Introduction to Sequence Analysis

Transcription

1 References Introducton to Seuence Analyss Chaters 2 & 7 of Bologcal Seuence Analyss (Durbn et al., 2001) Utah State Unversty Srng 2012 STAT 5570: Statstcal Bonformatcs Notes Revew Genes are: - seuences of DNA that do somethng - can be exressed as a strng of: nuclec acds: A,C,G,T (4-letter alhabet) Central Dogma of Molecular Bology DNA mrna roten bo. acton rotens can be exressed as a strng of: amno acds: (20-letter alhabet) (sometme 24 due to smlartes ) Why look at roten seuence? Levels of roten structure rmary structure: order of amno acds Secondary structure: reeatng structures (beta-sheets and alha-helces) n backbone Tertary structure: full three-dmensonal folded structure Quartenary structure: nteracton of multle backbones Seuence shae functon Smlar seuence smlar functon -? 3 4

2 Consder smle arwse algnment Seuence 1: HEAGAWGHEE Seuence 2: AWHEAE ossble algnments Seuence 1: HEAGAWGHEE Seuence 2: AWHEAE How smlar are these two seuences? Match u exactly? Subseuences smlar? Whch ostons could be ossbly matched wthout severe enalty? Algnment 1: HEAGAWGHEE AWHEAE Algnment 2: HEAGAWGHEE AW-HE-AE Algnment 3: HEA-GAWGHEE AWHEAE Algnment 4: HEAGAWGHE-E AW-HEAE To fnd the best algnment, need some way to: rate algnments Thnk of gas n algnment as: mutatonal nserton or deleton 5 6 Basc dea of scorng otental algnments + score: denttes and conservatve substtutons - score: non- conservatve changes - (not exected n real algnments) Add score at each oston Euvalent to assumng mutatons are: ndeendent Reasonable assumton for DNA and rotens but not structural RNA s Some Notaton a ab { a, b from common ancestor} Let x be seuence 1, and Random Model : Matched Model : assume ndeendence of seuences fre. of letter a n seuence, x, y R y be seuence 2. x, y M x j x y assume resdues a & b are algned as a ar wth rob. ab y j 7 8

3 Comare these two models Odds Rato : Need : ab x, y M x, y R Log Odds Rato : S x s( x, y ), x y ab where s( a, b) log a y b log lkelhood rato of ar (a,b) occurrng as algned ar, as oosed to unalgned ar Score Matrx or substtuton matrx A R N D... Y V A R N D s(a,b) Y V 0 3 Ths s a orton of the BLOSUM50 substtuton matrx; others exst. These are scaled and rounded log-odds values (for comutatonal effcency) 9 10 How to get these substtuton values? Basc dea: Look at exstng, known algnments Comare seuences of algned rotens and look at substtuton freuences Ths s a chcken-or-the-egg roblem: - algnment - - scorng scheme - Maybe better to base algnment on: tertary structures (or some other algnment) Some substtuton matrx tyes BLOSUM (Henkoff) BLOCK substtuton matrx derved from BLOCKS database set of algned ungaed roten famles, clustered accordng to threshold ercentage (L) of dentcal resdues comare resdue freuences between clusters L=50 BLOSUM50 AM (Dayhoff) ercentage of accetable ont mutatons er 10 8 years derved from a general model for roten evoluton, based on number L of AMs (evolutonary dstance) AM1 from comarng seuences wth <1% dvergence L=250 AM250 = AM1^

4 Whch substtuton matrx to use? No unversal best way In general: low AM fnd short algnments of smlar se. hgh AM fnd longer, weaker local algnments BLOSUM standards: BLOSUM50 for algnment wth gas BLOSUM62 for ungaed algnments hgher AM, lower BLOSUM more dvergent (lookng for more dstantly related rotens) A reasonable strategy: BLOSUM62 comlemented wth AM250 Whch matrx for algnng DNA seuences? The BLOSUM and AM matrces are based on smlartes between amno acds - no such smlarty assumed for nuclec acds; resdues ether match or they don t Untary matrx: dentty matrx +1 for dentcal match (or +3 or ) 0 for non-match (or -2 or ) How to score gas? Tabular reresentaton of algnment One way: affne ga enalty length of ga lnear transformaton followed by a translaton ( g ) d ( g 1) e ga oenng enalty ga extenson enalty (e < d) Thnk of gas n algnment as: mutatonal nserton or deleton start wth 0 0 A W H E A E H E A G A W G H E E begn (or contnue) ga: -d (or -e) match letters (resdues): + s(a,b) Fll n table to gve max. of ossble values at each successve element kee track of whch drecton generated max. then use the ath that gves hghest fnal score (lower rght corner) 15 16

5 Algnment algorthms Global: Needleman-Wunsch - fnd otmal algnment for entre seuences (rev. slde) Local: Smth-Waterman - fnd otmal algnment for subseuences Reeated matches - allow for startng over seuences (fnd motfs n long seuences) Overla matches - allow for one seuence to contan or overla the other (for comarng fragments) Heurstc: BLAST, FASTA - for comarng a sngle seuence aganst a large database of seuences Comare global and local algnments Seuence 1: HEAGAWGHEE Seuence 2: AWHEAE Global arwse Algnment (1 of 1) attern: [1] HEAGAWGHE-E subject: [1] ---AW-HEAE score: 23 Local arwse Algnment (1 of 1) attern: [5] AWGHE-E subject: [2] AW-HEAE score: Smle arwse algnment n R lbrary(bostrngs) # Defne seuences se1 <- "HEAGAWGHEE" se2 <- "AWHEAE" # erform global algnment g.algn <- arwsealgnment(se1, se2, substtutonmatrx='blosum50', gaoenng=-4, gaextenson=-1, tye='global') g.algn # erform local algnment l.algn <- arwsealgnment(se1, se2, substtutonmatrx='blosum50', gaoenng=-4, gaextenson=-1, tye='local') l.algn Look at a bgger examle The arsesm ackage (not n current Boconductor) has a comanon fle (ex.fasta) wth seuence data for 67 roten seuences n FASTA format: >At1g01010 NAC doman roten, utatve MEDQVGFGFRNDEELVGHYLRNKIEGNTSRDVEVAISEVNICSYDWNLRFQSKYKSRD... VISWIILVG >At1g01020 unknown roten MAASEHRCVGCGFRVKSLFIQYSGNIRLMKCGNCKEVADEYIECERMIIFIDLILHRK VYRHVLYNAINATVNIQHLLWKLVFAYLLLDCYRSLLLRKSDEESSFSDSVLLSIKVR SFLFNGLN >At1g01030 DNA-bndng roten, utatve MDLSLATTTTSSDQEQDRDQELTSNIGASSSSGSGNNNNLMMMIEKEHMFDKVV... EESWLVRGEIGASSSSSSALRLNLSTDHDDDNDDGDDGDDDQFAKKGKSSLSLNFN >At1g01040 CAF roten MVMEDEREATIKSYWLDACEDISCDLIDDLVSEFDSSVAVNESTDENGVINDFFGGI... DKDRKRARVCSYQSERSNLSGRGHVNNSREGDRFMNRKRTRNWDEAGNNKKKRECNNYRR htt:// 20

6 Bgger examle: For a gven seuence (subject), "At1g01010 NAC doman roten, utatve" fnd the most smlar seuence n a lst (attern) "At1g01190 cytochrome 450, utatve" Global arwse Algnment (1 of 1) attern: [1] MRTEIESLWVF-----ALASKFNIYMQQHFASLL---VAIAITWFTITI... subject: [1] MEDQVG--FGFRNDEELVGH---YLRNKIEGNTSRDVEVAIS EVNIC... score: 313 # read n data n FASTA format f1 <- "C://folder//ex.fasta" # fle saved from webste (slde 20) ff <- read.aastrngset(f1, "fasta") # comare frst seuence (subject) wth the others (attern) sub <- ff[1] names(sub) # "At1g01010 NAC doman roten, utatve" at <- ff[2:length(ff)] # get scores of all global algnments s <- arwsealgnment(at, sub, substtutonmatrx='am250', gaoenng=-4, gaextenson=-1, tye='global', scoreonly=true) hst(s, man=c('global algnment scores wth',names(sub))) # look at best algnment k <- whch.max(s) names(at[k]) # "At1g01190 cytochrome 450, utatve" arwsealgnment(at[k], sub, substtutonmatrx='am250', gaoenng=-4, gaextenson=-1, tye='global') (names refer to gene name or locus) hylogenetc trees ntro & motvaton hylogeny: relatonsh among seces hylogenetc tree: vsualzaton of hylogeny (usually a dendrogram) How can we do ths here? Consder multle seuences (maybe from dfferent seces) Smlar seuences are called homologues - descended from common ancestor seuence? - smlar functon? Want to vsualze these relatonshs Quck revew of agglomeratve clusterng - defne dstance between onts - each ont (seuence here) starts as ts own cluster - fnd closest clusters and merge them - Lnkage: how to defne dstance between new cluster and exstng clusters 23 24

7 Recall lnkage methods (a few) Defnng dstance between seuences & j Let,, be clusters, d d be the dstance, be thedstance between and the new, cluster, and n be thenumber of onts n cluster. Sngle (nearest neghbor) : d mn d Average : d Ward : d n n d n n d nd UGMA : d n d n n d n / 2 n n d, d n d Why not Eucldean, earson, etc.? - seuences are not onts n sace Could use (after arwse algnment): 1 normalzed score {score (or 0) dvded by smaller selfscore} 1 %dentty based on length of shorter seuence 1 %smlarty Makng use of models for resdue substtuton (for DNA): Let f = fracton of stes n arwse algnment where resdues dffer = 1 - %dentty Jukes-Cantor dstance: d j log1 4 f / Vsualze relatonshs among 11 seuences from ex.fasta fle # Functon to get hylogenetc dstance matrx for multle seuences # -- don't worry about syntax here; just see next slde for usage get.hylo.dst <- functon(ses,subm='blosum62',oen=-4,ext=-1,tye='local') { # Get matrx of arwse local algnment scores num.se <- length(ses) s.mat <- matrx(ncol=num.se, nrow=num.se) for( n 1:num.se) { for(j n :num.se) { s.mat[,j] <- s.mat[j,] <- arwsealgnment(ses[], ses[j], substtutonmatrx=subm, gaoenng=oen, gaextenson=ext, tye=tye, scoreonly=true) } } # Convert scores to normalzed scores norm.mat <- matrx(ncol=num.se, nrow=num.se) for( n 1:num.se) { for(j n :num.se) { mn.self <- mn(s.mat[,],s.mat[j,j]) norm.mat[,j] <- norm.mat[j,] <- s.mat[,j]/mn.self } norm.mat[,] <- 0 } } # Return dstance matrx colnames(norm.mat) <- rownames(norm.mat) <- substr(names(ses),1,9) return(as.dst(1-norm.mat)) 27 28

8 R code for hylogenetc trees from arwse dstances # Choose seuences ses <- ff[50:60] # recall ff object from slde 22 # hylogenetc tree dmat <- get.hylo.dst(ses,subm='blosum62',tye='local') lot(hclust(dmat,method="average"),man='hylogenetc Tree', xlab='normalzed Score') # heatma reresentaton lbrary(cluster) lbrary(rcolorbrewer) hmcol <- colorramalette(brewer.al(10,"uor"))(256) hclust.ave <- functon(d){hclust(d,method="average")} heatma(as.matrx(dmat),sym=true,col=hmcol, cexrow=4,cexcol=1,hclustfun=hclust.ave) Asde: vsualzng seuence content tab <- table(strslt(as.character(ff[1]),"")) use.col <- re('yellow',length(tab)) t <- names(tab)=='s' use.col[t] <- 'blue' barlot(tab,col=use.col,man=names(ff[1])) robably more useful for: assessng C-G counts n DNA seuences lbrary(affy); lbrary(hgu95av2.db); lbrary(annotate) GI <- as.lst(hgu95av2accnum) n.gi <- names(gi) t <- n.gi=="1950_s_at" se <- getseq(gi[t]) tab <- table(strslt(se,"")) use.col <- re('yellow', length(tab)) t <- names(tab)=='g' use.col[t] <- 'blue' barlot(tab,col=use.col, man="seuence content of 1950_s_at on hgu95av2") Summary Look at seuence smlarty to fnd: functonal smlarty -? arwse algnment bascs Scorng matrx BLOSUM, AM, etc. Algnment algorthm global, local, etc. Comng u: searchng onlne databases (BLAST) multle algnments attern (motf) fndng usng seuencng to measure gene exresson 31 32