Flexible refinement of protein-ligand docking on manifolds

Abstract

Our work is motivated by energy minimization of biological macromolecules, an essential step in computational docking. By allowing some ligand flexibility, we generalize a recently introduced novel representation of rigid body minimization as an optimization on the SO(3)×double-struckR3 manifold, rather than on the commonly used Special Euclidean group SE(3). We show that the resulting flexible docking can also be formulated as an optimization on a Lie group that is the direct product of simpler Lie groups for which geodesics and exponential maps can be easily obtained. Our computational results for a local optimization algorithm developed based on this formulation show that it is about an order of magnitude faster than the state-of-the-art local minimization algorithms for computational protein-small molecule docking.

Optimization on the space of rigid and flexible motions: An alternative manifold optimization approach

“…This is a formulation used in a number of engineering applications such as workpiece or camera localization or calibration (see, e.g., [1], [2], [3], [4]) or computer vision (see, e.g., [5], [6]). Our interest in this problem comes from the local optimization problems encountered in the area of computational docking of biological macromolecules (see, e.g., [7], [8], [9], [10]).…”