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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. April 2002, Volume 1, Number 4, 185-192 |
Solving the Geometric Docking Problem for Planar and Spatial Sets
Michel Petitjean
Internet Electron. J. Mol. Des. 2002, 1, 185-192
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Abstract:
A docking algorithm working without charge
calculations is needed for molecular modeling studies. Two sets of n
points in the d-dimensional Euclidean space are considered. The
optimal translation and/or rotation minimizing the variance of the sum
of the n squared distances between the fixed and the moving set is
computed. An analytical solution is provided for d-dimensional
translations and for planar rotations. The use of the quaternion
representation of spatial rotations leads to the solving of a
quadratically constrained non-linear system. When both spatial
translations and rotations are considered, the system is solved using a
projected Lagrangian method requiring only 4-dimensional initial
starting tuples.
The projected Lagrangian method was used in the docking algorithm.
The automatic positioning of the moving set is performed
without any a priori information about the initial orientation.
Minimizing the variance of the squared distances is an
original and simple geometric docking criterion, which avoids any
charge calculation. The FORTRAN source is available within framework of
scientific collaborations. Contact: petitjean@itodys.jussieu.fr.
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