1. CS 5263 Bioinformatics Lecture 7: Heuristic Sequence Alignment Algorithms (BLAST)

2. Roadmap Last lecture review –Sequence alignment statistics Today –Gene finding by alignment –Heuristic alignment algorithms Basic Local Alignment Search Tools

3. Sequence Alignment Statistics Substitution matrices –How is the BLOSUM matrix made –How to make your own substitution matrix –What’s the meaning of an arbitrary substitution matrix Significance of sequence alignments –P-value estimation for Global alignment scores Local alignment scores

4. What is a p-value? The probability of observing an effect as strong or stronger than you observed, given the null hypothesis. i.e., “How likely is this effect to occur by chance?” Pr(x > S | null)

5. What is a null-hypothesis? A statistician’s way of characterizing “chance.” Generally, a mathematical model of randomness with respect to a particular set of observations. The purpose of most statistical tests is to determine whether the observed data can be explained by the null hypothesis.

6. For sequence alignment Your null hypothesis is “the two sequences are unrelated” Your alternative hypothesis is “the two sequences are related” You obtained a score S –how likely that you can obtain such a score if the null hypothesis is true?

7. How to test that null-hypothesis? Randomly generate some pairs of “unrelated” sequences See what alignment scores you may get for those “unrelated” sequences Must keep other factors in mind –Your random sequences must be as close as possible to your true sequences –Except that they are “unrelated” (i.e., not from a common ancestor)

8. Possible ways to get unrelated sequences Which is better? –Randomly pick some sequences from a database –Randomly pick some sequences from a database and truncate to the same length as your real sequences –Generate random sequences according to the frequency that each letter is used by your real sequences –Randomly shuffle your sequences

9. Possible ways to get random sequences Which is better? –Randomly pick some sequences from a database –Randomly pick some sequences from a database and truncate to the same length as your real sequences –Generate random sequences according to the frequency that each letter is used by your real sequences –Randomly shuffle your sequences

10. Random shuffling is what we do to estimate p-values for global alignment

11. …………………………………………………… Mouse HEXA Human HEXA Score = 732

12. 732 Distribution of the alignment scores between mouse HEXA and 200 randomly shuffled human HEXA sequences P-value: less than 1/200 = 0.005

13. Advantages –Easy to implement –You don’t need to know a lot of theories to do this Disadvantages –Slow –Cannot estimate small p-values –If we had repeated 1,000 times, would we get a score as high 732? Based on what I’ve already seen, I would guess probably no What about 1,000,000 times?

14. When theory exists It gets much better You don’t really need to go there to know what’s there (I know roughly how many times you can get a score as high as 732 if you repeat your experiments a billion times…) That is what happened for local alignment

15. For ungapped alignment between two sequences of lengths M and N E(S) = KMN exp[- S] (Expected value, E-value. ) K, depends on sequence composition and substitution matrix –Can be obtained either empirically or analytically

16. when P is small.

17. Theory says my score distribution should have this shape Distribution of alignment scores for 1000 random sequence pairs Extreme value distribution My experiment shows me that the theory seems correct

18. Example You are aligning two sequences, each has 1000 bases m = 1, s = -1, d = -inf (ungapped alignment) You obtain a score 20 Is this score significant?

19. = ln3 = 1.1 E(S) = K MN exp{- S} E(20) = 0.1 * 1000 * 1000 * 3 -20 = 3 x 10 -5 P-value = 3 x 10 -5 << 0.05 The alignment is significant

20. Distribution of 1000 random sequence pairs 20

21. Multiple-testing problem You are searching a 1000-base sequence against a database of 10 6 sequences (average length 1000 bases) You get a score 20 You are essentially comparing 1000 bases with 1000x10 6 = 10 9 bases (ignore edge effect) E(20) = 0.1 * 1000 * 10 9 * 3 -20 = 30 By chance we would expect to see 30 matches P-value = 1 – e -30 = 0.9999999999 Not significant at all

22. Interpretation of p-value Your null hypothesis is: the two sequences are not related Your p-value is 0.999999999, so you cannot reject your null hypothesis –Which means you cannot exclude the possibility that the two sequence may be unrelated –But can you conclude that the two sequences are unrelated? –No! your did not test that!

23. A better way to understand p-value Your p-value is 0.99999 You have very low confidence (<0.00001) to say that the null hypothesis is wrong Is the null hypothesis true then (i.e., the two sequences are unrelated)? –You don’t know –Your test was not designed to tell you that

24. In practice You search the sequence against a database of 10 6 sequences You get 35 matches You expect to get about 30 by chance It could be all 35 are real, or none, or some You already reduced your target from 10 6 sequences to 35 sequences Take all 35 sequences with caution. Look for other evidences

25. Statistics for gapped local alignment Theory not well developed Extreme value distribution works well empirically Need to estimate K and empirically

26. Exercising FSA How do you make an FSA for the Needleman-Wunsch algorithm?

27. Exercising FSA How do you make an FSA for the Needleman-Wunsch algorithm? F Ix Iy (x i,y j ) /  (x i,-) / d (-, y j ) / d (x i,-)/d (-, y j ) / d

28. Simplify F I (x i,y j ) /  (x i,-) / d (-, y j ) / d (x i,-) / d

29. Simplify more F (x i,y j ) /  (-, y j ) / d (x i,-) / d F(i-1, j-1) +  (x i, y j ) F(i,j) = max F(i-1, j) + d F(i, j-1) + d

30. A more difficult alignment problem (A gene finder indeed!) X is a genomic sequence (DNA) –X encodes a gene –May contain introns Y is an ORF from another species –Contains only exons We want to compare X against Y –Conservation is on the level of amino acids

31. 5’ UTR 3’ UTRexon intron Start codonStop codon Open reading frame (ORF) Pre-mRNA Mature mRNA (mRNA) Splice DNA

32. We have a predicted gene We know the positions of the start codon and stop codon But we don’t know where are the splicing sites –Not even the number of introns exon intron Start codon Stop codon intron

33. Mouse putative gene human ORF 1.Most splicing sites start at GT and end at AG 2.But there are lots of GT and AG in the sequence 3.Aligning to a orthologous gene with known ORF may help us determine the splicing sites Orthologous genes: two genes evolved from the same ancestor Coding region are likely conserved on amino acid level UUA, UUG encode the same amino acid So do UCA, UCU, UCG, UCC GT…………AG

34. The Genetic Code Third letter

35. Easy Remove introns Global alignment Mouse putative gene human ORF Mouse putative ORF translate If know where are the exons

36. Or directly align triplets Remove introns Global alignment Mouse putative gene human ORF Mouse putative ORF

37. Codon substitution scores AAAAAGAAUAAC………UCUUCC AAA43 AAG34 AAU 4311 AAC 3411 … … … UCU 1143 UCC 1134 64 x 64 substitution matrix

38. FSA for aligning genomic DNA to ORF A B (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / e (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / d Considering only exons

39. Mouse putative gene human ORF 1.We don’t know exactly where are the splicing sites 2.Length of introns may not be a multiple of 3 - If convert the whole seq into triplets, may result in ORF shift 17 bases?

40. Model introns Mouse putative gene human ORF 1.Most splicing sites start at GT and end at AG 2.For simplicity, assume length of exon is a multiple of 3 Not true in reality Only a little more work without this assumption GT…………AG 120 nt = 40 aa 126 nt = 42 aa

41. Aligning genomic DNA to ORF Fixed cost to have an intron Alignment with Affine gap penalty

42. FSA for aligning genomic DNA to ORF A B (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / e Considering only exons (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / d

43. FSA for aligning genomic DNA to ORF A B C (-, GT) / s Start an intron (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / d (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / e

44. FSA for aligning genomic DNA to ORF A B C (-, GT) / s (-, y i ) / 0 Start an intron Continue in intron (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / d (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / e

45. FSA for aligning genomic DNA to ORF A B C (-, GT) / s (-, y i ) / 0 (-, AG) / s Close an intron Start an intron Continue in intron (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / d (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / e

46. A B C (-, GT) / s (-, y j ) / 0 (-, AG) / s A(i-3,j-3) +  (x i-2 x i-1 x i, y j-2 y j-1 y j ) A(i, j) = max B(i-3,j-3) +  (x i-2 x i-1 x i, y j-2 y j-1 y j ) C(i, j-2) + s, if y j-1 y j == ‘AG’ (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / d (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / e

47. A B C (-, GT) / s (-, AG) / s A(i, j-3) + d A(i-3, j) + d B(i, j) = max B(i, j-3) + e B(i-3, j) + e (-, y j ) / 0 (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / d (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / e

48. A B C (-, GT) / s (-, AG) / s B(i, j-2) + s, if y j-1 y j == ‘GT’ C(i, j) = max C(i, j-1) (-, y j ) / 0 (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / d (x i-2 x i-1 x i, y j-2 y j-1 y j ) /  (x i-2 x i-1 x i, - ) or (-, y j-2 y j-1 y j ) / e

49. ACGGATGCGATCAGTTGTACTACGAGCTGACGGTCCTCAGACTTGATTA

50. There is a close relationship between dynamic programming, FSA, regular expression, and regular grammar Using FSA, you can design more complex alignment algorithms If you can draw the state diagram for a problem, it can be easily formulated into a DP problem –In particular, Hidden Markov Models –Will discuss more in a few weeks

51. Heuristic Local Aligners BLAST and alike

52. State of biological databases Sequenced Genomes: Human 3  10 9 Yeast1.2  10 7 Mouse2.7  10 9 Rat2.6  10 9 Neurospora 4  10 7 Fugu fish3.3  10 8 Tetraodon3  10 8 Mosquito 2.8  10 8 Drosophila1.2  10 8 Worm 1.0  10 8 Rice1.0  10 9 Arabidopsis1.2  10 8 sea squirts 1.6  10 8 Current rate of sequencing: 4 big labs  3  10 9 bp /year/lab 10s small labs

53. State of biological databases Number of genes in these genomes: Vertebrate: ~30,000 Insects: ~14,000 Worm: ~17,000 Fungi: ~6,000-10,000 Small organisms: 100s-1,000s Each known or predicted gene has an associated protein sequence >1,000,000 known / predicted protein sequences

54. Some useful applications of alignments Given a newly discovered gene, - Does it occur in other species? - How fast does it evolve? Assume we try Smith-Waterman: The entire genomic database Our new gene 10 4 10 10 - 10 11 May take several weeks!

55. Some useful applications of alignments Given a newly sequenced organism, - Which subregions align with other organisms? -Potential genes - Other biological characteristics Assume we try Smith-Waterman: The entire genomic database Our newly sequenced mammal 3  10 9 10 10 - 10 11 > 1000 years ???

56. BLAST Basic Local Alignment Search Tool –Altschul, Gish, Miller, Myers, Lipman, J Mol Biol 1990 –The most widely used comp bio tool –The most cited paper Which is better: long mediocre match or a few nearby, short, strong matches with the same total score? –score-wise, exactly equivalent –biologically, later may be more interesting, & is common –at least, if must miss some, rather miss the former BLAST is a heuristic emphasizing the later –speed/sensitivity tradeoff: BLAST may miss former, but gains greatly in speed

57. BLAST Main idea: 1.Construct a dictionary of all the words in the query 2.Initiate a local alignment for each word match between query and DB Running Time: O(MN) However, orders of magnitude faster than Smith-Waterman query DB

58. BLAST  Original Version Dictionary: All words of length k (~11 for DNA, 3 for proteins) Alignment initiated between words of alignment score  T (typically T = k) Alignment: Ungapped extensions until score below statistical threshold Output: All local alignments with score > statistical threshold …… query DB query scan

59. BLAST  Original Version A C G A A G T A A G G T C C A G T C C C T T C C T G G A T T G C G A Example: k = 4, T = 4 The matching word GGTC initiates an alignment Extension to the left and right with no gaps until alignment falls < 50% Output: GTAAGGTCC GTTAGGTCC

60. Gapped BLAST A C G A A G T A A G G T C C A G T C T G A T C C T G G A T T G C G A Added features: Pairs of words can initiate alignment Extensions with gaps in a band around anchor Output: GTAAGGTCCAGT GTTAGGTC-AGT

61. Example Query: gattacaccccgattacaccccgattaca (29 letters) [2 mins] Database: All GenBank+EMBL+DDBJ+PDB sequences (but no EST, STS, GSS, or phase 0, 1 or 2 HTGS sequences) 1,726,556 sequences; 8,074,398,388 total letters >gi|28570323|gb|AC108906.9| Oryza sativa chromosome 3 BAC OSJNBa0087C10 genomic sequence, complete sequence Length = 144487 Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plusgi|28570323|gb|AC108906.9| Query: 4 tacaccccgattacaccccga 24 ||||||| ||||||||||||| Sbjct: 125138 tacacccagattacaccccga 125158 Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plus Query: 4 tacaccccgattacaccccga 24 ||||||| ||||||||||||| Sbjct: 125104 tacacccagattacaccccga 125124 >gi|28173089|gb|AC104321.7| Oryza sativa chromosome 3 BAC OSJNBa0052F07 genomic sequence, complete sequence Length = 139823 Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plusgi|28173089|gb|AC104321.7| Query: 4 tacaccccgattacaccccga 24 ||||||| ||||||||||||| Sbjct: 3891 tacacccagattacaccccga 3911

62. Example Query: Human atoh enhancer, 179 letters[1.5 min] Result: 57 blast hits 1. gi|7677270|gb|AF218259.1|AF218259 Homo sapiens ATOH1 enhanc... 355 1e-95 gi|7677270|gb|AF218259.1|AF218259355 2.gi|22779500|gb|AC091158.11| Mus musculus Strain C57BL6/J ch... 264 4e-68gi|22779500|gb|AC091158.11|264 3.gi|7677269|gb|AF218258.1|AF218258 Mus musculus Atoh1 enhanc... 256 9e-66gi|7677269|gb|AF218258.1|AF218258256 4.gi|28875397|gb|AF467292.1| Gallus gallus CATH1 (CATH1) gene... 78 5e-12gi|28875397|gb|AF467292.1|78 5.gi|27550980|emb|AL807792.6| Zebrafish DNA sequence from clo... 54 7e-05gi|27550980|emb|AL807792.6|54 6.gi|22002129|gb|AC092389.4| Oryza sativa chromosome 10 BAC O... 44 0.068gi|22002129|gb|AC092389.4|44 7.gi|22094122|ref|NM_013676.1| Mus musculus suppressor of Ty... 42 0.27gi|22094122|ref|NM_013676.1|42 8.gi|13938031|gb|BC007132.1| Mus musculus, Similar to suppres... 42 0.27gi|13938031|gb|BC007132.1|42 gi|7677269|gb|AF218258.1|AF218258gi|7677269|gb|AF218258.1|AF218258 Mus musculus Atoh1 enhancer sequence Length = 1517 Score = 256 bits (129), Expect = 9e-66 Identities = 167/177 (94%), Gaps = 2/177 (1%) Strand = Plus / Plus Query: 3 tgacaatagagggtctggcagaggctcctggccgcggtgcggagcgtctggagcggagca 62 ||||||||||||| ||||||||||||||||||| |||||||||||||||||||||||||| Sbjct: 1144 tgacaatagaggggctggcagaggctcctggccccggtgcggagcgtctggagcggagca 1203 Query: 63 cgcgctgtcagctggtgagcgcactctcctttcaggcagctccccggggagctgtgcggc 122 |||||||||||||||||||||||||| ||||||||| |||||||||||||||| ||||| Sbjct: 1204 cgcgctgtcagctggtgagcgcactc-gctttcaggccgctccccggggagctgagcggc 1262 Query: 123 cacatttaacaccatcatcacccctccccggcctcctcaacctcggcctcctcctcg 179 ||||||||||||| || ||| |||||||||||||||||||| ||||||||||||||| Sbjct: 1263 cacatttaacaccgtcgtca-ccctccccggcctcctcaacatcggcctcctcctcg 1318

63. Different types of BLAST blastn: search nucleic acid database blastp: search protein database blastx: you give a nucleic acid sequence, search protein database Tblastn: you give a protein sequence, search nucleic acid database tblastx: you give a nucleic database, search nucleic acid database, implicitly translate both into protein sequences

64. Variants of BLAST MEGABLAST: Optimized to align very similar sequences Linear gap penalty NCBI-BLAST: WU-BLAST: (Wash Univ BLAST) Optimized, added features BLAT: Blast-Like Alignment Tool BlastZ: Optimized for aligning two genomes PSI-BLAST: BLAST produces many hits Those are aligned, and a pattern is extracted Pattern is used for next search; above steps iterated Sensitive for weak homologies Slower

65. Pattern hunter Instead of exact matches of consecutive matches of k-mer, we can look for discontinuous matches –My query sequence looks like: ACGTAGACTAGCAGTTAAG –Search for sequences in database that match AXGXAGXCTAXC X stands for don’t care Seed: 101011011101

66. Pattern hunter A good seed may give you both a higher sensitivity and higher specificity You may think 110110110110 is the best seed Because mutation in the third position of a codon often doesn’t change the amino acid Best seed is actually –110100110010101111 How to design such seed is an open problem May combine multiple random seeds