1
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Shinkle E, Pachalieva A, Bahl R, Matin S, Gifford B, Craven GT, Lubbers N. Thermodynamic Transferability in Coarse-Grained Force Fields Using Graph Neural Networks. J Chem Theory Comput 2024; 20:10524-10539. [PMID: 39579131 PMCID: PMC11635977 DOI: 10.1021/acs.jctc.4c00788] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2024] [Revised: 11/12/2024] [Accepted: 11/15/2024] [Indexed: 11/25/2024]
Abstract
Coarse-graining is a molecular modeling technique in which an atomistic system is represented in a simplified fashion that retains the most significant system features that contribute to a target output while removing the degrees of freedom that are less relevant. This reduction in model complexity allows coarse-grained molecular simulations to reach increased spatial and temporal scales compared with corresponding all-atom models. A core challenge in coarse-graining is to construct a force field that represents the interactions in the new representation in a way that preserves the atomistic-level properties. Many approaches to building coarse-grained force fields have limited transferability between different thermodynamic conditions as a result of averaging over internal fluctuations at a specific thermodynamic state point. Here, we use a graph-convolutional neural network architecture, the Hierarchically Interacting Particle Neural Network with Tensor Sensitivity (HIP-NN-TS), to develop a highly automated training pipeline for coarse-grained force fields, which allows for studying the transferability of coarse-grained models based on the force-matching approach. We show that this approach yields not only highly accurate force fields but also that these force fields are more transferable through a variety of thermodynamic conditions. These results illustrate the potential of machine learning techniques, such as graph neural networks, to improve the construction of transferable coarse-grained force fields.
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Affiliation(s)
- Emily Shinkle
- Computer,
Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Aleksandra Pachalieva
- Earth
and Environmental Sciences Division, Los
Alamos National Laboratory, Los
Alamos, New Mexico 87545, United States
- Center
for Nonlinear Studies, Los Alamos National
Laboratory, Los Alamos, New Mexico 87545, United States
| | - Riti Bahl
- Department
of Mathematics, Emory University, Atlanta, Georgia 30322, United States
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sakib Matin
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Brendan Gifford
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Galen T. Craven
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Nicholas Lubbers
- Computer,
Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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2
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Ghaffarizadeh SA, Wang GJ. A Picture is Worth a Thousand Timesteps: Excess Entropy Scaling for Rapid Estimation of Diffusion Coefficients in Molecular-Dynamics Simulations of Fluids. J Chem Theory Comput 2024; 20:10362-10370. [PMID: 39508678 PMCID: PMC11635976 DOI: 10.1021/acs.jctc.4c00760] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2024] [Revised: 10/20/2024] [Accepted: 10/21/2024] [Indexed: 11/15/2024]
Abstract
In molecular-dynamics simulations of fluids, the Einstein-Helfand (EH) and Green-Kubo (GK) relationships are frequently used to compute a variety of transport coefficients, including diffusion coefficients. These relationships are formally valid in the limit of infinite sampling time: The error in the estimate of a transport coefficient (relative to an infinitely long simulation) asymptotically approaches zero as more dynamics are simulated and recorded. In practice, of course, one can only simulate a finite number of particles for a finite amount of time. In this work, we show that in this pre-asymptotic regime, an approach for estimating diffusion coefficients based upon excess entropy scaling (EES) achieves a significantly lower error than either EH or GK relationships at fixed online sampling time. This approach requires access only to structural information at the level of the radial distribution function (RDF). We further demonstrate that the use of a recently developed RDF mollification scheme significantly reduces the amount of sampling time needed to converge to the long-time value of the diffusion coefficient. We also demonstrate favorable sample-to-sample variances in the diffusion coefficient estimate obtained using EES as compared to those obtained using EH and GK.
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Affiliation(s)
- S. Arman Ghaffarizadeh
- Department
of Mechanical Engineering, Carnegie Mellon
University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, United States
| | - Gerald J. Wang
- Department
of Civil and Environmental Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, United States
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3
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Ma S, Li D, Li X, Hu G. Neural network-assisted model of interfacial fluids with explicit coarse-grained molecular structures. J Chem Phys 2024; 161:174110. [PMID: 39494790 DOI: 10.1063/5.0230195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2024] [Accepted: 10/17/2024] [Indexed: 11/05/2024] Open
Abstract
Interfacial fluids are ubiquitous in systems ranging from biological membranes to chemical droplets and exhibit a complex behavior due to their nonlinear, multiphase, and multicomponent nature. The development of accurate coarse-grained (CG) models for such systems poses significant challenges, as these models must effectively capture the intricate many-body interactions, both inter- and intramolecular, arising from atomic-level phenomena, and account for the diverse density distributions and fluctuations at the interface. In this study, we use advanced machine learning techniques incorporating force matching and diffusion probabilistic models to construct a robust CG model of interfacial fluids. We evaluate our model through simulations in various settings, including the water-air interface, bulk decane, and dipalmitoylphosphatidylcholine monolayer membranes. Our results show that our CG model accurately reproduces the essential many-body and interfacial properties of interfacial fluids and proves effective across different CG mapping strategies. This work not only validates the utility of our model for multiscale simulations, but also lays the groundwork for future improvements in the simulation of complex interfacial systems.
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Affiliation(s)
- Shuhao Ma
- Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Dechang Li
- Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Xuejin Li
- Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Guoqing Hu
- Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, People's Republic of China
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4
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Jin J, Voth GA. Understanding dynamics in coarse-grained models. IV. Connection of fine-grained and coarse-grained dynamics with the Stokes-Einstein and Stokes-Einstein-Debye relations. J Chem Phys 2024; 161:034114. [PMID: 39012809 DOI: 10.1063/5.0212973] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2024] [Accepted: 06/28/2024] [Indexed: 07/18/2024] Open
Abstract
Applying an excess entropy scaling formalism to the coarse-grained (CG) dynamics of liquids, we discovered that missing rotational motions during the CG process are responsible for artificially accelerated CG dynamics. In the context of the dynamic representability between the fine-grained (FG) and CG dynamics, this work introduces the well-known Stokes-Einstein and Stokes-Einstein-Debye relations to unravel the rotational dynamics underlying FG trajectories, thereby allowing for an indirect evaluation of the effective rotations based only on the translational information at the reduced CG resolution. Since the representability issue in CG modeling limits a direct evaluation of the shear stress appearing in the Stokes-Einstein and Stokes-Einstein-Debye relations, we introduce a translational relaxation time as a proxy to employ these relations, and we demonstrate that these relations hold for the ambient conditions studied in our series of work. Additional theoretical links to our previous work are also established. First, we demonstrate that the effective hard sphere radius determined by the classical perturbation theory can approximate the complex hydrodynamic radius value reasonably well. Furthermore, we present a simple derivation of an excess entropy scaling relationship for viscosity by estimating the elliptical integral of molecules. In turn, since the translational and rotational motions at the FG level are correlated to each other, we conclude that the "entropy-free" CG diffusion only depends on the shape of the reference molecule. Our results and analyses impart an alternative way of recovering the FG diffusion from the CG description by coupling the translational and rotational motions at the hydrodynamic level.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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5
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Klippenstein V, Wolf N, van der Vegt NFA. A Gauss-Newton method for iterative optimization of memory kernels for generalized Langevin thermostats in coarse-grained molecular dynamics simulations. J Chem Phys 2024; 160:204115. [PMID: 38804493 DOI: 10.1063/5.0203832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Accepted: 05/08/2024] [Indexed: 05/29/2024] Open
Abstract
In molecular dynamics simulations, dynamically consistent coarse-grained (CG) models commonly use stochastic thermostats to model friction and fluctuations that are lost in a CG description. While Markovian, i.e., time-local, formulations of such thermostats allow for an accurate representation of diffusivities/long-time dynamics, a correct description of the dynamics on all time scales generally requires non-Markovian, i.e., non-time-local, thermostats. These thermostats typically take the form of a Generalized Langevin Equation (GLE) determined by a memory kernel. In this work, we use a Markovian embedded formulation of a position-independent GLE thermostat acting independently on each CG degree of freedom. Extracting the memory kernel of this CG model from atomistic reference data requires several approximations. Therefore, this task is best understood as an inverse problem. While our recently proposed approximate Newton scheme allows for the iterative optimization of memory kernels (IOMK), Markovian embedding remained potentially error-prone and computationally expensive. In this work, we present an IOMK-Gauss-Newton scheme (IOMK-GN) based on IOMK that allows for the direct parameterization of a Markovian embedded model.
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Affiliation(s)
- Viktor Klippenstein
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
| | - Niklas Wolf
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
| | - Nico F A van der Vegt
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
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6
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Duignan TT. The Potential of Neural Network Potentials. ACS PHYSICAL CHEMISTRY AU 2024; 4:232-241. [PMID: 38800721 PMCID: PMC11117678 DOI: 10.1021/acsphyschemau.4c00004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/18/2024] [Revised: 03/04/2024] [Accepted: 03/05/2024] [Indexed: 05/29/2024]
Abstract
In the next half-century, physical chemistry will likely undergo a profound transformation, driven predominantly by the combination of recent advances in quantum chemistry and machine learning (ML). Specifically, equivariant neural network potentials (NNPs) are a breakthrough new tool that are already enabling us to simulate systems at the molecular scale with unprecedented accuracy and speed, relying on nothing but fundamental physical laws. The continued development of this approach will realize Paul Dirac's 80-year-old vision of using quantum mechanics to unify physics with chemistry and providing invaluable tools for understanding materials science, biology, earth sciences, and beyond. The era of highly accurate and efficient first-principles molecular simulations will provide a wealth of training data that can be used to build automated computational methodologies, using tools such as diffusion models, for the design and optimization of systems at the molecular scale. Large language models (LLMs) will also evolve into increasingly indispensable tools for literature review, coding, idea generation, and scientific writing.
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7
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Jin J, Reichman DR. Hierarchical Framework for Predicting Entropies in Bottom-Up Coarse-Grained Models. J Phys Chem B 2024; 128:3182-3199. [PMID: 38507575 DOI: 10.1021/acs.jpcb.3c07624] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/22/2024]
Abstract
The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However, performing additional CG simulations on top of model construction often leads to significant additional computational overhead. In this work, we propose a simple hierarchical framework for predicting the thermodynamic entropies of various molecular CG systems. Our approach employs a decomposition of the CG interactions, enabling the estimation of the CG partition function and thermodynamic properties a priori. Starting from the ideal gas description, we leverage classical perturbation theory to systematically incorporate simple yet essential interactions, ranging from the hard sphere model to the generalized van der Waals model. Additionally, we propose an alternative approach based on multiparticle correlation functions, allowing for systematic improvements through higher-order correlations. Numerical applications to molecular liquids validate the high fidelity of our approach, and our computational protocols demonstrate that a reduced model with simple energetics can reasonably estimate the thermodynamic entropy of CG models without performing any CG simulations. Overall, our findings present a systematic framework for estimating not only the entropy but also other thermodynamic properties of CG models, relying solely on information from the reference system.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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8
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Zhang XZ, Shi R, Lu ZY, Qian HJ. Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties. JACS AU 2024; 4:1018-1030. [PMID: 38559727 PMCID: PMC10976574 DOI: 10.1021/jacsau.3c00756] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Revised: 02/23/2024] [Accepted: 02/28/2024] [Indexed: 04/04/2024]
Abstract
The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.
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Affiliation(s)
| | | | - Zhong-Yuan Lu
- State Key Laboratory of Supramolecular
Structure and Materials, Institute of Theoretical Chemistry, College
of Chemistry, Jilin University, Changchun 130021, China
| | - Hu-Jun Qian
- State Key Laboratory of Supramolecular
Structure and Materials, Institute of Theoretical Chemistry, College
of Chemistry, Jilin University, Changchun 130021, China
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9
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Nie Y, Zheng Z, Li C, Zhan H, Kou L, Gu Y, Lü C. Resolving the dynamic properties of entangled linear polymers in non-equilibrium coarse grain simulation with a priori scaling factors. NANOSCALE 2024. [PMID: 38494916 DOI: 10.1039/d3nr06185j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/19/2024]
Abstract
The molecular weight of polymers can influence the material properties, but the molecular weight at the experiment level sometimes can be a huge burden for property prediction with full-atomic simulations. The traditional bottom-up coarse grain (CG) simulation can reduce the computation cost. However, the dynamic properties predicted by the CG simulation can deviate from the full-atomic simulation result. Usually, in CG simulations, the diffusion is faster and the viscosity and modulus are much lower. The fast dynamics in CG are usually solved by a posteriori scaling on time, temperature, or potential modifications, which usually have poor transferability to other non-fitted physical properties because of a lack of fundamental physics. In this work, a priori scaling factors were calculated by the loss of degrees of freedom and implemented in the iterative Boltzmann inversion. According to the simulation results on 3 different CG levels at different temperatures and loading rates, such a priori scaling factors can help in reproducing some dynamic properties of polycaprolactone in CG simulation more accurately, such as heat capacity, Young's modulus, and viscosity, while maintaining the accuracy in the structural distribution prediction. The transferability of entropy-enthalpy compensation and a dissipative particle dynamics thermostat is also presented for comparison. The proposed method reveals the huge potential for developing customized CG thermostats and offers a simple way to rebuild multiphysics CG models for polymers with good transferability.
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Affiliation(s)
- Yihan Nie
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
| | - Zhuoqun Zheng
- School of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
| | - Chengkai Li
- School of Materials Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China
| | - Haifei Zhan
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
- Center for Materials Science, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
| | - Liangzhi Kou
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
- Center for Materials Science, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
| | - Yuantong Gu
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
- Center for Materials Science, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia
| | - Chaofeng Lü
- Faculty of Mechanical Engineering & Mechanics, Ningbo University, Ningbo 315211, China
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
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10
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Palma Banos M, Popov AV, Hernandez R. Representability and Dynamical Consistency in Coarse-Grained Models. J Phys Chem B 2024; 128:1506-1514. [PMID: 38315661 DOI: 10.1021/acs.jpcb.3c08054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2024]
Abstract
We address the challenge of representativity and dynamical consistency when unbonded fine-grained particles are collected together into coarse-grained particles. We implement a hybrid procedure for identifying and tracking the underlying fine-grained particles─e.g., atoms or molecules─by exchanging them between the coarse-grained particles periodically at a characteristic time. The exchange involves a back-mapping of the coarse-grained particles into fine-grained particles and a subsequent reassignment to coarse-grained particles conserving total mass and momentum. We find that an appropriate choice of the characteristic exchange time can lead to the correct effective diffusion rate of the fine-grained particles when simulated in hybrid coarse-grained dynamics. In the compressed (supercritical) fluid regime, without the exchange term, fine-grained particles remain associated with a given coarse-grained particle, leading to substantially lower diffusion rates than seen in all-atom molecular dynamics of the fine-grained particles. Thus, this work confirms the need for addressing the representativity of fine-grained particles within coarse-grained particles and offers a simple exchange mechanism so as to retain dynamical consistency between the fine- and coarse-grained scales.
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Affiliation(s)
- Manuel Palma Banos
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Alexander V Popov
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Rigoberto Hernandez
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
- Department of Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
- Department of Materials Science & Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
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11
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Lesniewski MC, Noid WG. Insight into the Density-Dependence of Pair Potentials for Predictive Coarse-Grained Models. J Phys Chem B 2024; 128:1298-1316. [PMID: 38271676 DOI: 10.1021/acs.jpcb.3c06890] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2024]
Abstract
We investigate the temperature- and density-dependence of effective pair potentials for 1-site coarse-grained (CG) models of two industrial solvents, 1,4-dioxane and tetrahydrofuran. We observe that the calculated pair potentials are much more sensitive to density than to temperature. The generalized-Yvon-Born-Green framework reveals that this striking density-dependence reflects corresponding variations in the many-body correlations that determine the environment-mediated indirect contribution to the pair mean force. Moreover, we demonstrate, perhaps surprisingly, that this density-dependence is not important for accurately modeling the intermolecular structure. Accordingly, we adopt a density-independent interaction potential and transfer the density-dependence of the calculated pair potentials into a configuration-independent volume potential. Furthermore, we develop a single global potential that accurately models the intermolecular structure and pressure-volume equation of state across a very wide range of liquid state points. Consequently, this work provides fundamental insight into the density-dependence of effective pair potentials and also provides a significant step toward developing predictive CG models for efficiently modeling industrial solvents.
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Affiliation(s)
- Maria C Lesniewski
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - W G Noid
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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12
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Knudsen PA, Heyes DM, Niss K, Dini D, Bailey NP. Invariant dynamics in a united-atom model of an ionic liquid. J Chem Phys 2024; 160:034503. [PMID: 38230811 DOI: 10.1063/5.0177373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 12/11/2023] [Indexed: 01/18/2024] Open
Abstract
We study a united-atom model of the ionic liquid 1-butyl-1-methylpyrrolidinium bis(trifluoromethyl)sulfonylamide to determine to what extent there exist curves in the phase diagram along which the microscopic dynamics are invariant when expressed in dimensionless, or reduced, form. The initial identification of these curves, termed isodynes, is made by noting that contours of reduced shear viscosity and reduced self-diffusion coefficient coincide to a good approximation. Choosing specifically the contours of reduced viscosity as nominal isodynes, further simulations were carried out for state points on these, and other aspects of dynamics were investigated to study their degree of invariance. These include the mean-squared displacement, shear-stress autocorrelation function, and various rotational correlation functions. These were invariant to a good approximation, with the main exception being rotations of the anion about its long axis. The dynamical features that are invariant have in common that they are aspects that would be relevant for a coarse-grained description of the system; specifically, removing the most microscopic degrees of freedom in principle leads to a simplification of the potential energy landscape, which allows for the existence of isodynes.
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Affiliation(s)
- Peter A Knudsen
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - David M Heyes
- Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Kristine Niss
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Daniele Dini
- Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Nicholas P Bailey
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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13
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Pretti E, Shell MS. Mapping the configurational landscape and aggregation phase behavior of the tau protein fragment PHF6. Proc Natl Acad Sci U S A 2023; 120:e2309995120. [PMID: 37983502 PMCID: PMC10691331 DOI: 10.1073/pnas.2309995120] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 10/17/2023] [Indexed: 11/22/2023] Open
Abstract
The PHF6 (Val-Gln-Ile-Val-Tyr-Lys) motif, found in all isoforms of the microtubule-associated protein tau, forms an integral part of ordered cores of amyloid fibrils formed in tauopathies and is thought to play a fundamental role in tau aggregation. Because PHF6 as an isolated hexapeptide assembles into ordered fibrils on its own, it is investigated as a minimal model for insight into the initial stages of aggregation of larger tau fragments. Even for this small peptide, however, the large length and time scales associated with fibrillization pose challenges for simulation studies of its dynamic assembly, equilibrium configurational landscape, and phase behavior. Here, we develop an accurate, bottom-up coarse-grained model of PHF6 for large-scale simulations of its aggregation, which we use to uncover molecular interactions and thermodynamic driving forces governing its assembly. The model, not trained on any explicit information about fibrillar structure, predicts coexistence of formed fibrils with monomers in solution, and we calculate a putative equilibrium phase diagram in concentration-temperature space. We also characterize the configurational and free energetic landscape of PHF6 oligomers. Importantly, we demonstrate with a model of heparin that this widely studied cofactor enhances the aggregation propensity of PHF6 by ordering monomers during nucleation and remaining associated with growing fibrils, consistent with experimentally characterized heparin-tau interactions. Overall, this effort provides detailed molecular insight into PHF6 aggregation thermodynamics and pathways and, furthermore, demonstrates the potential of modern multiscale modeling techniques to produce predictive models of amyloidogenic peptides simultaneously capturing sequence-specific effects and emergent aggregate structures.
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Affiliation(s)
- Evan Pretti
- Department of Chemical Engineering, University of California, Santa Barbara, CA93106-5080
| | - M. Scott Shell
- Department of Chemical Engineering, University of California, Santa Barbara, CA93106-5080
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14
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Jin J, Hwang J, Voth GA. Gaussian representation of coarse-grained interactions of liquids: Theory, parametrization, and transferability. J Chem Phys 2023; 159:184105. [PMID: 37942867 DOI: 10.1063/5.0160567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 10/06/2023] [Indexed: 11/10/2023] Open
Abstract
Coarse-grained (CG) interactions determined via bottom-up methodologies can faithfully reproduce the structural correlations observed in fine-grained (atomistic resolution) systems, yet they can suffer from limited extensibility due to complex many-body correlations. As part of an ongoing effort to understand and improve the applicability of bottom-up CG models, we propose an alternative approach to address both accuracy and transferability. Our main idea draws from classical perturbation theory to partition the hard sphere repulsive term from effective CG interactions. We then introduce Gaussian basis functions corresponding to the system's characteristic length by linking these Gaussian sub-interactions to the local particle densities at each coordination shell. The remaining perturbative long-range interaction can be treated as a collective solvation interaction, which we show exhibits a Gaussian form derived from integral equation theories. By applying this numerical parametrization protocol to CG liquid systems, our microscopic theory elucidates the emergence of Gaussian interactions in common phenomenological CG models. To facilitate transferability for these reduced descriptions, we further infer equations of state to determine the sub-interaction parameter as a function of the system variables. The reduced models exhibit excellent transferability across the thermodynamic state points. Furthermore, we propose a new strategy to design the cross-interactions between distinct CG sites in liquid mixtures. This involves combining each Gaussian in the proper radial domain, yielding accurate CG potentials of mean force and structural correlations for multi-component systems. Overall, our findings establish a solid foundation for constructing transferable bottom-up CG models of liquids with enhanced extensibility.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 S. Ellis Ave., Chicago, Illinois 60637, USA
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Jisung Hwang
- Department of Statistics, The University of Chicago, 5747 S. Ellis Ave., Chicago, Illinois 60637, USA
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 S. Ellis Ave., Chicago, Illinois 60637, USA
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15
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Jin J, Lee EK, Voth GA. Understanding dynamics in coarse-grained models. III. Roles of rotational motion and translation-rotation coupling in coarse-grained dynamics. J Chem Phys 2023; 159:164102. [PMID: 37870140 DOI: 10.1063/5.0167158] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 09/29/2023] [Indexed: 10/24/2023] Open
Abstract
This paper series aims to establish a complete correspondence between fine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I). While Paper II successfully captured translational motions in CG systems using a hard sphere mapping, the absence of rotational motions in single-site CG models introduces differences between FG and CG dynamics. In this third paper, our objective is to faithfully recover atomistic diffusion coefficients from CG dynamics by incorporating rotational dynamics. By extracting FG rotational diffusion, we unravel, for the first time reported to our knowledge, a universality in excess entropy scaling between the rotational and translational diffusion. Once the missing rotational dynamics are integrated into the CG translational dynamics, an effective translation-rotation coupling becomes essential. We propose two different approaches for estimating this coupling parameter: the rough hard sphere theory with acentric factor (temperature-independent) or the rough Lennard-Jones model with CG attractions (temperature-dependent). Altogether, we demonstrate that FG diffusion coefficients can be recovered from CG diffusion coefficients by (1) incorporating "entropy-free" rotational diffusion with translation-rotation coupling and (2) recapturing the missing entropy. Our findings shed light on the fundamental relationship between FG and CG dynamics in molecular fluids.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Eok Kyun Lee
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, South Korea
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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16
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Sorkin B, Diamant H, Ariel G. Universal Relation between Entropy and Kinetics. PHYSICAL REVIEW LETTERS 2023; 131:147101. [PMID: 37862659 DOI: 10.1103/physrevlett.131.147101] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 08/25/2023] [Indexed: 10/22/2023]
Abstract
Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle configurations. It is universal and applicable to steady states arbitrarily far from thermodynamic equilibrium. Applying the general relation to diffusive dynamics yields a relation between the entropy and the (normal or anomalous) diffusion coefficient. The relation can be used to obtain useful bounds for the late-time diffusion coefficient from the calculated steady-state entropy or, conversely, to estimate the entropy based on measured diffusion coefficients. We demonstrate the validity and usefulness of the relation through several examples and discuss its broad range of applications, in particular, for systems far from equilibrium.
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Affiliation(s)
- Benjamin Sorkin
- School of Chemistry and Center for Physics and Chemistry of Living Systems, Tel Aviv University, 69978 Tel Aviv, Israel
| | - Haim Diamant
- School of Chemistry and Center for Physics and Chemistry of Living Systems, Tel Aviv University, 69978 Tel Aviv, Israel
| | - Gil Ariel
- Department of Mathematics, Bar-Ilan University, 52000 Ramat Gan, Israel
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17
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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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18
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Jin J, Voth GA. Statistical Mechanical Design Principles for Coarse-Grained Interactions across Different Conformational Free Energy Surfaces. J Phys Chem Lett 2023; 14:1354-1362. [PMID: 36728761 PMCID: PMC9940719 DOI: 10.1021/acs.jpclett.2c03844] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Accepted: 01/27/2023] [Indexed: 06/18/2023]
Abstract
Systematic bottom-up coarse-graining (CG) of molecular systems provides a means to explore different coupled length and time scales while treating the molecular-scale physics at a reduced level. However, the configuration dependence of CG interactions often results in CG models with limited applicability for exploring the parametrized configurations. We propose a statistical mechanical theory to design CG interactions across different configurations and conditions. In order to span wide ranges of conformational space, distinct classical CG free energy surfaces for characteristic configurations are identified using molecular collective variables. The coupling interaction between different CG free energy surfaces can then be systematically determined by analogy to quantum mechanical approaches describing coupled states. The present theory can accurately capture the underlying many-body potentials of mean force in the CG variables for various order parameters applied to liquids, interfaces, and in principle proteins, uncovering the complex nature underlying the coupling interaction and imparting a new protocol for the design of predictive multiscale models.
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Affiliation(s)
| | - Gregory A. Voth
- Department of Chemistry,
Chicago Center for Theoretical Chemistry, Institute for Biophysical
Dynamics, and James Franck Institute, The
University of Chicago, Chicago, Illinois 60637, United States
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19
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Jin J, Schweizer KS, Voth GA. Understanding dynamics in coarse-grained models. II. Coarse-grained diffusion modeled using hard sphere theory. J Chem Phys 2023; 158:034104. [PMID: 36681632 DOI: 10.1063/5.0116300] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of the scaling relationship was not possible due to the semi-empirical nature. In this second paper, an analytical excess entropy scaling relation is derived for bottom-up CG systems. At the single-site CG resolution, effective hard sphere systems are constructed that yield near-identical dynamical properties as the target CG systems by taking advantage of how hard sphere dynamics and excess entropy can be analytically expressed in terms of the liquid packing fraction. Inspired by classical equilibrium perturbation theories and recent advances in constructing hard sphere models for predicting activated dynamics of supercooled liquids, we propose a new approach for understanding the diffusion of molecular liquids in the normal regime using hard sphere reference fluids. The proposed "fluctuation matching" is designed to have the same amplitude of long wavelength density fluctuations (dimensionless compressibility) as the CG system. Utilizing the Enskog theory to derive an expression for hard sphere diffusion coefficients, a bridge between the CG dynamics and excess entropy is then established. The CG diffusion coefficient can be roughly estimated using various equations of the state, and an accurate prediction of accelerated CG dynamics at different temperatures is also possible in advance of running any CG simulation. By introducing another layer of coarsening, these findings provide a more rigorous method to assess excess entropy scaling and understand the accelerated CG dynamics of molecular fluids.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Kenneth S Schweizer
- Department of Material Science, Department of Chemistry, Department of Chemical and Biomolecular Engineering, and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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