MoDock: A multi-objective strategy improves the accuracy for molecular docking
- Junfeng Gu^{1}Email author,
- Xu Yang^{1},
- Ling Kang^{2},
- Jinying Wu^{1} and
- Xicheng Wang^{1}
https://doi.org/10.1186/s13015-015-0034-8
© Gu et al.; licensee BioMed Central. 2015
Received: 28 October 2013
Accepted: 8 January 2015
Published: 18 February 2015
Abstract
Background
As a main method of structure-based virtual screening, molecular docking is the most widely used in practice. However, the non-ideal efficacy of scoring functions is thought as the biggest barrier which hinders the improvement of the molecular docking method.
Results
A new multi-objective strategy for molecular docking, named as MoDock, is presented to further improve the docking accuracy with available scoring functions. Instead of simple combination of multiple objectives with fixed weight factors, an aggregate function is adopted to approximate the real solution of the original multi-objective and multi-constraint problem, which will simultaneously smooth the energy surface of the combined scoring functions. Then, method of centers and genetic algorithm are used to find the optimal solution. Tests of MoDock against the GOLD test data set reveal the multi-objective strategy improves the docking accuracy over the individual scoring functions. Meanwhile, a 70% ratio of the good docking solutions with the RMSD value below 1.0 Å outperforms other 6 commonly used docking programs, even with a flexible receptor docking program included.
Conclusions
The results show MoDock is an effective strategy to overcome the deviations brought by single scoring function, and improves the prediction power of molecular docking.
Keywords
Multi-objective Molecular docking Scoring function OptimizationBackground
Structure-Based Virtual Screening (SBVS) has become a routine tool in both pharmaceutical companies and academic groups for early-stage drug discovery [1]. As a main method of SBVS, molecular docking is the most widely used in practice, and there have reported a number of successful examples [2]. As a result, the docking method has received increasing interest in recent times. To date, over 60 docking programs and 30 scoring functions (SFs) have been disclosed [3]. For comparing their efficiency, there have been many comparative studies to evaluate the relative performance of the most popular programs and SFs [4-22]. However, previous comparative studies have revealed that none of the docking programs and SFs truly outperforms the others, and a universally accurate docking method is still out of reach.
It is fundamentally an optimization problem of docking a ligand into the binding site of a receptor. As the objects during the optimization process, SFs estimate binding affinities between small ligands and proteins, and rank the compounds, playing an essential role in molecular docking. The non-ideal efficacy of SFs is thought as the biggest barrier which hinders the improvement of the molecular docking method. The conflict between the accuracy and speed of SF is a difficult problem need to make great efforts in. More recently, many techniques have been applied to further improve the efficacy of SF, such as including thermodynamic data [23,24], including data derived from quantum chemical calculation [25,26], application of modern computation technique and computational intelligence [27,28], etc. Despite many achievements have been obtained, the development of an ideal SF still has a long way to go. Therefore, how to improve the docking accuracy with available SFs is a practical and urgent task. Most docking methods are based on one single objective, i.e., a SF. However, due to the approximation adopted in the SF developing, deviations from the real binding energy are unavoidable. Based on this consideration, consensus scoring was developed by combining multiple SFs to reduce the deviations brought by individual SFs as possible. The critical step in consensus scoring is the design of an appropriate consensus scoring strategy of individual scores so that the true modes/binders can be discriminated from others accordingly. However, classic consensus strategy like linear combination is strongly dependent on the initial parameters, and simple combination of multiple SFs will make the energy curves discontinuous and non-smooth, and make the optimization problem more difficult to solve.
The application of multiple SFs makes docking become a multi-objective optimization problem. How to choose and combine the SFs, and design relevant optimization strategy to the multi-objective problem are crucial for improving the docking efficiency with consensus scoring. In this work, a multi-objective docking strategy MoDock is proposed to further improve the pose prediction with available SFs. The SFs used in consensus scoring are preferred to be not correlated, so that errors can be diminished. The available scoring functions can generally be divided into the following three types: force-field-based, empirical-based and knowledge-based SFs. They focus on diverse aspects of ligand binding, and are derived from different principles. Therefore, three representative scoring functions from these three types are introduced as the objectives, and then a multi-objective optimization method is designed to optimize these three objectives simultaneously. The publicly available GOLD test set containing 134 protein-ligand complexes is applied to evaluate the reliability of MoDock. The results indicate that the multi-objective strategy can enhance the pose prediction power of docking with the available SFs.
Models and Methods
The optimization model and scoring functions
where each term is a double sum over the ligand atom i and the receptor atom j. n _{ lig }, n _{ rec } are the number of atoms in the ligand and the receptor, respectively; A _{ ij }, B _{ ij } are van der Waals repulsion and attraction parameters, r _{ ij } is the distance between atoms i and j, q _{ i }, q _{ j } are the point charges on atoms i and j, D is dielectric function, and 332.0 is a factor that converts the electrostatic energy into kilocalories per mole.
where K _{ B } is the Boltzmann constant, T is the absolute temperature, \( {f}_{vol- corr}^j \) is the ligand volume correction factor, \( {\rho}_{seg}^{ij}(r) \) is the number density of atom pair ij that occurs in a spherical shell with a thickness of Δr ranging from r to r + Δr, and \( {\rho}_{bulk}^{ij} \) expresses the number density when no interaction between i and j occurs.
The multi-objective optimization strategy
Despite the multi-objective docking problem (1) has been simplified with the method of centers and aggregate function, the objective function of problem (10) is still nonlinear and the design space is non-convex, which means we still need a powerful optimization tool to solve this problem. Genetic algorithms (GA) provide such a capability, and they have been successful adapted and implemented in a series of optimal design problems. In this work, an improved adaptive genetic algorithm is adopted [34], in which an entropy-based searching technique with multi-population is developed to ensure rapid and steady convergence. The GA firstly generates arbitrary n populations with the same design space, and the design space is treated as the initial searching space. Information entropy is used to measure the uncertainty which population the optimal solution occurs in. During the optimization process, the uncertainty and information entropy will be decreased. Meanwhile, the position of the optimal solution in the design space will be gradually clear, and the searching space will be narrowed until the optimal solution is found. The detailed steps of the genetic algorithm used in this study are given in the Additional file 1. In traditional GA, fixed genetic parameters such as the crossover and mutation probabilities p _{ c } and p _{ m } will lead to an unsteady and slow convergence of the optimization process. In the applied GA, p _{ c } and p _{ m } are treated as another two design variables which will also evolve in the execution of the applied GA. Therefore, these two parameters are self-adaptive, and rational determination of their values will be obtained. In this work, p _{ c } and p _{ m } are defined in [0.6, 1.0] and [0.0, 0.1], respectively.
Preparation of the test data set
The main purpose of this study is to show the multi-objective strategy we proposed can improve the prediction accuracy with available popular SFs and the prediction accuracy are comparable with several popular docking programs. Therefore, the commonly used GOLD test data set, originally proposed by Jones et al. [35], was chosen for our studies. Each complex was separated into a probe molecule and a docking ligand according to the biological interacting pairs. Each protein molecule was obtained by excluding ligands, all structural water molecules, cofactors and metal ions from the receptor PDB file [36]. Next, a mol2 file was generated by adding hydrogen atoms and Kallman charge. Residues around the bound ligand within a radius of 6.5 Å were isolated from the protein to define as the active site. The ligands were then prepared by adding hydrogen atoms and Gasteiger-Marsili atomic charges. The heavy atoms number of the ligands ranged from 6 to 55, with 83.6% of the ligands possessing fewer than 30 such atoms. Besides, the rotatable bonds of the ligands ranged widely from 0 to 22, with greater than 88.8% of the ligands possessing fewer than 15 such bonds.
Results and discussion
The evaluation of the docking accuracy is based on the root-mean-square deviation (RMSD) value of the locations of all heavy atoms in the model from those of the crystal structure. In general, the docking accuracy is acceptable if the RMSD value between the docked pose and X-ray crystal structure is less than 2.0 Å. Depending on the RMSD values, the accuracy is assigned to seven categories. The first, excellent, is for those predictions the top scoring pose of which is within 0.5 Å RMSD from the experimental results. The following three are for those good results with values between 0.5 and 2.0 Å. The fifth category, close, is used for those predictions the RMSD values of which are between 2.0 and 2.5 Å. The sixth category, error, is used for those predictions the RMSD values of which are between 2.5 and 3.0 Å. Finally, the seventh category, wrong, is used for completely incorrect predictions with RMSD values larger than 3.0 Å.
The docking RMSD results on the test set with the multi-objective strategy are listed in the Additional file 1.
Multi-objective versus single-objective
The improvement of the multi-objective strategy against the single objectives is investigated first. Single-objective dockings with the above-mentioned three SFs separately are also performed on the test benchmark, and the RMSD values of the docking results are also listed in the Additional file 1.
Improvement over the other docking strategies
Docking accuracy comparison of MoDock with 6 commonly used docking programs
RMSD | Ratio | ||||||
---|---|---|---|---|---|---|---|
MoDock | Glide ^{ a } | GOLD ^{ b } | Surflex ^{ c } | FlexX ^{ d } | DOCK6 ^{ e } | Dock6-F ^{ f } | |
≤0.5 | 0.40 | 0.29 | 0.08 | 0.16 | 0.03 | 0.15 | 0.09 |
≥0.5, ≤1.0 | 0.30 | 0.19 | 0.27 | 0.32 | 0.18 | 0.15 | 0.32 |
≥1.0, ≤1.5 | 0.07 | 0.12 | 0.20 | 0.14 | 0.14 | 0.19 | 0.28 |
≥1.5, ≤2.0 | 0.01 | 0.11 | 0.11 | 0.15 | 0.14 | 0.13 | 0.11 |
≥2.0, ≤2.5 | 0.03 | 0.06 | 0.02 | 0.04 | 0.06 | 0.04 | 0.07 |
≥2.5, ≤3.0 | 0.04 | 0.03 | 0.03 | 0.02 | 0.04 | 0.08 | 0.03 |
≥3.0 | 0.16 | 0.20 | 0.28 | 0.17 | 0.40 | 0.27 | 0.09 |
Avg. RMSD | 1.53 | 1.98 | 3.19 | 2.15 | 3.69 | 2.13 | 1.46 |
From this point of view, flexible docking can decrease the ratio of wrong prediction by considering the conformational change of the receptor during the receptor-ligand binding process. However, the flexible docking method is also seriously limited by the accuracy of the score function it used, so the ratio of excellent docking cannot be increased.
Failure analysis
Conclusions
In this work, we present a new multi-objective strategy MoDock for improving the accuracy of the molecular docking. To reduce the correlations between each other, three scoring functions chosen from different categories—force-field-based, empirical-based and knowledge-based, are treated as the objectives during the docking optimization. Instead of simple combination with predefined weight factors, an aggregate function is adopted to combine the multiple objectives and to approximate the real solution of the original multi-objective and multi-constraint problem. Finally, method of centers and genetic algorithm are introduced to solve the optimization problem.
The results of the docking experiments on the 134 diverse complexes from the GOLD test data set have shown an obvious improvement of the docking accuracy. Detailed analysis shows that in about half of the cases, the multi-objective docking strategy outperforms all the single-objective dockings. In addition, MoDock yielded 93 (nearly 70%) good docking solutions with a RMSD value below 1.0 Å, which clearly outperforms 5 rigid receptor and 1 flexible receptor docking programs, and the average RMSD value is only slightly higher than the flexible receptor docking program. The results indicate that the multi-objective strategy can overcome the deviations brought by single scoring function, so it makes the strategy an effective method to improve the docking accuracy with available scoring functions. However, through the analysis of the failure cases, we find the multi-objective strategy still limited by the combined SFs. If the energy distribution of a scoring function is seriously deviated, then it will result in the failure of the multi-objective strategy. Therefore, continuous development of the docking scoring function will further improve the accuracy of the multi-objective strategy.
In this work, we only consider three diverse scoring functions—AMBER, X-Score and KScore to demonstrate the efficacy of the multi-objective strategy, but the strategy is not restricted to these scoring function and even not to the quantity of the scoring functions. Different scoring functions can be combined with this multi-objective strategy to research the best combinations, and this will be the direction of our next work.
Declarations
Acknowledgements
The authors gratefully acknowledge financial support for this work from the Fundamental Research Funds for the Central Universities, the National Natural Science Funds of China (No. 11202049), the National Basic Research Program of China (No. 2012CB025905), the 111 Project (B14013) and the Fundamental Research Funds for the Central Universities.
Authors’ Affiliations
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