#17 - Protein Motifs & Domain
Prediction
10/1/07
Required Reading
BCB 444/544
(before lecture)
Mon Oct 1 - Lecture 17
Lecture 17
Protein Motifs & Domain Prediction
• Chp 7 - pp 85-96
Finish HMMs
Wed Oct 3 - Lecture 18
Protein Structure: The Basics (Note chg in lecture Schedule!)
• Chp 12 - pp173-186
Protein Motifs &
Domain Prediction
Thurs Oct 4 - Lab 6
Protein Structure: Databases & Visualization
#17_Oct01
Fri Oct 5 - Lecture 19
Protein Structure: Classification & Comparison
• Chp 13 - pp187-199
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Assignments & Announcements
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BCB 544 - Extra Required Reading
Mon Sept 24
• HW544Extra #1 Due: Task 1.1 - Mon Oct 1 (today) by noon
Task 1.2 & Task 2 - Mon Oct 8 by 5 PM
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
• HomeWork #3 - posted online
Due: Mon Oct 8 by 5 PM
• PDF available on class website - under Required Reading Link
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A few Online Resources for:
Cell & Molecular Biology
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Statistical Inference (Hardcover)
George Casella, Roger L. Berger
• NCBI Science Primer: What is a genome?
StatWeb: A Guide to Basic Statistics for Biologists
• http://www.ncbi.nlm.nih.gov/About/primer/genetics_cell.html
http://www.dur.ac.uk/stat.web/
• http://www.ncbi.nlm.nih.gov/About/primer/genetics_genome.html
Basic Statistics:
http://www.statsoft.com/textbook/stbasic.html
(correlations, tests, frequencies, etc.)
• BioTech’s Life Science Dictionary
• http://biotech.icmb.utexas.edu/search/dict-search.html
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.)
• NCBI Bookshelf
• http://www.ncbi.nlm.nih.gov/sites/entrez?db=books
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Statistics References
• NCBI Science Primer: What is a cell?
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#17 - Protein Motifs & Domain
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Extra Credit Questions #2-#6:
Extra Credit Questions #7 & #8:
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?
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 1 pt total (0.2 pt each): Answer all questions correctly
For 0.6 pts total (0.2 pt each): Answer all questions correctly
For 2 pts total: Prepare a PPT slide with all correct answers
For 1 pts total: Prepare a PPT slide with all correct answers
• Choose one option - you can't earn 3 pts!
• Choose one option - you can't earn more than 1 pt for this!
& submit by to terrible@iastate.edu
& submit by to terrible@iastate.edu
& submit to ddobbs@iastate.edu before 9 AM on Mon Oct 1
& submit to ddobbs@iastate.edu before 9 AM on Mon Oct 1
• Partial credit for incorrect answers? only if they are truly amusing!
BCB 444/544 F07 ISU Dobbs #17- Protein Motifs & Domain Prediction
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• 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
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Sequence Motifs (Patterns)
Types of representations:
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,
Consensus Sequences
Sequence Logos
PSSMs - Position-Specific Scoring Matrices
Profiles
HMMs - Hidden Markov Models
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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#17 - Protein Motifs & Domain
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CpG Islands
HMM example: CpG Islands
Written CpG to distinguish
from a C G base pair)
Nucleotide frequencies in human genome:
A
C
T
G
20.4
29.5
20.5
29.6
• 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
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Different Types of Markov Models
Goal: Find most likely explanation for observed variables
Zero-order Markov Model: probability of current state
is independent of previous state(s)
Components:
• Observed variables
• Hidden variables
• Emitted symbols
First-order MM: probability of current state is
determined by the previous state
e.g., random sequence, each residue with equal frequency
e.g., frequencies of two linked residues (dimer) occurring
simultaneously
• Emission probabilities
• Transition probabilities
Second-order MM: describes situation in which
probability of current state is determined by the
previous two states
• Graphical representation to illustrate relationships among these
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?
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Hidden Markov Model (HMM)
- a more sophisticated model in which some of states
are hidden
- some "unobserved" factors influence the state
transition probabilities
For biological sequences:
- 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
• each letter = state
• linked together by transition probabilities
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So, What is a hidden 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
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#17 - Protein Motifs & Domain
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HMMs for Biological Sequences?
Hidden Markov Models - HMMs
Goal: Find most likely explanation for observed variables
• HMMs originally developed for speech recognition
• Now widely used in bioinformatics
• Many applications (motif/domain detection, sequence
alignment, phylogenetic
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
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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• 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
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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:
Transition probabilities
• Prob(Fair → Loaded) = 0.01
• Prob(Loaded → Fair) = 0.2
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• 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
HMM Notation
• Model assigns a probability to each explanation for the
observation, e.g.:
• x = sequence of symbols emitted by model
• xi = symbol emitted at time i
• π = path, a sequence of states
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
• i-th state in π is πi
• akr = transition probability, for making a transition
from state k to state r
• Maximum Likelihood: Determine which explanation is most likely
akr = Pr(" i = r | " i !1 = k )
• Find path most likely to have produced observed sequence
• ek ( b ) =
• Total Probability: Determine probability that observed sequence
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ek (b ) = Pr(xi = b | ! i = k )
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Calculating Different Paths to an
Observed Sequence
!
(1 )
! * = arg max Pr(x , ! )
!
To find π*, consider all possible ways the last "symbol"
of x could have been emitted
Let
Pr(x , " (2) ) = a0 LeL (6)aLLeL (2)aLLeL (6)
! (2) = LLL
= 0.5 ! 0.5 ! 0.8 ! 0.1 ! 0.8 ! 0.5
!
! (3) = LFL
v k (i ) = Prob. of path ! 1 , L, ! i most likely
= 0.008
Pr(x , #
( 3)
) = a0 LeL (6)aLF eF (2)aFLeL (6)aL 0
Then
1
= 0.5 " 0.5 " 0.2 " " 0.01 " 0.5
6
! 0.0000417
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Viterbi for Most Probable Path: Example
x
How: one way = Viterbi Algorithm
• Initialization (i = 0)
v 0 (0) = 1, v k (0) = 0 for k > 0
π
For each state k
v k (i ) = ek (xi ) max(v r (i ! 1)ark )
r
• Termination:
Pr(x , ! * ) = max(v k (L)ak 0 )
k
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ε
6
2
B
1
0
0
6
F
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
L
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
0
v k (i ) = ek (xi ) max(v r (i ! 1)ark )
r
To find π*, use trace-back, as in dynamic programming
BCB 444/544 Fall 07 Dobbs
v k (i ) = ek (xi ) max(v r (i ! 1)ark )
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probability values for every state at every residue
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to emit x1 , K, xi such that ! i = k
r
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Calculate optimal path? Construct a matrix of
• Recursion (i = 1, . . . , L ):
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The most likely path π* satisfies:
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
= FFF
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Identifying the Most Probable Path?
transition probability
x = x1 , x 2 , x 3 = 6,2,6
emission probability, that symbol b is emitted
when in state k
was produced by HMM
• Consider all paths that could have produced observed sequence
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Total Probability
Total Probability: Example
x
Several different paths can result in observation x
ε
Probability that our model will emit x is:
π
Pr(x ) = ! Pr(x , " )
2
6
B
1
0
0
F
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
L
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
6
Total probability =
! Pr(x, " )
0
= 0.004313 + 0.008144 = 0.012
"
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An HMM for CpG Islands?
Viterbi gets it right more often than not
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
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• Used to model a family of related sequences
• Derive probable paths for training data using Viterbi algorithm
• Re-estimate transition probabilities based on Viterbi path
• Iterate until paths stop changing
(or motif or domain)
• Derived from a MSA of family members
• Transition & emission probabilities are position-specific
• Other algorithms can be used
• Set parameters of model so that total probability peaks
at members of family
• e.g., "forward" algorithm
• (see text - or see Wikipedia re: HMMs)
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Profile HMMs
• Viterbi training
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• Sequences can be tested for family membership using
Viterbi algorithm to evaluate match against profile
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#17 - Protein Motifs & Domain
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Pfam: Protein Families
An HMM can represent a MSA
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
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Motifs & Domains
• e.g., zinc finger motif - in protein
• e.g., TATA box - in DNA
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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• Associated with distinct function in protein or DNA
• Avg = 10 residues (usually 6-20 residues)
Protein Motifs and Domain Prediction
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• Motif - short conserved sequence pattern
SEQUENCE ALIGNMENT
Xiong: Chp 7
•
•
•
•
•
•
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• 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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