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Dutkiewicz Z. Computational methods for calculation of protein-ligand binding affinities in structure-based drug design. PHYSICAL SCIENCES REVIEWS 2022. [DOI: 10.1515/psr-2020-0034] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Abstract
Drug design is an expensive and time-consuming process. Any method that allows reducing the time the costs of the drug development project can have great practical value for the pharmaceutical industry. In structure-based drug design, affinity prediction methods are of great importance. The majority of methods used to predict binding free energy in protein-ligand complexes use molecular mechanics methods. However, many limitations of these methods in describing interactions exist. An attempt to go beyond these limits is the application of quantum-mechanical description for all or only part of the analyzed system. However, the extensive use of quantum mechanical (QM) approaches in drug discovery is still a demanding challenge. This chapter briefly reviews selected methods used to calculate protein-ligand binding affinity applied in virtual screening (VS), rescoring of docked poses, and lead optimization stage, including QM methods based on molecular simulations.
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Affiliation(s)
- Zbigniew Dutkiewicz
- Department of Chemical Technology of Drugs , Poznan University of Medical Sciences , ul. Grunwaldzka 6 , 60-780 Poznań , Poznan , 60-780, Poland
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Rocha-Santos A, Chaves EJ, Grillo IB, de Freitas AS, Araújo DAM, Rocha GB. Thermochemical and Quantum Descriptor Calculations for Gaining Insight into Ricin Toxin A (RTA) Inhibitors. ACS OMEGA 2021; 6:8764-8777. [PMID: 33842748 PMCID: PMC8027999 DOI: 10.1021/acsomega.0c02588] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2020] [Accepted: 12/30/2020] [Indexed: 05/03/2023]
Abstract
In this work, we performed a study to assess the interactions between the ricin toxin A (RTA) subunit of ricin and some of its inhibitors using modern semiempirical quantum chemistry and ONIOM quantum mechanics/molecular mechanics (QM/MM) methods. Two approaches were followed (calculation of binding enthalpies, ΔH bind, and reactivity quantum chemical descriptors) and compared with the respective half-maximal inhibitory concentration (IC50) experimental data, to gain insight into RTA inhibitors and verify which quantum chemical method would better describe RTA-ligand interactions. The geometries for all RTA-ligand complexes were obtained after running classical molecular dynamics simulations in aqueous media. We found that single-point energy calculations of ΔH bind with the PM6-DH+, PM6-D3H4, and PM7 semiempirical methods and ONIOM QM/MM presented a good correlation with the IC50 data. We also observed, however, that the correlation decreased significantly when we calculated ΔH bind after full-atom geometry optimization with all semiempirical methods. Based on the results from reactivity descriptors calculations for the cases studied, we noted that both types of interactions, molecular overlap and electrostatic interactions, play significant roles in the overall affinity of these ligands for the RTA binding pocket.
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Affiliation(s)
- Acassio Rocha-Santos
- Department
of Chemistry, Federal University of Paraíba, Cidade Universitária, João Pessoa, PB 58051-900, Brazil
| | - Elton José
Ferreira Chaves
- Department
of Biotechnology, Federal University of
Paraíba, Cidade Universitária, João Pessoa, PB 58051-900, Brazil
| | - Igor Barden Grillo
- Department
of Chemistry, Federal University of Paraíba, Cidade Universitária, João Pessoa, PB 58051-900, Brazil
| | - Amanara Souza de Freitas
- Department
of Chemical Engineering, Federal University
of Paraíba, Cidade Universitária, João Pessoa, PB 58051-900, Brazil
| | | | - Gerd Bruno Rocha
- Department
of Chemistry, Federal University of Paraíba, Cidade Universitária, João Pessoa, PB 58051-900, Brazil
- . Phone/Fax: +55-83-3216-7437
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Wang M, Mei Y, Ryde U. Host-Guest Relative Binding Affinities at Density-Functional Theory Level from Semiempirical Molecular Dynamics Simulations. J Chem Theory Comput 2019; 15:2659-2671. [PMID: 30811192 DOI: 10.1021/acs.jctc.8b01280] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
Relative free energies for the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host were calculated at the combined density-functional theory and molecular mechanics (DFT/MM) level of theory. The DFT calculations employed the BLYP functional and the 6-31G* basis set for the ligand. We employed free-energy perturbations (FEP) with the reference-potential approach and used molecular dynamics (MD) simulations with the semiempirical quantum mechanical (SQM) PM6-DH+ method for the ligand as an intermediate level between MM and DFT/MM to improve the convergence. Thus, the relative binding free energy of two ligands was first calculated at the MM level by an alchemical transformation from one ligand to another in both the bound and unbound states. Then, for each ligand the free-energy correction for going from the MM to the SQM/MM potentials was calculated using explicit SQM/MM MD simulations. Finally, the free-energy correction for going from the SQM/MM to the DFT/MM potentials was estimated with FEP without running any DFT/MM simulations. Instead, the free energy was calculated by single-step exponential averaging (ssEA) or employing the cumulant approximation to the second order (CA). The results show that CA converges much better than ssEA, and with 500-4500 DFT/MM single-point energy calculations, converged free energies with a precision of 0.3 kJ/mol can be obtained. These free energies reproduce the experimental binding free energy differences with a mean absolute deviation of 3.4 kJ/mol, a correlation ( R2) of 0.97, and correct signs for all of the eight free-energy differences. This is appreciably better than the results obtained at the SQM/MM level of theory and also slightly better than those obtained with MM. We show that the convergence of the SQM/MM → DFT/MM perturbations can be monitored by the use of Wu and Kofke's bias metric Π and by the standard deviation of the difference between the SQM/MM and DFT/MM energies. Finally, we show that the use of the intermediate SQM/MM MD simulations improves the convergence of the free energies by a factor of at least two, compared to doing direct MM → DFT/MM perturbations.
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Affiliation(s)
- Meiting Wang
- State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science , East China Normal University , Shanghai 200062 , China.,Department of Theoretical Chemistry , Lund University, Chemical Centre , P.O. Box 124, SE-221 00 Lund , Sweden
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science , East China Normal University , Shanghai 200062 , China.,NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062 , China.,Collaborative Innovation Center of Extreme Optics , Shanxi University , Taiyuan , Shanxi 030006 , China
| | - Ulf Ryde
- Department of Theoretical Chemistry , Lund University, Chemical Centre , P.O. Box 124, SE-221 00 Lund , Sweden
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Caldararu O, Olsson MA, Misini Ignjatović M, Wang M, Ryde U. Binding free energies in the SAMPL6 octa-acid host-guest challenge calculated with MM and QM methods. J Comput Aided Mol Des 2018; 32:1027-1046. [PMID: 30203229 DOI: 10.1007/s10822-018-0158-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Accepted: 08/31/2018] [Indexed: 01/15/2023]
Abstract
We have estimated free energies for the binding of eight carboxylate ligands to two variants of the octa-acid deep-cavity host in the SAMPL6 blind-test challenge (with or without endo methyl groups on the four upper-rim benzoate groups, OAM and OAH, respectively). We employed free-energy perturbation (FEP) for relative binding energies at the molecular mechanics (MM) and the combined quantum mechanical (QM) and MM (QM/MM) levels, the latter obtained with the reference-potential approach with QM/MM sampling for the MM → QM/MM FEP. The semiempirical QM method PM6-DH+ was employed for the ligand in the latter calculations. Moreover, binding free energies were also estimated from QM/MM optimised structures, combined with COSMO-RS estimates of the solvation energy and thermostatistical corrections from MM frequencies. They were performed at the PM6-DH+ level of theory with the full host and guest molecule in the QM system (and also four water molecules in the geometry optimisations) for 10-20 snapshots from molecular dynamics simulations of the complex. Finally, the structure with the lowest free energy was recalculated using the dispersion-corrected density-functional theory method TPSS-D3, for both the structure and the energy. The two FEP approaches gave similar results (PM6-DH+/MM slightly better for OAM), which were among the five submissions with the best performance in the challenge and gave the best results without any fit to data from the SAMPL5 challenge, with mean absolute deviations (MAD) of 2.4-5.2 kJ/mol and a correlation coefficient (R2) of 0.77-0.93. This is the first time QM/MM approaches give binding free energies that are competitive to those obtained with MM for the octa-acid host. The QM/MM-optimised structures gave somewhat worse performance (MAD = 3-8 kJ/mol and R2 = 0.1-0.9), but the results were improved compared to previous studies of this system with similar methods.
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Affiliation(s)
- Octav Caldararu
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P. O. Box 124, 221 00, Lund, Sweden
| | - Martin A Olsson
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P. O. Box 124, 221 00, Lund, Sweden
| | - Majda Misini Ignjatović
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P. O. Box 124, 221 00, Lund, Sweden
| | - Meiting Wang
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P. O. Box 124, 221 00, Lund, Sweden
| | - Ulf Ryde
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P. O. Box 124, 221 00, Lund, Sweden.
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Steinmann C, Olsson MA, Ryde U. Relative Ligand-Binding Free Energies Calculated from Multiple Short QM/MM MD Simulations. J Chem Theory Comput 2018; 14:3228-3237. [PMID: 29768915 DOI: 10.1021/acs.jctc.8b00081] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
We have devised a new efficient approach to compute combined quantum mechanical (QM) and molecular mechanical (MM, i.e. QM/MM) ligand-binding relative free energies. Our method employs the reference-potential approach with free-energy perturbation both at the MM level (between the two ligands) and from MM to QM/MM (for each ligand). To ensure that converged results are obtained for the MM → QM/MM perturbations, explicit QM/MM molecular dynamics (MD) simulations are performed with two intermediate mixed states. To speed up the calculations, we utilize the fact that the phase space can be extensively sampled at the MM level. Therefore, we run many short QM/MM MD simulations started from snapshots of the MM simulations, instead of a single long simulation. As a test case, we study the binding of nine cyclic carboxylate ligands to the octa-acid deep cavitand. Only the ligand is in the QM system, treated with the semiempirical PM6-DH+ method. We show that for eight of the ligands, we obtain well converged results with short MD simulations (1-15 ps). However, in one case, the convergence is slower (∼50 ps) owing to a mismatch between the conformational preferences of the MM and QM/MM potentials. We test the effect of initial minimization, the need of equilibration, and how many independent simulations are needed to reach a certain precision. The results show that the present approach is about four times faster than using standard MM → QM/MM free-energy perturbations with the same accuracy and precision.
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Affiliation(s)
- Casper Steinmann
- Department of Chemistry and Bioscience , Aalborg University , Frederik Bajers Vej 7H , DK-9220 Aalborg , Denmark.,Department of Theoretical Chemistry , Lund University , Chemical Centre , P.O. Box 124, SE-221 00 Lund , Sweden
| | - Martin A Olsson
- Department of Theoretical Chemistry , Lund University , Chemical Centre , P.O. Box 124, SE-221 00 Lund , Sweden
| | - Ulf Ryde
- Department of Theoretical Chemistry , Lund University , Chemical Centre , P.O. Box 124, SE-221 00 Lund , Sweden
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Olsson MA, Ryde U. Comparison of QM/MM Methods To Obtain Ligand-Binding Free Energies. J Chem Theory Comput 2017; 13:2245-2253. [DOI: 10.1021/acs.jctc.6b01217] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Martin A. Olsson
- Department of Theoretical
Chemistry, Lund University, Chemical Centre, P.O. Box 124, SE-221
00 Lund, Sweden
| | - Ulf Ryde
- Department of Theoretical
Chemistry, Lund University, Chemical Centre, P.O. Box 124, SE-221
00 Lund, Sweden
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Liu W, Jia X, Wang M, Li P, Wang X, Hu W, Zheng J, Mei Y. Calculations of the absolute binding free energies for Ralstonia solanacearum lectins bound with methyl-α-l-fucoside at molecular mechanical and quantum mechanical/molecular mechanical levels. RSC Adv 2017. [DOI: 10.1039/c7ra06215j] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
In this work, both a molecular mechanical (MM) method and a hybrid quantum mechanical/molecular mechanical (QM/MM) method have been applied in the study of the binding affinities of methyl-α-l-fucoside to Ralstonia solanacearum lectins.
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Affiliation(s)
- Wei Liu
- State Key Laboratory of Precision Spectroscopy
- School of Physics and Materials Science
- East China Normal University
- Shanghai 200062
- China
| | - Xiangyu Jia
- State Key Laboratory of Precision Spectroscopy
- School of Physics and Materials Science
- East China Normal University
- Shanghai 200062
- China
| | - Meiting Wang
- State Key Laboratory of Precision Spectroscopy
- School of Physics and Materials Science
- East China Normal University
- Shanghai 200062
- China
| | - Pengfei Li
- State Key Laboratory of Precision Spectroscopy
- School of Physics and Materials Science
- East China Normal University
- Shanghai 200062
- China
| | - Xiaohui Wang
- State Key Laboratory of Precision Spectroscopy
- School of Physics and Materials Science
- East China Normal University
- Shanghai 200062
- China
| | - Wenxin Hu
- The Computer Center
- School of Computer Science and Software Engineering
- East China Normal University
- Shanghai 200062
- China
| | - Jun Zheng
- The Computer Center
- School of Computer Science and Software Engineering
- East China Normal University
- Shanghai 200062
- China
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy
- School of Physics and Materials Science
- East China Normal University
- Shanghai 200062
- China
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Olsson MA, Söderhjelm P, Ryde U. Converging ligand-binding free energies obtained with free-energy perturbations at the quantum mechanical level. J Comput Chem 2016; 37:1589-600. [PMID: 27117350 PMCID: PMC5074236 DOI: 10.1002/jcc.24375] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2016] [Revised: 03/08/2016] [Accepted: 03/09/2016] [Indexed: 12/15/2022]
Abstract
In this article, the convergence of quantum mechanical (QM) free-energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158-224 atoms). We use single-step exponential averaging (ssEA) and the non-Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi-empirical PM6-DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free-energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.
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Affiliation(s)
- Martin A Olsson
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P. O. Box 124, Lund, SE-221 00, Sweden
| | - Pär Söderhjelm
- Department of Biophysical Chemistry, Lund University, Chemical Centre, P. O. Box 124, Lund, SE-221 00, Sweden
| | - Ulf Ryde
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P. O. Box 124, Lund, SE-221 00, Sweden
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Ryde U, Söderhjelm P. Ligand-Binding Affinity Estimates Supported by Quantum-Mechanical Methods. Chem Rev 2016; 116:5520-66. [DOI: 10.1021/acs.chemrev.5b00630] [Citation(s) in RCA: 175] [Impact Index Per Article: 21.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ulf Ryde
- Department of Theoretical
Chemistry and ‡Department of Biophysical Chemistry, Lund University, Chemical Centre, P.O. Box 124, SE-221 00 Lund, Sweden
| | - Pär Söderhjelm
- Department of Theoretical
Chemistry and ‡Department of Biophysical Chemistry, Lund University, Chemical Centre, P.O. Box 124, SE-221 00 Lund, Sweden
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Genheden S, Ryde U, Söderhjelm P. Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model. J Comput Chem 2015; 36:2114-24. [PMID: 26280564 DOI: 10.1002/jcc.24048] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2015] [Revised: 06/13/2015] [Accepted: 07/17/2015] [Indexed: 12/19/2022]
Abstract
The most general way to improve the accuracy of binding-affinity calculations for protein-ligand systems is to use quantum-mechanical (QM) methods together with rigorous alchemical-perturbation (AP) methods. We explore this approach by calculating the relative binding free energy of two synthetic disaccharides binding to galectin-3 at a reasonably high QM level (dispersion-corrected density functional theory with a triple-zeta basis set) and with a sufficiently large QM system to include all short-range interactions with the ligand (744-748 atoms). The rest of the protein is treated as a collection of atomic multipoles (up to quadrupoles) and polarizabilities. Several methods for evaluating the binding free energy from the 3600 QM calculations are investigated in terms of stability and accuracy. In particular, methods using QM calculations only at the endpoints of the transformation are compared with the recently proposed non-Boltzmann Bennett acceptance ratio (NBB) method that uses QM calculations at several stages of the transformation. Unfortunately, none of the rigorous approaches give sufficient statistical precision. However, a novel approximate method, involving the direct use of QM energies in the Bennett acceptance ratio method, gives similar results as NBB but with better precision, ∼3 kJ/mol. The statistical error can be further reduced by performing a greater number of QM calculations.
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Affiliation(s)
- Samuel Genheden
- School of Chemistry, University of Southampton, Highfield, Southampton, SO17 1BJ, United Kingdom
| | - Ulf Ryde
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P. O. Box 124, Lund, SE-221 00, Sweden
| | - Pär Söderhjelm
- Department of Biophysical Chemistry, Lund University, Chemical Centre, P. O. Box 124, Lund, SE-221 00, Sweden
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Steinbrecher T, Case DA, Labahn A. Free energy calculations on the binding of novel thiolactomycin derivatives to E. coli fatty acid synthase I. Bioorg Med Chem 2012; 20:3446-53. [PMID: 22560835 DOI: 10.1016/j.bmc.2012.04.019] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2012] [Revised: 04/03/2012] [Accepted: 04/07/2012] [Indexed: 11/16/2022]
Abstract
Finding novel antibiotics to combat the rise of drug resistance in harmful bacteria is of enormous importance for human health. Computational drug design can be employed to aid synthetic chemists in the search for new potent inhibitors. In recent years, molecular dynamics based free energy calculations have emerged as a useful tool to accurately calculate receptor binding affinities of novel or modified ligands. While being significantly more demanding in computational resources than simpler docking algorithms, they can be employed to obtain reliable estimates of the effect individual functional groups have on protein-ligand complex binding constants. Beta-ketoacyl [acyl carrier protein] synthase I, KAS I, facilitates a critical chain elongation step in the fatty acid synthesis pathway. Since the bacterial type II lipid synthesis system is fundamentally different from the mammalian type I multi-enzyme complex, this enzyme represents a promising target for the design of specific antibiotics. In this work, we study the binding of several recently synthesized derivatives of the natural KAS I inhibitor thiolactomycin in detail based on atomistic modeling. From extensive thermodynamic integration calculations the effect of changing functional groups on the thiolactone scaffold was determined. Four ligand modifications were predicted to show improved binding to the E. coli enzyme, pointing the way towards the design of thiolactomycin derivatives with binding constants in the nanomolar range.
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Affiliation(s)
- Thomas Steinbrecher
- Institut für Physikalische Chemie, Abteilung Theoretische Chemische Biologie, Universität Karlsruhe, KIT, Kaiserstr. 12, 76131 Karlsruhe, Germany.
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