Motivation. 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. Method. The projected Lagrangian method was used in the docking algorithm. Results. The automatic positioning of the moving set is performed without any a priori information about the initial orientation. Conclusions. Minimizing the variance of the squared distances is an original and simple geometric docking criterion, which avoids any charge calculation.
Publié le : 2002-04-04
Classification:
Geometric docking,
constrained optimization,
optimal rotation and translation,
[CHIM.THEO]Chemical Sciences/Theoretical and/or physical chemistry,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-02115007,
author = {Petitjean, Michel},
title = {Solving the Geometric Docking Problem for Planar and Spatial Sets},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-02115007}
}
Petitjean, Michel. Solving the Geometric Docking Problem for Planar and Spatial Sets. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-02115007/