Setting Up a Replica Exchange Approach to Motif Discovery in DNA

1. Setting Up a Replica Exchange Approach to Motif Discovery in DNA Jeffrey Goett Advisor: Professor Sengupta

2. RNA polymerase Binding Proteins Regulation Transcription Binding sites gene Translation to Proteins Protein Synthesis from DNA

3. Binding Site Binding protein “A” Binding protein “A” T - T - C - A - A - C - C - A - A - A - C - G - A - C - Sequence A: T - T - G - C - T - G - A - A - G - T - T - G - G - T - code for protein C - G - T - T - G - C - T - C - A - A - G - G - A - C - Sequence B: T - T - C - C - T - G - G - C - A - A - C - G - A - G - code for protein Binding Sites

4. Discovering New Binding Motifs Motif: GCTCAG …ATCG GCTCAG CTAG… …CACT GATCAG AGTA… …TTCC GCTCTG TAAC… …GCTA GCTCAA ATCG… Motif Probability Model

5. Modeling Motifs in Sequences Assume: Break into N sequences Each sequence has one instance of motif embedded in random background Variations of motif by point mutation, but not insertion or deletion ATATCCGTA AATCGAGAC TCGATGTGT CCACCTGCA

6. Modeling Motifs in Sequences The “Alignment:”Starting position of motif in each sequence AT ATC CGTA A ATC GAGAC TCG ATG TGT CC ACC TGCA The “Motif Probability Distribution:”Probability of each letter occurring at each motif position

7. 0 0 0 0 0 0 0 0 0 0 pC pC pG pT pA pA pA pT pC pG p1,T p2,A p3,T 0 ATATCCGTA AATCGAGAC TCGATGTGT CCACCTGCA pA p1,A p2,G p3,A 0 pC 0 0 0 pT pC pG 0 0 0 pT pG pT p1,A p2,T p3,G 0 0 0 0 0 0 p1,C p2,C p3,A pC pC pT pG pC pA Scoring a Model “Log-likelihood” score:

8. {3, 2, 4, 3} {2, 4, 7, 3} Example Models A TAT CCGTA AAT CGA GAC TCGATG TGT CC ACC TGCA AT ATC CGTA A ATC GAGAC TCG ATG TGT CC ACC TGCA

9. The Gibbs Sampler that maximizes We want to find

10. The Gibbs Sampler

11. The Gibbs Sampler Times visited Over time, the frequency distribution approaches

12. Optimization Technique If we assume areas of local maximization contribute the most during “integration” to the local maximizations of Biasing our search to these areas may discover the pj,ro values which maximize faster.

13. Multiple Gibbs Samplers By combining results from Gibbs Samplers begun at random positions, find maximizing sooner

14. Replica Exchange/Parallel Tempering “Low-sensitivity” samplers which “scout out area” periodically swap with “high-sensitivity” samplers good at focused searches if swap appears promising.

15. Controlling Sensitivity Adjust the relative probability of sampling an xi by adjusting a new parameter in distribution: Large Small Search breadth of space Focused search of region

16. Betas 2 1 .9 .1 Testing the Sensitivity Running on randomly generated sequences to see motifs found, different sensitivity samplers converge to different scores.

17. Predicting Convergence Score Measure of Similarity: magnetization Ex: m=.5 “Configuration Score:” energy m=0 m=0 m=1 m=0 m=.5 E=2J E=2J E=-6J E=2J E=0

18. Alignment Analogue m=1 E=-9J A: B: m=.77 E=-5J C: m=.77 m=.77 E=-5J E=-5J

19. Test Results L<|alphabet|w

20. Test Results L>|alphabet|w

21. Test Results

22. Test Results

23. Hidden Motifs: Gibbs Sampler Beta = .1 Beta = .5 Beta = .9 Beta = 1.3 Beta = 1.7 Beta = 2 W=5, l=500

24. Betas .8 .9 .93 .96 1 1.5 Hidden Motifs: Replica Exchange