Profile-based String Kernels for Remote Homology Detection and Motif Extraction

Transcription

1 Profile-based String Kernels for Remote Homology Detection and Motif Extraction Ray Kuang, Eugene Ie, Ke Wang, Kai Wang, Mahira Siddiqi, Yoav Freund and Christina Leslie. Department of Computer Science Columbia University

2 Agenda Remote Protein Homology Detection Classification of SCOP Superfamilies SVM and Kernels Profile Kernel and its Family Tree Motif Extraction with Profile Kernel Conclusion and Future Work

3 Remote Protein Homology Detection Protein represented by sequence of amino acids Easy to sequence proteins, difficult to obtain structure Remote homologs: remote evolutionary relationship conserved structure/function, low sequence similarity <10% sequence identity ADTIVAVELDTYPNTDIGDPSYPHIGIDIKSVRSKKTAKW NMQNGKVGTAHIIYNSVDKRLSAVVSYPNADSATVSYDVD LDNVLPEWVRVGLSASTGLYKETNTILSWSFTSKLKSNST HETNALHFMFNQFSKDQKDLILQGDATTGTDGNLELTRVS SNGPQGSSVGRALFYAPVHIWESSAVVASFEATFTFLIKS PDSHPADGIAFFISNIDSSIPSGSTGRLLGLFPDAN MSLLPVPYTEAASLSTGSTVTIKGRPLVCFLNEPYLQV DFHTEMKEESDIVFHFQVCFGRRVVMNSREYGAWKQQV ESKNMPFQDGQEFLSISVLPDKYQVMVNGQSSYTFDHR IKPEAVKMVQVWRDISLTKFNVSYLKR

4 Classification of SCOP Superfamilies Fold SCOP Superfamily Family Positive Training Set Negative Training Set Positive Test Set Negative Test Set Remote homologs: sequences that belong to the same superfamily but not the same family Discriminative framework: use positive (+1) and negative (-1) training sequences to learn classifier

5 Support Vector Machine (SVM) Classifiers Training examples mapped to (usually high-dimensional) feature space by a feature map Φ(x) = (φ 1 (x),, φ N (x)) Learn linear classifier in feature space f(x) = w, Φ(x) + b by solving optimization problem: trade-off between maximizing geometric margin and minimizing margin violations Large margin: good generalization performance even in high dimensions b w +

6 Kernels for Discrete Objects Kernel trick: To train an SVM, can use kernel rather than explicit feature map Can define kernels for sequences, graphs, other discrete objects: { sequences } Φ R N Kernel value is inner product in feature space: K(x, y) = Φ(x), Φ(y) Original string kernels (Watkins, Haussler, Lodhi et al.) require quadratic time in sequence length, O( x y ), to compute each kernel value K(x, y) We introduce fast novel string kernels computed with a trie data structure

7 Profile Kernel and its Family Tree Three generations Spectrum Kernel Mismatch Kernel Profile Kernel Effective: one of the best performing methods Fast: computation scales linearly with sequence length

8 Spectrum Kernel (Leslie, Eskin and Noble, PSB 2002) Feature map indexed by all possible k-length subsequences ( k-mers ) from alphabet Σ of amino acids, Σ = 20 Q1:AKQDYYYYE AKQ KQD QDY DYY YYY YYY YYE Feature Space (AAA-YYY) 1 AKQ 1 1 DYY 1 0 EIA 1 0 IAK 1 1 KQD 0 0 KQY 1 1 QDY 0 0 YEI 1 1 YYE 1 2 YYY 0 Q2:DYYEIAKQY DYY YYE YEI EIA IAK AKQ KQY K(Q1,Q2)=<( ),( )>=3 Problem: K-mers capture some position-independent local similarity, but they do not model mutations

9 Mismatch Kernel (Leslie, Eskin, Weston and Noble, NIPS 2002) For k-mer s, the mismatch neighborhood N (k,m) (s) is the set of all k-mers t within m mismatches from s Size of mismatch neighborhood is O( Σ m k m ) AKQ CKQ DKQ AKQ AAQ AKY ( 0,, 1,, 1,, 1,, 1,, 0 ) AAQ AKY CKQ DKQ

10 Computing the Mismatch Kernel Use mismatch tree (trie) to organize lexical traversal of all instances of k-mers (with mismatches) in training set Traversal of trie for k=3, m=1 S 1 : S 2 : EADLALGKAVF ADLALGADQVFNG A

11 Computing the Mismatch Kernel Use mismatch tree (trie) to organize lexical traversal of all instances of k-mers (with mismatches) in training set Traversal of trie for k=3, m=1 S 1 : S 2 : EADLALGKAVF ADLALGADQVFNG D A

12 Computing the Mismatch Kernel Use mismatch tree (trie) to organize lexical traversal of all instances of k-mers (with mismatches) in training set Traversal of trie for k=3, m=1 S 1 : EADLALGKAVF A S 2 : ADLALGADQVFNG D L Update kernel value for K(s 1,s 2 ) by adding contribution for feature ADL Problem: Arbitrary mismatch does not model the mutation probability between amino acids

13 Profile Kernel Profile kernel: specialized to protein sequences, probabilistic profiles to capture homology information Semi-supervised approach: profiles are estimated using unlabeled data (sequences available for about 1 million proteins ) A Q K A C D Y query profile E.g. PSI-BLAST profiles: estimated by iteratively aligning database homologs to query sequence

14 Profile-based k-mer Map P(x) = { p j (b),b Σ, j =1K x} Use profile to define position-dependent mutation neighborhoods: E.g. k=3, σ=5 and a profile of negative log probabilities A K Q A C D K Q Y M k,σ ( ) YKQ (2+1+1<σ) AKQ (1+1+1<σ) [ ] ( P( x j+ 1: j + k ))= { b 1 b 2 Lb k : log( p j + i ( b i )) < σ} i AKQ YKC AKC (2+1+1<σ) (1+1+2<σ) AKQ ( 0,, 1,, 1,, 1,, 1,, 0 ) AKC AKQ YKC YKQ

15 Efficient Computing with Trie Use trie data structure to organize lexical traversal of all instances of k-mers training profile. Scales linearly with length, O(k m_max+1 Σ m_max ( x + y )), where m_max is maximum number of mismatches that occur in any mutation neighborhood. E.g. k=3, σ=5 Query x A Q K A C D Q Y C Q D A x: 1+1+1< σ x: < σ y: < σ y: > σ Update K(x, y) by adding contribution for feature AQC but not AQD Query y A Q Y A C D Q Y 3 3 3

16 Experiments SCOP benchmark with 54 experiments Train PSI-BLAST profiles on NR database Comparison against newer SVM methods: PSI-BLAST rank: use training sequence as query and rank testing sequences with PSI-BLAST e-value EMotif Kernel (Ben-Hur et al., 2003): features are known protein motifs, stored using trie SVM-pairwise (Liao & Noble, 2002): feature vectors of pairwise alignment scores (e.g. PSI-BLAST scores) Cluster Kernel (Weston et al., 2003): Implicitly average the feature vectors for sequences in the PSI-BLAST neighborhood of input sequence

17 Results

18 Performance Comparison Kernels PSI-BLAST EMOTIF Mismatch(5,1) SVM-Pairwise Cluster Profile(5,7.5)-2 Iteration Profile(5,7.5)-5 Iteration ROC ROC

19 Extracting Discriminative Motif Regions SVM training determines support vector sequence profiles and their weights: (P(x i ), α i ) SVM decision hyperplane normal vector: w = Σ i y i α i Φ(P(x i )) Positional contribution to classification score: Sxj+1: [ j + k] [ ] ( )= Φ( Pxj+1: ( j + k )),w Averaged positional score for positive sequences: S avg x[ j] q=1kk [ ] ( ) ( )= max Sxj ( k + q : j 1+ q ),0

20 Extracting Discriminative Motif Sort positional scores: about 40%- 50% of positions in positive training sequences contribute 90% of classification score Peaky positional plots discriminative motifs Regions

21 Mapping Discriminative Regions to Structure Ecoli MarA protein (1bl0) In examined examples, discriminative motif regions correspond to conserved structural features of the protein superfamily Example: Homeodomain-like protein superfamily.

22 Conclusions and Future Work Conclusions: Profile string kernels exploit compact representation of homology information Interpretation of profile-svm classifier by discriminative motif regions: conserved structural components Future work Use secondary structure information in profile kernel Extend profile kernel for multi-class protein homology detection problem

23 Acknowledgements Asa Ben-Hur University of Washington Chris Bystroff Rensselaer Polytechnic Institute Lan Xu The Scripps Research Institute HairuoLiu Columbia University Eleazar Eskin University of California, San Diego