1. Coarse and Reliable Geometric Alignment for Protein Docking Yusu Wang Stanford University Joint Work with P. K. Agarwal, P. Brown, H. Edelsbrunner, J. Rudolph Duke University

2. Motivation How proteins interact with each other? Docking problem Predict docking configuration

3. Challenges Physical and biochemical mechanism Binding sites? Energy function: hydrophobicity, electrostatics, etc High complexity Thousands of atoms High dimension, flexibility

4. Coarse alignment Rigid molecules Small sets of candidates Refinement Flexibility, chemical information Two-step Approach

5. Coarse Alignment Goal A relatively small set of possible configurations

6. not too tight, global fitting … Lock and Key Principle … To use an image, I would say that enzyme and glycoside have to fit into each other like a lock and a key, in order to exert a chemical effect on each other… --- Emil Fischer, 1894 Geometric complementary at a coarse level

7. Coarse Alignment Algorithm Capture features (protrusions, cavities) Align these features

8. Capture Features Previous work: f eature points Connolly function [Connolly, 83] Our work: feature pairs Describe more global features Specify importance

9. Capture Feature Pairs Height function as example Extend to all directions -- Elevation function

10. k-legged Maxima of Elevation 1-legged2-legged3-legged4-legged [Agarwal, Edelsbrunner, Harer, Wang, SOCG’04]

11. Examples 2-legged4-legged3-legged

12. 3-Legged Maximum

13. In Short : Each maximum captures a feature on surface Four types of features Collect feature pairs: Any two points within the same maximum A concise representation of meaningful features!

14. Surface Representation using Elevation

15. Coarse Alignment Algorithm Describe protrusions and cavities (via feature pairs) Align features

16. PairMatch Alg: Take a feature pair from each set Align two feature pairs, get T Rank T ’s by their scores Output ranked sequence of configurations Align Features

17. Reassembly of Known Complexes A test set of 25 protein complexes CoarseAlign: take top 100 ranked coarse alignments Refinement: using local improvement (Choi et al.)

18. Docking Results (CoarseAlign) pdb-idRankRMSD (Å) 1BRS11.59 1A2222.75 2PTC14.55 1MEE11.33 1CHO12.71 1JLT83.64 1CSE22.21 3SGB13.21 3HLA11.87

19. Docking Results (Refinement) pdb-idRank.refineRMSD.refine 1BRS10.54 1A2211.08 2PTC10.66 1MEE10.57 1CHO10.99 1JLT11.57 1CSE10.82 3SGB12.24 3HLA10.78

20. Overall 23/25 return a near-native configuration w/o false positives

21. Unbound Protein Docking Docking benchmark by [Chen et al.’03] Take 49 out of 59 complexes

22. Sample Results Top 2,000All outputs pdb-idRMSD(Å)HitsRMSD (Å)Size 1ACB3.70201.7514,426 1AVW5.51 85.4223,565 1BRC4.66354.6612,770 1BRS1.60 7 11,607 1CGI3.04 5 10,135 1CHO2.35272.3511,815 1CSE3.15 72.7421,068 1DFJ6.44 2 35,231 1MAH2.78 4 25,402

23. More Results Output size: All < ~50,000, most < 25,000 Quality Among top 2,000 ranked configurations 38/49 produce at least one with < 6Å Among all outputs 47/49 produce at least one with < 6Å

24. Summary Elevation function -> meaningful features Useful coarse alignments Combine with refinement for the unbound case

25. Sample proteins 1A221JLT3HLA

26. Related Docking Packages FTDock, DOT, ZDock: FFT-based Shape complementary, electrostatics HEX: Fourier correlation GRAMM: FFT (focus on low resolution docking) BiGGER PPD: Geometric Hashing