1
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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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2
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Champion C, Hünenberger PH, Riniker S. Multistate Method to Efficiently Account for Tautomerism and Protonation in Alchemical Free-Energy Calculations. J Chem Theory Comput 2024; 20:4350-4362. [PMID: 38742760 PMCID: PMC11137823 DOI: 10.1021/acs.jctc.4c00370] [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: 03/22/2024] [Revised: 04/25/2024] [Accepted: 04/29/2024] [Indexed: 05/16/2024]
Abstract
The majority of drug-like molecules contain at least one ionizable group, and many common drug scaffolds are subject to tautomeric equilibria. Thus, these compounds are found in a mixture of protonation and/or tautomeric states at physiological pH. Intrinsically, standard classical molecular dynamics (MD) simulations cannot describe such equilibria between states, which negatively impacts the prediction of key molecular properties in silico. Following the formalism described by de Oliveira and co-workers (J. Chem. Theory Comput. 2019, 15, 424-435) to consider the influence of all states on the binding process based on alchemical free-energy calculations, we demonstrate in this work that the multistate method replica-exchange enveloping distribution sampling (RE-EDS) is well suited to describe molecules with multiple protonation and/or tautomeric states in a single simulation. We apply our methodology to a series of eight inhibitors of factor Xa with two protonation states and a series of eight inhibitors of glycogen synthase kinase 3β (GSK3β) with two tautomeric states. In particular, we show that given a sufficient phase-space overlap between the states, RE-EDS is computationally more efficient than standard pairwise free-energy methods.
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Affiliation(s)
- Candide Champion
- Department of Chemistry and Applied
Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Philippe H. Hünenberger
- Department of Chemistry and Applied
Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Sereina Riniker
- Department of Chemistry and Applied
Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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3
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Robo MT, Hayes RL, Ding X, Pulawski B, Vilseck JZ. Fast free energy estimates from λ-dynamics with bias-updated Gibbs sampling. Nat Commun 2023; 14:8515. [PMID: 38129400 PMCID: PMC10740020 DOI: 10.1038/s41467-023-44208-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Accepted: 12/04/2023] [Indexed: 12/23/2023] Open
Abstract
Relative binding free energy calculations have become an integral computational tool for lead optimization in structure-based drug design. Classical alchemical methods, including free energy perturbation or thermodynamic integration, compute relative free energy differences by transforming one molecule into another. However, these methods have high operational costs due to the need to perform many pairwise perturbations independently. To reduce costs and accelerate molecular design workflows, we present a method called λ-dynamics with bias-updated Gibbs sampling. This method uses dynamic biases to continuously sample between multiple ligand analogues collectively within a single simulation. We show that many relative binding free energies can be determined quickly with this approach without compromising accuracy. For five benchmark systems, agreement to experiment is high, with root mean square errors near or below 1.0 kcal mol-1. Free energy results are consistent with other computational approaches and within statistical noise of both methods (0.4 kcal mol-1 or less). Notably, large efficiency gains over thermodynamic integration of 18-66-fold for small perturbations and 100-200-fold for whole aromatic ring substitutions are observed. The rapid determination of relative binding free energies will enable larger chemical spaces to be more readily explored and structure-based drug design to be accelerated.
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Affiliation(s)
- Michael T Robo
- Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, Indianapolis, IN, 46202, USA
- Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indianapolis, IN, 46202, USA
- Indiana Biosciences Research Institute, 1210 Waterway Blvd Ste. 2000, Indianapolis, IN, 46202, USA
| | - Ryan L Hayes
- Chemical and Biomolecular Engineering, University of California, Irvine, California, 92617, USA
- Pharmaceutical Sciences, University of California, Irvine, CA, 92617, USA
| | - Xinqiang Ding
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- Department of Chemistry, Tufts University, Medford, MA, 02144, USA
| | - Brian Pulawski
- Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, Indianapolis, IN, 46202, USA
| | - Jonah Z Vilseck
- Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, Indianapolis, IN, 46202, USA.
- Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indianapolis, IN, 46202, USA.
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4
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Champion C, Gall R, Ries B, Rieder SR, Barros EP, Riniker S. Accelerating Alchemical Free Energy Prediction Using a Multistate Method: Application to Multiple Kinases. J Chem Inf Model 2023; 63:7133-7147. [PMID: 37948537 PMCID: PMC10685456 DOI: 10.1021/acs.jcim.3c01469] [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: 09/13/2023] [Revised: 10/23/2023] [Accepted: 10/23/2023] [Indexed: 11/12/2023]
Abstract
Alchemical free-energy methods based on molecular dynamics (MD) simulations have become important tools to identify modifications of small organic molecules that improve their protein binding affinity during lead optimization. The routine application of pairwise free-energy methods to rank potential binders from best to worst is impacted by the combinatorial increase in calculations to perform when the number of molecules to assess grows. To address this fundamental limitation, our group has developed replica-exchange enveloping distribution sampling (RE-EDS), a pathway-independent multistate method, enabling the calculation of alchemical free-energy differences between multiple ligands (N > 2) from a single MD simulation. In this work, we apply the method to a set of four kinases with diverse binding pockets and their corresponding inhibitors (42 in total), chosen to showcase the general applicability of RE-EDS in prospective drug design campaigns. We show that for the targets studied, RE-EDS is able to model up to 13 ligands simultaneously with high sampling efficiency, leading to a substantial decrease in computational cost when compared to pairwise methods.
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Affiliation(s)
- Candide Champion
- Department of Chemistry and
Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - René Gall
- Department of Chemistry and
Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | | | - Salomé R. Rieder
- Department of Chemistry and
Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Emilia P. Barros
- Department of Chemistry and
Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Sereina Riniker
- Department of Chemistry and
Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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5
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Gracia Carmona O, Gillhofer M, Tomasiak L, De Ruiter A, Oostenbrink C. Accelerated Enveloping Distribution Sampling to Probe the Presence of Water Molecules. J Chem Theory Comput 2023. [PMID: 37167545 DOI: 10.1021/acs.jctc.3c00109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Determining the presence of water molecules at protein-ligand interfaces is still a challenging task in free-energy calculations. The inappropriate placement of water molecules results in the stabilization of wrong conformational orientations of the ligand. With classical alchemical perturbation methods, such as thermodynamic integration (TI), it is essential to know the amount of water molecules in the active site of the respective ligands. However, the resolution of the crystal structure and the correct assignment of the electron density do not always lead to a clear placement of water molecules. In this work, we apply the one-step perturbation method named accelerated enveloping distribution sampling (AEDS) to determine the presence of water molecules in the active site by probing them in a fast and straightforward way. Based on these results, we combined the AEDS method with standard TI to calculate accurate binding free energies in the presence of buried water molecules. The main idea is to perturb the water molecules with AEDS such that they are allowed to alternate between regular water molecules and non-interacting dummy particles while treating the ligand with TI over an alchemical pathway. We demonstrate the use of AEDS to probe the presence of water molecules for six different test systems. For one of these, previous calculations showed difficulties to reproduce the experimental binding free energies, and here, we use the combined TI-AEDS approach to tackle these issues.
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Affiliation(s)
- Oriol Gracia Carmona
- Institute for Molecular Modeling and Simulation, Department of Material Sciences and Process Engineering, University of Natural Resources and Life Sciences, Vienna, Muthgasse 18, 1190 Vienna, Austria
| | - Michael Gillhofer
- Institute for Molecular Modeling and Simulation, Department of Material Sciences and Process Engineering, University of Natural Resources and Life Sciences, Vienna, Muthgasse 18, 1190 Vienna, Austria
| | - Lisa Tomasiak
- Institute for Molecular Modeling and Simulation, Department of Material Sciences and Process Engineering, University of Natural Resources and Life Sciences, Vienna, Muthgasse 18, 1190 Vienna, Austria
| | - Anita De Ruiter
- Institute for Molecular Modeling and Simulation, Department of Material Sciences and Process Engineering, University of Natural Resources and Life Sciences, Vienna, Muthgasse 18, 1190 Vienna, Austria
| | - Chris Oostenbrink
- Institute for Molecular Modeling and Simulation, Department of Material Sciences and Process Engineering, University of Natural Resources and Life Sciences, Vienna, Muthgasse 18, 1190 Vienna, Austria
- Christian Doppler Laboratory for Molecular Informatics in the Biosciences, University of Natural Resources and Life Sciences, Vienna, Muthgasse 18, 1190 Vienna, Austria
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6
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Kasavajhala K, Simmerling C. Exploring the Transferability of Replica Exchange Structure Reservoirs to Accelerate Generation of Ensembles for Alternate Hamiltonians or Protein Mutations. J Chem Theory Comput 2023; 19:1931-1944. [PMID: 36861842 PMCID: PMC10658647 DOI: 10.1021/acs.jctc.3c00005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/03/2023]
Abstract
Generating precise ensembles is commonly a prerequisite to understand the energetics of biological processes using Molecular Dynamics (MD) simulations. Previously, we have shown how unweighted reservoirs built from high temperature MD simulations can accelerate convergence of Boltzmann-weighted ensembles by at least 10× with the Reservoir Replica Exchange MD (RREMD) method. Therefore, in this work, we explore whether an unweighted structure reservoir generated with one Hamiltonian (solute force field plus solvent model) can be reused to quickly generate accurately weighted ensembles for Hamiltonians other than the one that was used to generate the reservoir. We also extended this methodology to rapidly estimate the effects of mutations on peptide stability by using a reservoir of diverse structures obtained from wild-type simulations. These results suggest that structures generated via fast methods such as coarse-grained models or structures predicted by Rosetta or deep learning approaches could be integrated into a reservoir to accelerate generation of ensembles using more accurate representations.
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Affiliation(s)
- Koushik Kasavajhala
- Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, United States
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, United States
| | - Carlos Simmerling
- Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, United States
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, United States
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7
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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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8
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Rieder SR, Ries BJ, Kubincová A, Champion C, Barros EP, Hünenberger PH, Riniker S. Leveraging the Sampling Efficiency of RE-EDS in OpenMM Using a Shifted Reaction-Field With an Atom-Based Cutoff. J Chem Phys 2022; 157:104117. [DOI: 10.1063/5.0107935] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Replica-exchange enveloping distribution sampling (RE-EDS) is a pathway-independent multistate free-energy method, currently implemented in the GROMOS software package for molecular dynamics (MD) simulations. It has a high intrinsic sampling efficiency as the interactions between the unperturbed particles have to be calculated only once for multiple end-states. As a result, RE-EDS is an attractive method for the calculation of relative solvation and binding free energies. An essential requirement for reaching this high efficiency is the separability of the nonbonded interactions into solute-solute, solute-environment, and environment-environment contributions. Such a partitioning is trivial when using a Coulomb term with a reaction-field (RF) correction to model the electrostatic interactions, but not when using lattice- sum schemes. To avoid cutoff artifacts, the RF correction is typically used in combination with a charge-group based cutoff, which is not supported by most small-molecule force fields and other MD engines. To address this issue, we investigate the combination of RE-EDS simulations with a recently introduced RF scheme including a shifting function that enables the rigorous calculation of RF electrostatics with atom-based cutoffs. The resulting approach is validated by calculating solvation free energies with the generalized AMBER force field (GAFF) in water and chloroform using both the GROMOS software package and a proof-of-concept implementation in OpenMM.
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Affiliation(s)
| | | | | | | | | | | | - Sereina Riniker
- Laboratory of Physical Chemistry, ETH Zurich D-CHAB, Switzerland
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9
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Rieder SR, Ries B, Schaller K, Champion C, Barros EP, Hünenberger PH, Riniker S. Replica-Exchange Enveloping Distribution Sampling Using Generalized AMBER Force-Field Topologies: Application to Relative Hydration Free-Energy Calculations for Large Sets of Molecules. J Chem Inf Model 2022; 62:3043-3056. [PMID: 35675713 PMCID: PMC9241072 DOI: 10.1021/acs.jcim.2c00383] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
![]()
Free-energy differences
between pairs of end-states can be estimated
based on molecular dynamics (MD) simulations using standard pathway-dependent
methods such as thermodynamic integration (TI), free-energy perturbation,
or Bennett’s acceptance ratio. Replica-exchange enveloping
distribution sampling (RE-EDS), on the other hand, allows for the
sampling of multiple end-states in a single simulation without the
specification of any pathways. In this work, we use the RE-EDS method
as implemented in GROMOS together with generalized AMBER force-field
(GAFF) topologies, converted to a GROMOS-compatible format with a
newly developed GROMOS++ program amber2gromos, to
compute relative hydration free energies for a series of benzene derivatives.
The results obtained with RE-EDS are compared to the experimental
data as well as calculated values from the literature. In addition,
the estimated free-energy differences in water and in vacuum are compared
to values from TI calculations carried out with GROMACS. The hydration
free energies obtained using RE-EDS for multiple molecules are found
to be in good agreement with both the experimental data and the results
calculated using other free-energy methods. While all considered free-energy
methods delivered accurate results, the RE-EDS calculations required
the least amount of total simulation time. This work serves as a validation
for the use of GAFF topologies with the GROMOS simulation package
and the RE-EDS approach. Furthermore, the performance of RE-EDS for
a large set of 28 end-states is assessed with promising results.
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Affiliation(s)
- Salomé R Rieder
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Benjamin Ries
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Kay Schaller
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Candide Champion
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Emilia P Barros
- 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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10
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Vilseck JZ, Cervantes LF, Hayes RL, Brooks CL. Optimizing Multisite λ-Dynamics Throughput with Charge Renormalization. J Chem Inf Model 2022; 62:1479-1488. [PMID: 35286093 PMCID: PMC9700484 DOI: 10.1021/acs.jcim.2c00047] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
With the ability to sample combinations of alchemical perturbations at multiple sites off a small molecule core, multisite λ-dynamics (MSλD) has become an attractive alternative to conventional alchemical free energy methods for exploring large combinatorial chemical spaces. However, current software implementations dictate that combinatorial sampling with MSλD must be performed with a multiple topology model (MTM), which is nontrivial to create by hand, especially for a series of ligand analogues which may have diverse functional groups attached. This work introduces an automated workflow, referred to as msld_py_prep, to assist in the creation of a MTM for use with MSλD. One approach for partitioning partial atomic charges between ligands to create a MTM, called charge renormalization, is also presented and rigorously evaluated. We find that msld_py_prep greatly accelerates the preparation of MSλD ready-to-use files and that charge renormalization can provide a successful approach for MTM generation, as long as bookending calculations are applied to correct small differences introduced by charge renormalization. Charge renormalization also facilitates the use of many different force field parameters with MSλD, broadening the applicability of MSλD for computer-aided drug design.
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Affiliation(s)
- Jonah Z. Vilseck
- Department of Chemistry, University of Michigan, Ann Arbor, MI 48109
- Department of Biochemistry and Molecular Biology, Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indianapolis, Indiana, 46202, United States
| | - Luis F. Cervantes
- Department of Medicinal Chemistry College of Pharmacy, University of Michigan, Ann Arbor, MI 48109, United States
| | - Ryan L. Hayes
- Department of Chemistry, University of Michigan, Ann Arbor, MI 48109
| | - Charles L. Brooks
- Department of Chemistry, University of Michigan, Ann Arbor, MI 48109
- Biophysics Program, University of Michigan, Ann Arbor, MI 48109
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11
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Ries B, Normak K, Weiß RG, Rieder S, Barros EP, Champion C, König G, Riniker S. Relative free-energy calculations for scaffold hopping-type transformations with an automated RE-EDS sampling procedure. J Comput Aided Mol Des 2022; 36:117-130. [PMID: 34978000 PMCID: PMC8907147 DOI: 10.1007/s10822-021-00436-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Accepted: 11/23/2021] [Indexed: 11/29/2022]
Abstract
The calculation of relative free-energy differences between different compounds plays an important role in drug design to identify potent binders for a given protein target. Most rigorous methods based on molecular dynamics simulations estimate the free-energy difference between pairs of ligands. Thus, the comparison of multiple ligands requires the construction of a “state graph”, in which the compounds are connected by alchemical transformations. The computational cost can be optimized by reducing the state graph to a minimal set of transformations. However, this may require individual adaptation of the sampling strategy if a transformation process does not converge in a given simulation time. In contrast, path-free methods like replica-exchange enveloping distribution sampling (RE-EDS) allow the sampling of multiple states within a single simulation without the pre-definition of alchemical transition paths. To optimize sampling and convergence, a set of RE-EDS parameters needs to be estimated in a pre-processing step. Here, we present an automated procedure for this step that determines all required parameters, improving the robustness and ease of use of the methodology. To illustrate the performance, the relative binding free energies are calculated for a series of checkpoint kinase 1 inhibitors containing challenging transformations in ring size, opening/closing, and extension, which reflect changes observed in scaffold hopping. The simulation of such transformations with RE-EDS can be conducted with conventional force fields and, in particular, without soft bond-stretching terms.
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Affiliation(s)
- Benjamin Ries
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093, Zürich, Switzerland
| | - Karl Normak
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093, Zürich, Switzerland
| | - R Gregor Weiß
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093, Zürich, Switzerland
| | - Salomé Rieder
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093, Zürich, Switzerland
| | - Emília P Barros
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093, Zürich, Switzerland
| | - Candide Champion
- 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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12
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Reinhardt M, Grubmüller H. Small-sample limit of the Bennett acceptance ratio method and the variationally derived intermediates. Phys Rev E 2021; 104:054133. [PMID: 34942806 DOI: 10.1103/physreve.104.054133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2021] [Accepted: 10/28/2021] [Indexed: 11/07/2022]
Abstract
Free energy calculations based on atomistic Hamiltonians provide microscopic insight into the thermodynamic driving forces of biophysical or condensed matter systems. Many approaches use intermediate Hamiltonians interpolating between the two states for which the free energy difference is calculated. The Bennett acceptance ratio (BAR) and variationally derived intermediates (VI) methods are optimal estimator and intermediate states in that the mean-squared error of free energy calculations based on independent sampling is minimized. However, BAR and VI have been derived based on several approximations that do not hold for very few sample points. Analyzing one-dimensional test systems, we show that in such cases BAR and VI are suboptimal and that established uncertainty estimates are inaccurate. Whereas for VI to become optimal, less than seven samples per state suffice in all cases; for BAR the required number increases unboundedly with decreasing configuration space densities overlap of the end states. We show that for BAR, the required number of samples is related to the overlap through an inverse power law. Because this relation seems to hold universally and almost independent of other system properties, these findings can guide the proper choice of estimators for free energy calculations.
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Affiliation(s)
- Martin Reinhardt
- Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
| | - Helmut Grubmüller
- Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
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13
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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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14
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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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15
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Wade AD, Huggins DJ. Identification of Optimal Ligand Growth Vectors Using an Alchemical Free-Energy Method. J Chem Inf Model 2020; 60:5580-5594. [PMID: 32810401 DOI: 10.1021/acs.jcim.0c00610] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In this work, a novel method to rationally design inhibitors with improved steric contacts and enhanced binding free energies is presented. This new method uses alchemical single step perturbation calculations to rapidly optimize the van der Waals interactions of a small molecule in a protein-ligand complex in order to maximize its binding affinity. The results of the optimizer are used to predict beneficial growth vectors on the ligand, and good agreement is found between the predictions from the optimizer and a more rigorous free energy calculation, with a Spearman's rank order correlation of 0.59. The advantage of the method presented here is the significant speed up of over 10-fold compared to traditional free energy calculations and sublinear scaling with the number of growth vectors assessed. Where experimental data were available, mutations from hydrogen to a methyl group at sites highlighted by the optimizer were calculated with MBAR, and the mean unsigned error between experimental and calculated values of the binding free energy was 0.83 kcal/mol.
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Affiliation(s)
- Alexander D Wade
- TCM Group, Cavendish Laboratory, University of Cambridge, 19 J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - David J Huggins
- Tri-Institutional Therapeutics Discovery Institute, Belfer Research Building, 413 East 69th Street, 16th Floor, Box 300, New York, United States.,Department of Physiology and Biophysics, Weill Cornell Medical College of Cornell University, New York, New York 10065, United States
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16
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Reinhardt M, Grubmüller H. Variationally derived intermediates for correlated free-energy estimates between intermediate states. Phys Rev E 2020; 102:043312. [PMID: 33212581 DOI: 10.1103/physreve.102.043312] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Accepted: 09/28/2020] [Indexed: 01/18/2023]
Abstract
Free-energy difference calculations based on atomistic simulations generally improve in accuracy when sampling from a sequence of intermediate equilibrium thermodynamic states that bridge the configuration space between two states of interest. For reasons of efficiency, usually the same samples are used to calculate the stepwise difference of such an intermediate to both adjacent intermediates. However, this procedure violates the assumption of uncorrelated estimates that is necessary to derive both the optimal sequence of intermediate states and the widely used Bennett acceptance ratio estimator. In this work, via a variational approach, we derive the sequence of intermediate states and the corresponding estimator with minimal mean-squared error that account for these correlations and assess its accuracy.
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Affiliation(s)
- Martin Reinhardt
- Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
| | - Helmut Grubmüller
- Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
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17
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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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18
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Perthold JW, Petrov D, Oostenbrink C. Toward Automated Free Energy Calculation with Accelerated Enveloping Distribution Sampling (A-EDS). J Chem Inf Model 2020; 60:5395-5406. [PMID: 32492343 PMCID: PMC7686955 DOI: 10.1021/acs.jcim.0c00456] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
![]()
Free-energy
perturbation (FEP) methods are commonly used in drug
design to calculate relative binding free energies of different ligands
to a common host protein. Alchemical ligand transformations are usually
performed in multiple steps which need to be chosen carefully to ensure
sufficient phase-space overlap between neighboring states. With one-step
or single-step FEP techniques, a single reference state is designed
that samples phase-space not only representative of a full transformation
but also ideally resembles multiple ligand end states and hence allows
for efficient multistate perturbations. Enveloping distribution sampling
(EDS) is one example for such a method in which the reference state
is created by a mathematical combination of the different ligand end
states based on solid statistical mechanics. We have recently proposed
a novel approach to EDS which enables efficient barrier crossing between
the different end states, termed accelerated EDS (A-EDS). In this
work, we further simplify the parametrization of the A-EDS reference
state and demonstrate the automated calculation of multiple free-energy
differences between different ligands from a single simulation in
three different well-described drug design model systems.
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Affiliation(s)
- Jan Walther Perthold
- Institute for Molecular Modeling and Simulation, Department for Material Sciences and Process Engineering, University of Natural Resources and Life Sciences (BOKU), Vienna, Muthgasse 18, 1190 Vienna, Austria
| | - Dražen Petrov
- Institute for Molecular Modeling and Simulation, Department for Material Sciences and Process Engineering, University of Natural Resources and Life Sciences (BOKU), Vienna, Muthgasse 18, 1190 Vienna, Austria
| | - Chris Oostenbrink
- Institute for Molecular Modeling and Simulation, Department for Material Sciences and Process Engineering, University of Natural Resources and Life Sciences (BOKU), Vienna, Muthgasse 18, 1190 Vienna, Austria
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19
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de Ruiter A, Oostenbrink C. Advances in the calculation of binding free energies. Curr Opin Struct Biol 2020; 61:207-212. [PMID: 32088376 DOI: 10.1016/j.sbi.2020.01.016] [Citation(s) in RCA: 39] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Revised: 01/21/2020] [Accepted: 01/24/2020] [Indexed: 01/19/2023]
Abstract
In recent years, calculations of binding affinities from molecular simulations seem to have matured significantly. While the number of applications of such methods in drug design and biotechnology increases, the number of truly new methodological developments decreases. This review provides an overview of the current status of the field as reflected in recent publications. The focus is on the challenges that remain when using endstate, alchemical and pathway methods. For endstate methods this is the calculation of entropic contributions. For alchemical methods there are unsolved problems associated with the solvation of the active site, sampling slow degrees of freedom and when modifying the net charge. For pathway methods achieving sufficient sampling remains challenging. New trends are also highlighted, including the use of pathway methods for the quantification of protein-protein interactions.
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Affiliation(s)
- Anita de Ruiter
- Institute for Molecular Modeling and Simulation, University of Natural Resources and Life Sciences (BOKU), Vienna, Austria
| | - Chris Oostenbrink
- Institute for Molecular Modeling and Simulation, University of Natural Resources and Life Sciences (BOKU), Vienna, Austria.
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20
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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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21
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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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22
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Yang YI, Shao Q, Zhang J, Yang L, Gao YQ. Enhanced sampling in molecular dynamics. J Chem Phys 2019; 151:070902. [PMID: 31438687 DOI: 10.1063/1.5109531] [Citation(s) in RCA: 172] [Impact Index Per Article: 34.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Abstract
Although molecular dynamics simulations have become a useful tool in essentially all fields of chemistry, condensed matter physics, materials science, and biology, there is still a large gap between the time scale which can be reached in molecular dynamics simulations and that observed in experiments. To address the problem, many enhanced sampling methods were introduced, which effectively extend the time scale being approached in simulations. In this perspective, we review a variety of enhanced sampling methods. We first discuss collective-variables-based methods including metadynamics and variationally enhanced sampling. Then, collective variable free methods such as parallel tempering and integrated tempering methods are presented. At last, we conclude with a brief introduction of some newly developed combinatory methods. We summarize in this perspective not only the theoretical background and numerical implementation of these methods but also the new challenges and prospects in the field of the enhanced sampling.
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Affiliation(s)
- Yi Isaac Yang
- Institute of Systems Biology, Shenzhen Bay Laboratory, Shenzhen 518055, Guangdong, China
| | - Qiang Shao
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, 555 Zuchongzhi Road, Shanghai 201203, China
| | - Jun Zhang
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, Berlin 14195, Germany
| | - Lijiang Yang
- Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Yi Qin Gao
- Institute of Systems Biology, Shenzhen Bay Laboratory, Shenzhen 518055, Guangdong, China
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23
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Maurer M, Hansen N, Oostenbrink C. Comparison of free-energy methods using a tripeptide-water model system. J Comput Chem 2018; 39:2226-2242. [PMID: 30280398 PMCID: PMC6220940 DOI: 10.1002/jcc.25537] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2018] [Revised: 06/29/2018] [Accepted: 06/30/2018] [Indexed: 11/24/2022]
Abstract
We investigate the ability of several free-energy calculation methods to combine two alchemical changes. We use Bennett acceptance ratio (BAR), thermodynamic integration (TI), extended TI (X-TI), and enveloping distribution sampling (EDS) to perturb a water molecule, which is restrained to an amino acid that is also being perturbed. In addition to these pairwise methods, we present two two-dimensional approaches, EDS-TI and two-dimensional TI (2D-TI). We compare feasibility, efficiency and usability of these methods in regard to our simple model system, which mimics the displacement of a water molecule in the active site of a protein on residue mutation. The correct treatment of structural water has been shown to greatly aid binding affinity calculations in some cases that remained elusive otherwise. This is of broad interest in, for example, drug design, and we conclude that thus far, the pairwise method BAR and also the newer X-TI remain the most suitable methods to treat this problem as long as few end states are involved. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Manuela Maurer
- Department of Material Sciences and Process EngineeringInstitute of Molecular Modeling and Simulation, University of Natural Resources and Life SciencesMuthgasse 18, A‐1190, ViennaAustria
| | - Niels Hansen
- Department of Energy‐, Process‐ and Bio‐Engineering, University of StuttgartInstitute of Thermodynamics and Thermal Process EngineeringPfaffenwaldring 9, 70569, StuttgartGermany
| | - Chris Oostenbrink
- Department of Material Sciences and Process EngineeringInstitute of Molecular Modeling and Simulation, University of Natural Resources and Life SciencesMuthgasse 18, A‐1190, ViennaAustria
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