A lignment Class III

1. Alignment Class III We continue where we stopped last week: FASTA – BLAST

2. FASTA-Stages • Find k-tups in the two sequences (k=1,2 for proteins, 4-6 for DNA sequences) • Score and select top 10 scoring “local diagonals” • For proteins, each k-tup found is scored using the PAM250 matrix • For DNA, the number of k-tups found • Penalize intervening gaps

3. Finding k-tups position 1 2 3 4 5 6 7 8 9 10 11 protein 1 n c s p t a . . . . . protein 2 . . . . . a c s p r k position in offset amino acid protein A protein B pos A - posB ----------------------------------------------------- a 6 6 0 c 2 7 -5 k - 11 n 1 - p 4 9 -5 r - 10 s 3 8 -5 t 5 - ----------------------------------------------------- Note the common offset for the 3 amino acids c,s and p A possible alignment is thus quickly found - protein 1 n c s p t a | | | protein 2 a c s p r k

4. FASTA, K-tups with common offset

5. FASTA-Stages • Rescan top 10 regions, score with PAM250 (proteins) or DNA scoring matrix. Trim off the ends of the regions to achieve highest scores. • Try to join regions with gapped alignments. Join if similarity score is one standard deviation above average expected score • After finding the best initial region, FASTA performs a global alignment of a 32 residue wide region centered on the best initial region, and uses the score as the optimized score.

6. BLAST • Basic Local Alignment Search Tool • Altschul et al. 1990,1994,1997 • Heuristic method for local alignment • Designed specifically for database searches • Idea: Good alignments contain short lengths of exact matches

7. Query: DNA Protein Database: DNA Protein Blast Application • Blast is a family of programs: BlastN, BlastP, BlastX, tBlastN, tBlastX • BlastN - nt versus nt database • BlastP - protein versus protein database • BlastX - translated nt versus protein database • tBlastN - protein versus translated nt database • tBlastX - translated nt versus translated nt database

8. Mathematical Basis of BLAST • Model matches as a sequence of coin tosses • Let p be the probability of a “head” • For a “fair” coin, p = 0.5 • (Erdös-Rényi) If there are n throws, then the expected length R of the longest run of heads is R = log1/p (n). • Example: Suppose n = 20 for a “fair” coin R=log2(20)=4.32 • Trick is how to model DNA (or amino acid) sequence alignments as coin tosses.

9. Mathematical Basis of BLAST • To model random sequence alignments, replace a match with a “head” and mismatch with a “tail”. • For DNA, the probability of a “head” is 1/4 • Same logic applies to amino acids AATCAT ATTCAG HTHHHT

10. Mathematical Basis of BLAST • So, for one particular alignment, the Erdös-Rényi property can be applied • What about for all possible alignments? • Consider that sequences are being shifted back and forth, dot matrix plot • The expected length of the longest match is R=log1/p(mn) where m and n are the lengths of the two sequences.

11. Steps of BLAST • Filter out low-complexity regions where L is length, N is alphabet size, ni is the number of letter i appearing in sequence. Example: AAAT K=1/4 log4(24/(3!*1!*0!*0!))=0.25

12. Steps of BLAST • Query words of length 3 (for proteins) or 11 (for DNA) are created from query sequence using a sliding window MEFPGLGSLGTSEPLPQFVDPALVSS MEF EFP FPG PGL GLG

13. Steps of BLAST • Using BLOSUM62 (for proteins) or scores of +5/-4 (DNA, PAM40), score all possible words of length 3 or 11 respectively against a query word. • Select a neighborhood word score threshold (T) so that only most significant sequences are kept. Approximately 50 hits per query word. • Repeat 3 and 4 for each query word in step 2. Total number of high scoring words is approximately 50 * sequence length.

14. M E E P F G Steps of BLAST • Organize the high-scoring words into a search tree • Scan each database sequence for match to high-scoring words. Each match is a seed for an ungapped alignment.

15. Steps of BLAST • (Original BLAST) extend matching words to the left and right using ungapped alignments. Extension continues as long as score increases or stays same. This is a HSP (high scoring pair). (BLAST2) Matches along the same diagonal within a distance A of each other are joined and then the longer sequence extended as before.

16. Steps of BLAST • Using a cutoff score S, keep only the extended matches that have a score at least S. • Determine statistical significance of each remaining match (from last time). • Try to extend the HSPs if possible. • Show Smith-Waterman local alignments.

17. Information theory Shanon Entropy and information

18. Entropy • X: discrete Random Variable (RV), p(X) • Entropy (or self-information) • Entropy measures the amount of information in a RV

19. Entropy (cont) i.e when the value of X is determinate, hence providing no new information

20. Joint Entropy • The joint entropy of 2 RV X,Y is the amount of the information needed on average to specify both their values

21. Conditional Entropy • The conditional entropy of a RV Y given another X, expresses how much extra information one still needs to supply on average to communicate Y given that the other party knows X

22. Chain Rule

23. Mutual Information • I(X,Y) is the mutual information between X and Y. It is the reduction of uncertainty of one RV due to knowing about the other, or the amount of information one RV contains about the other

24. Mutual Information (cont) • I is 0 only when X,Y are independent: H(X|Y)=H(X) • H(X)=H(X)-H(X|X)=I(X,X) Entropy is the self-information

25. Kullback-Leibler Divergence • Relative entropy or KL (Kullback-Leibler) divergence

26. Scoring matrices Identity PAM BLOSUM

27. Scoring Matrices Types • Identity matrix – exact matches receive one score and non-exat matches a different score (say 1 and 0, or 6 and –1 for local alignment.). • Mutation data matrix – a scoring matrix compiled based on observation of protein point mutation (PAM, BLOSUM). • Physical properties matrix – amino acids with with similar properties (e.G. hydrophobicity ) receive high score. • Genetic code matrix – amino acids are scored based on similarities in the coding triple (codons).

28. Substitution Matrix • Amino acids substitute easily for another due to similar physicochemical properties • Isoleucine for Valine (both small, hydrophobic) • Serine for Threonine (both polar) • Such changes – “conservative” • Thus, need a way to increase sensitivity of the alignment algorithm • Solution – substitution matrix • Therefore, we need a range of values that depend on the nature of sequences being compared • Identical amino acids > Conservative substitutions > Nonconservative substitutions

29. Choice of scoring matrix is dictated by the alignment goals • Two proteins are homologous if (and only if) they are evolutionarily related (have a common ancestor) • Homologous proteins are likely to have related functions (and have the same fold) • Scoring matrices must in some way model our understanding of protein evolution. • Based on the result of the search we have to be able to decide if the discovered sequence similarity could happen by chance or is a signature of likely homology.