Rigid Body Energy Minimization on Manifolds for Molecular Docking

Abstract

Virtually all docking methods include some local continuous minimization of an energy/scoring function in order to remove steric clashes and obtain more reliable energy values. In this paper, we describe an efficient rigid-body optimization algorithm that, compared to the most widely used algorithms, converges approximately an order of magnitude faster to conformations with equal or slightly lower energy. The space of rigid body transformations is a nonlinear manifold, namely, a space which locally resembles a Euclidean space. We use a canonical parametrization of the manifold, called the exponential parametrization, to map the Euclidean tangent space of the manifold onto the manifold itself. Thus, we locally transform the rigid body optimization to an optimization over a Euclidean space where basic optimization algorithms are applicable. Compared to commonly used methods, this formulation substantially reduces the dimension of the search space. As a result, it requires far fewer costly function and gradient evaluations and leads to a more efficient algorithm. We have selected the LBFGS quasi-Newton method for local optimization since it uses only gradient information to obtain second order information about the energy function and avoids the far more costly direct Hessian evaluations. Two applications, one in protein-protein docking, and the other in protein-small molecular interactions, as part of macromolecular docking protocols are presented. The code is available to the community under open source license, and with minimal effort can be incorporated into any molecular modeling package.

Interaction Of Platelet Activating Factor Acetyl Hydrolase (Paf Ah) Enzyme In Gln281 To Arg281 Mutation Toward Paf And Its Molecular Dynamic

“…The affinity energy from this process was -4.0 kcal/mol to -2.2 kcal/mol for wild-type and mutant structures respectively. This value has an important meaning since alteration Glutamine to Arginin may disturb binding process and cause more steric clashes [23,24]. Using LIGPLUS and LigandScout, all interactions between PAF AH (wild type and mutant) and PAF can be mapped (Figure 2A).…”

Flexible refinement of protein-ligand docking on manifolds

“…We use our formulation of rigid body motion introduced in [4], [5], and briefly described in the next section, for this purpose. In this formulation of rigid body motion, we have the freedom of choosing the center of rotation.…”

“…In this paper, we generalize the manifold (local) optimization approach introduced in [4], [5] by allowing some molecular flexibility while following the same basic optimization approach.…”

“…In [4], [5] we presented a manifold optimization approach to rigid body minimization with application to rigid molecular docking. Instead of the common Special Euclidean Group SE (3), we introduced an alternative group of rigid body transformations that corresponds to the Lie group $SO\left(3\right)\times {\mathrm{double-struckR}}^3$.…”

“…We show that the corresponding conformation space is a Riemannian manifold and a Lie group. As a result, an optimization approach similar to that presented in [4], [5] can be applied. Our computational results show that the algorithm is about an order of magnitude faster than a full-atomic optimization algorithm.…”