Search sequence databases 2 10/25/2016

Transcription

1 Search sequence databases 2 10/25/2016

2 The BLAST algorthms Ø BLAST fnds local matches between two sequences, called hgh scorng segment pars (HSPs). Step 1: Break down the query sequence and the database sequences nto k-mers. I: GCATCGGC GCATC CATCG ATCGG TCGGC J: CCATCGCCATCG CCATC CATCG ATCGC TCGCC Step 2: Sort them n a unque lst for each sequence I and J. For each unque k(5)-mer w n I, construct all ts neghbor sequences that can score at least T = 4 when algned wth w. CGCCA GCCAT CCATC CATCG When w = GCATC, there are 3x5 neghbor sequences for t: A C T CATC G A G T ATC GC C G T TC GCA A C G T GCAT C G T

3 The BLAST algorthms Thus, we have a total of (3x5+1)x4=64 neghbor sequences for I; ths has O(n) tme complexty; Step 3: Search each neghbor sequence of w of I for matches n the unque k-mers of the sequence J usng an exact match algorthm and the merger procedure; 5-mer n I, W(I) Postons n I, L(I) 5-mer n J, W(J) Postons n J L(J) Score GCATC 1 CCATC 1,7 4 CATCG 2 CATCG 2, 8 5 ATCGG 3 ATCGC 3 4 TCGGC 4 TCGCC 4 4 If number of hts for a sequence n the database s blow a predefned value, the sequence wll not be examned further; Step 4: If two non-overlappng hts are on the same dagonal and the dstance between them s less than n resdues, then extend each hts n the two drectons untl the score drops from the maxmum scores up to that ponts to a specfed amount, the resultng local algnment s an HSP.

4 The BLAST algorthms Both PAM and BLOSUM matrces can be used for the match and msmatch scorng; Gaps are allowed n the later versons of BLAST, meanng that matches on dfferent dagonals can be jonted by ntroducng gap penaltes. Step 5: The output of BLAST s the HSPs that score above a predefned cutoff value. The sgnfcance of each HSPs s evaluated by the so-called E value of the algnment score. E values are computed based on the dstrbuton of the scores of algnments of rrelevant sequences (the NULL model), whch follows an extreme value dstrbuton.

5 The BLAST algorthms Ø There are a few varants of the BLAST algorthm for dfferent applcaton purposes ( 1. blastp: search a proten database usng a proten sequence; 2. blastn: search a DNA database usng a DNA sequence; 3. blastx: search a proten database usng a DNA sequence by translatng t n sx possble open readng frames; (DNA à Proten) > Proten 4. tblastn: search a translated DNA database usng a proten sequence; Proten > (DNA à Proten) 5. tblastx: search translated DNA database usng a translated nucleotde query (DNA à Proten) > (DNA à Proten) 6. ps-blast (poston-specfc teratng blast): s a profle-based database search algorthm, therefore t s lkely to be more senstve n fndng dstantly related sequences. 7. makeblastdb: format the database, a replacement for the former formatdb program.

6 Profle representaton of sequence famles Examples of σ 70 bndng stes n E. col TACGAT TATAAT TATAAT GATACT TATGAT TATGTT TATAGT Consensus sequence Regular expresson TATAAT [TG]A[TC][GA]XT Frequency matrx A C G T To avod 0 countng, add a pseudo count of A C G T

7 Profle representaton of sequence famles Ø Profle: for a motf of n samples (sequences), the probablty of resdue b at poston s p b, = n n b, + + k 4k where n b, s the frequency of resdue b at poston ; and k s a pseudocount to avod zero probablty. Profle p b,, of the σ 70 bndng stes n E. col, pseudocount k = A C G T ,

8 Profle representaton of sequence famles Ø Poston specfc wegh (scorng) matrx (PSWM): for a motf of n samples, the weght of resdue b at poston s defned as w = b, log 2 where p b, s the probablty of resdue b at poston ; and p b s the probablty of resdue b n the background sequences. PSWM of the σ 70 bndng stes n E. col, assumng p A =p C =p G =p T = A C G T p b, p b

9 Profle representaton of sequence famles Ø Informaton content at poston of the sequence profle s gven by: p, I = p log b, Ø Logo representaton: b, b { A, C, G, T } Ø Informaton contents of a motf: I = 2 l p b p b, = 1 b { A, C, G, T} log A C G T I I = 2 + pb, log2 pb, + e( n), b { A, C, G, T} where e(n) s a correcton factor requred when one only has a few (n) samples. A pseudo count s not added when computng p b,. The heght of each base s h b, = pb, I Pb, Pb

10 Profle representaton of sequence famles Ø If we represent a sequence S = {b 1 b 2 b j b n } as a Lx4 bnary matrx: S =TATAAT {s j,b } nx4 = A C G T Ø The score a sequence S = { s j,b } aganst a profle (or PSWM) s defned as W = score( S) = { w b, j } l j= 1 s j. w. j

11 Profle representaton of sequence famles TATAAT = {S j,b } = A C G T W = { w b, j } = A C G T score ( S ) l = j= 1 s w j.. j = =

12 The PSI-BLAST algorthm for database search Ø Use a profle generated dynamcally durng the search. Ø The frst profle s generated based on a BLAST search. BlOSUM64 BLAST Results above a smlarty cutoff Profle Search usng the profle Untl no more new sequence are found or a specfed number of teratons have been done

13 Algnment statstcs Ø We need to have a statstcs framework to evaluate whether or not a ht wth a certan score n a database search s sgnfcant compared to the algnment of two unrelated sequences. Ø The goal s to derve the probablty dstrbuton of the scores for algnng two unrelated sequences for the database search algorthm. Ø If such a dstrbuton s known, then we can calculate the p-value for a gven algnment score, whch s the probablty to have a better score than ths for two unrelated sequences. Dstrbuton of scores of unrelated sequence pars p(s) s S S s

14 Dstrbuton of parwse match scores Ø We start wth a very smple case for algnng random DNA sequences wth the same length N, and we score a parwse algnment by the number of matches. A C C G T T A G G G A C T T T T A G G A * * * * * * * Ø Assume that the frequency of A, C, G and T n the database s π A, π C, π G and π T, respectvely. Then the probablty to have a match at a poston by chance s, a 2 A 2 C 2 G = π + π + π + π Ø The probablty that a parwse algnment wth a length of N has m matches by chance s gven by a bnomal dstrbuton, P( M N m m 2 T = m) = C a (1 a). N m Ø The mean and varance of ths dstrbuton s µ = Na and σ = Na (1-a), respectvely.

15 Dstrbuton of parwse match scores Ø When N s large, ths bnomal dstrbuton can be approxmated by a normal dstrbuton wth the same mean and varance. Ø Ths dstrbuton can be transformed to the standard normal dstrbuton, m µ m Na z = = σ Na( 1 a) Ø We can thnk that we convert the score m to a score z. Ø If a = 0.25, then µ = 0.25N, and σ 2 = N. Ø If two sequences of length 400 bases have m =120 match stes, then, m µ m Na z = = = = σ Na(1 a) p value = P( Z > 2.309) = Bnomal Normal µ = 4 σ 2 = 2 N = 8