations on the question Small sequence vs small sequence (how close are these two?) A small sequence against a very long sequence (Is this gene’s relative in the database?) Closest subsequences (does these sequences share a motif?)

Blast-style searches Answers the ‘relative’ question Heuristic (but statistically good, for the simplest model) Method: –Find local alignments –Find paths close to local alignments

P score Probability that alignment would arise by chance What if short vs long search gives a P-value of 10E-2? 10E-4?

Z-score, E-value Z-value is measure of ‘unlikelihood’ of match, from known mean and deviation E-value is expected number of sequences that give same Z-score or better with random probe E is usual Blast statistic E <= 0.02 is ‘good’

The Blast family Blast Blastp (protein-protein) Blastx (nucleotide-protein) Tblastn (amino-nucleotide) Tblastx (n-n) Psi-blast (improved a-a)