profiles for sequences. sequence profiles often, sequences are characterized by similarities that...
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Profiles for Sequences
Sequence Profiles
• Often, sequences are characterized by similarities that are not well captured through matching algorithms.
• For example, identification of genes in the presence of exons/introns, gene features (CpG islands, etc.), domain profiles in proteins, among others.
• For such sequences, Markov chains provide useful abstractions.
Markov Chains
Sunny
Rain
Cloudy
State transition matrix : The probability of
the weather given the previous day's weather.
Initial Distribution : Defining the probability of the system being in each of the states at time 0.
States : Three states - sunny, cloudy, rainy.
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Hidden Markov Models
Hidden states : the (TRUE) states of a system that may be described by a Markov process (e.g., the weather).
Observable states : the states of the process that are `visible’.
Hidden Markov Models
Initial Distribution : Initial state probability vector.
State transition Matrix
Emission Probabilities: containing the probability of observing a particular observable state given that the hidden model is in a particular hidden state.
Hidden Markov Models
Observed sequences can be scored if their state transitions are known.
The probability of ACCY along this path is:
.4 * .3 * .46 * .6 * .97 * .5 * .015 * .73 *.01 * 1 = 1.76x10-6.
Transition Prob.
Output Prob.
Methods for Hidden Markov Models
Scoring problem:
Given an existing HMM and observed sequence , what is the probability that the HMM can generate the sequence
Methods, contd.
Alignment ProblemGiven a sequence, what is the optimal state sequence that the HMM would use to generate it
Methods, contd.
Training ProblemHow do we estimate the structure and parameters of a HMM from
data.
HMMs– Some Applications
• Gene finding and prediction
• Protein-Profile Analysis
• Secondary Structure prediction
• Copy Number Variation
• Characterizing SNPs
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Gene Template
(Removed)
(Left)
HMMs: Applications• Classification: Classifying observations within a
sequence• Order: A DNA sequence is a set of ordered observations
• Structure : can be intuitively defined:
• Measure of success: # of complete exons correctly labeled
• Training data: Available from various genome annotation projects
HMMs for Gene Finding
An HMM for unspliced genes.x : non-coding DNAc : coding state
• Training - Expectation Maximization (EM)• Parsing – Viterbi algorithm
Genefinders: a Comparison
Method Sn Sp AC Sn Sp(Sn+Sp)/
2ME WE
GENSCAN 0.93 0.93 0.91 0.78 0.81 0.8 0.09 0.05FGENEH 0.77 0.85 0.78 0.61 0.61 0.61 0.15 0.11GeneID 0.63 0.81 0.67 0.44 0.45 0.45 0.28 0.24
GeneParser2 0.66 0.79 0.66 0.35 0.39 0.37 0.29 0.17GenLang 0.72 0.75 0.69 0.5 0.49 0.5 0.21 0.21GRAILII 0.72 0.84 0.75 0.36 0.41 0.38 0.25 0.1
SORFIND 0.71 0.85 0.73 0.42 0.47 0.45 0.24 0.14Xpound 0.61 0.82 0.68 0.15 0.17 0.16 0.32 0.13
Accuracy per nucleotide Accuracy per exon
Sn = SensitivitySp = SpecificityAc = Approximate CorrelationME = Missing ExonsWE = Wrong Exons
GENSCAN Performance Data, http://genes.mit.edu/Accuracy.html
Protein Profile HMMs• Motivation
– Given a single amino acid target sequence of unknown structure, we want to infer the structure of the resulting protein. Use Profile Similarity
• What is a Profile?– Proteins families of related sequences and structures– Same function– Clear evolutionary relationship– Patterns of conservation, some positions are more
conserved than the others
A HMM model for a DNA motif alignments, The transitions are shown with arrows whose thickness indicate their probability. In each state, the histogram shows the probabilities of the four bases.
ACA - - - ATG TCA ACT ATCACA C - - AGCAGA - - - ATCACC G - - ATC
HMMs From Alignment
Transition probabilities
Output Probabilities
insertion
Matching states
Insertion states
Deletion states
No of matching states = average sequence length in the familyPFAM Database - of Protein families (http://pfam.wustl.edu)
HMMs from Alignments
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• Given HMM, M, for a sequence family, find all members of the family in data base.
• LL – score LL(x) = log P(x|M)(LL score is length dependent – must
normalize or use Z-score)
Database Searching
Consensus sequence: P (ACACATC) = 0.8x1 x 0.8x1 x 0.8x0.6 x 0.4x0.6 x 1x1 x 0.8x1 x 0.8 = 4.7 x 10 -2
Suppose I have a query protein sequence, and I am interested in which family it belongs to? There can be many paths leading to the generation of this sequence. Need to find all these paths and sum the probabilities.
ACAC - - ATC
Querying a Sequence
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Multiple Alignments• Try every possible path through the
model that would produce the target sequences – Keep the best one and its probability.– Output : Sequence of match, insert and
delete states
• Viterbi alg. Dynamic Programming
HMMs from Unaligned Sequences
• Baum-Welch Expectation-maximization method– Start with a model whose length matches the
average length of the sequences and with random output and transition probabilities.
– Align all the sequences to the model.– Use the alignment to alter the output and transition
probabilities– Repeat. Continue until the model stops changing
• By-product: a multiple alignment
PHMM Example
An alignment of 30 short amino acid sequences chopped out of a alignment of the SH3 domain. The shaded area are the most conserved and were represented by the main states in the HMM. The unshaded area was represented by an insert state.