Gene prediction and HMM Computational Genomics 2005/6 Lecture 9b Slides taken (and rapidly mixed) from William Stafford Noble, Larry Hunter, and Eyal Pribman. Partially modified by Benny Chor.

Annotation of Genomic Sequence Given the sequence of an organism ’ s genome, we would like to be able to identify: –Genes –Exon boundaries & splice sites –Beginning and end of translation –Alternative splicings –Regulatory elements (e.g. promoters) The only certain way to do this is experimentally, but it is time consuming and expensive. Computational methods can achieve reasonable accuracy quickly, and help direct experimental approaches. primary goals secondary goals

Prokaryotic Gene Structure Promoter CDS Terminator transcription Genomic DNA mRNA  Most bacterial promoters contain the Shine-Delgarno signal, at about -10 that has the consensus sequence: 5'-TATAAT-3'.  The terminator: a signal at the end of the coding sequence that terminates the transcription of RNA  The coding sequence is composed of nucleotide triplets. Each triplet codes for an amino acid. The AAs are the building blocks of proteins.

Pieces of a (Eukaryotic) Gene (on the genome) 5’ 3’ 5’ ~ Mbp 5’ 3’ 5’ … … … … ~ kbp exons (cds & utr) / introns (~ bp) (~ bp) Polyadenylation site promoter (~10 3 bp) enhancers (~ bp) other regulatory sequences (~ bp)

What is it about genes that we can measure (and model)? Most of our knowledge is biased towards protein-coding characteristics –ORF (Open Reading Frame): a sequence defined by in- frame AUG and stop codon, which in turn defines a putative amino acid sequence. –Codon Usage: most frequently measured by CAI (Codon Adaptation Index) Other phenomena –Nucleotide frequencies and correlations: value and structure –Functional sites: splice sites, promoters, UTRs, polyadenylation sites

A simple measure: ORF length Comparison of Annotation and Spurious ORFs in S. cerevisiae Basrai MA, Hieter P, and Boeke J Genome Research :

Codon Adaptation Index (CAI) Parameters are empirically determined by examining a “large” set of example genes This is not perfect –Genes sometimes have unusual codons for a reason –The predictive power is dependent on length of sequence

CAI Example: Counts per 1000 codons

Splice signals (mice): GT, AG

General Things to Remember about (Protein-coding) Gene Prediction Software It is, in general, organism-specific It works best on genes that are reasonably similar to something seen previously It finds protein coding regions far better than non- coding regions In the absence of external (direct) information, alternative forms will not be identified It is imperfect! (It’s biology, after all…)

Simple HMM : Prokaryotes x m (i) = probability of being in state m at position i; H(m,y i ) = probability of emitting character y i in state m;  mk = probability of transition from state k to m.

Outline: Rest of Lecture Eukaryotic gene structure Modeling gene structure Using the model to make predictions Improving the model topology Modeling fixed-length signals

A eukaryotic gene This is the human p53 tumor suppressor gene on chromosome 17. Genscan is one of the most popular gene prediction algorithms.

A eukaryotic gene 3’ untranslated region Final exon Initial exon Introns Internal exons This particular gene lies on the reverse strand.

An Intron 3’ splice site 5’ splice site revcomp(CT)=AG revcomp(AC)=GT GT: signals start of intron AG: signals end of intron

Signals vs contents In gene finding, a small pattern within the genomic DNA is referred to as a signal, whereas a region of genomic DNA is a content. Examples of signals: splice sites, starts and ends of transcription or translation, branch points, transcription factor binding sites Examples of contents: exons, introns, UTRs, promoter regions

Prior knowledge We want to build a probabilistic model of a gene that incorporates our prior knowledge. E.g., the translated region must have a length that is a multiple of 3.

Prior knowledge The translated region must have a length that is a multiple of 3. Some codons are more common than others. Exons are usually shorter than introns. The translated region begins with a start signal and ends with a stop codon. 5’ splice sites (exon to intron) are usually GT; 3’ splice sites (intron to exon) are usually AG. The distribution of nucleotides and dinucleotides is usually different in introns and exons.

A simple gene model Transcription stop Transcription start StartEnd Gene Intergenic

A probabilistic gene model Transcription stop Transcription start StartEnd Gene Intergenic Every box stores transition probabilities for outgoing arrows. Every arrow stores emission probabilities for emitted nucleotides Pr(TACAGTAGATATGA) = Pr(AACAGT) = Pr(AACAGTAC) = …

Parse For a given sequence, a parse is an assignment of gene structure to that sequence. In a parse, every base is labeled, corresponding to the content it (is predicted to) belongs to. In our simple model, the parse contains only “I” (intergenic) and “G” (gene). A more complete model would contain, e.g., “-” for intergenic, “E” for exon and “I” for intron. S = ACTGACTACTACGACTACGATCTACTACGGGCGCGACCTATGCG P = IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIGGGGG TATGTTTTGAACTGACTATGCGATCTACGACTCGACTAGCTAC GGGGGGGGGGIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

The probability of a parse Transcription stop Transcription start StartEnd Gene Intergenic Pr(ACTGACTACTACGACTACGAT CTACTACGGGCGCGACCT) = Pr(ATGCGTATGTTTTGA) = Pr(ACTGACTATGCGATCTACGAC TCGACTAGCTAC) = Pr(parse P| sequence S, model M) = 0.67   1.00   0.75 x =  S = ACTGACTACTACGACTACGATCTACTACGGGCGCGACCTATGCGTATGTTTTGAACTGACTATGCGATCTACGACTCGACTAGCTAC P = IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIGGGGGGGGGGGGGGGIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

Finding the best parse For a given sequence S, the model M assigns a probability Pr(P|S,M) to every parse P. We want to find the parse P* that receives the highest probability.

Beyond Simplest Model Improving the gene model topology Fixed-length signals –PSSMs –Dependencies between positions Variable-length contents –Using HMMs –Semi-Markov models Parsing algorithms –Viterbi –Posterior decoding Including other types of data –Expressed sequence tags –Orthology

Improved model topology Draw a model that includes introns Transcription stop Transcription start StartEnd Gene Intergenic 2 Intergenic 1 Intergenic 4 Intergenic 3

Improved model topology Transcription stop Transcription start Start End 5’ splice site 3’ splice site

Improved model topology Transcription stop Transcription start Start End 5’ splice site 3’ splice site 4 intergenics 1 intron 4 exons

Improved model topology Transcription stop Transcription start Start End 5’ splice site 3’ splice site Single exonInitial exon Intron Internal exon Final exon

Modeling the 5’ splice site Most introns begin with the letters “GT.” We can add this signal to the model. 5’ splice site 3’ splice site Intron GT

Modeling the 5’ splice site Most introns begin with the letters “GT.” We can add this signal to the model. Indeed, we can model each nucleotide with its own arrow. 5’ splice site 3’ splice site Intron GT Pr(A)=0 Pr(C)=0 Pr(G)=0 Pr(T)=1 Pr(A)=0 Pr(C)=0 Pr(G)=1 Pr(T)=0

Modeling the 5’ splice site Like most biological phenomenon, the splice site signal admits exceptions. The resulting model of the 5’ splice site is a length-2 PSSM. 5’ splice site 3’ splice site Intron GT Pr(A)=0.01 Pr(C)=0.01 Pr(G)=0.01 Pr(T)=0.97 Pr(A)=0.01 Pr(C)=0.01 Pr(G)=0.97 Pr(T)=0.01

Real splice sites Real splice sites show some conservation at positions beyond the first two. We can add additional arrows to model these states. weblogo.berkeley.edu

Modeling the 5’ splice site 5’ splice site 3’ splice site Intron

Adding signals Transcription stop Transcription start Start End 5’ splice site 3’ splice site Single exonInitial exon Intron Internal exon Final exon Red ellipses correspond to signal models like this:

Positional Independence Pr(“ACTT”|M) = Pr(“A” at position 1 and “C” at position 2 and “T” at position 3 and “T” at position 4|M) = Pr(“A” at position 1|M)  Pr(“C” at position 2|M)  Pr(“T” at position 3|M)  Pr(“T” at position 4|M) In general, probabilities of independent events get multiplied. A PSSM assumes independence among nucleotides at different positions.

Positional dependence In this data, every time a “G” appears in position 1, an “A” appears in position 3. Conversely, an “A” in position 1 always occurs with a “T” in position 3. ACTGACTTGCACACTTACTAGCATACTAACTTACTGACTTGCACACTTACTAGCATACTAACTT

n th -order PSSM Normally, PSSM entry (i,j) gives the score for observing the i th letter in position j. In an n th -order PSSM, each score is conditioned on the preceding letters in the sequence. The entries A|A, C|A, G|A and T|A should sum to A|A A|C A|G A|T C|A … T|T nd -order PSSM

n th -order PSSM Normally, PSSM entry (i,j) gives the score for observing the i th letter in position j. In an n th -order PSSM, each score is conditioned on the preceding letters in the sequence. How many rows are in a 3 rd -order PSSM for nucleotides? n th -order? 1234 A|A A|C A|G A|T C|A … T|T nd -order PSSM The probability of observing an “A” in position 3, given that we already observed a “C” in position 2.

Conditional probability What is the probability of observing an “A” at position 2, given that we observed a “C” at the previous position? GCG CAG CCG GCG CCG CCG GCG CCT CCG GGG CGG GCG AGG CAG CCT CAT CCT GCG

Conditional probability What is the probability of observing an “A” at position 2, given that we observed a “C” at the previous position? Answer: total number of CA’s divided by total number of C’s in position 1. 3/11 = 27% Probability of observing CA = 3/18 = 17%. GCG CAG CCG GCG CCG CCG GCG CCT CCG GGG CGG GCG AGG CAG CCT CAT CCT GCG

Conditional probability The conditional probability Pr(x|y) = Number of occurrences of y:x Number of occurrences of y:* where * is any letter. GCG CAG CCG GCG CCG CCG GCG CCT CCG GGG CGG GCG AGG CAG CCT CAT CCT GCG

Conditional probability What is the probability of observing a “G” at position 3, given that we observed a “C” at the previous position? GCG CAG CCG GCG CCG CCG GCG CCT CCG GGG CGG GCG AGG CAG CCT CAT CCT GCG

Conditional probability What is the probability of observing a “G” at position 3, given that we observed a “C” at the previous position? Answer: 9/12 = 75%. GCG CAG CCG GCG CCG CCG GCG CCT CCG GGG CGG GCG AGG CAG CCT CAT CCT GCG

Modeling signals Transcription stop Transcription start Start End 5’ splice site 3’ splice site Single exonInitial exon Intron Internal exon Final exon Red ellipses may correspond to n th -order PSSMs.

Modeling variable-length regions Exon length

Modeling variable-length regions 1.The easy way, using standard HMMs. 2.And why that’s not so great. How are variable-length insertions modeled in protein HMMs?

The HMM solution 5’ splice site 3’ splice site Intron Fixed-length signals Variable-length content 5’ splice site 3’ splice site Intron

Codons start translation end translation Single exon start translation end translation Single exon

The complete model Transcription stop Transcription start Start End 5’ splice site 3’ splice site Single exonInitial exon Intron Internal exon Final exon Red ellipses correspond to n th -order PSSMs. Every arrow contains an invisible box with a self-loop.

A small problem Say that each blue arrow emits one letter. What is the probability that the intron will be exactly 2 letters long? 3 letters long? 4 letters long? 5’ splice site 3’ splice site Intron

A small problem Say that each blue arrow emits one letter. What is the probability that the intron will be exactly 2 letters long? 10% 3 letters long? 9% 4 letters long? 8.1% 5’ splice site 3’ splice site Intron

A small problem HMMs tend to produce geometric distributions Real contents are not necessarily geometric.

Building an HMM Input: annotated gene sequences Output: HMM parameters –Emission distributions within each content –Length distributions of contents –Transition distributions between contents

A more realistic (and complex) HMM model for Gene Prediction (Genie) Kulp, D., PhD Thesis, UCSC 2003

Assessing performance: Sensitivity and Specificity Testing of predictions is performed on sequences where the gene structure is known Sensitivity is the fraction of known genes (or bases or exons) correctly predicted –“Am I finding the things that I’m supposed to find” Specificity is the fraction of predicted genes (or bases or exons) that correspond to true genes –“What fraction of my predictions are true?” In general, increasing one decreases the other

Graphic View of Specificity and Sensitivity

Quantifying the tradeoff: Correlation Coefficient

Specificity/Sensitivity Tradeoffs Ideal Distribution of Scores More Realistically…

Bayesian Statistics Bayes’ Rule M: the model, D: data or evidence posterior likelihoodprior marginal

Basic Bayesian Statistics Bayes’ Rule is at the heart of much predictive software In the simplest example, we can simply compare two models, and reduce it to a log-odds ratio

Genetic + Genetic - short + short - intergenic Initiation + Initiation - Termination - Termination + overlap 0 overlap 1 overlap 2 overlap 3 Prokaryotes HMMs: Taking Overlaps on Two Strands into Account

Genetic + Genetic - short + short - Initiation + Initiation - Termination - Termination + overlap 0 overlap 1 overlap 2 overlap 3 Coding region (genes) intergenic

AAAAACAAG …. TTT Transition from any codon to any other. Model of all possible 64 codons Coding region (genes)

Integenic regions and overlap regions: Model Design (3)  Two consecutive genes either overlap each other or separated by an itergenic region.  The overlaping segment or the intergenic region is bordered in one of 4 possible ways. 5' 3' 5' 3' 5' 3' 5' 3' 5' 3' 5' 3' 5' 3' 5' 3' 5' Tail–Head Head–Tail Tail–Tail Head–Head Intermediate intergenic regionOverlapping Region TailHead

Example 1 Genetic + Genetic - short + short - Initiation + Initiation - Termination - Termination + overlap 0 overlap 1 overlap 2 overlap 3 Transition between two genes on the same strand. 5' 3' 5' intergenic

Example 2 Genetic + Genetic - short + short - Initiation + Initiation - Termination - Termination + overlap 0 overlap 1 overlap 2 overlap 3 Two genes on the opposite strands. 5' 3' 5' intergenic

Transitions between genes Genetic + Genetic - short + short - intergenic Initiation + Initiation - Termination - Termination + overlap 0 overlap 1 overlap 2 overlap 3 5' 3' 5'

Intergenic regions are modeled by profile HMMs. Intergenic Regions 5' 3' 5' We model two different types of intergenic regions: 1. Short intergenic sequences:  9 bases long.  Model situations where two same strand genes are close together.  This situation is common in polycistronic operons. 2. Long intergenic sequences are the more common case. They are modeled by the following 2 profile HMMs:  Transcription termination signal: 18 bases long.  Promoter region including the Shine-Dalgarno signal: 25 bases long.

A C G T---- A-- C G-- T A---- C G T A C G---- T A C G T---- Weight matrix models[i] (WMM) are used to represent overlapping regions of 1 or 4 bases, consisting of the stop codon of the previous gene and the start codon of the next one.[i]. TA A GT NNATGANN A- C- G- T- A- C- G- T- A--- C G- T A C G---- T A C G T---- A---- C G T A- C- G- T- A- C- G- T- Overlap Regions (1) 1 base overlap of stop codon TAA or TGA, with init codon ATG: 4 bases overlap: First gene terminated by TGA, second gene starts with [AG]TG: WMM format bases WMM format Overlap regions of 1 or 4 bases:

For each one of the 4 possible paths described (head  head, head  tail, tail  tail, tail  head), all possible frame differences are allowed. For example: a tail  head transition allows a 1 or 2 bases' shift of the reading frame. Overlap Regions (2) Overlap regions of 6 or more bases: Frame 1 Stop codon Frame 1 Stop codon Frame 1 Frame 2 Frame 3 Init codon Init codon Frame 2/3 5' 3' 5'