1
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Zhao S, Cieplak P, Duan Y, Luo R. Assessment of Amino Acid Electrostatic Parametrizations of the Polarizable Gaussian Multipole Model. J Chem Theory Comput 2024; 20:2098-2110. [PMID: 38394331 PMCID: PMC11060985 DOI: 10.1021/acs.jctc.3c01347] [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] [Indexed: 02/25/2024]
Abstract
Accurate parametrization of amino acids is pivotal for the development of reliable force fields for molecular modeling of biomolecules such as proteins. This study aims to assess amino acid electrostatic parametrizations with the polarizable Gaussian Multipole (pGM) model by evaluating the performance of the pGM-perm (with atomic permanent dipoles) and pGM-ind (without atomic permanent dipoles) variants compared to the traditional RESP model. The 100-conf-combterm fitting strategy on tetrapeptides was adopted, in which (1) all peptide bond atoms (-CO-NH-) share identical set of parameters and (2) the total charges of the two terminal N-acetyl (ACE) and N-methylamide (NME) groups were set to neutral. The accuracy and transferability of electrostatic parameters across peptides with varying lengths and real-world examples were examined. The results demonstrate the enhanced performance of the pGM-perm model in accurately representing the electrostatic properties of amino acids. This insight underscores the potential of the pGM-perm model and the 100-conf-combterm strategy for the future development of the pGM force field.
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Affiliation(s)
- Shiji Zhao
- Nurix Therapeutics, Inc., 1700 Owens St. Suite 205, San Francisco, CA 94158, USA
| | - Piotr Cieplak
- SBP Medical Discovery Institute, 10901 North Torrey Pines Road, La Jolla, California 92037, United States
| | - Yong Duan
- UC Davis Genome Center and Department of Biomedical Engineering, University of California, Davis, One Shields Avenue, Davis, California 95616, United States
| | - Ray Luo
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine. Irvine, California 92697, United States
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2
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Huang Z, Zhao S, Cieplak P, Duan Y, Luo R, Wei H. Optimal Scheme to Achieve Energy Conservation in Induced Dipole Models. J Chem Theory Comput 2023; 19:5047-5057. [PMID: 37441805 PMCID: PMC10434752 DOI: 10.1021/acs.jctc.3c00226] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/15/2023]
Abstract
Induced dipole models have proven to be effective tools for simulating electronic polarization effects in biochemical processes, yet their potential has been constrained by energy conservation issue, particularly when historical data is utilized for dipole prediction. This study identifies error outliers as the primary factor causing this failure of energy conservation and proposes a comprehensive scheme to overcome this limitation. Leveraging maximum relative errors as a convergence metric, our data demonstrates that energy conservation can be upheld even when using historical information for dipole predictions. Our study introduces the multi-order extrapolation method to quicken induction iteration and optimize the use of historical data, while also developing the preconditioned conjugate gradient with local iterations to refine the iteration process and effectively remove error outliers. This scheme further incorporates a "peek" step via Jacobi under-relaxation for optimal performance. Simulation evidence suggests that our proposed scheme can achieve energy convergence akin to that of point-charge models within a limited number of iterations, thus promising significant improvements in efficiency and accuracy.
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Affiliation(s)
- Zhen Huang
- Chemical and Materials Physics Graduate Program, University of California, Irvine. Irvine, California 92697, United States
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine. Irvine, California 92697, United States
| | - Shiji Zhao
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine. Irvine, California 92697, United States
- Nurix Therapeutics, Inc., 1700 Owens St. Suite 205, San Francisco, CA 94158, United States
| | - Piotr Cieplak
- SBP Medical Discovery Institute, 10901 North Torrey Pines Road, La Jolla, California 92037, United States
| | - Yong Duan
- UC Davis Genome Center and Department of Biomedical Engineering, University of California, Davis, One Shields Avenue, Davis, California 95616, United States
| | - Ray Luo
- Chemical and Materials Physics Graduate Program, University of California, Irvine. Irvine, California 92697, United States
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine. Irvine, California 92697, United States
| | - Haixin Wei
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine. Irvine, California 92697, United States
- Department of Chemistry & Biochemistry, University of California, San Diego. 9500 Gilman Drive, La Jolla, California 92093, United States
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3
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Zhao S, Cieplak P, Duan Y, Luo R. Transferability of the Electrostatic Parameters of the Polarizable Gaussian Multipole Model. J Chem Theory Comput 2023; 19:924-941. [PMID: 36696564 PMCID: PMC10152989 DOI: 10.1021/acs.jctc.2c01048] [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] [Indexed: 01/26/2023]
Abstract
Accuracy and transferability are the two highly desirable properties of molecular mechanical force fields. Compared with the extensively used point-charge additive force fields that apply fixed atom-centered point partial charges to model electrostatic interactions, polarizable force fields are thought to have the advantage of modeling the atomic polarization effects. Previous works have demonstrated the accuracy of the recently developed polarizable Gaussian multipole (pGM) models. In this work, we assessed the transferability of the electrostatic parameters of the pGM models with (pGM-perm) and without (pGM-ind) atomic permanent dipoles in terms of reproducing the electrostatic potentials surrounding molecules/oligomers absent from electrostatic parameterizations. Encouragingly, both the pGM-perm and pGM-ind models show significantly improved transferability than the additive model in the tests (1) from water monomer to water oligomer clusters; (2) across different conformations of amino acid dipeptides and tetrapeptides; (3) from amino acid tetrapeptides to longer polypeptides; and (4) from nucleobase monomers to Watson-Crick base pair dimers and tetramers. Furthermore, we demonstrated that the double-conformation fittings using amino acid tetrapeptides in the αR and β conformations can result in good transferability not only across different tetrapeptide conformations but also from tetrapeptides to polypeptides with lengths ranging from 1 to 20 repetitive residues for both the pGM-ind and pGM-perm models. In addition, the observation that the pGM-ind model has significantly better accuracy and transferability than the point-charge additive model, even though they have an identical number of parameters, strongly suggest the importance of intramolecular polarization effects. In summary, this and previous works together show that the pGM models possess both accuracy and transferability, which are expected to serve as foundations for the development of next-generation polarizable force fields for modeling various polarization-sensitive biological systems and processes.
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Affiliation(s)
- Shiji Zhao
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine, Irvine, California 92697, United States
| | - Piotr Cieplak
- SBP Medical Discovery Institute, 10901 North Torrey Pines Road, La Jolla, California 92037, United States
| | - Yong Duan
- UC Davis Genome Center and Department of Biomedical Engineering, University of California, Davis, One Shields Avenue, Davis, California 95616, United States
| | - Ray Luo
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine, Irvine, California 92697, United States
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4
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Zhao S, Wei H, Cieplak P, Duan Y, Luo R. Accurate Reproduction of Quantum Mechanical Many-Body Interactions in Peptide Main-Chain Hydrogen-Bonding Oligomers by the Polarizable Gaussian Multipole Model. J Chem Theory Comput 2022; 18:6172-6188. [PMID: 36094401 PMCID: PMC10152986 DOI: 10.1021/acs.jctc.2c00710] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A key advantage of polarizable force fields is their ability to model the atomic polarization effects that play key roles in the atomic many-body interactions. In this work, we assessed the accuracy of the recently developed polarizable Gaussian Multipole (pGM) models in reproducing quantum mechanical (QM) interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions for peptide main-chain hydrogen-bonding conformers, using glycine dipeptide oligomers as the model systems. Two types of pGM models were considered, including that with (pGM-perm) and without (pGM-ind) permanent atomic dipoles. The performances of the pGM models were compared with several widely used force fields, including two polarizable (Amoeba13 and ff12pol) and three additive (ff19SB, ff15ipq, and ff03) force fields. Encouragingly, the pGM models outperform all other force fields in terms of reproducing QM interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions, as measured by the root-mean-square errors (RMSEs) and mean absolute errors (MAEs). Furthermore, we tested the robustness of the pGM models against polarizability parameterization errors by employing alternative polarizabilities that are either scaled or obtained from other force fields. The results show that the pGM models with alternative polarizabilities exhibit improved accuracy in reproducing QM many-body interaction energies as well as the nonadditive and additive contributions compared with other polarizable force fields, suggesting that the pGM models are robust against the errors in polarizability parameterizations. This work shows that the pGM models are capable of accurately modeling polarization effects and have the potential to serve as templates for developing next-generation polarizable force fields for modeling various biological systems.
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Affiliation(s)
- Shiji Zhao
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine, Irvine, California 92697, United States
| | - Haixin Wei
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine, Irvine, California 92697, United States
| | - Piotr Cieplak
- SBP Medical Discovery Institute, 10901 North Torrey Pines Road, La Jolla, California 92037, United States
| | - Yong Duan
- UC Davis Genome Center and Department of Biomedical Engineering, University of California, Davis, One Shields Avenue, Davis, California 95616, United States
| | - Ray Luo
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine, Irvine, California 92697, United States
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5
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Zhao S, Wei H, Cieplak P, Duan Y, Luo R. PyRESP: A Program for Electrostatic Parameterizations of Additive and Induced Dipole Polarizable Force Fields. J Chem Theory Comput 2022; 18:3654-3670. [PMID: 35537209 DOI: 10.1021/acs.jctc.2c00230] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Molecular modeling at the atomic level has been applied in a wide range of biological systems. The widely adopted additive force fields typically use fixed atom-centered partial charges to model electrostatic interactions. However, the additive force fields cannot accurately model polarization effects, leading to unrealistic simulations in polarization-sensitive processes. Numerous efforts have been invested in developing induced dipole-based polarizable force fields. Whether additive atomic charge models or polarizable induced dipole models are used, proper parameterization of the electrostatic term plays a key role in the force field developments. In this work, we present a Python program called PyRESP for performing atomic multipole parameterizations by reproducing ab initio electrostatic potential (ESP) around molecules. PyRESP provides parameterization schemes for several electrostatic models, including the RESP model with atomic charges for the additive force fields and the RESP-ind and RESP-perm models with additional induced and permanent dipole moments for the polarizable force fields. PyRESP is a flexible and user-friendly program that can accommodate various needs during force field parameterizations for molecular modeling of any organic molecules.
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Affiliation(s)
- Shiji Zhao
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine, Irvine, California 92697, United States
| | - Haixin Wei
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine, Irvine, California 92697, United States
| | - Piotr Cieplak
- SBP Medical Discovery Institute, 10901 North Torrey Pines Road, La Jolla, California 92037, United States
| | - Yong Duan
- UC Davis Genome Center and Department of Biomedical Engineering, University of California, Davis, One Shields Avenue, Davis, California 95616, United States
| | - Ray Luo
- Departments of Molecular Biology and Biochemistry, Chemical and Biomolecular Engineering, Materials Science and Engineering, and Biomedical Engineering, University of California, Irvine, Irvine, California 92697, United States
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6
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Corrigan RA, Qi G, Thiel AC, Lynn JR, Walker BD, Casavant TL, Lagardere L, Piquemal JP, Ponder JW, Ren P, Schnieders MJ. Implicit Solvents for the Polarizable Atomic Multipole AMOEBA Force Field. J Chem Theory Comput 2021; 17:2323-2341. [PMID: 33769814 DOI: 10.1021/acs.jctc.0c01286] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Computational protein design, ab initio protein/RNA folding, and protein-ligand screening can be too computationally demanding for explicit treatment of solvent. For these applications, implicit solvent offers a compelling alternative, which we describe here for the polarizable atomic multipole AMOEBA force field based on three treatments of continuum electrostatics: numerical solutions to the nonlinear and linearized versions of the Poisson-Boltzmann equation (PBE), the domain-decomposition conductor-like screening model (ddCOSMO) approximation to the PBE, and the analytic generalized Kirkwood (GK) approximation. The continuum electrostatics models are combined with a nonpolar estimator based on novel cavitation and dispersion terms. Electrostatic model parameters are numerically optimized using a least-squares style target function based on a library of 103 small-molecule solvation free energy differences. Mean signed errors for the adaptive Poisson-Boltzmann solver (APBS), ddCOSMO, and GK models are 0.05, 0.00, and 0.00 kcal/mol, respectively, while the mean unsigned errors are 0.70, 0.63, and 0.58 kcal/mol, respectively. Validation of the electrostatic response of the resulting implicit solvents, which are available in the Tinker (or Tinker-HP), OpenMM, and Force Field X software packages, is based on comparisons to explicit solvent simulations for a series of proteins and nucleic acids. Overall, the emergence of performative implicit solvent models for polarizable force fields opens the door to their use for folding and design applications.
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Affiliation(s)
- Rae A Corrigan
- Roy J Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, United States
| | - Guowei Qi
- Department of Biochemistry, University of Iowa, Iowa City, Iowa 52242, United States
| | - Andrew C Thiel
- Roy J Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, United States
| | - Jack R Lynn
- Roy J Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, United States
| | - Brandon D Walker
- Department of Biomedical Engineering, University of Texas in Austin, Austin, Texas 78712, United States
| | - Thomas L Casavant
- Roy J Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, United States
| | - Louis Lagardere
- Department of Chemistry, Sorbonne Université, F-75005 Paris, France
| | | | - Jay W Ponder
- Department of Chemistry, Washington University in St. Louis, St. Louis, Missouri 63130, United States
| | - Pengyu Ren
- Department of Biomedical Engineering, University of Texas in Austin, Austin, Texas 78712, United States
| | - Michael J Schnieders
- Roy J Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, United States.,Department of Biochemistry, University of Iowa, Iowa City, Iowa 52242, United States
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7
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Cooper CD. A Boundary-Integral Approach for the Poisson-Boltzmann Equation with Polarizable Force Fields. J Comput Chem 2019; 40:1680-1692. [PMID: 30889283 DOI: 10.1002/jcc.25820] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2018] [Revised: 01/11/2019] [Accepted: 02/26/2019] [Indexed: 12/14/2022]
Abstract
Implicit-solvent models are widely used to study the electrostatics in dissolved biomolecules, which are parameterized using force fields. Standard force fields treat the charge distribution with point charges; however, other force fields have emerged which offer a more realistic description by considering polarizability. In this work, we present the implementation of the polarizable and multipolar force field atomic multipole optimized energetics for biomolecular applications (AMOEBA), in the boundary integral Poisson-Boltzmann solver PyGBe. Previous work from other researchers coupled AMOEBA with the finite-difference solver APBS, and found difficulties to effectively transfer the multipolar charge description to the mesh. A boundary integral formulation treats the charge distribution analytically, overlooking such limitations. This becomes particularly important in simulations that need high accuracy, for example, when the quantity of interest is the difference between solvation energies obtained from separate calculations, like happens for binding energy. We present verification and validation results of our software, compare it with the implementation on APBS, and assess the efficiency of AMOEBA and classical point-charge force fields in a Poisson-Boltzmann solver. We found that a boundary integral approach performs similarly to a volumetric method on CPU. Also, we present a GPU implementation of our solver. Moreover, with a boundary element method, the mesh density to correctly resolve the electrostatic potential is the same for standard point-charge and multipolar force fields. Finally, we saw that for binding energy calculations, a boundary integral approach presents more consistent results than a finite difference approximation for multipolar force fields. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Christopher D Cooper
- Departmento de Ingeniería Mecánica and Centro Científico Tecnológico de Valparaíso (CCTVal), Universidad Técnica Federico Santa María, Valparaíso, Chile
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8
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Aleksandrov A, Lin FY, Roux B, MacKerell AD. Combining the polarizable Drude force field with a continuum electrostatic Poisson-Boltzmann implicit solvation model. J Comput Chem 2018; 39:1707-1719. [PMID: 29737546 DOI: 10.1002/jcc.25345] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2017] [Revised: 02/26/2018] [Accepted: 04/08/2018] [Indexed: 12/13/2022]
Abstract
In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson-Boltzmann/solvent-accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self-consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well-experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas-phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute-solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non-polar solvation effects. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Alexey Aleksandrov
- Laboratoire d'Optique et Biosciences, CNRS, INSERM, Ecole Polytechnique, Palaiseau F-91128, France
| | - Fang-Yu Lin
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, Maryland 21201
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, Gordon Center for Integrative Science, 929 E57th Street, University of Chicago, Chicago, Illinois 60637
| | - Alexander D MacKerell
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, Maryland 21201
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9
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Li A, Voronin A, Fenley AT, Gilson MK. Evaluation of Representations and Response Models for Polarizable Force Fields. J Phys Chem B 2016; 120:8668-84. [PMID: 27248842 PMCID: PMC5002935 DOI: 10.1021/acs.jpcb.6b03392] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2016] [Revised: 05/31/2016] [Indexed: 12/02/2022]
Abstract
For classical simulations of condensed-phase systems, such as organic liquids and biomolecules, to achieve high accuracy, they will probably need to incorporate an accurate, efficient model of conformation-dependent electronic polarization. Thus, it is of interest to understand what determines the accuracy of a polarizable electrostatics model. This study approaches this problem by breaking polarization models down into two main components: the representation of electronic polarization and the response model used for mapping from an inducing field to the polarization within the chosen representation. Among the most common polarization representations are redistribution of atom-centered charges, such as those used in the fluctuating charge model, and atom-centered point dipoles, such as those used in a number of different polarization models. Each of these representations has been combined with one or more response models. The response model of fluctuating charge, for example, is based on the idea of electronegativity equalization in the context of changing electrostatic potentials (ESPs), whereas point-dipole representations typically use a response model based on point polarizabilities whose induced dipoles are computed based on interaction with other charges and dipoles. Here, we decouple polarization representations from their typical response models to analyze the strengths and weaknesses of various polarization approximations. First, we compare the maximal possible accuracies achievable by the charge redistribution and point-dipole model representations, by testing their ability to replicate quantum mechanical (QM) ESPs around small molecules polarized by external inducing charges. Perhaps not surprisingly, the atom-centered dipole model can yield higher accuracy. Next, we test two of the most commonly used response functions used for the point-dipole representations, self-consistent and direct (or first-order) inducible point polarizabilities, where the polarizabilities are optimized to best fit the full set of polarized QM potentials for each molecule studied. Strikingly, the induced-dipole response model markedly degrades accuracy relative to that obtainable with optimal point dipoles. In fact, the maximal accuracy achievable with this response model is even lower than that afforded by an optimal charge-redistribution representation. This means that, if coupled with a sufficiently accurate response function, the point-charge representation could outperform the standard induced-dipole model. Furthermore, although a key advantage of the point-dipole representation, relative to charge redistribution, is its ability to capture out-of-plane polarization, the inducible dipole response model causes it to be less accurate than optimal charge redistribution for out-of-plane induction of the planar nitrobenzene molecule. Thus, the widely used inducible dipole response function falls short of the full potential accuracy achievable with the point-dipole representation it employs. Additional results reported here bear on the relative accuracy of self-consistent inducible dipoles versus that of the first-order, or direct, approximation and on methods for assigning partial atomic charges for use in conjunction with inducible dipole models. In sum, these results point to the improvement of polarization response models as an important direction for future research aimed at improving the accuracy of molecular simulations.
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Affiliation(s)
- Amanda Li
- Department
of Bioengineering, University of California,
San Diego, 9500 Gilman
Drive, La Jolla, California 92093-0419, United States
| | - Alexey Voronin
- Skaggs
School of Pharmacy and Pharmaceutical Sciences, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0736, United States
- Lawrence
Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States
| | - Andrew T. Fenley
- Skaggs
School of Pharmacy and Pharmaceutical Sciences, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0736, United States
| | - Michael K. Gilson
- Skaggs
School of Pharmacy and Pharmaceutical Sciences, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0736, United States
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10
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Zhang R, Chen J, Mi J. Evaluation of solvent effect on the amine-based CO2 absorbents by theory and experiment. Theor Chem Acc 2015. [DOI: 10.1007/s00214-015-1637-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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11
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Xiao L, Cai Q, Li Z, Zhao H, Luo R. A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation. Chem Phys Lett 2014; 616-617:67-74. [PMID: 25404761 DOI: 10.1016/j.cplett.2014.10.033] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.
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Affiliation(s)
- Li Xiao
- Department of Biomedical Engineering, University of California, Irvine, CA 92697 ; Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697
| | - Qin Cai
- Department of Biomedical Engineering, University of California, Irvine, CA 92697 ; Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697
| | - Zhilin Li
- Department of Mathematics, North Carolina State University, Raleigh, NC 27695
| | - Hongkai Zhao
- Department of Mathematics, University of California, Irvine, CA 92697
| | - Ray Luo
- Department of Biomedical Engineering, University of California, Irvine, CA 92697 ; Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697 ; Department of Chemical Engineering and Materials Science, University of California, Irvine, CA 92697
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12
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Botello-Smith WM, Cai Q, Luo R. Biological applications of classical electrostatics methods. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2014. [DOI: 10.1142/s0219633614400082] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Continuum electrostatics modeling of solvation based on the Poisson–Boltzmann (PB) equation has gained wide acceptance in biomolecular applications such as energetic analysis and structural visualization. Successful application of the PB solvent models requires careful calibration of the solvation parameters. Extensive testing and validation is also important to ensure accuracy in their applications. Limitation in the continuum modeling of solvation is also a known issue in certain biomolecular applications. Growing interest in membrane systems has further spurred developmental efforts to allow inclusion of membrane in the PB solvent models. Despite their past successes due to careful parameterization, algorithm development and parallel implementation, there is still much to be done to improve their transferability from the small molecular systems upon which they were developed and validated to complex macromolecular systems as advances in technology continue to push forward, providing ever greater computational resources to researchers to study more interesting biological systems of higher complexity.
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Affiliation(s)
- Wesley M. Botello-Smith
- Chemical Physics and Material Physics Graduate Program, University of California, Irvine, CA 92697, USA
- Department of Chemistry, University of California, Irvine, CA 92697, USA
- Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697, USA
| | - Qin Cai
- Department of Biomedical Engineering, University of California, Irvine, CA 92697, USA
- Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697, USA
| | - Ray Luo
- Department of Biomedical Engineering, University of California, Irvine, CA 92697, USA
- Department of Molecular Biology and Biochemistry, University of California, Irvine, CA 92697, USA
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13
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Koehl P, Poitevin F, Orland H, Delarue M. Modified Poisson–Boltzmann equations for characterizing biomolecular solvation. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2014. [DOI: 10.1142/s021963361440001x] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Methods for computing electrostatic interactions often account implicitly for the solvent, due to the much smaller number of degrees of freedom involved. In the Poisson–Boltzmann (PB) approach the electrostatic potential is obtained by solving the Poisson–Boltzmann equation (PBE), where the solvent region is modeled as a homogeneous medium with a high dielectric constant. PB however is not exempt of problems. It does not take into account for example the sizes of the ions in the atmosphere surrounding the solute, nor does it take into account the inhomogeneous dielectric response of water due to the presence of a highly charged surface. In this paper we review two major modifications of PB that circumvent these problems, namely the size-modified PB (SMPB) equation and the Dipolar Poisson–Boltzmann Langevin (DPBL) model. In SMPB, steric effects between ions are accounted for with a lattice gas model. In DPBL, the solvent region is no longer modeled as a homogeneous dielectric media but rather as an assembly of self-orienting interacting dipoles of variable density. This model results in a dielectric profile that transits smoothly from the solute to the solvent region as well as in a variable solvent density that depends on the charges of the solute. We show successful applications of the DPBL formalism to computing the solvation free energies of isolated ions in water. Further developments of more accurately modified PB models are discussed.
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Affiliation(s)
- Patrice Koehl
- Department of Computer Science and Genome Center, University of California, Davis, CA 95616, USA
| | - Frederic Poitevin
- Unité de Dynamique Structurale des Macromolécules, UMR 3528 du CNRS, Institut Pasteur, 75015 Paris, France
| | - Henri Orland
- Service de Physique Théorique, CEA-Saclay, 91191 Gif/Yvette Cedex, France
| | - Marc Delarue
- Unité de Dynamique Structurale des Macromolécules, UMR 3528 du CNRS, Institut Pasteur, 75015 Paris, France
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14
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Bergonzo C, Galindo-Murillo R, Cheatham TE. Molecular modeling of nucleic acid structure: energy and sampling. CURRENT PROTOCOLS IN NUCLEIC ACID CHEMISTRY 2013; 54:7.8.1-7.8.21. [PMID: 24510800 DOI: 10.1002/0471142700.nc0708s54] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
An overview of computer simulation techniques as applied to nucleic acid systems is presented. This unit discusses methods used to treat energy and to sample representative configurations. Emphasis is placed on molecular mechanics and empirical force fields.
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Affiliation(s)
- Christina Bergonzo
- Department of Medicinal Chemistry, College of Pharmacy, University of Utah, Salt Lake City, Utah
| | - Rodrigo Galindo-Murillo
- Department of Medicinal Chemistry, College of Pharmacy, University of Utah, Salt Lake City, Utah
| | - Thomas E Cheatham
- Department of Medicinal Chemistry, College of Pharmacy, University of Utah, Salt Lake City, Utah
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15
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Abstract
This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects.
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16
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Abstract
This chapter provides an overview of the most common methods for including an explicit description of electronic polarization in molecular mechanics force fields: the induced point dipole, shell, and fluctuating charge models. The importance of including polarization effects in biomolecular simulations is discussed, and some of the most important achievements in the development of polarizable biomolecular force fields to date are highlighted.
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Affiliation(s)
- Hanne S Antila
- Department of Chemistry, Aalto University, Espoo, Finland
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17
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Designing electrostatic interactions in biological systems via charge optimization or combinatorial approaches: insights and challenges with a continuum electrostatic framework. Theor Chem Acc 2012. [DOI: 10.1007/s00214-012-1252-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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18
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Overview of computational methods employed in early-stage drug discovery. Future Med Chem 2011; 1:49-63. [PMID: 21426070 DOI: 10.4155/fmc.09.7] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
BACKGROUND The understanding of biomolecular interactions ultimately depends on knowledge about the structural and dynamic details of the interacting system. Rational structure-based drug design implements computational methodology in this rationale. DISCUSSION Together with increasing throughput of structural biology, molecular modeling has progressively contributed to rational drug design and elucidation of nontoxic and patient-tailored interventions, helping to make drug development more cost-efficient. But in this challenging time for the pharmaceutical industry, the successful discovery of novel therapeutics should rely on integration of computational modeling with experimentation when it comes to ligand-binding energetics, system flexibility and genetic diversity/heterogeneity of the target. Moreover, it appears that many drugs--even those for which specific receptors have been identified--intercalate in biological membranes, which could also become the actual target. CONCLUSIONS Understanding the drug-target and drug-unwanted-target interactions at the atomic level is fundamental in the initial phases of the drug development process. Molecular dynamics simulations and complementary computational methods are already contributing in this endeavor for the soluble pharmacological targets and show an increasing importance in the understanding of membrane-ligand interactions.
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Wang J, Cieplak P, Li J, Hou T, Luo R, Duan Y. Development of polarizable models for molecular mechanical calculations I: parameterization of atomic polarizability. J Phys Chem B 2011; 115:3091-9. [PMID: 21391553 DOI: 10.1021/jp112133g] [Citation(s) in RCA: 118] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
In this work, four types of polarizable models have been developed for calculating interactions between atomic charges and induced point dipoles. These include the Applequist, Thole linear, Thole exponential model, and the Thole Tinker-like. The polarizability models have been optimized to reproduce the experimental static molecular polarizabilities obtained from the molecular refraction measurements on a set of 420 molecules reported by Bosque and Sales. We grouped the models into five sets depending on the interaction types, that is, whether the interactions of two atoms that form the bond, bond angle, and dihedral angle are turned off or scaled down. When 1-2 (bonded) and 1-3 (separated by two bonds) interactions are turned off, 1-4 (separated by three bonds) interactions are scaled down, or both, all models including the Applequist model achieved similar performance: the average percentage error (APE) ranges from 1.15 to 1.23%, and the average unsigned error (AUE) ranges from 0.143 to 0.158 Å(3). When the short-range 1-2, 1-3, and full 1-4 terms are taken into account (set D models), the APE ranges from 1.30 to 1.58% for the three Thole models, whereas the Applequist model (DA) has a significantly larger APE (3.82%). The AUE ranges from 0.166 to 0.196 Å(3) for the three Thole models, compared with 0.446 Å(3) for the Applequist model. Further assessment using the 70-molecule van Duijnen and Swart data set clearly showed that the developed models are both accurate and highly transferable and are in fact have smaller errors than the models developed using this particular data set (set E models). The fact that A, B, and C model sets are notably more accurate than both D and E model sets strongly suggests that the inclusion of 1-2 and 1-3 interactions reduces the transferability and accuracy.
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Affiliation(s)
- Junmei Wang
- Department of Pharmacology, University of Texas Southwestern Medical Center at Dallas, Dallas, Texas 75390, USA
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20
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Zhou Y, Duan Y, Yang Y, Faraggi E, Lei H. Trends in template/fragment-free protein structure prediction. Theor Chem Acc 2011; 128:3-16. [PMID: 21423322 PMCID: PMC3030773 DOI: 10.1007/s00214-010-0799-2] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2010] [Accepted: 08/15/2010] [Indexed: 12/13/2022]
Abstract
Predicting the structure of a protein from its amino acid sequence is a long-standing unsolved problem in computational biology. Its solution would be of both fundamental and practical importance as the gap between the number of known sequences and the number of experimentally solved structures widens rapidly. Currently, the most successful approaches are based on fragment/template reassembly. Lacking progress in template-free structure prediction calls for novel ideas and approaches. This article reviews trends in the development of physical and specific knowledge-based energy functions as well as sampling techniques for fragment-free structure prediction. Recent physical- and knowledge-based studies demonstrated that it is possible to sample and predict highly accurate protein structures without borrowing native fragments from known protein structures. These emerging approaches with fully flexible sampling have the potential to move the field forward.
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Affiliation(s)
- Yaoqi Zhou
- School of Informatics, Indiana Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indiana University Purdue University, 719 Indiana Ave #319, Walker Plaza Building, Indianapolis, IN 46202 USA
| | - Yong Duan
- UC Davis Genome Center and Department of Applied Science, University of California, One Shields Avenue, Davis, CA USA
- College of Physics, Huazhong University of Science and Technology, 1037 Luoyu Road, 430074 Wuhan, China
| | - Yuedong Yang
- School of Informatics, Indiana Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indiana University Purdue University, 719 Indiana Ave #319, Walker Plaza Building, Indianapolis, IN 46202 USA
| | - Eshel Faraggi
- School of Informatics, Indiana Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indiana University Purdue University, 719 Indiana Ave #319, Walker Plaza Building, Indianapolis, IN 46202 USA
| | - Hongxing Lei
- UC Davis Genome Center and Department of Applied Science, University of California, One Shields Avenue, Davis, CA USA
- Beijing Institute of Genomics, Chinese Academy of Sciences, 100029 Beijing, China
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21
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Anandakrishnan R, Onufriev AV. An N log N approximation based on the natural organization of biomolecules for speeding up the computation of long range interactions. J Comput Chem 2010; 31:691-706. [PMID: 19569183 PMCID: PMC2818067 DOI: 10.1002/jcc.21357] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Presented here is a method, the hierarchical charge partitioning (HCP) approximation, for speeding up computation of pairwise electrostatic interactions in biomolecular systems. The approximation is based on multiple levels of natural partitioning of biomolecular structures into a hierarchical set of its constituent structural components. The charge distribution in each component is systematically approximated by a small number of point charges, which, for the highest level component, are much fewer than the number of atoms in the component. For short distances from the point of interest, the HCP uses the full set of atomic charges available. For long-distance interactions, the approximate charge distributions with smaller sets of charges are used instead. For a structure consisting of N charges, the computational cost of computing the pairwise interactions via the HCP scales as O(N log N), under assumptions about the structural organization of biomolecular structures generally consistent with reality. A proof-of-concept implementation of the HCP shows that for large structures it can lead to speed-up factors of up to several orders of magnitude relative to the exact pairwise O(N(2)) all-atom computation used as a reference. For structures with more than 2000-3000 atoms the relative accuracy of the HCP (relative root-mean-square force error per atom), approaches the accuracy of the particle mesh Ewald (PME) method with parameter settings typical for biomolecular simulations. When averaged over a set of 600 representative biomolecular structures, the relative accuracies of the two methods are roughly equal. The HCP is also significantly more accurate than the spherical cutoff method. The HCP has been implemented in the freely available nucleic acids builder (NAB) molecular dynamics (MD) package in Amber tools. A 10 ns simulation of a small protein indicates that the HCP based MD simulation is stable, and that it can be faster than the spherical cutoff method. A critical benefit of the HCP approximation is that it is algorithmically very simple, and unlike the PME, the HCP is straightforward to use with implicit solvent models.
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Affiliation(s)
- Ramu Anandakrishnan
- Department of Computer Science, Virginia Tech 2050 Torgersen Hall (0106), Blacksburg, VA 24061 USA
| | - Alexey V. Onufriev
- Departments of Computer Science and Physics, Virginia Tech 2050 Torgersen Hall (0106), Blacksburg, VA 24061
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22
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Cieplak P, Dupradeau FY, Duan Y, Wang J. Polarization effects in molecular mechanical force fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:333102. [PMID: 21828594 PMCID: PMC4020598 DOI: 10.1088/0953-8984/21/33/333102] [Citation(s) in RCA: 195] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
The focus here is on incorporating electronic polarization into classical molecular mechanical force fields used for macromolecular simulations. First, we briefly examine currently used molecular mechanical force fields and the current status of intermolecular forces as viewed by quantum mechanical approaches. Next, we demonstrate how some components of quantum mechanical energy are effectively incorporated into classical molecular mechanical force fields. Finally, we assess the modeling methods of one such energy component-polarization energy-and present an overview of polarizable force fields and their current applications. Incorporating polarization effects into current force fields paves the way to developing potentially more accurate, though more complex, parameterizations that can be used for more realistic molecular simulations.
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Affiliation(s)
- Piotr Cieplak
- Burnham Institute for Medical Research, 10901 North Torrey Pines Road, La Jolla, CA 92120, USA
| | - François-Yves Dupradeau
- UMR CNRS 6219—Faculté de Pharmacie, Université de Picardie Jules Verne, 1 rue des Louvels, F-80037 Amiens, France
| | - Yong Duan
- Genome Center and Department of Applied Science, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA
| | - Junmei Wang
- Department of Pharmacology, University of Texas Southwestern Medical Center, 6001 Forest Park Boulevard, ND9.136, Dallas, TX 75390-9050, USA
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23
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Truchon JF, Nicholls A, Roux B, Iftimie RI, Bayly CI. Integrated Continuum Dielectric Approaches to treat Molecular Polarizability and the Condensed Phase: Refractive Index and Implicit Solvation. J Chem Theory Comput 2009; 5:1785-1802. [PMID: 24826083 DOI: 10.1021/ct900029d] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jean-François Truchon
- Département de chimie, Université de Montréal, C.P. 6128 Succursale centreville, Montréal, Québec, Canada H3C 3J7 ; Merck Frosst Canada Ltd., 16711 TransCanada Highway, Kirkland, Québec, Canada H9H 3L1
| | | | - Benoît Roux
- Institute of Molecular Pediatric Sciences, Gordon Center for Integrative Science, University of Chicago, Illinois 929 East 57 Street, Chicago, Illinois 60637
| | - Radu I Iftimie
- Département de chimie, Université de Montréal, C.P. 6128 Succursale centreville, Montréal, Québec, Canada H3C 3J7
| | - Christopher I Bayly
- Merck Frosst Canada Ltd., 16711 TransCanada Highway, Kirkland, Québec, Canada H9H 3L1
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Cheatham TE, Brooks BR, Kollman PA. Molecular modeling of nucleic acid structure: energy and sampling. CURRENT PROTOCOLS IN NUCLEIC ACID CHEMISTRY 2001; Chapter 7:Unit-7.8. [PMID: 18428876 PMCID: PMC4029503 DOI: 10.1002/0471142700.nc0708s04] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
An overview of computer simulation techniques as applied to nucleic acid systems is presented. This unit expands an accompanying overview unit (UNIT 7.5) by discussing methods used to treat the energy and sample representative configurations. Emphasis is placed on molecular mechanics and empirical force fields.
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