(H)MMs in gene prediction and similarity searches

What is an HMM? (Eddy2004)

•States

•Transition Probabilities

•Emission Probabilities

What is hidden? (Eddy2004)

•State Path

Log (product of transition and emission probabilities)Log (1 x 0.25 x 0.9 x 0.25 x 0.9 x 0.25 …0.9 x 0.4) = -41.22

What is hidden? (Eddy2004)

•State Path

Using HMMs• Given the parameters of the model, compute the probability of

a particular output sequence. This problem is solved by the forward algorithm.

• Given the parameters of the model, find the most likely sequence of hidden states that could have generated a given output sequence. This problem is solved by the Viterbi algorithm.

• Given an output sequence or a set of such sequences, find the most likely set of state transition and output probabilities. In other words, train the parameters of the HMM given a dataset of sequences. This problem is solved by the Baum-Welch algorithm.

Profile Hidden Markov Models

• Statistical model of multiple sequence alignments

• Position-specific description of the level of conservation and the probabilities of observing each type of amino acid (nucleotide) at that position

• Protein domain alignments (PFAM, TIGRFams,…)• Regulator binding site alignments

Simple Profile HMM – no gaps

Emission Probabilities determined from distribution of amino acids at each site of the alignment

Allowing gaps in a position-specific way

Need to allow a sequence to contain one or more residues not found in the model (Insert) and also be missing regions that are present in the model (Delete)

Pfam

• Database of protein domains and families available as multiple alignments and HMMs

• Pfam-A is curated. Pfam-B is automated.

A sample Pfam: MCPsignal

Pfam- Seed Alignment

Pfam – scoring members

• Trusted cut-off– Bit score for lowest

scoring match included in the full alignment

• Noise cut-off– Bit score for highest

scoring match not included in the full alignment

• Gathering cut-off

ATTTATCCGCCGAAGCCATTACATAGTATCGCGCTTGGCAGTCGGATTCCGGCGCTGCGTGAAGACTATA AACTTGGGCGTTTATGCGGTCGTTATTTCCTCGCCACGGTTGGCAAGCTATTAACTGAAAAAGCGCCGCT TACCCGCCATCTGGTGCCAGTGGTGACGCCGGAATCGATTGTCATTCCGCCTGCGCCAGTCGCCAACGAT ACGCTGGTTGCCGAAGTGAGCGACGCTCCGCAGGCGAACGACCCGACATTTAACAATGAGGATCTGGCTT GATTTGCCGTTTTATCGACACCCACTGCCATTTTGATTTCCCGCCGTTTAGTGGCGATGAAGAGGCCAGC CTGCAACGCGCGGCACAAGCGGGCGTAGGCAAGATCATTGTTCCGGCAACAGAGGCGGAAAATTTTGCCC GTGTGTTGGCATTAGCGGAAAATTATCAACCGCTGTATGCCGCATTGGGCTTGCATCCTGGTATGTTGGA AAAACATAGCGATGTGTCTCTTGAGCAGCTACAGCAGGCGCTGGAAAGGCGTCCGGCGAAGGTGGTGGCG GTGGGGGAGATCGGTCTGGATCTCTTTGGCGACGATCCGCAATTTGAGAGGCAGCAGTGGTTACTCGACG AACAACTGAAACTGGCGAAACGCTACGATCTGCCGGTGATCCTGCATTCACGGCGCACGCACGACAAACT GGCGATGCATCTTAAACGCCACGATTTACCGCGCACTGGCGTGGTTCACGGTTTTTCCGGCAGCCTGCAA CAGGCCGAACGGTTTGTACAGCTGGGCTACAAAATTGGCGTAGGCGGTACTATCACCTATCCACGCGCCA GTAAAACCCGCGATGTCATCGCAAAATTACCGCTGGCATCGTTATTGCTGGAAACCGACGCGCCGGATAT GCCGCTCAACGGTTTTCAGGGGCAGCCTAACCGCCCGGAGCAGGCTGCCCGTGTGTTCGCCGTGCTTTGC GAGTTGCGCCGGGAACCGGCGGATGAGATTGCGCAAGCGTTGCTTAATAACACGTATACGTTGTTTAACG TGCCGTAGGCCGGATAAGGCGTTCACGCCGCATCCGGCAGTTGGCGCACAATGCCTGATGCGACGCTTAA CGCGTCTTATCATGCCTACAGGTTTGTGCCGAACCGTAGGCCGGATAAGGCGTTCACGCCGCATCCGGCA GTTGGCGCACAATGCCTGATGCGACGCTTGTCGCGTCTTATCATGCCTACAAGTCTGTGCCGAACCGTAG GCCGGATAAGGCGTTCACGCCGCATCCGGCAGTCGGCGCATAATGCCTGATGCGACGCTTGTCGCGTCTT ATCATGCCTACAGGTTTGTGCCGAACCGTAGGCCGGATAAGGCGTTCGCGCCGCATCCGGCAGTTGGCGC ACAATGCCTGATGCGACGCTTGACGCGTCTTATCAGGCCTACAAGTCTGTGCCGAACCGTAGGCCGTATC CGGCATGTCACAAATAGAGCGCCGGAAATATCAACCGGCTCACCCCGCGCACCTTTAACGCATCAGCCAA CGGCTCAACGTCTTCCGGCGTGGCGCTCGCCCAGCTTTGCGCCTCGCCATACACGCCGTGGGCATGAAAC GCGTTCAGGCGTACCGGAACATCGCCGAGTCCCTTGATAAACGCCGCCAGTTCTTCGATGTGTTGCAAAT AATCCACCTGGCCAGGGATCACCAGCAAACGCAGTTCCGCCAGCTTGCCGCGCTCTGCCAGCAAATAGAT GCTGCGCTTAATCTGCTGATTATCGCGTCCGGTGAGTTGTTGATGACATTCGCTCCCCCACGCTTTGAGA TCGAGCATTGCGCCGTCGCACACCGGGAGCAATTTTTCCCAGCCGGTTTCGCTCAACATGCCGTTACTGT CCACCAGACAGGTGAGATGGCGCAGTTGCGGATCGTTTTTGATAGCAGTAAACAGCGCCACCACAAACGG CAGCTGGGTCGTGGCTTCACCGCCACTCACCGTTATCCCTTCGATAAACAGCACTGCTTTGCGGACATGG CTAAGCACTTCGTCCACGCTCATGGATTGCGCCATGGGCGTGGCATGTTGCGGACACCTCTTCAGGCAGG TATCACACTGCTCGCAAACCACAGCGTTCCACACCACTTTGCCGTCAACAATCTGCAACGCCTGATGCGG ACACTGTGGCACGCACTCCCCACAGTCATTGCAACGTCCCATCGTCCACGGATTGTGACAGTTTTTGCAG CGCAGATTGCAGCCCTGCAAAAACAGAGCCAGACGACTGCCTGGCCCGTCAACGCAGGAGAAGGGGATAA TCTTACTGACTAAAGCGCATCTGCTGTTCATGGCTTATCACGCGCGGCTGGCGTTCCAGAATACGAGTGT TGCGTGCGGCTTCTTCGCCCAGCCAGGTGGTGTTGGTGCGTGAACCTTCGGCGCGATATTTTTCTAAATC CGACAAACGCACCATATAACCGGTAACGCGAACCAGATCGTTACCGCTGACATTGGCGGTAAATTCACGC ATTCCGGCTTTAAAGGCACCGAGGCAAAGCTGTACCAGTGCCTGCGGGTTACGTTTGATGGTTTCGTCGA

Gene Discovery

Prokaryotes: 10 kb

Eukaryotes: 10 kb

DNA

DNA

3 mRNAs

9 proteins

Unprocessed mRNA

Processed mRNA

1 protein

Two Approaches

• Ab initio– Based exclusively on computational models– Error prone, esp. for eukaryotes– Generally requires manual clean up

• Comparative– Find genes corresponding to sequenced cDNAs– Find the genes already predicted for a closely related organism

• If you can...use both strategies

Attributes that prove useful for gene prediction

Begin with a start codonEnd with a stop codonHave a length divisible by 3

Splice sites

Tend to have a species specific codon usageExhibit even higher order biases in composition

Tend to be more conserved between organisms than non-coding regions

ORFOpen Reading Frame

Detecting Signal Amid the NoiseEach sequence can be translated in each of 6 reading frames, 3 for the sequenced strand and 3 for the reverse complement.

There are far more open reading frames than there are genes.

How do we know which reading frame contains real genes?

Organism-specific Composition Biases

51.8%GC coding 38.1%GC coding

Codon usage in the E. coli K-12 and H. influenzae genomes

Preference for GGC glycine codons

Preference for GGU glycine codons

Example of a 1st order Markov model for gene prediction:

The probability that base X is part of a coding region depends only on the base immediately preceding X.

AX, TX, CX, GX

How frequently does AX occur in a coding region vs. a non-coding region?

A 5th order model: AAAAAX, AAAATX, AAAACX, … GGGGGX

Gene Discovery using Markov Models and HMMs

Model Order – which is best?

• In general, higher order models better describe the properties of real genes, but training higher order models requires more data and the training sets are limiting.

• The probabilities of rare sequences in higher order models can be low enough that the model performs worse.

Gene Prediction Models based on Markov Chains

Basic Method:

•Build at least 6 submodels (one for each reading frame) for coding regions and 1 for noncoding

•Find ORFs -Start, Stop, mod(3)

•Score each ORF by calculating the probability that it was generated by each model. Choose the model with the highest probability – if it exceeds a user-specified threshold, you have a gene.

Two popular applications: GLIMMER, GeneMark

Hidden Markov Models add modeling the gene boundaries as transitions between “hidden” states.

GLIMMERReference:A.L. Delcher, D. Harmon, S. Kasif, O. White and S.L. Salzberg. Improved microbial gene identificaton with GLIMMER NAR, 1999, Vol. 27, No. 23, pp. 4636-4641.

• GLIMMER can be “trained” using the genome itself

Finds the longest ORFs in the genome and assumes they are real genes to estimate emission probabilities

• Interpolated Markov model•Not necessary to “fix” the order of the model

•Analysis of 10 microbial genomes:

GLIMMER 2 finds 97.4-99.7% of annotated genes

PLUS another 7-25% !!!

•GLIMMER 3 has a much lower False Positive Rate

Specificity vs.

Sensitivity

W.H. Majoros, M. Pertea, and S.L. Salzberg. TigrScan and GlimmerHMM: two open-source ab initio eukaryotic gene-findershttp://www.tigr.org/software/GlimmerHMM/index.shtml

Sensitivity: TP/(TP+FN)How much of what you hoped to detect did you get?

Specificity: TP/(TP+FP)How much of what you detected is real?