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Zhang S, Giese TJ, Lee TS, York DM. Alchemical Enhanced Sampling with Optimized Phase Space Overlap. J Chem Theory Comput 2024; 20:3935-3953. [PMID: 38666430 PMCID: PMC11157682 DOI: 10.1021/acs.jctc.4c00251] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/15/2024]
Abstract
An alchemical enhanced sampling (ACES) method has recently been introduced to facilitate importance sampling in free energy simulations. The method achieves enhanced sampling from Hamiltonian replica exchange within a dual topology framework while utilizing new smoothstep softcore potentials. A common sampling problem encountered in lead optimization is the functionalization of aromatic rings that exhibit distinct conformational preferences when interacting with the protein. It is difficult to converge the distribution of ring conformations due to the long time scale of ring flipping events; however, the ACES method addresses this issue by modeling the syn and anti ring conformations within a dual topology. ACES thereby samples the conformer distributions by alchemically tunneling between states, as opposed to traversing a physical pathway with a high rotational barrier. We demonstrate the use of ACES to overcome conformational sampling issues involving ring flipping in ML300-derived noncovalent inhibitors of SARS-CoV-2 Main Protease (Mpro). The demonstrations explore how the use of replica exchange and the choice of softcore selection affects the convergence of the ring conformation distributions. Furthermore, we examine how the accuracy of the calculated free energies is affected by the degree of phase space overlap (PSO) between adjacent states (i.e., between neighboring λ-windows) and the Hamiltonian replica exchange acceptance ratios. Both of these factors are sensitive to the spacing between the intermediate states. We introduce a new method for choosing a schedule of λ values. The method analyzes short "burn-in" simulations to construct a 2D map of the nonlocal PSO. The schedule is obtained by optimizing an alchemical pathway on the 2D map that equalizes the PSO between the λ intervals. The optimized phase space overlap λ-spacing method (Opt-PSO) leads to more numerous end-to-end single passes and round trips due to the correlation between PSO and Hamiltonian replica exchange acceptance ratios. The improved exchange statistics enhance the efficiency of ACES method. The method has been implemented into the FE-ToolKit software package, which is freely available.
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Affiliation(s)
- Shi Zhang
- 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
| | - 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
| | - 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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2
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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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3
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Brickel S, Demkiv AO, Crean RM, Pinto GP, Kamerlin SCL. Q-RepEx: A Python pipeline to increase the sampling of empirical valence bond simulations. J Mol Graph Model 2023; 119:108402. [PMID: 36610324 DOI: 10.1016/j.jmgm.2022.108402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Revised: 12/17/2022] [Accepted: 12/26/2022] [Indexed: 12/31/2022]
Abstract
The exploration of chemical systems occurs on complex energy landscapes. Comprehensively sampling rugged energy landscapes with many local minima is a common problem for molecular dynamics simulations. These multiple local minima trap the dynamic system, preventing efficient sampling. This is a particular challenge for large biochemical systems with many degrees of freedom. Replica exchange molecular dynamics (REMD) is an approach that accelerates the exploration of the conformational space of a system, and thus can be used to enhance the sampling of complex biomolecular processes. In parallel, the empirical valence bond (EVB) approach is a powerful approach for modeling chemical reactivity in biomolecular systems. Here, we present an open-source Python-based tool that interfaces with the Q simulation package, and increases the sampling efficiency of the EVB free energy perturbation/umbrella sampling approach by means of REMD. This approach, Q-RepEx, both decreases the computational cost of the associated REMD-EVB simulations, and opens the door to more efficient studies of biochemical reactivity in systems with significant conformational fluctuations along the chemical reaction coordinate.
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Affiliation(s)
- Sebastian Brickel
- Department of Chemistry - BMC, Uppsala University, BMC Box 576, S-751 23, Uppsala, Sweden
| | - Andrey O Demkiv
- Department of Chemistry - BMC, Uppsala University, BMC Box 576, S-751 23, Uppsala, Sweden
| | - Rory M Crean
- Department of Chemistry - BMC, Uppsala University, BMC Box 576, S-751 23, Uppsala, Sweden
| | - Gaspar P Pinto
- Department of Chemistry - BMC, Uppsala University, BMC Box 576, S-751 23, Uppsala, Sweden
| | - Shina Caroline Lynn Kamerlin
- Department of Chemistry - BMC, Uppsala University, BMC Box 576, S-751 23, Uppsala, Sweden; School of Chemistry and Biochemistry, Georgia Institute of Technology, 901 Atlantic Drive NW, Atlanta, GA, 30332-0400, USA.
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4
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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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5
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Sakae Y, Zhang BW, Levy RM, Deng N. Absolute Protein Binding Free Energy Simulations for Ligands with Multiple Poses, a Thermodynamic Path That Avoids Exhaustive Enumeration of the Poses. J Comput Chem 2020; 41:56-68. [PMID: 31621932 PMCID: PMC7140983 DOI: 10.1002/jcc.26078] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Revised: 08/07/2019] [Accepted: 08/31/2019] [Indexed: 12/28/2022]
Abstract
We propose a free energy calculation method for receptor-ligand binding, which have multiple binding poses that avoids exhaustive enumeration of the poses. For systems with multiple binding poses, the standard procedure is to enumerate orientations of the binding poses, restrain the ligand to each orientation, and then, calculate the binding free energies for each binding pose. In this study, we modify a part of the thermodynamic cycle in order to sample a broader conformational space of the ligand in the binding site. This modification leads to more accurate free energy calculation without performing separate free energy simulations for each binding pose. We applied our modification to simple model host-guest systems as a test, which have only two binding poses, by using a single decoupling method (SDM) in implicit solvent. The results showed that the binding free energies obtained from our method without knowing the two binding poses were in good agreement with the benchmark results obtained by explicit enumeration of the binding poses. Our method is applicable to other alchemical binding free energy calculation methods such as the double decoupling method (DDM) in explicit solvent. We performed a calculation for a protein-ligand system with explicit solvent using our modified thermodynamic path. The results of the free energy simulation along our modified path were in good agreement with the results of conventional DDM, which requires a separate binding free energy calculation for each of the binding poses of the example of phenol binding to T4 lysozyme in explicit solvent. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Yoshitake Sakae
- Center for Biophysics and Computational Biology, Temple University, Philadelphia, Pennsylvania, 19122
| | - Bin W Zhang
- Center for Biophysics and Computational Biology, Temple University, Philadelphia, Pennsylvania, 19122
| | - Ronald M Levy
- Center for Biophysics and Computational Biology, Temple University, Philadelphia, Pennsylvania, 19122
- Department of Chemistry, Institute for Computational Molecular Science, Temple University, Philadelphia, Pennsylvania, 19122
| | - Nanjie Deng
- Department of Chemistry and Physical Sciences, Pace University, New York, New York, 10038
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6
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Min D, Zheng L, Harris W, Chen M, Lv C, Yang W. Practically Efficient QM/MM Alchemical Free Energy Simulations: The Orthogonal Space Random Walk Strategy. J Chem Theory Comput 2015; 6:2253-66. [PMID: 26613484 DOI: 10.1021/ct100033s] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The difference between free energy changes occurring at two chemical states can be rigorously estimated via alchemical free energy (AFE) simulations. Traditionally, most AFE simulations are carried out under the classical energy potential treatment; then, accuracy and applicability of AFE simulations are limited. In the present work, we integrate a recent second-order generalized ensemble strategy, the orthogonal space random walk (OSRW) method, into the combined quantum mechanical/molecular mechanical (QM/MM) potential based AFE simulation scheme. Thereby, within a commonly affordable simulation length, accurate QM/MM alchemical free energy simulations can be achieved. As revealed by the model study on the equilibrium of a tautomerization process of hydrated 3-hydroxypyrazole and by the model calculations of the redox potentials of two flavin derivatives, lumichrome (LC) and riboflavin (RF) in aqueous solution, the present OSRW-based scheme could be a viable path toward the realization of practically efficient QM/MM AFE simulations.
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Affiliation(s)
- Donghong Min
- Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306
| | - Lianqing Zheng
- Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306
| | - William Harris
- Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306
| | - Mengen Chen
- Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306
| | - Chao Lv
- Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306
| | - Wei Yang
- Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306
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7
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Burusco KK, Bruce NJ, Alibay I, Bryce RA. Free Energy Calculations using a Swarm-Enhanced Sampling Molecular Dynamics Approach. Chemphyschem 2015; 16:3233-41. [PMID: 26418190 PMCID: PMC4676921 DOI: 10.1002/cphc.201500524] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2015] [Indexed: 11/19/2022]
Abstract
Free energy simulations are an established computational tool in modelling chemical change in the condensed phase. However, sampling of kinetically distinct substates remains a challenge to these approaches. As a route to addressing this, we link the methods of thermodynamic integration (TI) and swarm-enhanced sampling molecular dynamics (sesMD), where simulation replicas interact cooperatively to aid transitions over energy barriers. We illustrate the approach by using alchemical alkane transformations in solution, comparing them with the multiple independent trajectory TI (IT-TI) method. Free energy changes for transitions computed by using IT-TI grew increasingly inaccurate as the intramolecular barrier was heightened. By contrast, swarm-enhanced sampling TI (sesTI) calculations showed clear improvements in sampling efficiency, leading to more accurate computed free energy differences, even in the case of the highest barrier height. The sesTI approach, therefore, has potential in addressing chemical change in systems where conformations exist in slow exchange.
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Affiliation(s)
- Kepa K Burusco
- Manchester Pharmacy School, University of Manchester, Oxford Road, Manchester, M13 9PT, UK
| | - Neil J Bruce
- Manchester Pharmacy School, University of Manchester, Oxford Road, Manchester, M13 9PT, UK.,Heidelberg Institute for Theoretical Studies (HITS gGmbH), Schloss-Wolfsbrunnenweg 35, 69118, Heidelberg, Germany
| | - Irfan Alibay
- Manchester Pharmacy School, University of Manchester, Oxford Road, Manchester, M13 9PT, UK
| | - Richard A Bryce
- Manchester Pharmacy School, University of Manchester, Oxford Road, Manchester, M13 9PT, UK.
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8
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Molecular dynamics and Monte Carlo simulations for protein-ligand binding and inhibitor design. Biochim Biophys Acta Gen Subj 2014; 1850:966-971. [PMID: 25196360 DOI: 10.1016/j.bbagen.2014.08.018] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2014] [Revised: 08/26/2014] [Accepted: 08/28/2014] [Indexed: 11/24/2022]
Abstract
BACKGROUND Non-nucleoside inhibitors of HIV reverse transcriptase are an important component of treatment against HIV infection. Novel inhibitors are sought that increase potency against variants that contain the Tyr181Cys mutation. METHODS Molecular dynamics based free energy perturbation simulations have been run to study factors that contribute to protein-ligand binding, and the results are compared with those from previous Monte Carlo based simulations and activity data. RESULTS Predictions of protein-ligand binding modes are very consistent for the two simulation methods; the accord is attributed to the use of an enhanced sampling protocol. The Tyr181Cys binding pocket supports large, hydrophobic substituents, which is in good agreement with experiment. CONCLUSIONS Although some discrepancies exist between the results of the two simulation methods and experiment, free energy perturbation simulations can be used to rapidly test small molecules for gains in binding affinity. GENERAL SIGNIFICANCE Free energy perturbation methods show promise in providing fast, reliable and accurate data that can be used to complement experiment in lead optimization projects. This article is part of a Special Issue entitled "Recent developments of molecular dynamics".
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9
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Lin Z, van Gunsteren WF. Enhanced conformational sampling using enveloping distribution sampling. J Chem Phys 2013; 139:144105. [DOI: 10.1063/1.4824391] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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10
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Zeifman AA, Stroylov VV, Novikov FN, Stroganov OV, Kulkov V, Chilov GG. Alchemical FEP Calculations of Ligand Conformer Focusing in Explicit Solvent. J Chem Theory Comput 2013; 9:1093-102. [DOI: 10.1021/ct300796g] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Alexey A. Zeifman
- N. D. Zelinsky Institute
Of
Organic Chemistry (ZIOC RAS), Leninsky avenue, 47, 119991 Moscow,
Russian Federation
- National Research Centre “Kurchatov Instititute”, Akademika
Kurchatova pl., 1, 123182 Moscow, Russia
| | - Victor V. Stroylov
- N. D. Zelinsky Institute
Of
Organic Chemistry (ZIOC RAS), Leninsky avenue, 47, 119991 Moscow,
Russian Federation
- Molecular Technologies, Ltd., Leninskie gory, 1/75G, 119992, Moscow, Russian
Federation
| | - Fedor N. Novikov
- N. D. Zelinsky Institute
Of
Organic Chemistry (ZIOC RAS), Leninsky avenue, 47, 119991 Moscow,
Russian Federation
- Molecular Technologies, Ltd., Leninskie gory, 1/75G, 119992, Moscow, Russian
Federation
| | - Oleg V. Stroganov
- N. D. Zelinsky Institute
Of
Organic Chemistry (ZIOC RAS), Leninsky avenue, 47, 119991 Moscow,
Russian Federation
- Molecular Technologies, Ltd., Leninskie gory, 1/75G, 119992, Moscow, Russian
Federation
| | - Val Kulkov
- BioMolTech Corp., 226 York Mills Road, Toronto, Ontario
M2L 1L1, Canada
| | - Ghermes G. Chilov
- N. D. Zelinsky Institute
Of
Organic Chemistry (ZIOC RAS), Leninsky avenue, 47, 119991 Moscow,
Russian Federation
- Molecular Technologies, Ltd., Leninskie gory, 1/75G, 119992, Moscow, Russian
Federation
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11
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Abstract
Free energy calculations are extremely useful for investigating small-molecule biophysical properties such as protein-ligand binding affinities and partition coefficients. However, these calculations are also notoriously difficult to implement correctly. In this chapter, we review standard methods for computing free energy via simulation, discussing current best practices and examining potential pitfalls for computational researchers performing them for the first time. We include a variety of examples and tips for how to set up and conduct these calculations, including applications to relative binding affinities and small-molecule solvation free energies.
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Affiliation(s)
- Michael R Shirts
- Department of Chemical Engineering, University of Virginia, Charlottesville, VA, USA.
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12
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Ripoll DR, Khavrutskii IV, Chaudhury S, Liu J, Kuschner RA, Wallqvist A, Reifman J. Quantitative predictions of binding free energy changes in drug-resistant influenza neuraminidase. PLoS Comput Biol 2012; 8:e1002665. [PMID: 22956900 PMCID: PMC3431292 DOI: 10.1371/journal.pcbi.1002665] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2012] [Accepted: 07/15/2012] [Indexed: 12/26/2022] Open
Abstract
Quantitatively predicting changes in drug sensitivity associated with residue mutations is a major challenge in structural biology. By expanding the limits of free energy calculations, we successfully identified mutations in influenza neuraminidase (NA) that confer drug resistance to two antiviral drugs, zanamivir and oseltamivir. We augmented molecular dynamics (MD) with Hamiltonian Replica Exchange and calculated binding free energy changes for H274Y, N294S, and Y252H mutants. Based on experimental data, our calculations achieved high accuracy and precision compared with results from established computational methods. Analysis of 15 µs of aggregated MD trajectories provided insights into the molecular mechanisms underlying drug resistance that are at odds with current interpretations of the crystallographic data. Contrary to the notion that resistance is caused by mutant-induced changes in hydrophobicity of the binding pocket, our simulations showed that drug resistance mutations in NA led to subtle rearrangements in the protein structure and its dynamics that together alter the active-site electrostatic environment and modulate inhibitor binding. Importantly, different mutations confer resistance through different conformational changes, suggesting that a generalized mechanism for NA drug resistance is unlikely. The capacity of the influenza virus to rapidly mutate and render resistance to a handful of FDA approved neuraminidase (NA) inhibitors represents a significant human health concern. To gain an atomic-level understanding of the mechanisms behind drug resistance, we applied a novel computational approach to characterize resistant NA mutations. These results are comparable in accuracy and precision with the best experimental measurements presently available. To the best of our knowledge, this is the first time that a rigorous computational method has attained the level of certainty needed to predict subtle changes in binding free energies conferred by mutations. Analysis of our simulation data provided a thorough description of the thermodynamics of the binding process for different NA-inhibitor complexes, with findings that in some cases challenge current views based on interpretations of the crystallographic data. While we did not find a generalized mechanism of NA resistance, we identified key differences between oseltamivir and zanamivir that discriminate their responses to the three mutations we considered, namely H274Y, N294S and Y252H. It is worth noting that our approach can be broadly applied to predict resistant mutations to existing and newly developed drugs in other important drug targets.
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Affiliation(s)
- Daniel R. Ripoll
- Department of Defense Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Materiel Command, Fort Detrick, Frederick, Maryland, United States of America
| | - Ilja V. Khavrutskii
- Department of Defense Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Materiel Command, Fort Detrick, Frederick, Maryland, United States of America
| | - Sidhartha Chaudhury
- Department of Defense Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Materiel Command, Fort Detrick, Frederick, Maryland, United States of America
| | - Jin Liu
- Department of Defense Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Materiel Command, Fort Detrick, Frederick, Maryland, United States of America
| | - Robert A. Kuschner
- Walter Reed Army Institute of Research, Emerging Infectious Diseases Research Unit, Silver Spring, Maryland, United States of America
| | - Anders Wallqvist
- Department of Defense Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Materiel Command, Fort Detrick, Frederick, Maryland, United States of America
| | - Jaques Reifman
- Department of Defense Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Materiel Command, Fort Detrick, Frederick, Maryland, United States of America
- * E-mail:
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13
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Cuendet MA, Tuckerman ME. Alchemical Free Energy Differences in Flexible Molecules from Thermodynamic Integration or Free Energy Perturbation Combined with Driven Adiabatic Dynamics. J Chem Theory Comput 2012; 8:3504-12. [DOI: 10.1021/ct300090z] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Michel A. Cuendet
- Department of Chemistry, New York
University, New York,
New York 10003, United States
| | - Mark E. Tuckerman
- Department of Chemistry, New York
University, New York,
New York 10003, United States
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14
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On achieving high accuracy and reliability in the calculation of relative protein-ligand binding affinities. Proc Natl Acad Sci U S A 2012; 109:1937-42. [PMID: 22308365 DOI: 10.1073/pnas.1114017109] [Citation(s) in RCA: 186] [Impact Index Per Article: 15.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We apply a free energy perturbation simulation method, free energy perturbation/replica exchange with solute tempering, to two modifications of protein-ligand complexes that lead to significant conformational changes, the first in the protein and the second in the ligand. The approach is shown to facilitate sampling in these challenging cases where high free energy barriers separate the initial and final conformations and leads to superior convergence of the free energy as demonstrated both by consistency of the results (independence from the starting conformation) and agreement with experimental binding affinity data. The second case, consisting of two neutral thrombin ligands that are taken from a recent medicinal chemistry program for this interesting pharmaceutical target, is of particular significance in that it demonstrates that good results can be obtained for large, complex ligands, as opposed to relatively simple model systems. To achieve quantitative agreement with experiment in the thrombin case, a next generation force field, Optimized Potentials for Liquid Simulations 2.0, is required, which provides superior charges and torsional parameters as compared to earlier alternatives.
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15
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Assessment of enveloping distribution sampling to calculate relative free enthalpies of binding for eight netropsin-DNA duplex complexes in aqueous solution. J Comput Chem 2012; 33:640-51. [DOI: 10.1002/jcc.22879] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2011] [Accepted: 10/28/2011] [Indexed: 12/25/2022]
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16
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Abstract
Free energy calculations are increasingly of interest for computing biophysical properties of novel small molecules of interest in drug design, such as protein-ligand binding affinities and small molecule partition coefficients. However, these calculations are also notoriously difficult to implement correctly. In this article, we review standard methods for computing free energy differences via simulation, discuss current best practices, and examine potential pitfalls for computational researchers without extensive experience in such calculations. We include a variety of examples and tips for how to set up and conduct these calculations, including applications to relative binding affinities and absolute binding free energies.
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Affiliation(s)
- Michael R Shirts
- Department of Chemical Engineering, University of Virginia, Charlottesville, VA, USA.
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17
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Meng Y, Dashti DS, Roitberg AE. Computing Alchemical Free Energy Differences with Hamiltonian Replica Exchange Molecular Dynamics (H-REMD) Simulations. J Chem Theory Comput 2011; 7:2721-2727. [PMID: 22125475 PMCID: PMC3223983 DOI: 10.1021/ct200153u] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Alchemical free energy calculations play a very important role in the field of molecular modeling. Efforts have been made to improve the accuracy and precision of those calculations. One of the efforts is to employ a Hamiltonian replica exchange molecular dynamics (H-REMD) method to enhance conformational sampling. In this paper, we demonstrated that HREMD method not only improves convergence in alchemical free energy calculations but also can be used to compute free energy differences directly via the Free Energy Perturbation (FEP)algorithm. We show a direct mapping between the H-REMD and the usual FEP equations, which are then used directly to compute free energies. The H-REMD alchemical free energy calculation (Replica exchange Free Energy Perturbation, REFEP) was tested on predicting the pK(a) value of the buried Asp26 in thioredoxin. We compare the results of REFEP with TI and regular FEP simulations. REFEP calculations converged faster than those from TI and regular FEP simulations. The final predicted pK(a) value from the H-REMD simulation was also very accurate, only 0.4 pK(a) unit above the experimental value. Utilizing the REFEP algorithm significantly improves conformational sampling, and this in turn improves the convergence of alchemical free energy simulations.
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Affiliation(s)
- Yilin Meng
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois, 60637
| | - Danial Sabri Dashti
- Department of Physics and Quantum Theory Project, University of Florida, Gainesville, Florida, 32611-8435
| | - Adrian E. Roitberg
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida, 32611-8435
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18
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Khavrutskii IV, Wallqvist A. Improved Binding Free Energy Predictions from Single-Reference Thermodynamic Integration Augmented with Hamiltonian Replica Exchange. J Chem Theory Comput 2011; 7:3001-3011. [PMID: 22046108 PMCID: PMC3200539 DOI: 10.1021/ct2003786] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Reliable predictions of relative binding free energies are essential in drug discovery, where chemists modify promising compounds with the aim of increasing binding affinity. Conventional Thermodynamic Integration (TI) approaches can estimate corresponding changes in binding free energies, but suffer from inadequate sampling due to ruggedness of the molecular energy surfaces. Here, we present an improved TI strategy for computing relative binding free energies of congeneric ligands. This strategy employs a specific, unphysical single-reference (SR) state and Hamiltonian replica exchange (HREX) to locally enhance sampling. We then apply this strategy to compute relative binding free energies of twelve ligands in the L99A mutant of T4 Lysozyme. Besides the ligands, our approach enhances hindered rotations of the important V111, as well as V87 and L118 sidechains. Concurrently, we devise practical strategies to monitor and improve HREX-SRTI efficiency. Overall, the HREX-SRTI results agree well (R(2) = 0.76, RMSE = 0.3 kcal/mol) with available experimental data. When optimized for efficiency, the HREX-SRTI precision matches that of experimental measurements.
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Affiliation(s)
- Ilja V Khavrutskii
- Biotechnology HPC Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Materiel Command, Fort Detrick, MD 21702
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19
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Grosdidier A, Zoete V, Michielin O. Fast docking using the CHARMM force field with EADock DSS. J Comput Chem 2011; 32:2149-59. [PMID: 21541955 DOI: 10.1002/jcc.21797] [Citation(s) in RCA: 318] [Impact Index Per Article: 24.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2010] [Revised: 01/24/2011] [Accepted: 02/27/2011] [Indexed: 01/22/2023]
Abstract
The prediction of binding modes (BMs) occurring between a small molecule and a target protein of biological interest has become of great importance for drug development. The overwhelming diversity of needs leaves room for docking approaches addressing specific problems. Nowadays, the universe of docking software ranges from fast and user friendly programs to algorithmically flexible and accurate approaches. EADock2 is an example of the latter. Its multiobjective scoring function was designed around the CHARMM22 force field and the FACTS solvation model. However, the major drawback of such a software design lies in its computational cost. EADock dihedral space sampling (DSS) is built on the most efficient features of EADock2, namely its hybrid sampling engine and multiobjective scoring function. Its performance is equivalent to that of EADock2 for drug-like ligands, while the CPU time required has been reduced by several orders of magnitude. This huge improvement was achieved through a combination of several innovative features including an automatic bias of the sampling toward putative binding sites, and a very efficient tree-based DSS algorithm. When the top-scoring prediction is considered, 57% of BMs of a test set of 251 complexes were reproduced within 2 Å RMSD to the crystal structure. Up to 70% were reproduced when considering the five top scoring predictions. The success rate is lower in cross-docking assays but remains comparable with that of the latest version of AutoDock that accounts for the protein flexibility.
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Affiliation(s)
- Aurélien Grosdidier
- Swiss Institute of Bioinformatics (SIB), Quartier Sorge, Bâtiment Génopode, CH-1015 Lausanne, Switzerland
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20
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Bruckner S, Boresch S. Efficiency of alchemical free energy simulations. I. A practical comparison of the exponential formula, thermodynamic integration, and Bennett's acceptance ratio method. J Comput Chem 2010; 32:1303-19. [DOI: 10.1002/jcc.21713] [Citation(s) in RCA: 87] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2010] [Revised: 10/01/2010] [Accepted: 10/17/2010] [Indexed: 01/17/2023]
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21
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Khavrutskii IV, Wallqvist A. Computing Relative Free Energies of Solvation using Single Reference Thermodynamic Integration Augmented with Hamiltonian Replica Exchange. J Chem Theory Comput 2010; 6:3427-3441. [PMID: 21151738 PMCID: PMC2998072 DOI: 10.1021/ct1003302] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
This paper introduces an efficient single-topology variant of Thermodynamic Integration (TI) for computing relative transformation free energies in a series of molecules with respect to a single reference state. The presented TI variant that we refer to as Single-Reference TI (SR-TI) combines well-established molecular simulation methodologies into a practical computational tool. Augmented with Hamiltonian Replica Exchange (HREX), the SR-TI variant can deliver enhanced sampling in select degrees of freedom. The utility of the SR-TI variant is demonstrated in calculations of relative solvation free energies for a series of benzene derivatives with increasing complexity. Noteworthy, the SR-TI variant with the HREX option provides converged results in a challenging case of an amide molecule with a high (13-15 kcal/mol) barrier for internal cis/trans interconversion using simulation times of only 1 to 4 ns.
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Affiliation(s)
- Ilja V Khavrutskii
- Biotechnology HPC Software Applications Institute, Telemedicine and Advanced Technology Research Center, US Army Medical Research and Materiel Command, Fort Detrick, MD 21702
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22
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Hansen HS, Hünenberger PH. Using the local elevation method to construct optimized umbrella sampling potentials: Calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water. J Comput Chem 2010; 31:1-23. [DOI: 10.1002/jcc.21253] [Citation(s) in RCA: 91] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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23
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Hritz J, Oostenbrink C. Efficient free energy calculations for compounds with multiple stable conformations separated by high energy barriers. J Phys Chem B 2009; 113:12711-20. [PMID: 19722597 DOI: 10.1021/jp902968m] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Compounds with high intramolecular energy barriers represent challenging targets for free energy calculations because of the difficulty to obtain sufficient conformational sampling. Existing approaches are therefore computationally very demanding, thus preventing practical applications for such compounds. We present an enhanced sampling-one step perturbation method (ES-OS) to tackle this problem in a highly efficient way. A single molecular dynamics simulation of a judiciously chosen reference state (using two sets of soft-core interactions) is sufficient to determine conformational distributions of chemically similar compounds and the free energy differences between them. The ES-OS method is applied to a set of five biologically relevant 8-substituted GTP analogs having high energy barriers between the anti and the syn conformations of the base with respect to the ribose part. The reliability of ES-OS is verified by comparing the results to Hamiltonian replica exchange simulations of GTP and 8-Br-GTP and the experimentally determined 3J(C4,H1') coupling constant for GMP in water. Additional simulations in vacuum and octanol allow us to calculate differences in the solvation free energies and in lipophilicities (log P). Free energy contributions from individual conformational regions are also calculated, and their relationship with the overall free energy is derived leading to a set of multiconformational free energy formulas. These relationships are of general applicability and can be used in free energy calculations for a more diverse set of compounds.
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Affiliation(s)
- Jozef Hritz
- Leiden Amsterdam Center for Drug Research, Division of Molecular Toxicology, VU University Amsterdam, The Netherlands
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24
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Jiang W, Hodoscek M, Roux B. Computation of Absolute Hydration and Binding Free Energy with Free Energy Perturbation Distributed Replica-Exchange Molecular Dynamics (FEP/REMD). J Chem Theory Comput 2009; 5:2583-2588. [PMID: 21857812 DOI: 10.1021/ct900223z] [Citation(s) in RCA: 104] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Distributed Replica (REPDSTR) is a powerful parallelization technique enabling simulations of a group of replicas in a parallel/parallel fashion, where each replica is distributed to different nodes of a large cluster [Theor. Chem. Acc. 109: 140 (2003)]. Here, we use the framework provided by REPDSTR to combine a staged free energy perturbation protocol with different values of the thermodynamic coupling parameters with replica-exchange molecular dynamics (FEP/REMD. The structure of REPDSTR, which allows multiple parallel input/output (I/O), facilitates the treatment of replica-exchange to couple the N window simulations. As a result, each of the N synchronous window simulations benefit from the sampling carried out by the N-1 others. As illustrative examples of the FEP/REMD strategy, calculations of the absolute hydration and binding free energy of small molecules were performed using the biomolecular simulation program CHARMM adapted for the IBM Blue Gene/P platform. The computations show that a FEP/REMD strategy significantly improves the sampling and accelerate the convergence of absolute free energy computations.
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Affiliation(s)
- Wei Jiang
- Biosciences Division, Argonne National Laboratory, 9700 South Cass Avenue, Building 221, Argonne, Illinois 60439, USACenter for Molecular Modeling, National Institute of Chemistry, Hajdrihova 19, SI-1000 Ljubljana, Slovenia,Department of Biochemistry and Molecular Biology, Gordon Center for Integrative Science, University of Chicago, 929 57th Street, Chicago, Illinois 60637, USA
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25
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Brooks B, Brooks C, MacKerell A, Nilsson L, Petrella R, Roux B, Won Y, Archontis G, Bartels C, Boresch S, Caflisch A, Caves L, Cui Q, Dinner A, Feig M, Fischer S, Gao J, Hodoscek M, Im W, Kuczera K, Lazaridis T, Ma J, Ovchinnikov V, Paci E, Pastor R, Post C, Pu J, Schaefer M, Tidor B, Venable RM, Woodcock HL, Wu X, Yang W, York D, Karplus M. CHARMM: the biomolecular simulation program. J Comput Chem 2009; 30:1545-614. [PMID: 19444816 PMCID: PMC2810661 DOI: 10.1002/jcc.21287] [Citation(s) in RCA: 6011] [Impact Index Per Article: 400.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.
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Affiliation(s)
- B.R. Brooks
- Laboratory of Computational Biology, National Heart, Lung, and
Blood Institute, National Institutes of Health, Bethesda, MD 20892
| | - C.L. Brooks
- Departments of Chemistry & Biophysics, University of
Michigan, Ann Arbor, MI 48109
| | - A.D. MacKerell
- Department of Pharmaceutical Sciences, School of Pharmacy,
University of Maryland, Baltimore, MD, 21201
| | - L. Nilsson
- Karolinska Institutet, Department of Biosciences and Nutrition,
SE-141 57, Huddinge, Sweden
| | - R.J. Petrella
- Department of Chemistry and Chemical Biology, Harvard University,
Cambridge, MA 02138
- Department of Medicine, Harvard Medical School, Boston, MA
02115
| | - B. Roux
- Department of Biochemistry and Molecular Biology, University of
Chicago, Gordon Center for Integrative Science, Chicago, IL 60637
| | - Y. Won
- Department of Chemistry, Hanyang University, Seoul
133–792 Korea
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - M. Karplus
- Department of Chemistry and Chemical Biology, Harvard University,
Cambridge, MA 02138
- Laboratoire de Chimie Biophysique, ISIS, Université de
Strasbourg, 67000 Strasbourg France
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26
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Random walk in orthogonal space to achieve efficient free-energy simulation of complex systems. Proc Natl Acad Sci U S A 2008; 105:20227-32. [PMID: 19075242 DOI: 10.1073/pnas.0810631106] [Citation(s) in RCA: 249] [Impact Index Per Article: 15.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
In the past few decades, many ingenious efforts have been made in the development of free-energy simulation methods. Because complex systems often undergo nontrivial structural transition during state switching, achieving efficient free-energy calculation can be challenging. As identified earlier, the "Hamiltonian" lagging, which reveals the fact that necessary structural relaxation falls behind the order parameter move, has been a primary problem for generally low free-energy simulation efficiency. Here, we propose an algorithm by achieving a random walk in both the order parameter space and its generalized force space; thereby, the order parameter move and the required conformational relaxation can be efficiently synchronized. As demonstrated in both the alchemical transition and the conformational transition, a leapfrog improvement in free-energy simulation efficiency can be obtained; for instance, (i) it allows us to solve a notoriously challenging problem: accurately predicting the pK(a) value of a buried titratable residue, Asp-66, in the interior of the V66E staphylococcal nuclease mutant, and (ii) it allows us to gain superior efficiency over the metadynamics algorithm.
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27
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Zheng L, Yang W. On the simulated scaling based free energy simulations: Adaptive optimization of the scaling parameter intervals. J Chem Phys 2008; 129:124107. [DOI: 10.1063/1.2982161] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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de Oliveira CAF, Hamelberg D, McCammon JA. Coupling Accelerated Molecular Dynamics Methods with Thermodynamic Integration Simulations. J Chem Theory Comput 2008; 4:1516-1525. [PMID: 19461868 PMCID: PMC2646661 DOI: 10.1021/ct800160q] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2008] [Indexed: 12/03/2022]
Abstract
In this work we propose a straightforward and efficient approach to improve accuracy and convergence of free energy simulations in condensed-phase systems. We also introduce a new accelerated Molecular Dynamics (MD) approach in which molecular conformational transitions are accelerated by lowering the energy barriers while the potential surfaces near the minima are left unchanged. All free energy calculations were performed on the propane-to-propane model system. The accuracy of free energy simulations was significantly improved when sampling of internal degrees of freedom of solute was enhanced. However, accurate and converged results were only achieved when the solvent interactions were taken into account in the accelerated MD approaches. The analysis of the distribution of boost potential along the free energy simulations showed that the new accelerated MD approach samples efficiently both low- and high-energy regions of the potential surface. Since this approach also maintains substantial populations in regions near the minima, the statistics are not compromised in the thermodynamic integration calculations, and, as a result, the ensemble average can be recovered.
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Affiliation(s)
- César Augusto F de Oliveira
- Howard Hughes Medical Institute, Center for Theoretical Biological Physics, Department of Chemistry and Biochemistry and Department of Pharmacology, University of California at San Diego, La Jolla, California 92093-0365
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29
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Min D, Yang W. Energy difference space random walk to achieve fast free energy calculations. J Chem Phys 2008; 128:191102. [PMID: 18500847 DOI: 10.1063/1.2927744] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A method is proposed to efficiently obtain free energy differences. In the present algorithm, free energy calculations proceed by the realization of an energy difference space random walk. Thereby, this algorithm can greatly improve the sampling of the regions in phase space where target states overlap.
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Affiliation(s)
- Donghong Min
- School of Computational Science, Florida State University, Tallahassee, Florida 32306, USA
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30
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Zheng L, Carbone IO, Lugovskoy A, Berg BA, Yang W. A hybrid recursion method to robustly ensure convergence efficiencies in the simulated scaling based free energy simulations. J Chem Phys 2008; 129:034105. [DOI: 10.1063/1.2953321] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Min D, Yang W. A divide-and-conquer strategy to improve diffusion sampling in generalized ensemble simulations. J Chem Phys 2008; 128:094106. [DOI: 10.1063/1.2834500] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Okur A, Wickstrom L, Simmerling C. Evaluation of Salt Bridge Structure and Energetics in Peptides Using Explicit, Implicit, and Hybrid Solvation Models. J Chem Theory Comput 2008; 4:488-98. [DOI: 10.1021/ct7002308] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Asim Okur
- Department of Chemistry and Graduate Program in Biochemistry and Structural Biology, Stony Brook University, Stony Brook, New York 11794
| | - Lauren Wickstrom
- Department of Chemistry and Graduate Program in Biochemistry and Structural Biology, Stony Brook University, Stony Brook, New York 11794
| | - Carlos Simmerling
- Department of Chemistry and Graduate Program in Biochemistry and Structural Biology, Stony Brook University, Stony Brook, New York 11794
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33
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Woods CJ, Manby FR, Mulholland AJ. An efficient method for the calculation of quantum mechanics/molecular mechanics free energies. J Chem Phys 2008; 128:014109. [DOI: 10.1063/1.2805379] [Citation(s) in RCA: 85] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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34
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Li H, Min D, Liu Y, Yang W. Essential energy space random walk via energy space metadynamics method to accelerate molecular dynamics simulations. J Chem Phys 2007; 127:094101. [PMID: 17824726 DOI: 10.1063/1.2769356] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
To overcome the possible pseudoergodicity problem, molecular dynamic simulation can be accelerated via the realization of an energy space random walk. To achieve this, a biased free energy function (BFEF) needs to be priori obtained. Although the quality of BFEF is essential for sampling efficiency, its generation is usually tedious and nontrivial. In this work, we present an energy space metadynamics algorithm to efficiently and robustly obtain BFEFs. Moreover, in order to deal with the associated diffusion sampling problem caused by the random walk in the total energy space, the idea in the original umbrella sampling method is generalized to be the random walk in the essential energy space, which only includes the energy terms determining the conformation of a region of interest. This essential energy space generalization allows the realization of efficient localized enhanced sampling and also offers the possibility of further sampling efficiency improvement when high frequency energy terms irrelevant to the target events are free of activation. The energy space metadynamics method and its generalization in the essential energy space for the molecular dynamics acceleration are demonstrated in the simulation of a pentanelike system, the blocked alanine dipeptide model, and the leucine model.
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Affiliation(s)
- Hongzhi Li
- School of Computational Science, Florida State University, Tallahassee, Florida 32306, USA
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35
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Yang W, Nymeyer H, Zhou HX, Berg B, Brüschweiler R. Quantitative computer simulations of biomolecules: A snapshot. J Comput Chem 2007; 29:668-72. [PMID: 17708535 DOI: 10.1002/jcc.20819] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
A recent workshop titled "Quantitative Computational Biophysics" at Florida State University provided an overview of the state of the art in quantitative modeling of biomolecular systems. The presentations covered a wide range of interrelated topics, including the development and validation of force fields, the modeling of protein-protein interactions, the sampling of conformational space, and the assessment of equilibration and statistical errors. Substantial progress in all these areas was reported.
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Affiliation(s)
- Wei Yang
- School of Computational Science, Florida State University, Tallahassee, Florida 32306, USA
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36
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Li H, Yang W. Forging the missing link in free energy estimations: λ-WHAM in thermodynamic integration, overlap histogramming, and free energy perturbation. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.04.009] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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