MIT6_047f08_lec08_slide08

Cerevisiae s pombe nucleotides figure by mit

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Unformatted text preview: cerevisiae S. pombe Nucleotides Figure by MIT OpenCourseWare. 31-40 71-80 111-120 151-160 191-200 231-240 271-280 311-320 351-360 391-400 431-440 471-480 511-520 551-560 591-600 631-640 671-680 711-720 751-760 791-800 Kupfer et al., (2004) Eukaryotic Cell HMM Emissions Donor T Intron Acceptor A HMMs typically emit a single nucleotide per state Donor G Exon Acceptor G P(T)=1 P(A),P(G),P(C)=0 Intergenic q0 Generalized HMMs (GHMMs) • GHMMs emit more than one symbol per state • Emissions probabilities modeled by any arbitrary probabilistic model • Feature lengths are explicitly modeled W.H. Majaros (http://geneprediction.org/book/classroom.html) Courtesy of William Majoros. Used with permission. Human Introns Courtesy of Elsevier, Inc. http://www.sciencedirect.com. Used with permission. Burge, Karlin (1997) GHMM Elements • • • • States Observations Initial state probabilities Transition Probabilities Q V πi = P(q0=i) ajk= P(qi=k|qi-1=j) Like HMMs • Duration Probabilities fk(d)=P(state k of length d) • Emission Probabilities ek(Xα,α+d)=Pk(Xα…Xα+d| qk,d) Now emit a subsequence Model Abstraction in GHMMs W.H. Majaros (http://geneprediction.org/book/classroom.html) Models must return the probability of a subsequence given a state and duration Courtesy of William Majoros. Used with permission. GHMM Submodel Examples 1. WMM (Weight Matrix) ∏ P (x ) i i i=0 L−1 2. Nth-order Markov Chain (MC) ∏ P( x | x ...x )∏ P( x | x i 0 i−1 i i=0 i= n n−1 L−1 i− n ...xi−1 ) 3. Three-Periodic Markov Chain (3PMC) 5. Codon Bias 6. MDD ∏P i= 0 L−1 ( f + i)(mod 3) (xi ) ∏ P( xα i=0 n−1 +3 i α +3 i+1 α +3 i+2 x x ) Ref: Burge C (1997) Identification of complete gene structures in human genomic DNA. PhD thesis. Stanford University. PeIMM (s | g0 ...g k −1 ) = 7. Interpolated Markov Model ⎧ λG P (s | g ...g ) + (1− λG )P IMM (s | g ...g ) 0 k −1 k e 1 k −1 Ref: Salzberg SL, Delcher AL, Kasif S, White O (1998) ⎨ke Microbial gene identification using interpolate...
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