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Research Overview III

Research Overview III. Jack Snoeyink UNC Chapel Hill. 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]

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Research Overview III

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

  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. 2380 lines later… 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 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

  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 Algorithm Crystal

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

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

  16. Difference in torsional angles • Local • O(n) running time • Difference in RMS distances • Global • O(n3) running time Previous work

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

  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. 4-tuples that may become Delaunay by perturbing points by at most e>0. Check robustness of statistical potential Search for motifs Almost-Delaunay tetrahedra [Bandyopadhyay]

  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 [Mascarenhas]

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

  28. 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 I've mentioned:

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