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] –Mining structure DB Structure determination (Carter) –Electron density modification [Carr,Kettner, Mascarenhas ] Packing (Edelsbrunner) –Alpha-shapes, skin surfaces [Kettner,Mascarenhas]

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

PXR: Pregnane Xenobiotic Receptor SR12813

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

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…

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 ATOM 2 O GLY ATOM 3 N GLY ATOM 4 CA GLY ATOM 5 N LEU ATOM 6 CA LEU ATOM 7 CB LEU ATOM 8 CG LEU ATOM 9 CD1 LEU ATOM 10 CD2 LEU ATOM 11 C LEU ATOM 12 O LEU ATOM 13 N THR ATOM 14 CA THR ATOM 2395 O HOH ATOM 2396 O HOH ATOM 2397 O HOH ATOM 2398 O HOH ATOM 2399 O HOH ATOM 2400 O HOH ATOM 2401 O HOH ATOM 2402 O HOH ATOM 2403 O HOH ATOM 2404 O HOH ATOM 2405 O HOH ATOM 2406 O HOH END 2380 lines later…

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

PXR binding pockets

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

SR12813 Results AlgorithmCrystal

Coumestrol results

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

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

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

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

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

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

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

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

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.

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.

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

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.

Surface Mesh Compression [Isenburg]

Topology for visualization Contour tree

Topology for visualization [Mascarenhas]

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

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