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