1
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Gilardoni I, Fröhlking T, Bussi G. Boosting Ensemble Refinement with Transferable Force-Field Corrections: Synergistic Optimization for Molecular Simulations. J Phys Chem Lett 2024; 15:1204-1210. [PMID: 38272001 DOI: 10.1021/acs.jpclett.3c03423] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2024]
Abstract
A novel method combining the force-field fitting approach and ensemble refinement by the maximum entropy principle is presented. Its formulation allows us to continuously interpolate between these two methods, which can thus be interpreted as two limiting cases. A cross-validation procedure enables us to correctly assess the relative weight of both of them, distinguishing scenarios in which the combined approach is meaningful from those in which either ensemble refinement or force-field fitting separately prevails. The efficacy of their combination is examined for a realistic case study of RNA oligomers. Within the new scheme, molecular dynamics simulations are integrated with experimental data provided by nuclear magnetic resonance measures. We show that force-field corrections are in general superior when applied to the appropriate force-field terms but are automatically discarded by the method when applied to inappropriate force-field terms.
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Affiliation(s)
- Ivan Gilardoni
- Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy
| | - Thorben Fröhlking
- Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy
| | - Giovanni Bussi
- Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy
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2
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Ballabio F, Paissoni C, Bollati M, de Rosa M, Capelli R, Camilloni C. Accurate and Efficient SAXS/SANS Implementation Including Solvation Layer Effects Suitable for Molecular Simulations. J Chem Theory Comput 2023; 19:8401-8413. [PMID: 37923304 PMCID: PMC10687869 DOI: 10.1021/acs.jctc.3c00864] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2023] [Revised: 10/11/2023] [Accepted: 10/24/2023] [Indexed: 11/07/2023]
Abstract
Small-angle X-ray and neutron scattering (SAXS/SANS) provide valuable insights into the structure and dynamics of biomolecules in solution, complementing a wide range of structural techniques, including molecular dynamics simulations. As contrast-based methods, they are sensitive not only to structural properties but also to solvent-solute interactions. Their use in molecular dynamics simulations requires a forward model that should be as fast and accurate as possible. In this work, we demonstrate the feasibility of calculating SAXS and SANS intensities using a coarse-grained representation consisting of one bead per amino acid and three beads per nucleic acid, with form factors that can be corrected on the fly to account for solvation effects at no additional computational cost. By coupling this forward model with molecular dynamics simulations restrained with SAS data, it is possible to determine conformational ensembles or refine the structure and dynamics of proteins and nucleic acids in agreement with the experimental results. To assess the robustness of this approach, we applied it to gelsolin, for which we acquired SAXS data on its closed state, and to a UP1-microRNA complex, for which we used previously collected measurements. Our hybrid-resolution small-angle scattering (hySAS) implementation, being distributed in PLUMED, can be used with atomistic and coarse-grained simulations using diverse restraining strategies.
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Affiliation(s)
- Federico Ballabio
- Dipartimento
di Bioscienze, Università degli Studi
di Milano, via Celoria 26, 20133 Milano, Italy
| | - Cristina Paissoni
- Dipartimento
di Bioscienze, Università degli Studi
di Milano, via Celoria 26, 20133 Milano, Italy
| | - Michela Bollati
- Dipartimento
di Bioscienze, Università degli Studi
di Milano, via Celoria 26, 20133 Milano, Italy
- Istituto
di Biofisica, Consiglio Nazionale delle
Ricerche (IBF-CNR), via
Alfonso Corti 12, 20133 Milano, Italy
| | - Matteo de Rosa
- Dipartimento
di Bioscienze, Università degli Studi
di Milano, via Celoria 26, 20133 Milano, Italy
- Istituto
di Biofisica, Consiglio Nazionale delle
Ricerche (IBF-CNR), via
Alfonso Corti 12, 20133 Milano, Italy
| | - Riccardo Capelli
- Dipartimento
di Bioscienze, Università degli Studi
di Milano, via Celoria 26, 20133 Milano, Italy
| | - Carlo Camilloni
- Dipartimento
di Bioscienze, Università degli Studi
di Milano, via Celoria 26, 20133 Milano, Italy
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3
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Scalone E, Broggini L, Visentin C, Erba D, Bačić Toplek F, Peqini K, Pellegrino S, Ricagno S, Paissoni C, Camilloni C. Multi-eGO: An in silico lens to look into protein aggregation kinetics at atomic resolution. Proc Natl Acad Sci U S A 2022; 119:e2203181119. [PMID: 35737839 PMCID: PMC9245614 DOI: 10.1073/pnas.2203181119] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Accepted: 05/17/2022] [Indexed: 12/25/2022] Open
Abstract
Protein aggregation into amyloid fibrils is the archetype of aberrant biomolecular self-assembly processes, with more than 50 associated diseases that are mostly uncurable. Understanding aggregation mechanisms is thus of fundamental importance and goes in parallel with the structural characterization of the transient oligomers formed during the process. Oligomers have been proven elusive to high-resolution structural techniques, while the large sizes and long time scales, typical of aggregation processes, have limited the use of computational methods to date. To surmount these limitations, we here present multi-eGO, an atomistic, hybrid structure-based model which, leveraging the knowledge of monomers conformational dynamics and of fibril structures, efficiently captures the essential structural and kinetics aspects of protein aggregation. Multi-eGO molecular dynamics simulations can describe the aggregation kinetics of thousands of monomers. The concentration dependence of the simulated kinetics, as well as the structural features of the resulting fibrils, are in qualitative agreement with in vitro experiments carried out on an amyloidogenic peptide from Transthyretin, a protein responsible for one of the most common cardiac amyloidoses. Multi-eGO simulations allow the formation of primary nuclei in a sea of transient lower-order oligomers to be observed over time and at atomic resolution, following their growth and the subsequent secondary nucleation events, until the maturation of multiple fibrils is achieved. Multi-eGO, combined with the many experimental techniques deployed to study protein aggregation, can provide the structural basis needed to advance the design of molecules targeting amyloidogenic diseases.
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Affiliation(s)
- Emanuele Scalone
- Dipartimento di Bioscienze, Università degli Studi di Milano, 20133 Milano, Italy
| | - Luca Broggini
- Dipartimento di Bioscienze, Università degli Studi di Milano, 20133 Milano, Italy
- Institute of Molecular and Translational Cardiology, IRCCS Policlinico San Donato, 20097 San Donato Milanese, Italy
| | - Cristina Visentin
- Dipartimento di Bioscienze, Università degli Studi di Milano, 20133 Milano, Italy
- Institute of Molecular and Translational Cardiology, IRCCS Policlinico San Donato, 20097 San Donato Milanese, Italy
| | - Davide Erba
- Dipartimento di Bioscienze, Università degli Studi di Milano, 20133 Milano, Italy
| | - Fran Bačić Toplek
- Dipartimento di Bioscienze, Università degli Studi di Milano, 20133 Milano, Italy
| | - Kaliroi Peqini
- Dipartimento di Scienze Farmaceutiche, Sezione Chimica Generale e Organica, Università degli Studi di Milano, 20133 Milano, Italy
| | - Sara Pellegrino
- Dipartimento di Scienze Farmaceutiche, Sezione Chimica Generale e Organica, Università degli Studi di Milano, 20133 Milano, Italy
| | - Stefano Ricagno
- Dipartimento di Bioscienze, Università degli Studi di Milano, 20133 Milano, Italy
- Institute of Molecular and Translational Cardiology, IRCCS Policlinico San Donato, 20097 San Donato Milanese, Italy
| | - Cristina Paissoni
- Dipartimento di Bioscienze, Università degli Studi di Milano, 20133 Milano, Italy
| | - Carlo Camilloni
- Dipartimento di Bioscienze, Università degli Studi di Milano, 20133 Milano, Italy
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4
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Lin X, Qi Y, Latham AP, Zhang B. Multiscale modeling of genome organization with maximum entropy optimization. J Chem Phys 2021; 155:010901. [PMID: 34241389 PMCID: PMC8253599 DOI: 10.1063/5.0044150] [Citation(s) in RCA: 34] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Accepted: 04/28/2021] [Indexed: 12/15/2022] Open
Abstract
Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.
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Affiliation(s)
- Xingcheng Lin
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Yifeng Qi
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Andrew P. Latham
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Bin Zhang
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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5
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Brotzakis ZF, Vendruscolo M, Bolhuis PG. A method of incorporating rate constants as kinetic constraints in molecular dynamics simulations. Proc Natl Acad Sci U S A 2021; 118:e2012423118. [PMID: 33376207 PMCID: PMC7812743 DOI: 10.1073/pnas.2012423118] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
From the point of view of statistical mechanics, a full characterization of a molecular system requires an accurate determination of its possible states, their populations, and the respective interconversion rates. Toward this goal, well-established methods increase the accuracy of molecular dynamics simulations by incorporating experimental information about states using structural restraints and about populations using thermodynamics restraints. However, it is still unclear how to include experimental knowledge about interconversion rates. Here, we introduce a method of imposing known rate constants as constraints in molecular dynamics simulations, which is based on a combination of the maximum-entropy and maximum-caliber principles. Starting from an existing ensemble of trajectories, obtained from either molecular dynamics or enhanced trajectory sampling, this method provides a minimally perturbed path distribution consistent with the kinetic constraints, as well as modified free energy and committor landscapes. We illustrate the application of the method to a series of model systems, including all-atom molecular simulations of protein folding. Our results show that by combining experimental rate constants and molecular dynamics simulations, this approach enables the determination of transition states, reaction mechanisms, and free energies. We anticipate that this method will extend the applicability of molecular simulations to kinetic studies in structural biology and that it will assist the development of force fields to reproduce kinetic and thermodynamic observables. Furthermore, this approach is generally applicable to a wide range of systems in biology, physics, chemistry, and material science.
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Affiliation(s)
- Z Faidon Brotzakis
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Michele Vendruscolo
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Peter G Bolhuis
- van't Hoff Institute for Molecular Sciences, University of Amsterdam, 1090 GD Amsterdam, The Netherlands
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6
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Fuchigami S, Niina T, Takada S. Particle Filter Method to Integrate High-Speed Atomic Force Microscopy Measurements with Biomolecular Simulations. J Chem Theory Comput 2020; 16:6609-6619. [PMID: 32805119 DOI: 10.1021/acs.jctc.0c00234] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
High-speed atomic force microscopy (HS-AFM) can be used to observe the structural dynamics of biomolecules at the single-molecule level in real time under near-physiological conditions; however, its spatiotemporal resolution is limited. Complementarily, molecular dynamics (MD) simulations have higher spatiotemporal resolutions, albeit with some artifacts. Here, to integrate HS-AFM data and coarse-grained molecular dynamics (CG-MD) simulations, we develop a particle filter method that implements a sequential Bayesian data assimilation approach. We test the method in a twin experiment. First, we generate a reference HS-AFM movie from the CG-MD trajectory of a test molecule, a nucleosome; this serves as the "experimental measurement". Then, we perform a particle filter simulation with 512 particles, which captures the large-scale nucleosome structural dynamics compatible with the AFM movie. Comparing particle filter simulations with 8-8192 particles, we find that using greater numbers of particles consistently increases the likelihood of the whole AFM movie. By comparing the likelihoods for different ionic concentrations and time scale mappings, we find that the "true" concentration and time scale mapping can be inferred as the largest likelihood of the whole AFM movie but not that of each AFM image. The particle filter method provides a general approach for integrating HS-AFM data with MD simulations.
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Affiliation(s)
- Sotaro Fuchigami
- Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Toru Niina
- Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Shoji Takada
- Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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7
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Geraets JA, Pothula KR, Schröder GF. Integrating cryo-EM and NMR data. Curr Opin Struct Biol 2020; 61:173-181. [PMID: 32028106 DOI: 10.1016/j.sbi.2020.01.008] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2019] [Revised: 01/13/2020] [Accepted: 01/14/2020] [Indexed: 01/06/2023]
Abstract
Single-particle cryo-electron microscopy (cryo-EM) is increasingly used as a technique to determine the atomic structure of challenging biological systems. Recent advances in microscope engineering, electron detection, and image processing have allowed the structural determination of bigger and more flexible targets than possible with the complementary techniques X-ray crystallography and NMR spectroscopy. However, there exist many biological targets for which atomic resolution cannot be currently achieved with cryo-EM, making unambiguous determination of the protein structure impossible. Although determining the structure of large biological systems using solely NMR is often difficult, highly complementary experimental atomic-level data for each molecule can be derived from the spectra, and used in combination with cryo-EM data. We review here strategies with which both techniques can be synergistically combined, in order to reach detail and understanding unattainable by each technique acting alone; and the types of biological systems for which such an approach would be desirable.
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Affiliation(s)
- James A Geraets
- Institute of Biological Information Processing (IBI-7: Structural Biochemistry) and JuStruct, Jülich Center for Structural Biology, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Karunakar R Pothula
- Institute of Biological Information Processing (IBI-7: Structural Biochemistry) and JuStruct, Jülich Center for Structural Biology, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Gunnar F Schröder
- Institute of Biological Information Processing (IBI-7: Structural Biochemistry) and JuStruct, Jülich Center for Structural Biology, Forschungszentrum Jülich, 52425 Jülich, Germany; Physics Department, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany.
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8
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Orioli S, Larsen AH, Bottaro S, Lindorff-Larsen K. How to learn from inconsistencies: Integrating molecular simulations with experimental data. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2020; 170:123-176. [PMID: 32145944 DOI: 10.1016/bs.pmbts.2019.12.006] [Citation(s) in RCA: 48] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modeling tool to interpret experimental measurements, and to use experimental data to refine our biophysical models. Thus, explicit integration and synergy between molecular simulations and experiments is fundamental for furthering our understanding of biological processes. This is especially true in the case where discrepancies between measured and simulated observables emerge. In this chapter, we provide an overview of some of the core ideas behind methods that were developed to improve the consistency between experimental information and numerical predictions. We distinguish between situations where experiments are used to refine our understanding and models of specific systems, and situations where experiments are used more generally to refine transferable models. We discuss different philosophies and attempt to unify them in a single framework. Until now, such integration between experiments and simulations have mostly been applied to equilibrium data, and we discuss more recent developments aimed to analyze time-dependent or time-resolved data.
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Affiliation(s)
- Simone Orioli
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark; Structural Biophysics, Niels Bohr Institute, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
| | - Andreas Haahr Larsen
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark; Structural Biophysics, Niels Bohr Institute, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
| | - Sandro Bottaro
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark; Atomistic Simulations Laboratory, Istituto Italiano di Tecnologia, Genova, Italy
| | - Kresten Lindorff-Larsen
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark.
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9
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Smith CA, Mazur A, Rout AK, Becker S, Lee D, de Groot BL, Griesinger C. Enhancing NMR derived ensembles with kinetics on multiple timescales. JOURNAL OF BIOMOLECULAR NMR 2020; 74:27-43. [PMID: 31838619 PMCID: PMC7015964 DOI: 10.1007/s10858-019-00288-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2019] [Accepted: 11/11/2019] [Indexed: 05/14/2023]
Abstract
Nuclear magnetic resonance (NMR) has the unique advantage of elucidating the structure and dynamics of biomolecules in solution at physiological temperatures, where they are in constant movement on timescales from picoseconds to milliseconds. Such motions have been shown to be critical for enzyme catalysis, allosteric regulation, and molecular recognition. With NMR being particularly sensitive to these timescales, detailed information about the kinetics can be acquired. However, nearly all methods of NMR-based biomolecular structure determination neglect kinetics, which introduces a large approximation to the underlying physics, limiting both structural resolution and the ability to accurately determine molecular flexibility. Here we present the Kinetic Ensemble approach that uses a hierarchy of interconversion rates between a set of ensemble members to rigorously calculate Nuclear Overhauser Effect (NOE) intensities. It can be used to simultaneously refine both temporal and structural coordinates. By generalizing ideas from the extended model free approach, the method can analyze the amplitudes and kinetics of motions anywhere along the backbone or side chains. Furthermore, analysis of a large set of crystal structures suggests that NOE data contains a surprising amount of high-resolution information that is better modeled using our approach. The Kinetic Ensemble approach provides the means to unify numerous types of experiments under a single quantitative framework and more fully characterize and exploit kinetically distinct protein states. While we apply the approach here to the protein ubiquitin and cross validate it with previously derived datasets, the approach can be applied to any protein for which NOE data is available.
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Affiliation(s)
- Colin A Smith
- Department for Theoretical and Computational Biophysics, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
- Department of Chemistry, Wesleyan University, Middletown, USA.
| | - Adam Mazur
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany
- Biozentrum, University of Basel, Basel, Switzerland
| | - Ashok K Rout
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany
| | - Stefan Becker
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany
| | - Donghan Lee
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
- James Graham Brown Cancer Center, University of Louisville, Louisville, USA.
| | - Bert L de Groot
- Department for Theoretical and Computational Biophysics, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
| | - Christian Griesinger
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
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10
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Bottaro S, Lindorff-Larsen K. Biophysical experiments and biomolecular simulations: A perfect match? Science 2018; 361:355-360. [DOI: 10.1126/science.aat4010] [Citation(s) in RCA: 135] [Impact Index Per Article: 22.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
A fundamental challenge in biological research is achieving an atomic-level description and mechanistic understanding of the function of biomolecules. Techniques for biomolecular simulations have undergone substantial developments, and their accuracy and scope have expanded considerably. Progress has been made through an increasingly tight integration of experiments and simulations, with experiments being used to refine simulations and simulations used to interpret experiments. Here we review the underpinnings of this progress, including methods for more efficient conformational sampling, accuracy of the physical models used, and theoretical approaches to integrate experiments and simulations. These developments are enabling detailed studies of complex biomolecular assemblies.
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