Finding Subtle Motifs by Branching from Sample Strings

1. Finding Subtle Motifs by Branching from Sample Strings Xuan Qi Computer Science Dept. Utah State Univ.

2. Preface • This presentation is based on paper “Finding subtle motifs by branching from sample strings” by Alkes Price, Sriram Ramabhadran and Pavel A. Pevzner.

3. Outline • Motif finding problem. • Methods that have been proposed to address this problem. • The contribution of the method presented in this paper. • The algorithms proposed in this paper. • Experiment results. • Discussion of the advantages and disadvantages of the method proposed in this paper. • Future research direction.

4. Motif Finding Problem • Given a set of DNA sequences, find a set of l-mers, one from each sequence, that maximizes the consensus score. Input: A t*n matrix of DNA, and l, the length of the pattern to find. Output: An array of t starting positions s = (s1, s2, …, st) maximizing Score(s, DNA). • Subtle motif: low score, not significant pattern among the sequences, and thus more difficult to identify

5. Methods Proposed • Category1: Searching possible starting points of the motif Methods: CONSENSUS, GibbsSampling Disadvantages: Search space is very large. They are not always capable to find optimal motifs. • Category2: Searching possible samples of the motif Methods: Vanet et al. 2000, Marsan and Sagot 2000, Pavesi et al. 2001, Apostolico et al. 2002, Eskin and Pevzner 2002 Advantages: Reduce down the search space. Disadvantages: Still have high computational cost especially for long motifs. The selected sample may only converge to local optima instead of global optimal point. An alternative: extended sample-driven approach Search the neighbors of all samples with exhaustive search.

6. Contribution of This Paper • Basic idea: branching from the sample strings • Contribution: Much more efficient than previous algorithms. Very powerful to find subtle motifs.

7. Comparison between the Methods

8. The Algorithms Proposed • Two ways to model a motif: 1. as a pattern 2. as a profile: 4*l matrix • Two algorithms proposed: 1. Pattern-Branching algorithm 2. Profile-Branching algorithm

9. Pattern-Branching Algorithm • Distance between M and a sample A0: d(M,A0) = k • D = k(A0): a set of patterns of distance exactly k from A0 • Neighbor: D = 1(A0), changing a single nucleotide of A E.g., ATTGCCAG, ATTGCCTG, GTTGCCAG • Score of a pattern: total distance from the sequences 1. For each sequence si, d(A, si) = min{d(A, P)|Psi}, p is a l- mer (a pattern of length n). 2. The total distance of A from S is d(A, S) = ∑ siS d(A, si) • BestNeighbor(A): the pattern B  D = 1(A0) with the lowest total distance d(B, S)

10. Pattern-Branching Algorithm • Input: A set of sequences S, the length of the motif l and * of mutations k. • Output: motif of length l with k mutations. • Algorithm: PatternBranching(S, l, k) 1. Motif M arbitrary motif pattern 2. Get a set of samples of M in the sequences (S) 3. For each l-mer A0 in S 4. For j  0 to k 5. { 6. if d(Aj, S) < d(M, S) 7. M  Aj 8. Aj+1  Bestneighbour(Aj) 9. Output M 10. }

11. Profile-Branching Algorithm • Similar to Pattern-Branching • Some changes: 1. convert each sample string to a profile X(A0) 2. generalize the scoring method to score profiles 3. modify the branching method to apply to profiles 4. use the top-scoring profile we find as a seed to the EM algorithm

12. Profile-Branching Algorithm • Convert a sample string to a profile X(A0):

13. Profile-Branching Algorithm • Use entropy to score profiles: Given a profile X = (xvw)and a pattern P =p1…pl, let e(X, P) be the log probability of sampling P from X, i.e. e(X, P) = ∑wlog(xpww). G T G A C A T 1/6 1/2 1/2 1/6 1/2 1/2 1/2

14. Profile-Branching Algorithm • For each sequence Si in the sample S = {S1, …, Sn}, let e(X, Si) = max{e(X, P)|PSi}. • Then the entropy score of X is e(X, S) = ∑siS e(X, si). • Intuitively, e(X, S) describes how well X matches its best occurrence in each sequence of the sample.

15. Profile-Branching Algorithm • Branching from the sample string: 1. Amplify only one column in the profile (which corresponds to one position in the sample pattern), and we only amplify a nucleotide v if xvw < 0.5. 2. Make sure that the relative entropy ∑v xvwlog(x’vm/xvm) = . We use  = -0.3.

16. Profile-Branching Algorithm • Algorithm: ProfileBranching(S, l, k) 1. M  arbitrary motif profile 2. For each l-mer A0 in S 3. { 4. X0  X(A0) 5. For j  0 to k 6. { 7. if e(Xj, S) > e(Motif, S) 8. Motif  Xj 9. Xj+1 BestNeighbor(Xj) 10. } 11. Run EM algorithm with Motif as seed

17. Results on Implanted Motifs • Pattern-Branching algorithm VS previous pattern-based motif finding algorithms WINNOWER, SP-STAR: unable to find subtle motifs PROJECTION, MITRA, MULTIPROFILER

18. Results on Implanted Motifs • Profile-Branching algorithm VS previous profile-based motif finding algorithms • Performance coefficient: Let k be the set of n implanted motifs found, and let p be the set of predicted motif positions,the performance coefficient is defined to be |K ∩ P|/|K ∪ P|.

19. Results on Biological Samples • Pattern-Branching Algorithm: • Profile-Branching Algorithm: The pattern returned by profile-branching matches the reference motif.

20. Discussion • Advantages: Much more efficient than previous algorithms. Very powerful to find subtle motifs. • Disadvantages: 1. Pattern-Branching has difficulty finding motifs with many degenerate positions. But profile-Branching works well on it. 2. Profile-Branching is very powerful to find subtle motifs but is comparatively slow.

21. Future Work • Apply Pattern-Branching and Profile-Branching algorithms to more challenging biological samples 1. Larger samples 2. Corrupted samples • Extend the algorithms to address the motif finding problem which involves not only A, T, G, C, but purine(R), pryrimidine(Y), weak bond(W) and strong bond(S).