BCB 444/544
Lecture 18
More details: HMMs
Protein Motifs & Domain Prediction
Maybe: Protein Structure - The Basics
#18_Oct03
BCB 444/544 F07 ISU Dobbs #18- Protein Motifs & Domains
10/3/07
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Required Reading
(before lecture)
√Mon Oct 1 - Lecture 17
Protein Motifs & Domain Prediction
• Chp 7 - pp 85-96
Wed Oct 3 - Lecture 18
Protein Structure: The Basics (Note chg in lecture Schedule!)
• Chp 12 - pp 173-186
Thurs Oct 4 - Lab 6
Protein Structure: Databases & Visualization
Fri Oct 5 - Lecture 19
Protein Structure: Classification & Comparison
• Chp 13 - pp 187-199
BCB 444/544 F07 ISU Dobbs #18- Protein Motifs & Domains
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Assignments & Announcements
• HW544Extra #1 √Due: Task 1.1 - Mon Oct 1 (today) by noon
Task 1.2 & Task 2 - Mon Oct 8 by 5 PM
• HomeWork #3 - posted online
Due: Mon Oct 8 by 5 PM
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BCB 544 - Extra Required Reading
Mon Sept 24
BCB 544 Extra Required Reading Assignment:
• Pollard KS, Salama SR, Lambert N, Lambot MA, Coppens S, Pedersen JS,
Katzman S, King B, Onodera C, Siepel A, Kern AD, Dehay C, Igel H, Ares M Jr,
Vanderhaeghen P, Haussler D. (2006) An RNA gene expressed during cortical
development evolved rapidly in humans. Nature 443: 167-172.
• http://www.nature.com/nature/journal/v443/n7108/abs/nature05113.html
doi:10.1038/nature05113
• PDF available on class website - under Required Reading Link
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A few Online Resources for:
Cell & Molecular Biology
• NCBI Science Primer: What is a cell?
• http://www.ncbi.nlm.nih.gov/About/primer/genetics_cell.html
• NCBI Science Primer: What is a genome?
• http://www.ncbi.nlm.nih.gov/About/primer/genetics_genome.html
• BioTech’s Life Science Dictionary
• http://biotech.icmb.utexas.edu/search/dict-search.html
• NCBI Bookshelf
• http://www.ncbi.nlm.nih.gov/sites/entrez?db=books
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Statistics References
Statistical Inference (Hardcover)
George Casella, Roger L. Berger
StatWeb: A Guide to Basic Statistics for Biologists
http://www.dur.ac.uk/stat.web/
Basic Statistics:
http://www.statsoft.com/textbook/stbasic.html
(correlations, tests, frequencies, etc.)
Electronic Statistics Textbook: StatSoft
http://www.statsoft.com/textbook/stathome.html
(from basic statistics to ANOVA to discriminant analysis, clustering,
regression, data mining, machine learning, etc.)
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Extra Credit Questions #2-#6:
2. What is the size of the dystrophin gene (in kb)?
Is it still the largest known human protein?
3. What is the largest protein encoded in human genome (i.e.,
longest single polypeptide chain)?
4. What is the largest protein complex for which a structure is
known (for any organism)?
5. What is the most abundant protein (naturally occurring) on
earth?
6. Which state in the US has the largest number of mobile
genetic elements (transposons) in its living population?
For 1 pt total (0.2 pt each): Answer all questions correctly
& submit by to terrible@iastate.edu
For 2 pts total: Prepare a PPT slide with all correct answers
& submit to ddobbs@iastate.edu before 9 AM on Mon Oct 1
• Choose one option - you can't earn 3 pts!
• Partial credit for incorrect answers? only if they are truly amusing!
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Extra Credit Questions #7 & #8:
Given that each male attending our BCB 444/544 class on a typical
day is healthy (let's assume MH=7), and is generating sperm at a
rate equal to the average normal rate for reproductively
competent males (dSp/dT = ? per minute):
7a. How many rounds of meiosis will occur during our 50 minute class
period?
7b. How many total sperm will be produced by our BCB 444/544 class
during that class period?
8. How many rounds of meiosis will occur in the reproductively
competent females in our class? (assume FH=5)
For 0.6 pts total (0.2 pt each): Answer all questions correctly
& submit by to terrible@iastate.edu
For 1 pts total: Prepare a PPT slide with all correct answers
& submit to ddobbs@iastate.edu before 9 AM on Mon Oct 1
• Choose one option - you can't earn more than 1 pt for this!
• Partial credit for incorrect answers? only if they are truly amusing!
BCB 444/544 F07 ISU Dobbs #18- Protein Motifs & Domains
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Answers?
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Chp 6 - Profiles & Hidden Markov Models
SECTION II
SEQUENCE ALIGNMENT
Xiong: Chp 6
Profiles & HMMs
•
•
•
•
Position Specific Scoring Matrices (PSSMs)
PSI-BLAST
Profiles
Markov Models & Hidden Markov Models
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Statistical Models for Representing
Biological Sequences
3 types of probabilistic models, all of which:
• Are based on MSA
• Capture both observed frequencies & predicted frequencies of
unobserved characters
In order of "sensitivity":
1.PSSM - scoring table derived from an ungapped MSA; stores
frequencies (log odds scores) for each amino acid in each position
of a protein sequence,
2.Profile - A PSSM with gaps: based on gapped MSA with
penalties for insertions & delations
3.HMM - hidden Markov Model - more complex mathematical model
(than PSSMs or Profiles) because it also differentiates between
insertions and deletions
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HMMs for Biological Sequences?
• HMMs originally developed for speech recognition
• Now widely used in bioinformatics
• Many applications (motif/domain detection, sequence
alignment, phylogenetic
HMMs are "machine learning" algorithms - must be
"trained" to obtain optimal statistical parameters
• For Biological sequences:
• each character of a sequence is considered a state in
a Markov process
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But, What is a Markov Model?
Markov Model (or Markov chain)
= mathematical model used to describe a sequence of
events that occur one after another in a chain
= a process that moves in one direction from one state to
the next with a certain transition probability
For biological sequences:
• each letter = state
• linked together by transition probabilities
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Different Types of Markov Models
Zero-order Markov Model: probability of current state
is independent of previous state(s)
e.g., random sequence, each residue with equal frequency
First-order MM: probability of current state is
determined by the previous state
e.g., frequencies of two linked residues (dimer) occurring
simultaneously
Second-order MM: describes situation in which
probability of current state is determined by the
previous two states
e.g., frequencies of thee linked residues (trimers) occurring simultaneously, as in a codon
Higher orders? Also possible, later…
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So, What is a hidden Markov Model?
Hidden Markov Model (HMM)
- a more sophisticated model in which some of states
are hidden
- some "unobserved" factors influence the state
transition probabilities
- MM which: combines 2 or more Markov chains:
• only 1 chain is made up of observed states
• other chains are made up of unobserved or "hidden"
states
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Hidden Markov Models - HMMs
Goal: Find most likely explanation for observed variables
Components:
• States - composed of a number of elements or "symbols" (e.g.,
A,C,G,T)
• Observed variables - sequence (or outcome) we can "see"
• Hidden variables - insertions/deletions/transition probabilities
that can't be "seen"
• Emission probability - probability value associated with each
"symbol" in each state
• Transition probability - probability of going from one state to
another
• Special graphical representation used to illustrate
relationships
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An HMM for CpG Islands?
Emission probabilities are 0 or 1 e.g., eG-(G) = 1, eG-(T) = 0
See Durbin et al., Biological Sequence Analysis, Cambridge, 1998
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This is a new slide
HMM example from Eddy HMM paper:
Toy HMM for Splice Site Prediction
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An HMM for Occasionally Dishonest Casino
Transition probabilities
• Prob(Fair  Loaded) = 0.01
• Prob(Loaded  Fair) = 0.2
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This slide has been changed
Calculating Different Paths to an
Observed Sequence
Calculations such as those shown below are used to fill a matrix
with probability values for every state at every position
x  x1, x2, x3  6,2,6

 LLL
 (3)  LFL
emission probability
Pr(x,  (1) )  a0F eF (6)aFF eF (2)aFF eF (6)
1
1
1
 0.5   0.99   0.99 
6
6
6
 0.00227
 (1)  FFF
( 2)
transition probability
Pr(x ,  (2) )  a0 LeL (6)aLLeL (2)aLLeL (6)

 0.5  0.5  0.8  0.1  0.8  0.5
 0.008
Pr(x ,  (3) )  a0LeL (6)aLF eF (2)aFL eL (6)aL 0
 0.5  0.5  0.2 
 0.0000417
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 0.01  0.5
6
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This slide has been changed
Calculating the Most Probable Path*, using
Viterbi algorithm (using traceback as in DP)
* Path within HMM that matches query sequence with highest probability
x
6
2
1
0
0
0
(1/6)(1/2)
= 1/12
0
(1/2)(1/2)
= 1/4

B

F
L
(1/6)max{(1/12)0.99
,
(1/4)0.2}
= 0.01375
(1/10)max{(1/12)0.01,
(1/4)0.8}
= 0.02
6
0
(1/6)max{0.013750.99,
0.020.2}
= 0.00226875
(1/2)max{0.013750.01,
0.020.8}
= 0.08
v k (i )  ek (xi ) max v r (i  1)ark 
r
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This slide has been changed
Calculating the Total Probability:
Note: This not the same as matrix on previous slide!
Here, last column contains sums for each row
x
B

F
L

6
2
1
0
0
0
(1/6)(1/2)
= 1/12
(1/6)sum{(1/12)0.99,
(1/4)0.2}
= 0.022083
(1/6)sum{0.0220830.99,
0.0200830.2}
= 0.004313
0
(1/2)(1/2)
= 1/4
(1/10)sum{(1/12)0.01,
(1/4)0.8}
= 0.020083
(1/2)sum{0.0220830.01,
0.0200830.8}
= 0.008144
Total probability =
Pr(x,  )


6
0
= 0 + 0.004313 + 0.008144 = 0.012
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This slide has been changed
Estimating the Probabilities
or “Training” the HMM
• Calculate frequencies in each column of MSA built from set of
related sequences
• Use frequency values to fill the emission and transition
probabilities in the model (use two matrices for this)
• Viterbi training
• Derive probable paths for training data using Viterbi algorithm
• Re-estimate transition probabilities based on Viterbi path
• Iterate until paths stop changing
• Other algorithms can be used
• e.g., "forward" & "backward" algorithms
• (see text - or see Wikipedia re: HMMs)
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Profile HMMs
• Used to model a family of related sequences
(or motif or domain)
• Derived from a MSA of family members
• Transition & emission probabilities are position-specific
• Set parameters of model so that total probability peaks at members
of family
• Sequences can be tested for family membership using
Viterbi algorithm to evaluate match against profile
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This slide has been changed
Profile HMM represents a gapped MSA
Character in alignment can
be in one of 3 states:
Match - observed
Insert - hidden
Delete - hidden
Hidden chains
Observed chain
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Example: Pfam: Protein Families
http://pfam.sanger.ac.uk/
• “A comprehensive collection of protein domains and families,
with a range of well-established uses including genome
annotation.”
•
Pfam: clans, web tools and services: R.D. Finn, …A. Bateman (2006)
Nucleic Acids Res Database Issue 34:D247-D5
• Each family is represented by:
• 2 MSAs
• 2 Hidden Markov Models (profile-HMMs)
• cf. Superfamily - from Lab 5
• similar collection of curated MSAs & HMMs, focuses on
superfamily level
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A few more Details re: Profiles & HMMs
• Smoothing or "Regularization" - method used to avoid "over-fitting"
• Common problem in machine learning (data-driven) approaches
• Limited training sample size causes over-representation of observed
characters while "ignoring" unobserved characters
• Result? Miss members of family not yet sampled
(too many false negative hits)
• Pseudocounts - adding artificial values for 'extra' amino acid(s) not
observed in the training set
• Treated as a 'real' values in calculating probabilities
• Improve predictive power of profiles & HMMs
• Dirichlet mixture - commonly used mathematical model to simulate
the aa distribution in a sequence alignment
• To "correct" problems in an observed alignment based on limited
number of sequences
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Applications (of PSSMs, Profiles, HMMs)
• HMMer - for building & using HMMs
• developed by Sean Eddy's group
• Not a web-based server; must download the software
• 9 related programs
• but check out the site - it's fun!
• Psi-BLAST - you've heard enough about this!
• Uses Profiles (not actually PSSMs) - iteratively
• In previous lab: used SuperFam (HMMs)
• http://supfam.mrc-lmb.cam.ac.uk/SUPERFAMILY/
• Prosite - includes patterns (regular expressions) & profiles
for motifs & domains
• http://ca.expasy.org/prosite
• Pfam (MSAs & HMMs)
• http://pfam.sanger.ac.uk/
(new URL)
• Many others
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Chp 7 - Protein Motifs & Domain Prediction
SECTION II
SEQUENCE ALIGNMENT
Xiong: Chp 7
Protein Motifs and Domain Prediction
•
•
•
•
•
•
Identification of Motifs & Domains in MSAs
Motif & Domain Databases Using Regular Expressions
Motif & Domain Databases Using Statistical Models
Protein Family Databases
Motif Discovery in Unaligned Sequences
√Sequence Logos
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Motifs & Domains
• Motif - short conserved sequence pattern
• Associated with distinct function in protein or DNA
• Avg = 10 residues (usually 6-20 residues)
• e.g., zinc finger motif - in protein
• e.g., TATA box - in DNA
• Domain - "longer" conserved sequence pattern, defined
as a independent functional and/or structural unit
• Avg = 100 residues (range from 40-700 in proteins)
• e.g., kinase domain or transmembrane domain - in protein
• Domains may (or may not) include motifs
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2 Approaches for Representing "Consensus"
Information in Motifs & Domains
• Regular expression - reduce information from MSA
• e.g., protein phosphorylation site motif: [S,T]- X- [R,K]
• Symbols represent specific or unspecified residues, spaces,
etc.
• 2 mechanisms for matching:
• Exact
• "Fuzzy" (inexact, approximate) - flexible, more permissive
to detect "near matches"
• Statistical model - includes probability information
derived from MSA
• e.g., PSSM, Profile or HMM
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Motif & Domain Databases
Based on regular expressions:
• Prosite (Interpro)
• Emofit
Limitation: these don't take probability info into account
Based on statistical models:
•
•
•
•
•
•
•
PRINTS
BLOCKS
ProDom
Pfam
SMART
CDART
Reverse PsiBLAST
• READ your textbook & try some
of these at home; there are
distinct advantages/disadvantages
associated with each
• TAKE HOME LESSON:
Always try several methods!
(not just one!)
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Chp 12 - Protein Structure Basics
SECTION V
STRUCTURAL BIOINFORMATICS
Xiong: Chp 12
Protein Structure Basics
• Introduction to the Protein DataBank - PDB
• NEXT lecture!
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