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Corrigan RA, Thiel AC, Lynn JR, Casavant TL, Ren P, Ponder JW, Schnieders MJ. A generalized Kirkwood implicit solvent for the polarizable AMOEBA protein model. J Chem Phys 2023; 159:054102. [PMID: 37526158 PMCID: PMC10396400 DOI: 10.1063/5.0158914] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 07/17/2023] [Indexed: 08/02/2023] Open
Abstract
Computational simulation of biomolecules can provide important insights into protein design, protein-ligand binding interactions, and ab initio biomolecular folding, among other applications. Accurate treatment of the solvent environment is essential in such applications, but the use of explicit solvents can add considerable cost. Implicit treatment of solvent effects using a dielectric continuum model is an attractive alternative to explicit solvation since it is able to describe solvation effects without the inclusion of solvent degrees of freedom. Previously, we described the development and parameterization of implicit solvent models for small molecules. Here, we extend the parameterization of the generalized Kirkwood (GK) implicit solvent model for use with biomolecules described by the AMOEBA force field via the addition of corrections to the calculation of effective radii that account for interstitial spaces that arise within biomolecules. These include element-specific pairwise descreening scale factors, a short-range neck contribution to describe the solvent-excluded space between pairs of nearby atoms, and finally tanh-based rescaling of the overall descreening integral. We then apply the AMOEBA/GK implicit solvent to a set of ten proteins and achieve an average coordinate root mean square deviation for the experimental structures of 2.0 Å across 500 ns simulations. Overall, the continued development of implicit solvent models will help facilitate the simulation of biomolecules on mechanistically relevant timescales.
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Affiliation(s)
- Rae A. Corrigan
- Roy J. Carver Department of Biomedical Engineering, The University of Iowa, Iowa City, Iowa 52242, USA
| | - Andrew C. Thiel
- Roy J. Carver Department of Biomedical Engineering, The University of Iowa, Iowa City, Iowa 52242, USA
| | - Jack R. Lynn
- Roy J. Carver Department of Biomedical Engineering, The University of Iowa, Iowa City, Iowa 52242, USA
| | - Thomas L. Casavant
- Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, Iowa 52242, USA
| | - Pengyu Ren
- Department of Biomedical Engineering, The University of Texas in Austin, Austin, Texas 78712, USA
| | - Jay W. Ponder
- Department of Chemistry, Washington University in St. Louis, St. Louis, Missouri 63130, USA
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2
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King E, Aitchison E, Li H, Luo R. Recent Developments in Free Energy Calculations for Drug Discovery. Front Mol Biosci 2021; 8:712085. [PMID: 34458321 PMCID: PMC8387144 DOI: 10.3389/fmolb.2021.712085] [Citation(s) in RCA: 49] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 07/27/2021] [Indexed: 01/11/2023] Open
Abstract
The grand challenge in structure-based drug design is achieving accurate prediction of binding free energies. Molecular dynamics (MD) simulations enable modeling of conformational changes critical to the binding process, leading to calculation of thermodynamic quantities involved in estimation of binding affinities. With recent advancements in computing capability and predictive accuracy, MD based virtual screening has progressed from the domain of theoretical attempts to real application in drug development. Approaches including the Molecular Mechanics Poisson Boltzmann Surface Area (MM-PBSA), Linear Interaction Energy (LIE), and alchemical methods have been broadly applied to model molecular recognition for drug discovery and lead optimization. Here we review the varied methodology of these approaches, developments enhancing simulation efficiency and reliability, remaining challenges hindering predictive performance, and applications to problems in the fields of medicine and biochemistry.
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Affiliation(s)
- Edward King
- Department of Molecular Biology and Biochemistry, University of California, Irvine, CA, United States
| | - Erick Aitchison
- Department of Molecular Biology and Biochemistry, University of California, Irvine, CA, United States
| | - Han Li
- Department of Chemical and Biomolecular Engineering, University of California, Irvine, CA, United States
| | - Ray Luo
- Department of Molecular Biology and Biochemistry, University of California, Irvine, CA, United States
- Department of Chemical and Biomolecular Engineering, University of California, Irvine, CA, United States
- Department of Materials Science and Engineering, University of California, Irvine, CA, United States
- Department of Biomedical Engineering, University of California, Irvine, CA, United States
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3
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Fortuna A, Costa PJ. Optimized Halogen Atomic Radii for PBSA Calculations Using Off-Center Point Charges. J Chem Inf Model 2021; 61:3361-3375. [PMID: 34185532 DOI: 10.1021/acs.jcim.1c00177] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
In force-field methods, the usage of off-center point charges, also called extra points (EPs), is a common strategy to tackle the anisotropy of the electrostatic potential of covalently bonded halogens (X), thus allowing the description of halogen bonds (XBs) at the molecular mechanics/molecular dynamics (MM/MD) level. Diverse EP implementations exist in the literature differing on the charge sets and/or the X-EP distances. Poisson-Boltzmann and surface area (PBSA) calculations can be used to obtain solvation free energies (ΔGsolv) of small molecules, often to compute binding free energies (ΔGbind) at the MM-PBSA level. This method depends, among other parameters, on the empirical assignment of atomic radii (PB radii). Given the multiplicity of off-center point-charge models and the lack of specific PB radii for halogens compatible with such implementations, in this work, we assessed the performance of PBSA calculations for the estimation of ΔGsolv values in water (ΔGhyd), also conducting an optimization of the halogen PB radii (Cl, Br, and I) for each EP model. We not only expand the usage of EP models in the scope of the general AMBER force field (GAFF) but also provide the first optimized halogen PB radii in the context of the CHARMM general force field (CGenFF), thus contributing to improving the description of halogenated compounds in PBSA calculations.
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Affiliation(s)
- Andreia Fortuna
- BioISI-Biosystems & Integrative Sciences Institute, Faculty of Sciences, University of Lisboa, 1749-016 Lisboa, Portugal.,Research Institute for Medicines (iMed.ULisboa), Faculty of Pharmacy, University of Lisbon, Av. Professor Gama Pinto, 1649-003 Lisbon, Portugal
| | - Paulo J Costa
- BioISI-Biosystems & Integrative Sciences Institute, Faculty of Sciences, University of Lisboa, 1749-016 Lisboa, Portugal
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4
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Lind C, Pandey P, Pastor RW, MacKerell AD. Functional Group Distributions, Partition Coefficients, and Resistance Factors in Lipid Bilayers Using Site Identification by Ligand Competitive Saturation. J Chem Theory Comput 2021; 17:3188-3202. [PMID: 33929848 DOI: 10.1021/acs.jctc.1c00089] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Small molecules such as metabolites and drugs must pass through the membrane of the cell, a barrier primarily comprising phospholipid bilayers and embedded proteins. To better understand the process of passive diffusion, knowledge of the ability of various functional groups to partition across bilayers and the associated energetics would be of utility. In the present study, the site identification by ligand competitive saturation (SILCS) methodology has been applied to sample the distributions of a diverse set of chemical solutes representing the functional groups of small molecules across phospholipid bilayers composed of 0.9:0.1 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine/cholesterol and a mixture of 0.52:0.18:0.3 1,2-dioleoyl-sn-glycero-3-phospho-l-serine/1,2-dioleoyl-sn-glycero-3-phosphocholine/cholesterol used in parallel artificial membrane permeability assay experiments. A combination of oscillating chemical potential grand canonical Monte Carlo and molecular dynamics in the SILCS simulations was applied to achieve solute sampling through the bilayers and surrounding aqueous environment from which the distribution of solutes and the functional groups they represent were obtained. Results show differential distribution of aliphatic versus aromatic groups with the former having increased sampling in the center of the bilayers versus in the region of the glycerol linker for the latter. Variations in the distribution of different polar groups are evident, with large differences between negative acetate and positive methylammonium with accumulation of the polar-neutral and acetate solutes above the bilayer head groups. Conversion of the distributions to absolute free energies allows for a detailed understanding of energetics of functional groups in different regions of the bilayers and for calculation of absolute free-energy profiles of multifunctional drug-like molecules across the bilayers from which partition coefficients and resistance factors suitable for insertion into the homogenous solubility-diffusion equation for calculation of permeability were obtained. Comparisons of the calculated bilayer/solution partition coefficients with 1-octanol/water experimental data for both drug-like molecules and the solutes show overall good agreement, validating the calculated distributions and associated absolute free-energy profiles.
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Affiliation(s)
- Christoffer Lind
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, Baltimore, Baltimore, Maryland 21201, United States
| | - Poonam Pandey
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, Baltimore, Baltimore, Maryland 21201, United States
| | - Richard W Pastor
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, United States
| | - Alexander D MacKerell
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, Baltimore, Baltimore, Maryland 21201, United States
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5
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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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6
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Aleksandrov A, Roux B, MacKerell AD. p Ka Calculations with the Polarizable Drude Force Field and Poisson-Boltzmann Solvation Model. J Chem Theory Comput 2020; 16:4655-4668. [PMID: 32464053 DOI: 10.1021/acs.jctc.0c00111] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Electronic polarization effects have been suggested to play an important role in proton binding to titratable residues in proteins. In this work, we describe a new computational method for pKa calculations, using Monte Carlo (MC) simulations to sample protein protonation states with the Drude polarizable force field and Poisson-Boltzmann (PB) continuum electrostatic solvent model. While the most populated protonation states at the selected pH, corresponding to residues that are half-protonated at that pH, are sampled using the exact relative free energies computed with Drude particles optimized in the field of the PB implicit solvation model, we introduce an approximation for the protein polarization of low-populated protonation states to reduce the computational cost. The highly populated protonation states used to compute the polarization and pKa's are then iteratively improved until convergence. It is shown that for lysozyme, when considering 9 of the 18 titratable residues, the new method converged within two iterations with computed pKa's differing only by 0.02 pH units from pKa's estimated with the exact approach. Application of the method to predict pKa's of 94 titratable side chains in 8 proteins shows the Drude-PB model to produce physically more correct results as compared to the additive CHARMM36 (C36) force field (FF). With a dielectric constant of two assigned to the protein interior the Root Mean Square (RMS) deviation between computed and experimental pKa's is 2.07 and 3.19 pH units with the Drude and C36 models, respectively, and the RMS deviation using the Drude-PB model is relatively insensitive to the choice of the internal dielectric constant in contrast to the additive C36 model. At the higher internal dielectric constant of 20, pKa's computed with the additive C36 model converge to the results obtained with the Drude polarizable force field, indicating the need to artificially overestimate electrostatic screening in a nonphysical way with the additive FF. In addition, inclusion of both syn and anti orientations of the proton in the neutral state of acidic groups is shown to yield improved agreement with experiment. The present work, which is the first example of the use of a polarizable model for the prediction of pKa's in proteins, shows that the use of a polarizable model represents a more physically correct model for the treatment of electrostatic contributions to pKa shifts in proteins.
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Affiliation(s)
- Alexey Aleksandrov
- Laboratoire d'Optique et Biosciences, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, Gordon Center for Integrative Science, University of Chicago, 929 E57th Street, Chicago, Illinois 60637, United States
| | - Alexander D MacKerell
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, Maryland 21201, United States
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7
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Lin FY, Huang J, Pandey P, Rupakheti C, Li J, Roux B, MacKerell AD. Further Optimization and Validation of the Classical Drude Polarizable Protein Force Field. J Chem Theory Comput 2020; 16:3221-3239. [PMID: 32282198 PMCID: PMC7306265 DOI: 10.1021/acs.jctc.0c00057] [Citation(s) in RCA: 49] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
The CHARMM Drude-2013 polarizable force field (FF) was developed to include the explicit treatment of induced electronic polarizability, resulting in a more accurate description of the electrostatic interactions in molecular dynamics (MD) simulations. While the Drude-2013 protein FF has shown success in improving the folding properties of α-helical peptides and to reproduce experimental observables in simulations up to 1 μs, some limitations were noted regarding the stability of β-sheet structures in simulations longer than 100 ns as well as larger deviations from crystal structures in simulations of a number of proteins compared to the additive CHARMM36 protein FF. The origin of the instability has been identified and appears to be primarily due to overestimated atomic polarizabilities and induced dipole-dipole interactions on the Cβ, Cγ, and Cδ side chain atoms. To resolve this and other issues, a number of aspects of the model were revisited, resulting in Drude-2019 protein FF. Backbone parameters were optimized targeting the conformational properties of the (Ala)5 peptide in solution along with gas phase properties of the alanine dipeptide. Dipeptides that contain N-acetylated and N'-methylamidated termini, excluding Gly, Pro, and Ala, were used as models to optimize the atomic polarizabilities and Thole screening factors on selected Cβ, Cγ, and Cδ carbons by targeting quantum mechanical (QM) dipole moments and molecular polarizabilities. In addition, to obtain better conformational properties, side chain χ1 and χ2 dihedral parameters were optimized targeting QM data for the respective side chain dipeptide conformations as well as Protein Data Bank survey data based on the χ1, χ2 sampling from Hamiltonian replica-exchange MD simulations of (Ala)4-X-(Ala)4 in solution, where X is the amino acid of interest. Further improvements include optimizing nonbonded interactions between charged residues to reproduce QM interaction energies of the charged-protein model compounds and experimental osmotic pressures. Validation of the optimized Drude protein FF includes MD simulations of a collection of peptides and proteins including β-sheet structures, as well as transmembrane ion channels. Results showed that the updated Drude-2019 protein FF yields smaller overall root-mean-square differences of proteins as compared to the additive CHARMM36m and Drude-2013 FFs as well as similar or improved agreement with experimental NMR properties, allowing for long time scale simulation studies of proteins and more complex biomolecular systems in conjunction with the remainder of the Drude polarizable FF.
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Affiliation(s)
- Fang-Yu Lin
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, MD 21201, USA
| | - Jing Huang
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, MD 21201, USA
- Westlake University, 18 Shilongshan Road, Hangzhou 310024, Zhejiang, China
| | - Poonam Pandey
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, MD 21201, USA
| | - Chetan Rupakheti
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, IL, 60637, USA
| | - Jing Li
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, IL, 60637, USA
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, IL, 60637, USA
| | - Alexander D. MacKerell
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, MD 21201, USA
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8
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Kirby BJ, Jungwirth P. Charge Scaling Manifesto: A Way of Reconciling the Inherently Macroscopic and Microscopic Natures of Molecular Simulations. J Phys Chem Lett 2019; 10:7531-7536. [PMID: 31743030 DOI: 10.1021/acs.jpclett.9b02652] [Citation(s) in RCA: 65] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Electronic polarization effects play an important role in the interactions of charged species in biologically relevant aqueous solutions, such as those involving salt ions, proteins, nucleic acids, or phospholipid membranes. Explicit inclusion of electronic polarization in molecular modeling is tedious both from the point of view of force field parametrization and actual performance of the simulations. Therefore, the vast majority of biomolecular simulations is performed using nonpolarizable force fields, which can lead to artifacts such as dramatically overestimated ion pairing, particularly when polyvalent ions are involved. Here, we show that many of these issues can be remedied without extra computational costs by including electronic polarization in a mean field way via charge rescaling. We also lay the solid physical foundations of this approach and reconcile from this perspective the microscopic versus macroscopic natures of nonpolarizable force fields.
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Affiliation(s)
- Brian J Kirby
- Sibley School of Mechanical and Aerospace Engineering , Cornell University , Ithaca , New York 14853 , United States
- Weill-Cornell Medicine , New York , New York 10065 , United States
| | - Pavel Jungwirth
- Institute of Organic Chemistry and Biochemistry , Academy of Sciences of the Czech Republic , Flemingovo nam. 2 , 16610 Prague 6 , Czech Republic
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9
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Poier PP, Jensen F. Including implicit solvation in the bond capacity polarization model. J Chem Phys 2019; 151:114118. [DOI: 10.1063/1.5120873] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Pier Paolo Poier
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus, Denmark
| | - Frank Jensen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus, Denmark
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10
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Tollefson MR, Litman JM, Qi G, O'Connell CE, Wipfler MJ, Marini RJ, Bernabe HV, Tollefson WTA, Braun TA, Casavant TL, Smith RJH, Schnieders MJ. Structural Insights into Hearing Loss Genetics from Polarizable Protein Repacking. Biophys J 2019; 117:602-612. [PMID: 31327459 DOI: 10.1016/j.bpj.2019.06.030] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2019] [Revised: 06/10/2019] [Accepted: 06/25/2019] [Indexed: 12/21/2022] Open
Abstract
Hearing loss is associated with ∼8100 mutations in 152 genes, and within the coding regions of these genes are over 60,000 missense variants. The majority of these variants are classified as "variants of uncertain significance" to reflect our inability to ascribe a phenotypic effect to the observed amino acid change. A promising source of pathogenicity information is biophysical simulation, although input protein structures often contain defects because of limitations in experimental data and/or only distant homology to a template. Here, we combine the polarizable atomic multipole optimized energetics for biomolecular applications force field, many-body optimization theory, and graphical processing unit acceleration to repack all deafness-associated proteins and thereby improve average structure MolProbity score from 2.2 to 1.0. We then used these optimized wild-type models to create over 60,000 structures for missense variants in the Deafness Variation Database, which are being incorporated into the Deafness Variation Database to inform deafness pathogenicity prediction. Finally, this work demonstrates that advanced polarizable atomic multipole force fields are efficient enough to repack the entire human proteome.
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Affiliation(s)
- Mallory R Tollefson
- Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa; Molecular Otolaryngology & Renal Research Laboratories, Department of Otolaryngology-Head and Neck Surgery, University of Iowa Hospitals and Clinics, Iowa City, Iowa
| | - Jacob M Litman
- Department of Biochemistry, University of Iowa, Iowa City, Iowa
| | - Guowei Qi
- Department of Biochemistry, University of Iowa, Iowa City, Iowa
| | - Claire E O'Connell
- Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa
| | - Matthew J Wipfler
- Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa
| | - Robert J Marini
- Molecular Otolaryngology & Renal Research Laboratories, Department of Otolaryngology-Head and Neck Surgery, University of Iowa Hospitals and Clinics, Iowa City, Iowa
| | - Hernan V Bernabe
- Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa; Molecular Otolaryngology & Renal Research Laboratories, Department of Otolaryngology-Head and Neck Surgery, University of Iowa Hospitals and Clinics, Iowa City, Iowa
| | | | - Terry A Braun
- Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa
| | - Thomas L Casavant
- Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa
| | - Richard J H Smith
- Molecular Otolaryngology & Renal Research Laboratories, Department of Otolaryngology-Head and Neck Surgery, University of Iowa Hospitals and Clinics, Iowa City, Iowa.
| | - Michael J Schnieders
- Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa; Department of Biochemistry, University of Iowa, Iowa City, Iowa.
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11
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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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12
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Molina JE, Vasquez-Echeverri A, Schwartz DC, Hernández-Ortiz JP. Discrete and Continuum Models for the Salt in Crowded Environments of Suspended Charged Particles. J Chem Theory Comput 2018; 14:4901-4913. [PMID: 30044624 DOI: 10.1021/acs.jctc.8b00221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Electrostatic forces greatly affect the overall dynamics and diffusional activities of suspended charged particles in crowded environments. Accordingly, the concentration of counter- or co-ions in a fluid-''the salt"-determines the range, strength, and order of electrostatic interactions between particles. This environment fosters engineering routes for controlling directed assembly of particles at both the micro- and nanoscale. Here, we analyzed two computational modeling schemes that considered salt within suspensions of charged particles, or polyelectrolytes: discrete and continuum. Electrostatic interactions were included through a Green's function formalism, where the confined fundamental solution for Poisson's equation is resolved by the general geometry Ewald-like method. For the discrete model, the salt was considered as regularized point-charges with a specific valence and size, while concentration fields were defined for each ionic species for the continuum model. These considerations were evolved using Brownian dynamics of the suspended charged particles and the discrete salt ions, while a convection-diffusion transport equation, including the Nernst-Planck diffusion mechanism, accounted for the dynamics of the concentration fields. The salt/particle models were considered as suspensions under slit-confinement conditions for creating crowded "macro-ions", where density distributions and radial distribution functions were used to compare and differentiate computational models. Importantly, our analysis shows that disparate length scales or increased system size presented by the salt and suspended particles are best dealt with using concentration fields to model the ions. These findings were then validated by novel simulations of a semipermeable polyelectrolyte membrane, at the mesoscale, from which ionic channels emerged and enable ion conduction.
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Affiliation(s)
- Jarol E Molina
- Departamento de Materiales y Nanotecnología , Universidad Nacional de Colombia-Medellín , Medellín 050034 , Colombia
| | - Alejandro Vasquez-Echeverri
- Departamento de Materiales y Nanotecnología , Universidad Nacional de Colombia-Medellín , Medellín 050034 , Colombia
| | - David C Schwartz
- Laboratory for Molecular and Computational Genomics, Department of Chemistry, Laboratory of Genetics , University of Wisconsin-Madison , Madison , Wisconsin 53706-1396 , United States.,The Biotechnology Center , University of Wisconsin-Madison , Madison , Wisconsin 53706-1396 , United States
| | - Juan P Hernández-Ortiz
- Departamento de Materiales y Nanotecnología , Universidad Nacional de Colombia-Medellín , Medellín 050034 , Colombia.,The Biotechnology Center , University of Wisconsin-Madison , Madison , Wisconsin 53706-1396 , United States.,Institute for Molecular Engineering , University of Chicago , Chicago , Illinois 60637 , United States
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