Alignments BLAST, BLAT

Transcription

1 Alignments BLAST, BLAT

2 Genome Genome Gene vs Built of DNA DNA Describes Organism Protein gene Stored as Circular/ linear Single molecule, or a few of them Both (depending on the species) Part of genome Linear Life cycle DNA-DNA-DNA- DNA-RNA-protein Size Amount per cell Information content 05Mb *) 3500Mb 100b b % 100% ~30%

3 The amount of genetic information in organisms Name Mycoplasma genitalium Escherichia coli Saccharomyces cerevisiae Drosophila melanogaster Caenorhabtitis Genome size (Mb) # genes elegans Homo sapiens Zea mays

4 The amount of genetic information in organisms Largest genome: amoeba Chaos chaos (200x human genome)

5 Sequence searching - challenges Exponential growth of databases

6 Sequence searching definition Task: Query: short, new sequence (~1000 letters) Database (searching space): very many sequences Goal: find seqs homologous to the query

7 Sequence searching definition We want: fast tool primarily a filter: most sequences will be unrelated to the query fine-tune the alignment later

8 Database Search Algorithms: Sensitivity, Selectivity True Positive (TP) a homology detected (positive) correctly (true) Signal Detected Name Yes Yes True Positive No No True Negative Yes No False Negative No Yes False Positive

9 Courtesy of Gary Benson (ISSCB 2003) Database Search Algorithms: Sensitivity, Selectivity Sensitivity =TP/(TP+FN) Selectivity =TN/(TN+FP) Sensitivity Selectivity

10 What is BLAST Basic Local Alignment Search Tool Bad news: it is only a heuristics Heuristics: A rule of thumb that often helps in solving a certain class of problems, but makes no guarantees Perkins, DN (1981) The Mind's Best Work Basic idea: High scoring segments have well conserved (almost identical) part As well conserved part are identified, extend it to the real alignment - s e q - s e q u e

11 What means well conserved for BLAST? BLAST works with k-words (words of length k) k is a parameter different for DNA (>10) and proteins (24) word w 1 is T-similar to w 2 if the sum of pair scores is at least T (eg T=12) Similar 3-words W 1 : R K P W 2 : R R P Score: = 15

12 BLAST algorithm 3 basic steps 1)Preprocess 2)Scan 3)Extend 1)Preprocess the query: extract all the k-words 2)Scan for T-similar matches in database 3)Extend them to alignments

13 BLAST, Step 1: Preprocess the query 1)Preprocess 2)Scan 3)Extend Take the query (eg LVNRKPVVP) Chop it into overlapping k-words (k=3 in this case) Query: LVNRKPVVP Word1: LVN Word2: VNR Word3: NRK For each word find all similar words (scoring at least T) Eg for RKP the following 3-words are similar: QKP KKP RQP REP RRP RKP

14 Finite state machine abstract machine constant amount of memory (states) used in computation and languages recognizes regular expressions cp dmt*pdf /home/john 1)Preprocess 2)Scan 3)Extend AC*T GGC

15 BLAST, Step 2: Find exact matches 1)Preprocess 2)Scan 3)Extend with scanning Use all the T-similar k-words to build the Finite State Machine Scan for exact matches QKP KKP RQP movement REP RRP RKP VLQKPLKKPPLVKRQPCCEVVRKPLVKVIRCLA

16 BLAST, Step 3: 1)Preprocess 2)Scan 3)Extend Extending exact matches Having the list of exact matches we extend alignment in both directions Query: L V N R K P V V P T-similar: R R P Subject: G V C R R P L K C Score: till the sum of scores drops below some level X (eg X=-100) from the best known - what with gaps?

17 Gapped BLAST (now standard) 1)Preprocess 2)Scan 3)Extend gapped local alignments are computed: much, much, much slower therefore: modified Hit criteria

18 Hit criteria query pos Extends the alignment only if there are close two hits on the same diagonal sensitivity would drop without lowering T reduces extensions (90% time is spend on extensions) Gapped local alignments are computed increased sensitivity allows us raise T raising T speeds up the search close hit, same diag dbpos 1)Preprocess 2)Scan 3)Extend

19 Gapped BLAST v BLAST We end up with same speed gapped alignments! much higher sensitivity

20 BLAST flavours blastp: protein query, protein db blastn: DNA query, DNA db blastx: DNA query, protein db in all reading frames Used to find potential translation products of an unknown nucleotide sequence tblastn: protein query, DNA db database dynamically translated in all reading frames tblastx: DNA query, DNA db all translations of query against all translations of db

21 PSI-BLAST Position-Specific Iterated BLAST A profile is derived from the result of the first search Database is searched against the profile (instead of a sequence) Up to 3 iterations

22 Profile Profile is generalized form of sequence probabilities instead of a letter A C D W Y Score of the profile scorep,i, A= B p[i,b]score blosum62 A,B profile position letter

23 Constructing a profile Take significant BLAST results Make an alignment Assign weights to sequences Construct the profile A C D W Y

24 BLAT The Blast-Like Alignment Tool Large-scale genome comparison: query can be large Preprocessing phase: BLAST: query BLAT: db

25 BLAT, Step 1: Preprocess the 1)Preprocess 2)Scan 3)Extend database Index the database with k-words k=816 for nucleotides k=35 for proteins For each k-word store in which sequences it appears k-word: RKP Hashed DB: QKP: HUgn , Gene14, IG0, KKP: haemoglobin, Gene134, IG_30, RQP: HSPHOSR1, GeneA22 RKP: galactosyltransferase, IG_1 REP: haemoglobin, Gene134, IG_30, RRP: Z17368, Creatine kinase,

26 Hashing associative arrays 1)Preprocess 2)Scan 3)Extend Indexing with the object Hash function: hash: small (fits in memory) possible objects - large Objects should be well spread x

27 Hashing - examples 1)Preprocess 2)Scan 3)Extend T9 Predictive Text in mobile phones hello in Multitap: 4, 4, 3, 3, 5, 5, 5, (pause) 5, 5, 5, 6, 6, 6 hello in T9: 4, 3, 5, 5, 6 Collisions: 4, 6: in, go

28 BLAT, Step 1: Index to find exact matches with hashing 1)Preprocess 2)Scan 3)Extend The database is preprocessed only once! (independent from the query) k-word: RKP Hashed DB: QKP: HUgn , Gene14, IG0, KKP: haemoglobin, Gene134, IG_30, RQP: HSPHOSR1, GeneA22 RKP: galactosyltransferase, IG_1 REP: haemoglobin, Gene134, IG_30, RRP: Z17368, Creatine kinase,

29 BLAT, Step 2: 1)Preprocess 2)Scan 3)Extend Hit criteria In a constant time we can get the sequences with a certain k-word relaxing hit definition -> improve sensitivity allow imperfect hits costly, huge hash grows a few times! shorten k (would lead to FP), but expect two hits (see BLAST)

30 BLAT, Step 3: Identifying homologous 1)Preprocess 2)Scan 3)Extend regions Exclude common k-words For all k-words from query find out the position in db For results (qpos, dbpos): split into buckets (64kbp) sort on the diagonal (diag=qposdbpos)

31 BLAT, Step 3: Identifying homologous 1)Preprocess 2)Scan 3)Extend regions continued from diagonally close hits (gap limit) create pre-clusters sort each pre-cluster on dbpos create clusters from close hits run Local Alignment for each cluster

32 Seeds improving sensitivity More general form of k-word is a seed The seed CTGTAT gives hits with both sequences CTCGTTATA CTAGTAATG

33 How to detect homology? Take the score of an maximal local alignment can it be obtained by chance? any score can be obtained from comparing (long enough) random sequences

34 What is a chance? Extracting local alignments from random sequences P-value (eg =001) The probability of obtaining the result by pure chance An alignment giving lower P-value than set by user is considered a hit

35 Best Local Alignments by chance Create random seqs, each 1000aa long Find the max local align Repeat # Alignments Score

36 The Statistics of local alignment Subst matrix must guarantee E(score(a,b)) < 0 for random a, b Analytical solution sum of iid variables -> normal distribution max of iid -> extreme value distribution (EVD)

37 Expected number of aligns E-value: the expected number of alignments scoring >= S E=K m n e S 2x size of seq -> 2x number aligns 2x S -> E drops exponentially

38 E-value depends on n, m E=K m n e S Example For comparing seqa with seqb: S=88 -> E = 0001 For comparing seqa with 1000 seqs: score 88 -> E=1 Important for db searching: n size of query, m - size of db

39 Deriving K, L E=Kmne S The above eq is theoretical result for gapless (g=inf) alignment K, L can be derived from the subst table For gapped case it seems that the equation holds we can derive K, L from experiments # Alignments Score

40 Bit score S' E=Kmne S Score S depends on the substitution table What if we want table-independent score? E=mn2 S' where S'= S ln K ln 2

41 Why does the BLAST work? Relevant riddle Are there at least 2 people in Amsterdam with the same number of hairs? At most hairs on each head people living in Amsterdam

42 Why does the BLAST work? Pigeons pigeonhole principle: having 9 boxes and 10 pigeons, there is at least one box with more than 1 pigeon n=9, k=7 case:

43 Why does the BLAST work? Average case pigeonhole principle describes the worst case! On average we'll expect two pigeons in the same box much earlier Birthday paradox: among 23 people, probability that they have the same birthday is > 05 note: 365 boxes and only 23 pigeons!

44 Birthday paradox

45 Why does the BLA[S]T work? Forget the T-similar words, now use only identities 2 sequences, 100 nucleotides each: What's the minimal sequence identity for which there's a string of 3 consecutive identities? 0 identities, 100 mismatches: 67 identities, 33 mismatches: 68st? but if seqs are 50% id, we'll detect it with prob 99% 28% id -> we'll detect it with prob 50% how is it calculated?

46 Expected sensitivity We assume that letters are independent I identity between seqs, for human-mouse 86% for DNA, 89% for proteins p word id =I k

47 Expected sensitivity Q - query size number of non-overlapping words R= Q k prob of a hit p detect =1 1 p wordid R

48 Expected specificity How many matches by chance (C)? G genome size C=Q k1 G k 1 4 k For h-m, to get 99% sensitivity we have to set k=7, and for Q=1000 C ~= 25,000,000 7h assuming 1/1000 per alignment