BCB 444/544
Lecture 17
Finish HMMs
Protein Motifs &
Domain Prediction
#17_Oct01
BCB 444/544 F07 ISU Dobbs #17- Protein Motifs & Domain Prediction
10/1/07
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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 - pp173-186
Thurs Oct 4 - Lab 6
Protein Structure: Databases & Visualization
Fri Oct 5 - Lecture 19
Protein Structure: Classification & Comparison
• Chp 13 - pp187-199
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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!
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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
TODAY:
• 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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Sequence Motifs (Patterns)
Types of representations:
•√
•√
•√
•√
Consensus Sequences
Sequence Logos
PSSMs - Position-Specific Scoring Matrices
Profiles
HMMs - Hidden Markov Models
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HMM example: CpG Islands
Nucleotide frequencies in human genome:
A
C
T
G
20.4
29.5
20.5
29.6
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CpG Islands
Written CpG to distinguish
from a C≡G base pair)
• CpG dinucleotides are rarer than would be expected
from independent probabilities of C and G (given the
background frequencies in human genome)
• High CpG frequency is sometimes biologically
significant; e.g., sometimes associated with promoter
regions (“start sites”for genes)
• CpG island - a region where CpG dinucleotides are
much more abundant than elsewhere
How can we represent or model CpG islands?
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Hidden Markov Models - HMMs
Goal: Find most likely explanation for observed variables
Components:
• Observed variables
• Hidden variables
• Emitted symbols
• Emission probabilities
• Transition probabilities
• Graphical representation to illustrate relationships among these
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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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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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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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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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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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HMM example from Eddy HMM paper:
Toy HMM for Splice Site Prediction
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The Occasionally Dishonest Casino
A casino uses a fair die most of the time, but occasionally
switches to a "loaded" one
• Fair die:
Prob(1) = Prob(2) = . . . = Prob(6) = 1/6
• Loaded die: Prob(1) = Prob(2) = . . . = Prob(5) = 1/10, Prob(6) = ½
• These are emission probabilities
Transition probabilities
• Prob(Fair  Loaded) = 0.01
• Prob(Loaded  Fair) = 0.2
• Transitions between states obey a Markov process
a linear chain of events linked by probability values such that the
occurrence of one event (state) depends on the occurrence of
previous event(s) or state(s)
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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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The Occasionally Dishonest Casino
• Known:
• Structure of the model
• Transition probabilities
• Hidden: What casino actually did
• FFFFFLLLLLLLFFFF...
• Observable: Series of die tosses
• 3415256664666153...
• What we must infer:
• When was a fair die used?
• When was a loaded one used?
• Answer is a sequence
FFFFFFFLLLLLLFFF...
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HMM: Making the Inference
• Model assigns a probability to each explanation for the
observation, e.g.:
P(326|FFL)
= P(3|F) · P(FF) · P(2|F) · P(FL) · P(6|L)
= 1/6 · 0.99 · 1/6
· 0.01 · ½
• Maximum Likelihood: Determine which explanation is most likely
• Find path most likely to have produced observed sequence
• Total Probability: Determine probability that observed sequence
was produced by HMM
• Consider all paths that could have produced observed sequence
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HMM Notation
• x = sequence of symbols emitted by model
• xi = symbol emitted at time i
•  = path, a sequence of states
• i-th state in  is i
• akr = transition probability, for making a transition
from state k to state r
akr  Pr( i  r |  i 1  k )
• ek(b) = emission probability, that symbol b is emitted
when in state k
ek (b )  Pr(xi  b |  i  k )
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Calculating Different Paths to an
Observed Sequence
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
1
 0.5  0.5  0.2   0.01  0.5
6
 0.0000417
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Identifying the Most Probable Path?
The most likely path * satisfies:
  arg max Pr(x ,  )
*

To find *, consider all possible ways the last "symbol"
of x could have been emitted
Let
v k (i )  Prob. of path  1 , ,  i most likely
Then
to emit x1 , , xi such that  i  k
v k (i )  ek (xi ) max v r (i  1)ark 
r
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Calculate optimal path? Construct a matrix of
probability values for every state at every residue
How: one way = Viterbi Algorithm
• Initialization (i = 0)
v 0 (0)  1, vk (0)  0 for k  0
• Recursion (i = 1, . . . , L):
For each state k
v k (i )  ek (xi ) max v r (i  1)ark 
r
• Termination:
Pr(x ,  * )  max vk (L)ak 0 
k
To find *, use trace-back, as in dynamic programming
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Viterbi for Most Probable Path: Example
x
6
2
1
0
0
0
(1/6)(1/2)
= 1/12
(1/6)max{(1/12)0.99,
(1/4)0.2}
= 0.01375
(1/6)max{0.013750.99,
0.020.2}
= 0.00226875
0
(1/2)(1/2)
= 1/4
(1/10)max{(1/12)0.01,
(1/4)0.8}
= 0.02
(1/2)max{0.013750.01,
0.020.8}
= 0.08

B

F
L
6
0
v k (i )  ek (xi ) max v r (i  1)ark 
r
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Total Probability
Several different paths can result in observation x
Probability that our model will emit x is:
Pr(x )   Pr(x ,  )

Total
Probability
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Total Probability: Example
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
= 0.004313 + 0.008144 = 0.012
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Viterbi gets it right more often than not
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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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Estimating the Probabilities
or “Training” the HMM
• 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" algorithm
• (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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An HMM can represent a MSA
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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, J. Mistry, B. SchusterBkler, S. Griffiths-Jones, V. Hollich, T. Lassmann, S. Moxon, M.
Marshall, A. Khanna, R. Durbin, S.R. Eddy, E.L.L. Sonnhammer and 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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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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