Interpolated Markov Models for Gene Finding

Transcription

1 Interpolated Markov Models for Gene Fndng BMI/CS Sprng 208 Anthony Gtter hese sldes, ecludng thrd-party materal, are lcensed under CC BY-NC 4.0 by Mark Craven, Coln Dewey, and Anthony Gtter

2 Goals for Lecture Key concepts the gene-fndng task the trade-off between potental predctve value and parameter uncertanty n choosng the order of a Markov model nterpolated Markov models 2

3 he Gene Fndng ask Gven: an uncharacterzed DNA sequence Do: locate the genes n the sequence, ncludng the coordnates of ndvdual eons and ntrons 3

4 Sources of Evdence for Gene Fndng Sgnals: the sequence sgnals e.g. splce junctons nvolved n gene epresson Content: statstcal propertes that dstngush proten-codng DNA from non-codng DNA Conservaton: sgnal and content propertes that are conserved across related sequences e.g. orthologous regons of the mouse and human genome 4

5 Gene Fndng: Search by Content Encodng a proten affects the statstcal propertes of a DNA sequence some amno acds are used more frequently than others Leu more prevalent than rp dfferent numbers of codons for dfferent amno acds Leu has 6, rp has for a gven amno acd, usually one codon s used more frequently than others ths s termed codon preference these preferences vary by speces 5

6 Codon reference n E. Col AA codon / Gly GGG.89 Gly GGA 0.44 Gly GGU Gly GGC Glu GAG 5.68 Glu GAA Asp GAU 2.63 Asp GAC

7 Readng Frames A gven sequence may encode a proten n any of the s readng frames G C A C G G A G C C G G A G C C G A G C C C G A A G C C C G 7

8 Open Readng Frames ORFs An ORF s a sequence that starts wth a potental start codon ends wth a potental stop codon, n the same readng frame doesn t contan another stop codon n-frame and s suffcently long say > 00 bases G A G G C C G G A An ORF meets the mnmal requrements to be a proten-codng gene n an organsm wthout ntrons 8

9 Markov Models & Readng Frames Consder modelng a gven codng sequence For each word we evaluate, we ll want to consder ts poston wth respect to the readng frame we re assumng readng frame G C A C G G A G C C G G A G C G C A C G C A C G G A C G G A G s n 3 rd codon poston G s n st poston A s n 2nd poston Can do ths usng an nhomogeneous model 9

10 Inhomogeneous Markov Model Homogenous Markov model: transton probablty matr does not change over tme or poston Inhomogenous Markov model: transton probablty matr depends on the tme or poston 0

11 Hgher Order Markov Models Hgher order models remember more hstory Addtonal hstory can have predctve value Eample: predct the net word n ths sentence fragment you are, gve, passed, say, see, too,? now predct t gven more hstory can you say can you oh say can you Youube

12 A Ffth Order Inhomogeneous Markov Model AAAAA start CACA CACC CACG CAC,...,, poston 5 GCAC poston 2 2

13 A Ffth Order Inhomogeneous Markov Model AAAAA AAAAA AAAAA CACA CACC CACA CACC CACA start CACG CAC CACG CAC ACAA ACAC ACAG rans. to states n pos. 2 GCAC GCAC ACA poston 2 poston 3 poston 3

14 Selectng the Order of a Markov Model But the number of parameters we need to estmate grows eponentally wth the order n+ for modelng DNA we need O4 parameters for an nth order model he hgher the order, the less relable we can epect our parameter estmates to be Suppose we have 00k bases of sequence to estmate parameters of a model for a 2 nd order homogeneous Markov chan, we d see each hstory 6250 tmes on average for an 8 th order chan, we d see each hstory ~.5 tmes on average 4

15 Interpolated Markov Models he IMM dea: manage ths trade-off by nterpolatng among models of varous orders Smple lnear nterpolaton:,...,...,..., 0 IMM n n n where 5

16 Interpolated Markov Models We can make the weghts depend on the hstory for a gven order, we may have sgnfcantly more data to estmate some words than others General lnear nterpolaton,...,,...,...,..., 0 IMM n n n n λ s a functon of the gven hstory 6

17 he GLIMMER System [Salzberg et al., Nuclec Acds Research, 998] System for dentfyng genes n bacteral genomes Uses 8 th order, nhomogeneous, nterpolated Markov models 7

18 IMMs n GLIMMER How does GLIMMER determne the values? Frst, let s epress the IMM probablty calculaton recursvely l IMM,n n n [ n n,..., n,...,,..., ] n IMM,n-,..., n,..., c,..., n,..., Let n be the number of tmes we see the hstory n our tranng set n n,..., f c n,..., 400 8

19 IMMs n GLIMMER,..., If we haven t seen n more than 400 tmes, then compare the counts for the followng: nth order hstory + base n,..., a n,..., n,..., n,..., c g t n-th order hstory + base n..., a n..., n..., n..., c g t Use a statstcal test to assess whether the dstrbutons of depend on the order 9

20 IMMs n GLIMMER nth order hstory + base n,..., a n,..., n,..., n,..., c g t n-th order hstory + base n..., a n..., n..., n..., 2 Null hypothess n test: dstrbuton s ndependent of order Defne d d pvalue If s small we don t need the hgher order hstory c g t 20

21 IMMs n GLIMMER uttng t all together c d 0,..., n n n,..., 400 f c n,..., else f d 0. 5 otherwse 400 where d 0, 2

22 ACGA 25 ACGC 40 ACGG 5 ACG IMM Eample Suppose we have the followng counts from our tranng set CGA 00 CGC 90 CGG 35 CG GA 75 GC 40 GG 65 G χ 2 test: d = χ 2 test: d = 0.40 λ 3 ACG = /400 = 0.24 λ 2 CG = 0 d < 0.5, ccg < 400 λ G = cg >

23 IMM Eample Contnued Now suppose we want to calculate IMM,0 IMM, G G G G G IMM, 2 2 IMM,2 G G CG CG CG CG IMM,2 3 3 IMM,3 G ACG CG ACG ACG ACG ACG IMM,3 ACG 23

24 Gene Recognton n GLIMMER Essentally ORF classfcaton For each ORF calculate the probablty of the ORF sequence n each of the 6 possble readng frames f the hghest scorng frame corresponds to the readng frame of the ORF, mark the ORF as a gene For overlappng ORFs that look lke genes score overlappng regon separately predct only one of the ORFs as a gene 24

25 Gene Recognton n GLIMMER ORF meetng length requrement JCVI Low scorng ORF Hgh scorng ORF 25

26 GLIMMER Eperment 8 th order IMM vs. 5 th order Markov model raned on 68 genes ORFs really ested on 77 annotated more or less known genes 26

27 GLIMMER Results FN F &? GLIMMER has greater senstvty than the baselne It s not clear whether ts precson/specfcty s better 27