1. Placing hydrogens by dynamic programming By Xueyi Wang Department of Computer Science UNC-Chapel Hill

2. Outline Reduce program Improvements -- Convert data structures to STL. -- Apply dynamic programming algorithm in large groups. -- Fix inconsistent results. Future Work

3. Reduce J. Michael Word, Simon C. Lovell, Jane S. Richardson and David C. Richardson. Asparagine and glutamine: using hydrogen atom contacts in the choice of sidechain amide orientation. J. Mol. Biol. (1999) 285, 1735-1747 Causes -- X-ray crystal structures lack hydrogen atoms. -- Structural ambiguity. Goals -- Understand hydrophobic core packing. -- Understand the role of hydrogen bonding in protein stability.

4. Movers: Rotations of Methyl, NH3+ and Donor CC S Methionine Lysine CC CC Og1 CC

5. Movers: Ambiguous Structure Glutamine (Asparagine, Histidine) ON CC ON CC

6. Approach of Reduce Find the placement of hydrogen atoms that -- maximize the number of hydrogen bonds -- minimize the number of clashes

7. Score Function in Reduce Maximize the function: 4 Vol (H-bond) - 10 Vol (overlap) -- Approximate to the van der Waals function for an isolated pair-wise interaction. -- Volume is approximated by summing dots and spikes

8. Improvements Convert the basic data structures to STL structures. Apply dynamic programming algorithm in large groups (more than 2 movers). Fix inconsistent results caused by different executing orders of atoms in groups.

9. Convert Data structures Original data structure is quite inefficient. STL provides a very good data structure for manipulating data. -- Separate data, iterator and algorithm. -- Easy for further improvements.

10. Improvements Convert the basic data structures to STL structures. Apply dynamic programming algorithm in large groups (more than 2 movers). Fix inconsistent results caused by different executing orders of atoms in groups.

11. Old algorithm used by Reduce Partition the movers into groups that have no interactions between them. Maximize the score within each group by brute force. Several groups have > 2-3 movers.

12. Dynamic Programming Problem: -- proteins with large groups exist and Brute force approach is very inefficient. Solution: -- Use the interaction graph to divide the problem and do dynamic programming. Leaver-Fay, A., Liu, Y., and Snoeyink, J., Faster placement of hydrogens in protein structures by dynamic programming, Proc. ALENEX'04, LNCS, Springer Verlag, 2004.

13. Demo Og1 From 1SBP.pdb angle 170 77 21 -219 Thr 62 Thr 13 Ser 9 angle 170 82 39 -94 -141 angle 17626 72-71 57-110 42

14. Interaction Graph

15. Experiments For proteins with large groups, dynamic programming algorithm can significantly reduce the calculation time.

16. Improvements Convert the basic data structures to STL structures. Apply dynamic programming algorithm in large groups (more than 2 movers). Fix inconsistent results caused by different executing orders of atoms in groups.

17. Inconsistent results Inconsistent results can be caused by different execution order of atoms in two stages: -- Setting initial angle stage -- Finding optimal angle stage Solution: Algorithm based on dynamic programming.

18. Inconsistent Result Angle 2 Angle 1 θ1θ1 θ1θ1 θ2θ2 Θ 1 +Δθ Θ 1 -Δθ Θ 2 -ΔθΘ 2 +Δθ Different calculation sequences cause different result.

19. New Algorithm Angle 2 Angle 1 θ1θ1 θ1θ1 θ2θ2 Θ 1 +Δθ Θ 1 -Δθ Θ 2 -ΔθΘ 2 +Δθ Different calculation sequences cause the same result.

20. Future Work Apply continuous scores instead of contact dots for the score function Enhance efficiency -- Rewrite and reorganize some inefficient subroutines.

21. Continuous Score Calculate the exact overlap volume.

22. Contact dots vs. Continuous Score Absolute and relative errors for all pairs of radii

23. Acknowledgements: -- Dr. Michael Word in GlaxoSmithKline. -- Andrew Leaver-Fay, Yuanxin (Leo) Liu and Jack Snoeyink. -- NSF grant 0076984. The End