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Abstract
Advances in machine learned interatomic potentials (MLIPs), such as those using neural networks, have resulted in short-range models that can infer interaction energies with near ab initio accuracy and orders of magnitude reduced computational cost. For many atom systems, including macromolecules, biomolecules, and condensed matter, model accuracy can become reliant on the description of short- and long-range physical interactions. The latter terms can be difficult to incorporate into an MLIP framework. Recent research has produced numerous models with considerations for nonlocal electrostatic and dispersion interactions, leading to a large range of applications that can be addressed using MLIPs. In light of this, we present a Perspective focused on key methodologies and models being used where the presence of nonlocal physics and chemistry are crucial for describing system properties. The strategies covered include MLIPs augmented with dispersion corrections, electrostatics calculated with charges predicted from atomic environment descriptors, the use of self-consistency and message passing iterations to propagated nonlocal system information, and charges obtained via equilibration schemes. We aim to provide a pointed discussion to support the development of machine learning-based interatomic potentials for systems where contributions from only nearsighted terms are deficient.
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Affiliation(s)
- Dylan M Anstine
- Department of Chemistry, Mellon College of Science, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Olexandr Isayev
- Department of Chemistry, Mellon College of Science, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
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2
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Burn M, Popelier PLA. Gaussian Process Regression Models for Predicting Atomic Energies and Multipole Moments. J Chem Theory Comput 2023; 19:1370-1380. [PMID: 36757024 PMCID: PMC9979601 DOI: 10.1021/acs.jctc.2c00731] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
Abstract
Developing a force field is a difficult task because its design is typically pulled in opposite directions by speed and accuracy. FFLUX breaks this trend by utilizing Gaussian process regression (GPR) to predict, at ab initio accuracy, atomic energies and multipole moments as obtained from the quantum theory of atoms in molecules (QTAIM). This work demonstrates that the in-house FFLUX training pipeline can generate successful GPR models for six representative molecules: peptide-capped glycine and alanine, glucose, paracetamol, aspirin, and ibuprofen. The molecules were sufficiently distorted to represent configurations from an AMBER-GAFF2 molecular dynamics run. All internal degrees of freedom were covered corresponding to 93 dimensions in the case of the largest molecule ibuprofen (33 atoms). Benefiting from active learning, the GPR models contain only about 2000 training points and return largely sub-kcal mol-1 prediction errors for the validation sets. A proof of concept has been reached for transferring the model produced through active learning on one atomic property to that of the remaining atomic properties. The prediction of electrostatic interaction can be assessed at the intermolecular level, and the vast majority of interactions have a root-mean-square error of less than 0.1 kJ mol-1 with a maximum value of ∼1 kJ mol-1 for a glycine and paracetamol dimer.
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3
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Yuan Y, Yan H, Cui Z, Liu Z, Su W, Zhang R. Quantum Chemical Calculations with Machine Learning for Multipolar Electrostatics Prediction in RNA: An Application to Pentose. J Chem Inf Model 2022; 62:4122-4133. [PMID: 36036609 DOI: 10.1021/acs.jcim.2c00747] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
To develop a realistic electrostatic model that allows for the anisotropy of the atomic electron density, high-rank atomic multipole moments computed by quantum chemical calculations have been studied extensively. However, it is hard to process huge RNA systems only relying on quantum chemical calculations due to its highly computational cost. In this study, we employ five machine learning methods of Gaussian process regression with automatic relevance determination (ARDGPR), Kriging, radial basis function neural networks, Bagging, and generalized regression neural network to predict atomic multipole moments. Atom-atom electrostatic interaction energies are subsequently computed using the predicted atomic multipole moments in the pilot system pentose of RNA. Here, the performance of the five methods is compared in terms of both the multipole moment prediction errors and the electrostatic energy prediction errors. For the predicted high-rank multipole moments of the four elements (O, C, N, and H) in capped pentose, ARDGPR and Kriging consistently outperform the other three methods. Therefore, the multipole moments predicted by the two best methods of ARDGPR and Kriging are then used to predict electrostatic interaction energy of each pentose. Finally, the absolute average energy errors of ARDGPR and Kriging are 1.83 and 4.33 kJ mol-1, respectively. Compared to Kriging, the ARDGPR method achieves a 58% decrease in the absolute average energy error. These satisfactory results demonstrated that the ARDGPR method with the strong feature extraction ability can predict the electrostatic interaction energy of pentose in RNA correctly and reliably.
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Affiliation(s)
- Yongna Yuan
- School of Information Science & Engineering, Lanzhou University, Lanzhou, China, 730000
| | - Haoqiu Yan
- School of Information Science & Engineering, Lanzhou University, Lanzhou, China, 730000
| | - Zeyang Cui
- School of Information Science & Engineering, Lanzhou University, Lanzhou, China, 730000
| | - Zhenyu Liu
- School of Cyberspace Security, Gansu University of Political Science and Law, Lanzhou, China, 730070
| | - Wei Su
- School of Information Science & Engineering, Lanzhou University, Lanzhou, China, 730000
| | - Ruisheng Zhang
- School of Information Science & Engineering, Lanzhou University, Lanzhou, China, 730000
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4
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Non-covalent interactions from a Quantum Chemical Topology perspective. J Mol Model 2022; 28:276. [PMID: 36006513 PMCID: PMC9411098 DOI: 10.1007/s00894-022-05188-7] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 02/07/2022] [Indexed: 11/12/2022]
Abstract
About half a century after its little-known beginnings, the quantum topological approach called QTAIM has grown into a widespread, but still not mainstream, methodology of interpretational quantum chemistry. Although often confused in textbooks with yet another population analysis, be it perhaps an elegant but somewhat esoteric one, QTAIM has been enriched with about a dozen other research areas sharing its main mathematical language, such as Interacting Quantum Atoms (IQA) or Electron Localisation Function (ELF), to form an overarching approach called Quantum Chemical Topology (QCT). Instead of reviewing the latter’s role in understanding non-covalent interactions, we propose a number of ideas emerging from the full consequences of the space-filling nature of topological atoms, and discuss how they (will) impact on interatomic interactions, including non-covalent ones. The architecture of a force field called FFLUX, which is based on these ideas, is outlined. A new method called Relative Energy Gradient (REG) is put forward, which is able, by computation, to detect which fragments of a given molecular assembly govern the energetic behaviour of this whole assembly. This method can offer insight into the typical balance of competing atomic energies both in covalent and non-covalent case studies. A brief discussion on so-called bond critical points is given, highlighting concerns about their meaning, mainly in the arena of non-covalent interactions.
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5
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Symons BCB, Bane MK, Popelier PLA. DL_FFLUX: A Parallel, Quantum Chemical Topology Force Field. J Chem Theory Comput 2021; 17:7043-7055. [PMID: 34617748 PMCID: PMC8582247 DOI: 10.1021/acs.jctc.1c00595] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
DL_FFLUX is a force
field based on quantum chemical topology that
can perform molecular dynamics for flexible molecules endowed with
polarizable atomic multipole moments (up to hexadecapole). Using the
machine learning method kriging (aka Gaussian process regression),
DL_FFLUX has access to atomic properties (energy, charge, dipole moment,
etc.) with quantum mechanical accuracy. Newly optimized and parallelized
using domain decomposition Message Passing Interface (MPI), DL_FFLUX
is now able to deliver this rigorous methodology at scale while still
in reasonable time frames. DL_FFLUX is delivered as an add-on to the
widely distributed molecular dynamics code DL_POLY 4.08. For the systems
studied here (103–105 atoms), DL_FFLUX
is shown to add minimal computational cost to the standard DL_POLY
package. In fact, the optimization of the electrostatics in DL_FFLUX
means that, when high-rank multipole moments are enabled, DL_FFLUX
is up to 1.25× faster than standard DL_POLY. The parallel DL_FFLUX
preserves the quality of the scaling of MPI implementation in standard
DL_POLY. For the first time, it is feasible to use the full capability
of DL_FFLUX to study systems that are large enough to be of real-world
interest. For example, a fully flexible, high-rank polarized (up to
and including quadrupole moments) 1 ns simulation of a system of 10 125
atoms (3375 water molecules) takes 30 h (wall time) on 18 cores.
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Affiliation(s)
- Benjamin C B Symons
- Manchester Institute of Biotechnology (MIB), 131 Princess Street, Manchester M1 7DN, Great Britain.,Department of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain
| | - Michael K Bane
- High End Compute LTD, 23 Welby Street, Manchester M13 0EL, Great Britainhttps://highendcompute.co.uk.,Department of Computing and Mathematics, Manchester Metropolitan University, Manchester M15 6BH, Great Britain
| | - Paul L A Popelier
- Manchester Institute of Biotechnology (MIB), 131 Princess Street, Manchester M1 7DN, Great Britain.,Department of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain
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6
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Cuevas-Zuviría B, Pacios LF. Machine Learning of Analytical Electron Density in Large Molecules Through Message-Passing. J Chem Inf Model 2021; 61:2658-2666. [PMID: 34009970 DOI: 10.1021/acs.jcim.1c00227] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Machine learning milestones in computational chemistry are overshadowed by their unaccountability and the overwhelming zoo of tools for each specific task. A promising path to tackle these problems is using machine learning to reproduce physical magnitudes as a basis to derive many other properties. By using a model of the electron density consisting of an analytical expansion on a linear set of isotropic and anisotropic functions, we implemented in this work a message-passing neural network able to reproduce electron density in molecules with just a 2.5% absolute error in complex cases. We also adapted our methodology to describe electron density in large biomolecules (proteins) and to obtain atomic charges, interaction energies, and DFT energies. We show that electron density learning is a new promising avenue with a variety of forthcoming applications.
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Affiliation(s)
- Bruno Cuevas-Zuviría
- Centro de Biotecnología y Genómica de Plantas (CBGP, UPM-INIA), Universidad Politécnica de Madrid (UPM), Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA), Campus de Montegancedo-UPM, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - Luis F Pacios
- Centro de Biotecnología y Genómica de Plantas (CBGP, UPM-INIA), Universidad Politécnica de Madrid (UPM), Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA), Campus de Montegancedo-UPM, 28223 Pozuelo de Alarcón, Madrid, Spain.,Departamento de Biotecnología-Biología Vegetal, Escuela Técnica Superior de Ingeniería Agraria, Alimentaria y de Biosistemas (ETSIAAB), Universidad Politécnica de Madrid (UPM), 28040 Madrid, Spain
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7
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Burn MJ, Popelier PLA. Creating Gaussian process regression models for molecular simulations using adaptive sampling. J Chem Phys 2020; 153:054111. [DOI: 10.1063/5.0017887] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Matthew J. Burn
- Manchester Institute of Biotechnology, The University of Manchester, Manchester M1 7DN, United Kingdom and Department of Chemistry, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Paul L. A. Popelier
- Manchester Institute of Biotechnology, The University of Manchester, Manchester M1 7DN, United Kingdom and Department of Chemistry, The University of Manchester, Manchester M13 9PL, United Kingdom
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8
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Cuevas-Zuviría B, Pacios LF. Analytical Model of Electron Density and Its Machine Learning Inference. J Chem Inf Model 2020; 60:3831-3842. [DOI: 10.1021/acs.jcim.0c00197] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Bruno Cuevas-Zuviría
- Centro de Biotecnologı́a y Genómica de Plantas (CBGP, UPM-INIA), Instituto Nacional de Investigación y Tecnologı́a Agraria y Alimentaria (INIA), Universidad Politécnica de Madrid (UPM), Campus de Montegancedo-UPM, Pozuelo de Alarcón, 28223 Madrid, Spain
| | - Luis F. Pacios
- Centro de Biotecnologı́a y Genómica de Plantas (CBGP, UPM-INIA), Instituto Nacional de Investigación y Tecnologı́a Agraria y Alimentaria (INIA), Universidad Politécnica de Madrid (UPM), Campus de Montegancedo-UPM, Pozuelo de Alarcón, 28223 Madrid, Spain
- Departamento de Biotecnologı́a-Biologı́a Vegetal, Escuela Técnica Superior de Ingenierı́a Agraria, Alimentaria y de Biosistemas (ETSIAAB), Universidad Politécnica de Madrid (UPM), 28040 Madrid, Spain
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9
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Devereux C, Smith JS, Huddleston KK, Barros K, Zubatyuk R, Isayev O, Roitberg AE. Extending the Applicability of the ANI Deep Learning Molecular Potential to Sulfur and Halogens. J Chem Theory Comput 2020; 16:4192-4202. [PMID: 32543858 DOI: 10.1021/acs.jctc.0c00121] [Citation(s) in RCA: 138] [Impact Index Per Article: 34.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Machine learning (ML) methods have become powerful, predictive tools in a wide range of applications, such as facial recognition and autonomous vehicles. In the sciences, computational chemists and physicists have been using ML for the prediction of physical phenomena, such as atomistic potential energy surfaces and reaction pathways. Transferable ML potentials, such as ANI-1x, have been developed with the goal of accurately simulating organic molecules containing the chemical elements H, C, N, and O. Here, we provide an extension of the ANI-1x model. The new model, dubbed ANI-2x, is trained to three additional chemical elements: S, F, and Cl. Additionally, ANI-2x underwent torsional refinement training to better predict molecular torsion profiles. These new features open a wide range of new applications within organic chemistry and drug development. These seven elements (H, C, N, O, F, Cl, and S) make up ∼90% of drug-like molecules. To show that these additions do not sacrifice accuracy, we have tested this model across a range of organic molecules and applications, including the COMP6 benchmark, dihedral rotations, conformer scoring, and nonbonded interactions. ANI-2x is shown to accurately predict molecular energies compared to density functional theory with a ∼106 factor speedup and a negligible slowdown compared to ANI-1x and shows subchemical accuracy across most of the COMP6 benchmark. The resulting model is a valuable tool for drug development which can potentially replace both quantum calculations and classical force fields for a myriad of applications.
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Affiliation(s)
- Christian Devereux
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States
| | - Justin S Smith
- Center for Non-Linear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States.,Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Kate K Huddleston
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States
| | - Kipton Barros
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Roman Zubatyuk
- Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Olexandr Isayev
- Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Adrian E Roitberg
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States
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10
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Vincent MA, Silva AF, Popelier PLA. A Comparison of the Interacting Quantum Atoms (IQA) Analysis of the Two‐Particle Density‐Matrices of MP4SDQ and CCSD. Z Anorg Allg Chem 2020. [DOI: 10.1002/zaac.202000169] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Affiliation(s)
- Mark A. Vincent
- Manchester Institute of Biotechnology The University of Manchester M1 7DN Manchester UK
- Department of Chemistry The University of Manchester M13 9PL Manchester UK
| | - Arnaldo F. Silva
- Manchester Institute of Biotechnology The University of Manchester M1 7DN Manchester UK
- Department of Chemistry The University of Manchester M13 9PL Manchester UK
| | - Paul L. A. Popelier
- Manchester Institute of Biotechnology The University of Manchester M1 7DN Manchester UK
- Department of Chemistry The University of Manchester M13 9PL Manchester UK
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11
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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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12
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Abbott AS, Turney JM, Zhang B, Smith DGA, Altarawy D, Schaefer HF. PES-Learn: An Open-Source Software Package for the Automated Generation of Machine Learning Models of Molecular Potential Energy Surfaces. J Chem Theory Comput 2019; 15:4386-4398. [DOI: 10.1021/acs.jctc.9b00312] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Adam S. Abbott
- Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602, United States
| | - Justin M. Turney
- Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602, United States
| | - Boyi Zhang
- Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602, United States
| | - Daniel G. A. Smith
- Molecular Sciences Software Institute, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Doaa Altarawy
- Molecular Sciences Software Institute, Virginia Tech, Blacksburg, Virginia 24061, United States
- Computer and Systems Engineering Department, Alexandria University, Alexandria, Egypt
| | - Henry F. Schaefer
- Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602, United States
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13
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Bose S, Dhawan D, Nandi S, Sarkar RR, Ghosh D. Machine learning prediction of interaction energies in rigid water clusters. Phys Chem Chem Phys 2018; 20:22987-22996. [PMID: 30156235 DOI: 10.1039/c8cp03138j] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
Classical force fields form a computationally efficient avenue for calculating the energetics of large systems. However, due to the constraints of the underlying analytical form, it is sometimes not accurate enough. Quantum mechanical (QM) methods, although accurate, are computationally prohibitive for large systems. In order to circumvent the bottle-neck of interaction energy estimation of large systems, data driven approaches based on machine learning (ML) have been employed in recent years. In most of these studies, the method of choice is artificial neural networks (ANN). In this work, we have shown an alternative ML method, support vector regression (SVR), that provides comparable accuracy with better computational efficiency. We have further used many body expansion (MBE) along with SVR to predict interaction energies in water clusters (decamers). In the case of dimer and trimer interaction energies, the root mean square errors (RMSEs) of the SVR based scheme are 0.12 kcal mol-1 and 0.34 kcal mol-1, respectively. We show that the SVR and MBE based scheme has a RMSE of 2.78% in the estimation of decamer interaction energy against the parent QM method in a computationally efficient way.
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Affiliation(s)
- Samik Bose
- School of Mathematical and Computational Sciences, Indian Association for the Cultivation of Science, Kolkata-700032, West Bengal, India.
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14
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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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15
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McDonagh JL, Silva AF, Vincent MA, Popelier PLA. Machine Learning of Dynamic Electron Correlation Energies from Topological Atoms. J Chem Theory Comput 2017; 14:216-224. [PMID: 29211469 DOI: 10.1021/acs.jctc.7b01157] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
We present an innovative method for predicting the dynamic electron correlation energy of an atom or a bond in a molecule utilizing topological atoms. Our approach uses the machine learning method Kriging (Gaussian Process Regression with a non-zero mean function) to predict these dynamic electron correlation energy contributions. The true energy values are calculated by partitioning the MP2 two-particle density-matrix via the Interacting Quantum Atoms (IQA) procedure. To our knowledge, this is the first time such energies have been predicted by a machine learning technique. We present here three important proof-of-concept cases: the water monomer, the water dimer, and the van der Waals complex H2···He. These cases represent the final step toward the design of a full IQA potential for molecular simulation. This final piece will enable us to consider situations in which dispersion is the dominant intermolecular interaction. The results from these examples suggest a new method by which dispersion potentials for molecular simulation can be generated.
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Affiliation(s)
- James L McDonagh
- Manchester Institute of Biotechnology, The University of Manchester , 131 Princess Street, Manchester M1 7DN, Great Britain
| | - Arnaldo F Silva
- Manchester Institute of Biotechnology, The University of Manchester , 131 Princess Street, Manchester M1 7DN, Great Britain
| | - Mark A Vincent
- School of Chemistry, The University of Manchester , Oxford Road, Manchester M13 9PL, Great Britain
| | - Paul L A Popelier
- Manchester Institute of Biotechnology, The University of Manchester , 131 Princess Street, Manchester M1 7DN, Great Britain.,School of Chemistry, The University of Manchester , Oxford Road, Manchester M13 9PL, Great Britain
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16
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Lošdorfer Božič A, Podgornik R. pH Dependence of Charge Multipole Moments in Proteins. Biophys J 2017; 113:1454-1465. [PMID: 28978439 DOI: 10.1016/j.bpj.2017.08.017] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2017] [Revised: 08/10/2017] [Accepted: 08/11/2017] [Indexed: 11/26/2022] Open
Abstract
Electrostatic interactions play a fundamental role in the structure and function of proteins. Due to ionizable amino acid residues present on the solvent-exposed surfaces of proteins, the protein charge is not constant but varies with the changes in the environment-most notably, the pH of the surrounding solution. We study the effects of pH on the charge of four globular proteins by expanding their surface charge distributions in terms of multipoles. The detailed representation of the charges on the proteins is in this way replaced by the magnitudes and orientations of the multipole moments of varying order. Focusing on the three lowest-order multipoles-the total charge, dipole, and quadrupole moment-we show that the value of pH influences not only their magnitudes, but more notably and importantly also the spatial orientation of their principal axes. Our findings imply important consequences for the study of protein-protein interactions and the assembly of both proteinaceous shells and patchy colloids with dissociable charge groups.
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Affiliation(s)
| | - Rudolf Podgornik
- Department of Theoretical Physics, Jožef Stefan Institute, Ljubljana, Slovenia; Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
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17
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Geometry Optimization with Machine Trained Topological Atoms. Sci Rep 2017; 7:12817. [PMID: 28993674 PMCID: PMC5634454 DOI: 10.1038/s41598-017-12600-3] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2017] [Accepted: 09/06/2017] [Indexed: 11/19/2022] Open
Abstract
The geometry optimization of a water molecule with a novel type of energy function called FFLUX is presented, which bypasses the traditional bonded potentials. Instead, topologically-partitioned atomic energies are trained by the machine learning method kriging to predict their IQA atomic energies for a previously unseen molecular geometry. Proof-of-concept that FFLUX’s architecture is suitable for geometry optimization is rigorously demonstrated. It is found that accurate kriging models can optimize 2000 distorted geometries to within 0.28 kJ mol−1 of the corresponding ab initio energy, and 50% of those to within 0.05 kJ mol−1. Kriging models are robust enough to optimize the molecular geometry to sub-noise accuracy, when two thirds of the geometric inputs are outside the training range of that model. Finally, the individual components of the potential energy are analyzed, and chemical intuition is reflected in the independent behavior of the three energy terms \documentclass[12pt]{minimal}
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\begin{document}$${E}_{{\rm{intra}}}^{{\rm{A}}}$$\end{document}EintraA(intra-atomic), \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
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\begin{document}$${V}_{{\rm{cl}}}^{\text{AA}\text{'}}$$\end{document}VclAA' (electrostatic) and \documentclass[12pt]{minimal}
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\begin{document}$${V}_{{\rm{x}}}^{\text{AA}\text{'}}$$\end{document}VxAA' (exchange), in contrast to standard force fields.
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18
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Fletcher TL, Popelier PLA. FFLUX: Transferability of polarizable machine-learned electrostatics in peptide chains. J Comput Chem 2017; 38:1005-1014. [DOI: 10.1002/jcc.24775] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2017] [Revised: 02/06/2017] [Accepted: 02/08/2017] [Indexed: 11/12/2022]
Affiliation(s)
- Timothy L. Fletcher
- Manchester Institute of Biotechnology (MIB); 131 Princess Street Manchester M1 7DN Great Britain
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Great Britain
| | - Paul L. A. Popelier
- Manchester Institute of Biotechnology (MIB); 131 Princess Street Manchester M1 7DN Great Britain
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Great Britain
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19
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Maxwell PI, Popelier PLA. Accurate prediction of the energetics of weakly bound complexes using the machine learning method kriging. Struct Chem 2017. [DOI: 10.1007/s11224-017-0928-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Fletcher TL, Popelier PLA. Toward amino acid typing for proteins in FFLUX. J Comput Chem 2016; 38:336-345. [PMID: 27991680 PMCID: PMC6681421 DOI: 10.1002/jcc.24686] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2016] [Revised: 11/14/2016] [Accepted: 11/14/2016] [Indexed: 01/18/2023]
Abstract
Continuing the development of the FFLUX, a multipolar polarizable force field driven by machine learning, we present a modern approach to atom-typing and building transferable models for predicting atomic properties in proteins. Amino acid atomic charges in a peptide chain respond to the substitution of a neighboring residue and this response can be categorized in a manner similar to atom-typing. Using a machine learning method called kriging, we are able to build predictive models for an atom that is defined, not only by its local environment, but also by its neighboring residues, for a minimal additional computational cost. We found that prediction errors were up to 11 times lower when using a model specific to the correct group of neighboring residues, with a mean prediction of ∼0.0015 au. This finding suggests that atoms in a force field should be defined by more than just their immediate atomic neighbors. When comparing an atom in a single alanine to an analogous atom in a deca-alanine helix, the mean difference in charge is 0.026 au. Meanwhile, the same difference between a trialanine and a deca-alanine helix is only 0.012 au. When compared to deca-alanine models, the transferable models are up to 20 times faster to train, and require significantly less ab initio calculation, providing a practical route to modeling large biological systems. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.
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Affiliation(s)
- Timothy L Fletcher
- Manchester Institute of Biotechnology (MIB), 131 Princess Street, Manchester, M1 7DN, United Kingdom
| | - Paul L A Popelier
- School of Chemistry, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
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Alborzpour JP, Tew DP, Habershon S. Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression. J Chem Phys 2016; 145:174112. [DOI: 10.1063/1.4964902] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jonathan P. Alborzpour
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - David P. Tew
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Scott Habershon
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
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