1
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Yao Y, Liu R, Li W, Huang W, Lai Y, Luo HB, Li Z. Convergence-Adaptive Roundtrip Method Enables Rapid and Accurate FEP Calculations. J Chem Theory Comput 2024. [PMID: 39236257 DOI: 10.1021/acs.jctc.4c00939] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/07/2024]
Abstract
The free energy perturbation (FEP) method is a powerful technique for accurate binding free energy calculations, which is crucial for identifying potent ligands with a high affinity in drug discovery. However, the widespread application of FEP is limited by the high computational cost required to achieve equilibrium sampling and the challenges in obtaining converged predictions. In this study, we present the convergence-adaptive roundtrip (CAR) method, which is an enhanced adaptive sampling approach, to address the key challenges in FEP calculations, including the precision-efficiency tradeoff, sampling efficiency, and convergence assessment. By employing on-the-fly convergence analysis to automatically adjust simulation times, enabling efficient traversal of the important phase space through rapid propagation of conformations between different states and eliminating the need for multiple parallel simulations, the CAR method increases convergence and minimizes computational overhead while maintaining calculation accuracy. The performance of the CAR method was evaluated through relative binding free energy (RBFE) calculations on benchmarks comprising four diverse protein-ligand systems. The results demonstrated a significant speedup of over 8-fold compared to conventional FEP methods while maintaining high accuracy. The overall R2 values of 0.65 and 0.56 were obtained using the combined-structure FEP approach and the single-step FEP approach, respectively, in conjunction with the CAR method. In-depth case studies further highlighted the superior performance of the CAR method in terms of convergence acceleration, improved predicted correlations, and reduced computational costs. The advancement of the CAR method makes it a highly effective approach, enhancing the applicability of FEP in drug discovery.
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Affiliation(s)
- Yufen Yao
- State Key Laboratory of Anti-Infective Drug Discovery and Development, School of Pharmaceutical Sciences, Sun Yat-Sen University, Guangzhou 510006, China
| | - Runduo Liu
- State Key Laboratory of Anti-Infective Drug Discovery and Development, School of Pharmaceutical Sciences, Sun Yat-Sen University, Guangzhou 510006, China
| | - Wenchao Li
- State Key Laboratory of Anti-Infective Drug Discovery and Development, School of Pharmaceutical Sciences, Sun Yat-Sen University, Guangzhou 510006, China
| | - Wanyi Huang
- State Key Laboratory of Anti-Infective Drug Discovery and Development, School of Pharmaceutical Sciences, Sun Yat-Sen University, Guangzhou 510006, China
| | - Yijun Lai
- State Key Laboratory of Anti-Infective Drug Discovery and Development, School of Pharmaceutical Sciences, Sun Yat-Sen University, Guangzhou 510006, China
| | - Hai-Bin Luo
- Key Laboratory of Tropical Biological Resources of Ministry of Education, School of Pharmaceutical Sciences, Hainan University, Haikou 570228, China
- Song Li' Academician Workstation of Hainan University (School of Pharmaceutical Sciences), Yazhou Bay, Sanya 572000, China
| | - Zhe Li
- State Key Laboratory of Anti-Infective Drug Discovery and Development, School of Pharmaceutical Sciences, Sun Yat-Sen University, Guangzhou 510006, China
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2
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Hahn DF, Gapsys V, de Groot BL, Mobley DL, Tresadern G. Current State of Open Source Force Fields in Protein-Ligand Binding Affinity Predictions. J Chem Inf Model 2024; 64:5063-5076. [PMID: 38895959 PMCID: PMC11234369 DOI: 10.1021/acs.jcim.4c00417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2024] [Revised: 04/23/2024] [Accepted: 04/25/2024] [Indexed: 06/21/2024]
Abstract
In drug discovery, the in silico prediction of binding affinity is one of the major means to prioritize compounds for synthesis. Alchemical relative binding free energy (RBFE) calculations based on molecular dynamics (MD) simulations are nowadays a popular approach for the accurate affinity ranking of compounds. MD simulations rely on empirical force field parameters, which strongly influence the accuracy of the predicted affinities. Here, we evaluate the ability of six different small-molecule force fields to predict experimental protein-ligand binding affinities in RBFE calculations on a set of 598 ligands and 22 protein targets. The public force fields OpenFF Parsley and Sage, GAFF, and CGenFF show comparable accuracy, while OPLS3e is significantly more accurate. However, a consensus approach using Sage, GAFF, and CGenFF leads to accuracy comparable to OPLS3e. While Parsley and Sage are performing comparably based on aggregated statistics across the whole dataset, there are differences in terms of outliers. Analysis of the force field reveals that improved parameters lead to significant improvement in the accuracy of affinity predictions on subsets of the dataset involving those parameters. Lower accuracy can not only be attributed to the force field parameters but is also dependent on input preparation and sampling convergence of the calculations. Especially large perturbations and nonconverged simulations lead to less accurate predictions. The input structures, Gromacs force field files, as well as the analysis Python notebooks are available on GitHub.
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Affiliation(s)
- David F. Hahn
- Computational
Chemistry, Janssen Research & Development, Turnhoutseweg 30, Beerse 2340, Belgium
| | - Vytautas Gapsys
- Computational
Chemistry, Janssen Research & Development, Turnhoutseweg 30, Beerse 2340, Belgium
- Computational
Biomolecular Dynamics Group, Max Planck
Institute for Multidisciplinary Sciences, Am Fassberg 11, Göttingen 37077, Germany
| | - Bert L. de Groot
- Computational
Biomolecular Dynamics Group, Max Planck
Institute for Multidisciplinary Sciences, Am Fassberg 11, Göttingen 37077, Germany
| | - David L. Mobley
- Department
of Chemistry, University of California, Irvine, California 92697, United States
- Department
of Pharmaceutical Sciences, University of
California, Irvine, California 92697, United States
| | - Gary Tresadern
- Computational
Chemistry, Janssen Research & Development, Turnhoutseweg 30, Beerse 2340, Belgium
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3
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Lagardère L, Maurin L, Adjoua O, El Hage K, Monmarché P, Piquemal JP, Hénin J. Lambda-ABF: Simplified, Portable, Accurate, and Cost-Effective Alchemical Free-Energy Computation. J Chem Theory Comput 2024; 20:4481-4498. [PMID: 38805379 DOI: 10.1021/acs.jctc.3c01249] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/30/2024]
Abstract
We introduce the lambda-Adaptive Biasing Force (lambda-ABF) method for the computation of alchemical free-energy differences. We propose a software implementation and showcase it on biomolecular systems. The method arises from coupling multiple-walker adaptive biasing force with λ-dynamics. The sampling of the alchemical variable is continuous and converges toward a uniform distribution, making manual optimization of the λ schedule unnecessary. Contrary to most other approaches, alchemical free-energy estimates are obtained immediately without any postprocessing. Free diffusion of λ improves orthogonal relaxation compared to fixed-λ thermodynamic integration or free-energy perturbation. Furthermore, multiple walkers provide generic orthogonal space coverage with minimal user input and negligible computational overhead. We show that our high-performance implementations coupling the Colvars library with NAMD and Tinker-HP can address real-world cases including ligand-receptor binding with both fixed-charge and polarizable models, with a demonstrably richer sampling than fixed-λ methods. The implementation is fully open-source, publicly available, and readily usable by practitioners of current alchemical methods. Thanks to the portable Colvars library, lambda-ABF presents a unified user interface regardless of the back-end (NAMD, Tinker-HP, or any software to be interfaced in the future), sparing users the effort of learning multiple interfaces. Finally, the Colvars Dashboard extension of the visual molecular dynamics (VMD) software provides an interactive monitoring and diagnostic tool for lambda-ABF simulations.
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Affiliation(s)
- Louis Lagardère
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, Paris 75005, France
- Sorbonne Université, Institut Parisien de Chimie Physique et Théorique, FR2622 CNRS, 75005 Paris, France
- Qubit Pharmaceuticals, 29 rue du Faubourg Saint Jacques, 75014 Paris, France
| | - Lise Maurin
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, Paris 75005, France
- Sorbonne Université, Laboratoire Jacques-Louis Lions, UMR 7589 CNRS, 75005 Paris, France
| | - Olivier Adjoua
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, Paris 75005, France
| | - Krystel El Hage
- Qubit Pharmaceuticals, 29 rue du Faubourg Saint Jacques, 75014 Paris, France
| | - Pierre Monmarché
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, Paris 75005, France
- Sorbonne Université, Laboratoire Jacques-Louis Lions, UMR 7589 CNRS, 75005 Paris, France
| | - Jean-Philip Piquemal
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, Paris 75005, France
- Qubit Pharmaceuticals, 29 rue du Faubourg Saint Jacques, 75014 Paris, France
| | - Jérôme Hénin
- Laboratoire de Biochimie Théorique, Université Paris Cité, CNRS, UPR 9080, 75005 Paris, France
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4
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Fu H, Chipot C, Shao X, Cai W. Standard Binding Free-Energy Calculations: How Far Are We from Automation? J Phys Chem B 2023; 127:10459-10468. [PMID: 37824848 DOI: 10.1021/acs.jpcb.3c04370] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2023]
Abstract
Recent success stories suggest that in silico protein-ligand binding free-energy calculations are approaching chemical accuracy. However, their widespread application remains limited by the extensive human intervention required, posing challenges for the neophyte. As such, it is critical to develop automated workflows for estimating protein-ligand binding affinities with minimum personal involvement. Key human efforts include setting up and tuning enhanced-sampling or alchemical-transformation algorithms as a preamble to computational binding free-energy estimations. Additionally, preparing input files, bookkeeping, and postprocessing represent nontrivial tasks. In this Perspective, we discuss recent progress in automating standard binding free-energy calculations, featuring the development of adaptive or parameter-free algorithms, standardization of binding free-energy calculation workflows, and the implementation of user-friendly software. We also assess the current state of automated standard binding free-energy calculations and evaluate the limitations of existing methods. Last, we outline the requirements for future algorithms and workflows to facilitate automated free-energy calculations for diverse protein-ligand complexes.
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Affiliation(s)
- Haohao Fu
- State Key Laboratory of Medicinal Chemical Biology, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Christophe Chipot
- Laboratoire International Associé CNRS and University of Illinois at Urbana-Champaign, UMR no. 7019, Université de Lorraine, BP 70239, F-54506 Vandoeuvre-lès-Nancy, France
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, United States
- Department of Chemistry, The University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637, United States
- Department of Chemistry, The University of Hawai'i at Ma̅noa, 2545 McCarthy Mall, Honolulu, Hawaii 96822, United States
| | - Xueguang Shao
- State Key Laboratory of Medicinal Chemical Biology, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Wensheng Cai
- State Key Laboratory of Medicinal Chemical Biology, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
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5
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Gheta SKO, Bonin A, Gerlach T, Göller AH. Predicting absolute aqueous solubility by applying a machine learning model for an artificially liquid-state as proxy for the solid-state. J Comput Aided Mol Des 2023; 37:765-789. [PMID: 37878216 DOI: 10.1007/s10822-023-00538-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 10/02/2023] [Indexed: 10/26/2023]
Abstract
In this study, we use machine learning algorithms with QM-derived COSMO-RS descriptors, along with Morgan fingerprints, to predict the absolute solubility of drug-like compounds. The QM-derived descriptors account for the molecular properties of the solute, i.e., the solute-solute interactions in an artificial-liquid-state (super-cooled liquid), and the solute-solvent interactions in solution. We employ two main approaches to predict solubility: (i) a hypothetical pathway that involves melting the solute at room temperature T = T¯ ([Formula: see text]) and mixing the artificially liquid solute into the solvent ([Formula: see text]). In this approach [Formula: see text] is predicted using machine learning models, and the [Formula: see text] is obtained from COSMO-RS calculations; (ii) direct solubility prediction using machine learning algorithms. The models were trained on a large number of Bayer in-house compounds for which water solubility data is available at physiological pH of 6.5 and ambient temperature. We also evaluated our models using external datasets from a solubility challenge. Our models present great improvements compared to the absolute solubility prediction with the QSAR model for the artificial liquid state as implemented in the COSMOtherm software, for both in-house and external datasets. We are furthermore able to demonstrate the superiority of QM-derived descriptors compared to cheminformatics descriptors. We finally present low-cost alternative models using fragment-based COSMOquick calculations with only marginal reduction in the quality of predicted solubility.
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Affiliation(s)
- Sadra Kashef Ol Gheta
- Bayer AG, Pharmaceuticals, R&D, Computational Molecular Design, 42096, Wuppertal, Germany
| | - Anne Bonin
- Bayer AG, Pharmaceuticals, R&D, Computational Molecular Design, 42096, Wuppertal, Germany
| | - Thomas Gerlach
- Bayer AG, Crop Science, R&D, Digital Transformation, 40789, Monheim, Germany
- Bayer AG, Engineering & Technology, Thermal Separation Technologies, 51368, Leverkusen, Germany
| | - Andreas H Göller
- Bayer AG, Pharmaceuticals, R&D, Computational Molecular Design, 42096, Wuppertal, Germany.
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6
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Barros EP, Ries B, Böselt L, Champion C, Riniker S. Recent developments in multiscale free energy simulations. Curr Opin Struct Biol 2021; 72:55-62. [PMID: 34534706 DOI: 10.1016/j.sbi.2021.08.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Revised: 08/06/2021] [Accepted: 08/16/2021] [Indexed: 11/26/2022]
Abstract
Physics-based free energy simulations enable the rigorous calculation of properties, such as conformational equilibria, solvation or binding free energies. While historically most applications have occurred at the atomistic level of resolution, a range of advances in the past years make it possible now to reliably cross the temporal, spatial and theory scales for the modeling of complex systems or the efficient prediction of results at the accuracy level of expensive quantum-mechanical calculations. In this mini-review, we discuss recent methodological advances as well as opportunities opened up by the introduction of machine learning approaches, which tackle the diverse challenges across the different scales, improve the accuracy and feasibility, and push the boundaries of multiscale free energy simulations.
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Affiliation(s)
- Emilia P Barros
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093, Zurich, Switzerland
| | - Benjamin Ries
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093, Zurich, Switzerland
| | - Lennard Böselt
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093, Zurich, Switzerland
| | - Candide Champion
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093, Zurich, Switzerland
| | - Sereina Riniker
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093, Zurich, Switzerland.
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7
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Gotzias A, Tocci E, Sapalidis A. On the Consistency of the Exfoliation Free Energy of Graphenes by Molecular Simulations. Int J Mol Sci 2021; 22:ijms22158291. [PMID: 34361058 PMCID: PMC8347420 DOI: 10.3390/ijms22158291] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2021] [Revised: 07/27/2021] [Accepted: 07/28/2021] [Indexed: 01/04/2023] Open
Abstract
Monolayer graphene is now produced at significant yields, by liquid phase exfoliation of graphites in solvents. This has increased the interest in molecular simulation studies to give new insights in the field. We use decoupling simulations to compute the exfoliation free energy of graphenes in a liquid environment. Starting from a bilayer graphene configuration, we decouple the Van der Waals interactions of a graphene monolayer in the presence of saline water. Then, we introduce the monolayer back into water by coupling its interactions with water molecules and ions. A different approach to compute the graphene exfoliation free energy is to use umbrella sampling. We apply umbrella sampling after pulling the graphene monolayer on the shear direction up to a distance from a bilayer. We show that the decoupling and umbrella methods give highly consistent free energy results for three bilayer graphene samples with different size. This strongly suggests that the systems in both methods remain closely in equilibrium as we move between the states before and after the exfoliation. Therefore, the amount of nonequilibrium work needed to peel the two layers apart is minimized efficiently.
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Affiliation(s)
- Anastasios Gotzias
- National Centre for Scientific Research “Demokritos”, Institute of Nanoscience and Nanotechnology INN, 15310 Athens, Greece;
- Correspondence: ; Tel.: +30-210-6503408
| | - Elena Tocci
- Institute on Membrane Technology ITM–CNR, National Research Council, 87036 Rende, Italy;
| | - Andreas Sapalidis
- National Centre for Scientific Research “Demokritos”, Institute of Nanoscience and Nanotechnology INN, 15310 Athens, Greece;
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8
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Vilseck JZ, Ding X, Hayes RL, Brooks CL. Generalizing the Discrete Gibbs Sampler-Based λ-Dynamics Approach for Multisite Sampling of Many Ligands. J Chem Theory Comput 2021; 17:3895-3907. [PMID: 34101448 DOI: 10.1021/acs.jctc.1c00176] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
In this work, the discrete λ variant of the Gibbs sampler-based λ-dynamics (d-GSλD) method is developed to enable multiple functional group perturbations to be investigated at one or more sites of substitution off a common ligand core. The theoretical framework and special considerations for constructing discrete λ states for multisite d-GSλD are presented. The precision and accuracy of the d-GSλD method is evaluated with three test cases of increasing complexity. Specifically, methyl → methyl symmetric perturbations in water, 1,4-benzene hydration free energies and protein-ligand binding affinities for an example HIV-1 reverse transcriptase inhibitor series are computed with d-GSλD. Complementary MSλD calculations were also performed to compare with d-GSλD's performance. Excellent agreement between d-GSλD and MSλD is observed, with mean unsigned errors of 0.12 and 0.22 kcal/mol for computed hydration and binding free energy test cases, respectively. Good agreement with experiment is also observed, with errors of 0.5-0.7 kcal/mol. These findings support the applicability of the d-GSλD free energy method for a variety of molecular design problems, including structure-based drug design. Finally, a discussion of d-GSλD versus MSλD approaches is presented to compare and contrast features of both methods.
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Affiliation(s)
- Jonah Z Vilseck
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States.,Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, Indianapolis, Indiana 46202, United States.,Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indianapolis, Indiana 46202, United States
| | - Xinqiang Ding
- Department of Computational Medicine & Bioinformatics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Ryan L Hayes
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Charles L Brooks
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States.,Biophysics Program, University of Michigan, Ann Arbor, Michigan 48109, United States
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9
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Ries B, Linker SM, Hahn DF, König G, Riniker S. Ensembler: A Simple Package for Fast Prototyping and Teaching Molecular Simulations. J Chem Inf Model 2021; 61:560-564. [PMID: 33512157 DOI: 10.1021/acs.jcim.0c01283] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Ensembler is a Python package that enables method prototyping using 1D and 2D model systems and allows deepening of the understanding of different molecular dynamics (MD) methods, starting from basic techniques to enhanced sampling and free-energy approaches. The ease of installing and using the package increases shareability, comparability, and reproducibility of scientific code developments. Here, we describe the implementation and usage of the package and provide an application example for free-energy calculation. The code of Ensembler is freely available on GitHub at https://github.com/rinikerlab/Ensembler.
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Affiliation(s)
- Benjamin Ries
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Stephanie M Linker
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - David F Hahn
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Gerhard König
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Sereina Riniker
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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10
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de Ruiter A, Petrov D, Oostenbrink C. Optimization of Alchemical Pathways Using Extended Thermodynamic Integration. J Chem Theory Comput 2021; 17:56-65. [PMID: 33351609 PMCID: PMC7872317 DOI: 10.1021/acs.jctc.0c01170] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Abstract
![]()
Thermodynamic
integration (TI) is a commonly used method to determine
free-energy differences. One of its disadvantages is that many intermediate
λ-states need to be sampled in order to be able to integrate
accurately over ⟨∂H/∂λ⟩.
Here, we use the recently introduced extended TI to study alternative
parameterizations of H(λ) and its influence
on the smoothness of the ⟨∂H/∂λ⟩
curves as well as the efficiency of the simulations. We find that
the extended TI approach can be used to select curves of low curvature.
An optimal parameterization is suggested for the calculation of hydration
free energies. For calculations of relative binding free energies,
we show that optimized parameterizations of the Hamiltonian in the
unbound state also effectively lower the curvature in the bound state
of the ligand.
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Affiliation(s)
- Anita de Ruiter
- Institute for Molecular Modeling and Simulation, University of Natural Resources and Life Science, Vienna Muthgasse 18, 1190 Vienna, Austria
| | - Drazen Petrov
- Institute for Molecular Modeling and Simulation, University of Natural Resources and Life Science, Vienna Muthgasse 18, 1190 Vienna, Austria
| | - Chris Oostenbrink
- Institute for Molecular Modeling and Simulation, University of Natural Resources and Life Science, Vienna Muthgasse 18, 1190 Vienna, Austria
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11
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Prediction of pKa in a system with high orthogonal barriers: Alchemical flying Gaussian method. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.138012] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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12
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Hu W, Li P, Wang JN, Xue Y, Mo Y, Zheng J, Pan X, Shao Y, Mei Y. Accelerated Computation of Free Energy Profile at Ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semiempirical Reference Potential. 3. Gaussian Smoothing on Density-of-States. J Chem Theory Comput 2020; 16:6814-6822. [PMID: 32975951 PMCID: PMC7658029 DOI: 10.1021/acs.jctc.0c00794] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Calculations of the free energy profile, also known as potential of mean force (PMF), along a chosen collective variable (CV) are now routinely applied in the studies of chemical processes, such as enzymatic reactions and chemical reactions in condensed phases. However, if the ab initio quantum mechanical/molecular mechanics (QM/MM) level of accuracy is required for the PMF, it can be formidably demanding even with the most advanced enhanced sampling methods, such as umbrella sampling. To ameliorate this difficulty, we developed a novel method for the computation of the free energy profile based on the reference-potential method recently, in which a low-level reference Hamiltonian is employed for phase space sampling and the free energy profile can be corrected to the level of interest (the target Hamiltonian) by energy reweighting in a nonparametric way. However, when the reference Hamiltonian is very different from the target Hamiltonian, the calculated ensemble averages, including the PMF, often suffer from numerical instability, which mainly comes from the overestimation of the density-of-states (DoS) in the low-energy region. Stochastic samplings of these low-energy configurations are rare events, and some low-energy conformations may get oversampled in simulations of a finite length. In this work, an assumption of Gaussian distribution is applied to the DoS in each CV bin, and the weight of each configuration is rescaled according to the accumulated DoS. The results show that this smoothing process can remarkably reduce the ruggedness of the PMF and increase the reliability of the reference-potential method.
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Affiliation(s)
- Wenxin Hu
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Pengfei Li
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Jia-Ning Wang
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Yuanfei Xue
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Yan Mo
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic 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
| | - Jun Zheng
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Xiaoliang Pan
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic 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
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13
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König G, Glaser N, Schroeder B, Kubincová A, Hünenberger PH, Riniker S. An Alternative to Conventional λ-Intermediate States in Alchemical Free Energy Calculations: λ-Enveloping Distribution Sampling. J Chem Inf Model 2020; 60:5407-5423. [PMID: 32794763 DOI: 10.1021/acs.jcim.0c00520] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Alchemical free energy calculations typically rely on intermediate states to bridge between the relevant phase spaces of the two end states. These intermediate states are usually created by mixing the energies or parameters of the end states according to a coupling parameter λ. The choice of the procedure has a strong impact on the efficiency of the calculation, as it affects both the encountered energy barriers and the phase space overlap between the states. The present work builds on the connection between the minimum variance pathway (MVP) and enveloping distribution sampling (EDS). It is shown that both methods can be regarded as special cases of a common scheme referred to as λ-EDS, which can also reproduce the behavior of conventional λ-intermediate states. A particularly attractive feature of λ-EDS is its ability to emulate the use of soft core potentials (SCP) while avoiding the associated computational overhead when applying efficient free energy estimators such as the multistate Bennett's acceptance ratio (MBAR). The method is illustrated for both relative and absolute free energy calculations considering five benchmark systems. The first two systems (charge inversion and cavity creation in a dipolar solvent) demonstrate the use of λ-EDS as an alternative coupling scheme in the context of thermodynamic integration (TI). The three other systems (change of bond length, change of dihedral angles, and cavity creation in water) investigate the efficiency and optimal choice of parameters in the context of free energy perturbation (FEP) and Bennett's acceptance ratio (BAR). It is shown that λ-EDS allows larger steps along the alchemical pathway than conventional intermediate states.
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Affiliation(s)
- Gerhard König
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Nina Glaser
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Benjamin Schroeder
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Alžbeta Kubincová
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Philippe H Hünenberger
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Sereina Riniker
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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14
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Kuhn M, Firth-Clark S, Tosco P, Mey ASJS, Mackey M, Michel J. Assessment of Binding Affinity via Alchemical Free-Energy Calculations. J Chem Inf Model 2020; 60:3120-3130. [DOI: 10.1021/acs.jcim.0c00165] [Citation(s) in RCA: 60] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Maximilian Kuhn
- Cresset, New Cambridge House, Bassingbourn Road, Litlington SG8 0SS, Cambridgeshire, U.K
- EaStCHEM School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh EH9 3FJ, U.K
| | - Stuart Firth-Clark
- Cresset, New Cambridge House, Bassingbourn Road, Litlington SG8 0SS, Cambridgeshire, U.K
| | - Paolo Tosco
- Cresset, New Cambridge House, Bassingbourn Road, Litlington SG8 0SS, Cambridgeshire, U.K
| | - Antonia S. J. S. Mey
- EaStCHEM School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh EH9 3FJ, U.K
| | - Mark Mackey
- Cresset, New Cambridge House, Bassingbourn Road, Litlington SG8 0SS, Cambridgeshire, U.K
| | - Julien Michel
- EaStCHEM School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh EH9 3FJ, U.K
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15
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Hahn DF, Zarotiadis RA, Hünenberger PH. The Conveyor Belt Umbrella Sampling (CBUS) Scheme: Principle and Application to the Calculation of the Absolute Binding Free Energies of Alkali Cations to Crown Ethers. J Chem Theory Comput 2020; 16:2474-2493. [DOI: 10.1021/acs.jctc.9b00998] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- David F. Hahn
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Rhiannon A. Zarotiadis
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Philippe H. Hünenberger
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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16
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Rogers TR, Wang F. Comparing Alchemical Free Energy Estimates to Experimental Values Based on the Ben-Naim Formula: How Much Agreement Can We Expect? J Phys Chem B 2020; 124:840-847. [PMID: 31922746 DOI: 10.1021/acs.jpcb.9b08965] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The solvation free energy (SFE) plays a key role in thermodynamics. One well-established method for computing the SFE is through an alchemical transformation. However, experimental SFEs are generally determined according to the Ben-Naim equations relying on vapor pressure or density ratios. It is important to establish whether, or to what extent, typical alchemical-based free energy computations provide results comparable to experimental SFEs. In this work, we mimic experimental measurements by simulating the liquid-vapor coexistence of water without alchemical operations. The SFEs measured through vapor pressure and density ratios are used to validate the SFEs obtained through alchemical transformations. It is shown that proper consideration of the nonideal behavior of the vapor is important to ensure that the alchemical SFEs are consistent with the Ben-Naim SFEs. Alchemical transformations in the vapor phase should be performed in addition to solution phase transformations for strongly interacting solutes, such as those with low boiling temperatures and large second virial coefficients. A formula based on the virial expansion of pressure is proposed to provide a better estimate of the true SFE from the simulated vapor pressures. The proposed formula is also applicable to experimental determinations of SFE when the pressure-based route is used.
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Affiliation(s)
- T Ryan Rogers
- Department of Chemistry and Biochemistry , University of Arkansas , Fayetteville , Arkansas 72703 , United States
| | - Feng Wang
- Department of Chemistry and Biochemistry , University of Arkansas , Fayetteville , Arkansas 72703 , United States
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17
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Hahn DF, König G, Hünenberger PH. Overcoming Orthogonal Barriers in Alchemical Free Energy Calculations: On the Relative Merits of λ-Variations, λ-Extrapolations, and Biasing. J Chem Theory Comput 2020; 16:1630-1645. [DOI: 10.1021/acs.jctc.9b00853] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- David F. Hahn
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Gerhard König
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Philippe H. Hünenberger
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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18
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Mey ASJS, Allen BK, Macdonald HEB, Chodera JD, Hahn DF, Kuhn M, Michel J, Mobley DL, Naden LN, Prasad S, Rizzi A, Scheen J, Shirts MR, Tresadern G, Xu H. Best Practices for Alchemical Free Energy Calculations [Article v1.0]. LIVING JOURNAL OF COMPUTATIONAL MOLECULAR SCIENCE 2020; 2:18378. [PMID: 34458687 PMCID: PMC8388617 DOI: 10.33011/livecoms.2.1.18378] [Citation(s) in RCA: 114] [Impact Index Per Article: 28.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Alchemical free energy calculations are a useful tool for predicting free energy differences associated with the transfer of molecules from one environment to another. The hallmark of these methods is the use of "bridging" potential energy functions representing alchemical intermediate states that cannot exist as real chemical species. The data collected from these bridging alchemical thermodynamic states allows the efficient computation of transfer free energies (or differences in transfer free energies) with orders of magnitude less simulation time than simulating the transfer process directly. While these methods are highly flexible, care must be taken in avoiding common pitfalls to ensure that computed free energy differences can be robust and reproducible for the chosen force field, and that appropriate corrections are included to permit direct comparison with experimental data. In this paper, we review current best practices for several popular application domains of alchemical free energy calculations performed with equilibrium simulations, in particular relative and absolute small molecule binding free energy calculations to biomolecular targets.
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Affiliation(s)
- Antonia S. J. S. Mey
- EaStCHEM School of Chemistry, David Brewster Road, Joseph Black Building, The King’s Buildings, Edinburgh, EH9 3FJ, UK
| | | | - Hannah E. Bruce Macdonald
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York NY, USA
| | - John D. Chodera
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York NY, USA
| | - David F. Hahn
- Computational Chemistry, Janssen Research & Development, Turnhoutseweg 30, Beerse B-2340, Belgium
| | - Maximilian Kuhn
- EaStCHEM School of Chemistry, David Brewster Road, Joseph Black Building, The King’s Buildings, Edinburgh, EH9 3FJ, UK
- Cresset, Cambridgeshire, UK
| | - Julien Michel
- EaStCHEM School of Chemistry, David Brewster Road, Joseph Black Building, The King’s Buildings, Edinburgh, EH9 3FJ, UK
| | - David L. Mobley
- Departments of Pharmaceutical Sciences and Chemistry, University of California, Irvine, Irvine, USA
| | - Levi N. Naden
- Molecular Sciences Software Institute, Blacksburg VA, USA
| | | | - Andrea Rizzi
- Silicon Therapeutics, Boston, MA, USA
- Tri-Institutional Training Program in Computational Biology and Medicine, New York, NY, USA
| | - Jenke Scheen
- EaStCHEM School of Chemistry, David Brewster Road, Joseph Black Building, The King’s Buildings, Edinburgh, EH9 3FJ, UK
| | | | - Gary Tresadern
- Computational Chemistry, Janssen Research & Development, Turnhoutseweg 30, Beerse B-2340, Belgium
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19
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Hahn DF, Milić JV, Hünenberger PH. Vase
‐
Kite
Equilibrium of Resorcin[4]arene Cavitands Investigated Using Molecular Dynamics Simulations with Ball‐and‐Stick Local Elevation Umbrella Sampling. Helv Chim Acta 2019. [DOI: 10.1002/hlca.201900060] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- David F. Hahn
- Laboratory of Physical Chemistry, Department of Chemistry and Applied BiosciencesETH Zürich Vladimir-Prelog-Weg 2 CH-8093 Zürich Switzerland
| | - Jovana V. Milić
- Laboratory of Photonics and InterfacesÉcole Polytechnique Fédérale de Lausanne, EPFL SB ISIC LPI, Station 6 CH-1015 Lausanne Switzerland
| | - Philippe H. Hünenberger
- Laboratory of Physical Chemistry, Department of Chemistry and Applied BiosciencesETH Zürich Vladimir-Prelog-Weg 2 CH-8093 Zürich Switzerland
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