research overview iii
DESCRIPTION
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] - PowerPoint PPT PresentationTRANSCRIPT
Research Overview III
Jack SnoeyinkUNC 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
ReceptorOH
P
P
O
O
O
O
O O
SR12813
Diagramatic representations
• PXR with bound ligandBall & stick /
van der Waals spheres
Model diagramSolvent 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 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…
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
Algorithm Crystal
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
Pfold: probability of folding
unfolded state folded state
Pfold1- Pfold
[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(n3) 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
n
n
iiiiiii
1
2,B,A
2,B,A
2,B,A
BA,
)ZZ()YY()XX(R
Distribution of random variations of RMS
distances• Density function of :
• For and ,
)2/exp()2/3(2
)( 2213312/3
2/3
R
nrrn
nrf n
nn
n
BA,R
1
)2exp()( 2111516
R rrrf
4n
• 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 [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