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Blazhynska M, Gumbart JC, Chen H, Tajkhorshid E, Roux B, Chipot C. A Rigorous Framework for Calculating Protein-Protein Binding Affinities in Membranes. J Chem Theory Comput 2023; 19:9077-9092. [PMID: 38091976 PMCID: PMC11145395 DOI: 10.1021/acs.jctc.3c00941] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2023]
Abstract
Calculating the binding free energy of integral transmembrane (TM) proteins is crucial for understanding the mechanisms by which they recognize one another and reversibly associate. The glycophorin A (GpA) homodimer, composed of two α-helical segments, has long served as a model system for studying TM protein reversible association. The present work establishes a methodological framework for calculating the binding affinity of the GpA homodimer in the heterogeneous environment of a membrane. Our investigation carefully considered a variety of protocols, including the appropriate choice of the force field, rigorous standardization reflecting the experimental conditions, sampling algorithm, anisotropic environment, and collective variables, to accurately describe GpA dimerization via molecular dynamics-based approaches. Specifically, two strategies were explored: (i) an unrestrained potential mean force (PMF) calculation, which merely enhances sampling along the separation of the two binding partners without any restraint, and (ii) a so-called "geometrical route", whereby the α-helices are progressively separated with imposed restraints on their orientational, positional, and conformational degrees of freedom to accelerate convergence. Our simulations reveal that the simplified, unrestrained PMF approach is inadequate for the description of GpA dimerization. Instead, the geometrical route, tailored specifically to GpA in a membrane environment, yields excellent agreement with experimental data within a reasonable computational time. A dimerization free energy of -10.7 kcal/mol is obtained, in fairly good agreement with available experimental data. The geometrical route further helps elucidate how environmental forces drive association before helical interactions stabilize it. Our simulations also brought to light a distinct, long-lived spatial arrangement that potentially serves as an intermediate state during dimer formation. The methodological advances in the generalized geometrical route provide a powerful tool for accurate and efficient binding-affinity calculations of intricate TM protein complexes in inhomogeneous environments.
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Affiliation(s)
- Marharyta Blazhynska
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n°7019, Université de Lorraine, B.P. 70239, Vandœuvre-lès-Nancy cedex 54506, France
| | - James C Gumbart
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332, United States
| | - Haochuan Chen
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n°7019, Université de Lorraine, B.P. 70239, Vandœuvre-lès-Nancy cedex 54506, France
| | - Emad Tajkhorshid
- Theoretical and Computational Biophysics Group, NIH Center for Macromolecular Modeling and Visualization, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Avenue, Urbana, Illinois 61801, United States
- Department of Biochemistry, University of Illinois at Urbana-Champaign, 600 S. Mathews Avenue, Urbana, Illinois 61801, United States
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, The University of Chicago, 929 E. 57th Street W225, Chicago, Illinois 60637, United States
- Department of Chemistry, The University of Chicago, 5735 S. Ellis Avenue, Chicago, Illinois 60637, United States
| | - Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n°7019, Université de Lorraine, B.P. 70239, Vandœuvre-lès-Nancy cedex 54506, France
- Theoretical and Computational Biophysics Group, NIH Center for Macromolecular Modeling and Visualization, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Avenue, Urbana, Illinois 61801, United States
- Department of Biochemistry and Molecular Biology, The University of Chicago, 929 E. 57th Street W225, Chicago, Illinois 60637, United States
- Department of Chemistry, The University of Hawai'i at Ma̅noa, 2545 McCarthy Mall, Honolulu, Hawaii 96822, United States
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2
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Pasarkar AP, Bencomo GM, Olsson S, Dieng AB. Vendi sampling for molecular simulations: Diversity as a force for faster convergence and better exploration. J Chem Phys 2023; 159:144108. [PMID: 37823459 DOI: 10.1063/5.0166172] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 09/25/2023] [Indexed: 10/13/2023] Open
Abstract
Molecular dynamics (MD) is the method of choice for understanding the structure, function, and interactions of molecules. However, MD simulations are limited by the strong metastability of many molecules, which traps them in a single conformation basin for an extended amount of time. Enhanced sampling techniques, such as metadynamics and replica exchange, have been developed to overcome this limitation and accelerate the exploration of complex free energy landscapes. In this paper, we propose Vendi Sampling, a replica-based algorithm for increasing the efficiency and efficacy of the exploration of molecular conformation spaces. In Vendi sampling, replicas are simulated in parallel and coupled via a global statistical measure, the Vendi Score, to enhance diversity. Vendi sampling allows for the recovery of unbiased sampling statistics and dramatically improves sampling efficiency. We demonstrate the effectiveness of Vendi sampling in improving molecular dynamics simulations by showing significant improvements in coverage and mixing between metastable states and convergence of free energy estimates for four common benchmarks, including Alanine Dipeptide and Chignolin.
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Affiliation(s)
- Amey P Pasarkar
- Vertaix, Department of Computer Science, Princeton University, 35 Olden Street, Princeton, New Jersey 08544, USA
| | - Gianluca M Bencomo
- Department of Computer Science, Princeton University, 35 Olden Street, Princeton, New Jersey 08544, USA
| | - Simon Olsson
- Department of Computer Science and Engineering, Chalmers University of Technology, Rännvägen 6, 41258 Gothenburg, Sweden
| | - Adji Bousso Dieng
- Vertaix, Department of Computer Science, Princeton University, 35 Olden Street, Princeton, New Jersey 08544, USA
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3
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Stevensson B, Edén M. Improved reweighting protocols for variationally enhanced sampling simulations with multiple walkers. Phys Chem Chem Phys 2023; 25:22063-22078. [PMID: 37560777 DOI: 10.1039/d2cp04009c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/11/2023]
Abstract
In molecular dynamics simulations utilizing enhanced-sampling techniques, reweighting is a central component for recovering the targeted ensemble averages of the "unbiased" system by calculating and applying a bias-correction function c(t). We present enhanced reweighting protocols for variationally enhanced sampling (VES) simulations by exploiting a recent reweighting method, originally introduced in the metadynamics framework [Giberti et al. J. Chem. Theory Comput., 2020, 16, 100-107], which was modified and extended to multiple-walker simulations: these may be implemented either as "independent" walkers (associated with one unique correction function per walker) or "cooperative" ones that all share one correction function, which is the hitherto only explored option. When each case is combined with the two possibilities of determining c(t) by time integration up to either t or over the entire simulation period , altogether four reweighting options result. Their relative merits were assessed by well-tempered VES simulations of two model problems: locating the free-energy difference between two metastable molecular conformations of the N-acetyl-L-alanine methylamide dipeptide, and the recovery of an a priori known distribution when one water molecule in the liquid phase is perturbed by a periodic free-energy function. The most rapid convergence occurred for large cooperative walkers, regardless of the upper integration limit, but integrating up to t proved advantageous for small walker ensembles. That novel reweighting method compared favorably to the standard VES reweighting, as well as to current state-of-the-art reweighting options introduced for metadynamics simulations that estimate c(t) by integration over the collective variables. For further gains in computational speed and accuracy, we also introduce analytical solutions for c(t), as well as offering further insight into its features by approximative analytical expressions in the "high-temperature" regime.
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Affiliation(s)
- Baltzar Stevensson
- Department of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden.
| | - Mattias Edén
- Department of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden.
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4
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Artiukhin DG, Godtliebsen IH, Schmitz G, Christiansen O. Gaussian process regression adaptive density-guided approach: Toward calculations of potential energy surfaces for larger molecules. J Chem Phys 2023; 159:024102. [PMID: 37428042 DOI: 10.1063/5.0152367] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Accepted: 06/15/2023] [Indexed: 07/11/2023] Open
Abstract
We present a new program implementation of the Gaussian process regression adaptive density-guided approach [Schmitz et al., J. Chem. Phys. 153, 064105 (2020)] for automatic and cost-efficient potential energy surface construction in the MidasCpp program. A number of technical and methodological improvements made allowed us to extend this approach toward calculations of larger molecular systems than those previously accessible and maintain the very high accuracy of constructed potential energy surfaces. On the methodological side, improvements were made by using a Δ-learning approach, predicting the difference against a fully harmonic potential, and employing a computationally more efficient hyperparameter optimization procedure. We demonstrate the performance of this method on a test set of molecules of growing size and show that up to 80% of single point calculations could be avoided, introducing a root mean square deviation in fundamental excitations of about 3 cm-1. A much higher accuracy with errors below 1 cm-1 could be achieved with tighter convergence thresholds still reducing the number of single point computations by up to 68%. We further support our findings with a detailed analysis of wall times measured while employing different electronic structure methods. Our results demonstrate that GPR-ADGA is an effective tool, which could be applied for cost-efficient calculations of potential energy surfaces suitable for highly accurate vibrational spectra simulations.
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Affiliation(s)
- Denis G Artiukhin
- Institut für Chemie und Biochemie, Freie Universität Berlin, Arnimallee 22, 14195 Berlin, Germany
| | - Ian H Godtliebsen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
| | - Gunnar Schmitz
- Lehrstuhl für Theoretische Chemie II, Ruhr-Universität Bochum, Universitätstraße 150, 44801 Bochum, Germany
| | - Ove Christiansen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
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5
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Bhatia H, Aydin F, Carpenter TS, Lightstone FC, Bremer PT, Ingólfsson HI, Nissley DV, Streitz FH. The confluence of machine learning and multiscale simulations. Curr Opin Struct Biol 2023; 80:102569. [PMID: 36966691 DOI: 10.1016/j.sbi.2023.102569] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Revised: 01/31/2023] [Accepted: 02/08/2023] [Indexed: 06/04/2023]
Abstract
Multiscale modeling has a long history of use in structural biology, as computational biologists strive to overcome the time- and length-scale limits of atomistic molecular dynamics. Contemporary machine learning techniques, such as deep learning, have promoted advances in virtually every field of science and engineering and are revitalizing the traditional notions of multiscale modeling. Deep learning has found success in various approaches for distilling information from fine-scale models, such as building surrogate models and guiding the development of coarse-grained potentials. However, perhaps its most powerful use in multiscale modeling is in defining latent spaces that enable efficient exploration of conformational space. This confluence of machine learning and multiscale simulation with modern high-performance computing promises a new era of discovery and innovation in structural biology.
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Affiliation(s)
- Harsh Bhatia
- Computing Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA. https://twitter.com/@harshbhatia85
| | - Fikret Aydin
- Physical and Life Sciences (PLS) Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA
| | - Timothy S Carpenter
- Physical and Life Sciences (PLS) Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA
| | - Felice C Lightstone
- Physical and Life Sciences (PLS) Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA
| | - Peer-Timo Bremer
- Computing Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA
| | - Helgi I Ingólfsson
- Physical and Life Sciences (PLS) Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA
| | - Dwight V Nissley
- RAS Initiative, The Cancer Research Technology Program, Frederick National Laboratory, Frederick, MD, 21701, USA.
| | - Frederick H Streitz
- Physical and Life Sciences (PLS) Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA.
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6
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Schmitz G, Schnieder B. Adaptive regularized Gaussian process regression for application in the context of hydrogen adsorption on graphene sheets. J Comput Chem 2023; 44:732-744. [PMID: 36382688 DOI: 10.1002/jcc.27035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Revised: 09/21/2022] [Accepted: 09/28/2022] [Indexed: 11/17/2022]
Abstract
We present a Gaussian process regression (GPR) scheme with an adaptive regularization scheme applied to the QM7 and QM9 test set, several protonated water clusters and specifically to the problem of atomic hydrogen adsorption on graphene sheets. For the last system our goal is to achieve good predictive accuracy with only a few training points. Therefore, we assess for these systems a self-correcting multilayer GPR model, in which the prediction is corrected by a chain of additional GPR models. In our adaptive regularization scheme, we impose no noise on the training data, but use an approach based on the data itself to account for its impurity. The strength of this strategy is that the data points are treated differently based on their importance and that the regularization can still be controlled by a single parameter. We assess how the accuracy of the prediction depends on this parameter. We can show that the new regularization scheme as well as the multilayer approach results in more robust predictors. Furthermore, we demonstrate that the predictor can be in good agreement with the density-functional theory results.
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Affiliation(s)
- Gunnar Schmitz
- Theoretische Chemie, Ruhr-Universität Bochum, Bochum, Germany
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7
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Ge P, Zhang L, Lei H. Machine learning assisted coarse-grained molecular dynamics modeling of meso-scale interfacial fluids. J Chem Phys 2023; 158:064104. [PMID: 36792498 DOI: 10.1063/5.0131567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
A hallmark of meso-scale interfacial fluids is the multi-faceted, scale-dependent interfacial energy, which often manifests different characteristics across the molecular and continuum scale. The multi-scale nature imposes a challenge to construct reliable coarse-grained (CG) models, where the CG potential function needs to faithfully encode the many-body interactions arising from the unresolved atomistic interactions and account for the heterogeneous density distributions across the interface. We construct the CG models of both single- and two-component polymeric fluid systems based on the recently developed deep coarse-grained potential [Zhang et al., J. Chem. Phys. 149, 034101 (2018)] scheme, where each polymer molecule is modeled as a CG particle. By only using the training samples of the instantaneous force under the thermal equilibrium state, the constructed CG models can accurately reproduce both the probability density function of the void formation in bulk and the spectrum of the capillary wave across the fluid interface. More importantly, the CG models accurately predict the volume-to-area scaling transition for the apolar solvation energy, illustrating the effectiveness to probe the meso-scale collective behaviors encoded with molecular-level fidelity.
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Affiliation(s)
- Pei Ge
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | | | - Huan Lei
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
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8
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Kawada R, Endo K, Yasuoka K, Kojima H, Matubayasi N. Prediction of Water Diffusion in Wide Varieties of Polymers with All-Atom Molecular Dynamics Simulations and Deep Generative Models. J Chem Inf Model 2023; 63:76-86. [PMID: 36475723 DOI: 10.1021/acs.jcim.2c01316] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Permeation through polymer membranes is an important technology in the chemical industry, and in its design, the self-diffusion coefficient is one of the physical quantities that determine permeability. Since the self-diffusion coefficient sensitively reflects intra- and intermolecular interactions, analysis using an all-atom model is required. However, all-atom simulations are computationally expensive and require long simulation times for the diffusion of small molecules dissolved in polymers. MD-GAN, a machine learning model, is effective in accelerating simulations and reducing computational costs. The target systems for MD-GAN prediction were limited to polyethylene melts in previous studies; therefore, this study extended MD-GAN to systems containing copolymers with branches and successfully predicted water diffusion in various polymers. The correlation coefficient between the predicted self-diffusion coefficient and that of the long-time simulation was 1.00. Additionally, we found that incorporating statistical domain knowledge into MD-GAN improved accuracy, reducing the mean-square displacement prediction outliers from 14.6% to 5.3%. Lastly, the distribution of latent variables with embedded dynamics information within the model was found to be strongly related to accuracy. We believe that these findings can be useful for the practical applications of MD-GAN.
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Affiliation(s)
- Ryo Kawada
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama223-8522, Japan
| | - Katsuhiro Endo
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama223-8522, Japan
| | - Kenji Yasuoka
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama223-8522, Japan
| | - Hidekazu Kojima
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka560-8531, Japan
| | - Nobuyuki Matubayasi
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka560-8531, Japan
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9
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Enhancing sampling with free-energy calculations. Curr Opin Struct Biol 2022; 77:102497. [PMID: 36410221 DOI: 10.1016/j.sbi.2022.102497] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2022] [Revised: 10/13/2022] [Accepted: 10/14/2022] [Indexed: 11/19/2022]
Abstract
In recent years, considerable progress has been made to enhance sampling and help address biological questions, including, but not limited to conformational transitions in biomolecules and protein-ligand reversible binding, hitherto intractable by brute-force computer simulations. Many of these advances result from the development of a palette of methods aimed at exploring rare events through reliable free-energy calculations. The advent of new, often conceptually related methods has also rendered difficult the choice of the best suited option for a given problem. Here, we focus on geometrical transformations and algorithms designed to enhance sampling along adequately chosen progress variables, tracing their theoretical foundations, and showing how they are connected and can be blended together for improved performance.
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10
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Depta PN, Dosta M, Wenzel W, Kozlowska M, Heinrich S. Hierarchical Coarse-Grained Strategy for Macromolecular Self-Assembly: Application to Hepatitis B Virus-Like Particles. Int J Mol Sci 2022; 23:ijms232314699. [PMID: 36499027 PMCID: PMC9740473 DOI: 10.3390/ijms232314699] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2022] [Revised: 11/01/2022] [Accepted: 11/14/2022] [Indexed: 11/27/2022] Open
Abstract
Macromolecular self-assembly is at the basis of many phenomena in material and life sciences that find diverse applications in technology. One example is the formation of virus-like particles (VLPs) that act as stable empty capsids used for drug delivery or vaccine fabrication. Similarly to the capsid of a virus, VLPs are protein assemblies, but their structural formation, stability, and properties are not fully understood, especially as a function of the protein modifications. In this work, we present a data-driven modeling approach for capturing macromolecular self-assembly on scales beyond traditional molecular dynamics (MD), while preserving the chemical specificity. Each macromolecule is abstracted as an anisotropic object and high-dimensional models are formulated to describe interactions between molecules and with the solvent. For this, data-driven protein-protein interaction potentials are derived using a Kriging-based strategy, built on high-throughput MD simulations. Semi-automatic supervised learning is employed in a high performance computing environment and the resulting specialized force-fields enable a significant speed-up to the micrometer and millisecond scale, while maintaining high intermolecular detail. The reported generic framework is applied for the first time to capture the formation of hepatitis B VLPs from the smallest building unit, i.e., the dimer of the core protein HBcAg. Assembly pathways and kinetics are analyzed and compared to the available experimental observations. We demonstrate that VLP self-assembly phenomena and dependencies are now possible to be simulated. The method developed can be used for the parameterization of other macromolecules, enabling a molecular understanding of processes impossible to be attained with other theoretical models.
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Affiliation(s)
- Philipp Nicolas Depta
- Institute of Solids Process Engineering and Particle Technology (SPE), Hamburg University of Technology, 21073 Hamburg, Germany
- Correspondence:
| | - Maksym Dosta
- Institute of Solids Process Engineering and Particle Technology (SPE), Hamburg University of Technology, 21073 Hamburg, Germany
- Boehringer Ingelheim Pharma GmbH & Co Kg., 88400 Biberach an der Riss, Germany
| | - Wolfgang Wenzel
- Institute of Nanotechnology (INT), Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany
| | - Mariana Kozlowska
- Institute of Nanotechnology (INT), Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany
| | - Stefan Heinrich
- Institute of Solids Process Engineering and Particle Technology (SPE), Hamburg University of Technology, 21073 Hamburg, Germany
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11
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Kawada R, Endo K, Yuhara D, Yasuoka K. MD-GAN with multi-particle input: the machine learning of long-time molecular behavior from short-time MD data. SOFT MATTER 2022; 18:8446-8455. [PMID: 36314893 DOI: 10.1039/d2sm00852a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Molecular dynamics simulation is a method of investigating the behavior of molecules, which is useful for analyzing a variety of structural and dynamic properties and mechanisms of phenomena. However, the huge computational cost of large-scale and long-time simulations is an enduring problem that must be addressed. MD-GAN is a machine learning-based method that can evolve part of the system at any time step, accelerating the generation of molecular dynamics data [Endo et al., Proceedings of the AAAI Conference on Artificial Intelligence, 2018, 32]. For the accurate prediction of MD-GAN, sufficient information on the dynamics of a part of the system should be included with the training data. Therefore, the selection of the part of the system is important for efficient learning. In a previous study, only one particle (or vector) of each molecule was extracted as part of the system. The effectiveness of adding information from other particles to the learning process is investigated in this study. When the dynamics of three particles of each molecule were used in the polyethylene experiment, the diffusion was successfully predicted using the training data with a time length of approximately 40%, compared to the single-particle input. Surprisingly, the unobserved transition of diffusion in the training data was also predicted using this method. The reduced cost for the generation of training MD data achieved in this study is useful for accelerating MD-GAN.
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Affiliation(s)
- Ryo Kawada
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan.
| | - Katsuhiro Endo
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan.
| | - Daisuke Yuhara
- Materials Design Laboratory, Science & Innovation Center, R&D Transformation Div., Mitsubishi Chemical Holdings Group, 1000 Kamoshida-cho, Aoba-ku, Yokohama, Kanagawa, 227-8502, Japan
| | - Kenji Yasuoka
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan.
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12
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Lee S, Ermanis K, Goodman JM. MolE8: finding DFT potential energy surface minima values from force-field optimised organic molecules with new machine learning representations. Chem Sci 2022; 13:7204-7214. [PMID: 35799803 PMCID: PMC9214916 DOI: 10.1039/d1sc06324c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2021] [Accepted: 05/23/2022] [Indexed: 11/21/2022] Open
Abstract
The use of machine learning techniques in computational chemistry has gained significant momentum since large molecular databases are now readily available. Predictions of molecular properties using machine learning have advantages over the traditional quantum mechanics calculations because they can be cheaper computationally without losing the accuracy. We present a new extrapolatable and explainable molecular representation based on bonds, angles and dihedrals that can be used to train machine learning models. The trained models can accurately predict the electronic energy and the free energy of small organic molecules with atom types C, H N and O, with a mean absolute error of 1.2 kcal mol-1. The models can be extrapolated to larger organic molecules with an average error of less than 3.7 kcal mol-1 for 10 or fewer heavy atoms, which represent a chemical space two orders of magnitude larger. The rapid energy predictions of multiple molecules, up to 7 times faster than previous ML models of similar accuracy, has been achieved by sampling geometries around the potential energy surface minima. Therefore, the input geometries do not have to be located precisely on the minima and we show that accurate density functional theory energy predictions can be made from force-field optimised geometries with a mean absolute error 2.5 kcal mol-1.
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Affiliation(s)
- Sanha Lee
- Yusuf Hamied Department of Chemistry, University of Cambridge Lensfield Road Cambridge CB2 1EW UK
| | | | - Jonathan M Goodman
- Yusuf Hamied Department of Chemistry, University of Cambridge Lensfield Road Cambridge CB2 1EW UK
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13
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Richings GW, Habershon S. Predicting Molecular Photochemistry Using Machine-Learning-Enhanced Quantum Dynamics Simulations. Acc Chem Res 2022; 55:209-220. [PMID: 34982533 DOI: 10.1021/acs.accounts.1c00665] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The processes which occur after molecules absorb light underpin an enormous range of fundamental technologies and applications, including photocatalysis to enable new chemical transformations, sunscreens to protect against the harmful effects of UV overexposure, efficient photovoltaics for energy generation from sunlight, and fluorescent probes to image the intricate details of complex biomolecular structures. Reflecting this broad range of applications, an enormously versatile set of experiments are now regularly used to interrogate light-driven chemical dynamics, ranging from the typical ultrafast transient absorption spectroscopy used in many university laboratories to the inspiring central facilities around the world, such as the next-generation of X-ray free-electron lasers.Computer simulations of light-driven molecular and material dynamics are an essential route to analyzing the enormous amount of transient electronic and structural data produced by these experimental sources. However, to date, the direct simulation of molecular photochemistry remains a frontier challenge in computational chemical science, simultaneously demanding the accurate treatment of molecular electronic structure, nuclear dynamics, and the impact of nonadiabatic couplings.To address these important challenges and to enable new computational methods which can be integrated with state-of-the-art experimental capabilities, the past few years have seen a burst of activity in the development of "direct" quantum dynamics methods, merging the machine learning of potential energy surfaces (PESs) and nonadiabatic couplings with accurate quantum propagation schemes such as the multiconfiguration time-dependent Hartree (MCTDH) method. The result of this approach is a new generation of direct quantum dynamics tools in which PESs are generated in tandem with wave function propagation, enabling accurate "on-the-fly" simulations of molecular photochemistry. These simulations offer an alternative route toward gaining quantum dynamics insights, circumventing the challenge of generating ab initio electronic structure data for PES fitting by instead only demanding expensive energy evaluations as and when they are needed.In this Account, we describe the chronological evolution of our own contributions to this field, focusing on describing the algorithmic developments that enable direct MCTDH simulations for complex molecular systems moving on multiple coupled electronic states. Specifically, we highlight active learning strategies for generating PESs during grid-based quantum chemical dynamics simulations, and we discuss the development and impact of novel diabatization schemes to enable direct grid-based simulations of photochemical dynamics; these developments are highlighted in a series of benchmark molecular simulations of systems containing multiple nuclear degrees of freedom moving on multiple coupled electronic states. We hope that the ongoing developments reported here represent a major step forward in tools for modeling excited-state chemistry such as photodissociation, proton and electron transfer, and ultrafast energy dissipation in complex molecular systems.
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Affiliation(s)
- Gareth W. Richings
- Department of Chemistry, University of Warwick, Coventry, United Kingdom CV4 7AL
| | - Scott Habershon
- Department of Chemistry, University of Warwick, Coventry, United Kingdom CV4 7AL
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14
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Machine-Learned Free Energy Surfaces for Capillary Condensation and Evaporation in Mesopores. ENTROPY 2022; 24:e24010097. [PMID: 35052123 PMCID: PMC8774451 DOI: 10.3390/e24010097] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Revised: 12/29/2021] [Accepted: 01/05/2022] [Indexed: 12/04/2022]
Abstract
Using molecular simulations, we study the processes of capillary condensation and capillary evaporation in model mesopores. To determine the phase transition pathway, as well as the corresponding free energy profile, we carry out enhanced sampling molecular simulations using entropy as a reaction coordinate to map the onset of order during the condensation process and of disorder during the evaporation process. The structural analysis shows the role played by intermediate states, characterized by the onset of capillary liquid bridges and bubbles. We also analyze the dependence of the free energy barrier on the pore width. Furthermore, we propose a method to build a machine learning model for the prediction of the free energy surfaces underlying capillary phase transition processes in mesopores.
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15
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Wang D, Wang Y, Chang J, Zhang L, Wang H, E W. Efficient sampling of high-dimensional free energy landscapes using adaptive reinforced dynamics. NATURE COMPUTATIONAL SCIENCE 2022; 2:20-29. [PMID: 38177702 DOI: 10.1038/s43588-021-00173-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2021] [Accepted: 11/15/2021] [Indexed: 01/06/2024]
Abstract
Enhanced sampling methods such as metadynamics and umbrella sampling have become essential tools for exploring the configuration space of molecules and materials. At the same time, they have long faced a number of issues such as the inefficiency when dealing with a large number of collective variables (CVs) or systems with high free energy barriers. Here we show that, with clustering and adaptive tuning techniques, the reinforced dynamics (RiD) scheme can be used to efficiently explore the configuration space and free energy landscapes with a large number of CVs or systems with high free energy barriers. We illustrate this by studying various representative and challenging examples. First we demonstrate the efficiency of adaptive RiD compared with other methods and construct the nine-dimensional (9D) free energy landscape of a peptoid trimer, which has energy barriers of more than 8 kcal mol-1. We then study the folding of the protein chignolin using 18 CVs. In this case, both the folding and unfolding rates are observed to be 4.30 μs-1. Finally, we propose a protein structure refinement protocol based on RiD. This protocol allows us to efficiently employ more than 100 CVs for exploring the landscape of protein structures and it gives rise to an overall improvement of 14.6 units over the initial global distance test-high accuracy (GDT-HA) score.
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Affiliation(s)
- Dongdong Wang
- Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, USA
- DP Technology, Beijing, People's Republic of China
| | - Yanze Wang
- DP Technology, Beijing, People's Republic of China
- College of Chemistry and Molecular Engineering, Peking University, Beijing, People's Republic of China
| | - Junhan Chang
- DP Technology, Beijing, People's Republic of China
- College of Chemistry and Molecular Engineering, Peking University, Beijing, People's Republic of China
| | - Linfeng Zhang
- Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, USA.
- DP Technology, Beijing, People's Republic of China.
| | - Han Wang
- Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, People's Republic of China.
| | - Weinan E
- School of Mathematical Sciences, Peking University, Beijing, People's Republic of China
- Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, USA
- Beijing Institute of Big Data Research, Beijing, People's Republic of China
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16
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Abstract
Mismatched base pairs alter the flexibility and intrinsic curvature of DNA. The role of such DNA features is not fully understood in the mismatch repair pathway. MutS/DNA complexes exhibit DNA bending, PHE intercalation, and changes of base-pair parameters near the mismatch. Recently, we have shown that base-pair opening in the absence of MutS can discriminate mismatches from canonical base pairs better than DNA bending. However, DNA bending in the absence of MutS was found to be rather challenging to describe correctly. Here, we present a computational study on the DNA bending of canonical and G/T mismatched DNAs. Five types of geometric parameters covering template-based bending toward the experimental DNA structure, global, and local geometry parameters were employed in biased molecular dynamics in the absence of MutS. None of these parameters showed higher discrimination than the base-pair opening. Only roll could induce a sharply localized bending of DNA as observed in the experimental MutS/DNA structure. Further, we demonstrated that the intercalation of benzene mimicking PHE decreases the energetic cost of DNA bending without any effect on mismatch discrimination.
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Affiliation(s)
- Tomáš Bouchal
- National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,CEITEC─Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
| | - Ivo Durník
- National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,CEITEC─Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
| | - Petr Kulhánek
- National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,CEITEC─Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
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17
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Bal KM. Reweighted Jarzynski Sampling: Acceleration of Rare Events and Free Energy Calculation with a Bias Potential Learned from Nonequilibrium Work. J Chem Theory Comput 2021; 17:6766-6774. [PMID: 34714088 DOI: 10.1021/acs.jctc.1c00574] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
We introduce a simple enhanced sampling approach for the calculation of free energy differences and barriers along a one-dimensional reaction coordinate. First, a small number of short nonequilibrium simulations are carried out along the reaction coordinate, and the Jarzynski equality is used to learn an approximate free energy surface from the nonequilibrium work distribution. This free energy estimate is represented in a compact form as an artificial neural network and used as an external bias potential to accelerate rare events in a subsequent molecular dynamics simulation. The final free energy estimate is then obtained by reweighting the equilibrium probability distribution of the reaction coordinate sampled under the influence of the external bias. We apply our reweighted Jarzynski sampling recipe to four processes of varying scales and complexities─spanning chemical reaction in the gas phase, pair association in solution, and droplet nucleation in supersaturated vapor. In all cases, we find reweighted Jarzynski sampling to be a very efficient strategy, resulting in rapid convergence of the free energy to high precision.
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Affiliation(s)
- Kristof M Bal
- Department of Chemistry and NANOlab Center of Excellence, University of Antwerp, Universiteitsplein 1, 2610 Antwerp, Belgium
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18
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Abstract
Enhanced sampling and free energy calculation algorithms of the thermodynamic integration family (such as the adaptive biasing force (ABF) method) are not based on the direct computation of a free energy surface but rather of its gradient. Integrating the free energy surface is nontrivial in dimensions higher than one. Here, the author introduces a flexible, portable implementation of a Poisson equation formalism to integrate free energy surfaces from estimated gradients in dimensions 2 and 3 using any combination of periodic and nonperiodic (Neumann) boundary conditions. The algorithm is implemented in portable C++ and provided as a standalone tool that can be used to integrate multidimensional gradient fields estimated on a grid using any algorithm, such as umbrella integration as a post-treatment of umbrella sampling simulations. It is also included in the implementation of ABF (and its extended-system variant eABF) in the Collective Variables Module, enabling the seamless computation of multidimensional free energy surfaces within ABF and eABF simulations. A Python-based analysis toolchain is provided to easily plot and analyze multidimensional ABF simulation results, including metrics to assess their convergence. The Poisson integration algorithm can also be used to perform Helmholtz decomposition of noisy gradient estimates on the fly, resulting in an efficient implementation of the projected ABF (pABF) method proposed by Leliévre and co-workers. In numerical tests, pABF is found to lead to faster convergence with respect to ABF in simple cases of low intrinsic dimension but seems detrimental to convergence in a more realistic case involving degenerate coordinates and hidden barriers due to slower exploration. This suggests that variance reduction schemes do not always yield convergence improvements when applied to enhanced sampling methods.
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Affiliation(s)
- Jérôme Hénin
- Laboratoire de Biochimie Théorique, UPR 9080, CNRS, Université de Paris, 75005 Paris, France.,Institut de Biologie Physico-Chimique-Fondation Edmond de Rothschild, PSL Research University, 75005 Paris, France
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19
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Escobedo FA. On the calculation of free energies over Hamiltonian and order parameters via perturbation and thermodynamic integration. J Chem Phys 2021; 155:114112. [PMID: 34551542 DOI: 10.1063/5.0061541] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, complementary formulas are presented to compute free-energy differences via perturbation (FEP) methods and thermodynamic integration (TI). These formulas are derived by selecting only the most statistically significant data from the information extractable from the simulated points involved. On the one hand, commonly used FEP techniques based on overlap sampling leverage the full information contained in the overlapping macrostate probability distributions. On the other hand, conventional TI methods only use information on the first moments of those distributions, as embodied by the first derivatives of the free energy. Since the accuracy of simulation data degrades considerably for high-order moments (for FEP) or free-energy derivatives (for TI), it is proposed to consider, consistently for both methods, data up to second-order moments/derivatives. This provides a compromise between the limiting strategies embodied by common FEP and TI and leads to simple, optimized expressions to evaluate free-energy differences. The proposed formulas are validated with an analytically solvable harmonic Hamiltonian (for assessing systematic errors), an atomistic system (for computing the potential of mean force with coordinate-dependent order parameters), and a binary-component coarse-grained model (for tracing a solid-liquid phase diagram in an ensemble sampled through alchemical transformations). It is shown that the proposed FEP and TI formulas are straightforward to implement, perform similarly well, and allow robust estimation of free-energy differences even when the spacing of successive points does not guarantee them to have proper overlapping in phase space.
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Affiliation(s)
- Fernando A Escobedo
- Robert Frederick Smith School of Chemistry and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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20
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Badin M, Martoňák R. Nucleating a Different Coordination in a Crystal under Pressure: A Study of the B1-B2 Transition in NaCl by Metadynamics. PHYSICAL REVIEW LETTERS 2021; 127:105701. [PMID: 34533357 DOI: 10.1103/physrevlett.127.105701] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 07/21/2021] [Indexed: 06/13/2023]
Abstract
Here we propose an NPT metadynamics simulation scheme for pressure-induced structural phase transitions, using coordination number and volume as collective variables, and apply it to the reconstructive structural transformation B1-B2 in NaCl. By studying systems with size up to 64 000 atoms we reach a regime beyond collective mechanism and observe transformations proceeding via nucleation and growth. We also reveal the crossover of the transition mechanism from Buerger-like for smaller systems to Watanabe-Tolédano for larger ones. The scheme is likely to be applicable to a broader class of pressure-induced structural transitions, allowing study of complex nucleation effects and bringing simulations closer to realistic conditions.
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Affiliation(s)
- Matej Badin
- SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
- Department of Experimental Physics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská Dolina F2, 842 48 Bratislava, Slovakia
| | - Roman Martoňák
- Department of Experimental Physics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská Dolina F2, 842 48 Bratislava, Slovakia
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21
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Keith JA, Vassilev-Galindo V, Cheng B, Chmiela S, Gastegger M, Müller KR, Tkatchenko A. Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems. Chem Rev 2021; 121:9816-9872. [PMID: 34232033 PMCID: PMC8391798 DOI: 10.1021/acs.chemrev.1c00107] [Citation(s) in RCA: 190] [Impact Index Per Article: 63.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Indexed: 12/23/2022]
Abstract
Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.
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Affiliation(s)
- John A. Keith
- Department
of Chemical and Petroleum Engineering Swanson School of Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States
| | - Valentin Vassilev-Galindo
- Department
of Physics and Materials Science, University
of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Bingqing Cheng
- Accelerate
Programme for Scientific Discovery, Department
of Computer Science and Technology, 15 J. J. Thomson Avenue, Cambridge CB3 0FD, United Kingdom
| | - Stefan Chmiela
- Department
of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, 10587, Berlin, Germany
| | - Michael Gastegger
- Department
of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, 10587, Berlin, Germany
| | - Klaus-Robert Müller
- Machine
Learning Group, Technische Universität
Berlin, 10587, Berlin, Germany
- Department
of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, Seoul, 02841, Korea
- Max-Planck-Institut für Informatik, 66123 Saarbrücken, Germany
- Google Research, Brain Team, 10117 Berlin, Germany
| | - Alexandre Tkatchenko
- Department
of Physics and Materials Science, University
of Luxembourg, L-1511 Luxembourg City, Luxembourg
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22
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Peterková K, Durník I, Marek R, Plavec J, Podbevšek P. c-kit2 G-quadruplex stabilized via a covalent probe: exploring G-quartet asymmetry. Nucleic Acids Res 2021; 49:8947-8960. [PMID: 34365512 PMCID: PMC8421218 DOI: 10.1093/nar/gkab659] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Revised: 07/12/2021] [Accepted: 07/22/2021] [Indexed: 11/23/2022] Open
Abstract
Several sequences forming G-quadruplex are highly conserved in regulatory regions of genomes of different organisms and affect various biological processes like gene expression. Diverse G-quadruplex properties can be modulated via their interaction with small polyaromatic molecules such as pyrene. To investigate how pyrene interacts with G-rich DNAs, we incorporated deoxyuridine nucleotide(s) with a covalently attached pyrene moiety (Upy) into a model system that forms parallel G-quadruplex structures. We individually substituted terminal positions and positions in the pentaloop of the c-kit2 sequence originating from the KIT proto-oncogene with Upy and performed a detailed NMR structural study accompanied with molecular dynamic simulations. Our results showed that incorporation into the pentaloop leads to structural polymorphism and in some cases also thermal destabilization. In contrast, terminal positions were found to cause a substantial thermodynamic stabilization while preserving topology of the parent c-kit2 G-quadruplex. Thermodynamic stabilization results from π–π stacking between the polyaromatic core of the pyrene moiety and guanine nucleotides of outer G-quartets. Thanks to the prevalent overall conformation, our structures mimic the G-quadruplex found in human KIT proto-oncogene and could potentially have antiproliferative effects on cancer cells.
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Affiliation(s)
- Kateřina Peterková
- Slovenian NMR Centre, National Institute of Chemistry, Hajdrihova 19, SI-1000 Ljubljana, Slovenia.,National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, CZ-625 00 Brno, Czechia.,Faculty of Chemistry and Chemical Technology, University of Ljubljana, Večna pot 113, SI-1000 Ljubljana, Slovenia
| | - Ivo Durník
- National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, CZ-625 00 Brno, Czechia.,CEITEC-Central European Institute of Technology, Masaryk University, Kamenice 5, CZ-62500 Brno, Czechia
| | - Radek Marek
- National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, CZ-625 00 Brno, Czechia.,CEITEC-Central European Institute of Technology, Masaryk University, Kamenice 5, CZ-62500 Brno, Czechia.,Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, CZ-62500 Brno, Czechia
| | - Janez Plavec
- Slovenian NMR Centre, National Institute of Chemistry, Hajdrihova 19, SI-1000 Ljubljana, Slovenia.,Faculty of Chemistry and Chemical Technology, University of Ljubljana, Večna pot 113, SI-1000 Ljubljana, Slovenia.,EN-FIST Centre of Excellence, Trg OF 13, SI-1000 Ljubljana, Slovenia
| | - Peter Podbevšek
- Slovenian NMR Centre, National Institute of Chemistry, Hajdrihova 19, SI-1000 Ljubljana, Slovenia
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23
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Lach D, Zhdan U, Smolinski A, Polanski J. Functional and Material Properties in Nanocatalyst Design: A Data Handling and Sharing Problem. Int J Mol Sci 2021; 22:ijms22105176. [PMID: 34068386 PMCID: PMC8153597 DOI: 10.3390/ijms22105176] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2021] [Revised: 05/06/2021] [Accepted: 05/11/2021] [Indexed: 11/16/2022] Open
Abstract
(1) Background: Properties and descriptors are two forms of molecular in silico representations. Properties can be further divided into functional, e.g., catalyst or drug activity, and material, e.g., X-ray crystal data. Millions of real measured functional property records are available for drugs or drug candidates in online databases. In contrast, there is not a single database that registers a real conversion, TON or TOF data for catalysts. All of the data are molecular descriptors or material properties, which are mainly of a calculation origin. (2) Results: Here, we explain the reason for this. We reviewed the data handling and sharing problems in the design and discovery of catalyst candidates particularly, material informatics and catalyst design, structural coding, data collection and validation, infrastructure for catalyst design and the online databases for catalyst design. (3) Conclusions: Material design requires a property prediction step. This can only be achieved based on the registered real property measurement. In reality, in catalyst design and discovery, we can observe either a severe functional property deficit or even property famine.
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Affiliation(s)
- Daniel Lach
- Institute of Chemistry, Faculty of Science and Technology, University of Silesia, Szkolna 9, 40-006 Katowice, Poland; (D.L.); (U.Z.)
| | - Uladzislau Zhdan
- Institute of Chemistry, Faculty of Science and Technology, University of Silesia, Szkolna 9, 40-006 Katowice, Poland; (D.L.); (U.Z.)
| | - Adam Smolinski
- Central Mining Institute, Plac Gwarkow 1, 40-166 Katowice, Poland;
| | - Jaroslaw Polanski
- Institute of Chemistry, Faculty of Science and Technology, University of Silesia, Szkolna 9, 40-006 Katowice, Poland; (D.L.); (U.Z.)
- Correspondence: ; Tel.: +48-32-259-9978
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24
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Lee EMY, Ludwig T, Yu B, Singh AR, Gygi F, Nørskov JK, de Pablo JJ. Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium. J Phys Chem Lett 2021; 12:2954-2962. [PMID: 33729797 DOI: 10.1021/acs.jpclett.1c00195] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In heterogeneous catalysis, free energy profiles of reactions govern the mechanisms, rates, and equilibria. Energetics are conventionally computed using the harmonic approximation (HA), which requires determination of critical states a priori. Here, we use neural networks to efficiently sample and directly calculate the free energy surface (FES) of a prototypical heterogeneous catalysis reaction-the dissociation of molecular nitrogen on ruthenium-at density-functional-theory-level accuracy. We find that the vibrational entropy of surface atoms, often neglected in HA for transition metal catalysts, contributes significantly to the reaction barrier. The minimum free energy path for dissociation reveals an "on-top" adsorbed molecular state prior to the transition state. While a previously reported flat-lying molecular metastable state can be identified in the potential energy surface, it is absent in the FES at relevant reaction temperatures. These findings demonstrate the importance of identifying critical points self-consistently on the FES for reactions that involve considerable entropic effects.
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Affiliation(s)
- Elizabeth M Y Lee
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
| | - Thomas Ludwig
- SUNCAT Center for Interface Science and Catalysis, Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States
- SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States
| | - Boyuan Yu
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
| | - Aayush R Singh
- SUNCAT Center for Interface Science and Catalysis, Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States
| | - François Gygi
- Department of Computer Science, University of California, Davis, California 95616, United States
| | - Jens K Nørskov
- SUNCAT Center for Interface Science and Catalysis, Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States
- SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States
- Department of Physics, Technical University of Denmark, Lyngby 2800, Denmark
| | - Juan J de Pablo
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
- Argonne National Laboratory, 9700 Cass Avenue, Lemont, Illinois 60439, United States
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25
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Tomeček J, Čablová A, Hromádková A, Novotný J, Marek R, Durník I, Kulhánek P, Prucková Z, Rouchal M, Dastychová L, Vícha R. Modes of Micromolar Host-Guest Binding of β-Cyclodextrin Complexes Revealed by NMR Spectroscopy in Salt Water. J Org Chem 2021; 86:4483-4496. [PMID: 33648337 DOI: 10.1021/acs.joc.0c02917] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Multitopic supramolecular guests with finely tuned affinities toward widely explored cucurbit[n]urils (CBs) and cyclodextrins (CDs) have been recently designed and tested as functional components of advanced supramolecular systems. We employed various spacers between the adamantane cage and a cationic moiety as a tool for tuning the binding strength toward CB7 to prepare a set of model guests with KCB7 and Kβ-CD values of (0.6-5.0) × 1010 M-1 and (0.6-2.6) × 106 M-1, respectively. These accessible adamantylphenyl-based binding motifs open a way toward supramolecular components with an outstanding affinity toward β-cyclodextrin. 1H NMR experiments performed in 30% CaCl2/D2O at 273 K along with molecular dynamics simulations allowed us to identify two arrangements of the guest@β-CD complexes. The approach, joining experimental and theoretical methods, provided a better understanding of the structure of cyclodextrin complexes and related molecular recognition, which is highly important for the rational design of drug delivery systems, molecular sensors and switches.
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Affiliation(s)
- Josef Tomeček
- Department of Chemistry, Faculty of Technology, Tomas Bata University in Zlín, Vavrečkova 275, 760 01 Zlín, Czech Republic
| | - Andrea Čablová
- Department of Chemistry, Faculty of Technology, Tomas Bata University in Zlín, Vavrečkova 275, 760 01 Zlín, Czech Republic
| | - Aneta Hromádková
- Department of Chemistry, Faculty of Technology, Tomas Bata University in Zlín, Vavrečkova 275, 760 01 Zlín, Czech Republic
| | - Jan Novotný
- CEITEC - Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
| | - Radek Marek
- CEITEC - Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
| | - Ivo Durník
- CEITEC - Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
| | - Petr Kulhánek
- CEITEC - Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
| | - Zdeňka Prucková
- Department of Chemistry, Faculty of Technology, Tomas Bata University in Zlín, Vavrečkova 275, 760 01 Zlín, Czech Republic
| | - Michal Rouchal
- Department of Chemistry, Faculty of Technology, Tomas Bata University in Zlín, Vavrečkova 275, 760 01 Zlín, Czech Republic
| | - Lenka Dastychová
- Department of Chemistry, Faculty of Technology, Tomas Bata University in Zlín, Vavrečkova 275, 760 01 Zlín, Czech Republic
| | - Robert Vícha
- Department of Chemistry, Faculty of Technology, Tomas Bata University in Zlín, Vavrečkova 275, 760 01 Zlín, Czech Republic
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26
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Bouchal T, Durník I, Illík V, Réblová K, Kulhánek P. Importance of base-pair opening for mismatch recognition. Nucleic Acids Res 2020; 48:11322-11334. [PMID: 33080020 PMCID: PMC7672436 DOI: 10.1093/nar/gkaa896] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Revised: 09/09/2020] [Accepted: 09/30/2020] [Indexed: 01/04/2023] Open
Abstract
Mismatch repair is a highly conserved cellular pathway responsible for repairing mismatched dsDNA. Errors are detected by the MutS enzyme, which most likely senses altered mechanical property of damaged dsDNA rather than a specific molecular pattern. While the curved shape of dsDNA in crystallographic MutS/DNA structures suggests the role of DNA bending, the theoretical support is not fully convincing. Here, we present a computational study focused on a base-pair opening into the minor groove, a specific base-pair motion observed upon interaction with MutS. Propensities for the opening were evaluated in terms of two base-pair parameters: Opening and Shear. We tested all possible base pairs in anti/anti, anti/syn and syn/anti orientations and found clear discrimination between mismatches and canonical base-pairs only for the opening into the minor groove. Besides, the discrimination gap was also confirmed in hotspot and coldspot sequences, indicating that the opening could play a more significant role in the mismatch recognition than previously recognized. Our findings can be helpful for a better understanding of sequence-dependent mutability. Further, detailed structural characterization of mismatches can serve for designing anti-cancer drugs targeting mismatched base pairs.
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Affiliation(s)
- Tomáš Bouchal
- CEITEC - Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
| | - Ivo Durník
- CEITEC - Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
| | - Viktor Illík
- National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
| | - Kamila Réblová
- CEITEC - Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
| | - Petr Kulhánek
- CEITEC - Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic.,National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
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27
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Kondo T, Sasaki T, Ruiz-Barragan S, Ribas-Ariño J, Shiga M. Refined metadynamics through canonical sampling using time-invariant bias potential: A study of polyalcohol dehydration in hot acidic solutions. J Comput Chem 2020; 42:156-165. [PMID: 33124054 DOI: 10.1002/jcc.26443] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Revised: 10/13/2020] [Accepted: 10/17/2020] [Indexed: 12/17/2022]
Abstract
We propose a canonical sampling method to refine metadynamics simulations a posteriori, where the hills obtained from metadynamics are used as a time-invariant bias potential. In this way, the statistical error in the computed reaction barriers is reduced by an efficient sampling of the collective variable space at the free energy level of interest. This simple approach could be useful particularly when two or more free energy barriers are to be compared among chemical reactions in different or competing conditions. The method was then applied to study the acid dependence of polyalcohol dehydration reactions in high-temperature aqueous solutions. It was found that the reaction proceeds consistently via an SN 2 mechanism, whereby the free energy of protonation of the hydroxyl group created as an intermediate is affected significantly by the acidic species. Although demonstration is shown for a specific problem, the computational method suggested herein could be generally used for simulations of complex reactions in the condensed phase.
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Affiliation(s)
- Tomomi Kondo
- Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Japan.,Center for Computational Science and e-Systems, Japan Atomic Energy Agency, Chiba, Japan
| | - Takehiko Sasaki
- Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Japan
| | - Sergi Ruiz-Barragan
- Center for Computational Science and e-Systems, Japan Atomic Energy Agency, Chiba, Japan
| | - Jordi Ribas-Ariño
- Departament de Ciència dels Materials i Química Física and IQTCUB, Universitat de Barcelona, Barcelona, Spain
| | - Motoyuki Shiga
- Center for Computational Science and e-Systems, Japan Atomic Energy Agency, Chiba, Japan
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28
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Christensen AS, von Lilienfeld OA. On the role of gradients for machine learning of molecular energies and forces. MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/abba6f] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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29
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Kulkarni SG, Jelínková K, Nečas M, Prucková Z, Rouchal M, Dastychová L, Kulhánek P, Vícha R. A Photochemical/Thermal Switch Based on 4,4'-Bis(benzimidazolio)stilbene: Synthesis and Supramolecular Properties. Chemphyschem 2020; 21:2084-2095. [PMID: 32672383 DOI: 10.1002/cphc.202000472] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Revised: 07/14/2020] [Indexed: 12/22/2022]
Abstract
Stilbene derivatives are well-recognised substructures of molecular switches based on photochemically and/or thermally induced (E)/(Z) isomerisation. We combined a stilbene motif with two benzimidazolium arms to prepare new sorts of supramolecular building blocks and examined their binding properties towards cucurbit[n]urils (n=7, 8) and cyclodextrins (β-CD, γ-CD) in water. Based on the 1 H NMR data and molecular dynamics simulations, we found that two distinct complexes with different stoichiometry, i. e., guest@β-CD and guest@β-CD2 , coexist in equilibrium in a water solution of the (Z)-stilbene-based guests. We also demonstrated that the bis(benzimidazolio)stilbene guests can be transformed from the (E) into the (Z) form via UV irradiation and back via thermal treatment in DMSO.
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Affiliation(s)
- Shantanu Ganesh Kulkarni
- Department of Chemistry, Faculty of Technology, Tomas Bata University Zlín, Vavrečkova 275, 760 01, Zlín, Czech Republic
| | - Kristýna Jelínková
- Department of Chemistry, Faculty of Technology, Tomas Bata University Zlín, Vavrečkova 275, 760 01, Zlín, Czech Republic
| | - Marek Nečas
- Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, 625 00, Brno, Czech Republic
| | - Zdeňka Prucková
- Department of Chemistry, Faculty of Technology, Tomas Bata University Zlín, Vavrečkova 275, 760 01, Zlín, Czech Republic
| | - Michal Rouchal
- Department of Chemistry, Faculty of Technology, Tomas Bata University Zlín, Vavrečkova 275, 760 01, Zlín, Czech Republic
| | - Lenka Dastychová
- Department of Chemistry, Faculty of Technology, Tomas Bata University Zlín, Vavrečkova 275, 760 01, Zlín, Czech Republic
| | - Petr Kulhánek
- CEITEC - Central European Institute of Technology, Masaryk University, Kamenice 5, 625 00, Brno, Czech Republic
| | - Robert Vícha
- Department of Chemistry, Faculty of Technology, Tomas Bata University Zlín, Vavrečkova 275, 760 01, Zlín, Czech Republic
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30
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Sinz P, Swift MW, Brumwell X, Liu J, Kim KJ, Qi Y, Hirn M. Wavelet scattering networks for atomistic systems with extrapolation of material properties. J Chem Phys 2020; 153:084109. [DOI: 10.1063/5.0016020] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
- Paul Sinz
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824-1226, USA
| | - Michael W. Swift
- Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, Michigan 48824-1226, USA
| | - Xavier Brumwell
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824-1226, USA
| | - Jialin Liu
- Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, Michigan 48824-1226, USA
| | - Kwang Jin Kim
- Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, Michigan 48824-1226, USA
| | - Yue Qi
- Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, Michigan 48824-1226, USA
| | - Matthew Hirn
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824-1226, USA
- Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1226, USA
- Center for Quantum Computing, Science and Engineering, Michigan State University, East Lansing, Michigan 48824-1226, USA
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31
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Schmitz G, Klinting EL, Christiansen O. A Gaussian process regression adaptive density guided approach for potential energy surface construction. J Chem Phys 2020; 153:064105. [DOI: 10.1063/5.0015344] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Gunnar Schmitz
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
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32
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Mandelli D, Hirshberg B, Parrinello M. Metadynamics of Paths. PHYSICAL REVIEW LETTERS 2020; 125:026001. [PMID: 32701329 DOI: 10.1103/physrevlett.125.026001] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2020] [Revised: 05/09/2020] [Accepted: 06/12/2020] [Indexed: 05/27/2023]
Abstract
We present a method to sample reactive pathways via biased molecular dynamics simulations in trajectory space. We show that the use of enhanced sampling techniques enables unconstrained exploration of multiple reaction routes. Time correlation functions are conveniently computed via reweighted averages along a single trajectory and kinetic rates are accessed at no additional cost. These abilities are illustrated analyzing a model potential and the umbrella inversion of NH_{3} in water. The algorithm allows a parallel implementation and promises to be a powerful tool for the study of rare events.
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Affiliation(s)
- Davide Mandelli
- Atomistic Simulations, Italian Institute of Technology, via Morego 30, 16163 Genova, Italy
| | - Barak Hirshberg
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8092 Zurich, Switzerland
- Institute of Computational Sciences, Università della Svizzera Italiana, 6900 Lugano, Switzerland
| | - Michele Parrinello
- Atomistic Simulations, Italian Institute of Technology, via Morego 30, 16163 Genova, Italy
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8092 Zurich, Switzerland
- Institute of Computational Sciences, Università della Svizzera Italiana, 6900 Lugano, Switzerland
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33
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Scherer C, Scheid R, Andrienko D, Bereau T. Kernel-Based Machine Learning for Efficient Simulations of Molecular Liquids. J Chem Theory Comput 2020; 16:3194-3204. [PMID: 32282206 PMCID: PMC7304872 DOI: 10.1021/acs.jctc.9b01256] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Indexed: 11/29/2022]
Abstract
Current machine learning (ML) models aimed at learning force fields are plagued by their high computational cost at every integration time step. We describe a number of practical and computationally efficient strategies to parametrize traditional force fields for molecular liquids from ML: the particle decomposition ansatz to two- and three-body force fields, the use of kernel-based ML models that incorporate physical symmetries, the incorporation of switching functions close to the cutoff, and the use of covariant meshing to boost the training set size. Results are presented for model molecular liquids: pairwise Lennard-Jones, three-body Stillinger-Weber, and bottom-up coarse-graining of water. Here, covariant meshing proves to be an efficient strategy to learn canonically averaged instantaneous forces. We show that molecular dynamics simulations with tabulated two- and three-body ML potentials are computationally efficient and recover two- and three-body distribution functions. Many-body representations, decomposition, and kernel regression schemes are all implemented in the open-source software package VOTCA.
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Affiliation(s)
- Christoph Scherer
- Max Planck Institute for
Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - René Scheid
- Max Planck Institute for
Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Denis Andrienko
- Max Planck Institute for
Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Tristan Bereau
- Max Planck Institute for
Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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34
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Richings GW, Habershon S. A new diabatization scheme for direct quantum dynamics: Procrustes diabatization. J Chem Phys 2020; 152:154108. [DOI: 10.1063/5.0003254] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gareth W. Richings
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Scott Habershon
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
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35
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Invernizzi M, Parrinello M. Rethinking Metadynamics: From Bias Potentials to Probability Distributions. J Phys Chem Lett 2020; 11:2731-2736. [PMID: 32191470 DOI: 10.1021/acs.jpclett.0c00497] [Citation(s) in RCA: 95] [Impact Index Per Article: 23.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Metadynamics is an enhanced sampling method of great popularity, based on the on-the-fly construction of a bias potential that is a function of a selected number of collective variables. We propose here a change in perspective that shifts the focus from the bias to the probability distribution reconstruction while retaining some of the key characteristics of metadynamics, such as flexible on-the-fly adjustments to the free energy estimate. The result is an enhanced sampling method that presents a drastic improvement in convergence speed, especially when dealing with suboptimal and/or multidimensional sets of collective variables. The method is especially robust and easy to use and in fact requires only a few simple parameters to be set, and it has a straightforward reweighting scheme to recover the statistics of the unbiased ensemble. Furthermore, it gives more control of the desired exploration of the phase space since the deposited bias is not allowed to grow indefinitely and it does not push the simulation to uninteresting high free energy regions. We demonstrate the performance of the method in a number of representative examples.
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Affiliation(s)
- Michele Invernizzi
- Department of Physics, ETH Zurich, c/o Università della Svizzera Italiana, Via Giuseppe Buffi 13, 6900 Lugano, Switzerland
- Facoltà di Informatica, Institute of Computational Science, National Center for Computational Design and Discovery of Novel Materials (MARVEL), Università della Svizzera Italiana, Via Giuseppe Buffi 13, 6900 Lugano, Switzerland
| | - Michele Parrinello
- Department of Chemistry and Applied Biosciences, ETH Zurich, c/o Università della Svizzera italiana, Via Giuseppe Buffi 13, 6900 Lugano, Switzerland
- Italian Institute of Technology, Via Morego 30, 16163 Genova, Italy
- Facoltà di Informatica, Institute of Computational Science, Università della Svizzera Italiana, 6900 Lugano, Switzerland
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36
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Abstract
Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for an ML revolution and have already been profoundly affected by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into ML structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation.
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Affiliation(s)
- Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany; .,Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany.,Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA;
| | - Alexandre Tkatchenko
- Physics and Materials Science Research Unit, University of Luxembourg, 1511 Luxembourg, Luxembourg;
| | - Klaus-Robert Müller
- Department of Computer Science, Technical University Berlin, 10587 Berlin, Germany; .,Max-Planck-Institut für Informatik, 66123 Saarbrücken, Germany.,Department of Brain and Cognitive Engineering, Korea University, Seoul 136-713, South Korea
| | - Cecilia Clementi
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany; .,Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA; .,Department of Physics, Rice University, Houston, Texas 77005, USA
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37
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Sevgen E, Guo AZ, Sidky H, Whitmer JK, de Pablo JJ. Combined Force-Frequency Sampling for Simulation of Systems Having Rugged Free Energy Landscapes. J Chem Theory Comput 2020; 16:1448-1455. [DOI: 10.1021/acs.jctc.9b00883] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Emre Sevgen
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Ashley Z. Guo
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Hythem Sidky
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Jonathan K. Whitmer
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, United States
| | - Juan J. de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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38
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Kananenka AA, Yao K, Corcelli SA, Skinner JL. Machine Learning for Vibrational Spectroscopic Maps. J Chem Theory Comput 2019; 15:6850-6858. [DOI: 10.1021/acs.jctc.9b00698] [Citation(s) in RCA: 43] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Alexei A. Kananenka
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, United States
| | - Kun Yao
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, United States
| | - Steven A. Corcelli
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, United States
| | - J. L. Skinner
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
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39
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Abstract
Sampling complex free-energy surfaces is one of the main challenges of modern atomistic simulation methods. The presence of kinetic bottlenecks in such surfaces often renders a direct approach useless. A popular strategy is to identify a small number of key collective variables and to introduce a bias potential that is able to favor their fluctuations in order to accelerate sampling. Here, we propose to use machine-learning techniques in conjunction with the recent variationally enhanced sampling method [O. Valsson, M. Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] in order to determine such potential. This is achieved by expressing the bias as a neural network. The parameters are determined in a variational learning scheme aimed at minimizing an appropriate functional. This required the development of a more efficient minimization technique. The expressivity of neural networks allows representing rapidly varying free-energy surfaces, removes boundary effects artifacts, and allows several collective variables to be handled.
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40
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Schmitz G, Godtliebsen IH, Christiansen O. Machine learning for potential energy surfaces: An extensive database and assessment of methods. J Chem Phys 2019; 150:244113. [DOI: 10.1063/1.5100141] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Gunnar Schmitz
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
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41
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Ceriotti M. Unsupervised machine learning in atomistic simulations, between predictions and understanding. J Chem Phys 2019; 150:150901. [PMID: 31005087 DOI: 10.1063/1.5091842] [Citation(s) in RCA: 82] [Impact Index Per Article: 16.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
Automated analyses of the outcome of a simulation have been an important part of atomistic modeling since the early days, addressing the need of linking the behavior of individual atoms and the collective properties that are usually the final quantity of interest. Methods such as clustering and dimensionality reduction have been used to provide a simplified, coarse-grained representation of the structure and dynamics of complex systems from proteins to nanoparticles. In recent years, the rise of machine learning has led to an even more widespread use of these algorithms in atomistic modeling and to consider different classification and inference techniques as part of a coherent toolbox of data-driven approaches. This perspective briefly reviews some of the unsupervised machine-learning methods-that are geared toward classification and coarse-graining of molecular simulations-seen in relation to the fundamental mathematical concepts that underlie all machine-learning techniques. It discusses the importance of using concise yet complete representations of atomic structures as the starting point of the analyses and highlights the risk of introducing preconceived biases when using machine learning to rationalize and understand structure-property relations. Supervised machine-learning techniques that explicitly attempt to predict the properties of a material given its structure are less susceptible to such biases. Current developments in the field suggest that using these two classes of approaches side-by-side and in a fully integrated mode, while keeping in mind the relations between the data analysis framework and the fundamental physical principles, will be key to realizing the full potential of machine learning to help understand the behavior of complex molecules and materials.
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Affiliation(s)
- Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute des Materiaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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42
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Schmitz G, Artiukhin DG, Christiansen O. Approximate high mode coupling potentials using Gaussian process regression and adaptive density guided sampling. J Chem Phys 2019; 150:131102. [DOI: 10.1063/1.5092228] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gunnar Schmitz
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
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43
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Di Pasquale N, Hudson T, Icardi M. Systematic derivation of hybrid coarse-grained models. Phys Rev E 2019; 99:013303. [PMID: 30780282 DOI: 10.1103/physreve.99.013303] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Indexed: 06/09/2023]
Abstract
Molecular dynamics represents a key enabling technology for applications ranging from biology to the development of new materials. However, many real-world applications remain inaccessible to fully resolved simulations due to their unsustainable computational costs and must therefore rely on semiempirical coarse-grained models. Significant efforts have been devoted in the last decade towards improving the predictivity of these coarse-grained models and providing a rigorous justification of their use, through a combination of theoretical studies and data-driven approaches. One of the most promising research efforts is the (re)discovery of the Mori-Zwanzig projection as a generic, yet systematic, theoretical tool for deriving coarse-grained models. Despite its clean mathematical formulation and generality, there are still many open questions about its applicability and assumptions. In this work, we propose a detailed derivation of a hybrid multiscale system, generalizing and further investigating the approach developed in Español [Europhys. Lett. 88, 40008 (2009)10.1209/0295-5075/88/40008]. Issues such as the general coexistence of atoms (fully resolved degrees of freedom) and beads (larger coarse-grained units), the role of the fine-to-coarse mapping chosen, and the approximation of effective potentials are discussed. The theoretical discussion is supported by numerical simulations of a monodimensional nonlinear periodic benchmark system with an open-source parallel Julia code, easily extensible to arbitrary potential models and fine-to-coarse mapping functions. The results presented highlight the importance of introducing, in the macroscopic model, nonconstant fluctuating and dissipative terms, given by the Mori-Zwanzig approach, to correctly reproduce the reference fine-grained results, without requiring ad hoc calibration of interaction potentials and thermostats.
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Affiliation(s)
- Nicodemo Di Pasquale
- Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom
| | - Thomas Hudson
- Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Matteo Icardi
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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44
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Hughes ZE, Thacker JCR, Wilson AL, Popelier PLA. Description of Potential Energy Surfaces of Molecules Using FFLUX Machine Learning Models. J Chem Theory Comput 2018; 15:116-126. [DOI: 10.1021/acs.jctc.8b00806] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Zak E. Hughes
- Manchester Institute of Biotechnology, The University of Manchester, Manchester M1 7DN, U.K
- School of Chemistry, The University of Manchester, Manchester M13 9PL, U.K
| | - Joseph C. R. Thacker
- Manchester Institute of Biotechnology, The University of Manchester, Manchester M1 7DN, U.K
- School of Chemistry, The University of Manchester, Manchester M13 9PL, U.K
| | - Alex L. Wilson
- Manchester Institute of Biotechnology, The University of Manchester, Manchester M1 7DN, U.K
- School of Chemistry, The University of Manchester, Manchester M13 9PL, U.K
| | - Paul L. A. Popelier
- Manchester Institute of Biotechnology, The University of Manchester, Manchester M1 7DN, U.K
- School of Chemistry, The University of Manchester, Manchester M13 9PL, U.K
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45
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Li P, Jia X, Pan X, Shao Y, Mei Y. Accelerated Computation of Free Energy Profile at ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semi-Empirical Reference Potential. I. Weighted Thermodynamics Perturbation. J Chem Theory Comput 2018; 14:5583-5596. [DOI: 10.1021/acs.jctc.8b00571] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- Pengfei Li
- State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science, East China Normal University, Shanghai 200062, China
| | - Xiangyu Jia
- State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science, East China Normal University, Shanghai 200062, China
| | - Xiaoliang Pan
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science, East China Normal University, Shanghai 200062, China
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
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46
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Fu H, Zhang H, Chen H, Shao X, Chipot C, Cai W. Zooming across the Free-Energy Landscape: Shaving Barriers, and Flooding Valleys. J Phys Chem Lett 2018; 9:4738-4745. [PMID: 30074802 DOI: 10.1021/acs.jpclett.8b01994] [Citation(s) in RCA: 78] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
A robust importance-sampling algorithm for mapping free-energy surfaces over geometrical variables, coined meta-eABF, is introduced. This algorithm shaves the free-energy barriers and floods valleys by incorporating a history-dependent potential term in the extended adaptive biasing force (eABF) framework. Numerical applications on both toy models and nontrivial examples indicate that meta-eABF explores the free-energy surface significantly faster than either eABF or metadynamics (MtD) alone, without the need to stratify the reaction pathway. In some favorable cases, meta-eABF can be as much as five times faster than other importance-sampling algorithms. Many of the shortcomings inherent to eABF and MtD, like kinetic trapping in regions of configurational space already adequately sampled, the requirement of prior knowledge of the free-energy landscape to set up the simulation, are readily eliminated in meta-eABF. Meta-eABF, therefore, represents an appealing solution for a broad range of applications, especially when both eABF and MtD fail to achieve the desired result.
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Affiliation(s)
- Haohao Fu
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition , Nankai University , Tianjin 300071 , China
| | - Hong Zhang
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition , Nankai University , Tianjin 300071 , China
| | - Haochuan Chen
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition , Nankai University , Tianjin 300071 , China
| | - Xueguang Shao
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition , Nankai University , Tianjin 300071 , China
- Collaborative Innovation Center of Chemical Science and Engineering (Tianjin) , Tianjin 300071 , China
- State Key Laboratory of Medicinal Chemical Biology , Tianjin 300071 , China
| | - Christophe Chipot
- Laboratoire International Associé CNRS and University of Illinois at Urbana-Champaign , Vandœuvre-lès-Nancy F-54506 , France
- LPCT, UMR 7019 Université de Lorraine CNRS , Vandœuvre-lès-Nancy F-54500 , France
- Department of Physics , University of Illinois at Urbana-Champaign , 1110 West Green Street , Urbana , Illinois 61801 , United States
| | - Wensheng Cai
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition , Nankai University , Tianjin 300071 , China
- Collaborative Innovation Center of Chemical Science and Engineering (Tianjin) , Tianjin 300071 , China
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47
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Zhang L, Han J, Wang H, Car R, E W. DeePCG: Constructing coarse-grained models via deep neural networks. J Chem Phys 2018; 149:034101. [PMID: 30037247 DOI: 10.1063/1.5027645] [Citation(s) in RCA: 98] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce a general framework for constructing coarse-grained potential models without ad hoc approximations such as limiting the potential to two- and/or three-body contributions. The scheme, called the Deep Coarse-Grained Potential (abbreviated DeePCG), exploits a carefully crafted neural network to construct a many-body coarse-grained potential. The network is trained with full atomistic data in a way that preserves the natural symmetries of the system. The resulting model is very accurate and can be used to sample the configurations of the coarse-grained variables in a much faster way than with the original atomistic model. As an application, we consider liquid water and use the oxygen coordinates as the coarse-grained variables, starting from a full atomistic simulation of this system at the ab initio molecular dynamics level. We find that the two-body, three-body, and higher-order oxygen correlation functions produced by the coarse-grained and full atomistic models agree very well with each other, illustrating the effectiveness of the DeePCG model on a rather challenging task.
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Affiliation(s)
- Linfeng Zhang
- Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
| | - Jiequn Han
- Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
| | - Han Wang
- Institute of Applied Physics and Computational Mathematics, Fenghao East Road 2, Beijing 100094, People's Republic of China and CAEP Software Center for High Performance Numerical Simulation, Huayuan Road 6, Beijing 100088, People's Republic of China
| | - Roberto Car
- Department of Chemistry, Department of Physics, Program in Applied and Computational Mathematics, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
| | - Weinan E
- Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA and Beijing Institute of Big Data Research, Beijing 100871, People's Republic of China
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48
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Schmitz G, Christiansen O. Gaussian process regression to accelerate geometry optimizations relying on numerical differentiation. J Chem Phys 2018; 148:241704. [DOI: 10.1063/1.5009347] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gunnar Schmitz
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
| | - Ove Christiansen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
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49
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Guo AZ, Sevgen E, Sidky H, Whitmer JK, Hubbell JA, de Pablo JJ. Adaptive enhanced sampling by force-biasing using neural networks. J Chem Phys 2018; 148:134108. [PMID: 29626875 DOI: 10.1063/1.5020733] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A machine learning assisted method is presented for molecular simulation of systems with rugged free energy landscapes. The method is general and can be combined with other advanced sampling techniques. In the particular implementation proposed here, it is illustrated in the context of an adaptive biasing force approach where, rather than relying on discrete force estimates, one can resort to a self-regularizing artificial neural network to generate continuous, estimated generalized forces. By doing so, the proposed approach addresses several shortcomings common to adaptive biasing force and other algorithms. Specifically, the neural network enables (1) smooth estimates of generalized forces in sparsely sampled regions, (2) force estimates in previously unexplored regions, and (3) continuous force estimates with which to bias the simulation, as opposed to biases generated at specific points of a discrete grid. The usefulness of the method is illustrated with three different examples, chosen to highlight the wide range of applicability of the underlying concepts. In all three cases, the new method is found to enhance considerably the underlying traditional adaptive biasing force approach. The method is also found to provide improvements over previous implementations of neural network assisted algorithms.
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Affiliation(s)
- Ashley Z Guo
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Emre Sevgen
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Hythem Sidky
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Jonathan K Whitmer
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Jeffrey A Hubbell
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Juan J de Pablo
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
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50
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Chen H, Fu H, Shao X, Chipot C, Cai W. ELF: An Extended-Lagrangian Free Energy Calculation Module for Multiple Molecular Dynamics Engines. J Chem Inf Model 2018; 58:1315-1318. [DOI: 10.1021/acs.jcim.8b00115] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Haochuan Chen
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University, Tianjin 300071, China
| | - Haohao Fu
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University, Tianjin 300071, China
| | - Xueguang Shao
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University, Tianjin 300071, China
- Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300071, China
- State Key Laboratory of Medicinal Chemical Biology, Nankai University, Tianjin 300071, China
| | - Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana−Champaign, Unité Mixte de Recherche No. 7565, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy cedex, France
- Theoretical and Computational Biophysics Group, Beckman Institute, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
- Department of Physics, University of Illinois at Urbana−Champaign, 1110 West Green Street, Urbana, Illinois 61801, United States
| | - Wensheng Cai
- Research Center for Analytical Sciences, College of Chemistry, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Nankai University, Tianjin 300071, China
- Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300071, China
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