Coarse and Reliable Geometric Alignment

for Protein Docking

Yusu WangStanford University

Joint Work with P. K. Agarwal, P. Brown, H. Edelsbrunner, J. Rudolph

Duke University

Motivation

How proteins interact with each other?

Docking problem Predict docking configuration

Challenges

Physical and biochemical mechanism Binding sites? Energy function: hydrophobicity, electrostatics, etc

High complexity Thousands of atoms High dimension, flexibility

Coarse alignment Rigid molecules Small sets of candidates

Refinement Flexibility, chemical information

Two-step Approach

Coarse Alignment

Goal

A relatively small set of possible configurations

not too tight, global fitting …

Lock and Key Principle

… To use an image, I would say that enzyme and glycoside have to fit into each other like a lock and a key, in order to exert a

chemical effect on each other…

--- Emil Fischer, 1894

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

Geometric complementary at a coarse level

Coarse Alignment Algorithm

Capture features (protrusions, cavities)

Align these features

Capture Features

Previous work: feature points Connolly function

[Connolly, 83]

Our work: feature pairs Describe more global features Specify importance

Capture Feature Pairs

Height function as example

Extend to all directions -- Elevation function

k-legged Maxima of Elevation

1-legged 2-legged 3-legged 4-legged

[Agarwal, Edelsbrunner, Harer, Wang, SOCG’04]

Examples

2-legged 4-legged3-legged

3-Legged Maximum

In Short :

Each maximum captures a feature on surface

Four types of features

Collect feature pairs: Any two points within the same maximum

A concise representation of meaningful features!

Surface Representation using Elevation

Coarse Alignment Algorithm

Describe protrusions and cavities (via feature pairs)

Align features

PairMatch Alg:

Take a feature pair from each set Align two feature pairs, get T Rank T ’s by their scores

Output ranked sequence of configurations

Align Features

Reassembly of Known Complexes

A test set of 25 protein complexes CoarseAlign: take top 100 ranked coarse alignments Refinement: using local improvement (Choi et al.)

Docking Results (CoarseAlign)

pdb-id Rank RMSD (Å)1BRS 1 1.591A22 2 2.752PTC 1 4.551MEE 1 1.331CHO 1 2.711JLT 8 3.641CSE 2 2.213SGB 1 3.213HLA 1 1.87

Docking Results (Refinement)

pdb-id Rank.refine RMSD.refine1BRS 1 0.541A22 1 1.082PTC 1 0.661MEE 1 0.571CHO 1 0.991JLT 1 1.571CSE 1 0.823SGB 1 2.243HLA 1 0.78

Overall

23/25 return a near-native configuration w/o false positives

Unbound Protein Docking

Docking benchmark by [Chen et al.’03] Take 49 out of 59 complexes

Sample ResultsTop 2,000 All outputs

pdb-id RMSD(Å) Hits RMSD (Å) Size1ACB 3.70 20 1.75 14,4261AVW 5.51 8 5.42 23,5651BRC 4.66 35 4.66 12,7701BRS 1.60 7 1.60 11,6071CGI 3.04 5 3.04 10,1351CHO 2.35 27 2.35 11,8151CSE 3.15 7 2.74 21,0681DFJ 6.44 2 6.44 35,231

1MAH 2.78 4 2.78 25,402

More Results

Output size: All < ~50,000, most < 25,000

Quality Among top 2,000 ranked configurations

38/49 produce at least one with < 6Å Among all outputs

47/49 produce at least one with < 6Å

Summary

Elevation function -> meaningful features Useful coarse alignments

Combine with refinement for the unbound case

Sample proteins

1A22 1JLT 3HLA

Related Docking Packages

FTDock, DOT, ZDock: FFT-based Shape complementary, electrostatics

HEX: Fourier correlation GRAMM: FFT (focus on low resolution docking) BiGGER PPD: Geometric Hashing