Predicting Protein Structures and Structural Features on a Genomic Scale Pierre Baldi School of Information and Computer Sciences Institute for Genomics and Bioinformatics University of California, Irvine

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Predicting Protein Structures and Structural
Features on a Genomic ScalePierre BaldiSchool
of Information and Computer SciencesInstitute
for Genomics and BioinformaticsUniversity of
California, Irvine
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UNDERSTANDING INTELLIGENCE

• Human intelligence (inverse problem)
• AI (direct problem)
• Choice of specific problems is key
• Protein structure prediction is a good problem

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PROTEINS

• R1
  R3
• 
  
  
• Ca N Cß
  Ca
• / \ / \ /
  \ / \
• N Cß Ca
  N Cß
• R2

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Utility of Structural Information
(Baker and Sali, 2001)
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CAVEAT
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REMARKS

• Structure/Folding
• Backbone/Full Atom
• Homology Modeling
• Fold Recognition (Threading)
• Ab Initio (Physical Potentials/Molecular
  Dynamics, Statistical Mechanics/Lattice Models)
• Statistical/Machine Learning (Training Sets, SS
  prediction)
• Mixtures ab-initio with statistical potentials,
  machine learning with profiles, etc.

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PROTEIN STRUCTURE PREDICTION (ab initio)
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Helices

• 1GRJ (Grea Transcript Cleavage Factor From
  Escherichia Coli)

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Antiparallel ß-sheets

• 1MSC (Bacteriophage Ms2 Unassembled Coat Protein
  Dimer)

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Parallel ß-sheets

• 1FUE (Flavodoxin)

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Contact map
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Secondary structure prediction
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GRAPHICAL MODELS BAYESIAN NETWORKS

• X1, ,Xn random variables associated with the
  vertices of a DAG Directed Acyclic Graph
• The local conditional distributions P(XiXj j
  parent of i) are the parameters of the model.
  They can be represented by look-up tables
  (costly) or other more compact parameterizations
  (Sigmoidal Belief Networks, XOR, etc).
• The global distribution is the product of the
  local characteristicsP(X1,,Xn) ?i P(XiXj
  j parent of i)

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DATA PREPARATION

•  
• Starting point PDB data base.
•        Remove sequences not determined by X ray
  diffraction.
•        Remove sequences where DSSP crashes.
•        Remove proteins with physical chain
  breaks (neighboring AA having
  distances exceeding 4 Angstroms)
•        Remove sequences with resolution worst
  than 2.5 Angstroms.
•        Remove chains with less than 30 AA.
•        Remove redundancy (Hobohms algorithm,
  Smith-Waterman, PAM 120, etc.)
• Build multiple alignments (BLAST,
  PSI-BLAST, etc.)

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SECONDARY STRUCTURE PROGRAMS

• DSSP (Kabsch and Sander, 1983) works by
  assigning potential backbone hydrogen bonds
  (based on the 3D coordinates of the backbone
  atoms) and subsequently by identifying repetitive
  bonding patterns.
•   STRIDE (Frishman and Argos, 1995) in addition
  to hydrogen bonds, it uses also dihedral angles.
•   DEFINE (Richards and Kundrot, 1988) uses
  difference distance matrices for evaluating the
  match of interatomic distances in the protein to
  those from idealized SS.

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SECONDARY STRUCTURE ASSIGNMENTS

• DSSP classes 
• H alpha helix
• E sheet
• G 3-10 helix
• S kind of turn
• T beta turn
• B beta bridge
• I pi-helix (very rare)
• C the rest
• CASP (harder) assignment 
• a H and G
• ß E and B
• ? the rest
• Alternative assignment 
• a H
• ß B
• ? the rest

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ENSEMBLES
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FUNDAMENTAL LIMITATIONS

• 100 CORRECT RECOGNITION IS PROBABLY IMPOSSIBLE
  FOR SEVERAL REASONS
• SOME PROTEINS DO NOT FOLD SPONTANEOUSLY OR MAY
  NEED CHAPERONES
• QUATERNARY STRUCTURE BETA-STRAND PARTNERS MAY BE
  ON A DIFFERENT CHAIN
• STRUCTURE MAY DEPEND ON OTHER VARIABLES
  ENVIRONMENT, PH
• DYNAMICAL ASPECTS
• FUZZINESS OF DEFINITIONS AND ERRORS IN DATABASES

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BB-RNNs
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2D RNNs
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2D INPUTS

• AA at positions i and j
• Profiles at positions i and j
• Correlated profiles at positions i and j
• Secondary Structure, Accessibility, etc.

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PERFORMANCE ()
6Å 8Å 10Å 12Å
non-contacts 99.9 99.8 99.2 98.9
contacts 71.2 65.3 52.2 46.6
all 98.5 97.1 93.2 88.5
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Protein Reconstruction
Using predicted secondary structure and predicted
contact map
PDB ID 1HCR, chain A Sequence
GRPRAINKHEQEQISRLLEKGHPRQQLAIIFGIGVSTLYRYFPASSIKKR
MN True SS CCCCCCCCHHHHHHHHHHHCCCCHHHHHHHCECCHHH
HHHHCCCCCCCCCCC Pred SS CCCCCCCHHHHHHHHHHHHCCCCH
HHHEEHECHHHHHHHHCCCHHHHHHHCC
PDB ID 1HCR Chain A (52 residues)
Model 147 RMSD 3.47Å
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Protein Reconstruction
Using predicted secondary structure and predicted
contact map
PDB ID 1BC8, chain C Sequence
MDSAITLWQFLLQLLQKPQNKHMICWTSNDGQFKLLQAEEVARLWGIRKN
KPNMNYDKLSRALRYYYVKNIIKKVNGQKFVYKFVSYPEILNM True
SS CCCCCCHHHHHHHHCCCHHHCCCCEECCCCCEEECCCHHHHHHHH
HHHHCCCCCCHHHHHHHHHHHHHHCCEEECCCCCCEEEECCCCHHHCC P
red SS CCCHHHHHHHHHHHHHCCCCCCEEEEECCCEEEEECCHHHH
HHHHHHHCCCCCCCHHHHHHHHHHHHHCCCEEECCCCEEEEEEECCHHHH
CC
PDB ID 1BC8 Chain C (93 residues)
Model 1714 RMSD 4.21Å
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CASP6 Self AssessmentEvaluation based on GDT_TS
of first submitted model GDT_TS Global
Distance Test Total ScoreGDT_TS (GDT_P1
GDT_P2 GDT_P4 GDT_P8 ) / 4 Pn percentage
of residues under distance cutoff n
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Hard Target Summary

• Top 10 groups displayed, of 65 registered servers
• Assessment on 25 new fold and fold recognition
  analogous target domains

N number of targets predicted Av.R.
average rank sumZ sum of Z scores on all
targets in set sumZpos sum of Z scores for
predictions with positive Z score group N Av.R.
sumZ sumZpos BAKER-ROBETTA 25 9.12 27.81 27.94 ba
ldi-group-server 24 10.04 20.47 22.33 Rokky 25
11.60 17.56 18.46 Pmodeller5 20 12.55 14.35 16.1
1 ZHOUSPARKS2 25 15.00 12.67 15.91 ACE 25 13.
08 11.63 14.89 Pcomb2 24 16.04 10.82 13.58 RAP
TOR 24 16.33 9.81 13.21 zhousp3 25 15.72 9.30
12.90 PROTINFO-AB 19 16.74 8.62 12.59
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Hard Target Summary

• Top 10 groups displayed, of 65 registered servers
• Assessment on 19 new fold and fold recognition
  analogous target domains less than 120 residues

N number of targets predicted Av.R.
average rank sumZ sum of Z scores on all
targets in set sumZpos sum of Z scores for
predictions with positive Z score group N Av.R.
sumZ sumZpos baldi-group-server 19 6.74 20.61 20.6
1 BAKER-ROBETTA 19 9.11 20.44 20.57 Rokky 19 1
2.11 12.30 13.20 PROTINFO-AB 16 12.63 11.53 12.5
9 ZHOUSPARKS2 19 15.32 8.91 11.87 Pcomb2 18 1
5.39 9.54 11.48 Pmodeller5 15 14.47 9.25 11.00
PROTINFO 18 16.22 8.66 10.56 ACE 19 14.21 6.98
10.24 RAPTOR 18 17.00 7.22 9.64
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Target T0281Detailed Target Analysis

• Target Information
• Length 70 amino acids
• Resolution 1.52 Å
• PDB code 1WHZ
• Description Hypothetical Protein From Thermus
  Thermophilus Hb8
• Domains single domain

• Assessment
• GDT_TS server rank of our 1st model 2
• GDT_TS 51.07
• RMSD to native 6.15

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Target T0281Contact Map Comparison
note true map is lower left
True Map vs. Predicted Map
True Map vs. Recovered Map
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Target T0281Structure Comparison
true structure
predicted structure
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Target T0281Structure Comparison Superposition
True structure thick trace Predicted structure
thin trace
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Target T0280_2Detailed Target Analysis

• Target Information
• Length 51 amino acids
• Resolution 2.00 Å
• PDB code 1WD5
• Description Putative phosphoribosyl transferase,
  T. thermophilus
• Domains 2nd domain, residues 53-103 of 208 AA
  sequence

• Assessment
• GDT_TS server rank of our 1st model 1 (also 1st
  among human groups)
• GDT_TS 54.41
• RMSD to native 5.81

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Target T0280_2Contact Map Comparison
note true map is lower left
True Map vs. Predicted Map
True Map vs. Recovered Map
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Target T0281Structure Comparison
true structure
predicted structure
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Target T0281Structure Comparison Superposition
True structure thick trace Predicted structure
thin trace
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THE SCRATCH SUITE

• www.igb.uci.edu
• DOMpro domains
• DISpro disordered regions
• SSpro secondary structure
• SSpro8 secondary structure
• ACCpro accessibility
• CONpro contact number
• DI-pro disulphide bridges
• BETA-pro beta partners
• CMAP-pro contact map
• CCMAP-pro coarse contact map
• CON23D-pro contact map to 3D
• 3D-pro 3D structure (homology fold recognition
  ab-initio)

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• SISQQTVWNQMATVRTPLNFDSSKQSFCQFSVDLLGGGISVDKTGDWITL
  VQNSPISNLL
• CCCECCCCCCEEEECCCCCCCCCCCCEEEEEEECCCCEEEECCCCCCEEE
  EECCHHHHHH
• CCCEEEEECEEEEECCCCCCCTCCCCEEEEEEEETCSEEEECTTTTEEEE
  EECCHHHHHH
• -----------------------------------
  ----
• --------------------------
  
• -------------------------------
  
• --------------------------
  
• eeeeee---e--e-e-eee-ee-eee---------e-e--eeeeee----
  ----------
• RVAAWKKGCLMVKVVMSGNAAVKRSDWASLVQVFLTNSNSTEHFDACRWT
  KSEPHSWELI
• HHHHHHCCCEEEEEEEEEECCEEECCCCCEEEEEEEECCCCCCCCCEEEE
  EECCCCCCCC
• HHHHHHTTCEEEEEEEEEEEEEEECCCCCEEEEEEEECCCTTCCCEEEEE
  EECCTCCEEE
• -----------------------
  ----------
• --------------------
  ----
• -----------------
  ----
• ------------------
  ----
• -----ee---e-------e-e-ee-e-e-e-----e--eeee--e-----
  --e-e-ee-e

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Advantage of Machine Learning

• Pitfalls of traditional ab-initio approaches
• Machine learning systems take time to train
  (weeks).
• Once trained however they can predict structures
  almost faster than proteins can fold.
• Predict or search protein structures on a genomic
  or bioengineering scale .

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DAG-RNNs APPROACH

• Two steps
• 1. Build relevant DAG to connect inputs, outputs,
  and hidden variables
• 2. Use a deterministic (neural network)
  parameterization together with appropriate
  stationarity assumptions/weight sharingoverall
  models remains probabilistic
• Process structured data of variable size,
  topology, and dimensions efficiently
• Sequences, trees, d-lattices, graphs, etc
• Convergence theorems
• Other applications

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Convergence Theorems

• Posterior Marginals
• sBN?dBN in distribution
• sBN?dBN in probability (uniformly)
• Belief Propagation
• sBN?dBN in distribution
• sBN?dBN in probability (uniformly)

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Structural Databases

• PPDB Poxvirus Proteomic Database
• ICBS Inter Chain Beta Sheet Database

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Strategies for drug design

• Block, modulate, mediate ß-sheet interactions
• Covalent modification of a chain to prevent
  ß-sheet formation

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Three-Stage Prediction of Protein Beta-Sheets
Using Neural Networks, Alignments, and Graph
Algorithms

• Jianlin Cheng and Pierre Baldi
• School of Info. and Computer Sci.
• University of California Irvine

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Beta-Sheet Architecture
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Importance of Predicting Beta-Sheet Structure

• AB-Initio Structure Prediction
• Fold Recognition
• Model Refinement
• Protein Design
• Protein Stability

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Previous Work

• Methods
• Statistical potential approach for strand
  alignment. (Hubbard, 1994 Zhu and Braun, 1999)
• Statistical potentials to improve beta-sheet
  secondary structure prediction.(Asogawa,1997)
• Information theory approach for strand alignment.
  (Steward and Thornton, 2000)
• Neural networks for beta-residue contacts.
  (Baldi, et.al, 2000)
• Shortcomings
• Focus on one single aspect not utilize
  structural contexts and evolutionary information
  not exploit constraints enough not publicly
  available.

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Three-Stage Prediction of Beta-Sheets

• Stage 1
• Predict beta-residue pairings using
  2D-Recursive Neural Networks (2D-RNN).
• Stage 2
• Align beta-strands using alignment algorithms.
• Stage 3
• Predict beta-strand pairs and beta-sheet
  architecture using graph algorithms.

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Dataset and Statistics
Num
Chains 916
Beta residues 48,996
Residue Pairs 31,638
Beta Strand 10,745
Strand Pairs 8,172
Beta Sheet 2,533
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Stage 1 Prediction of Beta-Residue Pairings
Using 2D-RNN
Target / Output Matrix (mm)
Input Matrix I (mm)
(i,j)
2D-RNN O f(I)
(i,j)
Tij 0/1 Oij Pairing Prob.
Iij
i-2 i-1 i i1 i2 j-2 j-1 j j1 j2 i-j
Total 251 inputs
20 profiles
3 SS
2 SA
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An Example Target
Protein 1VJG
Beta-Residue Pairing Map (Target Matrix)
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An Example Output
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Stage 2 Beta-Strand Alignment
Anti-parallel
1 m

• Use output probability matrix as scoring matrix
• Dynamic programming
• Disallow gaps and use simplified searching
  algorithms

n 1
Parallel
1 m
1 n
Total number of alignments 2(mn-1)
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Strand Alignment and Pairing Matrix

• The alignment score (Pseudo Binding Energy) is
  the sum of the probabilities of paired residues.
• The best alignment is the alignment with maximum
  score.
• Strand Pairing Matrix.

Strand Pairing Matrix of 1VJG
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Stage 3 Prediction of Beta-Strand Pairings and
Beta-Sheet Architecture
Strand Pairing Constraints
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Minimum Spanning Tree Like Algorithm
Strand Pairing Graph (SPG)
Goal Find a set of connected subgraphs that
maximize the sum of pseudo-energy and
satisfy the constraints. Algorithm Minimum
Spanning Tree Like Algorithm.
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Example of MST Like Algorithm
Assembly of beta-strands
1
2
3
4
5
6
7
Step 1 Pair strand 4 and 5
0
1.3 0
.94 .37 0
.02 .02 .04 0
.02 .02 .03 1.9 0
.10 .05 .74 .04 .04 0
.02 .02 .03 .02 .02 .20 0
1
2
3
4
5
4
5
6
7
Strand Pairing Matrix of 1VJG
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Example of MST Like Algorithm
Assembly of beta-strands
1
2
3
4
5
6
7
Step 2 Pair strand 1 and 2
0
1.3 0
.94 .37 0
.02 .02 .04 0
.02 .02 .03 1.9 0
.10 .05 .74 .04 .04 0
.02 .02 .03 .02 .02 .20 0
1
2
3
4
5
4
5
6
7
2
1
Strand Pairing Matrix of 1VJGA
N
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Example of MST Like Algorithm
Assembly of beta-strands
1
2
3
4
5
6
7
Step 3 Pair strand 1 and 3
0
1.3 0
.94 .37 0
.02 .02 .04 0
.02 .02 .03 1.9 0
.10 .05 .74 .04 .04 0
.02 .02 .03 .02 .02 .20 0
1
2
3
4
5
4
5
6
7
2
1
3
Strand Pairing Matrix of 1VJGA
N
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Example of MST Like Algorithm
Assembly of beta-strands
1
2
3
4
5
6
7
Step 4 Pair strand 3 and 6
0
1.3 0
.94 .37 0
.02 .02 .04 0
.02 .02 .03 1.9 0
.10 .05 .74 .04 .04 0
.02 .02 .03 .02 .02 .20 0
1
2
3
4
5
4
5
6
7
2
1
3
6
Strand Pairing Matrix of 1VJGA
N
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Example of MST Like Algorithm
Assembly of beta-strands
1
2
3
4
5
6
7
Step 5 Pair strand 6 and 7
0
1.3 0
.94 .37 0
.02 .02 .04 0
.02 .02 .03 1.9 0
.10 .05 .74 .04 .04 0
.02 .02 .03 .02 .02 .20 0
1
2
3
4
5
4
5
6
C
7
2
1
3
6
7
Strand Pairing Matrix of 1VJGA
N
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Beta-Residue Pairing Results

• Sensitivity Specificity 41
• Base-line 2.3. Ratio of improvement 17.8.
• ROC area 0.86
• At 5 FPR, TPR is 58
• CMAPpro
• Spec. and Sens. is 27. ROC area0.8.
• TPR42 at 5 FPR.

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Strand Pairing Results

• Naïve algorithm of pairing all adjacent strands
• Specificity 42
• Sensitivity 50
• MST like algorithm
• Specificity 53
• Sensitivity 59
• gt20 correctly predicted strand pairs are
  non-adjacent strand pairs

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Strand Alignment Results
On the correctly predicted pairs
Paring Direction Align. All Align. Anti-P Align. Para. Align. Bridge
Acc. 93 72 69 71 88
On all native pairs
Pairing Direction Align. All Align. Anti-P Align. Para. Align. Bridge
Acc. 84 66 63 66 73

• Pairing direction is 15 higher than
• of random algorithm.
• Alignment accuracy is improved by gt15.

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Application and Future Work

• New methods for beta-residue pairings (e.g.
  Linear Programming, SVM), and strand alignment
  and pairings. More inputs (Punta and Rost, 2005).
  
• Applications
• AB-Initio Structure Sampling (beta-sheet)
• Fold Recognition (conservation of beta-sheets)
• Contact Map
• Model Refinement (pairing direction/alignment)
• Web server and dataset
• http//www.ics.uci.edu/baldig/betasheet.html

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A New Fold Example (CASP6)

• 1S12 (T0201, 94 residues)

True SS
CEEEEECCCEEEEECCCCCHHHHHHHHHHHHHHHHHHHHCCCEEEEEECC
EEEEEECCCCHHHHHHHHHHHHHHHHHHHHCCCCEEEEECCCCCC
Predicted SS
CEEEEEECCEEEECCCCCCCCHHHHHHHHHHHHHHHHHHHHHHHEHHCCC
CEEEEHHHHHHHHHHHHHHHHHHHHHHHHHCCCCEEEEEEECCC
True 12, 2-4, 3-4, 1-5
Strand Pairing Matrix
1 2 3 4 5
1 0 1.71 .05 .29 .33
2 0 .06 .41 .12
3 0 .22 .04
4 0 .53
5 0
Predicted 1-2, 2-4, 3-4, 4-5
5
1
2
4
3
Rendered in Rasmol
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ACKNOWLEDGMENTS

• UCI
• Gianluca Pollastri, Pierre-Francois Baisnee,
  Michal Rosen-Zvi
• Arlo Randall, S. Joshua Swamidass, Jianlin Cheng,
  Yimeng Dou, Yann Pecout, Mike Sweredoski,
  Alessandro Vullo, Lin Wu
• James Nowick, Luis Villareal
• DTU Soren Brunak
• Columbia Burkhard Rost
• U of Florence Paolo Frasconi
• U of Bologna Rita Casadio, Piero Fariselli
• www.igb.uci.edu/
• www.ics.uci.edu/pfbaldi

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1DFN Defensin
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A Perfectly Predicted Example
Sequence with cysteine's position identified
MSNHTHHLKFKTLKRAWKASKYFIVGLSC29LYKFNLKSLVQTALST
LAMITLTSLVITAIIYISVGNAKAKPTSKPTIQQTQQPQNHTSPFFTEHN
YKSTHTSIQSTTLSQLLNIDTTRGITYGHSTNETQNRKIKGQSTLPATRK
PPINPSGSIPPENHQDHNNFQTLPYVPC173STC176EGNLAC18
2LSLC18 6HIETERAPSRAPTITLKKTPKPKTTKKPTKTTIHHRT
SPETKLQPKNNTATPQQG ILSSTEHHTNQSTTQI Length 257,
Total number of cysteines 5 Four bonded
cysteines form two disulfide bonds 173
-------186 ( red cysteine pair) 176 -------182
(blue cysteine pair)
Prediction Results from DIpro (http//contact.ics.
uci.edu/bridge.html) Predicted Bonded
Cysteines 173,176,182,186 Predicted disulfide
bonds Bond_Index Cys1_Position Cys2_Position 1 17
3 186 2 176 182 Prediction Accuracy for both
bond state and bond pair are 100.
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A Hard Example with Many Non-Bonded Cysteines
Sequence with cysteine's position identified
MTLGRRLAC9LFLAC14VLPALLLGGTALASEIVGGRRARPHAWP
FMVSLQLRGGHFC55GATLIAPNFVMSAAHC71VANVNVRAVRVVL
GAHNLSRREPTRQVFAVQRIFENGYDPVNLLNDIVILQLNGSATINANVQ
VAQLPAQGRRLGNGVQC151LAMGWGLLGRNRGIASVLQELNVTVVTS
LC181RRSNVC187TLVRGRQAGVC198FGDSGSPLVC208N
GLIHGIASFVRGGC223ASGLYPDAFAPVAQFVNWIDSIIQRSEDNPC
254PHPRDPDPASRTH Length 267, Total Cysteine
Number 11 Eight bonded cysteines form four
disulfide bonds 55 ----- 71 (Red), 151 -----
208 (Blue), 181 ----- 187 (Green), 198 ----- 223
(Purple)
Prediction Results from DIpro (http//contact.ics.
uci.edu/bridge.html) Predicted Bonded
Cysteines 9,14,55,71,181,187,223,254 Predicted
Disulfide Bonds Bond_Index Cys1_Position Cys2_Pos
ition 1 55 71 (correct) 2 9 14
(wrong) 3 223 254 (wrong) 4 181 187
(correct) Bond State Recall 5 / 8 0.625,
Bond State Precision 5 / 8 0.625 Pair Recall
2 / 4 0.5 Pair Precision 2 / 4 0.5 Bond
number is predicted correctly.
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Prediction Accuracy on SP51 Dataset on All
Cysteines
Bond Num Bond State Recall() Bond State Precision() Pair Recall() Pair Precision()
1 91 46 74 39
2 93 77 61 51
3 90 74 54 45
4 77 87 52 59
5 71 86 33 42
6 65 84 27 34
7 63 85 36 55
8 66 89 27 41
9 60 83 23 35
10 55 86 30 45
11 62 86 34 47
12 67 97 17 23
15 50 94 27 50
16 82 99 11 13
17 61 96 22 33
18 50 82 6 9
19 47 90 11 20
Overall bond state recall 78 overall bond
state precision 74 bond number prediction
accuracy 53 average difference between true
bond number and predicted bond number 1.1 .
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CURRENT WORK

• Feedback
• Ex SS ? Contacts ? SS ? Contacts
• Homology, homology, homology
• SSpro 4.0 performs at 88

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