CUDA-based triangulations of convolution molecular surfaces

ABSTRACT

Computing molecular surfaces is important to measure areas and volumes of molecules, as well as to infer useful information about interactions with other molecules. Over the years many algorithms have been developed to triangulate and to render molecular surfaces. However, triangulation algorithms usually are very expensive in terms of memory storage and time performance, and thus far from real-time performance. Fortunately, the massive computational power of the new generation of low-cost GPUs opens up an opportunity window to solve these problems: real-time performance and cheap computing commodities. This paper just presents a GPU-based algorithm to speed up the triangulation and rendering of molecular surfaces using CUDA. Our triangulation algorithm for molecular surfaces is based on a multi-threaded, parallel version of the Marching Cubes (MC) algorithm. However, the input of our algorithm is not the volume dataset of a given molecule as usual for Marching Cubes, but the atom centers provided by the PDB file of such a molecule. We also carry out a study that compares a serial version (CPU) and a parallel version (GPU) of the MC algorithm in triangulating molecular surfaces as a way to understand how real-time rendering of molecular surfaces can be achieved in the future.

References

1. }}CUDA Programming Guide 2. Available at: http://developer.download.nvidia.com, 2008.
2. }}Technical Brief: NVIDIA Geforce GTX 200 GPU Architectural Overview. Available at: http://developer.download.nvidia.com, 2008.
3. }}J. F. Blinn. A generalization of algebraic surface drawing. ACM Trans. Graph., 1(3):235--256, July 1982.
4. }}J. Bloomenthal and K. Shoemake. Convolution surfaces. Computer Graphics, 25(4):251--256, 1991.
5. }}T. Can, C.-I. Chen, and Y.-F. Wang. Efficient molecular surface generation using level-set methods. Journal of Molecular Graphics and Modelling, 25:442--454, 2006.
6. }}M. Connolly. Analytical molecular surface calculation. Journal of Applied Crystallography, 16(5):548--558, October 1983.
7. }}M. Connolly. Solvent-accessible surfaces of proteins and nucleic acids. Science, 221(4612):709--713, August 1983.
8. }}D. D'Agostino, I. Merelli, A. Clematis, L. Milanesi, and A. Orro. A parallel workflow for the reconstruction of molecular surfaces. In C. Bischof, M. Bücker, P. Gibbon, G. Joubert, T. Lippert, B. Mohr, and F. Peters, editors, Parallel Computing: Architectures, Algorithms and Applications, volume 15 of Advances in Parallel Computing, pages 147--154. IOS Press, 2008.
9. }}C. Dyken, G. Ziegler, C. Theobalt, and H.-P. Seidel. High-speed marching cubes using histopyramids. Computer Graphics Forum, 27(8):2028--2039, 2008.
10. }}R. Geiss. Generating complex procedural terrains using the GPU. In H. Nguyen, editor, GPU Gems 3. Addison-Wesley Professional, New Jersey, USA, 2007.
11. }}M. Harris, S. Sengupta, and J. D. Owens. Parallel prefix sum scan with cuda. In G. G. 3, editor, Hubert Nguyen. Addison-Wesley Professional, Upper Saddle River, New Jersey, Aug 2007.
12. }}W. Heiden and T. G. J. Brickmann. Fast generation of molecular surfaces from 3D data fields with an enhanced "marching cube" algorithm. Journal of Computational Chemistry, 14(2):246--250, 1993.
13. }}M. C. Lawrence and P. Bourki. Conscript: a program for generating electron density isosurfaces for presentation in protein crystallography. Journal of Applied Crystallography, 33:990--991, 2000.
14. }}B. Lee and F. Richards. The interpretation of protein structures: Estimation of static accessibility. Journal of Molecular Biology, 55(3):379--380, February 1971.
15. }}C. Levinthal. Molecular model-building by computer. Scientific American, 214(6):42--52, June 1966.
16. }}W. Lorensen and H. Cline. Marching cubes: A high resolution 3d surface construction algorithm. ACM SIGGRAPH Computer Graphics, 21(4):163--169, July 1987.
17. }}I. Merelli, L. Milanesi, D. D'Agostino, A. Clematis, M. Vanneschi, and M. Danelutto. Marching cubes: A high resolution 3d surface construction algorithm. In Proceedings of the 1st International Conference on Distributed Frameworks for Multimedia Applications (DFMA'05), pages 288--294, Washington, DC, USA, 2005. IEEE Computer Society.
18. }}T. Newman, J. Byrd, P. Emani, A. Narayanan, and A. Dastmalchi. High performance simd marching cubes isosurface extraction on commodity computers. Computers & Graphics, 28:213--233, 2004.
19. }}J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips. GPU computing. Proceedings of the IEEE, 96(5):879--899, 2008.
20. }}F. Richards. Areas, volumes, packing, and protein structure. Annual Review of Biophysics and Bioengineering, 6(3):151--176, February 1977.
21. }}N. Tang and T. Newman. A vector-parallel realization of the marching cubes. Technical Report TR-UAH-CS-1996-01, Computer Science Department, The University of Alabama in Huntsville, USA, 1996.
22. }}Y. Uralsky. DX 10: Pratical metaballs and implicit surfaces. In Game Developers Conference, 2006.
23. }}Y. Vorobjev and J. Hermans. Sims: Computation of a smooth invariant molecular surface. Biophysical Journal, 73(2):722--732, 1997.
24. }}G. Wyvill, C. McPheeters, and B. Wyvill. Data Structure for Soft Objects. The Visual Computer, 2(4):227--234, February 1986.
25. }}Z. Yu, M. Holst, Y. Cheng, and J. McCammon. Feature-preserving adaptive mesh generation for molecular shape modeling and simulation. Journal of Molecular Graphics and Modelling, 26:1370--1380, 2008.

Index Terms

• Applied computing

  • Life and medical sciences

  • Physical sciences and engineering

• Computing methodologies

  • Computer graphics

    • Graphics systems and interfaces

      • Graphics processors

    • Shape modeling

      • Parametric curve and surface models

      • Volumetric models

• Theory of computation

  • Randomness, geometry and discrete structures