1. Protein Family Classification using Sparse Markov Transducers Proceedings of Eighth International Conference on Intelligent Systems for Molecular Biology (ISMB2000), pp. 134-145 E. Eskin, W.N. Grundy, and Y. Singer Cho, Dong-Yeon

2. 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

3. 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). VAVIGSGTVGVLGLGTV*V*G*GT – wild cards

4. 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

5. Sparse Markov Transducers A Markov Transducer of Order L  Conditional probability distribution  X k are random variables over an input alphabet  Y k 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

6. 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.

7. 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 u 1 DACDADDDCAA, C CAAAACAD, D AACCAAA, ? C  0.5, D  0.5

8. 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.

9. 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_DEPTH=2 and MAX_PHI = 1

10.  Template tree  We only store these nodes which are reached during training. AA, AC and CD

11. 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.

12. 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(A), DACADAC(C), DACAAAC(D), ACACDAC(A), ADCADAC(D) ACDACAC(D)

13. 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 4:1 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.

14. Building SMT Prediction Models  A prediction model for each protein family  A sliding window of size 11  Prediction of the middle symbol a 6 using neighboring symbols  The input symbols are a 5 a 7 a 4 a 8 a 3 a 9 a 2 a 10 a 1 a 11.  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.

15. 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: a 1,…,a 10  MAX_DEPTH=5 and MAX_PHI=1 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.

16. Results  Time-Space-Performance tradeoffs

17.  Results of Protein Classification using SMTs  The SMT models outperform the PST models.  SMT Classifier > SMT Prediction > PST Prediction

18. 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