Protein Family Classification using Sparse Markov Transducers

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Protein Family Classification using Sparse Markov
Transducers

• E. Eskin, W.N. Grundy, and Y. Singer
• ISMB 00
• Talk by Cho, Dong-Yeon

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Abstract

• Classifying proteins into families using sparse
  Markov transducers (SMTs)
• Estimation of a probability distribution
  conditioned on an input sequence
• Similar to probability suffix trees
• Allowing for wild-cards
• Two models
• Efficient data structures

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Introduction

• Protein Classification
• Pairwise similarity
• Creating profiles for protein families
• Consensus patterns using motifs
• HMM-based approaches
• Probability suffix trees (PSTs)
• A PST is a model that predicts the next symbol in
  a sequence based on the previous symbols.
• This approach is based on the presence of common
  short sequences (motifs) through the protein
  family.
• One drawback of PSTs is that they rely on exact
  matches to the conditional sequences (e.g.,
  3-hydroxyacyl-CoA dehydrogenase).

VAVIGSGT
VGVLGLGT
VVGGT wild cards
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• Sparse Markov Transducers (SMTs)
• A generalization of PSTs
• It can condition the probability model over a
  sequence that contains wild-cards.
• In a transducer, the input symbol alphabet and
  output symbol alphabet can be different.
• Two methods
• Single amino acid
• Protein family
• Efficient data structure
• Experiments
• Pfam database of protein family

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Sparse Markov Transducers

• A Markov Transducer of Order L
• Conditional probability distribution
• Xk are random variables over an input alphabet
• Yk is a random variable over an output alphabet
• Sparse Markov Transducer
• Conditional probability distribution
• ? wild card
• Two approaches for SMT-based protein
  classification
• A prediction model for each family single amino
  acid
• A single model for the entire database protein
  family

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• Sparse Markov Trees
• Representationally equivalent to SMTs
• The topology of a tree encodes the positions of
  the wild-cards in the conditioning sequence of
  the probability distribution.

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• Training a Prediction Tree
• A set of training examples
• The input symbols are used to identify which leaf
  node is associated with that training example.
• The output symbol is then used to update the
  count of the appropriate predictor.
• The predictor kept counts of each output symbol
  seen by that predictor.
• We smooth each count by adding a constant value
  to the count of each output symbol. Cf) Dirichlet
  distribution

u1 DACDADDDCAA, C CAAAACAD, D AACCAAA, ?
C?0.5, D?0.5
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• Mixture of Sparse Prediction Trees
• We do not know which tree topology can best
  estimate the distribution.
• A mixture technique employs a weight sum of trees
  as a predictor.
• Updating the weight of each tree for each input
  string in the data set based on how well the tree
  preformed on predicting the output
• The prior probability of a tree is defined by the
  topology of the tree.

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• Implementation of SMTs
• Two important parameters
• MAX_DEPTH the maximum depth of the tree
• MAX_PHI the maximum number of wild-cards at
  every node

Ten tress in the mixture if MAX_DEPTH2 and
MAX_PHI 1
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• Template tree
• We only store these nodes which are reached
  during training.

AA, AC and CD
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Efficient Data Structures

• Performance of the SMT typically improves with
  higher MAX_PHI and MAX_DEPTH.
• The memory usage become bottleneck because it
  restricts these parameters to values that will
  allow the tree to fit in memory.

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• Lazy Evaluation
• We store the tails of the training sequence and
  recompute the part of the tree on demand when
  necessary.
• EXPAND_SEQUENCE_COUNT 4

ACDACAC(D)
ACDACAC(A), DACADAC(C), DACAAAC(D), ACACDAC(A),
ADCADAC(D)
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Methodology

• Data
• Two versions of the Pfam database
• Version 1.0 for comparing results to previous
  one
• Version 5.2 the latest version
• 175 protein families
• A total of 15610 single domain protein sequences
  containing a total 3560959 residues
• Training and test data with a ratio of 41 for
  each family
• ? transmembrane receptor 530 protein sequence
  (424 106)
• The 424 sequences of the training set give 108858
  subsequences that are used to train the model.

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• Building SMT Prediction Models
• A prediction model for each protein family
• A sliding window of size 11
• Prediction of the middle symbol a6 using
  neighboring symbols
• The input symbols are a5a7a4a8a3a9a2a10a1a11.
• MAX_DEPTH 7 and MAX_PHI 1
• Classification of a Sequence using a SMT
  Prediction Model
• Computation of the likelihood for an unknown
  sequence
• A sequence is classified into a family by
  computing the likelihood of the fit for each of
  the 175 models.

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• Building the SMT Classifier Model
• Estimation of the probability over protein
  families given a sequence of amino acids
• Input sequence an amino acid sequence from a
  protein family
• Output symbol the protein family name
• A sliding window of 10 amino acids a1,,a10
• MAX_DEPTH5 and MAX_PHI1
• Classification of a Sequence using an SMT
  Classifier
• Each position of the sequence gives us a
  probability over the 175 families measuring how
  likely the substring originated from each family.

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• Results
• Time-Space-Performance tradeoffs

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• Results of Protein Classification using SMTs
• The SMT models outperform the PST models.
• SMT Classifier gt SMT Prediction gt PST Prediction

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Discussion

• Sparse Markov Transducers (SMTs)
• We have presented two methods for protein
  classification using sparse Markov transducers
  (SMTs).
• Future Work
• Incorporating biological information into the
  model such as Dirichlet mixture priors
• Combining a generative and discriminative model
• Using both positive and negative examples in
  training