1
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Bosy M, Scroggs MW, Betcke T, Burman E, Cooper CD. Coupling finite and boundary element methods to solve the Poisson-Boltzmann equation for electrostatics in molecular solvation. J Comput Chem 2024; 45:787-797. [PMID: 38126925 DOI: 10.1002/jcc.27262] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Revised: 10/03/2023] [Accepted: 11/05/2023] [Indexed: 12/23/2023]
Abstract
The Poisson-Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to the accurate representation of the molecular surface and partial charges, and exact enforcement of the boundary conditions at infinity. However, the boundary element method is limited to linear equations and piecewise constant variations of the material properties. In this work, we present a scheme that couples finite and boundary elements for the linearised Poisson-Boltzmann equation, where the finite element method is applied in a confined solute region and the boundary element method in the external solvent region. As a proof-of-concept exercise, we use the simplest methods available: Johnson-Nédélec coupling with mass matrix and diagonal preconditioning, implemented using the Bempp-cl and FEniCSx libraries via their Python interfaces. We showcase our implementation by computing the polar component of the solvation free energy of a set of molecules using a constant and a Gaussian-varying permittivity. As validation, we compare against well-established finite difference solvers for an extensive binding energy data set, and with the finite difference code APBS (to 0.5%) for Gaussian permittivities. We also show scaling results from protein G B1 (955 atoms) up to immunoglobulin G (20,148 atoms). For small problems, the coupled method was efficient, outperforming a purely boundary integral approach. For Gaussian-varying permittivities, which are beyond the applicability of boundary elements alone, we were able to run medium to large-sized problems on a single workstation. The development of better preconditioning techniques and the use of distributed memory parallelism for larger systems remains an area for future work. We hope this work will serve as inspiration for future developments that consider space-varying field parameters, and mixed linear-nonlinear schemes for molecular electrostatics with implicit solvent models.
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Affiliation(s)
- Michał Bosy
- School of Computer Science and Mathematics, Kingston University London, Kingston upon Thames, UK
| | | | - Timo Betcke
- Department of Mathematics, University College London, London, UK
| | - Erik Burman
- Department of Mathematics, University College London, London, UK
| | - Christopher D Cooper
- Department of Mechanical Engineering and Centro Científico Tecnológico de Valparaíso, Universidad Técnica Federico Santa María, Valparaíso, Chile
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2
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Lolok N, Sumiwi SA, Ramadhan DSF, Levita J, Sahidin I. Molecular dynamics study of stigmasterol and beta-sitosterol of Morinda citrifolia L. towards α-amylase and α-glucosidase. J Biomol Struct Dyn 2024; 42:1952-1955. [PMID: 37539686 DOI: 10.1080/07391102.2023.2243519] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Accepted: 04/08/2023] [Indexed: 08/05/2023]
Abstract
Previous in vivo studies of Morinda citrifolia (Rubiaceae) reported that the extract inhibited α-amylase and reduced blood glucose levels in streptozotocin-induced diabetes mice. Moreover, molecular docking studies confirmed that ursolic acid and sterol compounds contained in the fruit interacted with important residues in the binding site of α-amylase and α-glucosidase. Our work aimed to study the complex stability of stigmasterol (which has been isolated from the M. citrifolia fruit for the first time) and beta-sitosterol towards α-amylase and α-glucosidase by employing molecular dynamics simulation on GROMACS 2016.3 embedded with the AMBER99SB-ILDN force field. The simulation was carried out for 100 ns at 310 oK. Based on the RMSD and RMSF graphs, the complexes of stigmasterol/α-amylase and stigmasterol/α-glucosidase are more stable compared to acarbose, the known inhibitor of both enzymes. Moreover, beta-sitosterol indicates a better stability complex with α-glucosidase compared to that of acarbose. Interestingly, the affinity of stigmasterol and beta-sitosterol to both enzymes, in terms of the total binding energy, is stronger than that of acarbose. Taken together, stigmasterol and beta-sitosterol in M. citrifolia fruit may have the potency to be developed as α-amylase and α-glucosidase inhibitors.Communicated by Ramaswamy H. Sarma.
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Affiliation(s)
- Nikeherpianti Lolok
- Faculty of Pharmacy, STIKES Mandala Waluya, Kendari, Southeast Sulawesi, Indonesia
- Department of Pharmacology and Clinical Pharmacy, Faculty of Pharmacy, Universitas Padjadjaran, Sumedang, West Java, Indonesia
| | - Sri Adi Sumiwi
- Department of Pharmacology and Clinical Pharmacy, Faculty of Pharmacy, Universitas Padjadjaran, Sumedang, West Java, Indonesia
| | | | - Jutti Levita
- Department of Pharmacology and Clinical Pharmacy, Faculty of Pharmacy, Universitas Padjadjaran, Sumedang, West Java, Indonesia
| | - I Sahidin
- Faculty of Pharmacy, Halu Oleo University, Kendari, Southeast Sulawesi, Indonesia
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3
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Vahid H, Scacchi A, Yang X, Ala-Nissila T, Sammalkorpi M. Modified Poisson–Boltzmann theory for polyelectrolytes in monovalent salt solutions with finite-size ions. J Chem Phys 2022; 156:214906. [DOI: 10.1063/5.0092273] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a soft-potential-enhanced Poisson–Boltzmann (SPB) theory to efficiently capture ion distributions and electrostatic potential around rodlike charged macromolecules. The SPB model is calibrated with a coarse-grained particle-based model for polyelectrolytes (PEs) in monovalent salt solutions as well as compared to a full atomistic molecular dynamics simulation with the explicit solvent. We demonstrate that our modification enables the SPB theory to accurately predict monovalent ion distributions around a rodlike PE in a wide range of ion and charge distribution conditions in the weak-coupling regime. These include excess salt concentrations up to 1M and ion sizes ranging from small ions, such as Na+ or Cl−, to softer and larger ions with a size comparable to the PE diameter. The work provides a simple way to implement an enhancement that effectively captures the influence of ion size and species into the PB theory in the context of PEs in aqueous salt solutions.
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Affiliation(s)
- Hossein Vahid
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
| | - Alberto Scacchi
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
| | - Xiang Yang
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
- Quantum Technology Finland Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
| | - Tapio Ala-Nissila
- Quantum Technology Finland Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland
- Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
| | - Maria Sammalkorpi
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Department of Bioproducts and Biosystems, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
- Academy of Finland Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
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4
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Zhou S, Wang W, Zhou X, Zhang Y, Lai Y, Tang Y, Xu J, Li D, Lin J, Yang X, Ran T, Chen H, Guddat LW, Wang Q, Gao Y, Rao Z, Gong H. Structure of Mycobacterium tuberculosis cytochrome bcc in complex with Q203 and TB47, two anti-TB drug candidates. eLife 2021; 10:69418. [PMID: 34819223 PMCID: PMC8616580 DOI: 10.7554/elife.69418] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2021] [Accepted: 11/05/2021] [Indexed: 01/10/2023] Open
Abstract
Pathogenic mycobacteria pose a sustained threat to global human health. Recently, cytochrome bcc complexes have gained interest as targets for antibiotic drug development. However, there is currently no structural information for the cytochrome bcc complex from these pathogenic mycobacteria. Here, we report the structures of Mycobacterium tuberculosis cytochrome bcc alone (2.68 Å resolution) and in complex with clinical drug candidates Q203 (2.67 Å resolution) and TB47 (2.93 Å resolution) determined by single-particle cryo-electron microscopy. M. tuberculosis cytochrome bcc forms a dimeric assembly with endogenous menaquinone/menaquinol bound at the quinone/quinol-binding pockets. We observe Q203 and TB47 bound at the quinol-binding site and stabilized by hydrogen bonds with the side chains of QcrBThr313 and QcrBGlu314, residues that are conserved across pathogenic mycobacteria. These high-resolution images provide a basis for the design of new mycobacterial cytochrome bcc inhibitors that could be developed into broad-spectrum drugs to treat mycobacterial infections.
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Affiliation(s)
- Shan Zhou
- State Key Laboratory of Medicinal Chemical Biology, College of Pharmacy, Nankai University, Tianjin, China.,State Key Laboratory of Medicinal Chemical Biology, College of Life Sciences, Nankai University, Tianjin, China
| | - Weiwei Wang
- Shanghai Institute for Advanced Immunochemical Studies and School of Life Science and Technology, ShanghaiTech University, Shanghai, China
| | - Xiaoting Zhou
- Shanghai Institute for Advanced Immunochemical Studies and School of Life Science and Technology, ShanghaiTech University, Shanghai, China
| | - Yuying Zhang
- State Key Laboratory of Medicinal Chemical Biology, College of Life Sciences, Nankai University, Tianjin, China
| | - Yuezheng Lai
- State Key Laboratory of Medicinal Chemical Biology, College of Life Sciences, Nankai University, Tianjin, China
| | - Yanting Tang
- State Key Laboratory of Medicinal Chemical Biology, College of Life Sciences, Nankai University, Tianjin, China
| | - Jinxu Xu
- State Key Laboratory of Medicinal Chemical Biology, College of Life Sciences, Nankai University, Tianjin, China
| | - Dongmei Li
- State Key Laboratory of Medicinal Chemical Biology, College of Pharmacy, Nankai University, Tianjin, China
| | - Jianping Lin
- State Key Laboratory of Medicinal Chemical Biology, College of Pharmacy, Nankai University, Tianjin, China
| | - Xiaolin Yang
- Shanghai Institute for Advanced Immunochemical Studies and School of Life Science and Technology, ShanghaiTech University, Shanghai, China
| | - Ting Ran
- Bioland Laboratory (Guangzhou Regenerative Medicine and Health - Guangdong Laboratory), Guangzhou, China
| | - Hongming Chen
- Bioland Laboratory (Guangzhou Regenerative Medicine and Health - Guangdong Laboratory), Guangzhou, China
| | - Luke W Guddat
- School of Chemistry and Molecular Biosciences, The University of Queensland, Brisbane, Australia
| | - Quan Wang
- Shanghai Institute for Advanced Immunochemical Studies and School of Life Science and Technology, ShanghaiTech University, Shanghai, China
| | - Yan Gao
- Shanghai Institute for Advanced Immunochemical Studies and School of Life Science and Technology, ShanghaiTech University, Shanghai, China
| | - Zihe Rao
- State Key Laboratory of Medicinal Chemical Biology, College of Pharmacy, Nankai University, Tianjin, China.,State Key Laboratory of Medicinal Chemical Biology, College of Life Sciences, Nankai University, Tianjin, China.,Shanghai Institute for Advanced Immunochemical Studies and School of Life Science and Technology, ShanghaiTech University, Shanghai, China.,National Laboratory of Biomacromolecules, CAS Center for Excellence in Biomacromolecules, Institute of Biophysics, Beijing, China.,Laboratory of Structural Biology, Tsinghua University, Beijing, China
| | - Hongri Gong
- State Key Laboratory of Medicinal Chemical Biology, College of Life Sciences, Nankai University, Tianjin, China
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5
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Ramm V, Chaudhry JH, Cooper CD. Efficient mesh refinement for the Poisson-Boltzmann equation with boundary elements. J Comput Chem 2021; 42:855-869. [PMID: 33751643 DOI: 10.1002/jcc.26506] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2020] [Revised: 01/20/2021] [Accepted: 02/17/2021] [Indexed: 11/11/2022]
Abstract
The Poisson-Boltzmann equation is a widely used model to study electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate representations of the solute, which is usually a complicated geometry. Here, we utilize adjoint-based analyses to form two goal-oriented error estimates that allow us to determine the contribution of each discretization element (panel) to the numerical error in the solvation free energy. This information is useful to identify high-error panels to then refine them adaptively to find optimal surface meshes. We present results for spheres and real molecular geometries, and see that elements with large error tend to be in regions where there is a high electrostatic potential. We also find that even though both estimates predict different total errors, they have similar performance as part of an adaptive mesh refinement scheme. Our test cases suggest that the adaptive mesh refinement scheme is very effective, as we are able to reduce the error one order of magnitude by increasing the mesh size less than 20% and come out to be more efficient than uniform refinement when computing error estimations. This result sets the basis toward efficient automatic mesh refinement schemes that produce optimal meshes for solvation energy calculations.
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Affiliation(s)
- Vicente Ramm
- Departamento de Ingeniería Mecánica, Universidad Técnica Federico Santa María, Valparaíso, Chile
| | - Jehanzeb H Chaudhry
- Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM, United States
| | - Christopher D Cooper
- Departamento de Ingeniería Mecánica, Universidad Técnica Federico Santa María, Valparaíso, Chile
- Centro Científico Tecnológico de Valparaíso (CCTVal), Universidad Técnica Federico Santa María, Valparaíso, Chile
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6
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Ying J, Xie D. An accelerated nonlocal Poisson-Boltzmann equation solver for electrostatics of biomolecule. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e3129. [PMID: 30021243 DOI: 10.1002/cnm.3129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2018] [Revised: 06/26/2018] [Accepted: 07/05/2018] [Indexed: 06/08/2023]
Abstract
The nonlocal modified Poisson-Boltzmann equation (NMPBE) is one important variant of a commonly used dielectric continuum model, the Poisson-Boltzmann equation (PBE), for computing electrostatics of biomolecules. In this paper, an accelerated NMPBE solver is constructed by finite element and finite difference hybrid techniques. It is then programmed as a software package for computing electrostatic solvation and binding free energies for a protein in a symmetric 1:1 ionic solvent. Numerical results validate the new solver and its numerical stability. They also demonstrate that the new solver has much better performance than the corresponding finite element solver in terms of computer CPU time. Furthermore, they show that the binding free energies produced by NMPBE can match chemical experiment data better than those by PBE.
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Affiliation(s)
- Jinyong Ying
- School of Mathematics and Statistics, Central South University, Changsha, Hunan, China
| | - Dexuan Xie
- Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin
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7
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Izadi S, Harris RC, Fenley MO, Onufriev AV. Accuracy Comparison of Generalized Born Models in the Calculation of Electrostatic Binding Free Energies. J Chem Theory Comput 2018; 14:1656-1670. [PMID: 29378399 DOI: 10.1021/acs.jctc.7b00886] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
The need for accurate yet efficient representation of the aqueous environment in biomolecular modeling has led to the development of a variety of generalized Born (GB) implicit solvent models. While many studies have focused on the accuracy of available GB models in predicting solvation free energies, a systematic assessment of the quality of these models in binding free energy calculations, crucial for rational drug design, has not been undertaken. Here, we evaluate the accuracies of eight common GB flavors (GB-HCT, GB-OBC, GB-neck2, GBNSR6, GBSW, GBMV1, GBMV2, and GBMV3), available in major molecular dynamics packages, in predicting the electrostatic binding free energies ( ΔΔ Gel) for a diverse set of 60 biomolecular complexes belonging to four main classes: protein-protein, protein-drug, RNA-peptide, and small complexes. The GB flavors are examined in terms of their ability to reproduce the results from the Poisson-Boltzmann (PB) model, commonly used as accuracy reference in this context. We show that the agreement with the PB of ΔΔ Gel estimates varies widely between different GB models and also across different types of biomolecular complexes, with R2 correlations ranging from 0.3772 to 0.9986. A surface-based "R6" GB model recently implemented in AMBER shows the closest overall agreement with reference PB ( R2 = 0.9949, RMSD = 8.75 kcal/mol). The RNA-peptide and protein-drug complex sets appear to be most challenging for all but one model, as indicated by the large deviations from the PB in ΔΔ Gel. Small neutral complexes present the least challenge for most of the GB models tested. The quantitative demonstration of the strengths and weaknesses of the GB models across the diverse complex types provided here can be used as a guide for practical computations and future development efforts.
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Affiliation(s)
- Saeed Izadi
- Early Stage Pharmaceutical Development , Genentech Inc. , 1 DNA Way , South San Francisco , California 94080 , United States
| | - Robert C Harris
- Department of Pharmaceutical Sciences , University of Maryland School of Pharmacy , Baltimore , Maryland 21201 , United States
| | - Marcia O Fenley
- Institute of Molecular Biophysics , Florida State University , Tallahassee , Florida 32306-3408 , United States
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8
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Forouzesh N, Izadi S, Onufriev AV. Grid-Based Surface Generalized Born Model for Calculation of Electrostatic Binding Free Energies. J Chem Inf Model 2017; 57:2505-2513. [DOI: 10.1021/acs.jcim.7b00192] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Saeed Izadi
- Early Stage Pharmaceutical
Development, Genentech Inc., 1 DNA
Way, South San Francisco, California 94080, United States
| | - Alexey V. Onufriev
- Center
for Soft Matter and Biological Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States
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9
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Li A, Gao K. Accurate estimation of electrostatic binding energy with Poisson-Boltzmann equation solver DelPhi program. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2016. [DOI: 10.1142/s0219633616500711] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Poisson–Boltzmann (PB) model is a widely used implicit solvent approximation in biophysical modeling because of its ability to provide accurate and reliable PB electrostatic salvation free energies ([Formula: see text] as well as electrostatic binding free energy ([Formula: see text] estimations. However, a recent study has warned that the 0.5[Formula: see text]Å grid spacing which is normally adopted can produce unacceptable errors in [Formula: see text] estimation with the solvent excluded surface (SES) (Harris RC, Boschitsch AH and Fenley MO, Influence of grid spacing in Poisson–Boltzmann equation binding energy estimation, J Chem Theory Comput 19: 3677–3685, 2013). In this work, we investigate the grid dependence of the widely used PB solver DelPhi v6.2 with molecular surface (MS) for estimating both electrostatic solvation free energies and electrostatic binding free energies. Our results indicate that, for the molecular complex and components the absolute errors of [Formula: see text] are smaller than that of [Formula: see text], and grid spacing of 0.8[Formula: see text]Å with DelPhi program ensures the accuracy and reliability of [Formula: see text]; however, the accuracy of [Formula: see text] largely relies on the order of magnitude of [Formula: see text] itself rather than that of [Formula: see text] or [Formula: see text]. Our findings suggest that grid spacing of 0.5[Formula: see text]Å is enough to produce accurate [Formula: see text] for molecules whose [Formula: see text] are large, but finer grids are needed when [Formula: see text] is very small.
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Affiliation(s)
- Anbang Li
- College of Physics Science and Technology, Central China Normal University, Wuhan, P.R. China, 430079, P.R. China
| | - Kaifu Gao
- College of Physics Science and Technology, Central China Normal University, Wuhan, P.R. China, 430079, P.R. China
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10
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Chakavorty A, Li L, Alexov E. Electrostatic component of binding energy: Interpreting predictions from poisson-boltzmann equation and modeling protocols. J Comput Chem 2016; 37:2495-507. [PMID: 27546093 PMCID: PMC5030180 DOI: 10.1002/jcc.24475] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2016] [Revised: 08/03/2016] [Accepted: 08/06/2016] [Indexed: 01/11/2023]
Abstract
Macromolecular interactions are essential for understanding numerous biological processes and are typically characterized by the binding free energy. Important component of the binding free energy is the electrostatics, which is frequently modeled via the solutions of the Poisson-Boltzmann Equations (PBE). However, numerous works have shown that the electrostatic component (ΔΔGelec ) of binding free energy is very sensitive to the parameters used and modeling protocol. This prompted some researchers to question the robustness of PBE in predicting ΔΔGelec . We argue that the sensitivity of the absolute ΔΔGelec calculated with PBE using different input parameters and definitions does not indicate PBE deficiency, rather this is what should be expected. We show how the apparent sensitivity should be interpreted in terms of the underlying changes in several numerous and physical parameters. We demonstrate that PBE approach is robust within each considered force field (CHARMM-27, AMBER-94, and OPLS-AA) once the corresponding structures are energy minimized. This observation holds despite of using two different molecular surface definitions, pointing again that PBE delivers consistent results within particular force field. The fact that PBE delivered ΔΔGelec values may differ if calculated with different modeling protocols is not a deficiency of PBE, but natural results of the differences of the force field parameters and potential functions for energy minimization. In addition, while the absolute ΔΔGelec values calculated with different force field differ, their ordering remains practically the same allowing for consistent ranking despite of the force field used. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Arghya Chakavorty
- Computational Biophysics and Bioinformatics, Department of Physics and Astronomy, Clemson University, Clemson, South Carolina, 29634
| | - Lin Li
- Computational Biophysics and Bioinformatics, Department of Physics and Astronomy, Clemson University, Clemson, South Carolina, 29634
| | - Emil Alexov
- Computational Biophysics and Bioinformatics, Department of Physics and Astronomy, Clemson University, Clemson, South Carolina, 29634.
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11
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Spiliotopoulos D, Kastritis PL, Melquiond ASJ, Bonvin AMJJ, Musco G, Rocchia W, Spitaleri A. dMM-PBSA: A New HADDOCK Scoring Function for Protein-Peptide Docking. Front Mol Biosci 2016; 3:46. [PMID: 27630991 PMCID: PMC5006095 DOI: 10.3389/fmolb.2016.00046] [Citation(s) in RCA: 49] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Accepted: 08/16/2016] [Indexed: 11/13/2022] Open
Abstract
Molecular-docking programs coupled with suitable scoring functions are now established and very useful tools enabling computational chemists to rapidly screen large chemical databases and thereby to identify promising candidate compounds for further experimental processing. In a broader scenario, predicting binding affinity is one of the most critical and challenging components of computer-aided structure-based drug design. The development of a molecular docking scoring function which in principle could combine both features, namely ranking putative poses and predicting complex affinity, would be of paramount importance. Here, we systematically investigated the performance of the MM-PBSA approach, using two different Poisson-Boltzmann solvers (APBS and DelPhi), in the currently rising field of protein-peptide interactions (PPIs), identifying the correct binding conformations of 19 different protein-peptide complexes and predicting their binding free energies. First, we scored the decoy structures from HADDOCK calculation via the MM-PBSA approach in order to assess the capability of retrieving near-native poses in the best-scoring clusters and of evaluating the corresponding free energies of binding. MM-PBSA behaves well in finding the poses corresponding to the lowest binding free energy, however the built-in HADDOCK score shows a better performance. In order to improve the MM-PBSA-based scoring function, we dampened the MM-PBSA solvation and coulombic terms by 0.2, as proposed in the HADDOCK score and LIE approaches. The new dampened MM-PBSA (dMM-PBSA) outperforms the original MM-PBSA and ranks the decoys structures as the HADDOCK score does. Second, we found a good correlation between the dMM-PBSA and HADDOCK scores for the near-native clusters of each system and the experimental binding energies, respectively. Therefore, we propose a new scoring function, dMM-PBSA, to be used together with the built-in HADDOCK score in the context of protein-peptide docking simulations.
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Affiliation(s)
| | - Panagiotis L Kastritis
- Faculty of Science - Chemistry, Bijvoet Center, Utrecht UniversityUtrecht, Netherlands; European Molecular Biology Laboratory HeidelbergHeidelberg, Germany
| | - Adrien S J Melquiond
- Faculty of Science - Chemistry, Bijvoet Center, Utrecht University Utrecht, Netherlands
| | | | - Giovanna Musco
- Biomolecular Nuclear Magnetic Resonance Unit, Ospedale S. Raffaele Milan, Italy
| | - Walter Rocchia
- CONCEPT Lab, Istituto Italiano di Tecnologia Genoa, Italy
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12
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Harris RC, Mackoy T, Fenley MO. Problems of robustness in Poisson-Boltzmann binding free energies. J Chem Theory Comput 2016; 11:705-12. [PMID: 26528091 PMCID: PMC4610304 DOI: 10.1021/ct5005017] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2014] [Indexed: 11/29/2022]
Abstract
Although models based on the Poisson–Boltzmann (PB) equation have been fairly successful at predicting some experimental quantities, such as solvation free energies (ΔG), these models have not been consistently successful at predicting binding free energies (ΔΔG). Here we found that ranking a set of protein–protein complexes by the electrostatic component (ΔΔGel) of ΔΔG was more difficult than ranking the same molecules by the electrostatic component (ΔGel) of ΔG. This finding was unexpected because ΔΔGel can be calculated by combining estimates of ΔGel for the complex and its components with estimates of the ΔΔGel in vacuum. One might therefore expect that if a theory gave reliable estimates of ΔGel, then its estimates of ΔΔGel would be reliable. However, ΔΔGel for these complexes were orders of magnitude smaller than ΔGel, so although estimates of ΔGel obtained with different force fields and surface definitions were highly correlated, similar estimates of ΔΔGel were often not correlated.
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Affiliation(s)
- Robert C Harris
- Sealy Center for Structural Biology and Molecular Biophysics, University of Texas Medical Branch, 301 University Boulevard, Galveston, Texas 77555-0304, United States
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13
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Cumberworth A, Bui JM, Gsponer J. Free energies of solvation in the context of protein folding: Implications for implicit and explicit solvent models. J Comput Chem 2015; 37:629-40. [DOI: 10.1002/jcc.24235] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Revised: 09/25/2015] [Accepted: 10/06/2015] [Indexed: 12/13/2022]
Affiliation(s)
| | | | - Jörg Gsponer
- Center for High-Throughput Biology, UBC; Vancouver Canada
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14
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Ritchie AW, Webb LJ. Understanding and Manipulating Electrostatic Fields at the Protein-Protein Interface Using Vibrational Spectroscopy and Continuum Electrostatics Calculations. J Phys Chem B 2015; 119:13945-57. [PMID: 26375183 DOI: 10.1021/acs.jpcb.5b06888] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Biological function emerges in large part from the interactions of biomacromolecules in the complex and dynamic environment of the living cell. For this reason, macromolecular interactions in biological systems are now a major focus of interest throughout the biochemical and biophysical communities. The affinity and specificity of macromolecular interactions are the result of both structural and electrostatic factors. Significant advances have been made in characterizing structural features of stable protein-protein interfaces through the techniques of modern structural biology, but much less is understood about how electrostatic factors promote and stabilize specific functional macromolecular interactions over all possible choices presented to a given molecule in a crowded environment. In this Feature Article, we describe how vibrational Stark effect (VSE) spectroscopy is being applied to measure electrostatic fields at protein-protein interfaces, focusing on measurements of guanosine triphosphate (GTP)-binding proteins of the Ras superfamily binding with structurally related but functionally distinct downstream effector proteins. In VSE spectroscopy, spectral shifts of a probe oscillator's energy are related directly to that probe's local electrostatic environment. By performing this experiment repeatedly throughout a protein-protein interface, an experimental map of measured electrostatic fields generated at that interface is determined. These data can be used to rationalize selective binding of similarly structured proteins in both in vitro and in vivo environments. Furthermore, these data can be used to compare to computational predictions of electrostatic fields to explore the level of simulation detail that is necessary to accurately predict our experimental findings.
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Affiliation(s)
- Andrew W Ritchie
- Department of Chemistry, Center for Nano- and Molecular Science and Technology, and Institute for Cell and Molecular Biology, The University of Texas at Austin , 105 East 24th Street STOP A5300, Austin, Texas 78712, United States
| | - Lauren J Webb
- Department of Chemistry, Center for Nano- and Molecular Science and Technology, and Institute for Cell and Molecular Biology, The University of Texas at Austin , 105 East 24th Street STOP A5300, Austin, Texas 78712, United States
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15
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Abstract
The calculation of electrostatic solute-solvent interactions in 3D RISM ("three-dimensional reference interaction site model") integral equation theory is recast in a form that allows for a computational treatment analogous to the "particle-mesh Ewald" formalism as used for molecular simulations. In addition, relations that connect 3D RISM correlation functions and interaction potentials with thermodynamic quantities such as the chemical potential and average solute-solvent interaction energy are reformulated in a way that calculations of expensive real-space electrostatic terms on the 3D grid are completely avoided. These methodical enhancements allow for both, a significant speedup particularly for large solute systems and a smoother convergence of predicted thermodynamic quantities with respect to box size, as illustrated for several benchmark systems.
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Affiliation(s)
- Jochen Heil
- Physikalische Chemie III, Technische Universität Dortmund, Otto-Hahn-Str. 6, 44227 Dortmund, Germany
| | - Stefan M Kast
- Physikalische Chemie III, Technische Universität Dortmund, Otto-Hahn-Str. 6, 44227 Dortmund, Germany
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16
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Lei H, Yang X, Zheng B, Lin G, Baker NA. CONSTRUCTING SURROGATE MODELS OF COMPLEX SYSTEMS WITH ENHANCED SPARSITY: QUANTIFYING THE INFLUENCE OF CONFORMATIONAL UNCERTAINTY IN BIOMOLECULAR SOLVATION. MULTISCALE MODELING & SIMULATION : A SIAM INTERDISCIPLINARY JOURNAL 2015; 13:1327-1353. [PMID: 26766929 PMCID: PMC4707684 DOI: 10.1137/140981587] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Biomolecules exhibit conformational fluctuations near equilibrium states, inducing uncertainty in various biological properties in a dynamic way. We have developed a general method to quantify the uncertainty of target properties induced by conformational fluctuations. Using a generalized polynomial chaos (gPC) expansion, we construct a surrogate model of the target property with respect to varying conformational states. To alleviate the high-dimensionality of the corresponding stochastic space, we propose a method to increase the sparsity of the gPC expansion by defining a set of conformational "active space" random variables. With the increased sparsity, we employ the compressive sensing method to accurately construct the surrogate model. We demonstrate the performance of the surrogate model by evaluating fluctuation-induced uncertainty in solvent-accessible surface area for the bovine trypsin inhibitor protein system and show that the new approach offers more accurate statistical information than standard Monte Carlo approaches. Furthermore, the constructed surrogate model also enables us to directly evaluate the target property under various conformational states, yielding a more accurate response surface than standard sparse grid collocation methods. In particular, the new method provides higher accuracy in high-dimensional systems, such as biomolecules, where sparse grid performance is limited by the accuracy of the computed quantity of interest. Our new framework is generalizable and can be used to investigate the uncertainty of a wide variety of target properties in biomolecular systems.
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Affiliation(s)
- H. Lei
- Pacific Northwest National Laboratory, Richland, Washington WA 99352, USA
| | - X. Yang
- Pacific Northwest National Laboratory, Richland, Washington WA 99352, USA
| | - B. Zheng
- Pacific Northwest National Laboratory, Richland, Washington WA 99352, USA
| | - G. Lin
- Department of Mathematics, Purdue University, West Lafayette, IN 47906, USA
| | - N. A. Baker
- Pacific Northwest National Laboratory, Richland, Washington WA 99352, USA
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17
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Tuszynski JA, Winter P, White D, Tseng CY, Sahu KK, Gentile F, Spasevska I, Omar SI, Nayebi N, Churchill CD, Klobukowski M, El-Magd RMA. Mathematical and computational modeling in biology at multiple scales. Theor Biol Med Model 2014; 11:52. [PMID: 25542608 PMCID: PMC4396153 DOI: 10.1186/1742-4682-11-52] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2014] [Accepted: 11/25/2014] [Indexed: 01/08/2023] Open
Abstract
A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields for protein simulations and methods for the calculation of solvation free energies. The utility of quantum mechanical methods in biophysical and biochemical modeling is explored. The field of computational enzymology is examined.
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Affiliation(s)
- Jack A Tuszynski
- Department of Physics and Department of Oncology, University of Alberta, Edmonton, Canada.
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18
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Wang N, Zhou S, Kekenes-Huskey PM, Li B, McCammon JA. Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers. J Phys Chem B 2014; 118:14827-32. [PMID: 25426875 PMCID: PMC4280115 DOI: 10.1021/jp511702w] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
![]()
Mean-field
methods, such as the Poisson–Boltzmann equation
(PBE), are often used to calculate the electrostatic properties of
molecular systems. In the past two decades, an enhancement of the
PBE, the size-modified Poisson–Boltzmann equation (SMPBE),
has been reported. Here, the PBE and the SMPBE are reevaluated for
realistic molecular systems, namely, lipid bilayers, under eight different
sets of input parameters. The SMPBE appears to reproduce the molecular
dynamics simulation results better than the PBE only under specific
parameter sets, but in general, it performs no better than the Stern
layer correction of the PBE. These results emphasize the need for
careful discussions of the accuracy of mean-field calculations on
realistic systems with respect to the choice of parameters and call
for reconsideration of the cost-efficiency and the significance of
the current SMPBE formulation.
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Affiliation(s)
- Nuo Wang
- Department of Chemistry and Biochemistry, ‡Department of Mathematics, §Department of Pharmacology, ⊥Howard Hughes Medical Institute, University of California-San Diego , La Jolla, California 92093, United States
| | - Shenggao Zhou
- Department of Chemistry and Biochemistry, ‡Department of Mathematics, §Department of Pharmacology, ⊥Howard Hughes Medical Institute, University of California-San Diego , La Jolla, California 92093, United States
| | - Peter M Kekenes-Huskey
- Department of Chemistry and Biochemistry, ‡Department of Mathematics, §Department of Pharmacology, ⊥Howard Hughes Medical Institute, University of California-San Diego , La Jolla, California 92093, United States
| | - Bo Li
- Department of Chemistry and Biochemistry, ‡Department of Mathematics, §Department of Pharmacology, ⊥Howard Hughes Medical Institute, University of California-San Diego , La Jolla, California 92093, United States
| | - J Andrew McCammon
- Department of Chemistry and Biochemistry, ‡Department of Mathematics, §Department of Pharmacology, ⊥Howard Hughes Medical Institute, University of California-San Diego , La Jolla, California 92093, United States
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19
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Fenley MO, Harris RC, Mackoy T, Boschitsch AH. Features of CPB: a Poisson-Boltzmann solver that uses an adaptive Cartesian grid. J Comput Chem 2014; 36:235-43. [PMID: 25430617 DOI: 10.1002/jcc.23791] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2014] [Revised: 09/14/2014] [Accepted: 10/12/2014] [Indexed: 11/10/2022]
Abstract
The capabilities of an adaptive Cartesian grid (ACG)-based Poisson-Boltzmann (PB) solver (CPB) are demonstrated. CPB solves various PB equations with an ACG, built from a hierarchical octree decomposition of the computational domain. This procedure decreases the number of points required, thereby reducing computational demands. Inside the molecule, CPB solves for the reaction-field component (ϕrf ) of the electrostatic potential (ϕ), eliminating the charge-induced singularities in ϕ. CPB can also use a least-squares reconstruction method to improve estimates of ϕ at the molecular surface. All surfaces, which include solvent excluded, Gaussians, and others, are created analytically, eliminating errors associated with triangulated surfaces. These features allow CPB to produce detailed surface maps of ϕ and compute polar solvation and binding free energies for large biomolecular assemblies, such as ribosomes and viruses, with reduced computational demands compared to other Poisson-Boltzmann equation solvers. The reader is referred to http://www.continuum-dynamics.com/solution-mm.html for how to obtain the CPB software.
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Affiliation(s)
- Marcia O Fenley
- Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida, 32306
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20
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Merino F, Ng C, Veerapandian V, Schöler H, Jauch R, Cojocaru V. Structural Basis for the SOX-Dependent Genomic Redistribution of OCT4 in Stem Cell Differentiation. Structure 2014; 22:1274-1286. [DOI: 10.1016/j.str.2014.06.014] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2014] [Revised: 06/03/2014] [Accepted: 06/18/2014] [Indexed: 01/12/2023]
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21
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Kumari R, Kumar R, Lynn A. g_mmpbsa--a GROMACS tool for high-throughput MM-PBSA calculations. J Chem Inf Model 2014; 54:1951-62. [PMID: 24850022 DOI: 10.1021/ci500020m] [Citation(s) in RCA: 2933] [Impact Index Per Article: 293.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Molecular mechanics Poisson-Boltzmann surface area (MM-PBSA), a method to estimate interaction free energies, has been increasingly used in the study of biomolecular interactions. Recently, this method has also been applied as a scoring function in computational drug design. Here a new tool g_mmpbsa, which implements the MM-PBSA approach using subroutines written in-house or sourced from the GROMACS and APBS packages is described. g_mmpbsa was developed as part of the Open Source Drug Discovery (OSDD) consortium. Its aim is to integrate high-throughput molecular dynamics (MD) simulations with binding energy calculations. The tool provides options to select alternative atomic radii and different nonpolar solvation models including models based on the solvent accessible surface area (SASA), solvent accessible volume (SAV), and a model which contains both repulsive (SASA-SAV) and attractive components (described using a Weeks-Chandler-Andersen like integral method). We showcase the effectiveness of the tool by comparing the calculated interaction energy of 37 structurally diverse HIV-1 protease inhibitor complexes with their experimental binding free energies. The effect of varying several combinations of input parameters such as atomic radii, dielectric constant, grid resolution, solute-solvent dielectric boundary definition, and nonpolar models was investigated. g_mmpbsa can also be used to estimate the energy contribution per residue to the binding energy. It has been used to identify those residues in HIV-1 protease that are most critical for binding a range of inhibitors.
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Affiliation(s)
- Rashmi Kumari
- School of Computational and Integrative Sciences, Jawaharlal Nehru University , New Delhi 110067, India
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22
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Li L, Li C, Alexov E. On the Modeling of Polar Component of Solvation Energy using Smooth Gaussian-Based Dielectric Function. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2014; 13. [PMID: 25018579 DOI: 10.1142/s0219633614400021] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Traditional implicit methods for modeling electrostatics in biomolecules use a two-dielectric approach: a biomolecule is assigned low dielectric constant while the water phase is considered as a high dielectric constant medium. However, such an approach treats the biomolecule-water interface as a sharp dielectric border between two homogeneous dielectric media and does not account for inhomogeneous dielectric properties of the macromolecule as well. Recently we reported a new development, a smooth Gaussian-based dielectric function which treats the entire system, the solute and the water phase, as inhomogeneous dielectric medium (J Chem Theory Comput. 2013 Apr 9; 9(4): 2126-2136.). Here we examine various aspects of the modeling of polar solvation energy in such inhomogeneous systems in terms of the solute-water boundary and the inhomogeneity of the solute in the absence of water surrounding. The smooth Gaussian-based dielectric function is implemented in the DelPhi finite-difference program, and therefore the sensitivity of the results with respect to the grid parameters is investigated, and it is shown that the calculated polar solvation energy is almost grid independent. Furthermore, the results are compared with the standard two-media model and it is demonstrated that on average, the standard method overestimates the magnitude of the polar solvation energy by a factor 2.5. Lastly, the possibility of the solute to have local dielectric constant larger than of a bulk water is investigated in a benchmarking test against experimentally determined set of pKa's and it is speculated that side chain rearrangements could result in local dielectric constant larger than 80.
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Affiliation(s)
- Lin Li
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, SC 29634, USA
| | - Chuan Li
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, SC 29634, USA
| | - Emil Alexov
- Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, SC 29634, USA
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23
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Kruse H, Havrila M, Šponer J. QM Computations on Complete Nucleic Acids Building Blocks: Analysis of the Sarcin–Ricin RNA Motif Using DFT-D3, HF-3c, PM6-D3H, and MM Approaches. J Chem Theory Comput 2014; 10:2615-29. [DOI: 10.1021/ct500183w] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Holger Kruse
- CEITEC
− Central European Institute of Technology, Campus Bohunice, Kamenice
5, 625 00 Brno, Czech Republic
| | - Marek Havrila
- CEITEC
− Central European Institute of Technology, Campus Bohunice, Kamenice
5, 625 00 Brno, Czech Republic
- Institute
of Biophysics, Academy of Sciences of the Czech Republic, Královopolská
135, 612 65 Brno, Czech Republic
| | - Jiřı́ Šponer
- CEITEC
− Central European Institute of Technology, Campus Bohunice, Kamenice
5, 625 00 Brno, Czech Republic
- Institute
of Biophysics, Academy of Sciences of the Czech Republic, Královopolská
135, 612 65 Brno, Czech Republic
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