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Noid WG, Szukalo RJ, Kidder KM, Lesniewski MC. Rigorous Progress in Coarse-Graining. Annu Rev Phys Chem 2024; 75:21-45. [PMID: 38941523 DOI: 10.1146/annurev-physchem-062123-010821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/30/2024]
Abstract
Low-resolution coarse-grained (CG) models provide remarkable computational and conceptual advantages for simulating soft materials. In principle, bottom-up CG models can reproduce all structural and thermodynamic properties of atomically detailed models that can be observed at the resolution of the CG model. This review discusses recent progress in developing theory and computational methods for achieving this promise. We first briefly review variational approaches for parameterizing interaction potentials and their relationship to machine learning methods. We then discuss recent approaches for simultaneously improving both the transferability and thermodynamic properties of bottom-up models by rigorously addressing the density and temperature dependence of these potentials. We also briefly discuss exciting progress in modeling high-resolution observables with low-resolution CG models. More generally, we highlight the essential role of the bottom-up framework not only for fundamentally understanding the limitations of prior CG models but also for developing robust computational methods that resolve these limitations in practice.
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Affiliation(s)
- W G Noid
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania, USA;
| | - Ryan J Szukalo
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania, USA;
- Current affiliation: Department of Chemistry, Princeton University, Princeton, New Jersey, USA
| | - Katherine M Kidder
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania, USA;
| | - Maria C Lesniewski
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania, USA;
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2
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Wu Z, Zhou T. Structural Coarse-Graining via Multiobjective Optimization with Differentiable Simulation. J Chem Theory Comput 2024; 20:2605-2617. [PMID: 38483262 DOI: 10.1021/acs.jctc.3c01348] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/27/2024]
Abstract
In the realm of multiscale molecular simulations, structure-based coarse-graining is a prominent approach for creating efficient coarse-grained (CG) representations of soft matter systems, such as polymers. This involves optimizing CG interactions by matching static correlation functions of the corresponding degrees of freedom in all-atom (AA) models. Here, we present a versatile method, namely, differentiable coarse-graining (DiffCG), which combines multiobjective optimization and differentiable simulation. The DiffCG approach is capable of constructing robust CG models by iteratively optimizing the effective potentials to simultaneously match multiple target properties. We demonstrate our approach by concurrently optimizing bonded and nonbonded potentials of a CG model of polystyrene (PS) melts. The resulting CG-PS model effectively reproduces both the structural characteristics, such as the equilibrium probability distribution of microscopic degrees of freedom and the thermodynamic pressure of the AA counterpart. More importantly, leveraging the multiobjective optimization capability, we develop a precise and efficient CG model for PS melts that is transferable across a wide range of temperatures, i.e., from 400 to 600 K. It is achieved via optimizing a pairwise potential with nonlinear temperature dependence in the CG model to simultaneously match target data from AA-MD simulations at multiple thermodynamic states. The temperature transferable CG-PS model demonstrates its ability to accurately predict the radial distribution functions and density at different temperatures, including those that are not included in the target thermodynamic states. Our work opens up a promising route for developing accurate and transferable CG models of complex soft-matter systems through multiobjective optimization with differentiable simulation.
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Affiliation(s)
- Zhenghao Wu
- Department of Chemistry, Xi'an Jiaotong-Liverpool University, Suzhou, Jiangsu 215123, P. R. China
| | - Tianhang Zhou
- College of Carbon Neutrality Future Technology, State Key Laboratory of Heavy Oil Processing, China University of Petroleum (Beijing), Beijing 102249, P. R. China
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3
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Matin S, Allen AEA, Smith J, Lubbers N, Jadrich RB, Messerly R, Nebgen B, Li YW, Tretiak S, Barros K. Machine Learning Potentials with the Iterative Boltzmann Inversion: Training to Experiment. J Chem Theory Comput 2024. [PMID: 38307009 DOI: 10.1021/acs.jctc.3c01051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2024]
Abstract
Methodologies for training machine learning potentials (MLPs) with quantum-mechanical simulation data have recently seen tremendous progress. Experimental data have a very different character than simulated data, and most MLP training procedures cannot be easily adapted to incorporate both types of data into the training process. We investigate a training procedure based on iterative Boltzmann inversion that produces a pair potential correction to an existing MLP using equilibrium radial distribution function data. By applying these corrections to an MLP for pure aluminum based on density functional theory, we observe that the resulting model largely addresses previous overstructuring in the melt phase. Interestingly, the corrected MLP also exhibits improved performance in predicting experimental diffusion constants, which are not included in the training procedure. The presented method does not require autodifferentiating through a molecular dynamics solver and does not make assumptions about the MLP architecture. Our results suggest a practical framework for incorporating experimental data into machine learning models to improve the accuracy of molecular dynamics simulations.
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Affiliation(s)
- Sakib Matin
- Department of Physics, Boston University, Boston, Massachusetts 02215, United States
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Alice E A Allen
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Justin Smith
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- NVIDIA Corp., Santa Clara, California 95051, United States
| | - Nicholas Lubbers
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ryan B Jadrich
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Richard Messerly
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Benjamin Nebgen
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Ying Wai Li
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Kipton Barros
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
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4
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Coste A, Slejko E, Zavadlav J, Praprotnik M. Developing an Implicit Solvation Machine Learning Model for Molecular Simulations of Ionic Media. J Chem Theory Comput 2024; 20:411-420. [PMID: 38118122 PMCID: PMC10782447 DOI: 10.1021/acs.jctc.3c00984] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Revised: 12/04/2023] [Accepted: 12/04/2023] [Indexed: 12/22/2023]
Abstract
Molecular dynamics (MD) simulations of biophysical systems require accurate modeling of their native environment, i.e., aqueous ionic solution, as it critically impacts the structure and function of biomolecules. On the other hand, the models should be computationally efficient to enable simulations of large spatiotemporal scales. Here, we present the deep implicit solvation model for sodium chloride solutions that satisfies both requirements. Owing to the use of the neural network potential, the model can capture the many-body potential of mean force, while the implicit water treatment renders the model inexpensive. We demonstrate our approach first for pure ionic solutions with concentrations ranging from physiological to 2 M. We then extend the model to capture the effective ion interactions in the vicinity and far away from a DNA molecule. In both cases, the structural properties are in good agreement with all-atom MD, showcasing a general methodology for the efficient and accurate modeling of ionic media.
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Affiliation(s)
- Amaury Coste
- Laboratory
for Molecular Modeling, National Institute of Chemistry, Ljubljana SI-1001, Slovenia
| | - Ema Slejko
- Laboratory
for Molecular Modeling, National Institute of Chemistry, Ljubljana SI-1001, Slovenia
- Department
of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana SI-1000, Slovenia
| | - Julija Zavadlav
- Professorship
of Multiscale Modeling of Fluid Materials, TUM School of Engineering
and Design, Technical University of Munich, Garching Near Munich DE-85748, Germany
| | - Matej Praprotnik
- Laboratory
for Molecular Modeling, National Institute of Chemistry, Ljubljana SI-1001, Slovenia
- Department
of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana SI-1000, Slovenia
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5
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Ivanov M, Posysoev M, Lyubartsev AP. Coarse-Grained Modeling Using Neural Networks Trained on Structural Data. J Chem Theory Comput 2023; 19:6704-6717. [PMID: 37712507 PMCID: PMC10569054 DOI: 10.1021/acs.jctc.3c00516] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Indexed: 09/16/2023]
Abstract
We propose a method of bottom-up coarse-graining, in which interactions within a coarse-grained model are determined by an artificial neural network trained on structural data obtained from multiple atomistic simulations. The method uses ideas of the inverse Monte Carlo approach, relating changes in the neural network weights with changes in average structural properties, such as radial distribution functions. As a proof of concept, we demonstrate the method on a system interacting by a Lennard-Jones potential modeled by a simple linear network and a single-site coarse-grained model of methanol-water solutions. In the latter case, we implement a nonlinear neural network with intermediate layers trained by atomistic simulations carried out at different methanol concentrations. We show that such a network acts as a transferable potential at the coarse-grained resolution for a wide range of methanol concentrations, including those not included in the training set.
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Affiliation(s)
- Mikhail Ivanov
- Department of Materials and
Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden
| | - Maksim Posysoev
- Department of Materials and
Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden
| | - Alexander P. Lyubartsev
- Department of Materials and
Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden
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6
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Arts M, Garcia Satorras V, Huang CW, Zügner D, Federici M, Clementi C, Noé F, Pinsler R, van den Berg R. Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics. J Chem Theory Comput 2023; 19:6151-6159. [PMID: 37688551 DOI: 10.1021/acs.jctc.3c00702] [Citation(s) in RCA: 15] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/11/2023]
Abstract
Coarse-grained (CG) molecular dynamics enables the study of biological processes at temporal and spatial scales that would be intractable at an atomistic resolution. However, accurately learning a CG force field remains a challenge. In this work, we leverage connections between score-based generative models, force fields, and molecular dynamics to learn a CG force field without requiring any force inputs during training. Specifically, we train a diffusion generative model on protein structures from molecular dynamics simulations, and we show that its score function approximates a force field that can directly be used to simulate CG molecular dynamics. While having a vastly simplified training setup compared to previous work, we demonstrate that our approach leads to improved performance across several protein simulations for systems up to 56 amino acids, reproducing the CG equilibrium distribution and preserving the dynamics of all-atom simulations such as protein folding events.
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Affiliation(s)
- Marloes Arts
- Department of Computer Science, University of Copenhagen, Universitetsparken 1, Copenhagen 2100, Denmark
| | - Victor Garcia Satorras
- AI4Science, Microsoft Research, Evert van de Beekstraat 354, Amsterdam 1118 CZ, The Netherlands
| | - Chin-Wei Huang
- AI4Science, Microsoft Research, Evert van de Beekstraat 354, Amsterdam 1118 CZ, The Netherlands
| | - Daniel Zügner
- AI4Science, Microsoft Research, Karl-Liebknecht-Straße 32, Berlin 10178, Germany
| | - Marco Federici
- Informatics Institute, University of Amsterdam, Science Park 904, Amsterdam 1098 XH, The Netherlands
| | - Cecilia Clementi
- AI4Science, Microsoft Research, Karl-Liebknecht-Straße 32, Berlin 10178, Germany
- Department of Physics, Freie Universität Berlin, Arnimalle 12, Berlin 14195, Germany
| | - Frank Noé
- AI4Science, Microsoft Research, Karl-Liebknecht-Straße 32, Berlin 10178, Germany
| | - Robert Pinsler
- AI4Science, Microsoft Research, 21 Station Road, Cambridge CB1 2FB, U.K
| | - Rianne van den Berg
- AI4Science, Microsoft Research, Evert van de Beekstraat 354, Amsterdam 1118 CZ, The Netherlands
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7
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Krämer A, Durumeric AEP, Charron NE, Chen Y, Clementi C, Noé F. Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics. J Phys Chem Lett 2023; 14:3970-3979. [PMID: 37079800 DOI: 10.1021/acs.jpclett.3c00444] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Machine-learned coarse-grained (CG) models have the potential for simulating large molecular complexes beyond what is possible with atomistic molecular dynamics. However, training accurate CG models remains a challenge. A widely used methodology for learning bottom-up CG force fields maps forces from all-atom molecular dynamics to the CG representation and matches them with a CG force field on average. We show that there is flexibility in how to map all-atom forces to the CG representation and that the most commonly used mapping methods are statistically inefficient and potentially even incorrect in the presence of constraints in the all-atom simulation. We define an optimization statement for force mappings and demonstrate that substantially improved CG force fields can be learned from the same simulation data when using optimized force maps. The method is demonstrated on the miniproteins chignolin and tryptophan cage and published as open-source code.
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Affiliation(s)
- Andreas Krämer
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
| | - Aleksander E P Durumeric
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
| | - Nicholas E Charron
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77251, United States
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
| | - Yaoyi Chen
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
- International Max Planck Research School for Biology and Computation (IMPRS-BAC), Max Planck Institute for Molecular Genetics, 14195 Berlin, Germany
| | - Cecilia Clementi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77251, United States
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Microsoft Research AI4Science, Karl-Liebknecht Straße 32, 10178 Berlin, Germany
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