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Abstract
The structures of biological macromolecules would not be known to their present extent without X-ray crystallography. Most simulations of globular proteins in solution begin by surrounding the crystal structure of the monomer in a bath of water molecules, but the standard simulation employing periodic boundary conditions is already close to a crystal lattice environment. With simple protocols, the same software and molecular models can perform simulations of the crystal lattice, including all asymmetric units and solvent to fill the box. Throughout the history of molecular dynamics, studies of crystal lattices have served to investigate the quality of the underlying force fields, correlate the simulated ensembles to experimental structure factors, and extrapolate the behavior in lattices to behavior in solution. Powerful new computers are enabling molecular simulations with greater realism and statistical convergence. Meanwhile, the advent of exciting new methods in crystallography, including femtosecond free-electron lasers and image reconstruction for time-resolved crystallography on slurries of small crystals, is expanding the range of structures accessible to X-ray diffraction. We review past fusions of simulations and crystallography, then look ahead to the ways that simulations of crystal structures will enhance structural biology in the future.
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Affiliation(s)
- David S Cerutti
- Department of Chemistry and Chemical Biology, Rutgers University, 174 Frelinghuysen Road, Piscataway, NJ 08854-8066
| | - David A Case
- Department of Chemistry and Chemical Biology, Rutgers University, 174 Frelinghuysen Road, Piscataway, NJ 08854-8066
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2
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Allison JR. Using simulation to interpret experimental data in terms of protein conformational ensembles. Curr Opin Struct Biol 2017; 43:79-87. [DOI: 10.1016/j.sbi.2016.11.018] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Revised: 11/15/2016] [Accepted: 11/21/2016] [Indexed: 01/03/2023]
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3
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van Gunsteren WF, Allison JR, Daura X, Dolenc J, Hansen N, Mark AE, Oostenbrink C, Rusu VH, Smith LJ. Bestimmung von Strukturinformation aus experimentellen Messdaten für Biomoleküle. Angew Chem Int Ed Engl 2016. [DOI: 10.1002/ange.201601828] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Wilfred F. van Gunsteren
- Laboratorium für Physikalische Chemie; Eidgenössische Technische Hochschule Zürich; 8093 Zürich Schweiz
| | - Jane R. Allison
- Centre for Theor. Chem. and Phys. & Institute of Natural and Mathematical Sciences; Massey Univ.; Auckland Neuseeland
- Biomolecular Interaction Centre; University of Canterbury, Christchurch; Neuseeland
- Maurice Wilkins Centre for Molecular Biodiscovery; Neuseeland
| | - Xavier Daura
- Institute of Biotechnology and Biomedicine; Universitat Autònoma de Barcelona (UAB); 08193 Barcelona Spanien
- Catalan Institution for Research and Advanced Studies (ICREA); 08010 Barcelona Spanien
| | - Jožica Dolenc
- Laboratorium für Physikalische Chemie; Eidgenössische Technische Hochschule Zürich; 8093 Zürich Schweiz
| | - Niels Hansen
- Institut für Technische Thermodynamik und Thermische Verfahrenstechnik; Universität Stuttgart; Pfaffenwaldring 9 70569 Stuttgart Deutschland
| | - Alan E. Mark
- School of Chemistry and Molecular Biosciences; University of Queensland; St. Lucia QLD 4072 Australien
| | - Chris Oostenbrink
- Institut für Molekulare Modellierung und Simulation; Universität für Bodenkultur Wien; Wien Österreich
| | - Victor H. Rusu
- Laboratorium für Physikalische Chemie; Eidgenössische Technische Hochschule Zürich; 8093 Zürich Schweiz
| | - Lorna J. Smith
- Department of Chemistry; University of Oxford, Inorganic Chemistry Laboratory; South Parks Road Oxford OX1 3QR Großbritannien
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4
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van Gunsteren WF, Allison JR, Daura X, Dolenc J, Hansen N, Mark AE, Oostenbrink C, Rusu VH, Smith LJ. Deriving Structural Information from Experimentally Measured Data on Biomolecules. Angew Chem Int Ed Engl 2016; 55:15990-16010. [PMID: 27862777 DOI: 10.1002/anie.201601828] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2016] [Revised: 07/08/2016] [Indexed: 12/27/2022]
Abstract
During the past half century, the number and accuracy of experimental techniques that can deliver values of observables for biomolecular systems have been steadily increasing. The conversion of a measured value Qexp of an observable quantity Q into structural information is, however, a task beset with theoretical and practical problems: 1) insufficient or inaccurate values of Qexp , 2) inaccuracies in the function Q(r→) used to relate the quantity Q to structure r→ , 3) how to account for the averaging inherent in the measurement of Qexp , 4) how to handle the possible multiple-valuedness of the inverse r→(Q) of the function Q(r→) , to mention a few. These apply to a variety of observable quantities Q and measurement techniques such as X-ray and neutron diffraction, small-angle and wide-angle X-ray scattering, free-electron laser imaging, cryo-electron microscopy, nuclear magnetic resonance, electron paramagnetic resonance, infrared and Raman spectroscopy, circular dichroism, Förster resonance energy transfer, atomic force microscopy and ion-mobility mass spectrometry. The process of deriving structural information from measured data is reviewed with an eye to non-experts and newcomers in the field using examples from the literature of the effect of the various choices and approximations involved in the process. A list of choices to be avoided is provided.
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Affiliation(s)
- Wilfred F van Gunsteren
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093, Zurich, Switzerland
| | - Jane R Allison
- Centre for Theor. Chem. and Phys. & Institute of Natural and Mathematical Sciences, Massey Univ., Auckland, New Zealand.,Biomolecular Interaction Centre, University of Canterbury, Christchurch, New Zealand.,Maurice Wilkins Centre for Molecular Biodiscovery, New Zealand
| | - Xavier Daura
- Institute of Biotechnology and Biomedicine, Universitat Autònoma de Barcelona (UAB), 08193, Barcelona, Spain.,Catalan Institution for Research and Advanced Studies (ICREA), 08010, Barcelona, Spain
| | - Jožica Dolenc
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093, Zurich, Switzerland
| | - Niels Hansen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany
| | - Alan E Mark
- School of Chemistry and Molecular Biosciences, University of Queensland, St. Lucia, QLD 4072, Australia
| | - Chris Oostenbrink
- Institute of Molecular Modeling and Simulation, University of Natural Resources and Life Sciences, Vienna, Austria
| | - Victor H Rusu
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093, Zurich, Switzerland
| | - Lorna J Smith
- Department of Chemistry, University of Oxford, Inorganic Chemistry Laboratory, South Parks Road, Oxford, OX1 3QR, UK
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5
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Pendrill R, Engström O, Volpato A, Zerbetto M, Polimeno A, Widmalm G. Flexibility at a glycosidic linkage revealed by molecular dynamics, stochastic modeling, and (13)C NMR spin relaxation: conformational preferences of α-L-Rhap-α-(1 → 2)-α-L-Rhap-OMe in water and dimethyl sulfoxide solutions. Phys Chem Chem Phys 2016; 18:3086-96. [PMID: 26741055 DOI: 10.1039/c5cp06288h] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The monosaccharide L-rhamnose is common in bacterial polysaccharides and the disaccharide α-L-Rhap-α-(1 → 2)-α-L-Rhap-OMe represents a structural model for a part of Shigella flexneri O-antigen polysaccharides. Utilization of [1'-(13)C]-site-specific labeling in the anomeric position at the glycosidic linkage between the two sugar residues facilitated the determination of transglycosidic NMR (3)JCH and (3)JCC coupling constants. Based on these spin-spin couplings the major state and the conformational distribution could be determined with respect to the ψ torsion angle, which changed between water and dimethyl sulfoxide (DMSO) as solvents, a finding mirrored by molecular dynamics (MD) simulations with explicit solvent molecules. The (13)C NMR spin relaxation parameters T1, T2, and heteronuclear NOE of the probe were measured for the disaccharide in DMSO-d6 at two magnetic field strengths, with standard deviations ≤1%. The combination of MD simulation and a stochastic description based on the diffusive chain model resulted in excellent agreement between calculated and experimentally observed (13)C relaxation parameters, with an average error of <2%. The coupling between the global reorientation of the molecule and the local motion of the spin probe is deemed essential if reproduction of NMR relaxation parameters should succeed, since decoupling of the two modes of motion results in significantly worse agreement. Calculation of (13)C relaxation parameters based on the correlation functions obtained directly from the MD simulation of the solute molecule in DMSO as solvent showed satisfactory agreement with errors on the order of 10% or less.
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Affiliation(s)
- Robert Pendrill
- Department of Organic Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm, Sweden.
| | - Olof Engström
- Department of Organic Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm, Sweden.
| | - Andrea Volpato
- Dipartimento di Scienze Chimiche, Università degli Studi di Padova, Padova 35131, Italy.
| | - Mirco Zerbetto
- Dipartimento di Scienze Chimiche, Università degli Studi di Padova, Padova 35131, Italy.
| | - Antonino Polimeno
- Dipartimento di Scienze Chimiche, Università degli Studi di Padova, Padova 35131, Italy.
| | - Göran Widmalm
- Department of Organic Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm, Sweden.
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6
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Smith LJ, van Gunsteren WF, Hansen N. On the use of time-averaging restraints when deriving biomolecular structure from ³ J -coupling values obtained from NMR experiments. J Biomol NMR 2016; 66:69-83. [PMID: 27627888 DOI: 10.1007/s10858-016-0058-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2016] [Accepted: 09/02/2016] [Indexed: 06/06/2023]
Abstract
Deriving molecular structure from [Formula: see text]-couplings obtained from NMR experiments is a challenge due to (1) the uncertainty in the Karplus relation [Formula: see text] connecting a [Formula: see text]-coupling value to a torsional angle [Formula: see text], (2) the need to account for the averaging inherent to the measurement of [Formula: see text]-couplings, and (3) the sampling road blocks that may emerge due to the multiple-valuedness of the inverse function [Formula: see text] of the function [Formula: see text]. Ways to properly handle these issues in structure refinement of biomolecules are discussed and illustrated using the protein hen egg white lysozyme as example.
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Affiliation(s)
- Lorna J Smith
- Inorganic Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford, OX1 3QR, UK
| | - Wilfred F van Gunsteren
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093, Zurich, Switzerland
| | - Niels Hansen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, 70569, Stuttgart, Germany.
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7
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Hansen N, Heller F, Schmid N, van Gunsteren WF. Time-averaged order parameter restraints in molecular dynamics simulations. J Biomol NMR 2014; 60:169-187. [PMID: 25312596 DOI: 10.1007/s10858-014-9866-7] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2014] [Accepted: 09/25/2014] [Indexed: 06/04/2023]
Abstract
A method is described that allows experimental S(2) order parameters to be enforced as a time-averaged quantity in molecular dynamics simulations. The two parameters that characterize time-averaged restraining, the memory relaxation time and the weight of the restraining potential energy term in the potential energy function used in the simulation, are systematically investigated based on two model systems, a vector with one end restrained in space and a pentapeptide. For the latter it is shown that the backbone N-H order parameter of individual residues can be enforced such that the spatial fluctuations of quantities depending on atomic coordinates are not significantly perturbed. The applicability to realistic systems is illustrated for the B3 domain of protein G in aqueous solution.
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Affiliation(s)
- Niels Hansen
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093, Zurich, Switzerland,
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8
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Cavalli A, Camilloni C, Vendruscolo M. Molecular dynamics simulations with replica-averaged structural restraints generate structural ensembles according to the maximum entropy principle. J Chem Phys 2013; 138:094112. [PMID: 23485282 DOI: 10.1063/1.4793625] [Citation(s) in RCA: 144] [Impact Index Per Article: 13.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
In order to characterise the dynamics of proteins, a well-established method is to incorporate experimental parameters as replica-averaged structural restraints into molecular dynamics simulations. Here, we justify this approach in the case of interproton distance information provided by nuclear Overhauser effects by showing that it generates ensembles of conformations according to the maximum entropy principle. These results indicate that the use of replica-averaged structural restraints in molecular dynamics simulations, given a force field and a set of experimental data, can provide an accurate approximation of the unknown Boltzmann distribution of a system.
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Affiliation(s)
- Andrea Cavalli
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
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9
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Allison JR. Assessing and refining molecular dynamics simulations of proteins with nuclear magnetic resonance data. Biophys Rev 2012; 4:189-203. [PMID: 28510078 DOI: 10.1007/s12551-012-0087-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2012] [Accepted: 06/12/2012] [Indexed: 11/28/2022] Open
Abstract
The sophistication of the force fields, algorithms and hardware used for molecular dynamics (MD) simulations of proteins is continuously increasing. No matter how advanced the methodology, however, it is essential to evaluate the appropriateness of the structures sampled in a simulation by comparison with quantitative experimental data. Solution nuclear magnetic resonance (NMR) data are particularly useful for checking the quality of protein simulations, as they provide both structural and dynamic information on a variety of temporal and spatial scales. Here, various features and implications of using NMR data to validate and bias MD simulations are outlined, including an overview of the different types of NMR data that report directly on structural properties and of relevant simulation techniques. The focus throughout is on how to properly account for conformational averaging, particularly within the context of the assumptions inherent in the relationships that link NMR data to structural properties.
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Affiliation(s)
- Jane R Allison
- Centre for Theoretical Chemistry and Physics, Institute of Natural Sciences, Massey University Albany, Albany Highway, Auckland, 0632, New Zealand.
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10
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Allison JR, Hertig S, Missimer JH, Smith LJ, Steinmetz MO, Dolenc J. Probing the Structure and Dynamics of Proteins by Combining Molecular Dynamics Simulations and Experimental NMR Data. J Chem Theory Comput 2012; 8:3430-44. [DOI: 10.1021/ct300393b] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jane R. Allison
- Laboratory of Physical Chemistry,
Swiss Federal Institute of Technology ETH, 8093 Zürich, Switzerland
| | - Samuel Hertig
- Department of Health Sciences
and Technology, Swiss Federal Institute of Technology ETH, 8093 Zürich,
Switzerland
| | - John H. Missimer
- Biomolecular
Research, Paul Scherrer
Institut, 5232 Villigen, Switzerland
| | - Lorna J. Smith
- Department of Chemistry, University
of Oxford, Oxford, United Kingdom
| | | | - Jožica Dolenc
- Laboratory of Physical Chemistry,
Swiss Federal Institute of Technology ETH, 8093 Zürich, Switzerland
- Faculty of Chemistry and Chemical
Technology, University of Ljubljana, 1000 Ljubljana, Slovenia
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11
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Zhao L, Liu Z, Cao Z, Liu H, Wang J. Determination of thermal intermediate state ensemble of box 5 with restrained molecular dynamics simulations. COMPUT THEOR CHEM 2011. [DOI: 10.1016/j.comptc.2011.10.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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12
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Fenwick RB, Esteban-Martín S, Salvatella X. Understanding biomolecular motion, recognition, and allostery by use of conformational ensembles. Eur Biophys J 2011; 40:1339-55. [PMID: 22089251 DOI: 10.1007/s00249-011-0754-8] [Citation(s) in RCA: 82] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/24/2011] [Revised: 09/06/2011] [Accepted: 09/14/2011] [Indexed: 10/31/2022]
Abstract
We review the role conformational ensembles can play in the analysis of biomolecular dynamics, molecular recognition, and allostery. We introduce currently available methods for generating ensembles of biomolecules and illustrate their application with relevant examples from the literature. We show how, for binding, conformational ensembles provide a way of distinguishing the competing models of induced fit and conformational selection. For allostery we review the classic models and show how conformational ensembles can play a role in unravelling the intricate pathways of communication that enable allostery to occur. Finally, we discuss the limitations of conformational ensembles and highlight some potential applications for the future.
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Kunz APE, Liu H, van Gunsteren WF. Enhanced sampling of particular degrees of freedom in molecular systems based on adiabatic decoupling and temperature or force scaling. J Chem Phys 2011; 135:104106. [DOI: 10.1063/1.3629450] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Säwén E, Massad T, Landersjö C, Damberg P, Widmalm G. Population distribution of flexible molecules from maximum entropy analysis using different priors as background information: application to the Φ, Ψ-conformational space of the α-(1-->2)-linked mannose disaccharide present in N- and O-linked glycoproteins. Org Biomol Chem 2010; 8:3684-95. [PMID: 20574564 DOI: 10.1039/c003958f] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The conformational space available to the flexible molecule α-D-Manp-(1-->2)-α-D-Manp-OMe, a model for the α-(1-->2)-linked mannose disaccharide in N- or O-linked glycoproteins, is determined using experimental data and molecular simulation combined with a maximum entropy approach that leads to a converged population distribution utilizing different input information. A database survey of the Protein Data Bank where structures having the constituent disaccharide were retrieved resulted in an ensemble with >200 structures. Subsequent filtering removed erroneous structures and gave the database (DB) ensemble having three classes of mannose-containing compounds, viz., N- and O-linked structures, and ligands to proteins. A molecular dynamics (MD) simulation of the disaccharide revealed a two-state equilibrium with a major and a minor conformational state, i.e., the MD ensemble. These two different conformation ensembles of the disaccharide were compared to measured experimental spectroscopic data for the molecule in water solution. However, neither of the two populations were compatible with experimental data from optical rotation, NMR (1)H,(1)H cross-relaxation rates as well as homo- and heteronuclear (3)J couplings. The conformational distributions were subsequently used as background information to generate priors that were used in a maximum entropy analysis. The resulting posteriors, i.e., the population distributions after the application of the maximum entropy analysis, still showed notable deviations that were not anticipated based on the prior information. Therefore, reparameterization of homo- and heteronuclear Karplus relationships for the glycosidic torsion angles Φ and Ψ were carried out in which the importance of electronegative substituents on the coupling pathway was deemed essential resulting in four derived equations, two (3)J(COCC) and two (3)J(COCH) being different for the Φ and Ψ torsions, respectively. These Karplus relationships are denoted JCX/SU09. Reapplication of the maximum entropy analysis gave excellent agreement between the MD- and DB-posteriors. The information entropies show that the current reparametrization of the Karplus relationships constitutes a significant improvement. The Φ(H) torsion angle of the disaccharide is governed by the exo-anomeric effect and for the dominating conformation Φ(H) = -40 degrees and Ψ(H) = 33 degrees. The minor conformational state has a negative Ψ(H) torsion angle; the relative populations of the major and the minor states are approximately 3 : 1. It is anticipated that application of the methodology will be useful to flexible molecules ranging from small organic molecules to large biomolecules.
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Affiliation(s)
- Elin Säwén
- Department of Organic Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91, Stockholm, Sweden
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15
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Abstract
Molecular dynamics (MD) simulations, in which experimental values such as nuclear Overhauser effects (NOEs), dipolar couplings, (3)J-coupling constants or crystallographic structure factors are used to bias the values of specific molecular properties towards experimental ones, are often carried out to study the structure refinement of peptides and proteins. However, (3)J-coupling constants are usually not employed because of the multiplicity of torsional angle values (phi) corresponding to each (3)J-coupling constant value. Here, we apply the method of adaptively enforced restraining using a local-elevation (LE) biasing potential energy function in which a memory function penalizes conformations in case both the average <(3)J> and the current (3)J-values deviate from the experimental target value. Then, the molecule is forced to sample other parts of the conformational space, thereby being able to cross high energy barriers and to bring the simulated average <(3)J> close to the measured <(3)J> value. Herein, we show the applicability of this method in structure refinement of a cyclo-beta-tetrapeptide by enforcing the (3)J-value restraining with LE on twelve backbone torsional angles. The resulting structural ensemble satisfies the experimental (3)J-coupling data better than the NMR model structure derived using conventional single-structure refinement based on these data. Thus, application of local-elevation search MD simulation in combination with biasing towards (3)J-coupling makes it possible to use (3)J-couplings quantitatively in structure determination of peptides.
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Affiliation(s)
- Zrinka Gattin
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093 Zürich, Switzerland
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16
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Abstract
Experimentally measured values of molecular properties or observables of biomolecules such as proteins are generally averages over time and space, which do not contain sufficient information to determine the underlying conformational distribution of the molecules in solution. The relationship between experimentally measured NMR (3)J-coupling values and the corresponding dihedral angle values is a particularly complicated case due to its nonlinear, multiple-valued nature. Molecular dynamics (MD) simulations at constant temperature can generate Boltzmann ensembles of molecular structures that are free from a priori assumptions about the nature of the underlying conformational distribution. They suffer, however, from limited sampling with respect to time and conformational space. Moreover, the quality of the obtained structures is dependent on the choice of force field and solvation model. A recently proposed method that uses time-averaging with local-elevation (LE) biasing of the conformational search provides an elegant means of overcoming these three problems. Using a set of side chain (3)J-coupling values for the FK506 binding protein (FKBP), we first investigate the uncertainty in the angle values predicted theoretically. We then propose a simple MD-based technique to detect inconsistencies within an experimental data set and identify degrees of freedom for which conformational averaging takes place or for which force field parameters may be deficient. Finally, we show that LE MD is the best method for producing ensembles of structures that, on average, fit the experimental data.
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Affiliation(s)
- Jane R Allison
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology ETH, 8093 Zurich, Switzerland
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17
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Kruschel D, Zagrovic B. Conformational averaging in structural biology: issues, challenges and computational solutions. Mol Biosyst 2009; 5:1606-16. [PMID: 20023721 DOI: 10.1039/b917186j] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Most experimental methods in structural biology provide time- and ensemble-averaged signals and, consequently, molecular structures based on such signals often exhibit only idealized, average features. Second, most experimental signals are only indirectly related to real, molecular geometries, and solving a structure typically involves a complicated procedure, which may not always result in a unique solution. To what extent do such conformationally-averaged, non-linear experimental signals and structural models derived from them accurately represent the underlying microscopic reality? Are there some structural motifs that are actually artificially more likely to be "seen" in an experiment simply due to the averaging artifact? Finally, what are the practical consequences of ignoring the averaging effects when it comes to functional and mechanistic implications that we try to glean from experimentally-based structural models? In this review, we critically address the work that has been aimed at studying such questions. We summarize the details of experimental methods typically used in structural biology (most notably nuclear magnetic resonance, X-ray crystallography and different types of spectroscopy), discuss their individual susceptibility to conformational (motional) averaging, and review several theoretical approaches, most importantly molecular dynamics simulations that are increasingly being used to aid experimentalists in interpreting structural biology experiments.
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Affiliation(s)
- Daniela Kruschel
- Laboratory of Computational Biophysics, Mediterranean Institute for Life Sciences, Mestrovicevo setaliste bb, Split, HR-21000, Croatia
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18
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Brooks B, Brooks C, MacKerell A, Nilsson L, Petrella R, Roux B, Won Y, Archontis G, Bartels C, Boresch S, Caflisch A, Caves L, Cui Q, Dinner A, Feig M, Fischer S, Gao J, Hodoscek M, Im W, Kuczera K, Lazaridis T, Ma J, Ovchinnikov V, Paci E, Pastor R, Post C, Pu J, Schaefer M, Tidor B, Venable RM, Woodcock HL, Wu X, Yang W, York D, Karplus M. CHARMM: the biomolecular simulation program. J Comput Chem 2009; 30:1545-614. [PMID: 19444816 PMCID: PMC2810661 DOI: 10.1002/jcc.21287] [Citation(s) in RCA: 5887] [Impact Index Per Article: 392.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.
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Affiliation(s)
- B.R. Brooks
- Laboratory of Computational Biology, National Heart, Lung, and
Blood Institute, National Institutes of Health, Bethesda, MD 20892
| | - C.L. Brooks
- Departments of Chemistry & Biophysics, University of
Michigan, Ann Arbor, MI 48109
| | - A.D. MacKerell
- Department of Pharmaceutical Sciences, School of Pharmacy,
University of Maryland, Baltimore, MD, 21201
| | - L. Nilsson
- Karolinska Institutet, Department of Biosciences and Nutrition,
SE-141 57, Huddinge, Sweden
| | - R.J. Petrella
- Department of Chemistry and Chemical Biology, Harvard University,
Cambridge, MA 02138
- Department of Medicine, Harvard Medical School, Boston, MA
02115
| | - B. Roux
- Department of Biochemistry and Molecular Biology, University of
Chicago, Gordon Center for Integrative Science, Chicago, IL 60637
| | - Y. Won
- Department of Chemistry, Hanyang University, Seoul
133–792 Korea
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- Department of Chemistry and Chemical Biology, Harvard University,
Cambridge, MA 02138
- Laboratoire de Chimie Biophysique, ISIS, Université de
Strasbourg, 67000 Strasbourg France
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Christen M, Keller B, van Gunsteren WF. Biomolecular structure refinement based on adaptive restraints using local-elevation simulation. J Biomol NMR 2007; 39:265-273. [PMID: 17929172 DOI: 10.1007/s10858-007-9194-2] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2007] [Accepted: 07/30/2007] [Indexed: 05/25/2023]
Abstract
Introducing experimental values as restraints into molecular dynamics (MD) simulation to bias the values of particular molecular properties, such as nuclear Overhauser effect intensities or distances, dipolar couplings, 3 J-coupling constants, chemical shifts or crystallographic structure factors, towards experimental values is a widely used structure refinement method. Because multiple torsion angle values varphi correspond to the same 3 J-coupling constant and high-energy barriers are separating those, restraining 3 J-coupling constants remains difficult. A method to adaptively enforce restraints using a local elevation (LE) potential energy function is presented and applied to 3 J-coupling constant restraining in an MD simulation of hen egg-white lysozyme (HEWL). The method succesfully enhances sampling of the restrained torsion angles until the 37 experimental 3 J-coupling constant values are reached, thereby also improving the agreement with the 1,630 experimental NOE atom-atom distance upper bounds. Afterwards the torsional angles varphi are kept restrained by the built-up local-elevation potential energies.
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Affiliation(s)
- Markus Christen
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology Zürich, ETH-Zürich, 8093 Zürich, Switzerland
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20
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Richter B, Gsponer J, Várnai P, Salvatella X, Vendruscolo M. The MUMO (minimal under-restraining minimal over-restraining) method for the determination of native state ensembles of proteins. J Biomol NMR 2007; 37:117-35. [PMID: 17225069 DOI: 10.1007/s10858-006-9117-7] [Citation(s) in RCA: 94] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2006] [Accepted: 11/03/2006] [Indexed: 05/13/2023]
Abstract
While reliable procedures for determining the conformations of proteins are available, methods for generating ensembles of structures that also reflect their flexibility are much less well established. Here we present a systematic assessment of the ability of ensemble-averaged molecular dynamics simulations with ensemble-averaged NMR restraints to simultaneously reproduce the average structure of proteins and their associated dynamics. We discuss the effects that under-restraining (overfitting) and over-restraining (underfitting) have on the structures generated in ensemble-averaged molecular simulations. We then introduce the MUMO (minimal under-restraining minimal over-restraining) method, a procedure in which different observables are averaged over a different number of molecules. As both over-restraining and under-restraining are significantly reduced in the MUMO method, it is possible to generate ensembles of conformations that accurately characterize both the structure and the dynamics of native states of proteins. The application of the MUMO method to the protein ubiquitin yields a high-resolution structural ensemble with an RDC Q-factor of 0.19.
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Affiliation(s)
- Barbara Richter
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
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Keller B, Christen M, Oostenbrink C, van Gunsteren WF. On using oscillating time-dependent restraints in MD simulation. J Biomol NMR 2007; 37:1-14. [PMID: 17180446 DOI: 10.1007/s10858-006-9081-2] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2006] [Accepted: 08/14/2006] [Indexed: 05/13/2023]
Abstract
The use of time-dependent restraints in molecular simulation in order to generate a conformational ensemble for molecules that is in accordance with measured ensemble averages for particular observable quantities is investigated. Using a model system consisting of liquid butane and the cyclic peptide antamanide the reproduction of particular average (3) J-coupling constant values in a molecular dynamics simulation is analysed. It is shown that the multiple-valuedness and the sizeable gradients of the Karplus curve relating (3) J-coupling constants measured in NMR experiments to the corresponding torsional-angle values cause severe problems when trying to restrain a (3) J-coupling constant to a value close to the extrema of the Karplus curve. The introduction of a factor oscillating with time into the restraining penalty function alleviates this problem and enhances the restrained conformational sampling.
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Affiliation(s)
- Bettina Keller
- Laboratorium für Physikalische Chemie, ETH Zürich, Zürich, CH-8093, Switzerland
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Glättli A, van Gunsteren WF. Are NMR-Derived Model Structures for β-Peptides Representative for the Ensemble of Structures Adopted in Solution? Angew Chem Int Ed Engl 2004. [DOI: 10.1002/ange.200460384] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Glättli A, van Gunsteren WF. Are NMR-Derived Model Structures for β-Peptides Representative for the Ensemble of Structures Adopted in Solution? Angew Chem Int Ed Engl 2004; 43:6312-6. [PMID: 15523681 DOI: 10.1002/anie.200460384] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Alice Glättli
- Laboratorium für Physikalische Chemie, ETH, ETH Hönggerberg, HCI, 8093 Zürich, Switzerland
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