1. Finding Recurrent Motifs in RNA 3D Structures Jesse Stombaugh Bowling Green State University RNA Society 2006

2. Outline  “Find RNA 3D” (FR3D)  Geometric Search  Screening Algorithm  Sample Search  Sarcin Query Motif  Sarcin Search Results  Summary

3. Outline  “Find RNA 3D” (FR3D)  Geometric Search  Screening Algorithm  Sample Search  Sarcin Query Motif  Sarcin Search Results  Summary

4. “Find RNA 3D” (FR3D)  We have developed a suite of Matlab programs, which allow for the search of RNA 3D structures.  Geometric search: given a query motif, find candidate motifs which are geometrically similar to the query motif, and rank them according to degree of similarity. (~ 2 min.)  Symbolic Search: Search for Candidates satisfying given basepairing and stacking constraints. (~ 5 sec.)  Combined search: geometric search with additional symbolic constraints. (~ 1 min.)

5. Outline  “Find RNA 3D” (FR3D)  Geometric Search  Screening Algorithm  Sample Search  Sarcin Query Motif  Sarcin Search Results  Summary

6. Geometric Search  Consider a query motif (blue) and a candidate motif (red).  Rigidly move candidate to align base centers (black dots).  The fitting error L is the RMS sum of distances between corresponding base centers.  The orientation error A is the RMS sum of angles required to rotate candidate bases onto query bases.  Geometric discrepancy

7. Geometric Search Discrepancies  In the 23S, there are 2754 bases.  For a 4–nucleotide query motif, that makes for: 2754 · 2753 · 2752 · 2751 = 5.7x10 13 possible candidate motifs.  You cannot calculate the discrepancy for every conceivable candidate motif.  Instead, set a cutoff discrepancy D 0 and find all candidates whose discrepancy with the query motif is smaller than D 0.

8. Outline  “Find RNA 3D” (FR3D)  Geometric Search  Screening Algorithm  Sample Search  Sarcin Query Motif  Sarcin Search Results  Summary

9. Screening Algorithm – Rejecting Candidates  (Q 12 -C 12 ) 2 ~ Large Discrepancy  Many candidates are nowhere close to the query motif.  We derive the inequality: where Q ij is the distance between centers of bases i and j in the query motif, and C ij for the candidate. Query Motif Candidate Motif 1 2 1 2

10. Screening Algorithm  Focusing on bases 1 and 2 in the query motif.  Find all pairs in the structure whose distances are similar.

11. Screening Algorithm  Focusing on bases 1, 2, and 3 in the query motif.  Find all triples in the structure whose distances are similar.

12. Screening Algorithm  Focusing on all in the query motif.  Find all quadruples in the structure whose distances are similar.

13. Outline  “Find RNA 3D” (FR3D)  Geometric Search  Screening Algorithm  Sample Search  Sarcin Query Motif  Sarcin Search Results  Summary

14. Sarcin Query Motif

15. Basepairing (Left) Identification of edges in the RNA bases. (Right) cis versus trans orientation of glycosidic bonds.

16. Sarcin Query Motif

17. Outline  “Find RNA 3D” (FR3D)  Geometric Search  Screening Algorithm  Sample Search  Sarcin Query Motif  Sarcin Search Results  Summary

18. Sarcin Search Results

19. Local vs. Composite Superposition of Local (black) and Composite (red, blue, cyan, green) Sarcin motifs Local Sarcin motif From DI of 23S rRNA Composite Sarcin motif from DII of 23S rRNA

20. Sarcin Search Results

21. Sarcin Search Results – Candidate 2

22. Sarcin Search Results – Candidate 3

23. Sarcin Search Results – Candidate 4

24. Sarcin Search Results – Candidate 5

25. Sarcin Search Results – Candidate 6

26. Sarcin Search Results – Candidate 7

27. Sarcin Search Results – Candidate 8

28. Outline  “Find RNA 3D” (FR3D)  Geometric Search  Screening Algorithm  Sample Search  Sarcin Query Motif  Sarcin Search Results  Summary

29. Summary  We can find and rank motifs similar to a given query motif  We can apply symbolic constraints to narrow the search and reduce search time  The program FR3D is available at: http://rna.bgsu.edu/FR3D

30. Acknowledgements Organizers of the RNA Society BGSU – Chemistry  Neocles Leontis, P.I.  Ali Mokdad (Poster #215)  Lorena Nasalean  Kirill Afonin BGSU – Math. And Stats.  Craig Zirbel  Mike Sarver