1. Research Overview III Jack Snoeyink UNC Chapel Hill

2. Geometric algorithms in: Docking (Redinbo) –PXR [Leaver-Fay, Berretty] Dynamic representations [Hsu] –p-fold (Latombe) –Hinge determination in TripRS (Carter) Folding (Tropsha) –Scoring with Delaunay [O’Brien,Bandyopadhyay] –Mining structure DB Structure determination (Carter) –Electron density modification [Carr,Kettner, Mascarenhas ] Packing (Edelsbrunner) –Alpha-shapes, skin surfaces [Kettner,Mascarenhas]

3. Other branches: Surface representation [Isenburg] –Compression of geometric models Topology for visualization (LLNL) –[Mascarenhas, Carr]

4. PXR: Pregnane Xenobiotic Receptor SR12813

5. Diagramatic representations PXR with bound ligand  Ball & stick / van der Waals spheres  Model diagram  Solvent accessible surface

6. Geometry on computers Where we can see structure, shape, connections, regions, The computer sees only coordinates For example, this PXR protein & ligand is in the Protein Data Bank as…

7. HEADER GENE REGULATION 08-MAY-01 1ILG TITLE CRYSTAL STRUCTURE OF APO HUMAN PREGNANE X RECEPTOR LIGAND. AUTHOR R.E.WATKINS,M.R.REDINBO. ATOM 1 C GLY 142 -5.808 44.753 13.561 1.00 58.97 6 ATOM 2 O GLY 142 -5.723 45.523 14.515 1.00 59.54 8 ATOM 3 N GLY 142 -4.377 43.177 14.842 1.00 59.37 7 ATOM 4 CA GLY 142 -5.307 43.330 13.685 1.00 59.68 6 ATOM 5 N LEU 143 -6.324 45.108 12.387 1.00 58.87 7 ATOM 6 CA LEU 143 -6.839 46.455 12.152 1.00 58.50 6 ATOM 7 CB LEU 143 -6.483 46.907 10.736 1.00 57.90 6 ATOM 8 CG LEU 143 -5.849 48.290 10.555 1.00 57.77 6 ATOM 9 CD1 LEU 143 -4.599 48.411 11.407 1.00 56.51 6 ATOM 10 CD2 LEU 143 -5.505 48.492 9.090 1.00 56.92 6 ATOM 11 C LEU 143 -8.352 46.446 12.333 1.00 58.92 6 ATOM 12 O LEU 143 -9.046 45.640 11.714 1.00 59.85 8 ATOM 13 N THR 144 -8.862 47.341 13.174 1.00 58.88 7 ATOM 14 CA THR 144 -10.299 47.407 13.444 1.00 59.76 6 ATOM 2395 O HOH 1600 29.442 64.461 -1.726 1.00 66.79 8 ATOM 2396 O HOH 1601 19.427 85.921 -22.662 1.00 60.16 8 ATOM 2397 O HOH 1602 5.344 90.815 7.154 1.00 54.96 8 ATOM 2398 O HOH 1603 -14.216 50.571 5.561 1.00 54.96 8 ATOM 2399 O HOH 1604 5.533 45.964 0.404 1.00 62.55 8 ATOM 2400 O HOH 1605 -1.394 63.145 20.705 1.00 40.08 8 ATOM 2401 O HOH 1606 -2.578 54.566 22.874 1.00 57.40 8 ATOM 2402 O HOH 1607 3.600 69.196 22.807 1.00 54.51 8 ATOM 2403 O HOH 1608 6.139 65.007 -18.611 1.00 54.86 8 ATOM 2404 O HOH 1609 4.202 75.224 -27.568 1.00 58.04 8 ATOM 2405 O HOH 1610 -5.421 61.703 24.061 1.00 57.88 8 ATOM 2406 O HOH 1611 -11.943 45.372 11.041 1.00 62.72 8 END 2380 lines later…

8. Pregnane Xenobiotic Receptor (PXR) Implicated in drug-drug interactions with St. John’s wort

9. PXR binding pockets

10. Successes: Educating ourselves Collaboration with Biochemistry Software integration and library building [Kettner, Hsu, …] Partial results

11. SR12813 Results AlgorithmCrystal

12. Coumestrol results

13. Difficulty Validation: –Molecular dynamics with standard energy models Most are designed for proteins –Evaluate against AutoDock general search by simulated annealing with many parameters –Crystallize with other bound ligands Incorporating flexibility

14. P fold : probability of folding unfolded state folded state P fold 1- P fold [Du, et al. 98]

15. Domain motion of TrpRS. Biological motivation: Understand the enzymatic mechanism Computational motivation: Compute motion for objects with many degrees of freedom TrpRS

16. Previous work  Difference in torsional angles  Local  O(n) running time  Difference in RMS distances  Global  O(n 3 ) running time

17. Random variations Random variations due to –Thermal motions –Measurement errors How to choose thresholds to detect significant torsional angle changes? Want –Robust: differentiate statistically significant changes from random variations –Efficient: O(n logn) running time

18. Distribution of random variations of RMS distances Minimum RMS distance Assumptions: –The effect of minimization is small. –X, Y, Z have errors with Gaussian distribution

19. Distribution of random variations of RMS distances Density function of : For and,

20. Statistical potential based on quadruples of nearby residues identified by Delaunay Tessellation Four-Body Statistical Potential [O'Brien] Convex hull formed by the tetrahedral edges Each tetrahedron corresponds to a cluster of four residues

21. Find quads incrementally Previous implementation could not use 4-body due to tessellation cost. Incremental algorithm in existing code already produces 2-3 orders of magnitude improvement. Rewrite in progress should be even faster.

22. Lattice Chain Growth Algo. Cubic lattice (311) w/ 24 possible moves {(3,1,1),(3,1,-1),…,(-3,1,1)} (Gan, Schlick, Tropsha) Grow chain by Monte Carlo, choosing next position based on empirical statistical potential.

23. Almost-Delaunay tetrahedra [Bandyopadhyay] 4-tuples that may become Delaunay by perturbing points by at most  Check robustness of statistical potential Search for motifs

24. Electron density refinement Structure from x-ray diffraction experiments Squaring relations give more accurate localization Combine information on fragments to further refine Talk by Carter.

25. Surface Mesh Compression [Isenburg]

26. Topology for visualization Contour tree 7 8 9 10 5 6 4 3 1 2

27. Topology for visualization [Mascarenhas]

28. UNC-CH Graphic Lab: NIH res. for molecular graphics

29. I've mentioned: PXR p-fold TrpRS motion Delaunay-based statistical potential –Fast evaluation –MC chain growing –Almost Delaunay Electron density refinement Surface compression Visualization Bio –shape representation –shape classification –docking –structure determination Modeling –shape representation Algorithms –deformation/flexibility –motion planning Software –library effort –visualization