1. Predicting Coaxial Stacking by Free Energy Minimization David Mathews Department of Biochemistry & Biophysics University of Rochester Medical Center

2. Predicting Coaxial Stacking: Rahul Tyagi

3. Multibranch Loops (MBL) http://www.stanford.edu/~esorin

4. A step towards tertiary structure prediction Secondary structure representation 1 stacked on 2 mediated by mismatch 2 flush stacked on 3

5. Flush and Mismatch-Mediated Stacking Mismatch-mediated stacking Flush stacking - Stacking stabilization: Thought to arise from hydrophobic effect, charge interactions and van der Waals interactions.

6. Predicting Coaxial Stacking -Find all the non-redundant RNA crystal structures from NDb. “The stacking configuration with lowest free energy as predicted by Nearest Neighbour Parameters exists in naturally occurring RNAs.” -Compare predictions with crystal structures. -Predict the coaxial stacking configuration by finding free energy of all possible configurations in all MBLs. Hypothesis

7. Finding Lowest Free Energy Configuration

8. Secondary structure to predicted stacks http://www.rna.icmb.utexas.edu/

9. Nearest Neighbor Model for Coaxial Stacking Model based on work by Walter, Kim and others in Turner lab.

10. Stacks with more than one Mismatch

11. Identifying Coaxial Stacks in Crystal Structures

12. Atom Coordinates to Identified Stacks http://rna.ucsc.edu/rnacenter/ribosome_images.html

13. Stacking Definition for Verification Basepair center and basepair plane definition from Biochemistry 2nd Ed. by Garrett & Grisham

14. Coaxial Stacking Discovery Criteria for stacking a. Basepair plane tilt < 26º for Flush / 32º for MM N1N1 N1N1 N2N2 D 1-2 b. Distance between basepair “centers” < 5 Å for Flush / 12 Å for MM (based on Gabb et al., J. Mol. Graph., 14, 6-11 Burkard et al., JMB, 290, 967-982 and Gendron at al., JMB, 308, 919-936

15. Stacking Definition for Verification c. Basepair shear angle between inter-center vector and baseplane normal vectors < 60º

16. Capturing Complex Stacks relaxed tilt and distance criteria: distance of basepair centers from normal to the other basepair < 10 Å

17. Capturing Complex Stacks Base Stack Cascade

18. Results : Comparison of Predictions with Reality

19. RNA structure dataset The ribosome RNA structures provide maximum data.

20. Results

21. Dependence on MBL Size (no. of branches)

22. Dependence on MBL Size (no. of bases)

23. A four way MBL:

24. Expanding to a partition function:

25. Suboptimal Configurations The Problem with Lowest Free Energy Consider, K 3 /2 < K 1, K 2 < K 3 A stack is more probable if it is part of many different configurations of low free energy. Just 4 out of 51 possible configurations!

26. Partition Function and Configuration Probabilities P T = Σ i exp(-ΔG i /RT) where i varies over ALL the possible configurations. P R,S = Σ j exp(-ΔG j /RT) where j varies over all the possible configurations that have stack S. p s = P R,S / P T

27. Probability Threshold for Prediction Both plots show a sharp drop at 0.70 So 70% was chosen to be the cut-off value for prediction

28. Partition Function Results

29. Conclusion: Predicting coaxial stacking by free energy minimization provides a method to predict the topology of tertiary structure.