1
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Gogal RA, Nessler AJ, Thiel AC, Bernabe HV, Corrigan Grove RA, Cousineau LM, Litman JM, Miller JM, Qi G, Speranza MJ, Tollefson MR, Fenn TD, Michaelson JJ, Okada O, Piquemal JP, Ponder JW, Shen J, Smith RJH, Yang W, Ren P, Schnieders MJ. Force Field X: A computational microscope to study genetic variation and organic crystals using theory and experiment. J Chem Phys 2024; 161:012501. [PMID: 38958156 PMCID: PMC11223778 DOI: 10.1063/5.0214652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2024] [Accepted: 06/17/2024] [Indexed: 07/04/2024] Open
Abstract
Force Field X (FFX) is an open-source software package for atomic resolution modeling of genetic variants and organic crystals that leverages advanced potential energy functions and experimental data. FFX currently consists of nine modular packages with novel algorithms that include global optimization via a many-body expansion, acid-base chemistry using polarizable constant-pH molecular dynamics, estimation of free energy differences, generalized Kirkwood implicit solvent models, and many more. Applications of FFX focus on the use and development of a crystal structure prediction pipeline, biomolecular structure refinement against experimental datasets, and estimation of the thermodynamic effects of genetic variants on both proteins and nucleic acids. The use of Parallel Java and OpenMM combines to offer shared memory, message passing, and graphics processing unit parallelization for high performance simulations. Overall, the FFX platform serves as a computational microscope to study systems ranging from organic crystals to solvated biomolecular systems.
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Affiliation(s)
- Rose A. Gogal
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, USA
| | - Aaron J. Nessler
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, USA
| | - Andrew C. Thiel
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, USA
| | - Hernan V. Bernabe
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, USA
| | - Rae A. Corrigan Grove
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Leah M. Cousineau
- Department of Biochemistry and Molecular Biology, University of Iowa, Iowa City, Iowa 52242, USA
| | - Jacob M. Litman
- Department of Biochemistry and Molecular Biology, University of Iowa, Iowa City, Iowa 52242, USA
| | - Jacob M. Miller
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, USA
| | - Guowei Qi
- Department of Biochemistry and Molecular Biology, University of Iowa, Iowa City, Iowa 52242, USA
| | - Matthew J. Speranza
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, USA
| | - Mallory R. Tollefson
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, USA
| | - Timothy D. Fenn
- Analytical Development, LEXEO Therapeutics, New York, New York 10010, USA
| | - Jacob J. Michaelson
- Department of Psychiatry, University of Iowa Hospitals and Clinics, Iowa City, Iowa 52242, USA
| | - Okimasa Okada
- Sohyaku Innovative Research Division, Mitsubishi Tanabe Pharma Corporation, 1000 Kamoshida-cho, Aoba-ku, Yokohama, Kanagawa 227-0033, Japan
| | | | - Jay W. Ponder
- Department of Chemistry, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Jana Shen
- Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, Baltimore, Maryland 21201, USA
| | - Richard J. H. Smith
- Molecular Otolaryngology and Renal Research Laboratories, Department of Otolaryngology, University of Iowa Hospitals and Clinics, Iowa City, Iowa 52242, USA
| | | | - Pengyu Ren
- Department of Biomedical Engineering, University of Texas, Austin, Texas 78712, USA
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2
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Corrigan RA, Thiel AC, Lynn JR, Casavant TL, Ren P, Ponder JW, Schnieders MJ. A generalized Kirkwood implicit solvent for the polarizable AMOEBA protein model. J Chem Phys 2023; 159:054102. [PMID: 37526158 PMCID: PMC10396400 DOI: 10.1063/5.0158914] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 07/17/2023] [Indexed: 08/02/2023] Open
Abstract
Computational simulation of biomolecules can provide important insights into protein design, protein-ligand binding interactions, and ab initio biomolecular folding, among other applications. Accurate treatment of the solvent environment is essential in such applications, but the use of explicit solvents can add considerable cost. Implicit treatment of solvent effects using a dielectric continuum model is an attractive alternative to explicit solvation since it is able to describe solvation effects without the inclusion of solvent degrees of freedom. Previously, we described the development and parameterization of implicit solvent models for small molecules. Here, we extend the parameterization of the generalized Kirkwood (GK) implicit solvent model for use with biomolecules described by the AMOEBA force field via the addition of corrections to the calculation of effective radii that account for interstitial spaces that arise within biomolecules. These include element-specific pairwise descreening scale factors, a short-range neck contribution to describe the solvent-excluded space between pairs of nearby atoms, and finally tanh-based rescaling of the overall descreening integral. We then apply the AMOEBA/GK implicit solvent to a set of ten proteins and achieve an average coordinate root mean square deviation for the experimental structures of 2.0 Å across 500 ns simulations. Overall, the continued development of implicit solvent models will help facilitate the simulation of biomolecules on mechanistically relevant timescales.
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Affiliation(s)
- Rae A. Corrigan
- Roy J. Carver Department of Biomedical Engineering, The University of Iowa, Iowa City, Iowa 52242, USA
| | - Andrew C. Thiel
- Roy J. Carver Department of Biomedical Engineering, The University of Iowa, Iowa City, Iowa 52242, USA
| | - Jack R. Lynn
- Roy J. Carver Department of Biomedical Engineering, The University of Iowa, Iowa City, Iowa 52242, USA
| | - Thomas L. Casavant
- Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, Iowa 52242, USA
| | - Pengyu Ren
- Department of Biomedical Engineering, The University of Texas in Austin, Austin, Texas 78712, USA
| | - Jay W. Ponder
- Department of Chemistry, Washington University in St. Louis, St. Louis, Missouri 63130, USA
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3
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Rackers JA, Silva RR, Wang Z, Ponder JW. Polarizable Water Potential Derived from a Model Electron Density. J Chem Theory Comput 2021; 17:7056-7084. [PMID: 34699197 DOI: 10.1021/acs.jctc.1c00628] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A new empirical potential for efficient, large scale molecular dynamics simulation of water is presented. The HIPPO (Hydrogen-like Intermolecular Polarizable POtential) force field is based upon the model electron density of a hydrogen-like atom. This framework is used to derive and parametrize individual terms describing charge penetration damped permanent electrostatics, damped polarization, charge transfer, anisotropic Pauli repulsion, and damped dispersion interactions. Initial parameter values were fit to Symmetry Adapted Perturbation Theory (SAPT) energy components for ten water dimer configurations, as well as the radial and angular dependence of the canonical dimer. The SAPT-based parameters were then systematically refined to extend the treatment to water bulk phases. The final HIPPO water model provides a balanced representation of a wide variety of properties of gas phase clusters, liquid water, and ice polymorphs, across a range of temperatures and pressures. This water potential yields a rationalization of water structure, dynamics, and thermodynamics explicitly correlated with an ab initio energy decomposition, while providing a level of accuracy comparable or superior to previous polarizable atomic multipole force fields. The HIPPO water model serves as a cornerstone around which similarly detailed physics-based models can be developed for additional molecular species.
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Affiliation(s)
- Joshua A Rackers
- Program in Computational & Molecular Biophysics, Washington University School of Medicine, Saint Louis, Missouri 63110, United States.,Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123, United States
| | - Roseane R Silva
- Program in Computational & Molecular Biophysics, Washington University School of Medicine, Saint Louis, Missouri 63110, United States
| | - Zhi Wang
- Department of Chemistry, Washington University in Saint Louis, Saint Louis, Missouri 63130, United States
| | - Jay W Ponder
- Department of Chemistry, Washington University in Saint Louis, Saint Louis, Missouri 63130, United States.,Department of Biochemistry & Molecular Biophysics, Washington University School of Medicine, Saint Louis, Missouri 63110, United States
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4
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Amin M, Barzegari E, Pourshohod A, Zeinali M, Jamalan M. 3D structure prediction, dynamic investigation and rational construction of an epitope-masked thermostable bovine hyaluronidase. Int J Biol Macromol 2021; 187:544-553. [PMID: 34298049 DOI: 10.1016/j.ijbiomac.2021.07.098] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2021] [Revised: 07/14/2021] [Accepted: 07/14/2021] [Indexed: 01/11/2023]
Abstract
Hyaluronidase (HAase) from bovine testes (BTH) has long been used in broad pharmaceutical areas, while it is associated with drawbacks in aspects of solubility, immunogenicity and pharmacokinetics. These issues can be addressed by gaining structural insights and designing rational modifications to the enzyme structure, as proposed in this study. A 3D structural model was built for HAase and underwent 40 ns of molecular dynamic simulation to examine its thermostability under normal, melting, and extreme conditions. The enzyme activity of BTH was measured against temperature and pH by kinetic assays. The interaction of bovine HAase with HA and chondroitin was defined by molecular docking. Furthermore, immunogenic properties of the enzyme were explored by immunoinformatics. Thermal effects on bovine HAase structural model and the HAase interactions with its substrates were described. We identified some B- and T-cell epitopes and showed that the protein could be recognized by human immune receptor molecules. Epitope masking by adding polyethylene glycol (PEG) to amine groups of residues presenting on the surface of the protein structure was adopted as a surface modification to enhance pharmacological properties of BTH. Assays showed that PEGylated BTH had higher thermostability and similar activity compared to the native enzyme.
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Affiliation(s)
- Mansour Amin
- Department of Microbiology, School of Medicine, Dezful University of Medical Sciences, Dezful, Iran
| | - Ebrahim Barzegari
- Medical Biology Research Center, Health Technology Institute, Kermanshah University of Medical Sciences, Kermanshah, Iran
| | - Aminollah Pourshohod
- Department of Biochemistry, Cellular and Molecular Research Center, Ahvaz Jundishapur University of Medical Science, Medical School, Ahvaz, Iran
| | - Majid Zeinali
- Biotechnology Research Center, Research Institute of Petroleum Industry (RIPI), Tehran, Iran
| | - Mostafa Jamalan
- Department of Biochemistry, Abadan University of Medical Sciences, Abadan, Iran.
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5
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Jamalan M, Barzegari E, Gholami-Borujeni F. Structure-Based Screening to Discover New Inhibitors for Papain-like Proteinase of SARS-CoV-2: An In Silico Study. J Proteome Res 2021; 20:1015-1026. [PMID: 33350309 PMCID: PMC7770893 DOI: 10.1021/acs.jproteome.0c00836] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Indexed: 12/23/2022]
Abstract
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) expresses a multifunctional papain-like proteinase (PLpro), which mediates the processing of the viral replicase polyprotein. Inhibition of PLpro has been shown to suppress the viral replication. This study aimed to explore new anti-PLpro candidates by applying virtual screening based on GRL0617, a known PLpro inhibitor of SARS coronavirus (SARS-CoV). The three-dimensional (3D) structure of SARS-CoV-2 PLpro was built by homology modeling, using SARS-CoV PLpro as the template. The model was refined and studied through molecular dynamic simulation. AutoDock Vina was then used to perform virtual screening where 50 chemicals with at least 65% similarity to GRL0617 were docked with the optimized SARS-CoV-2 PLpro. In this screening, 5-(aminomethyl)-2-methyl-N-[(1R)-1-naphthalen-1-ylethyl]benzamide outperformed GRL0617 in terms of binding affinity (-9.7 kcal/mol). Furthermore, 2-(4-fluorobenzyl)-5-nitro-1H-isoindole-1,3(2H)-dione (previously introduced as an inhibitor of cyclooxygenase-2), 3-nitro-N-[(1r)-1-phenylethyl]-5-(trifluoromethyl)benzamide (inhibitor against Mycobacterium tuberculosis), as well as the recently introduced SARS-CoV-2 PLpro inhibitor 5-acetamido-2-methyl-N-[(1S)-1-naphthalen-1-ylethyl]benzamide showed promising affinity for the viral proteinase. All of the identified compounds demonstrated an acceptable pharmacokinetic profile. In conclusion, our findings represent rediscovery of analgesic, anti-inflammatory, antibacterial, or antiviral drugs as promising pharmaceutical candidates against the ongoing coronavirus.
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Affiliation(s)
- Mostafa Jamalan
- Department
of Biochemistry, Abadan Faculty of Medical
Sciences, Abadan 6313833177, Iran
| | - Ebrahim Barzegari
- Medical
Biology Research Center, Health Technology Institute, Kermanshah University of Medical Sciences, Kermanshah 6715847141, Iran
| | - Fathollah Gholami-Borujeni
- Department
of Environmental Health, Mazandaran University
of Medical Sciences, Mazandaran 4815733971, Iran
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6
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Teng X, Liu B, Ichiye T. Understanding how water models affect the anomalous pressure dependence of their diffusion coefficients. J Chem Phys 2020; 153:104510. [PMID: 32933292 DOI: 10.1063/5.0021472] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
The self-diffusion coefficient of water shows an anomalous increase with increasing hydrostatic pressure up to a broad maximum (PmD) near 1 kbar at 298 K, which has been attributed to pressure effects on the tetrahedral hydrogen bond network of water. Moreover, the ability of a water model to reproduce anomalous properties of water is a signature that it is reproducing the network. Here, water was simulated between 1 bar and 5 kbar using three water models, two four-site (with all charges in the molecular plane) and one single-site multipole (which accounts for out-of-molecular plane charge), that have reasonable pressure-temperature properties. For these three models, the diffusion coefficients display a maximum in the pressure dependence and the radial distribution functions show good agreement with the limited experimental structural data at high pressure that are available. In addition, a variety of properties associated with the network are examined, including hydrogen bond lifetimes and occupancies, three-body angle distributions, and tetrahedral order parameters. Results suggest that the initial increasing diffusion with pressure is because hydrogen bonds are distorted and thus weakened by pressure, but above PmD, the hydrogen bonds are weakened to the point it behaves more like a normal liquid. In other words, the PmD may be a measure of the angular strength of hydrogen bonds. In addition, since the four-site models over-predict the values of PmD while the multipole model under-predicts it, out-of-plane charge may improve four-site models.
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Affiliation(s)
- Xiaojing Teng
- Department of Chemistry, Georgetown University, Washington, DC 20057, USA
| | - Bailang Liu
- Department of Chemistry, Georgetown University, Washington, DC 20057, USA
| | - Toshiko Ichiye
- Department of Chemistry, Georgetown University, Washington, DC 20057, USA
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7
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Burnham CJ, English NJ. A New Relatively Simple Approach to Multipole Interactions in Either Spherical Harmonics or Cartesians, Suitable for Implementation into Ewald Sums. Int J Mol Sci 2019; 21:ijms21010277. [PMID: 31906127 PMCID: PMC7017380 DOI: 10.3390/ijms21010277] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Revised: 12/12/2019] [Accepted: 12/20/2019] [Indexed: 11/16/2022] Open
Abstract
We present a novel derivation of the multipole interaction (energies, forces and fields) in spherical harmonics, which results in an expression that is able to exactly reproduce the results of earlier Cartesian formulations. Our method follows the derivations of Smith (W. Smith, CCP5 Newsletter 1998, 46, 18.) and Lin (D. Lin, J. Chem. Phys. 2015, 143, 114115), who evaluate the Ewald sum for multipoles in Cartesian form, and then shows how the resulting expressions can be converted into spherical harmonics, where the conversion is performed by establishing a relation between an inner product on the space of symmetric traceless Cartesian tensors, and an inner product on the space of harmonic polynomials on the unit sphere. We also introduce a diagrammatic method for keeping track of the terms in the multipole interaction expression, such that the total electrostatic energy can be viewed as a 'sum over diagrams', and where the conversion to spherical harmonics is represented by 'braiding' subsets of Cartesian components together. For multipoles of maximum rank n, our algorithm is found to have scaling of n 3.7 vs. n 4.5 for our most optimised Cartesian implementation.
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8
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Bedrov D, Piquemal JP, Borodin O, MacKerell AD, Roux B, Schröder C. Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields. Chem Rev 2019; 119:7940-7995. [PMID: 31141351 PMCID: PMC6620131 DOI: 10.1021/acs.chemrev.8b00763] [Citation(s) in RCA: 284] [Impact Index Per Article: 56.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 11/30/2022]
Abstract
Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.
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Affiliation(s)
- Dmitry Bedrov
- Department
of Materials Science & Engineering, University of Utah, 122 South Central Campus Drive, Room 304, Salt Lake City, Utah 84112, United States
| | - Jean-Philip Piquemal
- Laboratoire
de Chimie Théorique, Sorbonne Université,
UMR 7616 CNRS, CC137, 4 Place Jussieu, Tour 12-13, 4ème étage, 75252 Paris Cedex 05, France
- Institut
Universitaire de France, 75005, Paris Cedex 05, France
- Department
of Biomedical Engineering, The University
of Texas at Austin, Austin, Texas 78712, United States
| | - Oleg Borodin
- Electrochemistry
Branch, Sensors and Electron Devices Directorate, Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20703, United
States
| | - Alexander D. MacKerell
- Department
of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, Maryland 21201, United
States
| | - Benoît Roux
- Department
of Biochemistry and Molecular Biology, Gordon Center for Integrative
Science, University of Chicago, 929 57th Street, Chicago, Illinois 60637, United States
| | - Christian Schröder
- Department
of Computational Biological Chemistry, University
of Vienna, Währinger Strasse 17, A-1090 Vienna, Austria
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9
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Jing Z, Liu C, Cheng SY, Qi R, Walker BD, Piquemal JP, Ren P. Polarizable Force Fields for Biomolecular Simulations: Recent Advances and Applications. Annu Rev Biophys 2019; 48:371-394. [PMID: 30916997 DOI: 10.1146/annurev-biophys-070317-033349] [Citation(s) in RCA: 222] [Impact Index Per Article: 44.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Realistic modeling of biomolecular systems requires an accurate treatment of electrostatics, including electronic polarization. Due to recent advances in physical models, simulation algorithms, and computing hardware, biomolecular simulations with advanced force fields at biologically relevant timescales are becoming increasingly promising. These advancements have not only led to new biophysical insights but also afforded opportunities to advance our understanding of fundamental intermolecular forces. This article describes the recent advances and applications, as well as future directions, of polarizable force fields in biomolecular simulations.
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Affiliation(s)
- Zhifeng Jing
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
| | - Chengwen Liu
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
| | - Sara Y Cheng
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
| | - Rui Qi
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
| | - Brandon D Walker
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
| | - Jean-Philip Piquemal
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA; .,Sorbonne Université, CNRS, Laboratoire de Chimie Theórique, 75252 Paris CEDEX 05, France.,Institut Universitaire de France, 75005 Paris, France
| | - Pengyu Ren
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
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10
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Abstract
Molecular dynamics (MD) simulations have been widely applied to computer-aided drug design (CADD). While MD has been used in a variety of applications such as free energy perturbation and long-time simulations, the accuracy of the results from those methods depends strongly on the force field used. Force fields for small molecules are crucial, as they not only serve as building blocks for developing force fields for larger biomolecules but also act as model compounds that will be transferred to ligands used in CADD. Currently, a wide range of small molecule force fields based on additive or nonpolarizable models have been developed. While these nonpolarizable force fields can produce reasonable estimations of physical properties and have shown success in a variety of systems, there is still room for improvements due to inherent limitations in these models including the lack of an electronic polarization response. For this reason, incorporating polarization effects into the energy function underlying a force field is believed to be an important step forward, giving rise to the development of polarizable force fields. Recent simulations of biological systems have indicated that polarizable force fields are able to provide a better physical representation of intermolecular interactions and, in many cases, better agreement with experimental properties than nonpolarizable, additive force fields. Therefore, this chapter focuses on the development of small molecule force fields with emphasis on polarizable models. It begins with a brief introduction on the importance of small molecule force fields and their evolution from additive to polarizable force fields. Emphasis is placed on the additive CHARMM General Force Field and the polarizable force field based on the classical Drude oscillator. The theory for the Drude polarizable force field and results for small molecules are presented showing their improvements over the additive model. The potential importance of polarization for their application in a wide range of biological systems including CADD is then discussed.
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Affiliation(s)
- Fang-Yu Lin
- Department of Pharmaceutical Sciences, Computer-Aided Drug Design Center, School of Pharmacy, University of Maryland, Baltimore, MD, USA
| | - Alexander D MacKerell
- Department of Pharmaceutical Sciences, Computer-Aided Drug Design Center, School of Pharmacy, University of Maryland, Baltimore, MD, USA.
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11
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Stamm B, Lagardère L, Polack É, Maday Y, Piquemal JP. A coherent derivation of the Ewald summation for arbitrary orders of multipoles: The self-terms. J Chem Phys 2018; 149:124103. [PMID: 30278683 DOI: 10.1063/1.5044541] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we provide the mathematical elements we think essential for a proper understanding of the calculus of the electrostatic energy of point-multipoles of arbitrary order under periodic boundary conditions. The emphasis is put on the expressions of the so-called self-parts of the Ewald summation where different expressions can be found in the literature. Indeed, such expressions are of prime importance in the context of new generation polarizable force field where the self-field appears in the polarization equations. We provide a general framework, where the idea of the Ewald splitting is applied to the electric potential and, subsequently, all other quantities such as the electric field, the energy, and the forces are derived consistently thereof. Mathematical well-posedness is shown for all these contributions for any order of multipolar distribution.
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Affiliation(s)
- Benjamin Stamm
- Center for Computational Engineering Science, RWTH Aachen University, Aachen, Germany
| | - Louis Lagardère
- Institut des Sciences du Calcul et des Données, Sorbonne Université, Paris, France
| | - Étienne Polack
- Laboratoire de Chimie Théorique, Sorbonne Université, UMR 7616 CNRS, Paris, France
| | - Yvon Maday
- Laboratoire Jacques-Louis Lions, LJLL, Sorbonne Université, Université Paris-Diderot SPC, CNRS, F-75005 Paris, France
| | - Jean-Philip Piquemal
- Laboratoire de Chimie Théorique, Sorbonne Université, UMR 7616 CNRS, Paris, France
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12
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Huang J, Simmonett AC, Pickard FC, MacKerell AD, Brooks BR. Mapping the Drude polarizable force field onto a multipole and induced dipole model. J Chem Phys 2018; 147:161702. [PMID: 29096511 DOI: 10.1063/1.4984113] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
The induced dipole and the classical Drude oscillator represent two major approaches for the explicit inclusion of electronic polarizability into force field-based molecular modeling and simulations. In this work, we explore the equivalency of these two models by comparing condensed phase properties computed using the Drude force field and a multipole and induced dipole (MPID) model. Presented is an approach to map the electrostatic model optimized in the context of the Drude force field onto the MPID model. Condensed phase simulations on water and 15 small model compounds show that without any reparametrization, the MPID model yields properties similar to the Drude force field with both models yielding satisfactory reproduction of a range of experimental values and quantum mechanical data. Our results illustrate that the Drude oscillator model and the point induced dipole model are different representations of essentially the same physical model. However, results indicate the presence of small differences between the use of atomic multipoles and off-center charge sites. Additionally, results on the use of dispersion particle mesh Ewald further support its utility for treating long-range Lennard Jones dispersion contributions in the context of polarizable force fields. The main motivation in demonstrating the transferability of parameters between the Drude and MPID models is that the more than 15 years of development of the Drude polarizable force field can now be used with MPID formalism without the need for dual-thermostat integrators nor self-consistent iterations. This opens up a wide range of new methodological opportunities for polarizable models.
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Affiliation(s)
- Jing Huang
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, Baltimore, 20 Penn St., Baltimore, Maryland 21201, USA
| | - Andrew C Simmonett
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, 5635 Fishers Lane, Rockville, Maryland 20852, USA
| | - Frank C Pickard
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, 5635 Fishers Lane, Rockville, Maryland 20852, USA
| | - Alexander D MacKerell
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, Baltimore, 20 Penn St., Baltimore, Maryland 21201, USA
| | - Bernard R Brooks
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, 5635 Fishers Lane, Rockville, Maryland 20852, USA
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13
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Unke OT, Devereux M, Meuwly M. Minimal distributed charges: Multipolar quality at the cost of point charge electrostatics. J Chem Phys 2018; 147:161712. [PMID: 29096479 DOI: 10.1063/1.4993424] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
Most empirical force fields use atom-centered point charges (PCs) to represent the electrostatic potential (ESP) around molecules. While such PC models are computationally efficient, they are unable to capture anisotropic electronic features, such as σ holes or lone pairs. These features are better described using atomic multipole (MTP) moments, which significantly improve the quality of the resulting ESP. However, the improvement comes at the expense of a considerably increased computational complexity and cost for calculating the interaction energies and forces. In the present work, a novel minimal distributed charge model (MDCM) based on off-centered point charges is presented and the quality of the resulting ESP is compared to the performance of MTPs and atom-centered PC models for several test molecules. All three models are fitted using the same algorithm based on differential evolution, which is available as a Fortran90 program from the authors upon request. We show that the MDCM is capable of approximating the reference ab initio ESP with an accuracy as good as, or better than, MTPs without the need for computationally expensive higher order multipoles. Further it is demonstrated that the MDCM is numerically stable in molecular dynamics simulations and is able to reproduce electrostatic interaction energies and thermodynamic quantities with the same accuracy as MTPs at reduced computational cost.
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Affiliation(s)
- Oliver T Unke
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Mike Devereux
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Markus Meuwly
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
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14
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Boateng HA. Mesh-free hierarchical clustering methods for fast evaluation of electrostatic interactions of point multipoles. J Chem Phys 2018; 147:164104. [PMID: 29096477 DOI: 10.1063/1.4990552] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Electrostatic interactions involving point multipoles are being increasingly implemented to achieve higher accuracy in molecular simulations. A major drawback of multipolar electrostatics is the increased computational cost. Here we develop and compare two Cartesian tree algorithms which employ Taylor approximations and hierarchical clustering to speed up the evaluation of point multipole interactions. We present results from applying the algorithms to compute the free space Coulomb potential and forces of different sets of interacting point multipoles with different densities. The methods achieve high accuracy and speedup of more than an order of magnitude over direct sum calculations and scale well in parallel.
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Affiliation(s)
- H A Boateng
- Department of Mathematics, Bates College, 2 Andrews Rd., Lewiston, Maine 04240, USA
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15
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Dharmawardhana CC, Ichiye T. Building better water models using the shape of the charge distribution of a water molecule. J Chem Phys 2018; 147:194103. [PMID: 29166096 DOI: 10.1063/1.4986070] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
The unique properties of liquid water apparently arise from more than just the tetrahedral bond angle between the nuclei of a water molecule since simple three-site models of water are poor at mimicking these properties in computer simulations. Four- and five-site models add partial charges on dummy sites and are better at modeling these properties, which suggests that the shape of charge distribution is important. Since a multipole expansion of the electrostatic potential describes a charge distribution in an orthogonal basis set that is exact in the limit of infinite order, multipoles may be an even better way to model the charge distribution. In particular, molecular multipoles up to the octupole centered on the oxygen appear to describe the electrostatic potential from electronic structure calculations better than four- and five-site models, and molecular multipole models give better agreement with the temperature and pressure dependence of many liquid state properties of water while retaining the computational efficiency of three-site models. Here, the influence of the shape of the molecular charge distribution on liquid state properties is examined by correlating multipoles of non-polarizable water models with their liquid state properties in computer simulations. This will aid in the development of accurate water models for classical simulations as well as in determining the accuracy needed in quantum mechanical/molecular mechanical studies and ab initio molecular dynamics simulations of water. More fundamentally, this will lead to a greater understanding of how the charge distribution of a water molecule leads to the unique properties of liquid water. In particular, these studies indicate that p-orbital charge out of the molecular plane is important.
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Affiliation(s)
| | - Toshiko Ichiye
- Department of Chemistry, Georgetown University, Washington, DC 20057, USA
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16
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König G, Brooks BR, Thiel W, York DM. On the convergence of multi-scale free energy simulations. MOLECULAR SIMULATION 2018; 44:1062-1081. [PMID: 30581251 DOI: 10.1080/08927022.2018.1475741] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Abstract
In this work we employ simple model systems to evaluate the relative performance of two of the most important free energy methods: The Zwanzig equation (also known as "Free energy perturbation") and Bennett's acceptance ratio method (BAR). Although our examples should be transferable to other kinds of free energy simulations, we focus on applications of multi-scale free energy simulations. Such calculations are especially complex, since they connect two different levels of theory with very different requirements in terms of speed, accuracy, sampling and parallelizability. We try to reconcile all those different factors by developing some simple criteria to guide the early stages of the development of a free energy protocol. This is accomplished by quantifying how many λ intermediate steps and how many potential energy evaluations are necessary in order to reach a certain level of convergence.
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Affiliation(s)
- Gerhard König
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany, EU.,Laboratory for Biomolecular Simulation Research, Center for Integrative Proteomics Research, and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, USA.,Laboratory of Computational Biology, National Heart Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Bernard R Brooks
- Laboratory of Computational Biology, National Heart Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Walter Thiel
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany, EU
| | - Darrin M York
- Laboratory for Biomolecular Simulation Research, Center for Integrative Proteomics Research, and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, USA
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17
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Demerdash O, Wang L, Head‐Gordon T. Advanced models for water simulations. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1355] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Omar Demerdash
- Kenneth S. Pitzer Center for Theoretical Chemistry University of California Berkeley CA USA
- Department of Chemistry University of California Berkeley CA USA
| | - Lee‐Ping Wang
- Department of Chemistry University of California, Davis Davis CA USA
| | - Teresa Head‐Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry University of California Berkeley CA USA
- Department of Chemistry University of California Berkeley CA USA
- Department of Bioengineering University of California Berkeley CA USA
- Department of Chemical and Biomolecular Engineering University of California Berkeley CA USA
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18
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Albaugh A, Head-Gordon T. A New Method for Treating Drude Polarization in Classical Molecular Simulation. J Chem Theory Comput 2017; 13:5207-5216. [PMID: 28965397 DOI: 10.1021/acs.jctc.7b00838] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
With polarization becoming an increasingly common feature in classical molecular simulation, it is important to develop methods that can efficiently and accurately evaluate the many-body polarization solution. In this work, we expand the theoretical framework of our inertial extended Langrangian, self-consistent field iteration-free method (iEL/0-SCF), introduced for point induced dipoles, to the polarization model of a Drude oscillator. When applied to the polarizable simple point charge model (PSPC) for water, our iEL/0-SCF method for Drude polarization is as stable as a well-converged SCF solution and more stable than traditional extended Lagrangian (EL) approaches or EL formulations based on two temperature ensembles where Drude particles are kept "colder" than the real degrees of freedom. We show that the iEL/0-SCF method eliminates the need for mass repartitioning from parent atoms onto Drude particles, obeys system conservation of linear and angular momentum, and permits the extension of the integration time step of a basic molecular dynamics simulation to 6.0 fs for PSPC water.
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Affiliation(s)
- Alex Albaugh
- Departments of Chemical & Biomolecular Engineering, ‡Chemistry, and §Bioengineering, ∥Chemical Sciences Division, Lawrence Berkeley National Laboratory, University of California , Berkeley, California 94720, United States
| | - Teresa Head-Gordon
- Departments of Chemical & Biomolecular Engineering, ‡Chemistry, and §Bioengineering, ∥Chemical Sciences Division, Lawrence Berkeley National Laboratory, University of California , Berkeley, California 94720, United States
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19
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Giese TJ, York DM. Quantum mechanical force fields for condensed phase molecular simulations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:383002. [PMID: 28817382 PMCID: PMC5821073 DOI: 10.1088/1361-648x/aa7c5c] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Molecular simulations are powerful tools for providing atomic-level details into complex chemical and physical processes that occur in the condensed phase. For strongly interacting systems where quantum many-body effects are known to play an important role, density-functional methods are often used to provide the model with the potential energy used to drive dynamics. These methods, however, suffer from two major drawbacks. First, they are often too computationally intensive to practically apply to large systems over long time scales, limiting their scope of application. Second, there remain challenges for these models to obtain the necessary level of accuracy for weak non-bonded interactions to obtain quantitative accuracy for a wide range of condensed phase properties. Quantum mechanical force fields (QMFFs) provide a potential solution to both of these limitations. In this review, we address recent advances in the development of QMFFs for condensed phase simulations. In particular, we examine the development of QMFF models using both approximate and ab initio density-functional models, the treatment of short-ranged non-bonded and long-ranged electrostatic interactions, and stability issues in molecular dynamics calculations. Example calculations are provided for crystalline systems, liquid water, and ionic liquids. We conclude with a perspective for emerging challenges and future research directions.
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20
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Eastman P, Swails J, Chodera JD, McGibbon RT, Zhao Y, Beauchamp KA, Wang LP, Simmonett AC, Harrigan MP, Stern CD, Wiewiora RP, Brooks BR, Pande VS. OpenMM 7: Rapid development of high performance algorithms for molecular dynamics. PLoS Comput Biol 2017; 13:e1005659. [PMID: 28746339 PMCID: PMC5549999 DOI: 10.1371/journal.pcbi.1005659] [Citation(s) in RCA: 1364] [Impact Index Per Article: 194.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Revised: 08/09/2017] [Accepted: 06/27/2017] [Indexed: 01/22/2023] Open
Abstract
OpenMM is a molecular dynamics simulation toolkit with a unique focus on extensibility. It allows users to easily add new features, including forces with novel functional forms, new integration algorithms, and new simulation protocols. Those features automatically work on all supported hardware types (including both CPUs and GPUs) and perform well on all of them. In many cases they require minimal coding, just a mathematical description of the desired function. They also require no modification to OpenMM itself and can be distributed independently of OpenMM. This makes it an ideal tool for researchers developing new simulation methods, and also allows those new methods to be immediately available to the larger community.
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Affiliation(s)
- Peter Eastman
- Department of Chemistry, Stanford University, Stanford, California, United States of America
| | - Jason Swails
- Department of Chemistry and Chemical Biology and BioMaPS Institute, Rutgers University, Piscataway, New Jersey, United States of America
| | - John D Chodera
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York, United States of America
| | - Robert T McGibbon
- Department of Chemistry, Stanford University, Stanford, California, United States of America
| | - Yutong Zhao
- Department of Chemistry, Stanford University, Stanford, California, United States of America
| | - Kyle A Beauchamp
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York, United States of America
| | - Lee-Ping Wang
- Department of Chemistry, University of California, Davis, Davis, California, United States of America
| | - Andrew C Simmonett
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland, United States of America
| | - Matthew P Harrigan
- Department of Chemistry, Stanford University, Stanford, California, United States of America
| | - Chaya D Stern
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York, United States of America.,Tri-Institutional PhD Program in Chemical Biology, Memorial Sloan Kettering Cancer Center, New York, New York, United States of America
| | - Rafal P Wiewiora
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York, United States of America.,Tri-Institutional PhD Program in Chemical Biology, Memorial Sloan Kettering Cancer Center, New York, New York, United States of America
| | - Bernard R Brooks
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland, United States of America
| | - Vijay S Pande
- Department of Chemistry, Stanford University, Stanford, California, United States of America.,Department of Computer Science, Stanford University, Stanford, California, United States of America
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21
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Ojeda-May P, Nam K. Acceleration of Semiempirical QM/MM Methods through Message Passage Interface (MPI), Hybrid MPI/Open Multiprocessing, and Self-Consistent Field Accelerator Implementations. J Chem Theory Comput 2017. [PMID: 28628742 DOI: 10.1021/acs.jctc.7b00322] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The strategy and implementation of scalable and efficient semiempirical (SE) QM/MM methods in CHARMM are described. The serial version of the code was first profiled to identify routines that required parallelization. Afterward, the code was parallelized and accelerated with three approaches. The first approach was the parallelization of the entire QM/MM routines, including the Fock matrix diagonalization routines, using the CHARMM message passage interface (MPI) machinery. In the second approach, two different self-consistent field (SCF) energy convergence accelerators were implemented using density and Fock matrices as targets for their extrapolations in the SCF procedure. In the third approach, the entire QM/MM and MM energy routines were accelerated by implementing the hybrid MPI/open multiprocessing (OpenMP) model in which both the task- and loop-level parallelization strategies were adopted to balance loads between different OpenMP threads. The present implementation was tested on two solvated enzyme systems (including <100 QM atoms) and an SN2 symmetric reaction in water. The MPI version exceeded existing SE QM methods in CHARMM, which include the SCC-DFTB and SQUANTUM methods, by at least 4-fold. The use of SCF convergence accelerators further accelerated the code by ∼12-35% depending on the size of the QM region and the number of CPU cores used. Although the MPI version displayed good scalability, the performance was diminished for large numbers of MPI processes due to the overhead associated with MPI communications between nodes. This issue was partially overcome by the hybrid MPI/OpenMP approach which displayed a better scalability for a larger number of CPU cores (up to 64 CPUs in the tested systems).
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Affiliation(s)
| | - Kwangho Nam
- Department of Chemistry and Biochemistry, University of Texas at Arlington , Arlington, Texas 76019-0065, United States
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22
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Ruiz Pestana L, Mardirossian N, Head-Gordon M, Head-Gordon T. Ab initio molecular dynamics simulations of liquid water using high quality meta-GGA functionals. Chem Sci 2017; 8:3554-3565. [PMID: 30155200 PMCID: PMC6092720 DOI: 10.1039/c6sc04711d] [Citation(s) in RCA: 74] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2016] [Accepted: 02/24/2017] [Indexed: 01/23/2023] Open
Abstract
We have used ab initio molecular dynamics (AIMD) to characterize water properties using two meta-generalized gradient approximation (meta-GGA) functionals, M06-L-D3 and B97M-rV, and compared their performance against a standard GGA corrected for dispersion, revPBE-D3, at ambient conditions (298 K, and 1 g cm-3 or 1 atm). Simulations of the equilibrium density, radial distribution functions, self-diffusivity, the infrared spectrum, liquid dipole moments, and characterizations of the hydrogen bond network show that all three functionals have overcome the problem of the early AIMD simulations that erroneously found ambient water to be highly structured, but they differ substantially among themselves in agreement with experiment on this range of water properties. We show directly using water cluster data up through the pentamer that revPBE-D3 benefits from a cancellation of its intrinsic functional error by running classical trajectories, whereas the meta-GGA functionals are demonstrably more accurate and would require the simulation of nuclear quantum effects to realize better agreement with all cluster and condensed phase properties.
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Affiliation(s)
- Luis Ruiz Pestana
- Chemical Sciences Division , Lawrence Berkeley National Laboratory , Berkeley , USA .
| | - Narbe Mardirossian
- Kenneth S. Pitzer Center for Theoretical Chemistry , Department of Chemistry , University of California , Berkeley , USA
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry , Department of Chemistry , University of California , Berkeley , USA
| | - Teresa Head-Gordon
- Chemical Sciences Division , Lawrence Berkeley National Laboratory , Berkeley , USA .
- Kenneth S. Pitzer Center for Theoretical Chemistry , Department of Chemistry , University of California , Berkeley , USA
- Departments of Chemistry , Bioengineering , Chemical and Biomolecular Engineering , University of California , Berkeley , USA
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23
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Albaugh A, Niklasson AMN, Head-Gordon T. Accurate Classical Polarization Solution with No Self-Consistent Field Iterations. J Phys Chem Lett 2017; 8:1714-1723. [PMID: 28350167 DOI: 10.1021/acs.jpclett.7b00450] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We present a new solution for classical polarization that does not require any self-consistent field iterations, the aspect of classical polarization that makes it computationally expensive. The new method builds upon our iEL/SCF Lagrangian scheme that defines a set of auxiliary induced dipoles whose original purpose was to serve as a time-reversible initial guess to the SCF solution of the set of real induced dipoles. In the new iEL/0-SCF approach the auxiliary dipoles now drive the time evolution of the real induced dipoles such that they stay close to the Born-Oppenheimer surface in order to achieve a truly SCF-less method. We show that the iEL/0-SCF exhibits no loss of simulation accuracy when analyzed across bulk water, low to high concentration salt solutions, and small solutes to large proteins in water. In addition, iEL/0-SCF offers significant computational savings over more expensive SCF calculations based on traditional 1 fs time step integration using symplectic integrators and is as fast as reversible reference system propagator algorithms with an outer 2 fs time step.
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Affiliation(s)
| | - Anders M N Niklasson
- Theoretical Division, Los Alamos National Laboratory , Los Alamos, New Mexico 87545, United States
| | - Teresa Head-Gordon
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, University of California , Berkeley, California 94720, United States
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24
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Wu X, Pickard FC, Brooks BR. Isotropic periodic sum for multipole interactions and a vector relation for calculation of the Cartesian multipole tensor. J Chem Phys 2017; 145:164110. [PMID: 27802614 DOI: 10.1063/1.4966019] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
Isotropic periodic sum (IPS) is a method to calculate long-range interactions based on the homogeneity of simulation systems. By using the isotropic periodic images of a local region to represent remote structures, long-range interactions become a function of the local conformation. This function is called the IPS potential; it folds long-ranged interactions into a short-ranged potential and can be calculated as efficiently as a cutoff method. It has been demonstrated that the IPS method produces consistent simulation results, including free energies, as the particle mesh Ewald (PME) method. By introducing the multipole homogeneous background approximation, this work derives multipole IPS potentials, abbreviated as IPSMm, with m being the maximum order of multipole interactions. To efficiently calculate the multipole interactions in Cartesian space, we propose a vector relation that calculates a multipole tensor as a dot product of a radial potential vector and a directional vector. Using model systems with charges, dipoles, and/or quadrupoles, with and without polarizability, we demonstrate that multipole interactions of order m can be described accurately with the multipole IPS potential of order 2 or m - 1, whichever is higher. Through simulations with the multipole IPS potentials, we examined energetic, structural, and dynamic properties of the model systems and demonstrated that the multipole IPS potentials produce very similar results as PME with a local region radius (cutoff distance) as small as 6 Å.
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Affiliation(s)
- Xiongwu Wu
- Laboratory of Computational Biology, NHLBI, NIH, Bethesda, Maryland 20892, USA
| | - Frank C Pickard
- Laboratory of Computational Biology, NHLBI, NIH, Bethesda, Maryland 20892, USA
| | - Bernard R Brooks
- Laboratory of Computational Biology, NHLBI, NIH, Bethesda, Maryland 20892, USA
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25
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Simmonett AC, Pickard FC, Ponder JW, Brooks BR. An empirical extrapolation scheme for efficient treatment of induced dipoles. J Chem Phys 2017; 145:164101. [PMID: 27802661 DOI: 10.1063/1.4964866] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Many cutting edge force fields include polarization, to enhance their accuracy and range of applicability. In this work, we develop efficient strategies for the induced dipole polarization method. By fitting various orders of perturbation theory (PT) dipoles to a diverse training set, we arrive at a family of fully analytic methods - whose nth order is referred to OPTn - that span the full spectrum of polarization methods from the fast zeroth-order approach that neglects mutual dipole coupling, approaching the fully variational approach at high order. Our training set contains many difficult cases where the PT series diverges, and we demonstrate that our OPTn methods still deliver excellent results in these cases. Our tests show that the OPTn methods exhibit rapid convergence towards the exact answer with each increasing PT order. The fourth order OPT4 method, whose costs are commensurate with three iterations of the leading conjugate gradient method, is a particularly promising candidate to be used as a drop-in replacement for existing solvers without further parameterization.
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Affiliation(s)
- Andrew C Simmonett
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Frank C Pickard
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Jay W Ponder
- Department of Chemistry, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Bernard R Brooks
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
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26
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Rodgers JM, Ichiye T. Multipole moments of water molecules and the aqueous solvation of monovalent ions. J Mol Liq 2017. [DOI: 10.1016/j.molliq.2016.10.007] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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27
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Golze D, Benedikter N, Iannuzzi M, Wilhelm J, Hutter J. Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals. J Chem Phys 2017; 146:034105. [DOI: 10.1063/1.4973510] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Dorothea Golze
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Niels Benedikter
- QMath, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 København, Denmark
| | - Marcella Iannuzzi
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Jan Wilhelm
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Jürg Hutter
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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28
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Albaugh A, Bradshaw RT, Demerdash O, Dziedzic J, Mao Y, Margul DT, Swails J, Boateng HA, Case DA, Eastman P, Essex JW, Head-Gordon M, Pande VS, Ponder J, Shao Y, Skylaris C, Todorov IT, Tuckerman ME, Zeng Q, Head-Gordon T. Advanced Potential Energy Surfaces for Molecular Simulation. J Phys Chem B 2016; 120:9811-32. [PMID: 27513316 PMCID: PMC9113031 DOI: 10.1021/acs.jpcb.6b06414] [Citation(s) in RCA: 65] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Advanced potential energy surfaces are defined as theoretical models that explicitly include many-body effects that transcend the standard fixed-charge, pairwise-additive paradigm typically used in molecular simulation. However, several factors relating to their software implementation have precluded their widespread use in condensed-phase simulations: the computational cost of the theoretical models, a paucity of approximate models and algorithmic improvements that can ameliorate their cost, underdeveloped interfaces and limited dissemination in computational code bases that are widely used in the computational chemistry community, and software implementations that have not kept pace with modern high-performance computing (HPC) architectures, such as multicore CPUs and modern graphics processing units (GPUs). In this Feature Article we review recent progress made in these areas, including well-defined polarization approximations and new multipole electrostatic formulations, novel methods for solving the mutual polarization equations and increasing the MD time step, combining linear-scaling electronic structure methods with new QM/MM methods that account for mutual polarization between the two regions, and the greatly improved software deployment of these models and methods onto GPU and CPU hardware platforms. We have now approached an era where multipole-based polarizable force fields can be routinely used to obtain computational results comparable to state-of-the-art density functional theory while reaching sampling statistics that are acceptable when compared to that obtained from simpler fixed partial charge force fields.
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Affiliation(s)
- Alex Albaugh
- Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720
| | - Richard T. Bradshaw
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, UK
| | - Omar Demerdash
- Department of Chemistry, University of California, Berkeley, CA 94720
| | - Jacek Dziedzic
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, UK
- Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Poland
| | - Yuezhi Mao
- Department of Chemistry, University of California, Berkeley, CA 94720
| | - Daniel T. Margul
- Department of Chemistry, New York University, New York, NY 10003, USA
| | - Jason Swails
- Department of Chemistry and Chemical Biology and BioMaPS Institute, Rutgers University, Piscataway, New Jersey 08854-8066, United States
| | - Henry A. Boateng
- Department of Mathematics, Bates College, 2 Andrews Road, Lewiston, ME 04240
| | - David A. Case
- Department of Chemistry and Chemical Biology and BioMaPS Institute, Rutgers University, Piscataway, New Jersey 08854-8066, United States
| | - Peter Eastman
- Department of Chemistry, Stanford University, Stanford, CA 94305
| | - Jonathan W. Essex
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, UK
| | | | - Vijay S. Pande
- Department of Chemistry, Stanford University, Stanford, CA 94305
| | - Jay Ponder
- Department of Chemistry, Washington University in St. Louis, St. Louis, Missouri, 63130
| | - Yihan Shao
- Q-Chem Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588
| | - Chris Skylaris
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, UK
| | - Illian T. Todorov
- STFC Daresbury Laboratory, Keckwick Lane, Daresbury, Warrington WA4 4AD, UK
| | - Mark E. Tuckerman
- Department of Chemistry, New York University, New York, NY 10003, USA
- Courant Institute of Mathematical Sciences, New York University, New York, NY 10003, USA
- NYU-ECNU, Center for Computational Chemistry at NYU, Shanghai, Shanghai 200062, China
| | - Qiao Zeng
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892
| | - Teresa Head-Gordon
- Department of Chemistry, University of California, Berkeley, CA 94720
- Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720
- Bioengineering, University of California, Berkeley, CA 94720
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29
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König G, Pickard FC, Huang J, Simmonett AC, Tofoleanu F, Lee J, Dral PO, Prasad S, Jones M, Shao Y, Thiel W, Brooks BR. Calculating distribution coefficients based on multi-scale free energy simulations: an evaluation of MM and QM/MM explicit solvent simulations of water-cyclohexane transfer in the SAMPL5 challenge. J Comput Aided Mol Des 2016; 30:989-1006. [PMID: 27577746 DOI: 10.1007/s10822-016-9936-x] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2016] [Accepted: 08/09/2016] [Indexed: 11/29/2022]
Abstract
One of the central aspects of biomolecular recognition is the hydrophobic effect, which is experimentally evaluated by measuring the distribution coefficients of compounds between polar and apolar phases. We use our predictions of the distribution coefficients between water and cyclohexane from the SAMPL5 challenge to estimate the hydrophobicity of different explicit solvent simulation techniques. Based on molecular dynamics trajectories with the CHARMM General Force Field, we compare pure molecular mechanics (MM) with quantum-mechanical (QM) calculations based on QM/MM schemes that treat the solvent at the MM level. We perform QM/MM with both density functional theory (BLYP) and semi-empirical methods (OM1, OM2, OM3, PM3). The calculations also serve to test the sensitivity of partition coefficients to solute polarizability as well as the interplay of the quantum-mechanical region with the fixed-charge molecular mechanics environment. Our results indicate that QM/MM with both BLYP and OM2 outperforms pure MM. However, this observation is limited to a subset of cases where convergence of the free energy can be achieved.
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Affiliation(s)
- Gerhard König
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, MD, 20892, USA. .,Max-Planck-Institut für Kohlenforschung, 45470, Mülheim an der Ruhr, Germany.
| | - Frank C Pickard
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Jing Huang
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Andrew C Simmonett
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Florentina Tofoleanu
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Juyong Lee
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Pavlo O Dral
- Max-Planck-Institut für Kohlenforschung, 45470, Mülheim an der Ruhr, Germany
| | - Samarjeet Prasad
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Michael Jones
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Yihan Shao
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Walter Thiel
- Max-Planck-Institut für Kohlenforschung, 45470, Mülheim an der Ruhr, Germany
| | - Bernard R Brooks
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, MD, 20892, USA
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30
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Elking DM. Torque and atomic forces for Cartesian tensor atomic multipoles with an application to crystal unit cell optimization. J Comput Chem 2016; 37:2067-80. [PMID: 27349179 DOI: 10.1002/jcc.24427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2016] [Accepted: 05/17/2016] [Indexed: 01/31/2023]
Abstract
New equations for torque and atomic force are derived for use in flexible molecule force fields with atomic multipoles. The expressions are based on Cartesian tensors with arbitrary multipole rank. The standard method for rotating Cartesian tensor multipoles and calculating torque is to first represent the tensor with n indexes and 3(n) redundant components. In this work, new expressions for directly rotating the unique (n + 1)(n + 2)/2 Cartesian tensor multipole components Θpqr are given by introducing Cartesian tensor rotation matrix elements X(R). A polynomial expression and a recursion relation for X(R) are derived. For comparison, the analogous rotation matrix for spherical tensor multipoles are the Wigner functions D(R). The expressions for X(R) are used to derive simple equations for torque and atomic force. The torque and atomic force equations are applied to the geometry optimization of small molecule crystal unit cells. In addition, a discussion of computational efficiency as a function of increasing multipole rank is given for Cartesian tensors. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Dennis M Elking
- Openeye Scientific Software, Santa Fe, New Mexico, 87508.,Elking Scientific Modeling, Ballwin, Missouri, 63102
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31
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Hédin F, El Hage K, Meuwly M. A Toolkit to Fit Nonbonded Parameters from and for Condensed Phase Simulations. J Chem Inf Model 2016; 56:1479-89. [PMID: 27438992 DOI: 10.1021/acs.jcim.6b00280] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The quality of atomistic simulations depends decisively on the accuracy of the underlying energy function (force field). Of particular importance for condensed-phase properties are nonbonded interactions, including the electrostatic and Lennard-Jones terms. Permanent atomic multipoles (MTPs) are an extension to common point-charge (PC) representations in atomistic simulations. MTPs are commonly determined from and fitted to an ab initio Electrostatic Potential (ESP), and Lennard-Jones (LJ) parameters are obtained from comparison of experimental and computed observables using molecular dynamics (MD) simulations. For this a set of thermodynamic observables such as density, heat of vaporization, and hydration free energy is chosen, to which the parametrization is fitted. The current work introduces a comprehensive computing environment (Fitting Wizard (FW)) for optimizing nonbonded interactions for atomistic force fields of different qualities. The FW supports fitting of standard PC-based force fields and more physically motivated multipolar (MTP) force fields. A broader study including 20 molecules ranging from N-methyl-acetamide and benzene to halogenated benzenes, phenols, anilines, and pyridines yields a root mean squared deviation for hydration free energies of 0.36 kcal/mol over a range of 8 kcal/mol. It is furthermore shown that PC-based force fields are not necessarily inferior compared to MTP parametrizations depending on the molecule considered.
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Affiliation(s)
- Florent Hédin
- Department of Chemistry, University of Basel , Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Krystel El Hage
- Department of Chemistry, University of Basel , Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Markus Meuwly
- Department of Chemistry, University of Basel , Klingelbergstrasse 80, CH-4056 Basel, Switzerland.,Department of Chemistry, Brown University , Providence, Rhode Island 02912, United States
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32
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Tran KN, Tan ML, Ichiye T. A single-site multipole model for liquid water. J Chem Phys 2016; 145:034501. [DOI: 10.1063/1.4958621] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kelly N. Tran
- Department of Chemistry, Georgetown University, Washington, DC 20057, USA
| | - Ming-Liang Tan
- Department of Chemistry, Georgetown University, Washington, DC 20057, USA
| | - Toshiko Ichiye
- Department of Chemistry, Georgetown University, Washington, DC 20057, USA
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33
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Lin D. Generalized and efficient algorithm for computing multipole energies and gradients based on Cartesian tensors. J Chem Phys 2016; 143:114115. [PMID: 26395695 DOI: 10.1063/1.4930984] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
Accurate representation of intermolecular forces has been the central task of classical atomic simulations, known as molecular mechanics. Recent advancements in molecular mechanics models have put forward the explicit representation of permanent and/or induced electric multipole (EMP) moments. The formulas developed so far to calculate EMP interactions tend to have complicated expressions, especially in Cartesian coordinates, which can only be applied to a specific kernel potential function. For example, one needs to develop a new formula each time a new kernel function is encountered. The complication of these formalisms arises from an intriguing and yet obscured mathematical relation between the kernel functions and the gradient operators. Here, I uncover this relation via rigorous derivation and find that the formula to calculate EMP interactions is basically invariant to the potential kernel functions as long as they are of the form f(r), i.e., any Green's function that depends on inter-particle distance. I provide an algorithm for efficient evaluation of EMP interaction energies, forces, and torques for any kernel f(r) up to any arbitrary rank of EMP moments in Cartesian coordinates. The working equations of this algorithm are essentially the same for any kernel f(r). Recently, a few recursive algorithms were proposed to calculate EMP interactions. Depending on the kernel functions, the algorithm here is about 4-16 times faster than these algorithms in terms of the required number of floating point operations and is much more memory efficient. I show that it is even faster than a theoretically ideal recursion scheme, i.e., one that requires 1 floating point multiplication and 1 addition per recursion step. This algorithm has a compact vector-based expression that is optimal for computer programming. The Cartesian nature of this algorithm makes it fit easily into modern molecular simulation packages as compared with spherical coordinate-based algorithms. A software library based on this algorithm has been implemented in C++11 and has been released.
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Affiliation(s)
- Dejun Lin
- Department of Biochemistry and Biophysics, University of Rochester Medical Center, Rochester, New York 14642, USA
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34
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Giese TJ, York DM. Ambient-Potential Composite Ewald Method for ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulation. J Chem Theory Comput 2016; 12:2611-32. [PMID: 27171914 DOI: 10.1021/acs.jctc.6b00198] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
A new approach for performing Particle Mesh Ewald in ab initio quantum mechanical/molecular mechanical (QM/MM) simulations with extended atomic orbital basis sets is presented. The new approach, the Ambient-Potential Composite Ewald (CEw) method, does not perform the QM/MM interaction with Mulliken charges nor electrostatically fit charges. Instead the nuclei and electron density interact directly with the MM environment, but in a manner that avoids the use of dense Fourier transform grids. By performing the electrostatics with the underlying QM density, the CEw method avoids self-consistent field instabilities that have been encountered with simple charge mapping procedures. Potential of mean force (PMF) profiles of the p-nitrophenyl phosphate dissociation reaction in explicit solvent are computed from PBE0/6-31G* QM/MM molecular dynamics simulations with various electrostatic protocols. The CEw profiles are shown to be stable with respect to real-space Ewald cutoff, whereas the PMFs computed from truncated and switched electrostatics produce artifacts. PBE0/6-311G**, AM1/d-PhoT, and DFTB2 QM/MM simulations are performed to generate two-dimensional PMF profiles of the phosphoryl transesterification reactions with ethoxide and phenoxide leaving groups. The semiempirical models incorrectly produce a concerted ethoxide mechanism, whereas PBE0 correctly produces a stepwise mechanism. The ab initio reaction barriers agree more closely to experiment than the semiempirical models. The failure of Mulliken-charge QM/MM-Ewald is analyzed.
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Affiliation(s)
- Timothy J Giese
- Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology, Rutgers University , Piscataway, New Jersey 08854-8087, United States
| | - Darrin M York
- Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology, Rutgers University , Piscataway, New Jersey 08854-8087, United States
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35
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Simmonett AC, Pickard FC, Shao Y, Cheatham TE, Brooks BR. Efficient treatment of induced dipoles. J Chem Phys 2016; 143:074115. [PMID: 26298123 DOI: 10.1063/1.4928530] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Most existing treatments of induced dipoles in polarizable molecular mechanics force field calculations use either the self-consistent variational method, which is solved iteratively, or the "direct" approximation that is non-iterative as a result of neglecting coupling between induced dipoles. The variational method is usually implemented using assumptions that are only strictly valid under tight convergence of the induced dipoles, which can be computationally demanding to enforce. In this work, we discuss the nature of the errors that result from insufficient convergence and suggest a strategy that avoids such problems. Using perturbation theory to reintroduce the mutual coupling into the direct algorithm, we present a computationally efficient method that combines the precision of the direct approach with the accuracy of the variational approach. By analyzing the convergence of this perturbation series, we derive a simple extrapolation formula that delivers a very accurate approximation to the infinite order solution at the cost of only a few iterations. We refer to the new method as extrapolated perturbation theory. Finally, we draw connections to our previously published permanent multipole algorithm to develop an efficient implementation of the electric field and Thole terms and also derive some necessary, but not sufficient, criteria that force field parameters must obey.
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Affiliation(s)
- Andrew C Simmonett
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Frank C Pickard
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Yihan Shao
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Thomas E Cheatham
- Department of Medicinal Chemistry, University of Utah, Salt Lake City, Utah 84112, USA
| | - Bernard R Brooks
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
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36
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Tan ML, Tran KN, Pickard FC, Simmonett AC, Brooks BR, Ichiye T. Molecular Multipole Potential Energy Functions for Water. J Phys Chem B 2015; 120:1833-42. [DOI: 10.1021/acs.jpcb.5b09565] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ming-Liang Tan
- Department
of Chemistry, Georgetown University, Washington, DC 20057, United States
- Laboratory
of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Rockville, Maryland 20892, United States
| | - Kelly N. Tran
- Department
of Chemistry, Georgetown University, Washington, DC 20057, United States
| | - Frank C. Pickard
- Laboratory
of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Rockville, Maryland 20892, United States
| | - Andrew C. Simmonett
- Laboratory
of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Rockville, Maryland 20892, United States
| | - Bernard R. Brooks
- Laboratory
of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Rockville, Maryland 20892, United States
| | - Toshiko Ichiye
- Department
of Chemistry, Georgetown University, Washington, DC 20057, United States
- Laboratory
of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Rockville, Maryland 20892, United States
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37
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Lee J, Miller BT, Brooks BR. Computational scheme for pH-dependent binding free energy calculation with explicit solvent. Protein Sci 2015; 25:231-43. [PMID: 26189656 PMCID: PMC4815317 DOI: 10.1002/pro.2755] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2015] [Accepted: 07/16/2015] [Indexed: 01/25/2023]
Abstract
We present a computational scheme to compute the pH‐dependence of binding free energy with explicit solvent. Despite the importance of pH, the effect of pH has been generally neglected in binding free energy calculations because of a lack of accurate methods to model it. To address this limitation, we use a constant‐pH methodology to obtain a true ensemble of multiple protonation states of a titratable system at a given pH and analyze the ensemble using the Bennett acceptance ratio (BAR) method. The constant pH method is based on the combination of enveloping distribution sampling (EDS) with the Hamiltonian replica exchange method (HREM), which yields an accurate semi‐grand canonical ensemble of a titratable system. By considering the free energy change of constraining multiple protonation states to a single state or releasing a single protonation state to multiple states, the pH dependent binding free energy profile can be obtained. We perform benchmark simulations of a host‐guest system: cucurbit[7]uril (CB[7]) and benzimidazole (BZ). BZ experiences a large pKa shift upon complex formation. The pH‐dependent binding free energy profiles of the benchmark system are obtained with three different long‐range interaction calculation schemes: a cutoff, the particle mesh Ewald (PME), and the isotropic periodic sum (IPS) method. Our scheme captures the pH‐dependent behavior of binding free energy successfully. Absolute binding free energy values obtained with the PME and IPS methods are consistent, while cutoff method results are off by 2 kcal mol−1. We also discuss the characteristics of three long‐range interaction calculation methods for constant‐pH simulations.
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Affiliation(s)
- Juyong Lee
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute (NHLBI), National Institutes of Health (NIH), Bethesda, Maryland, 20892
| | - Benjamin T Miller
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute (NHLBI), National Institutes of Health (NIH), Bethesda, Maryland, 20892
| | - Bernard R Brooks
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute (NHLBI), National Institutes of Health (NIH), Bethesda, Maryland, 20892
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38
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Boateng HA, Todorov IT. Arbitrary order permanent Cartesian multipolar electrostatic interactions. J Chem Phys 2015; 142:034117. [PMID: 25612699 DOI: 10.1063/1.4905952] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Recently, there has been a concerted effort to implement advanced classical potential energy surfaces by adding higher order multipoles to fixed point charge electrostatics in a bid to increase the accuracy of simulations of condensed phase systems. One major hurdle is the unwieldy nature of the expressions which in part has limited developers mostly to including only dipoles and quadrupoles. In this paper, we present a generalization of the Cartesian formulation of electrostatic multipolar interactions that enables the specification of an arbitrary order of multipoles. Specifically, we derive formulas for arbitrary order implementation of the particle mesh Ewald method and give a closed form formula for the stress tensor in the reciprocal space. In addition, we provide recurrence relations for common electrostatic potentials employed in molecular simulations, which allows for the generalization to arbitrary order and guarantees a computational cost that scales as O(p(3)) for Cartesian multipole interactions of order p.
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Affiliation(s)
- H A Boateng
- STFC Daresbury Laboratory, Keckwick Lane, Daresbury, Warrington WA4 4AD, United Kingdom
| | - I T Todorov
- STFC Daresbury Laboratory, Keckwick Lane, Daresbury, Warrington WA4 4AD, United Kingdom
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39
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Giese T, Panteva MT, Chen H, York DM. Multipolar Ewald methods, 1: theory, accuracy, and performance. J Chem Theory Comput 2015; 11:436-50. [PMID: 25691829 PMCID: PMC4325605 DOI: 10.1021/ct5007983] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2014] [Indexed: 11/29/2022]
Abstract
The Ewald, Particle Mesh Ewald (PME), and Fast Fourier–Poisson (FFP) methods are developed for systems composed of spherical multipole moment expansions. A unified set of equations is derived that takes advantage of a spherical tensor gradient operator formalism in both real space and reciprocal space to allow extension to arbitrary multipole order. The implementation of these methods into a novel linear-scaling modified “divide-and-conquer” (mDC) quantum mechanical force field is discussed. The evaluation times and relative force errors are compared between the three methods, as a function of multipole expansion order. Timings and errors are also compared within the context of the quantum mechanical force field, which encounters primary errors related to the quality of reproducing electrostatic forces for a given density matrix and secondary errors resulting from the propagation of the approximate electrostatics into the self-consistent field procedure, which yields a converged, variational, but nonetheless approximate density matrix. Condensed-phase simulations of an mDC water model are performed with the multipolar PME method and compared to an electrostatic cutoff method, which is shown to artificially increase the density of water and heat of vaporization relative to full electrostatic treatment.
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Affiliation(s)
- Timothy
J. Giese
- Center for Integrative Proteomics
Research, BioMaPS Institute for Quantitative Biology and Department
of Chemistry and Chemical Biology, Rutgers
University, Piscataway, New Jersey 08854-8087, United States
| | - Maria T. Panteva
- Center for Integrative Proteomics
Research, BioMaPS Institute for Quantitative Biology and Department
of Chemistry and Chemical Biology, Rutgers
University, Piscataway, New Jersey 08854-8087, United States
| | - Haoyuan Chen
- Center for Integrative Proteomics
Research, BioMaPS Institute for Quantitative Biology and Department
of Chemistry and Chemical Biology, Rutgers
University, Piscataway, New Jersey 08854-8087, United States
| | - Darrin M. York
- Center for Integrative Proteomics
Research, BioMaPS Institute for Quantitative Biology and Department
of Chemistry and Chemical Biology, Rutgers
University, Piscataway, New Jersey 08854-8087, United States
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40
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Mills MJL, Popelier PLA. Electrostatic Forces: Formulas for the First Derivatives of a Polarizable, Anisotropic Electrostatic Potential Energy Function Based on Machine Learning. J Chem Theory Comput 2014; 10:3840-56. [DOI: 10.1021/ct500565g] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Matthew J. L. Mills
- Manchester
Institute of Biotechnology (MIB), University of Manchester, 131 Princess
Street, Manchester M1 7DN, Great Britain
| | - Paul L. A. Popelier
- School
of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain
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