1
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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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Lundborg M, Lidmar J, Hess B. On the Path to Optimal Alchemistry. Protein J 2023; 42:477-489. [PMID: 37651042 PMCID: PMC10480267 DOI: 10.1007/s10930-023-10137-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/04/2023] [Indexed: 09/01/2023]
Abstract
Alchemical free energy calculations have become a standard and widely used tool, in particular for calculating and comparing binding affinities of drugs. Although methods to compute such free energies have improved significantly over the last decades, the choice of path between the end states of interest is usually still the same as two decades ago. We will show that there is a fundamentally arbitrary, implicit choice of parametrization of this path. To address this, the notion of the length of a path or a metric is required. A metric recently introduced in the context of the accelerated weight histogram method also proves to be very useful here. We demonstrate that this metric can not only improve the efficiency of sampling along a given path, but that it can also be used to improve the actual choice of path. For a set of relevant use cases, the combination of these improvements can increase the efficiency of alchemical free energy calculations by up to a factor 16.
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Affiliation(s)
| | - Jack Lidmar
- Department of Physics, KTH Royal Institute of Technology, 10691, Stockholm, Sweden
| | - Berk Hess
- Department of Applied Physics, KTH Royal Institute of Technology, 10691, Stockholm, Science for Life Laboratory, Solna, Sweden.
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3
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Li XS, Van Koten B, Dinner AR, Thiede EH. Understanding the sources of error in MBAR through asymptotic analysis. J Chem Phys 2023; 158:214107. [PMID: 37259996 PMCID: PMC10845960 DOI: 10.1063/5.0147243] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 05/08/2023] [Indexed: 06/02/2023] Open
Abstract
Many sampling strategies commonly used in molecular dynamics, such as umbrella sampling and alchemical free energy methods, involve sampling from multiple states. The Multistate Bennett Acceptance Ratio (MBAR) formalism is a widely used way of recombining the resulting data. However, the error of the MBAR estimator is not well-understood: previous error analyses of MBAR assumed independent samples. In this work, we derive a central limit theorem for MBAR estimates in the presence of correlated data, further justifying the use of MBAR in practical applications. Moreover, our central limit theorem yields an estimate of the error that can be decomposed into contributions from the individual Markov chains used to sample the states. This gives additional insight into how sampling in each state affects the overall error. We demonstrate our error estimator on an umbrella sampling calculation of the free energy of isomerization of the alanine dipeptide and an alchemical calculation of the hydration free energy of methane. Our numerical results demonstrate that the time required for the Markov chain to decorrelate in individual states can contribute considerably to the total MBAR error, highlighting the importance of accurately addressing the effect of sample correlation.
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Affiliation(s)
- Xiang Sherry Li
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Brian Van Koten
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Aaron R. Dinner
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Erik H. Thiede
- Center for Computational Mathematics, Flatiron Institute, New York, New York 10010, USA
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4
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Decherchi S, Cavalli A. Optimal Transport for Free Energy Estimation. J Phys Chem Lett 2023; 14:1618-1625. [PMID: 36749941 PMCID: PMC9940200 DOI: 10.1021/acs.jpclett.2c03523] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
Optimal transport theory is a growing field of mathematics, which has recently found many applications. Here we take advantage of optimal transport for computational free energy estimation. We show analytically, and then via simulation, that this approach is effective in terms of optimizing the barriers of an alchemical transformation.
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5
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Lee TS, Tsai HC, Ganguly A, York DM. ACES: Optimized Alchemically Enhanced Sampling. J Chem Theory Comput 2023; 19:10.1021/acs.jctc.2c00697. [PMID: 36630672 PMCID: PMC10333454 DOI: 10.1021/acs.jctc.2c00697] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
We present an alchemical enhanced sampling (ACES) method implemented in the GPU-accelerated AMBER free energy MD engine. The methods hinges on the creation of an "enhanced sampling state" by reducing or eliminating selected potential energy terms and interactions that lead to kinetic traps and conformational barriers while maintaining those terms that curtail the need to otherwise sample large volumes of phase space. For example, the enhanced sampling state might involve transforming regions of a ligand and/or protein side chain into a noninteracting "dummy state" with internal electrostatics and torsion angle terms turned off. The enhanced sampling state is connected to a real-state end point through a Hamiltonian replica exchange (HREMD) framework that is facilitated by newly developed alchemical transformation pathways and smoothstep softcore potentials. This creates a counterdiffusion of real and enhanced-sampling states along the HREMD network. The effect of a differential response of the environment to the real and enhanced-sampling states is minimized by leveraging the dual topology framework in AMBER to construct a counterbalancing HREMD network in the opposite alchemical direction with the same (or similar) real and enhanced sampling states at inverted end points. The method has been demonstrated in a series of test cases of increasing complexity where traditional MD, and in several cases alternative REST2-like enhanced sampling methods, are shown to fail. The hydration free energy for acetic acid was shown to be independent of the starting conformation, and the values for four additional edge case molecules from the FreeSolv database were shown to have a significantly closer agreement with experiment using ACES. The method was further able to handle different rotamer states in a Cdk2 ligand identified as fractionally occupied in crystal structures. Finally, ACES was applied to T4-lysozyme and demonstrated that the side chain distribution of V111χ1 could be reliably reproduced for the apo state, bound to p-xylene, and in p-xylene→ benzene transformations. In these cases, the ACES method is shown to be highly robust and superior to a REST2-like enhanced sampling implementation alone.
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Affiliation(s)
- 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
| | - 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
| | - Abir Ganguly
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, 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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6
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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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7
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Pérez-Ramírez HA, Moncho-Jordá A, Odriozola G. Phenol release from pNIPAM hydrogels: scaling molecular dynamics simulations with dynamical density functional theory. SOFT MATTER 2022; 18:8271-8284. [PMID: 36278506 DOI: 10.1039/d2sm01083f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
We employed molecular dynamic simulations (MD) and the Bennett's acceptance ratio method to compute the free energy of transfer, ΔGtrans, of phenol, methane, and 5-fluorouracil (5-FU), between bulk water and water-pNIPAM mixtures of different polymer volume fractions, ϕp. For this purpose, we first calculate the solvation free energies in both media to obtain ΔGtrans. Phenol and 5-FU (a medication used to treat cancer) attach to the pNIPAM surface so that they show negative values of ΔGtrans irrespective of temperature (above or below the lower critical solution temperature of pNIPAM, Tc). Conversely, methane switches the ΔGtrans sign when considering temperatures below (positive) and above (negative) Tc. In all cases, and contrasting with some theoretical predictions, ΔGtrans maintains a linear behavior with the pNIPAM concentration up to large polymer densities. We have also employed MD to compute the diffusion coefficient, D, of phenol in water-pNIPAM mixtures as a function of ϕp in the diluted limit. Both ΔGtrans and D as a function of ϕp are required inputs to obtain the release halftime of hollow pNIPAM microgels through Dynamic Density Functional Theory (DDFT). Our scaling strategy captures the experimental value of 2200 s for 50 μm radius microgels with no cavity, for ϕp ≃ 0.83 at 315 K.
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Affiliation(s)
- H A Pérez-Ramírez
- Área de Física de Procesos Irreversibles, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Azcapotzalco, Avenida San Pablo 180, 02200 Ciudad de México, Mexico.
| | - A Moncho-Jordá
- Departamento de Física Aplicada, Universidad de Granada, Campus Fuentenueva S/N, 18071 Granada, Spain
| | - G Odriozola
- Área de Física de Procesos Irreversibles, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Azcapotzalco, Avenida San Pablo 180, 02200 Ciudad de México, Mexico.
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8
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Correa GB, Maciel JCSL, Tavares FW, Abreu CRA. A New Formulation for the Concerted Alchemical Calculation of van der Waals and Coulomb Components of Solvation Free Energies. J Chem Theory Comput 2022; 18:5876-5889. [PMID: 36189930 DOI: 10.1021/acs.jctc.2c00563] [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
Alchemical free energy calculations via molecular dynamics have been widely used to obtain thermodynamic properties related to protein-ligand binding and solute-solvent interactions. Although soft-core modeling is the most common approach, the linear basis function (LBF) methodology [Naden, L. N.; et al. J. Chem. Theory Comput.2014, 10 (3), 1128; 2015, 11 (6), 2536] has emerged as a suitable alternative. It overcomes the end-point singularity of the scaling method while maintaining essential advantages such as ease of implementation and high flexibility for postprocessing analysis. In the present work, we propose a simple LBF variant and formulate an efficient protocol for evaluating van der Waals and Coulomb components of an alchemical transformation in tandem, in contrast to the prevalent sequential evaluation mode. To validate our proposal, which results from a careful optimization study, we performed solvation free energy calculations and obtained octanol-water partition coefficients of small organic molecules. Comparisons with results obtained via the sequential mode using either another LBF approach or the soft-core model attest to the effectiveness and correctness of our method. In addition, we show that a reaction field model with an infinite dielectric constant can provide very accurate hydration free energies when used instead of a lattice-sum method to model solute-solvent electrostatics.
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Affiliation(s)
- Gabriela B Correa
- Chemical Engineering Program, Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa em Engenharia, Universidade Federal do Rio de Janeiro, 21941-909Rio de Janeiro, RJ, Brazil
| | - Jéssica C S L Maciel
- Chemical Engineering Department, Escola de Química, Universidade Federal do Rio de Janeiro, 21941-909Rio de Janeiro, RJ, Brazil
| | - Frederico W Tavares
- Chemical Engineering Program, Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa em Engenharia, Universidade Federal do Rio de Janeiro, 21941-909Rio de Janeiro, RJ, Brazil.,Chemical Engineering Department, Escola de Química, Universidade Federal do Rio de Janeiro, 21941-909Rio de Janeiro, RJ, Brazil
| | - Charlles R A Abreu
- Chemical Engineering Department, Escola de Química, Universidade Federal do Rio de Janeiro, 21941-909Rio de Janeiro, RJ, Brazil
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9
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Blaber S, Sivak DA. Optimal control with a strong harmonic trap. Phys Rev E 2022; 106:L022103. [PMID: 36110009 DOI: 10.1103/physreve.106.l022103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2022] [Accepted: 07/21/2022] [Indexed: 06/15/2023]
Abstract
Quadratic trapping potentials are widely used to experimentally probe biopolymers and molecular machines and drive transitions in steered molecular-dynamics simulations. Approximating energy landscapes as locally quadratic, we design multidimensional trapping protocols that minimize dissipation. The designed protocols are easily solvable and applicable to a wide range of systems. The approximation does not rely on either fast or slow limits and is valid for any duration provided the trapping potential is sufficiently strong. We demonstrate the utility of the designed protocols with a simple model of a periodically driven rotary motor. Our results elucidate principles of effective single-molecule manipulation and efficient nonequilibrium free-energy estimation.
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Affiliation(s)
- Steven Blaber
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
| | - David A Sivak
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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10
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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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11
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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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12
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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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13
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Gill SC, Mobley DL. Reversibly Sampling Conformations and Binding Modes Using Molecular Darting. J Chem Theory Comput 2021; 17:302-314. [PMID: 33289558 PMCID: PMC8121195 DOI: 10.1021/acs.jctc.0c00752] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Sampling multiple binding modes of a ligand in a single molecular dynamics simulation is difficult. A given ligand may have many internal degrees of freedom, along with many different ways it might orient itself in a binding site or across several binding sites, all of which might be separated by large energy barriers. We have developed a novel Monte Carlo move called molecular darting (MolDarting) to reversibly sample between predefined binding modes of a ligand. Here, we couple this with nonequilibrium candidate Monte Carlo (NCMC) to improve acceptance of moves. We apply this technique to a simple dipeptide system, a ligand binding to T4 lysozyme L99A, and ligand binding to HIV integrase to test this new method. We observe significant increases in acceptance compared to uniformly sampling the internal and rotational/translational degrees of freedom in these systems.
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Affiliation(s)
- Samuel C Gill
- Department of Chemistry, University of California, Irvine, California 92617, United States
| | - David L Mobley
- Department of Chemistry, University of California, Irvine, California 92617, United States
- Department of Pharmaceutical Sciences, University of California, Irvine, California 92617, United States
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14
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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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15
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Blaber S, Sivak DA. Skewed thermodynamic geometry and optimal free energy estimation. J Chem Phys 2020; 153:244119. [PMID: 33380076 DOI: 10.1063/5.0033405] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Abstract
Free energy differences are a central quantity of interest in physics, chemistry, and biology. We develop design principles that improve the precision and accuracy of free energy estimators, which have potential applications to screening for targeted drug discovery. Specifically, by exploiting the connection between the work statistics of time-reversed protocol pairs, we develop near-equilibrium approximations for moments of the excess work and analyze the dominant contributions to the precision and accuracy of standard nonequilibrium free-energy estimators. Within linear response, minimum-dissipation protocols follow the geodesics of the Riemannian metric induced by the Stokes friction tensor. We find that the next-order contribution arises from the rank-3 supra-Stokes tensor that skews the geometric structure such that minimum-dissipation protocols follow the geodesics of a generalized cubic Finsler metric. Thus, near equilibrium, the supra-Stokes tensor determines the leading-order contribution to the bias of bidirectional free-energy estimators.
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Affiliation(s)
- Steven Blaber
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - David A Sivak
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
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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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Abreu CRA, Tuckerman ME. Molecular Dynamics with Very Large Time Steps for the Calculation of Solvation Free Energies. J Chem Theory Comput 2020; 16:7314-7327. [PMID: 33197180 DOI: 10.1021/acs.jctc.0c00698] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In multiple time scale molecular dynamics, the use of isokinetic constraints along with massive thermostatting has enabled the adoption of very large integration steps, well beyond the limits imposed by resonance artifacts in standard algorithms. In this work, we present two new contributions to this topic. First, we investigate the velocity distribution and the temperature-kinetic energy relationship associated with the isokinetic Nosé-Hoover family of methods, showing how they depend on the number of thermostats attached to each atomic degree of freedom. Second, we investigate the performance of these methods in the calculation of solvation free energies, the determination of which is often key for understanding the partition of a chemical species among distinct environments. We show how one can extract this property from canonical (constant-NVT) simulations and compare the result to experimental data obtained at a specific pressure. Finally, we demonstrate that large time steps can, in fact, be used to improve the efficiency of these calculations and that attaching multiple thermostats per degree of freedom is beneficial for effectively exploring the configurational space of a molecular system.
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Affiliation(s)
- Charlles R A Abreu
- Chemical Engineering Department, Escola de Química, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-909, Brazil
| | - Mark E Tuckerman
- Department of Chemistry, New York University, New York, New York 10003, United States.,Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States.,NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
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18
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Lee TS, Lin Z, Allen BK, Lin C, Radak BK, Tao Y, Tsai HC, Sherman W, York DM. Improved Alchemical Free Energy Calculations with Optimized Smoothstep Softcore Potentials. J Chem Theory Comput 2020; 16:5512-5525. [PMID: 32672455 PMCID: PMC7494069 DOI: 10.1021/acs.jctc.0c00237] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
Progress in the development of GPU-accelerated free energy simulation software has enabled practical applications on complex biological systems and fueled efforts to develop more accurate and robust predictive methods. In particular, this work re-examines concerted (a.k.a., one-step or unified) alchemical transformations commonly used in the prediction of hydration and relative binding free energies (RBFEs). We first classify several known challenges in these calculations into three categories: endpoint catastrophes, particle collapse, and large gradient-jumps. While endpoint catastrophes have long been addressed using softcore potentials, the remaining two problems occur much more sporadically and can result in either numerical instability (i.e., complete failure of a simulation) or inconsistent estimation (i.e., stochastic convergence to an incorrect result). The particle collapse problem stems from an imbalance in short-range electrostatic and repulsive interactions and can, in principle, be solved by appropriately balancing the respective softcore parameters. However, the large gradient-jump problem itself arises from the sensitivity of the free energy to large values of the softcore parameters, as might be used in trying to solve the particle collapse issue. Often, no satisfactory compromise exists with the existing softcore potential form. As a framework for solving these problems, we developed a new family of smoothstep softcore (SSC) potentials motivated by an analysis of the derivatives along the alchemical path. The smoothstep polynomials generalize the monomial functions that are used in most implementations and provide an additional path-dependent smoothing parameter. The effectiveness of this approach is demonstrated on simple yet pathological cases that illustrate the three problems outlined. With appropriate parameter selection, we find that a second-order SSC(2) potential does at least as well as the conventional approach and provides vast improvement in terms of consistency across all cases. Last, we compare the concerted SSC(2) approach against the gold-standard stepwise (a.k.a., decoupled or multistep) scheme over a large set of RBFE calculations as might be encountered in drug discovery.
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Affiliation(s)
- Tai-Sung Lee
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Zhixiong Lin
- Silicon Therapeutics LLC, Boston, Massachusetts 02111, United States
| | - Bryce K Allen
- Silicon Therapeutics LLC, Boston, Massachusetts 02111, United States
| | - Charles Lin
- Silicon Therapeutics LLC, Boston, Massachusetts 02111, United States
| | - Brian K Radak
- Silicon Therapeutics LLC, Boston, Massachusetts 02111, United States
| | - Yujun Tao
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Hsu-Chun Tsai
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Woody Sherman
- Silicon Therapeutics LLC, Boston, Massachusetts 02111, United States
| | - 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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19
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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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20
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Reinhardt M, Grubmüller H. Determining Free-Energy Differences Through Variationally Derived Intermediates. J Chem Theory Comput 2020; 16:3504-3512. [PMID: 32392408 PMCID: PMC7303968 DOI: 10.1021/acs.jctc.0c00106] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Free-energy calculations based on atomistic Hamiltonians and sampling are key to a first-principles understanding of biomolecular processes, material properties, and macromolecular chemistry. Here, we generalize the free-energy perturbation method and derive nonlinear Hamiltonian transformation sequences yielding free-energy estimates with minimal mean squared error with respect to the exact values. Our variational approach applies to finite sampling and holds for any finite number of intermediate states. We show that our sequences are also optimal for the Bennett acceptance ratio (BAR) method, thereby generalizing BAR to small sampling sizes and non-Gaussian error distributions.
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Affiliation(s)
- Martin Reinhardt
- Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, Göttingen 37077, Germany
| | - Helmut Grubmüller
- Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, Göttingen 37077, Germany
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21
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Rizzi A, Jensen T, Slochower DR, Aldeghi M, Gapsys V, Ntekoumes D, Bosisio S, Papadourakis M, Henriksen NM, de Groot BL, Cournia Z, Dickson A, Michel J, Gilson MK, Shirts MR, Mobley DL, Chodera JD. The SAMPL6 SAMPLing challenge: assessing the reliability and efficiency of binding free energy calculations. J Comput Aided Mol Des 2020; 34:601-633. [PMID: 31984465 DOI: 10.1007/s10822-020-00290-5] [Citation(s) in RCA: 73] [Impact Index Per Article: 18.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2019] [Accepted: 01/13/2020] [Indexed: 12/22/2022]
Abstract
Approaches for computing small molecule binding free energies based on molecular simulations are now regularly being employed by academic and industry practitioners to study receptor-ligand systems and prioritize the synthesis of small molecules for ligand design. Given the variety of methods and implementations available, it is natural to ask how the convergence rates and final predictions of these methods compare. In this study, we describe the concept and results for the SAMPL6 SAMPLing challenge, the first challenge from the SAMPL series focusing on the assessment of convergence properties and reproducibility of binding free energy methodologies. We provided parameter files, partial charges, and multiple initial geometries for two octa-acid (OA) and one cucurbit[8]uril (CB8) host-guest systems. Participants submitted binding free energy predictions as a function of the number of force and energy evaluations for seven different alchemical and physical-pathway (i.e., potential of mean force and weighted ensemble of trajectories) methodologies implemented with the GROMACS, AMBER, NAMD, or OpenMM simulation engines. To rank the methods, we developed an efficiency statistic based on bias and variance of the free energy estimates. For the two small OA binders, the free energy estimates computed with alchemical and potential of mean force approaches show relatively similar variance and bias as a function of the number of energy/force evaluations, with the attach-pull-release (APR), GROMACS expanded ensemble, and NAMD double decoupling submissions obtaining the greatest efficiency. The differences between the methods increase when analyzing the CB8-quinine system, where both the guest size and correlation times for system dynamics are greater. For this system, nonequilibrium switching (GROMACS/NS-DS/SB) obtained the overall highest efficiency. Surprisingly, the results suggest that specifying force field parameters and partial charges is insufficient to generally ensure reproducibility, and we observe differences between seemingly converged predictions ranging approximately from 0.3 to 1.0 kcal/mol, even with almost identical simulations parameters and system setup (e.g., Lennard-Jones cutoff, ionic composition). Further work will be required to completely identify the exact source of these discrepancies. Among the conclusions emerging from the data, we found that Hamiltonian replica exchange-while displaying very small variance-can be affected by a slowly-decaying bias that depends on the initial population of the replicas, that bidirectional estimators are significantly more efficient than unidirectional estimators for nonequilibrium free energy calculations for systems considered, and that the Berendsen barostat introduces non-negligible artifacts in expanded ensemble simulations.
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Affiliation(s)
- Andrea Rizzi
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, NY, 10065, USA.
- Tri-Institutional Training Program in Computational Biology and Medicine, New York, NY, 10065, USA.
| | - Travis Jensen
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, CO, 80309, USA
| | - David R Slochower
- Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California, San Diego, La Jolla, CA, 92093, USA
| | - Matteo Aldeghi
- Max Planck Institute for Biophysical Chemistry, Computational Biomolecular Dynamics Group, Göttingen, Germany
| | - Vytautas Gapsys
- Max Planck Institute for Biophysical Chemistry, Computational Biomolecular Dynamics Group, Göttingen, Germany
| | - Dimitris Ntekoumes
- Biomedical Research Foundation, Academy of Athens, 4 Soranou Ephessiou, 11527, Athens, Greece
| | - Stefano Bosisio
- EaStCHEM School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh, EH9 3FJ, UK
| | - Michail Papadourakis
- EaStCHEM School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh, EH9 3FJ, UK
| | - Niel M Henriksen
- Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California, San Diego, La Jolla, CA, 92093, USA
- Atomwise, 717 Market St Suite 800, San Francisco, CA, 94103, USA
| | - Bert L de Groot
- Max Planck Institute for Biophysical Chemistry, Computational Biomolecular Dynamics Group, Göttingen, Germany
| | - Zoe Cournia
- Biomedical Research Foundation, Academy of Athens, 4 Soranou Ephessiou, 11527, Athens, Greece
| | - Alex Dickson
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI, USA
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, USA
| | - Julien Michel
- EaStCHEM School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh, EH9 3FJ, UK
| | - Michael K Gilson
- Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California, San Diego, La Jolla, CA, 92093, USA
| | - Michael R Shirts
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, CO, 80309, USA
| | - David L Mobley
- Department of Pharmaceutical Sciences and Department of Chemistry, University of California, Irvine, California, 92697, USA.
| | - John D Chodera
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, NY, 10065, USA.
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22
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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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23
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McDaniel JG, Verma A. On the Miscibility and Immiscibility of Ionic Liquids and Water. J Phys Chem B 2019; 123:5343-5356. [DOI: 10.1021/acs.jpcb.9b02187] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Jesse G. McDaniel
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States
| | - Archana Verma
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States
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24
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Hahn DF, Hünenberger PH. Alchemical Free-Energy Calculations by Multiple-Replica λ-Dynamics: The Conveyor Belt Thermodynamic Integration Scheme. J Chem Theory Comput 2019; 15:2392-2419. [PMID: 30821973 DOI: 10.1021/acs.jctc.8b00782] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
A new method is proposed to calculate alchemical free-energy differences based on molecular dynamics (MD) simulations, called the conveyor belt thermodynamic integration (CBTI) scheme. As in thermodynamic integration (TI), K replicas of the system are simulated at different values of the alchemical coupling parameter λ. The number K is taken to be even, and the replicas are equally spaced on a forward-turn-backward-turn path, akin to a conveyor belt (CB) between the two physical end-states; and as in λ-dynamics (λD), the λ-values associated with the individual systems evolve in time along the simulation. However, they do so in a concerted fashion, determined by the evolution of a single dynamical variable Λ of period 2π controlling the advance of the entire CB. Thus, a change of Λ is always associated with K/2 equispaced replicas moving forward and K/2 equispaced replicas moving backward along λ. As a result, the effective free-energy profile of the replica system along Λ is periodic of period 2 πK-1, and the magnitude of its variations decreases rapidly upon increasing K, at least as K-1 in the limit of large K. When a sufficient number of replicas is used, these variations become small, which enables a complete and quasi-homogeneous coverage of the λ-range by the replica system, without application of any biasing potential. If desired, a memory-based biasing potential can still be added to further homogenize the sampling, the preoptimization of which is computationally inexpensive. The final free-energy profile along λ is calculated similarly to TI, by binning of the Hamiltonian λ-derivative as a function of λ considering all replicas simultaneously, followed by quadrature integration. The associated quadrature error can be kept very low owing to the continuous and quasi-homogeneous λ-sampling. The CBTI scheme can be viewed as a continuous/deterministic/dynamical analog of the Hamiltonian replica-exchange/permutation (HRE/HRP) schemes or as a correlated multiple-replica analog of the λD or λ-local elevation umbrella sampling (λ-LEUS) schemes. Compared to TI, it shares the advantage of the latter schemes in terms of enhanced orthogonal sampling, i.e. the availability of variable-λ paths to circumvent conformational barriers present at specific λ-values. Compared to HRE/HRP, it permits a deterministic and continuous sampling of the λ-range, is expected to be less sensitive to possible artifacts of the thermo- and barostating schemes, and bypasses the need to carefully preselect a λ-ladder and a swapping-attempt frequency. Compared to λ-LEUS, it eliminates (or drastically reduces) the dead time associated with the preoptimization of a biasing potential. The goal of this article is to provide the mathematical/physical formulation of the proposed CBTI scheme, along with an initial application of the method to the calculation of the hydration free energy of methanol.
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Affiliation(s)
- David F Hahn
- 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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25
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Prasetyo N, Hünenberger PH, Hofer TS. Single-Ion Thermodynamics from First Principles: Calculation of the Absolute Hydration Free Energy and Single-Electrode Potential of Aqueous Li + Using ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations. J Chem Theory Comput 2018; 14:6443-6459. [PMID: 30284829 DOI: 10.1021/acs.jctc.8b00729] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
A recently proposed thermodynamic integration (TI) approach formulated in the framework of quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulations is applied to study the structure, dynamics, and absolute intrinsic hydration free energy Δs GM+,wat◦ of the Li+ ion at a correlated ab initio level of theory. Based on the results, standard values (298.15 K, ideal gas at 1 bar, ideal solute at 1 molal) for the absolute intrinsic hydration free energy [Formula: see text] of the proton, the surface electric potential jump χwat◦ upon entering bulk water, and the absolute single-electrode potential [Formula: see text] of the reference hydrogen electrode are calculated to be -1099.9 ± 4.2 kJ·mol-1, 0.13 ± 0.08 V, and 4.28 ± 0.04 V, respectively, in excellent agreement with the standard values recommended by Hünenberger and Reif on the basis of an extensive evaluation of the available experimental data (-1100 ± 5 kJ·mol-1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V). The simulation results for Li+ are also compared to those for Na+ and K+ from a previous study in terms of relative hydration free energies ΔΔs GM+,wat◦ and relative electrode potentials [Formula: see text]. The calculated values are found to agree extremely well with the experimental differences in standard conventional hydration free energies ΔΔs GM+,wat• and redox potentials [Formula: see text]. The level of agreement between simulation and experiment, which is quantitative within error bars, underlines the substantial accuracy improvement achieved by applying a highly demanding QM/MM approach at the resolution-of-identity second-order Møller-Plesset perturbation (RIMP2) level over calculations relying on purely molecular mechanical or density functional theory (DFT) descriptions. A detailed analysis of the structural and dynamical properties of the Li+ hydrate indicates that a correct description of the solvation structure and dynamics is achieved as well at this level of theory. Consideration of the QM/MM potential-energy components also shows that the partitioning into QM and MM zones does not induce any significant energetic artifact for the system considered.
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Affiliation(s)
- Niko Prasetyo
- Theoretical Chemistry Division, Institute of General, Inorganic and Theoretical Chemistry , University of Innsbruck , Innrain 80-82 , A-6020 Innsbruck , Austria.,Austria-Indonesia Centre (AIC) for Computational Chemistry , Universitas Gadjah Mada , Sekip Utara , Yogyakarta 55281 , Indonesia.,Department of Chemistry, Faculty of Mathematics and Natural Sciences , Universitas Gadjah Mada , Sekip Utara , Yogyakarta 55281 , Indonesia
| | - Philippe H Hünenberger
- Laboratorium für Physikalische Chemie , ETH Zürich, ETH-Hönggerberg , HCI Building , CH-8093 Zürich , Switzerland
| | - Thomas S Hofer
- Theoretical Chemistry Division, Institute of General, Inorganic and Theoretical Chemistry , University of Innsbruck , Innrain 80-82 , A-6020 Innsbruck , Austria
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26
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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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27
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Hofer TS, Hünenberger PH. Absolute proton hydration free energy, surface potential of water, and redox potential of the hydrogen electrode from first principles: QM/MM MD free-energy simulations of sodium and potassium hydration. J Chem Phys 2018; 148:222814. [DOI: 10.1063/1.5000799] [Citation(s) in RCA: 60] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Thomas S. Hofer
- Theoretical Chemistry Division, Institute of General, Inorganic and Theoretical Chemistry, Centre for Chemistry and Biomedicine, University of Innsbruck, Innrain 80-82, A-6020 Innsbruck, Austria
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28
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Athènes M, Terrier P. Estimating thermodynamic expectations and free energies in expanded ensemble simulations: Systematic variance reduction through conditioning. J Chem Phys 2018; 146:194101. [PMID: 28527448 DOI: 10.1063/1.4983164] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Abstract
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more accurate estimates are obtained by combining Monte Carlo integration and integration by numerical quadrature along particular coordinates. We show that this variance reduction technique, referred to as conditioning in probability theory, can be advantageously implemented in expanded ensemble simulations. These simulations aim at estimating thermodynamic expectations as a function of an external parameter that is sampled like an additional coordinate. Conditioning therein entails integrating along the external coordinate by numerical quadrature. We prove variance reduction with respect to alternative standard estimators and demonstrate the practical efficiency of the technique by estimating free energies and characterizing a structural phase transition between two solid phases.
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Affiliation(s)
- Manuel Athènes
- CEA, DEN, Service de Recherches de Métallurgie Physique, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
| | - Pierre Terrier
- CEA, DEN, Service de Recherches de Métallurgie Physique, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
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29
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Remsing RC, Xi E, Patel AJ. Protein Hydration Thermodynamics: The Influence of Flexibility and Salt on Hydrophobin II Hydration. J Phys Chem B 2018; 122:3635-3646. [DOI: 10.1021/acs.jpcb.7b12060] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Richard C. Remsing
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- Institute for Computational Molecular Science, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Erte Xi
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Amish J. Patel
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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30
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Matos GDR, Kyu DY, Loeffler HH, Chodera JD, Shirts MR, Mobley DL. Approaches for calculating solvation free energies and enthalpies demonstrated with an update of the FreeSolv database. JOURNAL OF CHEMICAL AND ENGINEERING DATA 2017; 62:1559-1569. [PMID: 29056756 PMCID: PMC5648357 DOI: 10.1021/acs.jced.7b00104] [Citation(s) in RCA: 129] [Impact Index Per Article: 18.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Solvation free energies can now be calculated precisely from molecular simulations, providing a valuable test of the energy functions underlying these simulations. Here, we briefly review "alchemical" approaches for calculating the solvation free energies of small, neutral organic molecules from molecular simulations, and illustrate by applying them to calculate aqueous solvation free energies (hydration free energies). These approaches use a non-physical pathway to compute free energy differences from a simulation or set of simulations and appear to be a particularly robust and general-purpose approach for this task. We also present an update (version 0.5) to our FreeSolv database of experimental and calculated hydration free energies of neutral compounds and provide input files in formats for several simulation packages. This revision to FreeSolv provides calculated values generated with a single protocol and software version, rather than the heterogeneous protocols used in the prior version of the database. We also further update the database to provide calculated enthalpies and entropies of hydration and some experimental enthalpies and entropies, as well as electrostatic and nonpolar components of solvation free energies.
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Affiliation(s)
- Guilherme Duarte Ramos Matos
- Department of Chemistry, University of California, Irvine, Department of Pharmaceutical Sciences, University of California, Irvine, Scientific Computing Department, STFC, UK, Computational and Systems Biology Program, Sloan Kettering Institute, Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, and Departments of Pharmaceutical Sciences and Chemistry, University of California, Irvine
| | - Daisy Y Kyu
- Department of Chemistry, University of California, Irvine, Department of Pharmaceutical Sciences, University of California, Irvine, Scientific Computing Department, STFC, UK, Computational and Systems Biology Program, Sloan Kettering Institute, Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, and Departments of Pharmaceutical Sciences and Chemistry, University of California, Irvine
| | - Hannes H Loeffler
- Department of Chemistry, University of California, Irvine, Department of Pharmaceutical Sciences, University of California, Irvine, Scientific Computing Department, STFC, UK, Computational and Systems Biology Program, Sloan Kettering Institute, Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, and Departments of Pharmaceutical Sciences and Chemistry, University of California, Irvine
| | - John D Chodera
- Department of Chemistry, University of California, Irvine, Department of Pharmaceutical Sciences, University of California, Irvine, Scientific Computing Department, STFC, UK, Computational and Systems Biology Program, Sloan Kettering Institute, Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, and Departments of Pharmaceutical Sciences and Chemistry, University of California, Irvine
| | - Michael R Shirts
- Department of Chemistry, University of California, Irvine, Department of Pharmaceutical Sciences, University of California, Irvine, Scientific Computing Department, STFC, UK, Computational and Systems Biology Program, Sloan Kettering Institute, Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, and Departments of Pharmaceutical Sciences and Chemistry, University of California, Irvine
| | - David L Mobley
- Department of Chemistry, University of California, Irvine, Department of Pharmaceutical Sciences, University of California, Irvine, Scientific Computing Department, STFC, UK, Computational and Systems Biology Program, Sloan Kettering Institute, Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, and Departments of Pharmaceutical Sciences and Chemistry, University of California, Irvine
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31
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Mecklenfeld A, Raabe G. Efficient solvation free energy simulations: impact of soft-core potential and a new adaptive λ-spacing method. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1292008] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Andreas Mecklenfeld
- Institut für Thermodynamik, Technische Universität Braunschweig, Braunschweig, Germany
- Center of Pharmaceutical Engineering, Technische Universität Braunschweig, Braunschweig, Germany
| | - Gabriele Raabe
- Institut für Thermodynamik, Technische Universität Braunschweig, Braunschweig, Germany
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32
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Graf MMH, Maurer M, Oostenbrink C. Free-energy calculations of residue mutations in a tripeptide using various methods to overcome inefficient sampling. J Comput Chem 2016; 37:2597-605. [PMID: 27634475 PMCID: PMC5082540 DOI: 10.1002/jcc.24488] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2016] [Revised: 08/22/2016] [Accepted: 08/24/2016] [Indexed: 01/19/2023]
Abstract
Previous free-energy calculations have shown that the seemingly simple transformation of the tripeptide KXK to KGK in water holds some unobvious challenges concerning the convergence of the forward and backward thermodynamic integration processes (i.e., hysteresis). In the current study, the central residue X was either alanine, serine, glutamic acid, lysine, phenylalanine, or tyrosine. Interestingly, the transformation from alanine to glycine yielded the highest hysteresis in relation to the extent of the chemical change of the side chain. The reason for that could be attributed to poor sampling of φ2 /ψ2 dihedral angles along the transformation. Altering the nature of alanine's Cβ atom drastically improved the sampling and at the same time led to the identification of high energy barriers as cause for it. Consequently, simple strategies to overcome these barriers are to increase simulation time (computationally expensive) or to use enhanced sampling techniques such as Hamiltonian replica exchange molecular dynamics and one-step perturbation. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.
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Affiliation(s)
- Michael M H Graf
- Institute of Molecular Modeling and Simulation, Department of Material Sciences and Process Engineering, BOKU, University of Natural Resources and Life Sciences, Muthgasse 18, AT-1190, Vienna, Austria
| | - Manuela Maurer
- Institute of Molecular Modeling and Simulation, Department of Material Sciences and Process Engineering, BOKU, University of Natural Resources and Life Sciences, Muthgasse 18, AT-1190, Vienna, Austria
| | - Chris Oostenbrink
- Institute of Molecular Modeling and Simulation, Department of Material Sciences and Process Engineering, BOKU, University of Natural Resources and Life Sciences, Muthgasse 18, AT-1190, Vienna, Austria.
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33
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Modak VP, Wyslouzil BE, Singer SJ. On the determination of the crystal-vapor surface free energy, and why a Gaussian expression can be accurate for a system far from Gaussian. J Chem Phys 2016; 145:054710. [PMID: 27497575 DOI: 10.1063/1.4959167] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The crystal-vapor surface free energy γ is an important physical parameter governing physical processes, such as wetting and adhesion. We explore exact and approximate routes to calculate γ based on cleaving an intact crystal into non-interacting sub-systems with crystal-vapor interfaces. We do this by turning off the interactions, ΔV, between the sub-systems. Using the soft-core scheme for turning off ΔV, we find that the free energy varies smoothly with the coupling parameter λ, and a single thermodynamic integration yields the exact γ. We generate another exact method, and a cumulant expansion for γ by expressing the surface free energy in terms of an average of e(-βΔV) in the intact crystal. The second cumulant, or Gaussian approximation for γ is surprisingly accurate in most situations, even though we find that the underlying probability distribution for ΔV is clearly not Gaussian. We account for this fact by developing a non-Gaussian theory for γ and find that the difference between the non-Gaussian and Gaussian expressions for γ consist of terms that are negligible in many situations. Exact and approximate methods are applied to the (111) surface of a Lennard-Jones crystal and are also tested for more complex molecular solids, the surface of octane and nonadecane. Alkane surfaces were chosen for study because their crystal-vapor surface free energy has been of particular interest for understanding surface freezing in these systems.
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Affiliation(s)
- Viraj P Modak
- Department of Chemical and Biomolecular Engineering, Ohio State University, Columbus, Ohio 43210, USA
| | - Barbara E Wyslouzil
- Department of Chemical and Biomolecular Engineering, Ohio State University, Columbus, Ohio 43210, USA
| | - Sherwin J Singer
- Department of Chemistry and Biochemistry, Ohio State University, Columbus, Ohio 43210, USA
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34
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Maurer M, de Beer SBA, Oostenbrink C. Calculation of Relative Binding Free Energy in the Water-Filled Active Site of Oligopeptide-Binding Protein A. Molecules 2016; 21:499. [PMID: 27092480 PMCID: PMC5881882 DOI: 10.3390/molecules21040499] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2016] [Revised: 03/30/2016] [Accepted: 04/11/2016] [Indexed: 11/19/2022] Open
Abstract
The periplasmic oligopeptide binding protein A (OppA) represents a well-known example of water-mediated protein-ligand interactions. Here, we perform free-energy calculations for three different ligands binding to OppA, using a thermodynamic integration approach. The tripeptide ligands share a high structural similarity (all have the sequence KXK), but their experimentally-determined binding free energies differ remarkably. Thermodynamic cycles were constructed for the ligands, and simulations conducted in the bound and (freely solvated) unbound states. In the unbound state, it was observed that the difference in conformational freedom between alanine and glycine leads to a surprisingly slow convergence, despite their chemical similarity. This could be overcome by increasing the softness parameter during alchemical transformations. Discrepancies remained in the bound state however, when comparing independent simulations of the three ligands. These difficulties could be traced to a slow relaxation of the water network within the active site. Fluctuations in the number of water molecules residing in the binding cavity occur mostly on a timescale larger than the simulation time along the alchemical path. After extensive simulations, relative binding free energies that were converged to within thermal noise could be obtained, which agree well with available experimental data.
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Affiliation(s)
- Manuela Maurer
- Institute of Molecular Modeling and Simulation, University of Natural Resources and Life Sciences, Muthgasse 18, A-1190 Vienna, Austria.
| | - Stephanie B A de Beer
- Institute of Molecular Modeling and Simulation, University of Natural Resources and Life Sciences, Muthgasse 18, A-1190 Vienna, Austria.
| | - Chris Oostenbrink
- Institute of Molecular Modeling and Simulation, University of Natural Resources and Life Sciences, Muthgasse 18, A-1190 Vienna, Austria.
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35
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Naden LN, Shirts MR. Rapid Computation of Thermodynamic Properties over Multidimensional Nonbonded Parameter Spaces Using Adaptive Multistate Reweighting. J Chem Theory Comput 2016; 12:1806-23. [DOI: 10.1021/acs.jctc.5b00869] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Levi N. Naden
- Department
of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, United States
| | - Michael R. Shirts
- Department
of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, United States
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36
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Sakuraba S, Asai K, Kameda T. Predicting RNA Duplex Dimerization Free-Energy Changes upon Mutations Using Molecular Dynamics Simulations. J Phys Chem Lett 2015; 6:4348-4351. [PMID: 26722970 DOI: 10.1021/acs.jpclett.5b01984] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The dimerization free energies of RNA-RNA duplexes are fundamental values that represent the structural stability of RNA complexes. We report a comparative analysis of RNA-RNA duplex dimerization free-energy changes upon mutations, estimated from a molecular dynamics simulation and experiments. A linear regression for nine pairs of double-stranded RNA sequences, six base pairs each, yielded a mean absolute deviation of 0.55 kcal/mol and an R(2) value of 0.97, indicating quantitative agreement between simulations and experimental data. The observed accuracy indicates that the molecular dynamics simulation with the current molecular force field is capable of estimating the thermodynamic properties of RNA molecules.
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Affiliation(s)
- Shun Sakuraba
- Graduate School of Frontier Sciences, The University of Tokyo , 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8561, Japan
| | - Kiyoshi Asai
- Graduate School of Frontier Sciences, The University of Tokyo , 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8561, Japan
- Biotechnology Research Institute for Drug Discovery, National Institute of Advanced Industrial Science and Technology (AIST) , 2-4-7 Aomi, Koto-ku, Tokyo 135-0064, Japan
| | - Tomoshi Kameda
- Biotechnology Research Institute for Drug Discovery, National Institute of Advanced Industrial Science and Technology (AIST) , 2-4-7 Aomi, Koto-ku, Tokyo 135-0064, Japan
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37
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Naden LN, Shirts MR. Linear Basis Function Approach to Efficient Alchemical Free Energy Calculations. 2. Inserting and Deleting Particles with Coulombic Interactions. J Chem Theory Comput 2015; 11:2536-49. [DOI: 10.1021/ct501047e] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Levi N. Naden
- Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, United States
| | - Michael R. Shirts
- Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, United States
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38
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Remsing RC, Patel AJ. Water density fluctuations relevant to hydrophobic hydration are unaltered by attractions. J Chem Phys 2015; 142:024502. [DOI: 10.1063/1.4905009] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Richard C. Remsing
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Amish J. Patel
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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39
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Naden LN, Pham TT, Shirts MR. Linear Basis Function Approach to Efficient Alchemical Free Energy Calculations. 1. Removal of Uncharged Atomic Sites. J Chem Theory Comput 2014; 10:1128-49. [DOI: 10.1021/ct4009188] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Levi N. Naden
- Department
of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22902, United States
| | - Tri T. Pham
- Biozentrum
University of Basel, Klingelbergstrasse, Basel, Switzerland
| | - Michael R. Shirts
- Department
of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22902, United States
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