1
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Stepanenko D, Wang Y, Simmerling C. Assessing pH-Dependent Conformational Changes in the Fusion Peptide Proximal Region of the SARS-CoV-2 Spike Glycoprotein. Viruses 2024; 16:1066. [PMID: 39066230 PMCID: PMC11281432 DOI: 10.3390/v16071066] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2024] [Revised: 06/26/2024] [Accepted: 06/28/2024] [Indexed: 07/28/2024] Open
Abstract
One of the entry mechanisms of the SARS-CoV-2 coronavirus into host cells involves endosomal acidification. It has been proposed that under acidic conditions, the fusion peptide proximal region (FPPR) of the SARS-CoV-2 spike glycoprotein acts as a pH-dependent switch, modulating immune response accessibility by influencing the positioning of the receptor binding domain (RBD). This would provide indirect coupling of RBD opening to the environmental pH. Here, we explored this possible pH-dependent conformational equilibrium of the FPPR within the SARS-CoV-2 spike glycoprotein. We analyzed hundreds of experimentally determined spike structures from the Protein Data Bank and carried out pH-replica exchange molecular dynamics to explore the extent to which the FPPR conformation depends on pH and the positioning of the RBD. A meta-analysis of experimental structures identified alternate conformations of the FPPR among structures in which this flexible regions was resolved. However, the results did not support a correlation between the FPPR conformation and either RBD position or the reported pH of the cryo-EM experiment. We calculated pKa values for titratable side chains in the FPPR region using PDB structures, but these pKa values showed large differences between alternate PDB structures that otherwise adopt the same FPPR conformation type. This hampers the comparison of pKa values in different FPPR conformations to rationalize a pH-dependent conformational change. We supplemented these PDB-based analyses with all-atom simulations and used constant-pH replica exchange molecular dynamics to estimate pKa values in the context of flexibility and explicit water. The resulting titration curves show good reproducibility between simulations, but they also suggest that the titration curves of the different FPPR conformations are the same within the error bars. In summary, we were unable to find evidence supporting the previously published hypothesis of an FPPR pH-dependent equilibrium: neither from existing experimental data nor from constant-pH MD simulations. The study underscores the complexity of the spike system and opens avenues for further exploration into the interplay between pH and SARS-CoV-2 viral entry mechanisms.
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Affiliation(s)
- Darya Stepanenko
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794, USA; (D.S.); (Y.W.)
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA
| | - Yuzhang Wang
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794, USA; (D.S.); (Y.W.)
- Department of Chemistry, Stony Brook University, Stony Brook, NY 11794, USA
| | - Carlos Simmerling
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794, USA; (D.S.); (Y.W.)
- Department of Chemistry, Stony Brook University, Stony Brook, NY 11794, USA
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2
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Wilson CJ, de Groot BL, Gapsys V. Resolving coupled pH titrations using alchemical free energy calculations. J Comput Chem 2024; 45:1444-1455. [PMID: 38471815 DOI: 10.1002/jcc.27318] [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: 09/17/2023] [Revised: 01/11/2024] [Accepted: 01/16/2024] [Indexed: 03/14/2024]
Abstract
In a protein, nearby titratable sites can be coupled: the (de)protonation of one may affect the other. The degree of this interaction depends on several factors and can influence the measured p K a . Here, we derive a formalism based on double free energy differences ( Δ Δ G ) for quantifying the individual site p K a values of coupled residues. As Δ Δ G values can be obtained by means of alchemical free energy calculations, the presented approach allows for a convenient estimation of coupled residue p K a s in practice. We demonstrate that our approach and a previously proposed microscopic p K a formalism, can be combined with alchemical free energy calculations to resolve pH-dependent protein p K a values. Toy models and both, regular and constant-pH molecular dynamics simulations, alongside experimental data, are used to validate this approach. Our results highlight the insights gleaned when coupling and microstate probabilities are analyzed and suggest extensions to more complex enzymatic contexts. Furthermore, we find that naïvely computed p K a values that ignore coupling, can be significantly improved when coupling is accounted for, in some cases reducing the error by half. In short, alchemical free energy methods can resolve the p K a values of both uncoupled and coupled residues.
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Affiliation(s)
- Carter J Wilson
- Department of Mathematics, The University of Western Ontario, London, Ontario, Canada
- Centre for Advanced Materials and Biomaterials Research (CAMBR), The University of Western Ontario, London, Ontario, Canada
- Computational Biomolecular Dynamics Group, Department of Theoretical and Computational Biophysics, Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
| | - Bert L de Groot
- Computational Biomolecular Dynamics Group, Department of Theoretical and Computational Biophysics, Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
| | - Vytautas Gapsys
- Computational Biomolecular Dynamics Group, Department of Theoretical and Computational Biophysics, Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
- Computational Chemistry, Janssen Research & Development, Beerse, Belgium
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3
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Pirnia A, Maqdisi R, Mittal S, Sener M, Singharoy A. Perspective on Integrative Simulations of Bioenergetic Domains. J Phys Chem B 2024; 128:3302-3319. [PMID: 38562105 DOI: 10.1021/acs.jpcb.3c07335] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/04/2024]
Abstract
Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.
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Affiliation(s)
- Adam Pirnia
- School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287-1004, United States
| | - Ranel Maqdisi
- School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287-1004, United States
| | - Sumit Mittal
- VIT Bhopal University, Sehore 466114, Madhya Pradesh, India
| | - Melih Sener
- School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287-1004, United States
- Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Abhishek Singharoy
- School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287-1004, United States
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4
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Thiel A, Speranza MJ, Jadhav S, Stevens LL, Unruh DK, Ren P, Ponder JW, Shen J, Schnieders MJ. Constant-pH Simulations with the Polarizable Atomic Multipole AMOEBA Force Field. J Chem Theory Comput 2024; 20:2921-2933. [PMID: 38507252 PMCID: PMC11008096 DOI: 10.1021/acs.jctc.3c01180] [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: 10/24/2023] [Revised: 03/05/2024] [Accepted: 03/05/2024] [Indexed: 03/22/2024]
Abstract
Accurately predicting protein behavior across diverse pH environments remains a significant challenge in biomolecular simulations. Existing constant-pH molecular dynamics (CpHMD) algorithms are limited to fixed-charge force fields, hindering their application to biomolecular systems described by permanent atomic multipoles or induced dipoles. This work overcomes these limitations by introducing the first polarizable CpHMD algorithm in the context of the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field. Additionally, our implementation in the open-source Force Field X (FFX) software has the unique ability to handle titration state changes for crystalline systems including flexible support for all 230 space groups. The evaluation of constant-pH molecular dynamics (CpHMD) with the AMOEBA force field was performed on 11 crystalline peptide systems that span the titrating amino acids (Asp, Glu, His, Lys, and Cys). Titration states were correctly predicted for 15 out of the 16 amino acids present in the 11 systems, including for the coordination of Zn2+ by cysteines. The lone exception was for a HIS-ALA peptide where CpHMD predicted both neutral histidine tautomers to be equally populated, whereas the experimental model did not consider multiple conformers and diffraction data are unavailable for rerefinement. This work demonstrates the promise polarizable CpHMD simulations for pKa predictions, the study of biochemical mechanisms such as the catalytic triad of proteases, and for improved protein-ligand binding affinity accuracy in the context of pharmaceutical lead optimization.
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Affiliation(s)
- Andrew
C. Thiel
- Department
of Biomedical Engineering, University of
Iowa, Iowa City, Iowa 52242, United States
| | - Matthew J. Speranza
- Department
of Biomedical Engineering, University of
Iowa, Iowa City, Iowa 52242, United States
| | - Sanika Jadhav
- Department
of Pharmaceutical Sciences and Experimental Therapeutics, University of Iowa, Iowa City, Iowa 52242, United States
| | - Lewis L. Stevens
- Department
of Pharmaceutical Sciences and Experimental Therapeutics, University of Iowa, Iowa City, Iowa 52242, United States
| | - Daniel K. Unruh
- Office
of the Vice President for Research, University
of Iowa, Iowa City, Iowa 52242, United
States
| | - Pengyu Ren
- Department
of Biomedical Engineering, University of
Texas, Austin, Texas 78712, United States
| | - Jay W. Ponder
- Department
of Chemistry, Washington University in St.
Louis, St. Louis, Missouri 63130, United
States
| | - Jana Shen
- Department
of Pharmaceutical Sciences, University of
Maryland School of Pharmacy, Baltimore, Maryland 21201, United States
| | - Michael J. Schnieders
- 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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5
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Jansen A, Aho N, Groenhof G, Buslaev P, Hess B. phbuilder: A Tool for Efficiently Setting up Constant pH Molecular Dynamics Simulations in GROMACS. J Chem Inf Model 2024; 64:567-574. [PMID: 38215282 PMCID: PMC10865341 DOI: 10.1021/acs.jcim.3c01313] [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: 08/16/2023] [Revised: 12/05/2023] [Accepted: 12/06/2023] [Indexed: 01/14/2024]
Abstract
Constant pH molecular dynamics (MD) is a powerful technique that allows the protonation state of residues to change dynamically, thereby enabling the study of pH dependence in a manner that has not been possible before. Recently, a constant pH implementation was incorporated into the GROMACS MD package. Although this implementation provides good accuracy and performance, manual modification and the preparation of simulation input files are required, which can be complicated, tedious, and prone to errors. To simplify and automate the setup process, we present phbuilder, a tool that automatically prepares constant pH MD simulations for GROMACS by modifying the input structure and topology as well as generating the necessary parameter files. phbuilder can prepare constant pH simulations from both initial structures and existing simulation systems, and it also provides functionality for performing titrations and single-site parametrizations of new titratable group types. The tool is freely available at www.gitlab.com/gromacs-constantph. We anticipate that phbuilder will make constant pH simulations easier to set up, thereby making them more accessible to the GROMACS user community.
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Affiliation(s)
- Anton Jansen
- Department
of Applied Physics and Swedish e-Science Research Center, Science
for Life Laboratory, KTH Royal Institute
of Technology, 100 44 Stockholm, Sweden
| | - Noora Aho
- Nanoscience
Center and Department of Chemistry, University
of Jyväskylä, 40014 Jyväskylä, Finland
| | - Gerrit Groenhof
- Nanoscience
Center and Department of Chemistry, University
of Jyväskylä, 40014 Jyväskylä, Finland
| | - Pavel Buslaev
- Nanoscience
Center and Department of Chemistry, University
of Jyväskylä, 40014 Jyväskylä, Finland
| | - Berk Hess
- Department
of Applied Physics and Swedish e-Science Research Center, Science
for Life Laboratory, KTH Royal Institute
of Technology, 100 44 Stockholm, Sweden
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6
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Harris J, Chipot C, Roux B. How is Membrane Permeation of Small Ionizable Molecules Affected by Protonation Kinetics? J Phys Chem B 2024; 128:795-811. [PMID: 38227958 DOI: 10.1021/acs.jpcb.3c06765] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2024]
Abstract
According to the pH-partition hypothesis, the aqueous solution adjacent to a membrane is a mixture of the ionization states of the permeating molecule at fixed Henderson-Hasselbalch concentrations, such that each state passes through the membrane in parallel with its own specific permeability. An alternative view, based on the assumption that the rate of switching ionization states is instantaneous, represents the permeation of ionizable molecules via an effective Boltzmann-weighted average potential (BWAP). Such an assumption is used in constant-pH molecular dynamics simulations. The inhomogeneous solubility-diffusion framework can be used to compute the pH-dependent membrane permeability for each of these two limiting treatments. With biased WTM-eABF molecular dynamics simulations, we computed the potential of mean force and diffusivity of each ionization state of two weakly basic small molecules: nicotine, an addictive drug, and varenicline, a therapeutic for treating nicotine addiction. At pH = 7, the BWAP effective permeability is greater than that determined by pH-partitioning by a factor of 2.5 for nicotine and 5 for varenicline. To assess the importance of ionization kinetics, we present a Smoluchowski master equation that includes explicitly the protonation and deprotonation processes coupled with the diffusive motion across the membrane. At pH = 7, the increase in permeability due to the explicit ionization kinetics is negligible for both nicotine and varenicline. This finding is reaffirmed by combined Brownian dynamics and Markov state model simulations for estimating the permeability of nicotine while allowing changes in its ionization state. We conclude that for these molecules the pH-partition hypothesis correctly captures the physics of the permeation process. The small free energy barriers for the permeation of nicotine and varenicline in their deprotonated neutral forms play a crucial role in establishing the validity of the pH-partitioning mechanism. Essentially, BWAP fails because ionization kinetics are too slow on the time scale of membrane crossing to affect the permeation of small ionizable molecules such as nicotine and varenicline. For the singly protonated state of nicotine, the computational results agree well with experimental measurements (P1 = 1.29 × 10-7 cm/s), but the agreement for neutral (P0 = 6.12 cm/s) and doubly protonated nicotine (P2 = 3.70 × 10-13 cm/s) is slightly worse, likely due to factors associated with the aqueous boundary layer (neutral form) or leaks through paracellular pathways (doubly protonated form).
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Affiliation(s)
- Jonathan Harris
- Department of Chemistry, The University of Chicago, 5735 S Ellis Avenue, Chicago, Illinois 60637, United States
| | - Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n◦7019, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy Cedex, France
- Theoretical and Computational Biophysics Group, Beckman Institute, and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Department of Biochemistry and Molecular Biology, Department of Chemistry, The University of Chicago, 5735 S Ellis Avenue, Chicago, Illinois 60637, United States
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, Department of Chemistry, The University of Chicago, 5735 S Ellis Avenue, Chicago, Illinois 60637, United States
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7
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Wilson C, Karttunen M, de Groot BL, Gapsys V. Accurately Predicting Protein p Ka Values Using Nonequilibrium Alchemy. J Chem Theory Comput 2023; 19:7833-7845. [PMID: 37820376 PMCID: PMC10653114 DOI: 10.1021/acs.jctc.3c00721] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Indexed: 10/13/2023]
Abstract
The stability, solubility, and function of a protein depend on both its net charge and the protonation states of its individual residues. pKa is a measure of the tendency for a given residue to (de)protonate at a specific pH. Although pKa values can be resolved experimentally, theory and computation provide a compelling alternative. To this end, we assess the applicability of a nonequilibrium (NEQ) alchemical free energy method to the problem of pKa prediction. On a data set of 144 residues that span 13 proteins, we report an average unsigned error of 0.77 ± 0.09, 0.69 ± 0.09, and 0.52 ± 0.04 pK for aspartate, glutamate, and lysine, respectively. This is comparable to current state-of-the-art predictors and the accuracy recently reached using free energy perturbation methods (e.g., FEP+). Moreover, we demonstrate that our open-source, pmx-based approach can accurately resolve the pKa values of coupled residues and observe a substantial performance disparity associated with the lysine partial charges in Amber14SB/Amber99SB*-ILDN, for which an underused fix already exists.
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Affiliation(s)
- Carter
J. Wilson
- Department
of Mathematics, The University of Western
Ontario, N6A 5B7 London, Canada
- Centre
for Advanced Materials and Biomaterials Research (CAMBR), The University of Western Ontario, N6A 5B7 London, Canada
| | - Mikko Karttunen
- Centre
for Advanced Materials and Biomaterials Research (CAMBR), The University of Western Ontario, N6A 5B7 London, Canada
- Department
of Physics & Astronomy, The University
of Western Ontario, N6A
5B7 London, Canada
- Department
of Chemistry, The University of Western
Ontario, N6A 5B7 London, Canada
| | - Bert L. de Groot
- Computational
Biomolecular Dynamics Group, Department of Theoretical and Computational
Biophysics, Max Planck Institute for Multidisciplinary
Sciences, 37077 Göttingen, Germany
| | - Vytautas Gapsys
- Computational
Biomolecular Dynamics Group, Department of Theoretical and Computational
Biophysics, Max Planck Institute for Multidisciplinary
Sciences, 37077 Göttingen, Germany
- Computational
Chemistry, Janssen Research & Development, Janssen Pharmaceutica N. V., Turnhoutseweg 30, B-2340 Beerse, Belgium
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8
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Mandalaparthy V, Tripathy M, van der Vegt NFA. Anions and Cations Affect Amino Acid Dissociation Equilibria via Distinct Mechanisms. J Phys Chem Lett 2023; 14:9250-9256. [PMID: 37812174 DOI: 10.1021/acs.jpclett.3c02062] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/10/2023]
Abstract
Salts reduce the pKa of weak acids by a mechanism sensitive to ion identity and concentration via charge screening of the deprotonated state. In this study, we utilize constant pH molecular dynamics simulations to understand the molecular mechanism behind the salt-dependent dissociation of aspartic acid (Asp). We calculate the pKa of Asp in the presence of a monovalent salt and investigate Hofmeister ion effects by systematically varying the ionic radii. We observe that increasing the anion size leads to a monotonic decrease in Asp pKa. Conversely, the cation size affects the pKa nonmonotonically, interpretable in the context of the law of matching water affinity. The net effect of salt on Asp acidity is governed by an interplay of solvation and competing ion interactions. The proposed mechanism is rather general and can be applicable to several problems in Hofmeister ion chemistry, such as pH effects on protein stability and soft matter interfaces.
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Affiliation(s)
- Varun Mandalaparthy
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
| | - Madhusmita Tripathy
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
| | - Nico F A van der Vegt
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
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9
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Donati L, Weber M. Assessing transition rates as functions of environmental variables. J Chem Phys 2022; 157:224103. [PMID: 36546809 DOI: 10.1063/5.0109555] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
Abstract
We present a method to estimate the transition rates of molecular systems under different environmental conditions that cause the formation or the breaking of bonds and require the sampling of the Grand Canonical Ensemble. For this purpose, we model the molecular system in terms of probable "scenarios," governed by different potential energy functions, which are separately sampled by classical MD simulations. Reweighting the canonical distribution of each scenario according to specific environmental variables, we estimate the grand canonical distribution, then use the Square Root Approximation method to discretize the Fokker-Planck operator into a rate matrix and the robust Perron Cluster Cluster Analysis method to coarse-grain the kinetic model. This permits efficiently estimating the transition rates of conformational states as functions of environmental variables, for example, the local pH at a cell membrane. In this work, we formalize the theoretical framework of the procedure, and we present a numerical experiment comparing the results with those provided by a constant-pH method based on non-equilibrium Molecular Dynamics Monte Carlo simulations. The method is relevant for the development of new drug design strategies that take into account how the cellular environment influences biochemical processes.
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Affiliation(s)
- Luca Donati
- Zuse Institute Berlin, Takustr. 7, D-14195 Berlin, Germany
| | - Marcus Weber
- Zuse Institute Berlin, Takustr. 7, D-14195 Berlin, Germany
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10
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de Oliveira VM, Liu R, Shen J. Constant pH molecular dynamics simulations: Current status and recent applications. Curr Opin Struct Biol 2022; 77:102498. [PMID: 36410222 PMCID: PMC9933785 DOI: 10.1016/j.sbi.2022.102498] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 10/10/2022] [Indexed: 11/19/2022]
Abstract
Many important protein functions are carried out through proton-coupled conformational dynamics. Thus, the ability to accurately model protonation states dynamically has wide-ranging implications. Over the past two decades, two main types of constant pH methods (discrete and continuous) have been developed to enable proton-coupled molecular dynamics (MD) simulations. In this short review, we discuss the current status of the development and highlight recent applications that have advanced our understanding of protein structure-function relationships. We conclude the review by outlining the remaining challenges in the method development and projecting important areas for future applications.
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Affiliation(s)
- Vinicius Martins de Oliveira
- Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, 20 Penn Street, Baltimore, 20201, Maryland, U.S.A
| | - Ruibin Liu
- Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, 20 Penn Street, Baltimore, 20201, Maryland, U.S.A
| | - Jana Shen
- Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, 20 Penn Street, Baltimore, 20201, MD, USA.
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11
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Aho N, Buslaev P, Jansen A, Bauer P, Groenhof G, Hess B. Scalable Constant pH Molecular Dynamics in GROMACS. J Chem Theory Comput 2022; 18:6148-6160. [PMID: 36128977 PMCID: PMC9558312 DOI: 10.1021/acs.jctc.2c00516] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Noora Aho
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, 40014Jyväskylä, Finland
| | - Pavel Buslaev
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, 40014Jyväskylä, Finland
| | - Anton Jansen
- Department of Applied Physics and Swedish e-Science Research Center, Science for Life Laboratory, KTH Royal Institute of Technology, 100 44Stockholm, Sweden
| | - Paul Bauer
- Department of Applied Physics and Swedish e-Science Research Center, Science for Life Laboratory, KTH Royal Institute of Technology, 100 44Stockholm, Sweden
| | - Gerrit Groenhof
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, 40014Jyväskylä, Finland
| | - Berk Hess
- Department of Applied Physics and Swedish e-Science Research Center, Science for Life Laboratory, KTH Royal Institute of Technology, 100 44Stockholm, Sweden
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12
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Buslaev P, Aho N, Jansen A, Bauer P, Hess B, Groenhof G. Best Practices in Constant pH MD Simulations: Accuracy and Sampling. J Chem Theory Comput 2022; 18:6134-6147. [PMID: 36107791 PMCID: PMC9558372 DOI: 10.1021/acs.jctc.2c00517] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
![]()
Various approaches
have been proposed to include the
effect of
pH in molecular dynamics (MD) simulations. Among these, the λ-dynamics approach proposed
by Brooks and
co-workers [Kong, X.; Brooks III, C. L. J. Chem. Phys.1996, 105, 2414−2423] can be performed
with little computational overhead and hfor each typeence be used
to routinely perform MD simulations at microsecond time scales, as
shown in the accompanying paper [Aho, N. et al. J. Chem. Theory
Comput.2022, DOI: 10.1021/acs.jctc.2c00516]. At
such time scales, however, the accuracy of the molecular mechanics
force field and the parametrization becomes critical. Here, we address
these issues and provide the community with guidelines on how to set
up and perform long time scale constant pH MD simulations. We found
that barriers associated with the torsions of side chains in the CHARMM36m
force field are too high for reaching convergence in constant pH MD
simulations on microsecond time scales. To avoid the high computational
cost of extending the sampling, we propose small modifications to
the force field to selectively reduce the torsional barriers. We demonstrate
that with such modifications we obtain converged distributions of
both protonation and torsional degrees of freedom and hence consistent
pKa estimates, while the sampling of the
overall configurational space accessible to proteins is unaffected
as compared to normal MD simulations. We also show that the results
of constant pH MD depend on the accuracy of the correction potentials.
While these potentials are typically obtained by fitting a low-order
polynomial to calculated free energy profiles, we find that higher
order fits are essential to provide accurate and consistent results.
By resolving problems in accuracy and sampling, the work described
in this and the accompanying paper paves the way to the widespread
application of constant pH MD beyond pKa prediction.
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Affiliation(s)
- Pavel Buslaev
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, 40014 Jyväskylä, Finland
| | - Noora Aho
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, 40014 Jyväskylä, Finland
| | - Anton Jansen
- Department of Applied Physics, Science for Life Laboratory, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden
| | - Paul Bauer
- Department of Applied Physics, Science for Life Laboratory, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden
| | - Berk Hess
- Department of Applied Physics and Swedish e-Science Research Center, Science for Life Laboratory, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden
| | - Gerrit Groenhof
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, 40014 Jyväskylä, Finland
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13
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Electrostatics in Computational Biophysics and Its Implications for Disease Effects. Int J Mol Sci 2022; 23:ijms231810347. [PMID: 36142260 PMCID: PMC9499338 DOI: 10.3390/ijms231810347] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2022] [Revised: 08/31/2022] [Accepted: 09/02/2022] [Indexed: 12/25/2022] Open
Abstract
This review outlines the role of electrostatics in computational molecular biophysics and its implication in altering wild-type characteristics of biological macromolecules, and thus the contribution of electrostatics to disease mechanisms. The work is not intended to review existing computational approaches or to propose further developments. Instead, it summarizes the outcomes of relevant studies and provides a generalized classification of major mechanisms that involve electrostatic effects in both wild-type and mutant biological macromolecules. It emphasizes the complex role of electrostatics in molecular biophysics, such that the long range of electrostatic interactions causes them to dominate all other forces at distances larger than several Angstroms, while at the same time, the alteration of short-range wild-type electrostatic pairwise interactions can have pronounced effects as well. Because of this dual nature of electrostatic interactions, being dominant at long-range and being very specific at short-range, their implications for wild-type structure and function are quite pronounced. Therefore, any disruption of the complex electrostatic network of interactions may abolish wild-type functionality and could be the dominant factor contributing to pathogenicity. However, we also outline that due to the plasticity of biological macromolecules, the effect of amino acid mutation may be reduced, and thus a charge deletion or insertion may not necessarily be deleterious.
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14
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Patel LA, Chau P, Debesai S, Darwin L, Neale C. Drug Discovery by Automated Adaptation of Chemical Structure and Identity. J Chem Theory Comput 2022; 18:5006-5024. [PMID: 35834740 DOI: 10.1021/acs.jctc.1c01271] [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
Computer-aided drug design offers the potential to dramatically reduce the cost and effort required for drug discovery. While screening-based methods are valuable in the early stages of hit identification, they are frequently succeeded by iterative, hypothesis-driven computations that require recurrent investment of human time and intuition. To increase automation, we introduce a computational method for lead refinement that combines concerted dynamics of the ligand/protein complex via molecular dynamics simulations with integrated Monte Carlo-based changes in the chemical formula of the ligand. This approach, which we refer to as ligand-exchange Monte Carlo molecular dynamics, accounts for solvent- and entropy-based contributions to competitive binding free energies by coupling the energetics of bound and unbound states during the ligand-exchange attempt. Quantitative comparison of relative binding free energies to reference values from free energy perturbation, conducted in vacuum, indicates that ligand-exchange Monte Carlo molecular dynamics simulations sample relevant conformational ensembles and are capable of identifying strongly binding compounds. Additional simulations demonstrate the use of an implicit solvent model. We speculate that the use of chemical graphs in which exchanges are only permitted between ligands with sufficient similarity may enable an automated search to capture some of the benefits provided by human intuition during hypothesis-guided lead refinement.
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15
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Chen AY, Lee J, Damjanovic A, Brooks BR. Protein p Ka Prediction by Tree-Based Machine Learning. J Chem Theory Comput 2022; 18:2673-2686. [PMID: 35289611 PMCID: PMC10510853 DOI: 10.1021/acs.jctc.1c01257] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Protonation states of ionizable protein residues modulate many essential biological processes. For correct modeling and understanding of these processes, it is crucial to accurately determine their pKa values. Here, we present four tree-based machine learning models for protein pKa prediction. The four models, Random Forest, Extra Trees, eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM), were trained on three experimental PDB and pKa datasets, two of which included a notable portion of internal residues. We observed similar performance among the four machine learning algorithms. The best model trained on the largest dataset performs 37% better than the widely used empirical pKa prediction tool PROPKA and 15% better than the published result from the pKa prediction method DelPhiPKa. The overall root-mean-square error (RMSE) for this model is 0.69, with surface and buried RMSE values being 0.56 and 0.78, respectively, considering six residue types (Asp, Glu, His, Lys, Cys, and Tyr), and 0.63 when considering Asp, Glu, His, and Lys only. We provide pKa predictions for proteins in human proteome from the AlphaFold Protein Structure Database and observed that 1% of Asp/Glu/Lys residues have highly shifted pKa values close to the physiological pH.
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Affiliation(s)
- Ada Y. Chen
- Department of Physics & Astronomy, Johns Hopkins
University, Baltimore, Maryland, 21218
- Laboratory of Computational Biology, National Heart, Lung
and Blood Institute, National Institutes of Health, Bethesda, Maryland, 20892
| | - Juyong Lee
- Department of Chemistry, Division of Chemistry and
Biochemistry, Kangwon National University, 1 Gangwondaehak-gil, Chuncheon, 24341,
Republic of Korea
| | - Ana Damjanovic
- Department of Biophysics, Johns Hopkins University,
Baltimore, Maryland, 21218
| | - Bernard R. Brooks
- Laboratory of Computational Biology, National Heart, Lung
and Blood Institute, National Institutes of Health, Bethesda, Maryland, 20892
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16
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Gokcan H, Isayev O. Prediction of protein p K a with representation learning. Chem Sci 2022; 13:2462-2474. [PMID: 35310485 PMCID: PMC8864681 DOI: 10.1039/d1sc05610g] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Accepted: 01/29/2022] [Indexed: 11/21/2022] Open
Abstract
The behavior of proteins is closely related to the protonation states of the residues. Therefore, prediction and measurement of pK a are essential to understand the basic functions of proteins. In this work, we develop a new empirical scheme for protein pK a prediction that is based on deep representation learning. It combines machine learning with atomic environment vector (AEV) and learned quantum mechanical representation from ANI-2x neural network potential (J. Chem. Theory Comput. 2020, 16, 4192). The scheme requires only the coordinate information of a protein as the input and separately estimates the pK a for all five titratable amino acid types. The accuracy of the approach was analyzed with both cross-validation and an external test set of proteins. Obtained results were compared with the widely used empirical approach PROPKA. The new empirical model provides accuracy with MAEs below 0.5 for all amino acid types. It surpasses the accuracy of PROPKA and performs significantly better than the null model. Our model is also sensitive to the local conformational changes and molecular interactions.
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Affiliation(s)
- Hatice Gokcan
- Department of Chemistry, Mellon College of Science, Carnegie Mellon University Pittsburgh PA USA
| | - Olexandr Isayev
- Department of Chemistry, Mellon College of Science, Carnegie Mellon University Pittsburgh PA USA
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17
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Chen AY, Brooks BR, Damjanovic A. Determinants of conductance of a bacterial voltage-gated sodium channel. Biophys J 2021; 120:3050-3069. [PMID: 34214541 DOI: 10.1016/j.bpj.2021.06.013] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Revised: 05/22/2021] [Accepted: 06/08/2021] [Indexed: 10/21/2022] Open
Abstract
Through molecular dynamics (MD) and free energy simulations in electric fields, we examine the factors influencing conductance of bacterial voltage-gated sodium channel NavMs. The channel utilizes four glutamic acid residues in the selectivity filter (SF). Previously, we have shown, through constant pH and free energy calculations of pKa values, that fully deprotonated, singly protonated, and doubly protonated states are all feasible at physiological pH, depending on how many ions are bound in the SF. With 173 MD simulations of 450 or 500 ns and additional free energy simulations, we determine that the conductance is highest for the deprotonated state and decreases with each additional proton bound. We also determine that the pKa value of the four glutamic residues for the transition between deprotonated and singly protonated states is close to the physiological pH and that there is a small voltage dependence. The pKa value and conductance trends are in agreement with experimental work on bacterial Nav channels, which show a decrease in maximal conductance with lowering of pH, with pKa in the physiological range. We examine binding sites for Na+ in the SF, compare with previous work, and note a dependence on starting structures. We find that narrowing of the gate backbone to values lower than the crystal structure's backbone radius reduces the conductance, whereas increasing the gate radius further does not affect the conductance. Simulations with some amount of negatively charged lipids as opposed to purely neutral lipids increases the conductance, as do simulations at higher voltages.
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Affiliation(s)
- Ada Y Chen
- Department of Physics & Astronomy, Johns Hopkins University, Baltimore, Maryland; Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland
| | - Bernard R Brooks
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland
| | - Ana Damjanovic
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland; Department of Biophysics, Johns Hopkins University, Baltimore, Maryland.
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18
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Michael E, Polydorides S, Simonson T, Archontis G. Hybrid MC/MD for protein design. J Chem Phys 2021; 153:054113. [PMID: 32770896 DOI: 10.1063/5.0013320] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Abstract
Computational protein design relies on simulations of a protein structure, where selected amino acids can mutate randomly, and mutations are selected to enhance a target property, such as stability. Often, the protein backbone is held fixed and its degrees of freedom are modeled implicitly to reduce the complexity of the conformational space. We present a hybrid method where short molecular dynamics (MD) segments are used to explore conformations and alternate with Monte Carlo (MC) moves that apply mutations to side chains. The backbone is fully flexible during MD. As a test, we computed side chain acid/base constants or pKa's in five proteins. This problem can be considered a special case of protein design, with protonation/deprotonation playing the role of mutations. The solvent was modeled as a dielectric continuum. Due to cost, in each protein we allowed just one side chain position to change its protonation state and the other position to change its type or mutate. The pKa's were computed with a standard method that scans a range of pH values and with a new method that uses adaptive landscape flattening (ALF) to sample all protonation states in a single simulation. The hybrid method gave notably better accuracy than standard, fixed-backbone MC. ALF decreased the computational cost a factor of 13.
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Affiliation(s)
- Eleni Michael
- Department of Physics, University of Cyprus, P.O 20537, CY678 Nicosia, Cyprus
| | - Savvas Polydorides
- Department of Physics, University of Cyprus, P.O 20537, CY678 Nicosia, Cyprus
| | - Thomas Simonson
- Laboratoire de Biochimie (CNRS UMR7654), Ecole Polytechnique, Palaiseau, France
| | - Georgios Archontis
- Department of Physics, University of Cyprus, P.O 20537, CY678 Nicosia, Cyprus
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19
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On the Use of the Discrete Constant pH Molecular Dynamics to Describe the Conformational Space of Peptides. Polymers (Basel) 2020; 13:polym13010099. [PMID: 33383731 PMCID: PMC7795291 DOI: 10.3390/polym13010099] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2020] [Revised: 12/18/2020] [Accepted: 12/24/2020] [Indexed: 12/02/2022] Open
Abstract
Solvent pH is an important property that defines the protonation state of the amino acids and, therefore, modulates the interactions and the conformational space of the biochemical systems. Generally, this thermodynamic variable is poorly considered in Molecular Dynamics (MD) simulations. Fortunately, this lack has been overcome by means of the Constant pH Molecular Dynamics (CPHMD) methods in the recent decades. Several studies have reported promising results from these approaches that include pH in simulations but focus on the prediction of the effective pKa of the amino acids. In this work, we want to shed some light on the CPHMD method and its implementation in the AMBER suitcase from a conformational point of view. To achieve this goal, we performed CPHMD and conventional MD (CMD) simulations of six protonatable amino acids in a blocked tripeptide structure to compare the conformational sampling and energy distributions of both methods. The results reveal strengths and weaknesses of the CPHMD method in the implementation of AMBER18 version. The change of the protonation state according to the chemical environment is presumably an improvement in the accuracy of the simulations. However, the simulations of the deprotonated forms are not consistent, which is related to an inaccurate assignment of the partial charges of the backbone atoms in the CPHMD residues. Therefore, we recommend the CPHMD methods of AMBER program but pointing out the need to compare structural properties with experimental data to bring reliability to the conformational sampling of the simulations.
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20
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Kasavajhala K, Lam K, Simmerling C. Exploring Protocols to Build Reservoirs to Accelerate Temperature Replica Exchange MD Simulations. J Chem Theory Comput 2020; 16:7776-7799. [PMID: 33142060 DOI: 10.1021/acs.jctc.0c00513] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Temperature replica exchange molecular dynamics (REMD) is a widely used enhanced sampling method for accelerating biomolecular simulations. During the past 2 decades, several variants of REMD have been developed to further improve the rate of conformational sampling of REMD. One such variant, reservoir REMD (RREMD), was shown to improve the rate of conformational sampling by around 5-20×. Despite the significant increase in the sampling speed, RREMD methods have not been widely used because of the difficulties in building the reservoir and also because of the code not being available on the graphics processing units (GPUs). In this work, we ported the Amber RREMD code onto GPUs making it 20× faster than the central processing unit code. Then, we explored protocols for building Boltzmann-weighted reservoirs as well as non-Boltzmann reservoirs and tested how each choice affects the accuracy of the resulting RREMD simulations. We show that, using the recommended protocols outlined here, RREMD simulations can accurately reproduce Boltzmann-weighted ensembles obtained by much more expensive conventional temperature-based REMD simulations, with at least 15× faster convergence rates even for larger proteins (>50 amino acids) compared to conventional REMD.
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Affiliation(s)
- Koushik Kasavajhala
- Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, United States.,Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, United States
| | - Kenneth Lam
- Molecular and Cellular Biology, Stony Brook University, Stony Brook, New York 11794, United States.,Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, United States
| | - Carlos Simmerling
- Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, United States.,Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, United States
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21
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Paul TJ, Vilseck JZ, Hayes RL, Brooks CL. Exploring pH Dependent Host/Guest Binding Affinities. J Phys Chem B 2020; 124:6520-6528. [PMID: 32628482 DOI: 10.1021/acs.jpcb.0c03671] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
When the electrostatic environment surrounding binding partners changes between unbound and bound states, the net uptake or release of a proton is possible by either binding partner. This process is pH-dependent in that the free energy required to uptake or release the proton varies with pH. This pH-dependence is typically not considered in conventional free energy methods where the use of fixed protonation states is the norm. In the present paper, we apply a simple two-step approach to calculate the pH-dependent binding free energy of a model cucubit[7]uril host/guest system. By use of λ-dynamics with an enhanced sampling protocol, adaptive landscape flattening, pKa shifts and reference binding free energies upon complexation were determined. This information enables the construction of pH-dependent binding profiles that accurately capture the pKa shifts and reproduce binding free energies at the different pH conditions that were observed experimentally. Our calculations illustrate a general framework for computing pH-dependent binding free energies but also point to some issues in modeling the molecular charge distributions within this series of molecules with CGenFF. However, by introducing some minor charge modifications to the CGenFF force field, we saw significant improvement in accuracy of the calculated pKa shifts.
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22
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Liao Q. Enhanced sampling and free energy calculations for protein simulations. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2020; 170:177-213. [PMID: 32145945 DOI: 10.1016/bs.pmbts.2020.01.006] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
Molecular dynamics simulation is a powerful computational technique to study biomolecular systems, which complements experiments by providing insights into the structural dynamics relevant to biological functions at atomic scale. It can also be used to calculate the free energy landscapes of the conformational transitions to better understand the functions of the biomolecules. However, the sampling of biomolecular configurations is limited by the free energy barriers that need to be overcome, leading to considerable gaps between the timescales reached by MD simulation and those governing biological processes. To address this issue, many enhanced sampling methodologies have been developed to increase the sampling efficiency of molecular dynamics simulations and free energy calculations. Usually, enhanced sampling algorithms can be classified into methods based on collective variables (CV-based) and approaches which do not require predefined CVs (CV-free). In this chapter, the theoretical basis of free energy estimation is briefly reviewed first, followed by the reviews of the most common CV-based and CV-free methods including the presentation of some examples and recent developments. Finally, the combination of different enhanced sampling methods is discussed.
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Affiliation(s)
- Qinghua Liao
- Science for Life Laboratory, Department of Chemistry-BMC, Uppsala University, Uppsala, Sweden.
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23
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Lim YY, Lim TS, Choong YS. Human IgG1 Fc pH-dependent optimization from a constant pH molecular dynamics simulation analysis. RSC Adv 2020; 10:13066-13075. [PMID: 35492131 PMCID: PMC9051383 DOI: 10.1039/c9ra10712f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2019] [Accepted: 03/11/2020] [Indexed: 11/21/2022] Open
Abstract
The binding of IgG Fc with FcRn enables the long circulating half-life of IgG, where the Fc–FcRn complex interacts in a pH-dependent manner. This complex shows stronger interaction at pH ≤ 6.5 and weaker interaction at pH ≥ 7.4. The Fc–FcRn binding mechanism that promotes the long circulating half-life of IgG has prompted several IgG Fc-related mutational studies to focus on the pH-dependent Fc–FcRn complex interactions in order to improve the pharmacokinetic properties of Fc. Hence, in this study, we applied the in silico constant pH molecular dynamics (CpHMD) simulation approach to evaluate the human Fc–FcRn complex binding (pH 6.0) and dissociating (pH 7.5) mechanism at the molecular level. The analysis showed that the protonated state of the titratable residues changes from pH 6.0 to pH 7.5, where the disrupting energy for Fc–FcRn complex formation was found to be due to the electrostatic repulsion between the complex. According to the analysis, an Fc variant was computationally designed with an improved binding affinity at pH 6.0, which is still able to dissociate at pH 7.5 with FcRn at the in silico level. The binding free energy calculation via the MMPB/GBSA approach showed that the designed Fc mutant (MutM4) has increased binding affinity only at pH 6.0 compared with the reported mutant (YTE) Fc. This work demonstrates an alternative Fc design with better binding properties for FcRn, which can be useful for future experimental evaluation and validation. An in silico IgG-Fc variant with better affinity at pH 6.0 but retained the dissociation at pH 7.5 was designed.![]()
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Affiliation(s)
- Yee Ying Lim
- Institute for Research in Molecular Medicine (INFORMM)
- Universiti Sains Malaysia
- 11800 Minden
- Malaysia
| | - Theam Soon Lim
- Institute for Research in Molecular Medicine (INFORMM)
- Universiti Sains Malaysia
- 11800 Minden
- Malaysia
| | - Yee Siew Choong
- Institute for Research in Molecular Medicine (INFORMM)
- Universiti Sains Malaysia
- 11800 Minden
- Malaysia
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24
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Harris RC, Shen J. GPU-Accelerated Implementation of Continuous Constant pH Molecular Dynamics in Amber: p Ka Predictions with Single-pH Simulations. J Chem Inf Model 2019; 59:4821-4832. [PMID: 31661616 DOI: 10.1021/acs.jcim.9b00754] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present a GPU implementation of the continuous constant pH molecular dynamics (CpHMD) based on the most recent generalized Born implicit-solvent model in the pmemd engine of the Amber molecular dynamics package. To test the accuracy of the tool for rapid pKa predictions, a series of 2 ns single-pH simulations were performed for over 120 titratable residues in 10 benchmark proteins that were previously used to test the various continuous CpHMD methods. The calculated pKa's showed a root-mean-square deviation of 0.80 and correlation coefficient of 0.83 with respect to experiment. Also, 90% of the pKa's were converged with estimated errors below 0.1 pH units. Surprisingly, this level of accuracy is similar to our previous replica-exchange simulations with 2 ns per replica and an exchange attempt frequency of 2 ps-1 (Huang, Harris, and Shen J. Chem. Inf. Model. 2018 , 58 , 1372 - 1383 ). Interestingly, for the linked titration sites in two enzymes, although residue-specific protonation state sampling in the single-pH simulations was not converged within 2 ns, the protonation fraction of the linked residues appeared to be largely converged, and the experimental macroscopic pKa values were reproduced to within 1 pH unit. Comparison with replica-exchange simulations with different exchange attempt frequencies showed that the splitting between the two macroscopic pKa's is underestimated with frequent exchange attempts such as 2 ps-1, while single-pH simulations overestimate the splitting. The same trend is seen for the single-pH vs replica-exchange simulations of a hydrogen-bonded aspartyl dyad in a much larger protein. A 2 ns single-pH simulation of a 400-residue protein takes about 1 h on a single NVIDIA GeForce RTX 2080 graphics card, which is over 1000 times faster than a CpHMD run on a single CPU core of a high-performance computing cluster node. Thus, we envision that GPU-accelerated continuous CpHMD may be used in routine pKa predictions for a variety of applications, from assisting MD simulations with protonation state assignment to offering pH-dependent corrections of binding free energies and identifying reactive hot spots for covalent drug design.
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Affiliation(s)
- Robert C Harris
- Department of Pharmaceutical Sciences , University of Maryland School of Pharmacy , Baltimore , Maryland 21201 , United States
| | - Jana Shen
- Department of Pharmaceutical Sciences , University of Maryland School of Pharmacy , Baltimore , Maryland 21201 , United States
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25
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González-Lebrero RM, Defelipe L, Modenutti C, Roitberg AE, Batastini NA, Noguera ME, Santos J, Roman EA. Folding and Dynamics Are Strongly pH-Dependent in a Psychrophile Frataxin. J Phys Chem B 2019; 123:7676-7686. [PMID: 31407901 DOI: 10.1021/acs.jpcb.9b05960] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Protein dynamics, folding, and thermodynamics represent a central aspect of biophysical chemistry. pH, temperature, and denaturant perturbations inform our understanding of diverse contributors to stability and rates. In this work, we performed a thermodynamic analysis using a combined experimental and computational approach to gain insights into the role of electrostatics in the folding reaction of a psychrophile frataxin variant from Psychromonas ingrahamii. This folding reaction is strongly modulated by pH with a single, narrow, and well-defined transition state with ∼80% compactness, ∼70% electrostatic interactions, and ∼60% hydration shell compared to the native state (αD = 0.82, αH = 0.67, and αΔCp = 0.59). Our results are best explained by a two-proton/two-state model with very different pKa values of the native and denatured states (∼5.5 and ∼8.0, respectively). As a consequence, the stability strongly increases from pH 8.0 to 6.0 (|ΔΔG°| = 5.2 kcal mol-1), mainly because of a decrease in the TΔS°. Variation of ΔH° and ΔS° at pH below 7.0 is dominated by a change in ΔHf⧧ and ΔSf⧧, while at pH above 7.0, it is governed by ΔHu⧧ and ΔSu⧧. Molecular dynamics simulations showed that these pH modulations could be explained by the fluctuations of two regions, rich in electrostatic contacts, whose dynamics are pH-dependent and motions are strongly correlated. Results presented herein contribute to the understanding of the stability and dynamics of this frataxin variant, pointing to an intrinsic feature of the family topology to support different folding mechanisms.
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Affiliation(s)
- Rodolfo M González-Lebrero
- Facultad de Farmacia y Bioquímica, Departamento de Química Biológica , Universidad de Buenos Aires , Buenos Aires C1113AAD , Argentina
- Consejo Nacional de Investigaciones Científicas y Técnicas , Instituto de Química y Fisicoquímica Biológicas , Buenos Aires C1113AAD , Argentina
| | | | | | - Adrian E Roitberg
- Department of Chemistry , University of Florida , Gainesville , Florida 32611 , United States
| | - Nicolas A Batastini
- Facultad de Farmacia y Bioquímica, Departamento de Química Biológica , Universidad de Buenos Aires , Buenos Aires C1113AAD , Argentina
| | - Martín E Noguera
- Facultad de Farmacia y Bioquímica, Departamento de Química Biológica , Universidad de Buenos Aires , Buenos Aires C1113AAD , Argentina
| | | | - Ernesto A Roman
- Consejo Nacional de Investigaciones Científicas y Técnicas , Instituto de Química y Fisicoquímica Biológicas , Buenos Aires C1113AAD , Argentina
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26
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Sarkar A, Gupta PL, Roitberg AE. pH-Dependent Conformational Changes Due to Ionizable Residues in a Hydrophobic Protein Interior: The Study of L25K and L125K Variants of SNase. J Phys Chem B 2019; 123:5742-5754. [DOI: 10.1021/acs.jpcb.9b03816] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Ankita Sarkar
- Department of Physics, University of Florida, Gainesville, Florida 32611, United States
| | - Pancham Lal Gupta
- Department of Chemistry, University of Florida, Gainesville, Florida 32603, United States
| | - Adrian E. Roitberg
- Department of Chemistry, University of Florida, Gainesville, Florida 32603, United States
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27
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Wang AH, Zhang ZC, Li GH. Advances in enhanced sampling molecular dynamics simulations for biomolecules. CHINESE J CHEM PHYS 2019. [DOI: 10.1063/1674-0068/cjcp1905091] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- An-hui Wang
- Laboratory of Molecular Modeling and Design, State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
- State Key Laboratory of Fine Chemicals, School of Chemistry, Dalian University of Technology, Dalian 116024, China
| | - Zhi-chao Zhang
- State Key Laboratory of Fine Chemicals, School of Chemistry, Dalian University of Technology, Dalian 116024, China
| | - Guo-hui Li
- Laboratory of Molecular Modeling and Design, State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
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28
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Cruzeiro VWD, Roitberg AE. Multidimensional Replica Exchange Simulations for Efficient Constant pH and Redox Potential Molecular Dynamics. J Chem Theory Comput 2019; 15:871-881. [DOI: 10.1021/acs.jctc.8b00935] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Adrian E. Roitberg
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States
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29
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Lee TS, Cerutti DS, Mermelstein D, Lin C, LeGrand S, Giese TJ, Roitberg A, Case DA, Walker RC, York DM. GPU-Accelerated Molecular Dynamics and Free Energy Methods in Amber18: Performance Enhancements and New Features. J Chem Inf Model 2018; 58:2043-2050. [PMID: 30199633 DOI: 10.1021/acs.jcim.8b00462] [Citation(s) in RCA: 255] [Impact Index Per Article: 42.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
We report progress in graphics processing unit (GPU)-accelerated molecular dynamics and free energy methods in Amber18. Of particular interest is the development of alchemical free energy algorithms, including free energy perturbation and thermodynamic integration methods with support for nonlinear soft-core potential and parameter interpolation transformation pathways. These methods can be used in conjunction with enhanced sampling techniques such as replica exchange, constant-pH molecular dynamics, and new 12-6-4 potentials for metal ions. Additional performance enhancements have been made that enable appreciable speed-up on GPUs relative to the previous software release.
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Affiliation(s)
- Tai-Sung Lee
- Laboratory for Biomolecular Simulation Research, Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology , Rutgers University , Piscataway , New Jersey 08854 , United States
| | - David S Cerutti
- Laboratory for Biomolecular Simulation Research, Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology , Rutgers University , Piscataway , New Jersey 08854 , United States
| | - Dan Mermelstein
- Department of Chemistry and Biochemistry , University of California, San Diego , La Jolla , California 92093 , United States
| | - Charles Lin
- Department of Chemistry and Biochemistry , University of California, San Diego , La Jolla , California 92093 , United States
| | - Scott LeGrand
- A9.com , Palo Alto , California 94301 , United States
| | - Timothy J Giese
- Laboratory for Biomolecular Simulation Research, Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology , Rutgers University , Piscataway , New Jersey 08854 , United States
| | - Adrian Roitberg
- Department of Chemistry , University of Florida , Gainesville , Florida 32611 , United States
| | - David A Case
- Laboratory for Biomolecular Simulation Research, Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology , Rutgers University , Piscataway , New Jersey 08854 , United States
| | - Ross C Walker
- GlaxoSmithKline PLC , 1250 South Collegeville Road , Collegeville , Pennsylvania 19426 , United States
| | - Darrin M York
- Laboratory for Biomolecular Simulation Research, Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology , Rutgers University , Piscataway , New Jersey 08854 , United States
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30
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Damjanovic A, Miller BT, Okur A, Brooks BR. Reservoir pH replica exchange. J Chem Phys 2018; 149:072321. [PMID: 30134701 PMCID: PMC6005788 DOI: 10.1063/1.5027413] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2018] [Accepted: 05/30/2018] [Indexed: 11/15/2022] Open
Abstract
We present the reservoir pH replica exchange (R-pH-REM) method for constant pH simulations. The R-pH-REM method consists of a two-step procedure; the first step involves generation of one or more reservoirs of conformations. Each reservoir is obtained from a standard or enhanced molecular dynamics simulation with a constrained (fixed) protonation state. In the second step, fixed charge constraints are relaxed, as the structures from one or more reservoirs are periodically injected into a constant pH or a pH-replica exchange (pH-REM) simulation. The benefit of this two-step process is that the computationally intensive part of conformational search can be decoupled from constant pH simulations, and various techniques for enhanced conformational sampling can be applied without the need to integrate such techniques into the pH-REM framework. Simulations on blocked Lys, KK, and KAAE peptides were used to demonstrate an agreement between pH-REM and R-pH-REM simulations. While the reservoir simulations are not needed for these small test systems, the real need arises in cases when ionizable molecules can sample two or more conformations separated by a large energy barrier, such that adequate sampling is not achieved on a time scale of standard constant pH simulations. Such problems might be encountered in protein systems that exploit conformational transitions for function. A hypothetical case is studied, a small molecule with a large torsional barrier; while results of pH-REM simulations depend on the starting structure, R-pH-REM calculations on this model system are in excellent agreement with a theoretical model.
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Affiliation(s)
- Ana Damjanovic
- Author to whom correspondence should be addressed: . Tel.: (410) 516-5390. FAX: (410) 516-4118
| | - Benjamin T. Miller
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892-5690, USA
| | - Asim Okur
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892-5690, USA
| | - Bernard R. Brooks
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892-5690, USA
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31
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Cruzeiro VWD, Amaral MS, Roitberg AE. Redox potential replica exchange molecular dynamics at constant pH in AMBER: Implementation and validation. J Chem Phys 2018; 149:072338. [DOI: 10.1063/1.5027379] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- Vinícius Wilian D. Cruzeiro
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
- CAPES Foundation, Ministry of Education of Brazil, Brasília, DF 70040-020, Brazil
| | - Marcos S. Amaral
- Institute of Physics, Federal University of Mato Grosso do Sul, Campo Grande, MS 79070-900, Brazil
| | - Adrian E. Roitberg
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
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32
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Huang Y, Harris RC, Shen J. Generalized Born Based Continuous Constant pH Molecular Dynamics in Amber: Implementation, Benchmarking and Analysis. J Chem Inf Model 2018; 58:1372-1383. [PMID: 29949356 DOI: 10.1021/acs.jcim.8b00227] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Solution pH plays an important role in structure and dynamics of biomolecular systems; however, pH effects cannot be accurately accounted for in conventional molecular dynamics simulations based on fixed protonation states. Continuous constant pH molecular dynamics (CpHMD) based on the λ-dynamics framework calculates protonation states on the fly during dynamical simulation at a specified pH condition. Here we report the CPU-based implementation of the CpHMD method based on the GBNeck2 generalized Born (GB) implicit-solvent model in the pmemd engine of the Amber molecular dynamics package. The performance of the method was tested using pH replica-exchange titration simulations of Asp, Glu and His side chains in 4 miniproteins and 7 enzymes with experimentally known p Ka's, some of which are significantly shifted from the model values. The added computational cost due to CpHMD titration ranges from 11 to 33% for the data set and scales roughly linearly as the ratio between the titrable sites and number of solute atoms. Comparison of the experimental and calculated p Ka's using 2 ns per replica sampling yielded a mean unsigned error of 0.70, a root-mean-squared error of 0.91, and a linear correlation coefficient of 0.79. Though this level of accuracy is similar to the GBSW-based CpHMD in CHARMM, in contrast to the latter, the current implementation was able to reproduce the experimental orders of the p Ka's of the coupled carboxylic dyads. We quantified the sampling errors, which revealed that prolonged simulation is needed to converge p Ka's of several titratable groups involved in salt-bridge-like interactions or deeply buried in the protein interior. Our benchmark data demonstrate that GBNeck2-CpHMD is an attractive tool for protein p Ka predictions.
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Affiliation(s)
- Yandong Huang
- Department of Pharmaceutical Sciences , University of Maryland School of Pharmacy , Baltimore , Maryland 21201 , United States
| | - Robert C Harris
- Department of Pharmaceutical Sciences , University of Maryland School of Pharmacy , Baltimore , Maryland 21201 , United States
| | - Jana Shen
- Department of Pharmaceutical Sciences , University of Maryland School of Pharmacy , Baltimore , Maryland 21201 , United States
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33
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34
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Pathak AK. Effect of pH on the hinge region of influenza viral protein: a combined constant pH and well-tempered molecular dynamics study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:195101. [PMID: 29578453 DOI: 10.1088/1361-648x/aab98c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Despite the knowledge that the influenza protein, hemagglutinin, undergoes a large conformational change at low pH during the process of fusion with the host cell, its molecular mechanism remains elusive. The present constant pH molecular dynamics (CpHMD) study identifies the residues responsible for large conformational change in acidic condition. Based on the pKa calculations, it is predicted that His-106 is much more responsible for the large conformational change than any other residues in the hinge region of hemagglutinin protein. Potential of mean force profile from well-tempered meta-dynamics (WT-MtD) simulation is also generated along the folding pathway by considering radius of gyration (R gyr) as a collective variable (CV). It is very clear from the present WT-MtD study, that the initial bending starts at that hinge region, which may trigger other conformational changes. Both the protein-protein and protein-water HB time correlation functions are monitored along the folding pathway. The protein-protein (full or hinge region) HB time correlation functions are always found to be stronger than those of the protein-water time correlation functions. The dynamical balance between protein-protein and protein-water HB interactions favors the stabilization of the folded state.
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Affiliation(s)
- Arup Kumar Pathak
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Mumbai 400085, India
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35
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Liu J, Swails J, Zhang JZH, He X, Roitberg AE. A Coupled Ionization-Conformational Equilibrium Is Required To Understand the Properties of Ionizable Residues in the Hydrophobic Interior of Staphylococcal Nuclease. J Am Chem Soc 2018; 140:1639-1648. [PMID: 29308643 DOI: 10.1021/jacs.7b08569] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Ionizable residues in the interior of proteins play essential roles, especially in biological energy transduction, but are relatively rare and seem incompatible with the complex and polar environment. We perform a comprehensive study of the internal ionizable residues on 21 variants of staphylococcal nuclease with internal Lys, Glu, or Asp residues. Using pH replica exchange molecular dynamics simulations, we find that, in most cases, the pKa values of these internal ionizable residues are shifted significantly from their values in solution. Our calculated results are in excellent agreement with the experimental observations of the Garcia-Moreno group. We show that the interpretation of the experimental pKa values requires the study of not only protonation changes but also conformational changes. The coupling between the protonation and conformational equilibria suggests a mechanism for efficient pH-sensing and regulation in proteins. This study provides new physical insights into how internal ionizable residues behave in the hydrophobic interior of proteins.
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Affiliation(s)
- Jinfeng Liu
- School of Chemistry and Molecular Engineering, Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, East China Normal University , Shanghai, 200062, China.,Department of Chemistry, University of Florida , Gainesville, Florida 32611, United States.,Department of Basic Medicine and Clinical Pharmacy, China Pharmaceutical University , Nanjing, 210009, China
| | - Jason Swails
- Department of Chemistry and Chemical Biology and BioMaPS Institute, Rutgers University , Piscataway, New Jersey 08854, United States
| | - John Z H Zhang
- School of Chemistry and Molecular Engineering, Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, East China Normal University , Shanghai, 200062, China.,NYU-ECNU Center for Computational Chemistry at NYU Shanghai , Shanghai, 200062, China
| | - Xiao He
- School of Chemistry and Molecular Engineering, Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, East China Normal University , Shanghai, 200062, China.,NYU-ECNU Center for Computational Chemistry at NYU Shanghai , Shanghai, 200062, China
| | - Adrian E Roitberg
- Department of Chemistry, University of Florida , Gainesville, Florida 32611, United States
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36
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Peck MT, Ortega G, De Luca-Johnson JN, Schlessman JL, Robinson AC, García-Moreno E B. Local Backbone Flexibility as a Determinant of the Apparent pKa Values of Buried Ionizable Groups in Proteins. Biochemistry 2017; 56:5338-5346. [DOI: 10.1021/acs.biochem.7b00678] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Affiliation(s)
- Meredith T. Peck
- Department
of Biophysics, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Gabriel Ortega
- Structural
Biology Unit, CIC bioGUNE, Bizkaia Technology Park Ed. 800, 48160 Derio, Spain
- Department
of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
| | | | - Jamie L. Schlessman
- Chemistry
Department, U.S. Naval Academy, Annapolis, Maryland 21402, United States
| | - Aaron C. Robinson
- Department
of Biophysics, Johns Hopkins University, Baltimore, Maryland 21218, United States
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37
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Wu X, Lee J, Brooks BR. Origin of pK a Shifts of Internal Lysine Residues in SNase Studied Via Equal-Molar VMMS Simulations in Explicit Water. J Phys Chem B 2016; 121:3318-3330. [PMID: 27700118 DOI: 10.1021/acs.jpcb.6b08249] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Protein internal ionizable groups can exhibit large shifts in pKa values. Although the environment and interaction changes have been extensively studied both experimentally and computationally, direct calculation of pKa values of these internal ionizable groups in explicit water is challenging due to energy barriers in solvent interaction and in conformational transition. The virtual mixture of multiple states (VMMS) method is a new approach designed to study chemical state equilibrium. This method constructs a virtual mixture of multiple chemical states in order to sample the conformational space of all states simultaneously and to avoid crossing energy barriers related to state transition. By applying VMMS to 25 variants of staphylococcal nuclease with lysine residues at internal positions, we obtained the pKa values of these lysine residues and investigated the physics underlining the pKa shifts. Our calculation results agree reasonably well with experimental measurements, validating the VMMS method for pKa calculation and providing molecular details of the protonation equilibrium for protein internal ionizable groups. Based on our analyses of protein conformation relaxation, lysine side chain flexibility, water penetration, and the microenvironment, we conclude that the hydrophobicity of the microenvironment around the lysine side chain (which affects water penetration differently for different protonation states) plays an important role in the pKa shifts.
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Affiliation(s)
- Xiongwu Wu
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute (NHLBI), National Institutes of Health (NIH) , Bethesda, Maryland 20892, United States
| | - Juyong Lee
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute (NHLBI), National Institutes of Health (NIH) , Bethesda, Maryland 20892, United States
| | - Bernard R Brooks
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute (NHLBI), National Institutes of Health (NIH) , Bethesda, Maryland 20892, United States
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38
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Chen Y, Roux B. Constant-pH Hybrid Nonequilibrium Molecular Dynamics-Monte Carlo Simulation Method. J Chem Theory Comput 2016; 11:3919-31. [PMID: 26300709 PMCID: PMC4535364 DOI: 10.1021/acs.jctc.5b00261] [Citation(s) in RCA: 70] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
A computational method is developed to carry out explicit solvent simulations of complex molecular systems under conditions of constant pH. In constant-pH simulations, preidentified ionizable sites are allowed to spontaneously protonate and deprotonate as a function of time in response to the environment and the imposed pH. The method, based on a hybrid scheme originally proposed by H. A. Stern (J. Chem. Phys. 2007, 126, 164112), consists of carrying out short nonequilibrium molecular dynamics (neMD) switching trajectories to generate physically plausible configurations with changed protonation states that are subsequently accepted or rejected according to a Metropolis Monte Carlo (MC) criterion. To ensure microscopic detailed balance arising from such nonequilibrium switches, the atomic momenta are altered according to the symmetric two-ends momentum reversal prescription. To achieve higher efficiency, the original neMD-MC scheme is separated into two steps, reducing the need for generating a large number of unproductive and costly nonequilibrium trajectories. In the first step, the protonation state of a site is randomly attributed via a Metropolis MC process on the basis of an intrinsic pKa; an attempted nonequilibrium switch is generated only if this change in protonation state is accepted. This hybrid two-step inherent pKa neMD-MC simulation method is tested with single amino acids in solution (Asp, Glu, and His) and then applied to turkey ovomucoid third domain and hen egg-white lysozyme. Because of the simple linear increase in the computational cost relative to the number of titratable sites, the present method is naturally able to treat extremely large systems.
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Affiliation(s)
- Yunjie Chen
- Department of Biochemistry and Molecular Biology, Department of Chemistry, University of Chicago , Chicago, Illinois 60637, United States
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, Department of Chemistry, University of Chicago , Chicago, Illinois 60637, United States
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39
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Suárez E, Adelman JL, Zuckerman DM. Accurate Estimation of Protein Folding and Unfolding Times: Beyond Markov State Models. J Chem Theory Comput 2016; 12:3473-81. [PMID: 27340835 PMCID: PMC5022777 DOI: 10.1021/acs.jctc.6b00339] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Because standard molecular dynamics (MD) simulations are unable to access time scales of interest in complex biomolecular systems, it is common to "stitch together" information from multiple shorter trajectories using approximate Markov state model (MSM) analysis. However, MSMs may require significant tuning and can yield biased results. Here, by analyzing some of the longest protein MD data sets available (>100 μs per protein), we show that estimators constructed based on exact non-Markovian (NM) principles can yield significantly improved mean first-passage times (MFPTs) for protein folding and unfolding. In some cases, MSM bias of more than an order of magnitude can be corrected when identical trajectory data are reanalyzed by non-Markovian approaches. The NM analysis includes "history" information, higher order time correlations compared to MSMs, that is available in every MD trajectory. The NM strategy is insensitive to fine details of the states used and works well when a fine time-discretization (i.e., small "lag time") is used.
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Affiliation(s)
- Ernesto Suárez
- Department of Computational and Systems Biology, University of Pittsburgh , Pittsburgh, Pennsylvania 15260, United States
| | - Joshua L Adelman
- Department of Biological Sciences, University of Pittsburgh , Pittsburgh, Pennsylvania 15260, United States
| | - Daniel M Zuckerman
- Department of Computational and Systems Biology, University of Pittsburgh , Pittsburgh, Pennsylvania 15260, United States
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40
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Yang M, Huang J, MacKerell AD. Enhanced conformational sampling using replica exchange with concurrent solute scaling and hamiltonian biasing realized in one dimension. J Chem Theory Comput 2016; 11:2855-67. [PMID: 26082676 PMCID: PMC4463548 DOI: 10.1021/acs.jctc.5b00243] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2015] [Indexed: 12/17/2022]
Abstract
![]()
Replica exchange (REX) is a powerful
computational tool for overcoming
the quasi-ergodic sampling problem of complex molecular systems. Recently,
several multidimensional extensions of this method have been developed
to realize exchanges in both temperature and biasing potential space
or the use of multiple biasing potentials to improve sampling efficiency.
However, increased computational cost due to the multidimensionality
of exchanges becomes challenging for use on complex systems under
explicit solvent conditions. In this study, we develop a one-dimensional
(1D) REX algorithm to concurrently combine the advantages of overall
enhanced sampling from Hamiltonian solute scaling and the specific
enhancement of collective variables using Hamiltonian biasing potentials.
In the present Hamiltonian replica exchange method, termed HREST-BP,
Hamiltonian solute scaling is applied to the solute subsystem, and
its interactions with the environment to enhance overall conformational
transitions and biasing potentials are added along selected collective
variables associated with specific conformational transitions, thereby
balancing the sampling of different hierarchical degrees of freedom.
The two enhanced sampling approaches are implemented concurrently
allowing for the use of a small number of replicas (e.g., 6 to 8)
in 1D, thus greatly reducing the computational cost in complex system
simulations. The present method is applied to conformational sampling
of two nitrogen-linked glycans (N-glycans) found
on the HIV gp120 envelope protein. Considering the general importance
of the conformational sampling problem, HREST-BP represents an efficient
procedure for the study of complex saccharides, and, more generally,
the method is anticipated to be of general utility for the conformational
sampling in a wide range of macromolecular systems.
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Affiliation(s)
- Mingjun Yang
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, Baltimore, Maryland 21201, United States
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41
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Pathak AK. Effect of a buried ion pair in the hydrophobic core of a protein: An insight from constant pH molecular dynamics study. Biopolymers 2016; 103:148-57. [PMID: 25363335 DOI: 10.1002/bip.22577] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2014] [Revised: 10/07/2014] [Accepted: 10/09/2014] [Indexed: 01/18/2023]
Abstract
Constant pH molecular dynamics (CpHMD) is a commonly used sampling method, which incorporates the coupling of conformational flexibility and protonation state of a protein during the simulation by using pH as an external parameter. The effects on the structure and stability of a hyperstable variant of staphylococcal nuclease (Δ+PHS) protein of an artificial charge pair buried in its hydrophobic core are investigated by applying both CpHMD and accelerated molecular dynamics coupled with constant pH (CpHaMD) methods. Generalized Born electrostatics is used to model the solvent water. Two sets of starting coordinates of V23E/L36K variant of Δ+PHS, namely, Maestro generated coordinates from Δ+PHS and crystal structure coordinates of the same are considered for detail investigations. On the basis of root mean square displacement (RMSD) and root mean square fluctuations (RMSF) calculations, it is observed that this variant is stable over a wide range of pH. The calculated pKa values for aspartate and glutamate residues based on both CpHMD and CpHaMD simulations are consistent with the reported experimental values (within ± 0.5 to ± 1.5 pH unit), which clearly indicates that the local chemical environment of the carboxylic acids in V23E/L36K variant are comparable to the parent form. The strong salt bridge interaction between the mutated pair, E23/K36 and additional hydrogen bonds formed in the V23E/L36K variant, may help to compensate for the unfavorable self-energy experienced by the burial of these residues in the hydrophobic core. However, from RMSD, RMSF, and pKa analysis, no significant change in the global conformation of V23E/L36K variant with respect to the parent form, Δ+PHS is noticed.
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Affiliation(s)
- Arup K Pathak
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Mumbai, 400085, India
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42
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Mimicking titration experiments with MD simulations: A protocol for the investigation of pH-dependent effects on proteins. Sci Rep 2016; 6:22523. [PMID: 26936826 PMCID: PMC4776130 DOI: 10.1038/srep22523] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2015] [Accepted: 02/15/2016] [Indexed: 11/08/2022] Open
Abstract
Protein structure and function are highly dependent on the environmental pH. However, the temporal or spatial resolution of experimental approaches hampers direct observation of pH-induced conformational changes at the atomic level. Molecular dynamics (MD) simulation strategies (e.g. constant pH MD) have been developed to bridge this gap. However, one frequent problem is the sampling of unrealistic conformations, which may also lead to poor pKa predictions. To address this problem, we have developed and benchmarked the pH-titration MD (pHtMD) approach, which is inspired by wet-lab titration experiments. We give several examples how the pHtMD protocol can be applied for pKa calculation including peptide systems, Staphylococcus nuclease (SNase), and the chaperone HdeA. For HdeA, pHtMD is also capable of monitoring pH-dependent dimer dissociation in accordance with experiments. We conclude that pHtMD represents a versatile tool for pKa value calculation and simulation of pH-dependent effects in proteins.
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43
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Lang EJM, Heyes LC, Jameson GB, Parker EJ. Calculated pKa Variations Expose Dynamic Allosteric Communication Networks. J Am Chem Soc 2016; 138:2036-45. [DOI: 10.1021/jacs.5b13134] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
| | | | - Geoffrey B. Jameson
- Institute
of Fundamental Sciences, Massey University, PO Box 11-222, Palmerston North 4422, New Zealand
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44
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A Virtual Mixture Approach to the Study of Multistate Equilibrium: Application to Constant pH Simulation in Explicit Water. PLoS Comput Biol 2015; 11:e1004480. [PMID: 26506245 PMCID: PMC4624693 DOI: 10.1371/journal.pcbi.1004480] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2015] [Accepted: 07/29/2015] [Indexed: 11/26/2022] Open
Abstract
Chemical and thermodynamic equilibrium of multiple states is a fundamental phenomenon in biology systems and has been the focus of many experimental and computational studies. This work presents a simulation method to directly study the equilibrium of multiple states. This method constructs a virtual mixture of multiple states (VMMS) to sample the conformational space of all chemical states simultaneously. The VMMS system consists of multiple subsystems, one for each state. The subsystem contains a solute and a solvent environment. The solute molecules in all subsystems share the same conformation but have their own solvent environments. Transition between states is implicated by the change of their molar fractions. Simulation of a VMMS system allows efficient calculation of relative free energies of all states, which in turn determine their equilibrium molar fractions. For systems with a large number of state transition sites, an implicit site approximation is introduced to minimize the cost of simulation. A direct application of the VMMS method is for constant pH simulation to study protonation equilibrium. Applying the VMMS method to a heptapeptide of 3 ionizable residues, we calculated the pKas of those residues both with all explicit states and with implicit sites and obtained consistent results. For mouse epidermal growth factor of 9 ionizable groups, our VMMS simulations with implicit sites produced pKas of all 9 ionizable groups and the results agree qualitatively with NMR measurement. This example demonstrates the VMMS method can be applied to systems of a large number of ionizable groups and the computational cost scales linearly with the number of ionizable groups. For one of the most challenging systems in constant pH calculation, SNase Δ+PHS/V66K, our VMMS simulation shows that it is the state-dependent water penetration that causes the large deviation in lysine66’s pKa. Computer simulation plays an important role to understand molecular systems and has been applied to problems of increasing complexity. Multistate equilibrium is a fundamental concept behind the structure and function of biological systems. Due to the limit in computing resources and lack of good alternative methods, computer simulation has been conducted for systems in a single state, sampling from one state to another to infer equilibrium properties. This sequential approach has been successful in many cases such as protonation equilibrium with implicit solvation model. However, state transition is difficult when explicit solvent is used for more accurate solvation description. Many efforts have been dedicated to overcome this difficulty. Analogous to real multistate systems, we proposed a virtual mixture of multiple states (VMMS) to directly simulate the equilibrium. State transitions are replaced by changes in state molar fractions. Mimicking a test tube environment, all states are simulated in parallel to equilibrate with each other. Application to constant pH simulation in explicit water demonstrates the capability of this method. It is expected that the VMMS method will find more applications in biological problems related to the equilibrium of competing states.
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45
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Xia J, Flynn WF, Gallicchio E, Zhang BW, He P, Tan Z, Levy RM. Large-scale asynchronous and distributed multidimensional replica exchange molecular simulations and efficiency analysis. J Comput Chem 2015; 36:1772-85. [PMID: 26149645 PMCID: PMC4512903 DOI: 10.1002/jcc.23996] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2015] [Revised: 06/10/2015] [Accepted: 06/11/2015] [Indexed: 01/25/2023]
Abstract
We describe methods to perform replica exchange molecular dynamics (REMD) simulations asynchronously (ASyncRE). The methods are designed to facilitate large scale REMD simulations on grid computing networks consisting of heterogeneous and distributed computing environments as well as on homogeneous high-performance clusters. We have implemented these methods on NSF (National Science Foundation) XSEDE (Extreme Science and Engineering Discovery Environment) clusters and BOINC (Berkeley Open Infrastructure for Network Computing) distributed computing networks at Temple University and Brooklyn College at CUNY (the City University of New York). They are also being implemented on the IBM World Community Grid. To illustrate the methods, we have performed extensive (more than 60 ms in aggregate) simulations for the beta-cyclodextrin-heptanoate host-guest system in the context of one- and two-dimensional ASyncRE, and we used the results to estimate absolute binding free energies using the binding energy distribution analysis method. We propose ways to improve the efficiency of REMD simulations: these include increasing the number of exchanges attempted after a specified molecular dynamics (MD) period up to the fast exchange limit and/or adjusting the MD period to allow sufficient internal relaxation within each thermodynamic state. Although ASyncRE simulations generally require long MD periods (>picoseconds) per replica exchange cycle to minimize the overhead imposed by heterogeneous computing networks, we found that it is possible to reach an efficiency similar to conventional synchronous REMD, by optimizing the combination of the MD period and the number of exchanges attempted per cycle.
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Affiliation(s)
- Junchao Xia
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University, Philadelphia, PA 19122
| | - William F. Flynn
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University, Philadelphia, PA 19122
- Department of Physics & Astronomy, Rutgers University, Piscataway, NJ 08854
| | | | - Bin W. Zhang
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University, Philadelphia, PA 19122
| | - Peng He
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University, Philadelphia, PA 19122
| | - Zhiqiang Tan
- Department of Statistics, Rutgers University, Piscataway, NJ 08854
| | - Ronald M. Levy
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University, Philadelphia, PA 19122
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46
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Zarzycki P, Smith DM, Rosso KM. Proton Dynamics on Goethite Nanoparticles and Coupling to Electron Transport. J Chem Theory Comput 2015; 11:1715-24. [DOI: 10.1021/ct500891a] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- Piotr Zarzycki
- Institute
of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
| | - Dayle M. Smith
- Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Kevin M. Rosso
- Pacific Northwest National Laboratory, Richland, Washington 99354, United States
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47
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Meng Y, Lin YL, Roux B. Computational study of the "DFG-flip" conformational transition in c-Abl and c-Src tyrosine kinases. J Phys Chem B 2015; 119:1443-56. [PMID: 25548962 PMCID: PMC4315421 DOI: 10.1021/jp511792a] [Citation(s) in RCA: 48] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
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Protein
tyrosine kinases are crucial to cellular signaling pathways
regulating cell growth, proliferation, metabolism, differentiation,
and migration. To maintain normal regulation of cellular signal transductions,
the activities of tyrosine kinases are also highly regulated. The
conformation of a three-residue motif Asp-Phe-Gly (DFG) near the N-terminus
of the long “activation” loop covering the catalytic
site is known to have a critical impact on the activity of c-Abl and
c-Src tyrosine kinases. A conformational transition of the DFG motif
can switch the enzyme from an active (DFG-in) to an inactive (DFG-out)
state. In the present study, the string method with swarms-of-trajectories
was used to computationally determine the reaction pathway connecting
the two end-states, and umbrella sampling calculations were carried
out to characterize the thermodynamic factors affecting the conformations
of the DFG motif in c-Abl and c-Src kinases. According to the calculated
free energy landscapes, the DFG-out conformation is clearly more favorable
in the case of c-Abl than that of c-Src. The calculations also show
that the protonation state of the aspartate residue in the DFG motif
strongly affects the in/out conformational transition in c-Abl, although
it has a much smaller impact in the case of c-Src due to local structural
differences.
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Affiliation(s)
- Yilin Meng
- Department of Biochemistry and Molecular Biology, The University of Chicago , 929 E. 57th Street, Chicago, Illinois, 60637, United States
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48
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Pathak AK. Constant pH molecular dynamics study on the doubly mutated staphylococcal nuclease: capturing the microenvironment. RSC Adv 2015. [DOI: 10.1039/c5ra17983a] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Small rearrangements of residues in the microenvironment of V23E/L36K variant of staphylococcal nuclease can effectively be captured by CpHMD method.
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Affiliation(s)
- Arup Kumar Pathak
- Theoretical Chemistry Section
- Bhabha Atomic Reserch Centre
- Mumbai-400085
- India
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49
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Bernardi RC, Melo MCR, Schulten K. Enhanced sampling techniques in molecular dynamics simulations of biological systems. Biochim Biophys Acta Gen Subj 2014; 1850:872-877. [PMID: 25450171 DOI: 10.1016/j.bbagen.2014.10.019] [Citation(s) in RCA: 410] [Impact Index Per Article: 41.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2014] [Revised: 10/17/2014] [Accepted: 10/20/2014] [Indexed: 01/29/2023]
Abstract
BACKGROUND Molecular dynamics has emerged as an important research methodology covering systems to the level of millions of atoms. However, insufficient sampling often limits its application. The limitation is due to rough energy landscapes, with many local minima separated by high-energy barriers, which govern the biomolecular motion. SCOPE OF REVIEW In the past few decades methods have been developed that address the sampling problem, such as replica-exchange molecular dynamics, metadynamics and simulated annealing. Here we present an overview over theses sampling methods in an attempt to shed light on which should be selected depending on the type of system property studied. MAJOR CONCLUSIONS Enhanced sampling methods have been employed for a broad range of biological systems and the choice of a suitable method is connected to biological and physical characteristics of the system, in particular system size. While metadynamics and replica-exchange molecular dynamics are the most adopted sampling methods to study biomolecular dynamics, simulated annealing is well suited to characterize very flexible systems. The use of annealing methods for a long time was restricted to simulation of small proteins; however, a variant of the method, generalized simulated annealing, can be employed at a relatively low computational cost to large macromolecular complexes. GENERAL SIGNIFICANCE Molecular dynamics trajectories frequently do not reach all relevant conformational substates, for example those connected with biological function, a problem that can be addressed by employing enhanced sampling algorithms. This article is part of a Special Issue entitled Recent developments of molecular dynamics.
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Affiliation(s)
| | - Marcelo C R Melo
- Center for Biophysics and Computational Biology, University of Illinois, Urbana, IL 61801, USA
| | - Klaus Schulten
- Beckman Institute, University of Illinois, Urbana, IL 61801, USA; Center for Biophysics and Computational Biology, University of Illinois, Urbana, IL 61801, USA; Department of Physics, University of Illinois, Urbana, IL 61801, USA.
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50
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Richman DE, Majumdar A, García-Moreno E B. pH dependence of conformational fluctuations of the protein backbone. Proteins 2014; 82:3132-43. [PMID: 25137073 DOI: 10.1002/prot.24673] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2014] [Revised: 06/25/2014] [Accepted: 08/04/2014] [Indexed: 01/08/2023]
Abstract
Proton binding equilibria (pK(a) values) of ionizable groups in proteins are exquisitely sensitive to their microenvironments. Apparent pK(a) values measured for individual ionizable residues with NMR spectroscopy are actually population-weighted averages of the pK(a) in different conformational microstates. NMR spectroscopy experiments with staphylococcal nuclease were used to test the hypothesis that pK(a) values of surface Glu and Asp residues are affected by pH-sensitive fluctuations of the backbone between folded and locally unfolded conformations. (15)N spin relaxation studies showed that as the pH decreases from the neutral into the acidic range the amplitudes of backbone fluctuations in the ps-ns timescale increase near carboxylic residues. Hydrogen exchange experiments suggested that backbone conformational fluctuations promoted by decreasing pH also reflect slower local or sub-global unfolding near carboxylic groups. This study has implications for structure-based pKa calculations: (1) The timescale of the backbone's response to ionization events in proteins can range from ps to ms, and even longer; (2) pH-sensitive fluctuations of the backbone can be localized to both the segment the ionizable residue is attached to or the one that occludes the ionizable group; (3) Structural perturbations are not necessarily propagated through Coulomb interactions; instead, local fluctuations appear to be coupled through the co-operativity inherent to elements of secondary structure and to networks of hydrogen bonds. These results are consistent with the idea that local conformational fluctuations and stabilities are important determinants of apparent pK(a) values of ionizable residues in proteins.
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Affiliation(s)
- Daniel E Richman
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland, 21218
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