Abstract
A novel efficient algorithm for searching for the optimum arrangement of two rigid bodies is proposed. Such a problem often arises in the analysis of the matching of three-dimensional shapes (e.g., in protein-protein docking). The proposed method is based on exhaustive enumeration of the possible arrangements in the spherical polar Fourier space and uses the generalized five-dimensional Fourier transform to speed up the calculations. The main advantage of the described method consists in the efficiency of calculations performed with multicomponent evaluation functions. This high efficiency allows one to obtain highly accurate results with low computational costs.
Similar content being viewed by others
References
N. Volkmann and D. Hanein, “Quantitative fitting of atomic models into observed densities derived by electron microscopy,” J. Struct. Biol. 125, 176–184 (1999).
D. Kozakov, R. Brenke, S. R. Comeau, and S. Vajda, “PIPER: An FFT-based protein docking program with pairwise potentials,” Proteins: Struct., Funct., Bioinform. 65, 392–406 (2006).
D. W. Ritchie, D. Kozakov, and S. Vajda, “Accelerating and focusing protein-protein docking correlations using multi-dimensional rotational FFT generating functions,” Bioinform. 24, 1865–1873 (2008).
D. W. Ritchie and G. J. Kemp, “Protein docking using spherical polar Fourier correlations,” Proteins 39, 178–194 (2000).
D. W. Ritchie, “High-order analytic translation matrix elements for real-space six-dimensional polar Fourier correlations,” J. Appl. Crystallogr. 38, 808–818 (2005).
M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93, 216–231 (2005).
L. Rabiner, “On the use of symmetry in FFT computation,” IEEE Trans. on Acoust., Speech Signal Process. 27, 233–239 (1979).
F. C. Bernstein, T. F. Koetzle, G. J. Williams, E. E. Meyer, Jr., M. D. Brice, J. R. Rodgers, O. Kennard, T. Shi- manouchi, and M. Tasumi, “The protein data bank: a computer-based archival file for macromolecular structures,” J. Mol. Biol. 112, 535–542 (1977).
H. K. Songa and S. W. Suh, “Kunitz-type soybean trypsin inhibitor revisited: refined structure of its complex with porcine trypsin reveals an insight into the interaction between a homologous inhibitor from Erythrina caffra and tissue-type plasminogen activator,” J. Mol. Biol. 275, 347–363 (1998).
J. Janin, K. Henrick, J. Moult, L. T. Eyck, M. J. Sternberg, S. Vajda, I. Vakser, and S. J. Wodak, “CAPRI: a critical assessment of predicted interactions,” Proteins 52, 2–9 (2003).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.M. Kazennov, A.E. Alekseenko, D. Kozakov, D.N. Padhorny, Y.A. Kholodov, 2014, published in Matematicheskoe Modelirovanie, 2014, Vol. 26, No. 12, pp. 3–13.
Rights and permissions
About this article
Cite this article
Kazennov, A.M., Alekseenko, A.E., Kozakov, D. et al. Efficient search for the possible mutual arrangements of two rigid bodies with the use of the generalized five-dimensional Fourier transform. Math Models Comput Simul 7, 315–322 (2015). https://doi.org/10.1134/S2070048215040043
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S2070048215040043