1. CMSC 828N lecture notes: Eukaryotic Gene Finding with Generalized HMMs Mihaela Pertea and Steven Salzberg Center for Bioinformatics and Computational Biology, University of Maryland

2. Eukaryotic Gene Finding Goals Given an uncharacterized DNA sequence, find out: –Which regions code for proteins? –Which DNA strand is used to encode each gene? –Where does the gene starts and ends? –Where are the exon-intron boundaries in eukaryotes? Overall accuracy usually below 50%

3. Gene Finding: Different Approaches Similarity-based methods. These use similarity to annotated sequences like proteins, cDNAs, or ESTs (e.g. Procrustes, GeneWise). Ab initio gene-finding. These don’t use external evidence to predict sequence structure (e.g. GlimmerHMM, GeneZilla, Genscan, SNAP). Comparative (homology) based gene finders. These align genomic sequences from different species and use the alignments to guide the gene predictions (e.g. TWAIN, SLAM, TWINSCAN, SGP-2). Integrated approaches. These combine multiple forms of evidence, such as the predictions of other gene finders (e.g. Jigsaw, EuGène, Gaze)

4. Why ab-initio gene prediction? Ab initio gene finders can predict novel genes not clearly homologous to any previously known gene.

5. …ACTGATGCGCGATTAGAGTCATGGCGATGCATCTAGCTAGCTATATCGCGTAGCTAGCTAGCTGATCTACTATCGTAGC… Signal sensor We slide a fixed-length model or “window” along the DNA and evaluate score(signal) at each point: When the score is greater than some threshold (determined empirically to result in a desired sensitivity), we remember this position as being the potential site of a signal. The most common signal sensor is the Weight Matrix: A 100% A = 31% T = 28% C = 21% G = 20% T 100% G 100% A = 18% T = 32% C = 24% G = 26% A = 19% T = 20% C = 29% G = 32% A = 24% T = 18% C = 26% G = 32% Identifying Signals In DNA with a Signal Sensor

6. Start and stop codon scoring Score all potential start/stop codons within a window of length 19. The probability of generating the sequence is given by: (WAM model or inhomogeneous Markov model) CATCCACCATGGAGAACCACCATGG Kozak consensus

7. Donor/Acceptor sites at location k: DS(k) = S comb (k,16) + (S cod (k-80)-S nc (k-80)) + (S nc (k+2)-S cod (k+2)) AS(k) = S comb (k,24) + (S nc (k-80)-S cod (k-80)) + (S cod (k+2)-S nc (k+2)) S comb (k,i) = score computed by the Markov model/MDD method using window of i bases S cod/nc (j) = score of coding/noncoding Markov model for 80bp window starting at j Splice Site Scoring

8. Coding Statistics Unequal usage of codons in the coding regions is a universal feature of the genomes We can use this feature to differentiate between coding and non- coding regions of the genome Coding statistics - a function that for a given DNA sequence computes a likelihood that the sequence is coding for a protein Many different ones ( codon usage, hexamer usage,GC content, Markov chains, IMM, ICM.)

9. A three-periodic ICM uses three ICMs in succession to evaluate the different codon positions, which have different statistics: ATC GAT CGA TCA GCT TAT CGC ATC ICM 0 ICM 1 ICM 2 P[C|M 0 ] P[G|M 1 ] P[A|M 2 ] The three ICMs correspond to the three phases. Every base is evaluated in every phase, and the score for a given stretch of (putative) coding DNA is obtained by multiplying the phase-specific probabilities in a mod 3 fashion: GlimmerHMM uses 3-periodic ICMs for coding and homogeneous (non-periodic) ICMs for noncoding DNA. 3-periodic ICMs

10. The Advantages of Periodicity and Interpolation

11. HMMs and Gene Structure Nucleotides {A,C,G,T} are the observables Different states generate nucleotides at different frequencies A simple HMM for unspliced genes: AAAGC ATG CAT TTA ACG AGA GCA CAA GGG CTC TAA TGCCG The sequence of states is an annotation of the generated string – each nucleotide is generated in intergenic, start/stop, coding state ATG TAA

12. An HMM is a following: An HMM is a stochastic machine M=(Q, , P t, P e ) consisting of the following: a finite set of states, Q={q 0, q 1,..., q m } a finite alphabet  ={s 0, s 1,..., s n } a transition distribution P t : Q×Q  [0,1] i.e., P t (q j | q i ) an emission distribution P e : Q×   [0,1] i.e., P e (s j | q i ) q 0q 0 100% 80% 15% 30% 70% 5% R =0% Y = 100% q 1 Y =0% R = 100% q 2 M 1 =({q 0,q 1,q 2 },{ Y, R },P t,P e ) P t ={(q 0,q 1,1), (q 1,q 1,0.8), (q 1,q 2,0.15), (q 1,q 0,0.05), (q 2,q 2,0.7), (q 2,q 1,0.3)} P e ={(q 1, Y,1), (q 1, R,0), (q 2, Y,0), (q 2, R,1) } An Example Recall: “Pure” HMMs

13. exon length geometric distribution geometric HMMs & Geometric Feature Lengths

14. Generalized Hidden Markov Models Advantages: * Submodel abstraction * Architectural simplicity * State duration modeling Disadvantages: * Decoding complexity

15. A GHMM is a following: A GHMM is a stochastic machine M=(Q, , P t, P e, P d ) consisting of the following: a finite set of states, Q={q 0, q 1,..., q m } a finite alphabet  ={s 0, s 1,..., s n } a transition distribution P t : Q×Q  [0,1] i.e., P t (q j | q i ) an emission distribution P e : Q×  * × N  [0,1] i.e., P e (s j | q i,d j ) a duration distribution P e : Q× N  [0,1] i.e., P d (d j | q i ) each state now emits an entire subsequence rather than just one symbol feature lengths are now explicitly modeled, rather than implicitly geometric emission probabilities can now be modeled by any arbitrary probabilistic model there tend to be far fewer states => simplicity & ease of modification Key Differences Ref: Kulp D, Haussler D, Reese M, Eeckman F (1996) A generalized hidden Markov model for the recognition of human genes in DNA. ISMB '96. Generalized HMMs

16. emission prob. transition prob. Recall: Decoding with an HMM

17. emission prob. transition prob. duration prob. Decoding with a GHMM

18. Given a sequence S, we would like to determine the parse  of that sequence which segments the DNA into the most likely exon/intron structure: The parse  consists of the coordinates of the predicted exons, and corresponds to the precise sequence of states during the operation of the GHMM (and their duration, which equals the number of symbols each state emits). This is the same as in an HMM except that in the HMM each state emits bases with fixed probability, whereas in the GHMM each state emits an entire feature such as an exon or intron. parse  exon 1exon 2exon 3 AGCTAGCAGTCGATCATGGCATTATCGGCCGTAGTACGTAGCAGTAGCTAGTAGCAGTCGATAGTAGCATTATCGGCCGTAGCTACGTAGCGTAGCTC sequence S prediction Gene Prediction with a GHMM

19. GHMMs generalize HMMs by allowing each state to emit a subsequence rather than just a single symbol Whereas HMMs model all feature lengths using a geometric distribution, coding features can be modeled using an arbitrary length distribution in a GHMM Emission models within a GHMM can be any arbitrary probabilistic model (“submodel abstraction”), such as a neural network or decision tree GHMMs tend to have many fewer states => simplicity & modularity GHMMs generalize HMMs by allowing each state to emit a subsequence rather than just a single symbol Whereas HMMs model all feature lengths using a geometric distribution, coding features can be modeled using an arbitrary length distribution in a GHMM Emission models within a GHMM can be any arbitrary probabilistic model (“submodel abstraction”), such as a neural network or decision tree GHMMs tend to have many fewer states => simplicity & modularity GHMMs Summary

20. GlimmerHMM architecture I2I1I0 Exon2Exon1Exon0 Exon Sngl Init Exon I1I2 Exon1Exon2 Term Exon I0 Exon0 Exon Sngl Init Exon + forward strand - backward strand Phase-specific introns Four exon types Uses GHMM to model gene structure (explicit length modeling) WAM and MDD for splice sites ICMs for exons, introns and intergenic regions Different model parameters for regions with different GC content Can emit a graph of high- scoring ORFS Intergenic

21. Key steps in the GHMM Dynamic Programming Algorithm Scan left to right At each signal, look bacward (left) –Find all compatible signals –Take MAX score –Repeat for all reading frames

22. Key steps in the GHMM Dynamic Programming Algorithm GT AG ATG Look back at all previous compatible signals

23. Key steps in the GHMM Dynamic Programming Algorithm GT AG  Retrieve score of best parse up to previous site  Compute score of the exon linking AG to GT  Use Markov chain or other methods  Look up probability of exon length  Multiply probabilities (or add logs)

24. Key steps in the GHMM Dynamic Programming Algorithm GT AG ATG MAX over all previous sites Store for each frame: MAX score Reading frame Pointer backward

25. GHMM Dynamic Programming Algorithm: Introns AG GT Huge number of potential signals: how far back to look?

26. AG GT  Limit look-back with maximum intron length  Or, use other techniques  Compute score of intron linking GT to AG  Score donor site with donor site model  Score intron with Markov chain  Score acceptor with acceptor site model  Look up probability of intron length  Multiply probabilities (or add logs) GHMM Dynamic Programming Algorithm: Introns

27. θ=(P t,P e,P d ) Training the Gene Finder

28. estimate via labeled training data construct a histogram of observed feature lengths Training for GHMMs

29. –parameter mismatching: train on a close relative –use a comparative GF trained on a close relative –use BLAST to find conserved genes & curate them, use as training set –augment training set with genes from related organisms, use weighting –manufacture artificial training data long ORFs –be sensitive to sample sizes during training by reducing the number of parameters (to reduce overtraining) fewer states (1 vs. 4 exon states, intron=intergenic) lower-order models –pseudocounts –smoothing (esp. for length distributions) Gene Finding in the Dark: Dealing with Small Sample Sizes

30. Evaluation of Gene Finding Programs Nucleotide level accuracy TN FPFNTN TPFN TP FN REALITY PREDICTION Sensitivity: Precision:

31. More Measures of Prediction Accuracy Exon level accuracy REALITY PREDICTION WRONG EXON CORRECT EXON MISSING EXON

32. Nuc Sens Nuc Prec Nuc Acc Exon Sens Exon Prec Exon Acc Exact Genes GlimmerHMM86%72%79%72%62%67% 17% Genscan86%68%77%69%60%65% 13% GlimmerHMM’s performace compared to Genscan on 963 human RefSeq genes selected randomly from all 24 chromosomes, non-overlapping with the training set. The test set contains 1000 bp of untranslated sequence on either side (5' or 3') of the coding portion of each gene. GlimmerHMM on human genes (circa 2002)

33. GlimmerHMM on other species Nucleotide Level Exon LevelCorretly Predicted Genes Size of test set SnPrSnPr Arabidopsis thaliana 97%99%84%89%60%809 genes Cryptococcus neoformans 96%99%86%88%53%350 genes Coccidoides posadasii 99% 84%86%60%503 genes Oryza sativa95%98%77%80%37%1323 genes GlimmerHMM has also been trained on: Aspergillus fumigatus, Entamoeba histolytica, Toxoplasma gondii, Brugia malayi, Trichomonas vaginalis, and many others.

34. Ab initio gene finding in the model plant Arabidopsis thaliana (circa 2004) All three programs were tested on a test data set of 809 genes, which did not overlap with the training data set of GlimmerHMM. All genes were confirmed by full-length Arabidopsis cDNAs and carefully inspected to remove homologues. Arabidopsis thaliana test results NucleotideExonGene SnPrAccSnPrAccSnPrAcc GlimmerHMM979998848986.5606160.5 SNAP969997.5838584605758.5 Genscan+939996748177.535