Solving Molecular Docking Problems with Multi-Objective Metaheuristics

María García-Godoy, Esteban López-Camacho, José García-Nieto, Antonio Nebro, José Aldana-Montes
2015 Molecules  
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
more » ... , 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 solutions are analyzed, showing promising results for the multi-objective approaches. In addition, a case study of application for aeroplysinin-1 is performed, showing the effectiveness of our multi-objective approach in drug discovery. Molecular docking is a hard optimization problem, which consists of predicting the orientation of a small molecule (ligand) to a receptor (macromolecule) when they are bound to each other to form an energetically-stable complex. The main goal is to find an optimal conformation between the ligand and receptor with a minimum binding energy, which is evaluated by an energy function. This problem has been tackled in the past with metaheuristics and other nature-inspired computational methods, demonstrating new and challenging results when looking for the minimum binding energy [1]. However, only a few papers can be found in the literature that deal with this problem by means of multi-objective approaches. The first attempt was carried out in 2006 by Oduguwa et al. [2], in which three evolutionary multi-objective optimization algorithms (non-dominated sorting genetic algorithm II (NSGA-II), the Pareto Archived Evolution Strategy algorithm (PAES) and the Strength Pareto Evolutionary algorithm (SPEA)) were evaluated on three molecular complexes. Grosdidier et al. [3] proposed a new hybrid evolutionary algorithm for docking (EADock), which was interfaced with the CHARMM package. In 2008, Janson et al. [4] designed a parallel multi-objective optimization algorithm based on PSO (Particle Swarm Optimization) using AutoDock energy function Version 3.05, called ClustMPSO, that used K-means to guide the migration strategy when dealing with six molecular complexes. Furthermore, in 2008, Boisson et al. [5] implemented a parallel evolutionary bi-objective model using ParadisEO platform and GOLD docking software for the docking of six instances. Recently, Sandoval-Perez et al. [6] used the implementation of NSGA-II provided by the jMetal framework [7] to optimize bound and non-bound energy terms as objectives applied to four docking instances. These publications, although proposing different approaches, performed only limited comparisons with other current multi-/single-objective techniques. Furthermore, a low number of molecular instances were used in these studies, and their complexities were also moderate in terms of flexibility. In the area of ligand design, there have been several studies that apply the multi-objective approach. proposed a bi-objective optimization approach using the S-metric evolutionary multi-objective optimization (SMS-EMOA) to solve the problem of finding a peptide ligand. The results obtained show the possibility to design a peptide ligand of the γ1 isoform of the 14-3-3 protein with predicted selectivity over the 1 isoform. Van der Horst et al. [9] used the multi-objective evolutionary algorithm (MOEA) for a de novo ligand design applied to the new adenosine receptor antagonists. The selection of the candidate A1 adenosine receptor antagonists was based on multiple criteria and several objectives, such as the high predicted affinity and the selectivity of the
doi:10.3390/molecules200610154 pmid:26042856 fatcat:h5llsmx7unecpdhqtucew5tb7i