Download Dynamic Programming: Sequence alignment

Gene finding with GeneMark.HMM
(Lukashin & Borodovsky, 1997)
CS 466
Saurabh Sinha
Gene finding in bacteria
• Large number of bacterial genomes sequenced (10
at the time of paper, 1997)
• Previous work: “Genemark” program identified gene
as ORF that looks more like genes than non-genes.
– Uses Markov chains of coding and non-coding sequence
• 5’ (starting) boundary not well predicted
– Resolution of start point ~ 100 nucleotides
Genemark.hmm
• Builds on Genemark, but uses HMM for better prediction of
start and stop
• Given DNA sequence S = {b1,b2,….bL}
• Find “functional sequence” A={a1,…aL} where each ai = 0 if
non-coding, 1 if coding in forward strand, 2 if coding in
reverse strand
• Sounds like the Fair Bet Casino problem (sequence of coin
types “fair” or “biased”)
• Find Pr(A | S) and report A that maximizes this
Functional sequence
• “A” carries information about where the coding
function switched into non-coding (stop of gene) and
vice versa.
• Model sequence by HMM with different states for
“coding” and “non-coding”
• Maximum likelihood “A” is the optimal path through
the HMM, given the sequence
• Viterbi algorithm to solve this problem
Hidden Markov Model
• In some states, choose (i) a length of
sequence to emit and (ii) the sequence
to emit
• This is different from the Fair Bet
Casino problem. There, each state
emitted exactly one observation (H or T)
Hidden Markov Model
• “Typical” and “Atypical” gene states (one for
each of forward and reverse strands)
• These two states emit coding sequence
(between and excluding start and stop
codons) with different codon usage patterns
• Clustering of E. coli genes showed that
– majority of genes belong to one cluster (“Typical”)
– many genes, believed to have been “horizontally
transferred” into the genome, belong to another
cluster (“Atypical”)
Hidden State Trajectory “A”
• This is similar to the “functional” sequence
defined earlier
– except that we have one for each state, not one
for each nucleotide
• Sequence of M hidden states ai having
duration di:
– A = {(a1d1), (a2d2), …. (aMdM)}
– ∑di = L
• Find A* that maximizes Pr(A|S)
Formulation
• Find trajectory (path) A that has the
highest probability of occurring
simultaneously with the sequence S
Pmax  P(A*,S) 
max
(a1 d1 )...( a M d M )
Pr[(a1d1 )...(aM dM ),b1,b2 ...bL ]
M
ds L
s 1
• Maximizing Pr(A,S) is the same as
maximizing Pr(A|S). Why ?
Solution
• Maximization problem solved by Viterbi
algorithm (seen in previous lecture)
Solution
maximizing over all possible trajectories
Solution
Define (for dynamic progamming):
transition prob.
prob. of duration prob. of sequence
the joint probability of a partial trajectory of m states (with the
last state being am) and a partial sequence of length l.
Solution
Parameters of the HMM
• Transition probability distributions, emission
probability distributions
• Fixed a priori
– What was the other possibility ?
– Learn parameters from data
• Emission probabilities of coding sequence state
obtained from previous statistical studies: “What does
a coding sequence look like in general?”
• Emission probabilities of non-coding sequence
obtained similarly
Parameters of the HMM
• Probability that a state “a” has duration “d” (i.e.,
length of emission is d) is learned from frequency
distribution of lengths of known coding sequences
Parameters of the HMM
•… and non-coding sequences
Parameters of the HMM
• Emission probabilities of start codon fixed from
previous studies
– Pr(ATG)=0.905, Pr(GTG)=0.090, Pr(TTG)=0.005
• Transition probabilities: Non-coding to
Typical/Atypical coding state = 0.85/0.15
Post-processing
• As per the HMM, two genes cannot
overlap. In reality, genes may overlap !
G1
G2
Post-processing
• As per the HMM, two genes cannot
overlap. In reality, genes may overlap !
G1
Will predict second gene to begin here
What about the start codon for that second gene?
G2
Post-processing
• As per the HMM, two genes cannot
overlap. In reality, genes may overlap !
G1
G2
• Look for an RBS somewhere here.
• Take each start codon here, and find RBS -19 to -4 bp
upstream of it
Ribosome binding site (RBS)
How to search for RBS?
• Take 325 genes from E. coli (bacterium) with
known RBS
• Align them using sequence alignment
• Use this as a PWM to scan for RBS
Gene prediction in different species
• The coding and non-coding state
emission probabilities need to be
trained from each species for predicting
genes in that species
Gene prediction accuracy
•
•
•
•
Data set #1: all annotated E. coli genes
Data set #2: non-overlapping genes
Data set #3: Genes with known RBS
Data set #4: Genes with known start
positions
Results
VA: Viterbi algorithm
PP: With post-processing
Results
• Gene overlap is an important factor
• Performance goes up from 58% to 71% when
overlapping genes are excluded from data set
• Post-processing helps a lot
– 58% --> 75% for data set #1
• Missing genes: “False negatives” < 5%
• “Wrong” gene predictions: “False positives” ~8%
– Are they really false positives, or are they unannotated
genes?
Results
• Compared with other programs
Results
• Robustness to parameter settings
• Alternative set of transition probability
values used
• Little change in performance (~20%
change in parameter values leads to <
5% change in performance)
Higher Order Markov models
• Sequence emissions were modeled by a second
order Markov chain.
– Pr (Xi|Xi-1, Xi-2,…X1) = Pr (Xi|Xi-1, Xi-2)
• Examined the effect of changing the “Markov
order” (0,1,3,4,5)
• Even zeroth order Markov chain does pretty well.
Higher Order Markov models