Solving the Geometric Docking Problem for Planar and Spatial Sets

Michel Petitjean (1)

1 BFA (UMR_8251 / U1133) - Unité de Biologie Fonctionnelle et Adaptative

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.

Mots clés: Geometric docking; constrained optimization; optimal rotation and translation

Domaines: Chimie théorique et/ou physique; Optimisation et contrôle [math.OC]

Michel Petitjean. Solving the Geometric Docking Problem for Planar and Spatial Sets. Internet Electronic Journal of Molecular Design, 2002, 1 (4), pp.185 - 192. ⟨hal-02115007⟩