BDOCK ： An Implementation of the FFT Protein-Protein Docking Method Using the BALL Library

Bingding Huang

Center of Bioinformatics

Saarland University

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Overview

Introduction of BALL(Biochemical Algorithms Library)

Protein-Protein docking FFT (Fast Fourier Transform) method Our implementation Result Conclusion

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BALL(Biochemical Algorithms Library)

by Dr. Oliver Kohlbacher and Prof. Hans-Peter Lenhof

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BALL

What is BALL BALL is a C++ application framework for rapid software

prototyping in the area of Molecular Modeling and computational bioiolgy

What can BALL do It provides an extensive set of data structures as well as classes for

molecular mechanics,advanced solvation methods,comparison and analysis of protein structure,file import/export and visualization of molecule ,etc

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Molecular Docking

The molecular docking problem Given two molecules with 3D conformation at

atomics level Do the molecules bind to each other?if yes How strong is the binding affinity How does the molecule-complex look like?

Docking problem in biochemistry Protein-Ligand docking Protein-Protein docking Protein-DNA docking DNA-Ligand docking

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Overview of a typical docking procedure

Coordinates of two molecules to be

docked

Perform a rigid-body search for

favorable complexes

Generate a number of

possible docked complexes

Re-rank complexes based on a scoring

function

Introduce flexibility to refine and re-rank complexes

List a few complexes for experimental

design and test

Generator Scoring function

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Protein-Protein Docking

Problem features Stable conformation(rigid) Large contact surface Good geometric shape complementarity

Applications Understanding Protein-Protein interaction Prediction of Protein-Protein interaction Predicting protein complex structures

classification Unbound docking Bound docking

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FFT method for protein-protein docking

First proposed by Katchalski-Katzir (1992)

Further developed by Sternberg and Gabb (1997)

Features Proteins are projected into 3D grids to measure geometric

shape complementarity Assign interior and surface grid cell values Use Fast Fourier Transform to decrease the computational

time

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FFT method

Surface:+1Surface:+1

Interior: -15Interior: -15

Interior: +1Interior: +1

Blank: 0Blank: 0

Protein AProtein A

Protein BProtein B

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FFT method

Good shape complementarityGood shape complementarity

complexcomplex

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FFT method

Protein A al,m,n = { 1, surface cell1, surface cell

p, interior cellp, interior cell

0, elsewhere0, elsewhere

Protein B bl,m,n =q, interior cellq, interior cell

0, elsewhere 0, elsewhere

Here we use p = -15Here we use p = -15

Here we use q = +1Here we use q = +1

Correlation:Correlation:

N

l

N

m

N

n

nmlnml bac1 1 1

,,,,,,

Find the grid step that maximise the correlation Overcost O(N6) – and have to rotate protein B and repeat..

,,

{

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FFT method

DFT Ap,q,r =

N

l

N

m

N

n

nmlaNrnqmpli1 1 1

,,]/)(2exp[

Forward FFT A = DFT (a)

Forward FFT B= DFT (b)

Computer C=A*B

Inversed FFT c=IFFT(C)

Totally, FFT can reduce O(N6) to O(N3 lnN3)

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The strategy for FFT Protein-Protein Docking

Protein A Protein B

static grid mobile grid

discretise discretise

Stack

FFTFFT

Inverse transformMultiply

loop

rotate protein B

discretise

Score complexes

finish loop

Filter

local refinement

Predicted complexes

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Rotational conformations

An uniformly distributed Euler angle set is used to ensure minimal orientations are required to cover the whole rotational space

A schematic diagram of rotational search

15o 4392

12o 8580

10o 14868

8o 29025

6o 68760

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Our implementation of FFT using BALL

Realize all the functionalities into a class:geometricfit initGridSize(Atomcontainer &pro_a,&pro_b) makeGrid(Atomcontainer &pro)

FindInsidePoints() FindSurfacePoints()

RotateProtein(Atomcontainer &pro_b) doFFT() FFTGridMulti() doIFFT() getPeakValue() ……….

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The main function

2int main(int agrc,char ** agrv){2PDBFile pdb_a(“recetor.pdb”) ;3PDBFile pdb_b(“ligand.pdb”) ;4System pro_a;5System pro_b;6pdb_a>>pro_a;7pdb_b>>pro_b;8GeometricFit geofit(pro_a,pro_b);9geofit.initGridSize(pro_a,pro_b);1geofit.makeFFTGrid(pro_a);1geofit.doFFT(pro_a);1RotationAngles rotAngle;

// the main docking program loop1for ( int i=0;i< rotAngle.getNumber();++i ){1float phi = rotAngle.getXAng(i);1float theta = rotAngle.getYAng(i);1float psi = rotAngle.getZAng(i);

1System sys_b = pro_b;1geofit. RotateProtein(sys_b,phi,theta,psi);2geofit.makeFFTGrid(sys_b);2geofit.doFFT(sys_b);2geofit.FFTMutil();2geofit.doIFFT();2float peak_value = geofit.getGlobalPeak();2Vector3 trans = geofit.getTranslation();2} // finish docking loop2}

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Distribute the rotational conformations

Each rotational conformation is independent ,so we can distribute the total rotational conformations to a number of different processors to perform docking together using MPI (Message Passing Interface)

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A good scoring function should be able to eliminate the false positives to screen the docked complexes

Initial stage of docking Geometric shape complementarity alone – very fast to compute

Re-ranking stage Empirical residue-residue pair potentials Binding free energy:

Scoring function

vdwconfcavelebind GGGGG

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Evaluate the docked Complex

Ideally, the prediction complexes having higher score should be near-native complex

Evaluation RMSD (Root mean square Deviation) of all C atoms

between prediction complex and native complex

RMSD below 3 Angstrom is acceptable

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We apply our implementation to an unbound/unbound protein-protein data set Enzyme / Inhibitor Antibody / Antigen

Parameters 1 Angstrom grid spacing 2 Angstrom surface thickness 15 degree interval

We obtain The number of hits (RMSD below 3.0 Angstrom )at top 2000 The rank of best hit The best RMSD value

Result

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Result

Complex ID Hits Rank Best rmsd Complex ID Hits Rank Best rmsd

1ACB 7 23 1.62 1FSS 2 190 2.22

1ATN 4 27 1.17 1MAH 4 10 0.94

1AVW 6 5 1.91 1PPE 66 1 0.64

1AY7 3 11 2.19 1PPF 2 7 1.78

1BRC 2 582 2.98 1TGS 13 13 1.37

1BRS 2 3 1.54 1UDI 78 2 0.90

1CGI 4 672 2.29 1UGH 86 6 1.67

1CHO 32 631 1.40 2KAI 2 692 1.66

1CLV 55 567 1.85 2PCC 6 4 2.98

1CSE 24 365 0.86 2PTC 2 1671 2.84

Table 1. The docking results at 15 degree based on shape complementarity

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Re-ranking

Table 2. The re-ranking results using residue-residue pair potential and binding free energy scoring functions

Complex ID shape rpscore Energy Complex ID Shape rpscore Energy

1ACB 23 1 3 1FSS 190 15 25

1ATN 27 15 9 1MAH 10 15 12

1AVW 5 2 1 1PPE 1 1 2

1AY7 11 6 6 1PPF 7 2 3

1BRC 282 27 24 1TGS 13 4 7

1BRS 3 1 2 1UDI 2 1 2

1CGI 672 54 67 1UGH 6 3 4

1CHO 631 16 13 2KAI 692 27 38

1CLV 567 36 53 2PCC 4 1 1

1CSE 365 14 34 2PTC 1671 34 45

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1PPE. Shape complementarity vs. RMSD

Fig1.1PPE shape complementarity vs. RMSD (unit Angstrom)

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1PPE. Pair potential vs. RMSD

Fig 2.1PPE. residue-residue pair potential vs. RMSD (unit Angstrom)

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1PPE. binding free energy vs. RMSD

Fig 3.1PPE. binding free energy (unit KJ/mol) vs. RMSD (unit Angstrom)

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Prediction Complex structures

Fig 4. 1PPE. RMSD 0.42 Fig 5. 1UGH. RMSD 1.67

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Only half an hour to two hours is needed at 15o on a single Xeon 2.8 G processor. Using 8 processors (connected by giganet) the general running time is about 5 to 15 minutes

When docking at 6o, the running time is 8 hours to two days. Using 8 processors, it is one hour to 6 hours

Running time

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We implemented the FFT protein-protein docking method using the BALL library

Our program can predict a number of near-native complex structures based on shape complementarity alone Pair potential and binding free energy can improve the

ranking Our program is more faster than FTDOCK The rapid prototyping capabilities of BALL saves us a lot of

time in implementation source codes and we only need to focus on the new technologies, algorithms and methods

BDOCK is freely available to academic users

Conclusion

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Prof. Volkhard Helms and Prof. Hans-Peter Lenhof

Dr. Julie Mitchell

Mr. Andreas Hildebrandt

Mr. Hongbo Zhu

Aknowledgement

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Thank you!

Questions?