Ligand-protein docking is an optimization problem based on predicting the position of a ligand with the lowest binding energy in the active site of the receptor. Molecular docking problems are traditionally tackled with single-objective, as well as with multi-objective approaches, to minimize the binding energy. In this paper, we propose a novel multi-objective formulation that considers: the Root Mean Square Deviation (RMSD) difference in the coordinates of ligands and the binding (intermolecular) energy, as two objectives to evaluate the quality of the ligand-protein interactions. To determine the kind of Pareto front approximations that can be obtained, we have selected a set of representative multi-objective algorithms such as NSGA-II, SMPSO, GDE3, and MOEA/D. Their performances have been assessed by applying two main quality indicators intended to measure convergence and diversity of the fronts. In addition, a comparison with LGA, a reference single-objective evolutionary algorithm for molecular docking (AutoDock) is carried out. In general, SMPSO shows the best overall results in terms of energy and and RMSD (value lower than 2Å for successful docking results). This new multi-objective approach shows an improvement over the ligand-protein docking predictions that could be promising in in silico docking studies to select new anticancer compounds for therapeutic targets that are multidrug resistant.

The main objective of the molecular docking problem is to find a conformation between a small molecule (ligand) and a receptor molecule with minimum binding energy. The quality of the docking score depends on two factors: the scoring function and the search method being used to find the lowest binding energy solution. In this context, AutoDock 4.2 is a popular C++ software package in the bioinformatics community providing both elements, including two genetic algorithms, one of them endowed with a local search strategy. This paper principally focuses on the search techniques for solving the docking problem. In using the AutoDock 4.2 scoring function, the approach in this study is twofold. On the one hand, a number of four metaheuristic techniques are analyzed within an extensive set of docking problems, looking for the best technique according to the quality of the binding energy solutions. These techniques are thoroughly evaluated and also compared with popular well-known docking algorithms in AutoDock 4.2. The metaheuristics selected are: generational and a steady-state Genetic Algorithm, Differential Evolution, and Particle Swarm Optimization. On the other hand, a C++ version of the jMetal optimization framework has been integrated inside AutoDock 4.2, so that all the algorithms included in jMetal are readily available to solve docking problems. The experiments reveal that Differential Evolution obtains the best overall results, even outperforming other existing algorithms specifically designed for molecular docking.

Molecular docking is a hard optimization problem that has been tackled in the past with metaheuristics, demonstrating new and challenging results when looking for one objective: the minimum binding energy. However, only a few papers can be found in the literature that deal with this problem by means of a multi-objective approach, and no experimental comparisons have been made in order to clarify which of them has the best overall performance. In this paper, we use and compare, for the first time, a set of representative multi-objective optimization algorithms applied to solve complex molecular docking problems. The approach followed is focused on optimizing the intermolecular and intramolecular energies as two main objectives to minimize. Specifically, these algorithms are: two variants of the non-dominated sorting genetic algorithm II (NSGA-II), speed modulation multi-objective particle swarm optimization (SMPSO), third evolution step of generalized differential evolution (GDE3), multi-objective evolutionary algorithm based on decomposition (MOEA/D) and S-metric evolutionary multi-objective optimization (SMS-EMOA). We assess the performance of the algorithms by applying quality indicators intended to measure convergence and the diversity of the generated Pareto front approximations. We carry out a comparison with another reference mono-objective algorithm in the problem domain (Lamarckian genetic algorithm (LGA) provided by the AutoDock tool). Furthermore, the ligand binding site and molecular interactions of computed In addition, a case study of application for aeroplysinin-1 is performed, showing the effectiveness of our multi-objective approach in drug discovery.

jMetalCpp software adapted to AutoDock is freely available as a C++ source code at http://khaos.uma.es/AutodockjMetal/.

In the last years, particle swarm optimizers have emerged as prominent search methods to solve the molecular docking problem. A new approach to address this problem consists in a multi-objective formulation, minimizing the intermolecular energy and the Root Mean Square Deviation (RMSD) between the atom coordinates of the cocrystallized and the predicted ligand conformations. In this paper, we analyze the performance of a set of multiobjective particle swarm optimization variants based on different archiving and leader selection strategies, in the scope of molecular docking. The conducted experiments involve a large set of 75 molecular instances from the Protein Data Bank database (PDB) characterized by different sizes of HIV-protease inhibitors. The main moti-vation is to provide molecular biologists with unbiased conclusions concerning which algorithmic variant should be used in drug discovery. Our study confirms that the multi-objective particle swarm algorithms SMPSOhv and MPSO/D show the best overall performance. An analysis of the resulting molecular ligand conformations, in terms of binding site and molecular interactions, is also performed to validate the solutions found, from a biological point of view.