Interpolated Markov Models for Gene Finding

Transcription

1 Iterpolated Markov Models for Gee Fdg BMI/CS Sprg 2009 Mark Crave The Gee Fdg Task Gve: a ucharacterzed DNA sequece Do: locate the gees the sequece, cludg the coordates of dvdual eos ad tros mage from the UCSC Geome Browser

2 Gee Epresso Revsted eukaryotes prokaryotes Sources of Evdece for Gee Fdg sgals: the sequece sgals (e.g. splce juctos volved gee epresso cotet: statstcal propertes that dstgush protecodg DNA from o-codg DNA coservato: sgal ad cotet propertes that are coserved across related sequeces (e.g. sytec regos of the mouse ad huma geome

3 Gee Fdg: Search by Cotet ecodg a prote affects the statstcal propertes of a DNA sequece some amo acds are used more frequetly tha others (Leu more popular tha Trp dfferet umbers of codos for dfferet amo acds (Leu has 6, Trp has for a gve amo acd, usually oe codo s used more frequetly tha others ths s termed codo preferece these prefereces vary by speces Codo eferece E. Col AA codo / Gly GGG.89 Gly GGA 0.44 Gly GGU Gly GGC Glu GAG 5.68 Glu GAA Asp GAU 2.63 Asp GAC 43.26

4 Readg Frames a gve sequece may ecode a prote ay of the s readg frames G C T A C G G A G C T T C G G A G C C G A T G C C T C G A A G C C T C G Ope Readg Frames (ORFs a ORF s a sequece that starts wth a potetal start codo eds wth a potetal stop codo, the same readg frame does t cota aother stop codo -frame ad s suffcetly log (say > 00 bases G T T A T G G C T T C G T G A T T a ORF meets the mmal requremets to be a prote-codg gee a orgasm wthout tros

5 Markov Models & Readg Frames cosder modelg a gve codg sequece for each word we evaluate, we ll wat to cosder ts posto wth respect to the readg frame we re assumg readg frame G C T A C G G A G C T T C G G A G C G C T A C G C T A C G G T A C G G A G s 3 rd codo posto G s st posto A s 2d posto ca do ths usg a homogeous model A Ffth Order Ihomogeous Markov Cha AAAAA AAAAA AAAAA CTACA CTACC CTACA CTACC start CTACG CTACT CTACG CTACT TACAA TACAC TACAG trastos to states pos 2 GCTAC GCTAC TACAT TTTTT TTTTT TTTTT posto 2 posto 3 posto

6 Selectg the Order of a Markov Cha Model hgher order models remember more hstory addtoal hstory ca have predctve value eample: predct the et word ths setece fragmet eds (up, t, well, of,? ow predct t gve more hstory that eds well that eds All s well that eds Selectg the Order of a Markov Cha Model but the umber of parameters we eed to estmate grows epoetally wth the order + for modelg DNA we eed O(4 parameters for a th order model the hgher the order, the less relable we ca epect our parameter estmates to be estmatg the parameters of a 2 d order homogeous Markov cha from the complete geome of E. Col, we d see each word > 72,000 tmes o average estmatg the parameters of a 8 th order cha, we d see each word ~ 5 tmes o average

7 Iterpolated Markov Models the IMM dea: maage ths trade-off by terpolatg amog models of varous orders smple lear terpolato: IMM where ( #" = = " + " ( " ( ( Iterpolated Markov Models we ca make the weghts deped o the hstory for a gve order, we may have sgfcatly more data to estmate some words tha others geeral lear terpolato IMM ( = " ( + " ( " ( ( (

8 The GLIMMER System Salzberg et al., 998 system for detfyg gees bacteral geomes uses 8 th order, homogeeous, terpolated Markov cha models IMMs GLIMMER how does GLIMMER determe the values? frst, let s epress the IMM probablty calculato recursvely IMM, ( " ( [! " ( c( ",..., " ",..., " ( = ] IMM,- (! + + let be the umber of tmes we see the hstory our trag set " ( #,..., # = f c( #,..., # > 400

9 IMMs GLIMMER! f we have t see! more tha 400 tmes, the compare the couts for the followg: th order hstory + base!, a!, c!, g!, t (-th order hstory + base! +, a! +, c! +, g! +, t 2 use a statstcal test (! to get a value d dcatg our cofdece that the dstrbutos represeted by the two sets of couts are dfferet IMMs GLIMMER puttg t all together $! c( # d &! " ' ' ' ( ( ',..., ' = else f d. f c( otherwse ' % 0 5 > 400 where d!(0,

10 ACGA 25 ACGC 40 ACGG 5 ACGT IMM Eample suppose we have the followg couts from our trag set CGA 00 CGC 90 CGG 35 CGT GA 75 GC 40 GG 65 GT ! 2 test: d = 0.857! 2 test: d = 0.4 " 3 (ACG = # 00/400 " 2 (CG = 0 (d < 0.5, c(cg < 400 " (G = (c(g > 400 IMM Eample (Cotued ow suppose we wat to calculate IMM, IMM,2 = ( T G (! ( G ( T G = " ( G ( T G + " ( T CG = " ( CG ( T CG + " 2 = ( T G IMM,0 (! ( CG 2 IMM,3 ( T ( T ACG IMM, ( T G IMM,3 (T ACG = " 3 (ACG(T ACG + ( # " 3 (ACG IMM,2 (T CG = 0.24 $ (T ACG + (# 0.24 $ (T G

11 Gee Recogto GLIMMER essetally ORF classfcato for each ORF calculate the prob of the ORF sequece each of the 6 possble readg frames f the hghest scorg frame correspods to the readg frame of the ORF, mark the ORF as a gee for overlappg ORFs that look lke gees score overlappg rego separately predct oly oe of the ORFs as a gee GLIMMER Epermet 8 th order IMM vs. 5 th order Markov model traed o 68 gees (ORFs really tested o 77 aotated (more or less kow gees

12 GLIMMER Results TP FN FP & TP? GLIMMER has greater sestvty tha the basele t s ot clear f ts precso/specfcty s better A Alteratve Approach: Back-off Models devsed for laguage modelg [Katz, IEEE Trasactos o Acoustcs, Speech ad Sgal ocessg, 987] % (" # c(,..., " c( ( ",..., " = ",..., ", f c(,..., > k " ' & (' $ ( "+,..., ", otherwse use th order probablty f we ve see ths sequece (hstory + curret character k tmes otherwse back off to lower-order

13 A Alteratve Approach: Back-off Models % (" # c(,..., " c( ( ",..., " = ",..., ", f c( ",..., > k ' & (' $ ( "+,..., ", otherwse why do we eed! ad "?!: save some probablty mass for sequeces we have t see ": dstrbute ths saved mass to lower-order sequeces (dfferet " for each hstory; really "(! + ths s mportat for atural laguage, where there are may words that could follow a partcular hstory Smple Back-off Eample ( % % $ c( %,...,!( %' = # c( %,...,! " & ( %, f % + % c(, % > k otherwse gve trag sequece: TAACGACACG suppose! = 0.2 ad k = 0 ( A = ( C = ( G = ( T = ( A A = (!" 4 = 3 ( C A = (!" 4 = ( G A = ' ( $ 0.2 % " ( =! 0.2 ( ( & G + T G # 0.3 ( T A = ' ( $ 0.2 % " ( =! 0. ( ( & G + T T # 0.3