Data Mining in Bioinformatics Day 9: String & Text Mining in Bioinformatics Karsten Borgwardt March 1 to March 12, 2010 Machine Learning & Computational Biology Research Group MPIs Tübingen Karsten Borgwardt: Data Mining in Bioinformatics, Page 1
Why compare sequences? Protein sequences Proteins are chains of amino acids. 20 different types of amino acids can be found in protein sequences. Protein sequence changes over time by mutations, deletion, insertions. Different protein sequences may diverge from one common ancestor. Their sequences may differ slightly, yet their function is often conserved. Karsten Borgwardt: Data Mining in Bioinformatics, Page 2
Why compare sequences? Biological Question: Biologists are interested in the reverse direction: Given two protein sequences, is it likely that they originate from the same common ancestor? Computational Challenge: How to measure similarity between two protein sequence, or equivalently: How to measure similarity between two strings Kernel Challenge: How to measure similarity between two strings via a kernel function In short: How to define a string kernel Karsten Borgwardt: Data Mining in Bioinformatics, Page 3
History of sequence comparison First phase Smith-Waterman BLAST Second phase Profiles Hidden Markov Models Third phase PSI-Blast SAM-T98 Fourth phase Kernels Karsten Borgwardt: Data Mining in Bioinformatics, Page 4
Sequence comparison: Phase 1 Idea Methods Measure pairwise similarities between sequences with gaps Smith-Waterman dynamic programming high accuracy slow (O(n 2 )) BLAST faster heuristic alternative with sufficient accuracy searches common substrings of fixed length extends these in both directions performs gapped alignment Karsten Borgwardt: Data Mining in Bioinformatics, Page 5
Sequence comparison: Phase 2 Idea Methods Collect aggregate statistics from a family of sequences Compare this statistics to a single unlabeled protein Hidden Markov Models (HMMs) Markov process with hidden and observable parameters Forward algorithm determines probability if given sequence is output of particular HMM Profiles Profiles of sequence families are derived by multiple sequence alignment Given sequence is compared to this profile Karsten Borgwardt: Data Mining in Bioinformatics, Page 6
Sequence comparison: Phase 3 Idea Methods Create single models from database collections of homologous sequences PSI-BLAST Position specific iterative BLAST Profile from highest scoring hits in initial BLAST runs Position weighting according to degree of conservation Iteration of these steps SAM-T98, now SAM-T02 database search with HMM from multiple sequence alignment Karsten Borgwardt: Data Mining in Bioinformatics, Page 7
Phase 4: Kernels and SVMs General idea Model differences between classes of sequences Use SVM classifier to distinguish classes Use kernel to measure similarity between strings Kernels for Protein Sequences SVM-Fisher kernel Composite kernel Motif kernel String kernel Karsten Borgwardt: Data Mining in Bioinformatics, Page 8
SVM-Fisher method General idea Combine HMMs and SVMs for sequence classification Won best-paper award at ISMB 1999 Sequence representation fixed-length vector components are transition and emission probabilities transformation into Fisher score Karsten Borgwardt: Data Mining in Bioinformatics, Page 9
SVM-Fisher method Algorithm Model protein family F as HMM Transform query protein X into fixed-length vector via HMM Compute kernel between X and positive and negative examples of the protein family Advantages allows to incorporate prior knowledge allows to deal with missing data is interpretable outperforms competing methods Karsten Borgwardt: Data Mining in Bioinformatics, Page 10
Composition kernels General idea Model sequence by amino acid content Bin amino acids w.r.t physico-chemical properties Sequence representation feature vector of amino acid frequencies physico-chemical properties include predicted secondary structure, hydrophobicity, normalized van der Waals volume, polarity, polarizability useful database: AAindex Karsten Borgwardt: Data Mining in Bioinformatics, Page 11
Motif kernels General idea Conserved motif in amino acid sequences indicate structural and functional relationship Model sequence s as a feature vector f representing motifs i-th component of f is 1 s contains i-th motif Motif databases PROSITE emotifs BLOCKS+ combines several databases Generated by manual construction multiple sequence alignment Karsten Borgwardt: Data Mining in Bioinformatics, Page 12
Pairwise comparison kernels General idea Employ empirical kernel map on Smith-Waterman/Blast scores Advantage Utilizes decades of practical experience with Blast Disadvantage High computational cost (O(m 3 )) Alleviation Employ Blast instead of Smith-Waterman Use vectorization set for empirical map only Karsten Borgwardt: Data Mining in Bioinformatics, Page 13
Phase 4: String Kernels General idea Count common substrings in two strings A substring of length k is a k-mer Variations Assign weights to k-mers Allow for mismatches Allow for gaps Include substitutions Include wildcards Karsten Borgwardt: Data Mining in Bioinformatics, Page 14
Spectrum Kernel General idea For each l-mer α Σ l, the coordinate indexed by α will be the number of times α occurs in sequence x. Then the l-spectrum feature map is Φ Spectrum l (x) = (φ α (x)) α Σ l Here φ α (x) is the # occurrences of α in x. The spectrum kernel is now the inner product in the feature space defined by this map: k Spectrum (x, x ) =< Φ Spectrum l (x), Φ Spectrum l (x ) > Sequences are deemed the more similar, the more common substrings they contain Karsten Borgwardt: Data Mining in Bioinformatics, Page 15
Spectrum Kernel Principle Spectrum kernel: Count exactly common k-mers Karsten Borgwardt: Data Mining in Bioinformatics, Page 16
Mismatch Kernel General idea Do not enforce strictly exact matches Define mismatch neighborhood of an l-mer α with up to m mismatches: φ Mismatch (l,m) (α) = (φ β (α)) β Σ l For a sequence x of any length, the map is then extended as φ Mismatch (l,m) (x) = (φ Mismatch (l,m) (α)) l mers α in x The mismatch kernel is now the inner product in feature space defined by: k Mismatch (l,m) (x, x ) =< Φ Mismatch (l,m) (x), Φ Mismatch (l,m) (x ) > Karsten Borgwardt: Data Mining in Bioinformatics, Page 17
Mismatch Kernel Principle Mismatch kernel: Count common k-mers with max. m mismatches Karsten Borgwardt: Data Mining in Bioinformatics, Page 18
Gappy Kernel General idea Allow for gaps in common substrings subsequences A g-mer then contributes to all its l-mer subsequences φ Gap (g,l) (α) = (φ β(α)) β Σ l For a sequence x of any length, the map is then extended as φ Gap (g,l) (x) = (φ Gap (g,l) (α)) g mers α in x The gappy kernel is now the inner product in feature space defined by: k Gap (g,l) (x, x ) =< Φ Gap (g,l) (x), ΦGap (g,l) (x ) > Karsten Borgwardt: Data Mining in Bioinformatics, Page 19
Gappy Kernel Principle Gappy kernel: Count common l-subsequences of g- mers Karsten Borgwardt: Data Mining in Bioinformatics, Page 20
Substitution Kernel General idea mismatch neighborhood substitution neighborhood An l-mer then contributes to all l-mers in its substitution neighborhood l M (l,σ) (α) = {β = b 1 b 2... b l Σ l : log P (a i b i ) < σ} For a sequence x of any length, the map is then extended as φ Sub (l,σ) (x) = (φ Sub (l,σ) (α)) l mers α in x The substitution kernel is now: k(l,σ) Sub (x, x ) =< Φ Sub (l,σ)(x), ΦSub (l,σ) (x ) > i Karsten Borgwardt: Data Mining in Bioinformatics, Page 21
Substitution Kernel Principle Substitution kernel: Count common l-subsequences in substitution neighborhood Karsten Borgwardt: Data Mining in Bioinformatics, Page 22
Wildcard Kernels General idea augment alphabet Σ by a wildcard character Σ { } given α from Σ l and β from {Σ { }} l with maximum m occurrences of l-mer α contributes to l-mer β if their non-wildcard characters match For a sequence x of any length, the map is then given by φ W (l,m,λ) ildcard (x) = (φ β (α)) β W l mers α in x where φ β (α) = λ j if α matches pattern β containing j wildcards, φ β (α) = 0 if α does not match β, and 0 λ 1. Karsten Borgwardt: Data Mining in Bioinformatics, Page 23
Wildcard Kernel Principle Wildcard kernel: Count l-mers that match except for wildcards Karsten Borgwardt: Data Mining in Bioinformatics, Page 24
References and further reading References [1] C. Leslie, E. Eskin, and W. S. Noble. The spectrum kernel: A string kernel for SVM protein classification. In PSB, pages 564 575, 2002. [2] C. Leslie, E. Eskin, J. Weston, and W. S. Noble. Mismatch string kernels for SVM protein classification. In NIPS 2002. MIT Press. [3] C. Leslie and R. Kuang. Fast kernels for inexact string matching. In COLT, 2003. [4] B. Schölkopf, K. Tsuda, and J.-P. Vert. Kernel Methods in Computational Biology, Chapter 3 and 4. MIT Press, Cambridge, MA, 2004. Karsten Borgwardt: Data Mining in Bioinformatics, Page 25