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 A 0 : d(M, A 0 ) = k  D = k (A 0 ): a set of patterns of distance exactly k from A 0  Neighbor: D = 1 (A 0 ), changing a single nucleotide of A E.g., ATTGCCAG, ATTGCCTG, GTTGCCAG  Score of a pattern: total distance from the sequences 1. For each sequence s i, d(A, s i ) = min{d(A, P)|P  s i }, p is a l- mer (a pattern of length n). 2. The total distance of A from S is d(A, S) = ∑ s i  S d(A, s i )  BestNeighbor(A): the pattern B  D = 1 (A 0 ) 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 A 0 in S 4. For j  0 to k 5. { 6. if d(A j, S) < d(M, S) 7. M  A j 8. A j+1  Bestneighbour(A j ) 9. Output M 10. }

11. Profile-Branching Algorithm  Similar to Pattern-Branching  Some changes: 1. convert each sample string to a profile X(A 0 ) 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(A 0 ): ATGCCAT A1/21/6 1/21/6 T 1/21/6 1/2 G1/6 1/21/6 C 1/2 1/6

13. Profile-Branching Algorithm  Use entropy to score profiles: Given a profile X = (x vw ) and a pattern P = p 1 … p l, let e(X, P) be the log probability of sampling P from X, i.e. e(X, P) = ∑ w log(x p w w ). ATGCCAT A1/21/6 1/21/6 T 1/21/6 1/2 G1/6 1/21/6 C 1/2 1/6 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 S i in the sample S = {S 1, …, S n }, let e(X, S i ) = max{e(X, P)|P  S i }.  Then the entropy score of X is e(X, S) = ∑ s i  S e(X, s i ).  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 x vw < 0.5. 2. Make sure that the relative entropy ∑ v x vw log(x’ vm /x vm ) = . We use  = -0.3. ATGCCAT A1/21/6 1/21/6 T 1/21/6 1/2 G1/6 1/21/6 C 1/2 1/6 ATGCCAT A0.271/6 1/21/6 T0.551/21/6 1/2 G0.091/61/21/6 C0.091/6 1/2 1/6

16. Profile-Branching Algorithm  Algorithm: ProfileBranching(S, l, k) 1. M  arbitrary motif profile 2. For each l-mer A 0 in S 3. { 4. X 0  X(A 0 ) 5. For j  0 to k 6. { 7. if e(X j, S) > e(Motif, S) 8. Motif  Xj 9. X j+1  BestNeighbor(X j ) 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).