Bayesian Segmentation of Protein Sequences

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Bayesian Segmentation of Protein Sequences
Paper A Graphical Model for Protein Secondary
Structure Prediction by Wei Chu, Zoubin
Ghahramani, and David L. Wild ICML(2003)

• Presentation by Jivko Sinapov

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Outline

• Introduction
• Background
• Naïve Bayes, HMM, HSMM
• Baysian Segmentation Model
• Experiments and Results
• Discussion

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Introduction

• Prediction of class labels for residues in a
  protein sequence

Secondary structure
Sequence VTSYTLSDVVSLKDVVPEWVRIGFSATTGAEYAAHEVLSW
SFHSELS Class -EEEEEEEE--HHHH---EEEEEEEEE-----
-EEEEEEEEEEEEE-
Protein-RNA interface
Sequence DSNPKYLGVKKFGGEVVKAGNILVRQRGTKFKAGQGVGMG
RDHTLFALSDGK Class 111111001111111001111100101
1111100000001111101000000
Protein-Protein interface
Sequence AVTTYKLVINGKTLKGETTTKAVDAETAEKAFKQYANDNG
VDGVWTYDDA Class 00000000000111111110100000000
000001011110000000000
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Background

• Naïve Assumption the label of a residue is
  independent of the labels of neighboring
  residues.
• e.g. Naïve Bayes on windows

c1
c2
c3
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Class labels
s1
s2
s3
s4
s5
s6
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s8
Sequence
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Background

• Hidden Markov Model
• Models dependencies between adjacent class labels
• Observation can be multi-dimensional (PSSM, or
  multiple sequence alignment)
• Efficient algorithms for learning and prediction
  of class labels
• Captures some local dependencies that are obvious
  from the data

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Class labels
s1
s2
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Sequence
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Previous methods

• Hidden semi-Markov Model
• Each state is a segment of the sequence
• Each state emits a sequence, rather than a single
  amino-acid

coil
sheet
coil
helix
coil
V TSYTLSDV VS LKDV VPE
More formally
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Sequence segmentation

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

• T2 E ß-strand S2 9 R2 S1 1 S2

in Bayesian Segmentation of Protein Secondary
Structure SC Schmidler, JS Liu, DL Brutlag -
Journal of Computational Biology, 2000
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Bayesian Segmentation of Protein Secondary
Structure

• Introduces a model that utilizes multiple
  sequence alignments or PSSM
• Efficient algorithms for learning and inference
• Improves accuracy by 10 against window-based
  methods
• Models long range interaction by beta-strands

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The Model

• Observation

where Oi is a 20 x 1 vector containing the
occurrence counts for each amino acid at position
i.

• Set of structure types

• Segment sequence

• Segment locations determined by position of last
  residue in the segments

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• The variables (m,e,T) describe the segmentation
• Bayesian approach

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• Prior

where
is specified by a 3x3 transition matrix.
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• Likelihood

and

• Likelihood function for each segment

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• Likelihood function for each residue

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• Dirichlet prior on

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• Likelihood function for each segment becomes

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Inference (i.e. classification)

• Bayes rule

• MAP estimate (use Viterbi)

• Marginal posterior mode estimate (use
  forward-backward)

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Long Range interactions
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• Long range interactions

where r is the number of interacting pairs
is a pair of interacting segments with their
alignment information
and

• Incorporate into model
• Prior
• Conditional
• Final segmental likelihood for strand

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Parameter estimation and inference

• Discrete parameters segment lengths, occurrence
  counts, state transition probabilities.
• Estimated directly from data

• Weight parameters for neighboring and
  long-distance dependencies
• Estimated using a MAP estimate
• Uses Variational method (!!!)

• Use Markov-Chain Monte Carlo for inference

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Experiments and Results

• Dataset CB513
• 513 non-homologous protein chains with solved
  structure
• Removed sequences shorter than 30 and longer than
  550.
• Do 7-fold cross validation

• Three types of features
• Sequence only
• Multiple sequence alignment profile
• PSSM

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Experiments and Results
window-based Naïve Bayes approach 60.5
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Predicting long range interactions

• A subset of 153 proteins with long range contact
  maps between beta-strands
• Good performance in predicting the contact maps
  between a pair of beta-strands AUC 0.89
• However, no clear difference between using MCMC
  with long range interaction and exact inference
  without such interactions

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Discussion

• The model achieves comparable performance to the
  state of the art
• Can be extended to other problems
• Can model short-distance and long-distance
  interaction between segments
• If using sequence only, model achieves 5
  improvement over Naïve Bayes