Protein Quaternary Fold Recognition Using Conditional Graphical Models

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Protein Quaternary Fold Recognition Using
Conditional Graphical Models

• Yan Liu
• IBM Research
• Jaime Carbonell (CMU), Vanathi Gopalakrishnan (U
  Pitt), Peter Weigele (MIT)
• ICML-2007 workshop

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Snapshot of Cell Biology
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Example Protein Structures
Triple beta-spiral fold in Adenovirus Fiber Shaft
Adenovirus Fibre Shaft
Virus Capsid
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Predicting Protein Structures

• Protein Structure is a key determinant of protein
  function
• Crystalography to resolve protein structures
  experimentally in-vitro is very expensive, NMR
  can only resolve very-small proteins
• The gap between the known protein sequences and
  structures
• 3,023,461 sequences v.s. 36,247 resolved
  structures (1.2)
• Therefore we need to predict structures in-silico

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Quaternary Folds and Alignments

• Protein fold
• Identifiable regular arrangement of secondary
  structural elements
• Thus far, a limited number of protein folds have
  been discovered (1000)
• Very few research work on quaternary folds
• Complex structures and few labeled data
• Quaternary fold recognition

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Related Work

• Previous Work in General Protein Structure
  Prediction
• Sequence similarity perspective Altschul et al,
  1997, Durbin et al, 1998, Karplus et al, 1998,
  Jones, 2001
• Physical forces perspective Jones, 1998
• Structural biology perspective Efimov, 1991
  Wilmot and Thornton, 1990 Bradley at al, 2001
• Previous Work in Quaternary Structure Prediction
• Mostly on partial tasks, e.g. classification of
  protein sequences, analysis of domain-domain
  docking or interaction types and geometric
  regularities and constraints
• Computational challenges in viral fold
  recognition
• Complex structures, insufficient data and less
  sequence similarities between membership proteins

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Conditional Random Fields

• Hidden Markov model (HMM) Rabiner, 1989
• Conditional random fields (CRFs) Lafferty et al,
  2001
• Model conditional probability directly
  (discriminative models, directly optimizable)
• Allow arbitrary dependencies in observation
• Adaptive to different loss functions and
  regularizers
• Promising results in multiple applications
• But, need to scale up (computationally) and
  extend to long-distance dependencies

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Our Solution Conditional Graphical Models
Long-range dependency
Local dependency

• Segmentation CRF
• Outputs Y M, Wi , where Wi pi, qi, si
• Feature definition
• Node feature
• Local interaction feature
• Long-range interaction feature

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Linked Segmentation CRF

• Node secondary structure elements and/or simple
  fold
• Edges Local interactions and long-range
  inter-chain and intra-chain interactions
• L-SCRF conditional probability of y given x is
  defined as

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Linked Segmentation CRF (II)

• Objective
• Training learn the model parameters ?
• Minimizing regularized negative log loss
• Iterative search algorithms by seeking the
  direction whose empirical values agree with the
  expectation
• Complex graphs results in huge computational
  complexity

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Approximate Inference - Learning

• Most approximation algorithms cannot handle
  variable number of nodes in the graph, but we
  need variable graph topologies, so
• Contrastive Divergence Hinton Welling, 2002
• ??k Ep0 fk E p1fk
• P0 estimated from empirical samples
• P1 estimated from a few samples starting the
  seeds from the empirical samples

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Approximate Inference - Inference

• Reversible jump MCMC sampling Greens, 1995,
  Schmidler et al, 2001 with Four types of
  Metropolis operators
• State switching
• Position switching
• Segment split
• Segment merge
• MAP estimate using simulated annealing reversible
  jump MCMC Andireu et al, 2000
• Replace the sample with RJ MCMC
• Theoretically converge on the global optimum

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Experiments Target Quaternary Fold

• Triple beta-spirals van Raaij et al. Nature
  1999
• Virus fibers in adenovirus, reovirus and PRD1
• Double barrel trimer Benson et al, 2004
• Coat protein of adenovirus, PRD1, STIV, PBCV

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Features for Protein Fold Recognition
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Experiment Results Fold Recognition

• Double barrel-trimer

Triple beta-spirals
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Experiment Results Alignment Prediction
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Experiment ResultsDiscovery of New Membership
Proteins

• Predicted membership proteins of triple
  beta-spirals can be accessed at
• http//www.cs.cmu.edu/yanliu/swissprot_list.xls
• Membership proteins of double barrel-trimer
  suggested by biologists Benson, 2005 compared
  with L-SCRF predictions

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Conclusion

• Conditional graphical models for protein
  structure prediction
• Effective representation for protein structural
  properties
• Feasibility to incorporate different kinds of
  informative features
• Efficient inference algorithms for large-scale
  applications
• A major extension compared with previous work
• Knowledge representation through graphical models
• Ability to handle long-range interactions within
  one chain and between chains
• Future work
• Automatic learning of graph topology
• Applications to other domains

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Tertiary Fold Recognition ß-Helix fold

• Histogram and ranks for known ß-helices against
  PDB-minus dataset

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Chain graph model reduces the real running time
of SCRFs model by around 50 times
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Fold Alignment Prediction ß-Helix

• Predicted alignment for known ß -helices on
  cross-family validation

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Discovery of New Potential ß-helices

• Run structural predictor seeking potential
  ß-helices from Uniprot (structurally unresolved)
  databases
• Full list (98 new predictions) can be accessed at
  www.cs.cmu.edu/yanliu/SCRF.html
• Verification on 3 proteins with later
  experimentally resolved structures from different
  organisms
• 1YP2 Potato Tuber ADP-Glucose Pyrophosphorylase
• 1PXZ The Major Allergen From Cedar Pollen
• GP14 of Shigella bacteriophage as a ß-helix
  protein
• No single false positive!

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Previous Work

• Sequence similarity perspective
• Sequence similarity searches, e.g. PSI-BLAST
  Altschul et al, 1997
• Profile HMM, .e.g. HMMER Durbin et al, 1998 and
  SAM Karplus et al, 1998
• Window-based methods, e.g. PSI_pred Jones, 2001
• Physical forces perspective
• Homology modeling or threading, e.g. Threader
  Jones, 1998
• Structural biology perspective
• Painstakingly hand-engineered methods for
  specific structures, e.g. aa- and ßß- hairpins,
  ß-turn and ß-helix Efimov, 1991 Wilmot and
  Thornton, 1990 Bradley at al, 2001

Fail to capture the structure properties and
long-range dependencies
Generative models based on rough approximation of
free-energy, perform very poorly on complex
structures
Very Hard to generalize due to built-in
constants, fixed features
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Graphical Models

• A graphical model is a graph representation of
  probability dependencies Pearl 1993 Jordan
  1999
• Node random variables
• Edges dependency relations
• Directed graphical model (Bayesian networks)
• Undirected graphical model (Markov random fields)