PROTEIN SEONDARY

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PROTEIN SEONDARY SUPER-SECONDARY STRUCTURE
PREDICTION WITH HMM By En-Shiun Annie Lee CS 882
Protein Folding Instructed by Professor Ming Li
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0. OUTLINE

• Introduction
• Problem
• Methods (4)
• HMM Examples (3)
• Segmentation HMM
• Profile HMM
• Conditional Random Field
• Proposal

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1. INTRODUCTION

• Introduction
• Problem
• Methods (4)
• HMM Examples (3)
• Segmentation HMM
• Profile HMM
• Conditional Random Field
• Proposal

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1. Genomics

• Achievements in Genomic
• BLAST (Basic Local Alignment Search Tool)
• most cited paper published in 1990s
• more than 15,000 times
• Human genome project
• Completion April 2003

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1. Proteomics

• Precedence to Proteomics
• Protein Data Bank (PDB)
• 40,132 structures
• cited more than 6,000 times

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1. Proteomics
Number of Protein Structures in Protein Data Bank
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1. Secondary Structure

• Importance
• The known secondary structure may be used as an
  input for the tertiary structure predictions.

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1. Protein Structure

• Primary Structure

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1. Protein Structure

• Secondary Structure

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1. Secondary Structure

• a-helix
• Interaction between i and (i4)th residue

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1. Secondary Structure

• ß-sheet/strand
• Parallel or Anti-parallel

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1. Secondary Structure

• Coil (loop)

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1. Protein Structure

• Tertiary Structure

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1. Protein Structure

• Super-Secondary (2.5) Structure

Super-Secondary (2.5) Structure
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1. Protein Structure

• Quaternary Structure

Super-Secondary (2.5) Structure
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2. PROBLEM

• Introduction
• Problem
• Methods (4)
• HMM Examples (3)
• Segmentation HMM
• Profile HMM
• Conditional Random Field
• Proposal

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2. Secondary Structure

• Problem
• Given
• A primary sequence of amino acids
• a1a2an
• Find
• Secondary structure of each ai as
• a-helix H
• ß-strand E
• coil C

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2. Secondary Structure

• Example
• Given
• Primary Sequence
• GHWIATRGQLIREAYEDYRHFSSECPFIP
• Find
• Secondary Structure Element
• CEEEEECHHHHHHHHHHHCCCHHCCCCCC
• Note segments

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2. Prediction Quality

• Three-state prediction accuracy
• Q3 of correctly predicted residues total
  of number of residues
• Q?, Qß, Qc
• Q3 for random prediction is 33
• Theoretical limit Q390.

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2. Prediction Quality

• Segment Overlap (SOV)
• Higher penalties for core segment regions
• Matthews Correlation Coefficients (MCC)
• Prediction errors made for each state

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2. True Structures

• Three dimensional PDB data
• DSSP (Dictionary of Secondary Structure of
  Proteins)
• 8 states
• H alpha helix H
• G 310 - helix H
• I 5 helix (pi helix) H
• E extended strand (beta ladder) E
• B residue in isolated beta-bridge E
• T hydrogen bonded turn C
• S bend C
• C coil C
• STRIDE

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3. METHODS

• Introduction
• Problem
• Methods (4)
• HMM Examples (3)
• Segmentation HMM
• Profile HMM
• Conditional Random Field
• Proposal

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3. Sliding Window

• Sliding-Window

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3. Sliding Window

• Sliding-Window

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3. Sliding Window

• Sliding-Window

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3. Sliding Window

• Sliding-Window

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3. Four Methods

• Statistical Method
• Neural Network
• Support Vector Machine
• Hidden Markov Model

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3a. Statistical Method

• Propensity
• Ex. Chou-Fasman 5053

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3b. Neural Network

• Ex. PHD 71

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3c. SVM

• Ex. PSIPRED 7678

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3d. HMM Definition

• State set Q
• Output alphabet S

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3d. HMM Definition

• Transition probabilities
• probability of entering the state p from state q
• Tq(p)
• ? q ? Q
• ? p ? Q

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3d. HMM Definition

• Emission probabilities
• probability emits each letter of S from state q
• Eq(ai)
• ? ai ? S
• ? q ? Q

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3d. HMM Decoding

• Problem
• Given
• HMM (Q,S,E,T) and
• Sequence S
• Where S S1, S2, , Sn
• Find
• Most probable path of state gone through to get S
• Where X X1, X2, , Xn state sequence

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4. HMM Decoding

• Optimize
• Pr S , X
• X X1, X2, , Xn state sequence
• S S1, S2, , Sn
• Pr S X

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4. HMM Decoding

• Dynamic programming
• Memoryless
• Pr XnSn Pr Xn-1Sn-1 Tn-1Xn EXn Sn

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4. HMM EXAMPLES

• Introduction
• Problem
• Methods (4)
• HMM Examples (3)
• Segmentation HMM
• Profile HMM
• Conditional Random Field
• Proposal

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4a. SEMI-HMM

• Introduction
• Problem
• Methods (4)
• HMM Examples (3)
• Semi-HMM
• Profile HMM
• Conditional Random Field
• Proposal

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4a. Semi-HMM

• Definition
• Each state can emit a sequence
• Move emission probabilities into states
• Model secondary structure segments

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4a. Segmentation

• Sequence Segments

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4a. Segmentation

• Sequence Segments

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4a. Segmentation

• Sequence Segments

• T secondary structural type of the segment, H,
  E, L
• S ends of each individual structural segments
• R known amino acid sequence

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4a. Segmentation

• Sequence Segments

• T2 E ß-strand
• S2 9
• R2 S1 1 S2

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4a. Bayesian

• Bayesian Formulation

• R Sequence of ALL amino acid residues
• S End of the segments
• T Secondary structural type of the segments
• H, E, L

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4a. Bayesian

• Bayesian Formulation

?
?
?

1. Likelihood
2. Priori Probability
3. Constant ? (S,T) ? ? dropped

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4a. Bayesian

• ? Likelihood

• m Total number of segments
• Sj End of the jth segments
• Tj Secondary structural type of the jth segments

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4a. Bayesian

• ? Likelihood

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4a. Bayesian

• ? Likelihood

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4a. Bayesian

• ? Likelihood

N-terminus
Internal
C-terminus
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4a. BSPPS

• Bayesian Segmentation PPS

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4a. BSPPS

• Bayesian Segmentation PPS

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4a. Results

• Better than PSIPRED
• (w/o homology information)

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4a. Results

• Better than PSIPRED
• (w/o homology information)

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4b. PROFILE-HMM

• Introduction
• Problem
• Methods (4)
• HMM Examples (3)
• Semi-HMM
• Profile HMM
• Conditional Random Field
• Proposal

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4b. Profile HMM

• Main States
• Columns of alignment

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4b. Profile HMM

• Insertion States

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4b. Profile HMM

• Deletion States
• Jump over 1 column in alignment

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4b. Profile HMM

• Combined

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4b. HMMSTR

• HMM for local protein STRucture

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4b. HMMSTR

• HMM for local protein STRucture
• Pronounced hamster

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4b. I-Site Library

• I-sites Library
• Motif short basic structural fragments
• 319 residues
• 262 motifs
• Highly predictable
• Non-redundant PDB data (lt25 similarity)
• Fold uniquely across protein family
• Exhaustive motif clustering

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4b. Build HMM

• States
• Amino acid sequence and
• Structural attribute
• Transition from state
• Adjacent positions in motif
• No gap or insertion states

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4b. Build HMM

• Emission probability distributions
• b observed amino acid
• (20 probability values)
• d secondary structure
• (helix, strand, loop)
• r backbone angle region
• (11 dihedral angle symbols)
• c structural context descriptor
• (10 context symbols)

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4b. Build HMM

• Model I-site Library
• Each 262 motif is a chain in HMM
• Merge states base on similarity of
• Sequence
• Structure

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4b. Build HMM

• Model I-site Library
• Merge states
• base on similarity of
• Sequence
• Structure

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4b. HMMSTR Merge

• Ex. ß-Hairpin

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4b. HMMSTR Merge

• Ex. ß-Hairpin

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4b. HMMSTR Merge

• Ex. ß-Hairpin

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4b. HMMSTR Merge

• Ex. ß-Hairpin

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4b. HMMSTR Training

• Input PDB proteins
• Find
• best state sequence for sequence
• probability distribution of one amino acid
• Integrate 3 data set
• Aligned probability distribution
• Amino acid and context information
• Contact map

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4b. HMMSTR Summary

• 282 nodes
• 317 transitions
• 31 merged motifs

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4b. HMMSTR Summary

• Introduce structural context on level of
  super-secondary structure
• Predict higher-order 3D tertiary structure
• Side-result predict 1D secondary structure

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4b. PROFILE-HMM

• Introduction
• Problem
• Methods (4)
• HMM Examples (3)
• Semi-HMM
• Profile HMM
• Conditional Random Field
• Proposal

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4c. HMM Disadvantages

• Does not model
• Multiple interacting features
• Long-range dependencies
• Strict independence assumptions

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4c. Conditional Model

• Allow
• Arbitrary features
• Non-independent features
• Transition probability
• With respect to past and future observations

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4c. Conditional Model
y1
y2
y3
y4
y5
y6

HMM
x1
x2
x3
x4
x5
x6
y1
y2
y3
y4
y5
y6

CRF
x1
x2
x3
x4
x5
x6
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4c. Random Field

• Random Field (Undirected graphical model)
• Let G (Y, E) be a graph
• Where each vertex Yv a random variable
• If P(Yvall other Y) P(Yvneighbours of Yv)Then
  Y is a random field

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4c. Random Field

• Example
• P(Y5 all other Y) P(Y5 Y4, Y6)

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4c. Conditional RF

• Conditional Random Field
• Let X r.v. data sequences to be labeled
• observations
• Let Y r.v. corresponding label sequences
• labels
• Let G (V, E) be a graph
• S.t. Y (Yv)v?Y so Y is indexed by vertices of G
• If P(Yv X, Yw w?v) P(Yv X, Yw, wv)Then
  (X, Y) is a random field

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4c. Conditional RF

• Example
• P(Y3 X, all other Y) P(Y3 X, Y2, Y4)

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4c. HMM vs. CRF

• HMM
• Maximize P(x,y?)P(yx,?)P(x?)
• Transition and emission probabilities
• Transition/emission base only one x
• CRF
• Maximize P(yx,?)
• Feature function f(i, j, k)
• Feature function base on all x

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4c. Beta-Wrap

• ß-Helix
• 3 parallel ß-strands
• Connected by coils
• Few solved structures
• 9 SCOP SuperFamilies
• 14 RH solved structures in PDB
• Solved structures differ widely

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4c. Graph Definition

• Let G (V,E1,E2) be a graph
• V Nodes/States Secondary structures
• Edges interactions
• E1
• Edges between adjacent neighbors
• Implied in the model
• E2
• Edges for long-term interactions
• Explicitly considered

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4c. Beta-Wrap Example

• Simple Example
• S2 first ß-strand
• S3 coil
• S4 second ß-strand
• S5 coil
• S6 ?-helix

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4c. Beta-Wrap

• ß-Helix Solution

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5. PROPOSAL

• Introduction
• Problem
• Methods (4)
• HMM Examples (3)
• Segmentation HMM
• Profile HMM
• Conditional Random Field
• Proposal

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5. Difficulties

• Do not infer global interaction
• i.e. Beta-sheet interactions
• Protein structure definition constraint

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5. Possible Future Work

• Novel methods of secondary structure prediction
• Model as Integer Programming
• Super-secondary structure prediction

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5. Acknowledgement

• Professor Ming Li
• Guidance in
• knowledge and
• expertise
• Bioinformatics lab
• Mentoring a rookie
• Class
• Attention and listening