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York DM. Modern Alchemical Free Energy Methods for Drug Discovery Explained. ACS PHYSICAL CHEMISTRY AU 2023; 3:478-491. [PMID: 38034038 PMCID: PMC10683484 DOI: 10.1021/acsphyschemau.3c00033] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Revised: 09/12/2023] [Accepted: 09/13/2023] [Indexed: 12/02/2023]
Abstract
This Perspective provides a contextual explanation of the current state-of-the-art alchemical free energy methods and their role in drug discovery as well as highlights select emerging technologies. The narrative attempts to answer basic questions about what goes on "under the hood" in free energy simulations and provide general guidelines for how to run simulations and analyze the results. It is the hope that this work will provide a valuable introduction to students and scientists in the field.
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Affiliation(s)
- Darrin M. York
- Laboratory for Biomolecular
Simulation Research, Institute for Quantitative Biomedicine, and Department
of Chemistry and Chemical Biology, Rutgers
University, Piscataway, New Jersey 08854, United States
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2
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Tsai HC, Lee TS, Ganguly A, Giese TJ, Ebert MCCJC, Labute P, Merz KM, York DM. AMBER Free Energy Tools: A New Framework for the Design of Optimized Alchemical Transformation Pathways. J Chem Theory Comput 2023; 19:10.1021/acs.jctc.2c00725. [PMID: 36622640 PMCID: PMC10329732 DOI: 10.1021/acs.jctc.2c00725] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
We develop a framework for the design of optimized alchemical transformation pathways in free energy simulations using nonlinear mixing and a new functional form for so-called "softcore" potentials. We describe the implementation and testing of this framework in the GPU-accelerated AMBER software suite. The new optimized alchemical transformation pathways integrate a number of important features, including (1) the use of smoothstep functions to stabilize behavior near the transformation end points, (2) consistent power scaling of Coulomb and Lennard-Jones (LJ) interactions with unitless control parameters to maintain balance of electrostatic attractions and exchange repulsions, (3) pairwise form based on the LJ contact radius for the effective interaction distance with separation-shifted scaling, and (4) rigorous smoothing of the potential at the nonbonded cutoff boundary. The new softcore potential form is combined with smoothly transforming nonlinear λ weights for mixing specific potential energy terms, along with flexible λ-scheduling features, to enable robust and stable alchemical transformation pathways. The resulting pathways are demonstrated and tested, and shown to be superior to the traditional methods in terms of numerical stability and minimal variance of the free energy estimates for all cases considered. The framework presented here can be used to design new alchemical enhanced sampling methods, and leveraged in robust free energy workflows for large ligand data sets.
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Affiliation(s)
- Hsu-Chun Tsai
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Tai-Sung Lee
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Abir Ganguly
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Timothy J. Giese
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Maximilian CCJC Ebert
- Congruence Therapeutics, 7171 Rue Frederick Banting #117, Saint-Laurent, Quebec, Canada H4S 1Z9
| | - Paul Labute
- Chemical Computing Group ULC, 910-1010 Sherbrooke West, Montreal, Quebec, Canada H3A 2R7
| | - Kenneth M. Merz
- Department of Chemistry and Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI 48824, USA
| | - Darrin M. York
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
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Gracia Carmona O, Oostenbrink C. Accelerated Enveloping Distribution Sampling (AEDS) Allows for Efficient Sampling of Orthogonal Degrees of Freedom. J Chem Inf Model 2023; 63:197-207. [PMID: 36512416 PMCID: PMC9832482 DOI: 10.1021/acs.jcim.2c01272] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
One of the most challenging aspects in the molecular simulation of proteins is the study of slowly relaxing processes, such as loop rearrangements or ligands that adopt different conformations in the binding site. State-of-the-art methods used to calculate binding free energies rely on performing several short simulations (lambda steps), in which the ligand is slowly transformed into the endstates of interest. This makes capturing the slowly relaxing processes even more difficult, as they would need to be observed in all of the lambda steps. One attractive alternative is the use of a reference state capable of sampling all of the endstates of interest in a single simulation. However, the energy barriers between the states can be too high to overcome, thus hindering the sampling of all of the relevant conformations. Accelerated enveloping distribution sampling (AEDS) is a recently developed reference state technique that circumvents the high-energy-barrier challenge by adding a boosting potential that flattens the energy landscape without distorting the energy minima. In the present work, we apply AEDS to the well-studied benchmark system T4 lysozyme L99A. The T4 lysozyme L99A mutant contains a hydrophobic pocket in which there is a valine (valine 111), whose conformation influences the binding efficiencies of the different ligands. Incorrectly sampling the dihedral angle can lead to errors in predicted binding free energies of up to 16 kJ mol-1. This protein constitutes an ideal scenario to showcase the advantages and challenges when using AEDS in the presence of slow relaxing processes. We show that AEDS is able to successfully sample the relevant degrees of freedom, providing accurate binding free energies, without the need of previous information of the system in the form of collective variables. Additionally, we showcase the capabilities of AEDS to efficiently screen a set of ligands. These results represent a promising first step toward the development of free-energy methods that can respond to more intricate molecular events.
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Wade A, Bhati AP, Wan S, Coveney PV. Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy, Precision, and Reproducibility. J Chem Theory Comput 2022; 18:3972-3987. [PMID: 35609233 PMCID: PMC9202356 DOI: 10.1021/acs.jctc.2c00114] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2022] [Indexed: 11/28/2022]
Abstract
The binding free energy between a ligand and its target protein is an essential quantity to know at all stages of the drug discovery pipeline. Assessing this value computationally can offer insight into where efforts should be focused in the pursuit of effective therapeutics to treat a myriad of diseases. In this work, we examine the computation of alchemical relative binding free energies with an eye for assessing reproducibility across popular molecular dynamics packages and free energy estimators. The focus of this work is on 54 ligand transformations from a diverse set of protein targets: MCL1, PTP1B, TYK2, CDK2, and thrombin. These targets are studied with three popular molecular dynamics packages: OpenMM, NAMD2, and NAMD3 alpha. Trajectories collected with these packages are used to compare relative binding free energies calculated with thermodynamic integration and free energy perturbation methods. The resulting binding free energies show good agreement between molecular dynamics packages with an average mean unsigned error between them of 0.50 kcal/mol. The correlation between packages is very good, with the lowest Spearman's, Pearson's and Kendall's tau correlation coefficients being 0.92, 0.91, and 0.76, respectively. Agreement between thermodynamic integration and free energy perturbation is shown to be very good when using ensemble averaging.
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Affiliation(s)
- Alexander
D. Wade
- Centre
for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, UK
| | - Agastya P. Bhati
- Centre
for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, UK
| | - Shunzhou Wan
- Centre
for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, UK
| | - Peter V. Coveney
- Centre
for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, UK
- Informatics
Institute, University of Amsterdam, Amsterdam 1098XH, The Netherlands
- Advanced
Research Computing Centre, University College
London, London WC1H 0AJ, UK
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Oshima H, Sugita Y. Modified Hamiltonian in FEP Calculations for Reducing the Computational Cost of Electrostatic Interactions. J Chem Inf Model 2022; 62:2846-2856. [PMID: 35639709 DOI: 10.1021/acs.jcim.1c01532] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The free-energy perturbation (FEP) method predicts relative and absolute free-energy changes of biomolecules in solvation and binding with other molecules. FEP is, therefore, one of the most essential tools in in silico drug design. In conventional FEP, to smoothly connect two thermodynamic states, the potential energy is modified as a linear combination of the end-state potential energies by introducing scaling factors. When the particle mesh Ewald is used for electrostatic calculations, conventional FEP requires two reciprocal-space calculations per time step, which largely decreases the computational performance. To overcome this problem, we propose a new FEP scheme by introducing a modified Hamiltonian instead of interpolation of the end-state potential energies. The scheme introduces nonuniform scaling into the electrostatic potential as used in Replica Exchange with Solute Tempering 2 (REST2) and does not require additional reciprocal-space calculations. We tested this modified Hamiltonian in FEP calculations in several biomolecular systems. In all cases, the calculated free-energy changes with the current scheme are in good agreement with those from conventional FEP. The modified Hamiltonian in FEP greatly improves the computational performance, which is particularly marked for large biomolecular systems whose reciprocal-space calculations are the major bottleneck of total computational time.
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Affiliation(s)
- Hiraku Oshima
- Laboratory for Biomolecular Function Simulation, RIKEN Center for Biosystems Dynamics Research, Integrated Innovation Building 7F, 6-7-1 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
| | - Yuji Sugita
- Laboratory for Biomolecular Function Simulation, RIKEN Center for Biosystems Dynamics Research, Integrated Innovation Building 7F, 6-7-1 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan.,Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan.,Computational Biophysics Research Team, RIKEN Center for Computational Science, Integrated Innovation Building 7F, 6-7-1 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
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Petrov D. Perturbation Free-Energy Toolkit: An Automated Alchemical Topology Builder. J Chem Inf Model 2021; 61:4382-4390. [PMID: 34415755 PMCID: PMC8479811 DOI: 10.1021/acs.jcim.1c00428] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Indexed: 11/30/2022]
Abstract
Free-energy calculations play an important role in the application of computational chemistry to a range of fields, including protein biochemistry, rational drug design, or materials science. Importantly, the free-energy difference is directly related to experimentally measurable quantities such as partition and adsorption coefficients, water activity, and binding affinities. Among several techniques aimed at predicting free-energy differences, perturbation approaches, involving the alchemical transformation of one molecule into another through intermediate states, stand out as rigorous methods based on statistical mechanics. However, despite the importance of free-energy calculations, the applicability of the perturbation approaches is still largely impeded by a number of challenges, including the definition of the perturbation path, i.e., alchemical changes leading to the transformation of one molecule to the other. To address this, an automatic perturbation topology builder based on a graph-matching algorithm is developed, which can identify the maximum common substructure (MCS) of two or multiple molecules and provide the perturbation topologies suitable for free-energy calculations using the GROMOS and the GROMACS simulation packages. Various MCS search options are presented leading to alternative definitions of the perturbation pathway. Moreover, perturbation topologies generated using the default multistate MCS search are used to calculate the changes in free energy between lysine and its two post-translational modifications, 3-methyllysine and acetyllysine. The pairwise free-energy calculations performed on this test system led to a cycle closure of 0.5 ± 0.3 and 0.2 ± 0.2 kJ mol-1, with GROMOS and GROMACS simulation packages, respectively. The same relative free energies between the three states are obtained by employing the enveloping distribution sampling (EDS) approach when compared to the pairwise perturbations. Importantly, this toolkit is made available online as an open-source Python package (https://github.com/drazen-petrov/SMArt).
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Affiliation(s)
- Drazen Petrov
- Department of Material Sciences
and Process Engineering, Institute of Molecular Modeling and Simulation, University of Natural Resources and Life Sciences
Vienna, Muthgasse 18, A-1190 Vienna, Austria
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König G, Ries B, Hünenberger PH, Riniker S. Efficient Alchemical Intermediate States in Free Energy Calculations Using λ-Enveloping Distribution Sampling. J Chem Theory Comput 2021; 17:5805-5815. [PMID: 34476947 DOI: 10.1021/acs.jctc.1c00418] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Alchemical free energy calculations generally require intermediate states along a coupling parameter λ to establish sufficient phase space overlap for obtaining converged results. Such intermediate states can also be engineered to lower the energy barriers and, consequently, reduce the required sampling time. The recently introduced λ-enveloping distribution sampling (λ-EDS) scheme combines the properties of the minimum variance pathway and the EDS methods to improve sampling and allow for larger steps along the alchemical pathway compared to conventional approaches. This scheme also eliminates the need for soft-core potentials and retains the behavior of conventional λ-intermediate states as a limiting case. In this study, an automated procedure is developed to select the parameters of λ-EDS for optimal performance. The underlying theory is illustrated based on simulations of simple test systems (bond length changes in harmonic oscillators, mutations of dihedral angles, and charge creation in water), as well as on the calculation of the absolute hydration free energies of 12 small organic molecules.
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Affiliation(s)
- Gerhard König
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland.,Centre for Enzyme Innovation, University of Portsmouth, St. Michael's Building, PO1 2DT Portsmouth, U.K
| | - Benjamin Ries
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Philippe H Hünenberger
- 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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