1. Profiles for Sequences
Hidden Markov Models in Computational Biology
Profiles for Sequences

2. 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.

3. Markov Chains State transition matrix : The probability of
Rain
Sunny
Cloudy
State transition matrix : The probability of
the weather given the previous day's weather.
States : Three states - sunny, cloudy, rainy.
Initial Distribution : Defining the probability of the system being in each of the states at time 0.

4. 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’.

5. 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.

6. Hidden Markov Models Output Prob.
Transition Prob.
Output Prob.
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.

7. 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

8. Methods, contd. Alignment Problem
Given a sequence, what is the optimal state sequence that the HMM would use to generate it

9. Methods, contd. Training Problem
How do we estimate the structure and parameters of a HMM from data.

10. HMMs– Some Applications
Gene finding and prediction
Protein-Profile Analysis
Secondary Structure prediction
Copy Number Variation
Characterizing SNPs

11. Gene Template
(Left)
(Removed)

12. 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

13. Hidden Markov Models in Computational Biology
HMMs for Gene Finding
Training - Expectation Maximization (EM)
Parsing – Viterbi algorithm
from Salzberg, Chapter 4. pp 50.
An HMM for unspliced genes.
x : non-coding DNA
c : coding state

14. Genefinders: a Comparison
Sn = Sensitivity
Sp = Specificity
Ac = Approximate Correlation
ME = Missing Exons
WE = Wrong Exons
GENSCAN Performance Data,

15. Protein Profile HMMs Motivation What is a Profile?
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

16. Transition probabilities
HMMs From Alignment
ACA ATG
TCA ACT ATC
ACA C - - AGC
AGA ATC
ACC G - - ATC
insertion
Transition probabilities
Output Probabilities
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.

17. HMMs from Alignments Deletion states Matching states Insertion states
No of matching states = average sequence length in the family
PFAM Database - of Protein families (

18. Database Searching
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)

19. Querying a Sequence
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.
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
ACAC - - ATC

20. 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

21. 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

22. 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.