51
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Lickert B, Wolf S, Stock G. Data-Driven Langevin Modeling of Nonequilibrium Processes. J Phys Chem B 2021; 125:8125-8136. [PMID: 34270245 DOI: 10.1021/acs.jpcb.1c03828] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Given nonstationary data from molecular dynamics simulations, a Markovian Langevin model is constructed that aims to reproduce the time evolution of the underlying process. While at equilibrium the free energy landscape is sampled, nonequilibrium processes can be associated with a biased energy landscape, which accounts for finite sampling effects and external driving. When the data-driven Langevin equation (dLE) approach [Phys. Rev. Lett. 2015, 115, 050602] is extended to the modeling of nonequilibrium processes, an efficient way to calculate multidimensional Langevin fields is outlined. The dLE is shown to correctly account for various nonequilibrium processes, including the enforced dissociation of sodium chloride in water, the pressure-jump induced nucleation of a liquid of hard spheres, and the conformational dynamics of a helical peptide sampled from nonstationary short trajectories.
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Affiliation(s)
- Benjamin Lickert
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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52
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Xi K, Hu Z, Wu Q, Wei M, Qian R, Zhu L. Assessing the Performance of Traveling-salesman based Automated Path Searching (TAPS) on Complex Biomolecular Systems. J Chem Theory Comput 2021; 17:5301-5311. [PMID: 34270241 DOI: 10.1021/acs.jctc.1c00182] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Though crucial for understanding the function of large biomolecular systems, locating the minimum free energy paths (MFEPs) between their key conformational states is far from trivial due to their high-dimensional nature. Most existing path-searching methods require a static collective variable space as input, encoding intuition or prior knowledge of the transition mechanism. Such information is, however, hardly available a priori and expensive to validate. To alleviate this issue, we have previously introduced a Traveling-salesman based Automated Path Searching method (TAPS) and demonstrated its efficiency on simple peptide systems. Having implemented a parallel version of this method, here we assess the performance of TAPS on three realistic systems (tens to hundreds of residues) in explicit solvents. We show that TAPS successfully located the MFEP for the ground/excited state transition of the T4 lysozyme L99A variant, consistent with previous findings. TAPS also helped identifying the important role of the two polar contacts in directing the loop-in/loop-out transition of the mitogen-activated protein kinase kinase (MEK1), which explained previous mutant experiments. Remarkably, at a minimal cost of 126 ns sampling, TAPS revealed that the Ltn40/Ltn10 transition of lymphotactin needs no complete unfolding/refolding of its β-sheets and that five polar contacts are sufficient to stabilize the various partially unfolded intermediates along the MFEP. These results present TAPS as a general and promising tool for studying the functional dynamics of complex biomolecular systems.
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Affiliation(s)
- Kun Xi
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China.,School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
| | - Zhenquan Hu
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China.,School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
| | - Qiang Wu
- School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
| | - Meihan Wei
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
| | - Runtong Qian
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
| | - Lizhe Zhu
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
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53
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Multiscale Models for Fibril Formation: Rare Events Methods, Microkinetic Models, and Population Balances. Life (Basel) 2021; 11:life11060570. [PMID: 34204410 PMCID: PMC8234428 DOI: 10.3390/life11060570] [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: 04/14/2021] [Revised: 05/30/2021] [Accepted: 06/09/2021] [Indexed: 11/17/2022] Open
Abstract
Amyloid fibrils are thought to grow by a two-step dock-lock mechanism. However, previous simulations of fibril formation (i) overlook the bi-molecular nature of the docking step and obtain rates with first-order units, or (ii) superimpose the docked and locked states when computing the potential of mean force for association and thereby muddle the docking and locking steps. Here, we developed a simple microkinetic model with separate locking and docking steps and with the appropriate concentration dependences for each step. We constructed a simple model comprised of chiral dumbbells that retains qualitative aspects of fibril formation. We used rare events methods to predict separate docking and locking rate constants for the model. The rate constants were embedded in the microkinetic model, with the microkinetic model embedded in a population balance model for “bottom-up” multiscale fibril growth rate predictions. These were compared to “top-down” results using simulation data with the same model and multiscale framework to obtain maximum likelihood estimates of the separate lock and dock rate constants. We used the same procedures to extract separate docking and locking rate constants from experimental fibril growth data. Our multiscale strategy, embedding rate theories, and kinetic models in conservation laws should help to extract docking and locking rate constants from experimental data or long molecular simulations with correct units and without compromising the molecular description.
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54
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Abstract
We describe a nonparametric approach for accurate determination of the slowest relaxation eigenvectors of molecular dynamics. The approach is blind as it uses no system specific information. In particular, it does not require a functional form with many parameters to closely approximate eigenvectors, e.g., linear combinations of molecular descriptors or a deep neural network, and thus no extensive expertise with the system. We suggest a rigorous and sensitive validation/optimality criterion for an eigenvector. The criterion uses only eigenvector time series and can be used to validate eigenvectors computed by other approaches. The power of the approach is illustrated on long atomistic protein folding trajectories. The determined eigenvectors pass the validation test at a time scale of 0.2 ns, much shorter than alternative approaches.
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Affiliation(s)
- Sergei V Krivov
- Astbury Center for Structural Molecular Biology, Faculty of Biological Sciences, University of Leeds, Leeds LS2 9JT, United Kingdom
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55
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Abstract
The ability to make sense of the massive amounts of high-dimensional data generated from molecular dynamics simulations is heavily dependent on the knowledge of a low-dimensional manifold (parameterized by a reaction coordinate or RC) that typically distinguishes between relevant metastable states, and which captures the relevant slow dynamics of interest. Methods based on machine learning and artificial intelligence have been proposed over the years to deal with learning such low-dimensional manifolds, but they are often criticized for a disconnect from more traditional and physically interpretable approaches. To deal with such concerns, in this work we propose a deep learning based state predictive information bottleneck approach to learn the RC from high-dimensional molecular simulation trajectories. We demonstrate analytically and numerically how the RC learnt in this approach is connected to the committor in chemical physics and can be used to accurately identify transition states. A crucial hyperparameter in this approach is the time delay or how far into the future the algorithm should make predictions about. Through careful comparisons for benchmark systems, we demonstrate that this hyperparameter choice gives useful control over how coarse-grained we want the metastable state classification of the system to be. We thus believe that this work represents a step forward in systematic application of deep learning based ideas to molecular simulations.
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Affiliation(s)
- Dedi Wang
- Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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56
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Bolhuis PG, Swenson DWH. Transition Path Sampling as Markov Chain Monte Carlo of Trajectories: Recent Algorithms, Software, Applications, and Future Outlook. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202000237] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Peter G. Bolhuis
- Amsterdam Center for Multiscale Modeling van 't Hoff Institute for Molecular Sciences University of Amsterdam PO Box 94157 1090 GD Amsterdam The Netherlands
| | - David W. H. Swenson
- Centre Blaise Pascal Ecole Normale Superieure 46, allée d'Italie 69364 Lyon Cedex 07 France
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57
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Silveira RL, Knott BC, Pereira CS, Crowley MF, Skaf MS, Beckham GT. Transition Path Sampling Study of the Feruloyl Esterase Mechanism. J Phys Chem B 2021; 125:2018-2030. [PMID: 33616402 DOI: 10.1021/acs.jpcb.0c09725] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Serine hydrolases cleave peptide and ester bonds and are ubiquitous in nature, with applications in biotechnology, in materials, and as drug targets. The serine hydrolase two-step mechanism employs a serine-histidine-aspartate/glutamate catalytic triad, where the histidine residue acts as a base to activate poor nucleophiles (a serine residue or a water molecule) and as an acid to allow the dissociation of poor leaving groups. This mechanism has been the subject of debate regarding how histidine shuttles the proton from the nucleophile to the leaving group. To elucidate the reaction mechanism of serine hydrolases, we employ quantum mechanics/molecular mechanics-based transition path sampling to obtain the reaction coordinate using the Aspergillus niger feruloyl esterase A (AnFaeA) as a model enzyme. The optimal reaction coordinates include terms involving nucleophilic attack on the carbonyl carbon and proton transfer to, and dissociation of, the leaving group. During the reaction, the histidine residue undergoes a reorientation on the time scale of hundreds of femtoseconds that supports the "moving histidine" mechanism, thus calling into question the "ring flip" mechanism. We find a concerted mechanism, where the transition state coincides with the tetrahedral intermediate with the histidine residue pointed between the nucleophile and the leaving group. Moreover, motions of the catalytic aspartate toward the histidine occur concertedly with proton abstraction by the catalytic histidine and help stabilize the transition state, thus partially explaining how serine hydrolases enable poor nucleophiles to attack the substrate carbonyl carbon. Rate calculations indicate that the second step (deacylation) is rate-determining, with a calculated rate constant of 66 s-1. Overall, these results reveal the pivotal role of active-site dynamics in the catalytic mechanism of AnFaeA, which is likely similar in other serine hydrolases.
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Affiliation(s)
- Rodrigo L Silveira
- Renewable Resources and Enabling Sciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States.,Institute of Chemistry and Center for Computing in Engineering and Sciences, University of Campinas, Campinas, Sao Paulo 13084-862, Brazil.,Institute of Chemistry, Federal University of Rio de Janeiro, Rio de Janeiro, RJ 21941-909, Brazil
| | - Brandon C Knott
- Renewable Resources and Enabling Sciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States
| | - Caroline S Pereira
- Renewable Resources and Enabling Sciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States.,Institute of Chemistry and Center for Computing in Engineering and Sciences, University of Campinas, Campinas, Sao Paulo 13084-862, Brazil
| | - Michael F Crowley
- Renewable Resources and Enabling Sciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States
| | - Munir S Skaf
- Institute of Chemistry and Center for Computing in Engineering and Sciences, University of Campinas, Campinas, Sao Paulo 13084-862, Brazil
| | - Gregg T Beckham
- Renewable Resources and Enabling Sciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States
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58
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Levintov L, Paul S, Vashisth H. Reaction Coordinate and Thermodynamics of Base Flipping in RNA. J Chem Theory Comput 2021; 17:1914-1921. [PMID: 33594886 DOI: 10.1021/acs.jctc.0c01199] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Base flipping is a key biophysical event involved in recognition of various ligands by ribonucleic acid (RNA) molecules. However, the mechanism of base flipping in RNA remains poorly understood, in part due to the lack of atomistic details on complex rearrangements in neighboring bases. In this work, we applied transition path sampling (TPS) methods to study base flipping in a double-stranded RNA (dsRNA) molecule that is known to interact with RNA-editing enzymes through this mechanism. We obtained an ensemble of 1000 transition trajectories to describe the base-flipping process. We used the likelihood maximization method to determine the refined reaction coordinate (RC) consisting of two collective variables (CVs), a distance and a dihedral angle between nucleotides that form stacking interactions with the flipping base. The free energy profile projected along the refined RC revealed three minima, two corresponding to the initial and final states and one for a metastable state. We suggest that the metastable state likely represents a wobbled conformation of nucleobases observed in NMR studies that is often characterized as the flipped state. The analyses of reactive trajectories further revealed that the base flipping is coupled to a global conformational change in a stem-loop of dsRNA.
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Affiliation(s)
- Lev Levintov
- Department of Chemical Engineering, University of New Hampshire, Durham 03824, New Hampshire, United States
| | - Sanjib Paul
- Department of Chemistry, New York University, New York 10003, New York, United States
| | - Harish Vashisth
- Department of Chemical Engineering, University of New Hampshire, Durham 03824, New Hampshire, United States
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59
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Lickert B, Stock G. Modeling non-Markovian data using Markov state and Langevin models. J Chem Phys 2020; 153:244112. [DOI: 10.1063/5.0031979] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Benjamin Lickert
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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60
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Prebiotic chemistry and origins of life research with atomistic computer simulations. Phys Life Rev 2020; 34-35:105-135. [DOI: 10.1016/j.plrev.2018.09.004] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2018] [Accepted: 09/10/2018] [Indexed: 02/02/2023]
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61
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Bubnis G, Grubmüller H. Sequential Water and Headgroup Merger: Membrane Poration Paths and Energetics from MD Simulations. Biophys J 2020; 119:2418-2430. [PMID: 33189685 PMCID: PMC7822740 DOI: 10.1016/j.bpj.2020.10.037] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2020] [Revised: 10/07/2020] [Accepted: 10/23/2020] [Indexed: 01/06/2023] Open
Abstract
Membrane topology changes such as poration, stalk formation, and hemifusion rupture are essential to cellular function, but their molecular details, energetics, and kinetics are still not fully understood. Here, we present a unified energetic and mechanistic picture of metastable pore defects in tensionless lipid membranes. We used an exhaustive committor analysis to test and select optimal reaction coordinates and also to determine the nucleation mechanism. These reaction coordinates were used to calculate free-energy landscapes that capture the full process and end states. The identified barriers agree with the committor analysis. To enable sufficient sampling of the complete transition path for our molecular dynamics simulations, we developed a “gizmo” potential biasing scheme. The simulations suggest that the essential step in the nucleation is the initial merger of lipid headgroups at the nascent pore center. To facilitate this event, an indentation pathway is energetically preferred to a hydrophobic defect. Continuous water columns that span the indentation were determined to be on-path transients that precede the nucleation barrier. This study gives a quantitative description of the nucleation mechanism and energetics of small metastable pores and illustrates a systematic approach to uncover the mechanisms of diverse cellular membrane remodeling processes.
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Affiliation(s)
- Greg Bubnis
- Department of Theoretical and Computational Biophysics, Max-Planck-Institute for Biophysical Chemistry, Göttingen, Germany; Weill Institute for Neurosciences and Department of Neurology, University of California San Francisco, San Francisco, California.
| | - Helmut Grubmüller
- Department of Theoretical and Computational Biophysics, Max-Planck-Institute for Biophysical Chemistry, Göttingen, Germany.
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62
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Gkeka P, Stoltz G, Barati Farimani A, Belkacemi Z, Ceriotti M, Chodera JD, Dinner AR, Ferguson AL, Maillet JB, Minoux H, Peter C, Pietrucci F, Silveira A, Tkatchenko A, Trstanova Z, Wiewiora R, Lelièvre T. Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems. J Chem Theory Comput 2020; 16:4757-4775. [PMID: 32559068 PMCID: PMC8312194 DOI: 10.1021/acs.jctc.0c00355] [Citation(s) in RCA: 82] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.
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Affiliation(s)
- Paraskevi Gkeka
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
| | - Gabriel Stoltz
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
| | | | - Zineb Belkacemi
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - John D Chodera
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Aaron R Dinner
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, United States
| | | | - Hervé Minoux
- Integrated Drug Discovery, Sanofi R&D, 94403 Vitry-sur-Seine, France
| | | | - Fabio Pietrucci
- UMR CNRS 7590, MNHN, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, 75005 Paris, France
| | - Ana Silveira
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Zofia Trstanova
- School of Mathematics, The University of Edinburgh, Edinburgh EH9 3FD, U.K
| | - Rafal Wiewiora
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Tony Lelièvre
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
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63
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Mori Y, Okazaki KI, Mori T, Kim K, Matubayasi N. Learning reaction coordinates via cross-entropy minimization: Application to alanine dipeptide. J Chem Phys 2020; 153:054115. [DOI: 10.1063/5.0009066] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Affiliation(s)
- Yusuke Mori
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | | | - Toshifumi Mori
- Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan
- The Graduate University for Advanced Studies, Okazaki, Aichi 444-8585, Japan
| | - Kang Kim
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
- Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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64
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Bailleul S, Dedecker K, Cnudde P, Vanduyfhuys L, Waroquier M, Van Speybroeck V. Ab initio enhanced sampling kinetic study on MTO ethene methylation reaction. J Catal 2020. [DOI: 10.1016/j.jcat.2020.04.015] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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65
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Levintov L, Vashisth H. Ligand Recognition in Viral RNA Necessitates Rare Conformational Transitions. J Phys Chem Lett 2020; 11:5426-5432. [PMID: 32551654 DOI: 10.1021/acs.jpclett.0c01390] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Ribonucleic acids (RNAs) are conformationally flexible molecules that fold into three-dimensional structures and play an important role in different cellular processes as well as in the development of many diseases. RNA has therefore become an important target for developing novel therapeutic approaches. The biophysical processes underlying RNA function are often associated with rare structural transitions that play a key role in ligand recognition. In this work, we probe these rarely occurring transitions using nonequilibrium simulations by characterizing the dissociation of a ligand molecule from an HIV-1 viral RNA element. Specifically, we observed base-flipping rare events that are coupled with ligand binding/unbinding and also provided mechanistic details underlying these transitions.
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Affiliation(s)
- Lev Levintov
- Department of Chemical Engineering, University of New Hampshire, Durham 03824, New Hampshire, United States
| | - Harish Vashisth
- Department of Chemical Engineering, University of New Hampshire, Durham 03824, New Hampshire, United States
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66
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Rogers JR, Geissler PL. Breakage of Hydrophobic Contacts Limits the Rate of Passive Lipid Exchange between Membranes. J Phys Chem B 2020; 124:5884-5898. [DOI: 10.1021/acs.jpcb.0c04139] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Julia R. Rogers
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Phillip L. Geissler
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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67
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Servis MJ, Martinez-Baez E, Clark AE. Hierarchical phenomena in multicomponent liquids: simulation methods, analysis, chemistry. Phys Chem Chem Phys 2020; 22:9850-9874. [PMID: 32154813 DOI: 10.1039/d0cp00164c] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Complex, multicomponent, solutions have often been studied solely through the lens of specific applications of interest. Yet advances to both simulation methodologies (enhanced sampling, etc.) and analysis techniques (network analysis algorithms and others), are creating a trove of data that reveal transcending characteristics across vast compositional phase space. This perspective discusses technical considerations of the reliable and accurate simulations of complex solutions, followed by the advances to analysis algorithms that elucidate coupling of different length and timescale behavior (hierarchical phenomena). The different manifestations of hierarchical phenomena are presented across an array of solution environments, emphasizing fundamental and ongoing science questions. With a more advanced molecular understanding in hand, a quintessential application (solvent extraction) is discussed, where significant opportunities exist to re-imagine the technical scope of an established technology.
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Affiliation(s)
- Michael J Servis
- Department of Chemistry, Washington State University, Pullman, WA 99164, USA.
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68
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Mori T, Saito S. Dissecting the Dynamics during Enzyme Catalysis: A Case Study of Pin1 Peptidyl-Prolyl Isomerase. J Chem Theory Comput 2020; 16:3396-3407. [PMID: 32268066 DOI: 10.1021/acs.jctc.9b01279] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
Free energy surfaces have played a central role in studying protein conformational changes and enzymatic reactions over decades. Yet, free energy barriers and kinetics are highly dependent on the coordinates chosen to define the surface, and furthermore, the dynamics during the reactions are often overlooked. Our recent study on the Pin1-catalyzed isomerization reaction has indicated that the isomerization transition events remarkably deviate from the free energy path, highlighting the need to understand the reaction dynamics in more detail. To this end, here we investigate the reaction coordinates that describe the transition states of the free energy and transition pathways by minimizing the cross-entropy function. We show that the isomerization transition events can be expressed by the concerted changes in the improper torsion angle ζ and nearby backbone torsional angles of the ligand, whereas the transition state of the free energy surface involves changes in a broad range of coordinates including multiple protein-ligand interactions. The current result supports the previous finding that the isomerization transitions occur quickly from the conformational excited states, which is in sharp contrast to the slow and collective changes suggested from the free energy path. Our results further indicate that the coordinates derived from the transition trajectories are not sufficient for finding the transition states on the free energy surfaces due to the lack of information from conformational excited states.
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Affiliation(s)
- Toshifumi Mori
- Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan.,School of Physical Sciences, The Graduate University for Advanced Studies, Okazaki, Aichi 444-8585, Japan
| | - Shinji Saito
- Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan.,School of Physical Sciences, The Graduate University for Advanced Studies, Okazaki, Aichi 444-8585, Japan
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69
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Wang Y, Tiwary P. Understanding the role of predictive time delay and biased propagator in RAVE. J Chem Phys 2020; 152:144102. [DOI: 10.1063/5.0004838] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Affiliation(s)
- Yihang Wang
- Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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70
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Schilling M, Cunha RA, Luber S. Zooming in on the O–O Bond Formation—An Ab Initio Molecular Dynamics Study Applying Enhanced Sampling Techniques. J Chem Theory Comput 2020; 16:2436-2449. [DOI: 10.1021/acs.jctc.9b01207] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mauro Schilling
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Richard A. Cunha
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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71
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Foglia NO, González Lebrero MC, Biekofsky RR, Estrin DA. Reaction Path Analysis from Potential Energy Contributions Using Forces: An Accessible Estimator of Reaction Coordinate Adequacy. J Chem Theory Comput 2020; 16:1618-1629. [PMID: 31999449 DOI: 10.1021/acs.jctc.9b01081] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The calculation of potential energy and free-energy profiles along complex chemical reactions or rare event processes is of great interest because of their importance for many areas in chemistry, molecular biology, and material science. One typical way to generate these profiles is to add a bias potential to modify the energy surface, which can act on a selected degree of freedom in the system. However, in these cases, the quality of the result is strongly dependent on the selection of the degree of freedom over which this bias potential acts. The present work introduces a simple method for the analysis of the degree of freedom selected to describe a chemical process. The proposed methodology is based on the decomposition of contributions to the potential energy profiles by the integration of forces along a reaction path, which allows evaluating the different contributions to the energy change. This could be useful for discriminating the contributions to the energy arising from different regions of the system, which is particularly useful in systems with complex environments that must be represented using hybrid quantum mechanics/molecular mechanics schemes. Furthermore, this methodology allows in generating a quick and simple analysis of the degree of freedom which is used to describe the potential energy profile associated with the reactive process. This is computationally more accessible than the corresponding free-energy profile and can therefore be used as a simple estimator of reaction coordinate adequacy.
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Affiliation(s)
- Nicolás O Foglia
- Departamento de Quı́mica Inorgánica, Analı́tica y Quı́mica Fı́sica/INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
| | - Mariano C González Lebrero
- Departamento de Quı́mica Inorgánica, Analı́tica y Quı́mica Fı́sica/INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
| | - Rodolfo R Biekofsky
- Moebius Research Ltd., Systems Biomedicine, 24 Chedworth House, West Green Rd, N15 5EH London, U.K
| | - Darío A Estrin
- Departamento de Quı́mica Inorgánica, Analı́tica y Quı́mica Fı́sica/INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
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72
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Sigg D, Voelz VA, Carnevale V. Microcanonical coarse-graining of the kinetic Ising model. J Chem Phys 2020; 152:084104. [PMID: 32113343 PMCID: PMC7042020 DOI: 10.1063/1.5139228] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2019] [Accepted: 02/06/2020] [Indexed: 11/15/2022] Open
Abstract
We propose a scheme for coarse-graining the dynamics of the 2-D kinetic Ising model onto the microcanonical ensemble. At subcritical temperatures, 2-D and higher-dimensional Ising lattices possess two basins of attraction separated by a free energy barrier. Projecting onto the microcanonical ensemble has the advantage that the dependence of the crossing rate constant on environmental conditions can be obtained from a single Monte Carlo trajectory. Using various numerical methods, we computed the forward rate constants of coarse-grained representations of the Ising model and compared them with the true value obtained from brute force simulation. While coarse-graining preserves detailed balance, the computed rate constants for barrier heights between 5 kT and 9 kT were consistently 50% larger than the true value. Markovianity testing revealed loss of dynamical memory, which we propose accounts for coarse-graining error. Committor analysis did not support the alternative hypothesis that microcanonical projection is incompatible with an optimal reaction coordinate. The correct crossing rate constant was obtained by spectrally decomposing the diffusion coefficient near the free energy barrier and selecting the slowest (reactive) component. The spectral method also yielded the correct rate constant in the 3-D Ising lattice, where coarse-graining error was 6% and memory effects were diminished. We conclude that microcanonical coarse-graining supplemented by spectral analysis of short-term barrier fluctuations provides a comprehensive kinetic description of barrier crossing in a non-inertial continuous-time jump process.
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Affiliation(s)
| | - Vincent A. Voelz
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Vincenzo Carnevale
- Institute for Computational Molecular Science, College of Science and Technology, Temple University, Philadelphia, Pennsylvania 19122, USA
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73
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Bharadwaj VS, Knott BC, Ståhlberg J, Beckham GT, Crowley MF. The hydrolysis mechanism of a GH45 cellulase and its potential relation to lytic transglycosylase and expansin function. J Biol Chem 2020; 295:4477-4487. [PMID: 32054684 DOI: 10.1074/jbc.ra119.011406] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2019] [Revised: 02/12/2020] [Indexed: 11/06/2022] Open
Abstract
Family 45 glycoside hydrolases (GH45) are endoglucanases that are integral to cellulolytic secretomes, and their ability to break down cellulose has been successfully exploited in textile and detergent industries. In addition to their industrial relevance, understanding the molecular mechanism of GH45-catalyzed hydrolysis is of fundamental importance because of their structural similarity to cell wall-modifying enzymes such as bacterial lytic transglycosylases (LTs) and expansins present in bacteria, plants, and fungi. Our understanding of the catalytic itinerary of GH45s has been incomplete because a crystal structure with substrate spanning the -1 to +1 subsites is currently lacking. Here we constructed and validated a putative Michaelis complex in silico and used it to elucidate the hydrolytic mechanism in a GH45, Cel45A from the fungus Humicola insolens, via unbiased simulation approaches. These molecular simulations revealed that the solvent-exposed active-site architecture results in lack of coordination for the hydroxymethyl group of the substrate at the -1 subsite. This lack of coordination imparted mobility to the hydroxymethyl group and enabled a crucial hydrogen bond with the catalytic acid during and after the reaction. This suggests the possibility of a nonhydrolytic reaction mechanism when the catalytic base aspartic acid is missing, as is the case in some LTs (murein transglycosylase A) and expansins. We calculated reaction free energies and demonstrate the thermodynamic feasibility of the hydrolytic and nonhydrolytic reaction mechanisms. Our results provide molecular insights into the hydrolysis mechanism in HiCel45A, with possible implications for elucidating the elusive catalytic mechanism in LTs and expansins.
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Affiliation(s)
- Vivek S Bharadwaj
- Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401
| | - Brandon C Knott
- Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401
| | - Jerry Ståhlberg
- Department of Molecular Sciences, Swedish University of Agricultural Sciences, P. O. Box 7015, 750 07 Uppsala, Sweden
| | - Gregg T Beckham
- National Bioenergy Center, National Renewable Energy Laboratory, Golden, Colorado 80401
| | - Michael F Crowley
- Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401
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74
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Meyer H, Pelagejcev P, Schilling T. Non-Markovian out-of-equilibrium dynamics: A general numerical procedure to construct time-dependent memory kernels for coarse-grained observables. ACTA ACUST UNITED AC 2020. [DOI: 10.1209/0295-5075/128/40001] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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75
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Yappert R, Kamat K, Peters B. The overdamped transmission coefficient: Recovering the true mean first passage time from an inaccurate reaction coordinate. J Chem Phys 2019; 151:184108. [DOI: 10.1063/1.5117237] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Affiliation(s)
- Ryan Yappert
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Kartik Kamat
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Baron Peters
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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76
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Metadynamics to Enhance Sampling in Biomolecular Simulations. Methods Mol Biol 2019. [PMID: 31396904 DOI: 10.1007/978-1-4939-9608-7_8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2023]
Abstract
Molecular dynamics is a powerful simulation method to provide detailed atomic-scale insight into a range of biological processes including protein folding, biochemical reactions, ligand binding, and many others. Over the last several decades, enhanced sampling methods have been developed to address the large separation in time scales between a molecular dynamics simulation (usually microseconds or shorter) and the time scales of biological processes (often orders of magnitude longer). This chapter specifically focuses on the metadynamics family of methods, which achieves enhanced sampling through the introduction of a history-dependent bias potential that is based on one or more slow degrees of freedom, called collective variables. We introduce the method and its recent variants related to biomolecular studies and then discuss frontier areas of the method. A large part of this chapter is devoted to helping new users of the method understand how to choose metadynamics parameters properly and apply the method to their system of interest.
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77
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Paul S, Nair NN, Vashisth H. Phase space and collective variable based simulation methods for studies of rare events. MOLECULAR SIMULATION 2019. [DOI: 10.1080/08927022.2019.1634268] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Sanjib Paul
- Department of Chemical Engineering, University of New Hampshire, Durham, NH, USA
| | - Nisanth N. Nair
- Department of Chemistry, Indian Institute of Technology, Kanpur, India
| | - Harish Vashisth
- Department of Chemical Engineering, University of New Hampshire, Durham, NH, USA
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78
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Post M, Wolf S, Stock G. Principal component analysis of nonequilibrium molecular dynamics simulations. J Chem Phys 2019; 150:204110. [PMID: 31153204 DOI: 10.1063/1.5089636] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Principal component analysis (PCA) represents a standard approach to identify collective variables {xi} = x, which can be used to construct the free energy landscape ΔG(x) of a molecular system. While PCA is routinely applied to equilibrium molecular dynamics (MD) simulations, it is less obvious as to how to extend the approach to nonequilibrium simulation techniques. This includes, e.g., the definition of the statistical averages employed in PCA as well as the relation between the equilibrium free energy landscape ΔG(x) and the energy landscapes ΔG(x) obtained from nonequilibrium MD. As an example for a nonequilibrium method, "targeted MD" is considered which employs a moving distance constraint to enforce rare transitions along some biasing coordinate s. The introduced bias can be described by a weighting function P(s), which provides a direct relation between equilibrium and nonequilibrium data, and thus establishes a well-defined way to perform PCA on nonequilibrium data. While the resulting distribution P(x) and energy ΔG∝lnP will not reflect the equilibrium state of the system, the nonequilibrium energy landscape ΔG(x) may directly reveal the molecular reaction mechanism. Applied to targeted MD simulations of the unfolding of decaalanine, for example, a PCA performed on backbone dihedral angles is shown to discriminate several unfolding pathways. Although the formulation is in principle exact, its practical use depends critically on the choice of the biasing coordinate s, which should account for a naturally occurring motion between two well-defined end-states of the system.
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Affiliation(s)
- Matthias Post
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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79
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Meyer H, Voigtmann T, Schilling T. On the dynamics of reaction coordinates in classical, time-dependent, many-body processes. J Chem Phys 2019; 150:174118. [DOI: 10.1063/1.5090450] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Hugues Meyer
- Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
- Research Unit in Engineering Science, Université du Luxembourg, L-4364 Esch-sur-Alzette, Luxembourg
| | - Thomas Voigtmann
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany
- Department of Physics, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Tanja Schilling
- Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
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80
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Marriott M, Lupi L, Kumar A, Molinero V. Following the nucleation pathway from disordered liquid to gyroid mesophase. J Chem Phys 2019; 150:164902. [PMID: 31042878 DOI: 10.1063/1.5081850] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Mesophases have order intermediate between liquids and crystals and arise in systems with frustration, such as surfactants, block copolymers, and Janus nanoparticles. The gyroid mesophase contains two interpenetrated, nonintersecting chiral networks that give it properties useful for photonics. It is challenging to nucleate a gyroid from the liquid. Elucidating the reaction coordinate for gyroid nucleation could assist in designing additives that facilitate the formation of the mesophase. However, the complexity of the gyroid structure and the extreme weakness of the first-order liquid to gyroid transition make this a challenging quest. Here, we investigate the pathway and transition states for the nucleation of a gyroid from the liquid in molecular simulations with a mesogenic binary mixture. We find that the gyroid nuclei at the transition states have a large degree of positional disorder and are not compact, consistent with the low surface free energy of the liquid-gyroid interface. A combination of bond-order parameters for the minor component is best to describe the passage from liquid to gyroid, among those we consider. The committor analyses, however, show that this best coordinate is not perfect and suggests that accounting for the relative ordering of the two interpenetrated networks in infant nuclei, as well as for signatures of ordering in the major component of the mesophase, would improve the accuracy of the reaction coordinate for gyroid formation and its use to evaluate nucleation barriers. To our knowledge, this study is the first to investigate the reaction coordinate and critical nuclei for the formation of any mesophase from an amorphous phase.
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Affiliation(s)
- Maile Marriott
- Department of Chemistry, The University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-085, USA
| | - Laura Lupi
- Department of Chemistry, The University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-085, USA
| | - Abhinaw Kumar
- Department of Chemistry, The University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-085, USA
| | - Valeria Molinero
- Department of Chemistry, The University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-085, USA
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81
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Zhu L, Sheong FK, Cao S, Liu S, Unarta IC, Huang X. TAPS: A traveling-salesman based automated path searching method for functional conformational changes of biological macromolecules. J Chem Phys 2019; 150:124105. [DOI: 10.1063/1.5082633] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
- Lizhe Zhu
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, China
| | - Fu Kit Sheong
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Siqin Cao
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Song Liu
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Ilona C. Unarta
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Xuhui Huang
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Bioengineering Program, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
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82
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Nagel D, Weber A, Lickert B, Stock G. Dynamical coring of Markov state models. J Chem Phys 2019; 150:094111. [DOI: 10.1063/1.5081767] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Daniel Nagel
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Anna Weber
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Benjamin Lickert
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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83
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DeFever RS, Sarupria S. Contour forward flux sampling: Sampling rare events along multiple collective variables. J Chem Phys 2019; 150:024103. [PMID: 30646707 DOI: 10.1063/1.5063358] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
Many rare event transitions involve multiple collective variables (CVs), and the most appropriate combination of CVs is generally unknown a priori. We thus introduce a new method, contour forward flux sampling (cFFS), to study rare events with multiple CVs simultaneously. cFFS places nonlinear interfaces on-the-fly from the collective progress of the simulations, without any prior knowledge of the energy landscape or appropriate combination of CVs. We demonstrate cFFS on analytical potential energy surfaces and a conformational change in alanine dipeptide.
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Affiliation(s)
- Ryan S DeFever
- Department of Chemical and Biomolecular Engineering, Clemson University, Clemson, South Carolina 29634, USA
| | - Sapna Sarupria
- Department of Chemical and Biomolecular Engineering, Clemson University, Clemson, South Carolina 29634, USA
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84
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Abstract
This chapter discusses how the PLUMED plugin for molecular dynamics can be used to analyze and bias molecular dynamics trajectories. The chapter begins by introducing the notion of a collective variable and by then explaining how the free energy can be computed as a function of one or more collective variables. A number of practical issues mostly around periodic boundary conditions that arise when these types of calculations are performed using PLUMED are then discussed. Later parts of the chapter discuss how PLUMED can be used to perform enhanced sampling simulations that introduce simulation biases or multiple replicas of the system and Monte Carlo exchanges between these replicas. This section is then followed by a discussion on how free-energy surfaces and associated error bars can be extracted from such simulations by using weighted histogram and block averaging techniques.
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Affiliation(s)
- Giovanni Bussi
- Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy.
| | - Gareth A Tribello
- Atomistic Simulation Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast, UK.
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85
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Schile AJ, Limmer DT. Studying rare nonadiabatic dynamics with transition path sampling quantum jump trajectories. J Chem Phys 2018; 149:214109. [DOI: 10.1063/1.5058281] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Addison J. Schile
- Department of Chemistry, University of California, Berkeley, California 94618, USA
- Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94618, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, California 94618, USA
- Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94618, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94618, USA
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86
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Dickson BM. Erroneous Rates and False Statistical Confirmations from Infrequent Metadynamics and Other Equivalent Violations of the Hyperdynamics Paradigm. J Chem Theory Comput 2018; 15:78-83. [DOI: 10.1021/acs.jctc.8b00848] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Bradley M. Dickson
- Center for Epigenetics, Van Andel Research Institute, Grand Rapids, Michigan 49503, United States
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87
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Demuynck R, Wieme J, Rogge SMJ, Dedecker KD, Vanduyfhuys L, Waroquier M, Van Speybroeck V. Protocol for Identifying Accurate Collective Variables in Enhanced Molecular Dynamics Simulations for the Description of Structural Transformations in Flexible Metal-Organic Frameworks. J Chem Theory Comput 2018; 14:5511-5526. [PMID: 30336016 PMCID: PMC6236469 DOI: 10.1021/acs.jctc.8b00725] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2018] [Indexed: 01/05/2023]
Abstract
Various kinds of flexibility have been observed in metal-organic frameworks, which may originate from the topology of the material or the presence of flexible ligands. The construction of free energy profiles describing the full dynamical behavior along the phase transition path is challenging since it is not trivial to identify collective variables able to identify all metastable states along the reaction path. In this work, a systematic three-step protocol to uniquely identify the dominant order parameters for structural transformations in flexible metal-organic frameworks and subsequently construct accurate free energy profiles is presented. Methodologically, this protocol is rooted in the time-structure based independent component analysis (tICA), a well-established statistical modeling technique embedded in the Markov state model methodology and often employed to study protein folding, that allows for the identification of the slowest order parameters characterizing the structural transformation. To ensure an unbiased and systematic identification of these order parameters, the tICA decomposition is performed based on information from a prior replica exchange (RE) simulation, as this technique enhances the sampling along all degrees of freedom of the system simultaneously. From this simulation, the tICA procedure extracts the order parameters-often structural parameters-that characterize the slowest transformations in the material. Subsequently, these order parameters are adopted in traditional enhanced sampling methods such as umbrella sampling, thermodynamic integration, and variationally enhanced sampling to construct accurate free energy profiles capturing the flexibility in these nanoporous materials. In this work, the applicability of this tICA-RE protocol is demonstrated by determining the slowest order parameters in both MIL-53(Al) and CAU-13, which exhibit a strongly different type of flexibility. The obtained free energy profiles as a function of this extracted order parameter are furthermore compared to the profiles obtained when adopting less-suited collective variables, indicating the importance of systematically selecting the relevant order parameters to construct accurate free energy profiles for flexible metal-organic frameworks, which is in correspondence with experimental findings. The method succeeds in mapping the full free energy surface in terms of appropriate collective variables for MOFs exhibiting linker flexibility. For CAU-13, we show the decreased stability of the closed pore phase by systematically adding adsorbed xylene molecules in the framework.
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Affiliation(s)
- Ruben Demuynck
- Center for Molecular Modeling, Ghent University, Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Jelle Wieme
- Center for Molecular Modeling, Ghent University, Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Sven M. J. Rogge
- Center for Molecular Modeling, Ghent University, Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Karen D. Dedecker
- Center for Molecular Modeling, Ghent University, Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Louis Vanduyfhuys
- Center for Molecular Modeling, Ghent University, Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Michel Waroquier
- Center for Molecular Modeling, Ghent University, Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Veronique Van Speybroeck
- Center for Molecular Modeling, Ghent University, Technologiepark 903, B-9052 Zwijnaarde, Belgium
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88
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Sittel F, Stock G. Perspective: Identification of collective variables and metastable states of protein dynamics. J Chem Phys 2018; 149:150901. [PMID: 30342445 DOI: 10.1063/1.5049637] [Citation(s) in RCA: 84] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
The statistical analysis of molecular dynamics simulations requires dimensionality reduction techniques, which yield a low-dimensional set of collective variables (CVs) {x i } = x that in some sense describe the essential dynamics of the system. Considering the distribution P( x ) of the CVs, the primal goal of a statistical analysis is to detect the characteristic features of P( x ), in particular, its maxima and their connection paths. This is because these features characterize the low-energy regions and the energy barriers of the corresponding free energy landscape ΔG( x ) = -k B T ln P( x ), and therefore amount to the metastable states and transition regions of the system. In this perspective, we outline a systematic strategy to identify CVs and metastable states, which subsequently can be employed to construct a Langevin or a Markov state model of the dynamics. In particular, we account for the still limited sampling typically achieved by molecular dynamics simulations, which in practice seriously limits the applicability of theories (e.g., assuming ergodicity) and black-box software tools (e.g., using redundant input coordinates). We show that it is essential to use internal (rather than Cartesian) input coordinates, employ dimensionality reduction methods that avoid rescaling errors (such as principal component analysis), and perform density based (rather than k-means-type) clustering. Finally, we briefly discuss a machine learning approach to dimensionality reduction, which highlights the essential internal coordinates of a system and may reveal hidden reaction mechanisms.
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Affiliation(s)
- Florian Sittel
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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89
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Richard D, Speck T. Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling. J Chem Phys 2018; 148:124110. [PMID: 29604868 DOI: 10.1063/1.5016277] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, and the second method is based on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow us to probe a wide range of supersaturations and to reconstruct the kinetics and the free energy landscape from the same simulation. Results are consistent with the scaling predicted by classical nucleation theory although a quantitative fit requires a rather large effective interfacial tension.
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Affiliation(s)
- David Richard
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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90
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Kappler J, Daldrop JO, Brünig FN, Boehle MD, Netz RR. Memory-induced acceleration and slowdown of barrier crossing. J Chem Phys 2018; 148:014903. [PMID: 29306292 DOI: 10.1063/1.4998239] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
We study the mean first-passage time τMFP for the barrier crossing of a single massive particle with non-Markovian memory by Langevin simulations in one dimension. In the Markovian limit of short memory time τΓ, the expected Kramers turnover between the overdamped (high-friction) and the inertial (low-friction) limits is recovered. Compared to the Markovian case, we find barrier crossing to be accelerated for intermediate memory time, while for long memory time, barrier crossing is slowed down and τMFP increases with τΓ as a power law τMFP∼τΓ2. Both effects are derived from an asymptotic propagator analysis: while barrier crossing acceleration at intermediate memory can be understood as an effective particle mass reduction, slowing down for long memory is caused by the slow kinetics of energy diffusion. A simple and globally accurate heuristic formula for τMFP in terms of all relevant time scales of the system is presented and used to establish a scaling diagram featuring the Markovian overdamped and the Markovian inertial regimes, as well as the non-Markovian intermediate memory time regime where barrier crossing is accelerated and the non-Markovian long memory time regime where barrier crossing is slowed down.
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Affiliation(s)
- Julian Kappler
- Freie Universität Berlin, Fachbereich Physik, 14195 Berlin, Germany
| | - Jan O Daldrop
- Freie Universität Berlin, Fachbereich Physik, 14195 Berlin, Germany
| | - Florian N Brünig
- Freie Universität Berlin, Fachbereich Physik, 14195 Berlin, Germany
| | - Moritz D Boehle
- Freie Universität Berlin, Fachbereich Physik, 14195 Berlin, Germany
| | - Roland R Netz
- Freie Universität Berlin, Fachbereich Physik, 14195 Berlin, Germany
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91
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Abstract
We introduce a method to obtain one-dimensional collective variables for studying rarely occurring transitions between two metastable states separated by a high free energy barrier. No previous information, not even approximated, on the path followed during the transition is needed. The only requirement is to know the fluctuations of the system while in the two metastable states. With this information in hand, we build the collective variable using a modified version of Fisher's linear discriminant analysis. The usefulness of this approach is tested on the metadynamics simulation of two representative systems. The first is the freezing of silver iodide into the superionic α-phase, and the second is the study of a classical Diels-Alder reaction. The collective variable works very well in these two diverse cases.
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Affiliation(s)
- Dan Mendels
- Department of Chemistry and Applied Biosciences , ETH Zurich, c/o USI Campus , Via Giuseppe Buffi 13 , CH-6900 Lugano , Ticino , Switzerland
- Facoltá di Informatica, Istituto di Scienze Computazionali , Universitá della Svizzera italiana (USI) , Via Giuseppe Buffi 13 , CH-6900 Lugano , Ticino , Switzerland
| | - GiovanniMaria Piccini
- Department of Chemistry and Applied Biosciences , ETH Zurich, c/o USI Campus , Via Giuseppe Buffi 13 , CH-6900 Lugano , Ticino , Switzerland
- Facoltá di Informatica, Istituto di Scienze Computazionali , Universitá della Svizzera italiana (USI) , Via Giuseppe Buffi 13 , CH-6900 Lugano , Ticino , Switzerland
| | - Michele Parrinello
- Department of Chemistry and Applied Biosciences , ETH Zurich, c/o USI Campus , Via Giuseppe Buffi 13 , CH-6900 Lugano , Ticino , Switzerland
- Facoltá di Informatica, Istituto di Scienze Computazionali , Universitá della Svizzera italiana (USI) , Via Giuseppe Buffi 13 , CH-6900 Lugano , Ticino , Switzerland
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92
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Wagner JW, Dannenhoffer-Lafage T, Jin J, Voth GA. Extending the range and physical accuracy of coarse-grained models: Order parameter dependent interactions. J Chem Phys 2018; 147:044113. [PMID: 28764380 DOI: 10.1063/1.4995946] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Order parameters (i.e., collective variables) are often used to describe the behavior of systems as they capture different features of the free energy surface. Yet, most coarse-grained (CG) models only employ two- or three-body non-bonded interactions between the CG particles. In situations where these interactions are insufficient for the CG model to reproduce the structural distributions of the underlying fine-grained (FG) model, additional interactions must be included. In this paper, we introduce an approach to expand the basis sets available in the multiscale coarse-graining (MS-CG) methodology by including order parameters. Then, we investigate the ability of an additive local order parameter (e.g., density) and an additive global order parameter (i.e., distance from a hard wall) to improve the description of CG models in interfacial systems. Specifically, we study methanol liquid-vapor coexistence, acetonitrile liquid-vapor coexistence, and acetonitrile liquid confined by hard-wall plates, all using single site CG models. We find that the use of order parameters dramatically improves the reproduction of structural properties of interfacial CG systems relative to the FG reference as compared with pairwise CG interactions alone.
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Affiliation(s)
- Jacob W Wagner
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Thomas Dannenhoffer-Lafage
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Jaehyeok Jin
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Gregory A Voth
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
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93
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Krivov SV. Protein Folding Free Energy Landscape along the Committor - the Optimal Folding Coordinate. J Chem Theory Comput 2018; 14:3418-3427. [PMID: 29791148 DOI: 10.1021/acs.jctc.8b00101] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Recent advances in simulation and experiment have led to dramatic increases in the quantity and complexity of produced data, which makes the development of automated analysis tools very important. A powerful approach to analyze dynamics contained in such data sets is to describe/approximate it by diffusion on a free energy landscape - free energy as a function of reaction coordinates (RC). For the description to be quantitatively accurate, RCs should be chosen in an optimal way. Recent theoretical results show that such an optimal RC exists; however, determining it for practical systems is a very difficult unsolved problem. Here we describe a solution to this problem. We describe an adaptive nonparametric approach to accurately determine the optimal RC (the committor) for an equilibrium trajectory of a realistic system. In contrast to alternative approaches, which require a functional form with many parameters to approximate an RC and thus extensive expertise with the system, the suggested approach is nonparametric and can approximate any RC with high accuracy without system specific information. To avoid overfitting for a realistically sampled system, the approach performs RC optimization in an adaptive manner by focusing optimization on less optimized spatiotemporal regions of the RC. The power of the approach is illustrated on a long equilibrium atomistic folding simulation of HP35 protein. We have determined the optimal folding RC - the committor, which was confirmed by passing a stringent committor validation test. It allowed us to determine a first quantitatively accurate protein folding free energy landscape. We have confirmed the recent theoretical results that diffusion on such a free energy profile can be used to compute exactly the equilibrium flux, the mean first passage times, and the mean transition path times between any two points on the profile. We have shown that the mean squared displacement along the optimal RC grows linear with time as for simple diffusion. The free energy profile allowed us to obtain a direct rigorous estimate of the pre-exponential factor for the folding dynamics.
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Affiliation(s)
- Sergei V Krivov
- Astbury Center for Structural Molecular Biology , University of Leeds , Leeds LS2 9JT , United Kingdom
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94
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Walker EA, Mitchell D, Terejanu GA, Heyden A. Identifying Active Sites of the Water–Gas Shift Reaction over Titania Supported Platinum Catalysts under Uncertainty. ACS Catal 2018. [DOI: 10.1021/acscatal.7b03531] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Eric A. Walker
- Department of Chemical Engineering, University of South Carolina, 301 Main Street, Columbia, South Carolina 29208, United States
| | - Donald Mitchell
- Department of Chemical Engineering, City College of New York, 160 Covenant Avenue, New York, New York 10031, United States
| | - Gabriel A. Terejanu
- Department of Computer Science and Engineering, University of South Carolina, 301 Main Street, Columbia, South Carolina 29208, United States
| | - Andreas Heyden
- Department of Chemical Engineering, University of South Carolina, 301 Main Street, Columbia, South Carolina 29208, United States
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95
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Shen L, Yang W. Molecular Dynamics Simulations with Quantum Mechanics/Molecular Mechanics and Adaptive Neural Networks. J Chem Theory Comput 2018; 14:1442-1455. [PMID: 29438614 PMCID: PMC6233882 DOI: 10.1021/acs.jctc.7b01195] [Citation(s) in RCA: 88] [Impact Index Per Article: 14.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Direct molecular dynamics (MD) simulation with ab initio quantum mechanical and molecular mechanical (QM/MM) methods is very powerful for studying the mechanism of chemical reactions in a complex environment but also very time-consuming. The computational cost of QM/MM calculations during MD simulations can be reduced significantly using semiempirical QM/MM methods with lower accuracy. To achieve higher accuracy at the ab initio QM/MM level, a correction on the existing semiempirical QM/MM model is an attractive idea. Recently, we reported a neural network (NN) method as QM/MM-NN to predict the potential energy difference between semiempirical and ab initio QM/MM approaches. The high-level results can be obtained using neural network based on semiempirical QM/MM MD simulations, but the lack of direct MD samplings at the ab initio QM/MM level is still a deficiency that limits the applications of QM/MM-NN. In the present paper, we developed a dynamic scheme of QM/MM-NN for direct MD simulations on the NN-predicted potential energy surface to approximate ab initio QM/MM MD. Since some configurations excluded from the database for NN training were encountered during simulations, which may cause some difficulties on MD samplings, an adaptive procedure inspired by the selection scheme reported by Behler [ Behler Int. J. Quantum Chem. 2015 , 115 , 1032 ; Behler Angew. Chem., Int. Ed. 2017 , 56 , 12828 ] was employed with some adaptions to update NN and carry out MD iteratively. We further applied the adaptive QM/MM-NN MD method to the free energy calculation and transition path optimization on chemical reactions in water. The results at the ab initio QM/MM level can be well reproduced using this method after 2-4 iteration cycles. The saving in computational cost is about 2 orders of magnitude. It demonstrates that the QM/MM-NN with direct MD simulations has great potentials not only for the calculation of thermodynamic properties but also for the characterization of reaction dynamics, which provides a useful tool to study chemical or biochemical systems in solution or enzymes.
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Affiliation(s)
- Lin Shen
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, P.R. China
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96
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Paul S, Paul TK, Taraphder S. Reaction Coordinate, Free Energy, and Rate of Intramolecular Proton Transfer in Human Carbonic Anhydrase II. J Phys Chem B 2018; 122:2851-2866. [DOI: 10.1021/acs.jpcb.7b10713] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sanjib Paul
- Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
| | - Tanmoy Kumar Paul
- Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
| | - Srabani Taraphder
- Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
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97
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Patra S, Keshavamurthy S. Detecting reactive islands using Lagrangian descriptors and the relevance to transition path sampling. Phys Chem Chem Phys 2018; 20:4970-4981. [PMID: 29387842 DOI: 10.1039/c7cp05912d] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
It has been known for sometime now that isomerization reactions, classically, are mediated by phase space structures called reactive islands (RI). RIs provide one possible route to correct for the nonstatistical effects in the reaction dynamics. In this work, we map out the reactive islands for the two dimensional Müller-Brown model potential and show that the reactive islands are intimately linked to the issue of rare event sampling. In particular, we establish the sensitivity of the so called committor probabilities, useful quantities in the transition path sampling technique, to the hierarchical RI structures. Mapping out the RI structure for high dimensional systems, however, is a challenging task. Here, we show that the technique of Lagrangian descriptors is able to effectively identify the RI hierarchy in the model system. Based on our results, we suggest that the Lagrangian descriptors can be useful for detecting RIs in high dimensional systems.
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Affiliation(s)
- Sarbani Patra
- Department of Chemistry, Indian Institute of Technology, Kanpur, U.P. 208 016, India.
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98
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Demuynck R, Rogge SMJ, Vanduyfhuys L, Wieme J, Waroquier M, Van Speybroeck V. Efficient Construction of Free Energy Profiles of Breathing Metal-Organic Frameworks Using Advanced Molecular Dynamics Simulations. J Chem Theory Comput 2017; 13:5861-5873. [PMID: 29131647 PMCID: PMC5729547 DOI: 10.1021/acs.jctc.7b01014] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
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In order to reliably
predict and understand the breathing behavior
of highly flexible metal–organic frameworks from thermodynamic
considerations, an accurate estimation of the free energy difference
between their different metastable states is a prerequisite. Herein,
a variety of free energy estimation methods are thoroughly tested
for their ability to construct the free energy profile as a function
of the unit cell volume of MIL-53(Al). The methods comprise free energy
perturbation, thermodynamic integration, umbrella sampling, metadynamics,
and variationally enhanced sampling. A series of molecular dynamics
simulations have been performed in the frame of each of the five methods
to describe structural transformations in flexible materials with
the volume as the collective variable, which offers a unique opportunity
to assess their computational efficiency. Subsequently, the most efficient
method, umbrella sampling, is used to construct an accurate free energy
profile at different temperatures for MIL-53(Al) from first principles
at the PBE+D3(BJ) level of theory. This study yields insight into
the importance of the different aspects such as entropy contributions
and anharmonic contributions on the resulting free energy profile.
As such, this thorough study provides unparalleled insight in the
thermodynamics of the large structural deformations of flexible materials.
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Affiliation(s)
- Ruben Demuynck
- Center for Molecular Modeling (CMM), Ghent University , Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Sven M J Rogge
- Center for Molecular Modeling (CMM), Ghent University , Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Louis Vanduyfhuys
- Center for Molecular Modeling (CMM), Ghent University , Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Jelle Wieme
- Center for Molecular Modeling (CMM), Ghent University , Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Michel Waroquier
- Center for Molecular Modeling (CMM), Ghent University , Technologiepark 903, B-9052 Zwijnaarde, Belgium
| | - Veronique Van Speybroeck
- Center for Molecular Modeling (CMM), Ghent University , Technologiepark 903, B-9052 Zwijnaarde, Belgium
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99
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DeFever RS, Sarupria S. Nucleation mechanism of clathrate hydrates of water-soluble guest molecules. J Chem Phys 2017; 147:204503. [DOI: 10.1063/1.4996132] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ryan S. DeFever
- Department of Chemical and Biomolecular Engineering, Clemson University, Clemson, South Carolina 29634, USA
| | - Sapna Sarupria
- Department of Chemical and Biomolecular Engineering, Clemson University, Clemson, South Carolina 29634, USA
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100
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Ernst M, Wolf S, Stock G. Identification and Validation of Reaction Coordinates Describing Protein Functional Motion: Hierarchical Dynamics of T4 Lysozyme. J Chem Theory Comput 2017; 13:5076-5088. [DOI: 10.1021/acs.jctc.7b00571] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Affiliation(s)
- Matthias Ernst
- Biomolecular Dynamics, Institute
of Physics, Albert Ludwigs University, Freiburg, 79104, Germany
| | - Steffen Wolf
- Biomolecular Dynamics, Institute
of Physics, Albert Ludwigs University, Freiburg, 79104, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute
of Physics, Albert Ludwigs University, Freiburg, 79104, Germany
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