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[其它] Finding Surface Atoms of a Protein Molecule on a GPU

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发表于 2012-1-3 10:14:39 |只看该作者 |倒序浏览

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SIGGRAPH Asia 2011, Hong Kong, China, December 12 – 15, 2011.

ISBN 978-1-4503-0807-6/11/0012

(a) (b)

Figure 1. An example for PDB ID 1O3Y. (a)a set of sampling

points, (b)surface atoms(red color) and

non-surface atoms(blue color)

1. Introduction

We present a real-time method to find the atoms at the boundary

surface of a protein molecule. Efficient finding of the atoms at the

surface of the molecule is important since most of interactions

between two protein molecules including docking and binding

occur at the boundary surface of molecules.

[Deanda, et al. 2002] proposed a method to extract surface atoms

based on solvent-accessible surfaces. Solvent-accessible surface is

a trajectory of the center of probe solvent, where the solvent

touches the molecule without interference. They defined surface

atoms as the atoms that touch the solvent probes.

We represent the protein molecule as a set of spheres with van der

Waals radii: M = {S(ci, ri)}, where S(ci, ri) is a sphere with center

point ci and radius ri. The probe solvent is represented as a sphere

with radius d. We compute the offset surface of M with offset

distance d. Then, we find the spheres in M, whose d-offset surface

has an intersection with the d-offset surface of M. To achieve the

real-time performance, our algorithm is implemented on a GPU.

2. Algorithm for Finding Surface Atoms

Let us denote the ball with center point c and radius r as B(c, r):

B(c, r) = { p ∈ R3 | ||c – p|| ≤ r }. The surface of B(c, r) is

denoted as a sphere S(c, r): S(c, r) = { p | ||c – p|| = r }. The protein

molecule is represented as follows:

M = { Bi | 0 ≤ i < n },

where Bi = B(ci, ri) corresponds to each atom with center ci and

Van der Waals radius ri. When the radius of given solvent probe is

d, the offset surface of M with offset distance d can be considered

as a boundary surface of Md:

Md = { Bd

i | 0 ≤ i < n },

where Bd

i = B(ci, ri + d) corresponds to the d-offset of Bi. We also

define Sd

i as follows:

Sd

i = S(ci, ri + d).

________________________

* This research was supported by Basic Science Research Program

through the National Research Foundation of Korea(NRF) funded

by the Ministry of Education, Science and Technology(2011-

0004094).

** Corresponding author

When we partition the bounding box of Md into nx × ny × nz voxels,

the bounding box can be represented as a set of voxels as follows:

V = { Vαβγ | 0 ≤ α < nx, 0 ≤ β < ny, 0 ≤ γ < nz}.

For each ball Bi

d in Md, we find every voxel Vαβγ it covers, and the

n add Bi

d to Vαβγ.balls:

Vαβγ.balls = { Bi

d | Bi

d ∩ Vαβγ.box ≠ ∅ },

where Vαβγ.box represents the voxel area. By using the voxel map

V, we can efficiently determine if the points embedded in Sd

i is

contained in the d-offset surface of M or not. For a point p ∈ Sd

i, if

there is a ball Bd

k, i ≠ k, which includes p inside, then p is not

embedded in the offset surface of M. After removing the sample

points which are inside other d-offset spheres, we can extract the

sample points embedded in the offset surface of the molecule

(Figure 1 (a)). If there are one or more sample points of an atom A

is contained in the d-offset surface of the molecule, A is classified

as a surface atom(Figure 1 (b)).

Both functions for constructing a voxel map and determining if

the sample points on a sphere, Sd

i is embedded in the offset surface

of M, are accelerated by GPU.

3. Experimental Results

We demonstrate the efficiency of the proposed algorithm through

experiments which were done on a PC equipped with a Intel i5

2.8GHz CPU with 4.0GB of memory and nVIDIA GeForce GTS

450 graphic card with 1GB Video RAM. The software was

developed using Microsoft Visual C++ and CUDA. The input

Protein Data Bank (PDB) files were downloaded from the PDB

website (http://www.pdb.org). As shown in Table1, we achieved

real-time performance when we partition the space into voxels of

size 2×2×2Å.

Table1. Execution times for our implementations

PDB id. 2PLT 1A19 1O3Y 1QB5 1EAI

# of atoms 727 1,438 2,664 3,750 4,540

# of surface

atoms 338 681 1,261 1,482 2,151

Computation

time (msec) 4.88 7.37 14.28 22.52 28.45

Frame rate(Fps) 204.92 135.69 70.03 44.40 35.15

4. Conclusions

In this paper, we presented a real-time algorithm to extract the

surface atoms of a protein molecule. We utilize the graphic

processor for achieving the real-time performance. Based on our

work, we expect to develop interactive-time algorithms for

molecular docking as further researches.

References

DEANDA, F., PEARLMAN, R.S. 2002. A novel approach for

identifying the surface atoms of macro-molecules. Journal of

Molecular Graphics and Modelling 20, 415-425.

Finding Surface Atoms of a Protein Molecule on a GPU*

Byungjoo Kim1 Ku-Jin Kim2,** Ji-Hoon Choi3 Nakhoon Baek4 Joon-Kyung Seong5 Yoo-Joo Choi6

1-4Kyungpook National University 5Soongsil University 6Korean German Institute of Technology

1kbj113@hotmail.com 2kujinkim@yahoo.com 3azureripple@yahoo.co.kr 4oceancru@gmail.com 5seong@ssu.ac.kr 6yjchoi@kgit.ac.kr