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2Lyle H Ungar, University of Pennsylvania
Markov ModelMarkov ModelMarkov ModelMarkov Model
Sequence of states E..g., exon, intron, …
Sequence of observations E.g., AATCGGCGT Called “emissions”
Probability of transition The Markov matrix Mij = p(Sj | Si)
Probability of emission P(Ok|Sj)
3Lyle H Ungar, University of Pennsylvania
Markov Matrix propertiesMarkov Matrix propertiesMarkov Matrix propertiesMarkov Matrix properties
Columns of M sum to one You must transition somewhere
Multiplying by M gives probilites of the state of the next item in the sequence
P(Sj) = Mij P(Si)
0.67 = 0.4 0.7 0.1
0.33 0.6 0.3 0.9
4Lyle H Ungar, University of Pennsylvania
Prokaryotic HMMProkaryotic HMMProkaryotic HMMProkaryotic HMM
6Lyle H Ungar, University of Pennsylvania
Hidden Markov ModelHidden Markov ModelHidden Markov ModelHidden Markov Model
Can’t observe the states Need to estimate using HMM using an
EM algorithm “Baum-Welsh” or “forward-backward”
Given an HMM, for a new sequence, find the most likely states Done using dynamic programming “Viterbi algorithm”
7Lyle H Ungar, University of Pennsylvania
More Realistic HMMsMore Realistic HMMsMore Realistic HMMsMore Realistic HMMs
Frame Shifts need more states
Generalized HMMs (GMMs) Distribution of exon lengths is not
geometric
Example gene finders Genscan
8Lyle H Ungar, University of Pennsylvania
How well do they work?How well do they work?How well do they work?How well do they work?
Define criteria for working wellBase level, exon level or
entire gene?
Sn: Sensitivity = fraction of correct exons over actual exons
Sp: Specificity = fraction of correct exons over predicted exons
9Lyle H Ungar, University of Pennsylvania
HMM accuraciesHMM accuraciesHMM accuraciesHMM accuracies
http://www1.imim.es/courses/SeqAnalysis/GeneIdentification/Evaluation.html
10Lyle H Ungar, University of Pennsylvania
Combined methodsCombined methodsCombined methodsCombined methods
HMM plus sequence similarity Twinscan
11Lyle H Ungar, University of Pennsylvania
Align using an HMMAlign using an HMMAlign using an HMMAlign using an HMM
ACCGGA__TTTG__CGGACGTAT_DDMMMMIIMMMD
ACCGGA__TTTG__CGGACGTAT_DDMMMMIIMMMD