Tai et al. J Cheminform (2018) 10:62 https://doi.org/10.1186/s13321-018-0320-9 Journal of Cheminformatics METHODOLOGY Open Access Chaos‑embedded particle swarm optimization approach for protein‑ligand docking and virtual screening Hio Kuan Tai1, Siti Azma Jusoh2 and Shirley W. I. Siu1* Abstract Background: Protein-ligand docking programs are routinely used in structure-based drug design to fnd the optimal binding pose of a ligand in the protein’s active site. These programs are also used to identify potential drug candidates by ranking large sets of compounds. As more accurate and efcient docking programs are always desirable, constant eforts focus on developing better docking algorithms or improving the scoring function. Recently, chaotic maps have emerged as a promising approach to improve the search behavior of optimization algorithms in terms of search diversity and convergence speed. However, their efectiveness on docking applications has not been explored. Herein, we integrated fve popular chaotic maps—logistic, Singer, sinusoidal, tent, and Zaslavskii maps—into PSOVina2LS , a recent variant of the popular AutoDock Vina program with enhanced global and local search capabilities, and evalu- ated their performances in ligand pose prediction and virtual screening using four docking benchmark datasets and two virtual screening datasets. Results: Pose prediction experiments indicate that chaos-embedded algorithms outperform AutoDock Vina and PSOVina in ligand pose RMSD, success rate, and run time. In virtual screening experiments, Singer map-embedded PSOVina2LS achieved a very signifcant fve- to sixfold speedup with comparable screening performances to AutoDock Vina in terms of area under the receiver operating characteristic curve and enrichment factor. Therefore, our results suggest that chaos-embedded PSOVina methods might be a better option than AutoDock Vina for docking and virtual screening tasks. The success of chaotic maps in protein-ligand docking reveals their potential for improving optimization algorithms in other search problems, such as protein structure prediction and folding. The Singer map- embedded PSOVina2LS which is named PSOVina-2.0 and all testing datasets are publicly available on https​://cbbio​.cis. umac.mo/softw​are/psovi​na. Keywords: Docking, Virtual screening, PSOVina, Autodock Vina, Chaotic maps, Singer map, Sinusoidal map Introduction protein-ligand docking [1]. Given the three-dimensional Small-molecule drugs exert their pharmacological efects structures of a target protein and a ligand, the main goal through binding to their biological targets and subse- of protein-ligand docking is to dock the ligand at the quently modulating the activities that are associated with active site of the protein and to score the diferent bind- diseases to be treated. To rationally design new drugs ing poses of the ligand. Ten, through a virtual screening for a target protein, specifc interactions of the binding process, a large library of ligands can be docked, ranked partners must be correctly predicted. Tis prediction and fltered according to their docking scores, enabling can be achieved with a computational approach called the rapid identifcation of lead candidates. Terefore, accurate and efcient docking tools are indispensable for reducing the cost and time in the drug discovery process. *Correspondence: [email protected] 1 Department of Computer and Information Science, University of Macau, From an algorithmic point of view, the docking prob- Avenida da Universidade, Taipa, Macau, China lem is a conformational search problem, which is to fnd Full list of author information is available at the end of the article the combination of parameters that yields the optimal © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creat​iveco​mmons​.org/licen​ses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creat​iveco​mmons​.org/ publi​cdoma​in/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Tai et al. J Cheminform (2018) 10:62 Page 2 of 13 ligand binding pose. Assuming fxed topologies of the in an attempt to further enhance the search capability protein and ligand, then the conformational parameters of the algorithm. A chaotic map is a function to mimic of the complex include the position and orientation of the dynamics of some nonlinear systems. Previous stud- the ligand with respect to the protein and the angles of ies [13–15] indicated that using chaotic variables rather all rotatable bonds of the ligand (and even the protein than the conventional random number generators might if fexibility of the protein is considered). Assessment of improve the search behavior of evolutionary algorithms a ligand binding pose is done by a scoring function of in terms of search diversity and convergence speed. To interaction types and distances of the atoms between evaluate the efectiveness of chaotic functions in dock- the protein and ligand, which can be force feld-based, ing applications, we implemented fve chaotic functions 2LS empirical-based or knowledge-based [2]. in PSOVina and analyzed their performances on four Various optimization strategies have been proposed to benchmark docking datasets and two virtual screening solve the protein-ligand docking problem. For example, a datasets. In our experiments, chaos-embedded methods Monte Carlo (MC)-based approach was implemented in outperformed AutoDock Vina and our previous PSOVina AutoDock Vina [3], and a genetic algorithm (GA)-based in both the success rate of ligand pose prediction and the approach was implemented in GOLD [4] and Auto- speed of virtual screening. Dock [5]. Recently, swarm-intelligence-based approaches using particle swarm optimization (PSO) and other Methods nature-inspired methods, such as artifcial bee colony PSOVina and PSOVina2LS (ABC) and ant colony optimization (ACO), have become PSOVina is a metaheuristic molecular docking program very popular for solving nonlinear and complex optimi- based on the AutoDock Vina software [3]. In PSOVina, zation problems. Te advantages of these metaheuris- the fast converging PSO algorithm was used as the global tic algorithms are that they tend to fnd good solutions optimizer integrated with the Broyden–Fletcher–Gold- quickly, they are easy to implement, and there are many farb–Shanno (BFGS) local search algorithm and the scor- variants to allow easy customization of the algorithm ft- ing function of Vina. PSO is a population-based search ting the domain of interest. Some metaheuristic docking method that is inspired by the social learning behaviors methods have been implemented, such as SODOCK [6], of bird focking and fsh schooling when searching for PSO@AutoDock [7], FIPSDock [8], PSOVina [9] based food [16]. Te population, called swarm, consists of N on the PSO algorithm and variants, PLANTS [10] based members, called particles. Each individual particle repre- on ACO and FlABCps [11] based on ABC. All of these sents a potential solution and moves in a D-dimensional docking methods have been shown to improve the pose search space based on its current position and velocity. prediction accuracy and docking efciency compared to During the search process, each particle adjusts its posi- traditional optimization methods. In these implementa- tion according to its own experience and the swarm’s tions, the metaheuristic algorithms were utilized as the experience. Te former is the best position that the global optimizer to quickly locate promising regions in particle has ever visited, called pbest, and the latter is the conformational search space. Some of these methods the best position that the swarm has ever visited, called included a local search algorithm to refne the solution gbest. Te velocity Vi and position Xi of the particle i are from the global search to the closest local minimum. updated iteratively over time t according to the following In this paper, we present an improvement of the equations: PSOVina docking method that was previously developed V (t + 1) = wV (t) + c r (pbest (t) − X (t)) in our group [9]. Te frst version of PSOVina imple- i i 1 1 i i (1) mented the canonical PSO algorithm with a convergence + c2r2(gbest(t) − Xi(t)), detection strategy to efectively reduce the execution time of AutoDock Vina docking by 51–60% [9]. Te sec- Xi(t + 1) = Xi(t) + Vi(t + 1), 2LS (2) ond version of PSOVina, named PSOVina [12], further where Vi =[vi1, ..., viD] and Xi =[xi1, ..., xiD] . w is a enhanced the docking performance by incorporating a constant parameter called the inertia weight, and it deter- novel two-stage local search (2LS) algorithm to quickly mines the contribution of the current velocity of the examine the potential of the global search solutions. particle to its new velocity. A large w encourages explora- Only promising solutions will be refned by the expen- tion of the entire search space, and a small w facilitates sive full-length local search. Our experimental results local exploitation and convergence. Terefore, a suitable showed that the 2LS achieved an approximate threefold value of w (typically between 0.8 and 1.2) will help main- acceleration in fnding optimal docking solutions rela- tain a proper balance between the global and local search tive to the conventional one-stage local search. In this capabilities of the swarm. Rather than using a predefned work, we investigate the use of chaotic maps in PSOVina constant value, many studies have proposed strategies to Tai et al. J Cheminform (2018) 10:62 Page 3 of 13 dynamically adjust w during the search process [17]. Two distribution) or to adaptively modify parameters in other coefcients c1 and c2 are the cognitive and social the metaheuristic optimization algorithm while the parameters, respectively. Te former controls the parti- search evolves.