1
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Kidder KM, Noid WG. Analysis of mapping atomic models to coarse-grained resolution. J Chem Phys 2024; 161:134113. [PMID: 39365018 DOI: 10.1063/5.0220989] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2024] [Accepted: 09/10/2024] [Indexed: 10/05/2024] Open
Abstract
Low-resolution coarse-grained (CG) models provide significant computational and conceptual advantages for simulating soft materials. However, the properties of CG models depend quite sensitively upon the mapping, M, that maps each atomic configuration, r, to a CG configuration, R. In particular, M determines how the configurational information of the atomic model is partitioned between the mapped ensemble of CG configurations and the lost ensemble of atomic configurations that map to each R. In this work, we investigate how the mapping partitions the atomic configuration space into CG and intra-site components. We demonstrate that the corresponding coordinate transformation introduces a nontrivial Jacobian factor. This Jacobian factor defines a labeling entropy that corresponds to the uncertainty in the atoms that are associated with each CG site. Consequently, the labeling entropy effectively transfers configurational information from the lost ensemble into the mapped ensemble. Moreover, our analysis highlights the possibility of resonant mappings that separate the atomic potential into CG and intra-site contributions. We numerically illustrate these considerations with a Gaussian network model for the equilibrium fluctuations of actin. We demonstrate that the spectral quality, Q, provides a simple metric for identifying high quality representations for actin. Conversely, we find that neither maximizing nor minimizing the information content of the mapped ensemble results in high quality representations. However, if one accounts for the labeling uncertainty, Q(M) correlates quite well with the adjusted configurational information loss, Îmap(M), that results from the mapping.
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Affiliation(s)
- Katherine M Kidder
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - W G Noid
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, 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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Izvekov S, Kroonblawd MP, Larentzos JP, Brennan JK, Rice BM. Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB). J Phys Chem B 2024. [PMID: 38489758 DOI: 10.1021/acs.jpcb.3c07078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/17/2024]
Abstract
The MSCG/FM (multiscale coarse-graining via force-matching) approach is an efficient supervised machine learning method to develop microscopically informed coarse-grained (CG) models. We present a theory based on the principle of maximum entropy (PME) enveloping the existing MSCG/FM approaches. This theory views the MSCG/FM method as a special case of matching the thermodynamic forces from the extended ensemble described by the set of thermodynamic (relevant) system coordinates. This set may include CG coordinates, the stress tensor, applied external fields, and so forth, and may be characterized by nonequilibrium conditions. Following the presentation of the theory, we discuss the consistent matching of both bonded and nonbonded interactions. The proposed PME formulation is used as a starting point to extend the MSCG/FM method to the constant strain ensemble, which together with the explicit matching of the bonded forces is better suited for coarse-graining anisotropic media at a submolecular resolution. The theory is demonstrated by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a well-known insensitive molecular energetic material, which exhibits highly anisotropic mechanical properties.
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Affiliation(s)
- Sergei Izvekov
- U.S. Army DEVCOM Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
| | - Matthew P Kroonblawd
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - James P Larentzos
- U.S. Army DEVCOM Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
| | - John K Brennan
- U.S. Army DEVCOM Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
| | - Betsy M Rice
- U.S. Army DEVCOM Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
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4
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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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5
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Kidder KM, Shell MS, Noid WG. Surveying the energy landscape of coarse-grained mappings. J Chem Phys 2024; 160:054105. [PMID: 38310476 DOI: 10.1063/5.0182524] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Accepted: 12/28/2023] [Indexed: 02/05/2024] Open
Abstract
Simulations of soft materials often adopt low-resolution coarse-grained (CG) models. However, the CG representation is not unique and its impact upon simulated properties is poorly understood. In this work, we investigate the space of CG representations for ubiquitin, which is a typical globular protein with 72 amino acids. We employ Monte Carlo methods to ergodically sample this space and to characterize its landscape. By adopting the Gaussian network model as an analytically tractable atomistic model for equilibrium fluctuations, we exactly assess the intrinsic quality of each CG representation without introducing any approximations in sampling configurations or in modeling interactions. We focus on two metrics, the spectral quality and the information content, that quantify the extent to which the CG representation preserves low-frequency, large-amplitude motions and configurational information, respectively. The spectral quality and information content are weakly correlated among high-resolution representations but become strongly anticorrelated among low-resolution representations. Representations with maximal spectral quality appear consistent with physical intuition, while low-resolution representations with maximal information content do not. Interestingly, quenching studies indicate that the energy landscape of mapping space is very smooth and highly connected. Moreover, our study suggests a critical resolution below which a "phase transition" qualitatively distinguishes good and bad representations.
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Affiliation(s)
- Katherine M Kidder
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - M Scott Shell
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - W G Noid
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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6
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Nguyen MVT, Dolph K, Delaney KT, Shen K, Sherck N, Köhler S, Gupta R, Francis MB, Shell MS, Fredrickson GH. Molecularly informed field theory for estimating critical micelle concentrations of intrinsically disordered protein surfactants. J Chem Phys 2023; 159:244904. [PMID: 38149742 PMCID: PMC10754628 DOI: 10.1063/5.0178910] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Accepted: 11/30/2023] [Indexed: 12/28/2023] Open
Abstract
The critical micelle concentration (CMC) is a crucial parameter in understanding the self-assembly behavior of surfactants. In this study, we combine simulation and experiment to demonstrate the predictive capability of molecularly informed field theories in estimating the CMC of biologically based protein surfactants. Our simulation approach combines the relative entropy coarse-graining of small-scale atomistic simulations with large-scale field-theoretic simulations, allowing us to efficiently compute the free energy of micelle formation necessary for the CMC calculation while preserving chemistry-specific information about the underlying surfactant building blocks. We apply this methodology to a unique intrinsically disordered protein platform capable of a wide variety of tailored sequences that enable tunable micelle self-assembly. The computational predictions of the CMC closely match experimental measurements, demonstrating the potential of molecularly informed field theories as a valuable tool to investigate self-assembly in bio-based macromolecules systematically.
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Affiliation(s)
- My. V. T. Nguyen
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Kate Dolph
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | | | | | | | - Rohini Gupta
- California Research Alliance (CARA) by BASF, Berkeley, California 94720, USA
| | | | - M. Scott Shell
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
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7
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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: 0] [Impact Index Per Article: 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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8
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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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9
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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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10
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Majewski M, Pérez A, Thölke P, Doerr S, Charron NE, Giorgino T, Husic BE, Clementi C, Noé F, De Fabritiis G. Machine learning coarse-grained potentials of protein thermodynamics. Nat Commun 2023; 14:5739. [PMID: 37714883 PMCID: PMC10504246 DOI: 10.1038/s41467-023-41343-1] [Citation(s) in RCA: 19] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 08/29/2023] [Indexed: 09/17/2023] Open
Abstract
A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics.
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Affiliation(s)
- Maciej Majewski
- Computational Science Laboratory, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Carrer Dr. Aiguader 88, 08003, Barcelona, Spain
- Acellera Labs, Doctor Trueta 183, 08005, Barcelona, Spain
| | - Adrià Pérez
- Computational Science Laboratory, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Carrer Dr. Aiguader 88, 08003, Barcelona, Spain
- Acellera Labs, Doctor Trueta 183, 08005, Barcelona, Spain
| | - Philipp Thölke
- Computational Science Laboratory, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Carrer Dr. Aiguader 88, 08003, Barcelona, Spain
| | - Stefan Doerr
- Acellera Labs, Doctor Trueta 183, 08005, Barcelona, Spain
| | - Nicholas E Charron
- Department of Physics, Rice University, Houston, TX, 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, TX, 77005, USA
- Department of Physics, FU Berlin, Arnimallee 12, 14195, Berlin, Germany
| | - Toni Giorgino
- Biophysics Institute, National Research Council (CNR-IBF), 20133, Milan, Italy
| | - Brooke E Husic
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany
- Lewis Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, 08540, USA
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, 08540, USA
- Center for the Physics of Biological Function, Princeton University, Princeton, NJ, 08540, USA
| | - Cecilia Clementi
- Department of Physics, Rice University, Houston, TX, 77005, USA.
- Center for Theoretical Biological Physics, Rice University, Houston, TX, 77005, USA.
- Department of Physics, FU Berlin, Arnimallee 12, 14195, Berlin, Germany.
- Department of Chemistry, Rice University, Houston, TX, 77005, USA.
| | - Frank Noé
- Department of Physics, FU Berlin, Arnimallee 12, 14195, Berlin, Germany.
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany.
- Department of Chemistry, Rice University, Houston, TX, 77005, USA.
- Microsoft Research AI4Science, Karl-Liebknecht Str. 32, 10178, Berlin, Germany.
| | - Gianni De Fabritiis
- Computational Science Laboratory, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Carrer Dr. Aiguader 88, 08003, Barcelona, Spain.
- Acellera Labs, Doctor Trueta 183, 08005, Barcelona, Spain.
- Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluis Companys 23, 08010, Barcelona, Spain.
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11
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Wang W, Wu Z, Dietschreit JCB, Gómez-Bombarelli R. Learning pair potentials using differentiable simulations. J Chem Phys 2023; 158:044113. [PMID: 36725529 DOI: 10.1063/5.0126475] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Learning pair interactions from experimental or simulation data is of great interest for molecular simulations. We propose a general stochastic method for learning pair interactions from data using differentiable simulations (DiffSim). DiffSim defines a loss function based on structural observables, such as the radial distribution function, through molecular dynamics (MD) simulations. The interaction potentials are then learned directly by stochastic gradient descent, using backpropagation to calculate the gradient of the structural loss metric with respect to the interaction potential through the MD simulation. This gradient-based method is flexible and can be configured to simulate and optimize multiple systems simultaneously. For example, it is possible to simultaneously learn potentials for different temperatures or for different compositions. We demonstrate the approach by recovering simple pair potentials, such as Lennard-Jones systems, from radial distribution functions. We find that DiffSim can be used to probe a wider functional space of pair potentials compared with traditional methods like iterative Boltzmann inversion. We show that our methods can be used to simultaneously fit potentials for simulations at different compositions and temperatures to improve the transferability of the learned potentials.
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Affiliation(s)
- Wujie Wang
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
| | - Zhenghao Wu
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany
| | - Johannes C B Dietschreit
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
| | - Rafael Gómez-Bombarelli
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
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12
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Schmid F. Understanding and Modeling Polymers: The Challenge of Multiple Scales. ACS POLYMERS AU 2022. [DOI: 10.1021/acspolymersau.2c00049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128Mainz, Germany
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13
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Jin J, Pak AJ, Durumeric AEP, Loose TD, Voth GA. Bottom-up Coarse-Graining: Principles and Perspectives. J Chem Theory Comput 2022; 18:5759-5791. [PMID: 36070494 PMCID: PMC9558379 DOI: 10.1021/acs.jctc.2c00643] [Citation(s) in RCA: 80] [Impact Index Per Article: 40.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Indexed: 01/14/2023]
Abstract
Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.
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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, United States
| | - Alexander J. Pak
- 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
| | - Aleksander E. P. Durumeric
- 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
| | - Timothy D. Loose
- 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
| | - 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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14
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Nkepsu Mbitou RL, Goujon F, Dequidt A, Latour B, Devémy J, Blaak R, Martzel N, Emeriau-Viard C, Tchoufag J, Garruchet S, Munch E, Hauret P, Malfreyt P. Consistent and Transferable Force Fields for Statistical Copolymer Systems at the Mesoscale. J Chem Theory Comput 2022; 18:6940-6951. [PMID: 36205431 DOI: 10.1021/acs.jctc.2c00945] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The statistical trajectory matching (STM) method was applied successfully to derive coarse grain (CG) models for bulk properties of homopolymers. The extension of the methodology for building CG models for statistical copolymer systems is much more challenging. We present here the strategy for developing CG models for styrene-butadiene-rubber, and we compare the quality of the resulting CG force fields on the structure and thermodynamics at different chemical compositions. The CG models are used through the use of a genuine mesoscopic method called the dissipative particle dynamics method and compared to high-resolution molecular dynamics simulations. We conclude that the STM method is able to produce coarse-grained potentials that are transferable in composition by using only a few reference systems. Additionally, this methodology can be applied on any copolymer system.
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Affiliation(s)
- R L Nkepsu Mbitou
- Université Clermont Auvergne, CNRS, Clermont Auvergne INP, Institut de Chimie de Clermont-Ferrand, F-63000Clermont-Ferrand, France.,Manufacture Française des Pneumatiques Michelin, 23, Place des Carmes, 63040Clermont-Ferrand, France
| | - F Goujon
- Université Clermont Auvergne, CNRS, Clermont Auvergne INP, Institut de Chimie de Clermont-Ferrand, F-63000Clermont-Ferrand, France
| | - A Dequidt
- Université Clermont Auvergne, CNRS, Clermont Auvergne INP, Institut de Chimie de Clermont-Ferrand, F-63000Clermont-Ferrand, France
| | - B Latour
- Manufacture Française des Pneumatiques Michelin, 23, Place des Carmes, 63040Clermont-Ferrand, France
| | - J Devémy
- Université Clermont Auvergne, CNRS, Clermont Auvergne INP, Institut de Chimie de Clermont-Ferrand, F-63000Clermont-Ferrand, France
| | - R Blaak
- Université Clermont Auvergne, CNRS, Clermont Auvergne INP, Institut de Chimie de Clermont-Ferrand, F-63000Clermont-Ferrand, France
| | - N Martzel
- Manufacture Française des Pneumatiques Michelin, 23, Place des Carmes, 63040Clermont-Ferrand, France
| | - C Emeriau-Viard
- Manufacture Française des Pneumatiques Michelin, 23, Place des Carmes, 63040Clermont-Ferrand, France
| | - J Tchoufag
- Manufacture Française des Pneumatiques Michelin, 23, Place des Carmes, 63040Clermont-Ferrand, France
| | - S Garruchet
- Manufacture Française des Pneumatiques Michelin, 23, Place des Carmes, 63040Clermont-Ferrand, France
| | - E Munch
- Manufacture Française des Pneumatiques Michelin, 23, Place des Carmes, 63040Clermont-Ferrand, France
| | - P Hauret
- Manufacture Française des Pneumatiques Michelin, 23, Place des Carmes, 63040Clermont-Ferrand, France
| | - P Malfreyt
- Université Clermont Auvergne, CNRS, Clermont Auvergne INP, Institut de Chimie de Clermont-Ferrand, F-63000Clermont-Ferrand, France
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15
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Kanekal KH, Rudzinski JF, Bereau T. Broad chemical transferability in structure-based coarse-graining. J Chem Phys 2022; 157:104102. [DOI: 10.1063/5.0104914] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Compared to top-down coarse-grained (CG) models, bottom-up approaches are capable of offering higher structural fidelity. This fidelity results from the tight link to a higher-resolution reference, making the CG model chemically specific. Unfortunately, chemical specificity can be at odds with compound-screening strategies, which call for transferable parametrizations. Here we present an approach to reconcile bottom-up, structure-preserving CG models with chemical transferability. We consider the bottom-up CG parametrization of 3,441 C7O2 small-molecule isomers. Our approach combines atomic representations, unsupervised learning, and a large-scale extended-ensemble force-matching parametrization. We first identify a subset of 19 representative molecules, which maximally encode the local environment of all gas-phase conformers. Reference interactions between the 19 representative molecules were obtained from both homogeneous bulk liquids and various binary mixtures. An extended-ensemble parametrization over all 703 state points leads to a CG model that is both structure-based and chemically transferable. Remarkably, the resulting force field is on average more structurally accurate than single-state-point equivalents. Averaging over the extended ensemble acts as a mean-force regularizer, smoothing out both force and structural correlations that are overly specific to a single state point. Our approach aims at transferability through a set of CG bead types that can be used to easily construct new molecules, while retaining the benefits of a structure-based parametrization.
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Affiliation(s)
- Kiran H. Kanekal
- AK Kremer - Theory Group, Max Planck Institute for Polymer Research, Germany
| | | | - Tristan Bereau
- Van 't Hoff Institute for Molecular Sciences and Informatics Institute, University of Amsterdam, Netherlands
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16
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Yu G, Wilson MR. Molecular simulation studies of self-assembly for a chromonic perylene dye: All-atom studies and new approaches to coarse-graining. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2021.118210] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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17
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Dhamankar S, Webb MA. Chemically specific coarse‐graining of polymers: Methods and prospects. JOURNAL OF POLYMER SCIENCE 2021. [DOI: 10.1002/pol.20210555] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Satyen Dhamankar
- Department of Chemical and Biological Engineering Princeton University Princeton New Jersey USA
| | - Michael A. Webb
- Department of Chemical and Biological Engineering Princeton University Princeton New Jersey USA
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18
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Pretti E, Shell MS. A microcanonical approach to temperature-transferable coarse-grained models using the relative entropy. J Chem Phys 2021; 155:094102. [PMID: 34496595 DOI: 10.1063/5.0057104] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Bottom-up coarse-graining methods provide systematic tools for creating simplified models of molecular systems. However, coarse-grained (CG) models produced with such methods frequently fail to accurately reproduce all thermodynamic properties of the reference atomistic systems they seek to model and, moreover, can fail in even more significant ways when used at thermodynamic state points different from the reference conditions. These related problems of representability and transferability limit the usefulness of CG models, especially those of strongly state-dependent systems. In this work, we present a new strategy for creating temperature-transferable CG models using a single reference system and temperature. The approach is based on two complementary concepts. First, we switch to a microcanonical basis for formulating CG models, focusing on effective entropy functions rather than energy functions. This allows CG models to naturally represent information about underlying atomistic energy fluctuations, which would otherwise be lost. Such information not only reproduces energy distributions of the reference model but also successfully predicts the correct temperature dependence of the CG interactions, enabling temperature transferability. Second, we show that relative entropy minimization provides a direct and systematic approach to parameterize such classes of temperature-transferable CG models. We calibrate the approach initially using idealized model systems and then demonstrate its ability to create temperature-transferable CG models for several complex molecular liquids.
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Affiliation(s)
- Evan Pretti
- Department of Chemical Engineering, Engineering II Building, University of California, Santa Barbara, Santa Barbara, California 93106-5080, USA
| | - M Scott Shell
- Department of Chemical Engineering, Engineering II Building, University of California, Santa Barbara, Santa Barbara, California 93106-5080, USA
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19
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Giulini M, Rigoli M, Mattiotti G, Menichetti R, Tarenzi T, Fiorentini R, Potestio R. From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules. Front Mol Biosci 2021; 8:676976. [PMID: 34164432 PMCID: PMC8215203 DOI: 10.3389/fmolb.2021.676976] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2021] [Accepted: 05/06/2021] [Indexed: 12/18/2022] Open
Abstract
The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.
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Affiliation(s)
- Marco Giulini
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Marta Rigoli
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Giovanni Mattiotti
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Roberto Menichetti
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Thomas Tarenzi
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Raffaele Fiorentini
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Raffaello Potestio
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
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20
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Szukalo RJ, Noid WG. Investigating the energetic and entropic components of effective potentials across a glass transition. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:154004. [PMID: 33498016 DOI: 10.1088/1361-648x/abdff8] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 01/26/2021] [Indexed: 06/12/2023]
Abstract
By eliminating unnecessary details, coarse-grained (CG) models provide the necessary efficiency for simulating scales that are inaccessible to higher resolution models. However, because they average over atomic details, the effective potentials governing CG degrees of freedom necessarily incorporate significant entropic contributions, which limit their transferability and complicate the treatment of thermodynamic properties. This work employs a dual-potential approach to consider the energetic and entropic contributions to effective interaction potentials for CG models. Specifically, we consider one- and three-site CG models for ortho-terphenyl (OTP) both above and below its glass transition. We employ the multiscale coarse-graining (MS-CG) variational principle to determine interaction potentials that accurately reproduce the structural properties of an all-atom (AA) model for OTP at each state point. We employ an energy-matching variational principle to determine an energy operator that accurately reproduces the intra- and inter-molecular energy of the AA model. While the MS-CG pair potentials are almost purely repulsive, the corresponding pair energy functions feature a pronounced minima that corresponds to contacting benzene rings. These energetic functions then determine an estimate for the entropic component of the MS-CG interaction potentials. These entropic functions accurately predict the MS-CG pair potentials across a wide range of liquid state points at constant density. Moreover, the entropic functions also predict pair potentials that quite accurately model the AA pair structure below the glass transition. Thus, the dual-potential approach appears a promising approach for modeling AA energetics, as well as for predicting the temperature-dependence of CG effective potentials.
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Affiliation(s)
- Ryan J Szukalo
- Department of Chemistry, Penn State University, University Park, PA 16802 United States of America
| | - W G Noid
- Department of Chemistry, Penn State University, University Park, PA 16802 United States of America
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21
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Wen C, Odle R, Cheng S. Coarse-Grained Molecular Dynamics Modeling of a Branched Polyetherimide. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c01440] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- Chengyuan Wen
- Department of Physics, Center for Soft Matter and Biological Physics, and Macromolecules Innovation Institute, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States
| | - Roy Odle
- SABIC, 1 Lexan Lane, Mt. Vernon, Indiana 47620, United States
| | - Shengfeng Cheng
- Department of Physics, Center for Soft Matter and Biological Physics, and Macromolecules Innovation Institute, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States
- Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States
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22
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DeLyser M, Noid WG. Bottom-up coarse-grained models for external fields and interfaces. J Chem Phys 2020; 153:224103. [PMID: 33317310 DOI: 10.1063/5.0030103] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Abstract
Bottom-up coarse-grained (CG) models accurately describe the structure of homogeneous systems but sometimes provide limited transferability and a poor description of thermodynamic properties. Consequently, inhomogeneous systems present a severe challenge for bottom-up models. In this work, we examine bottom-up CG models for interfaces and inhomogeneous systems. We first analyze the effect of external fields upon the many-body potential of mean force. We also demonstrate that the multiscale CG (MS-CG) variational principle for modeling the external field corresponds to a generalization of the first Yvon-Born-Green equation. This provides an important connection with liquid state theory, as well as physical insight into the structure of interfaces and the resulting MS-CG models. We then develop and assess MS-CG models for a film of liquid methanol that is adsorbed on an attractive wall and in coexistence with its vapor phase. While pair-additive potentials provide unsatisfactory accuracy and transferability, the inclusion of local-density (LD) potentials dramatically improves the accuracy and transferability of the MS-CG model. The MS-CG model with LD potentials quite accurately describes the wall-liquid interface, the bulk liquid density, and the liquid-vapor interface while simultaneously providing a much improved description of the vapor phase. This model also provides an excellent description of the pair structure and pressure-density equation of state for the bulk liquid. Thus, LD potentials hold considerable promise for transferable bottom-up models that accurately describe the structure and thermodynamic properties of both bulk and interfacial systems.
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Affiliation(s)
- Michael DeLyser
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
| | - W G Noid
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
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23
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Rudzinski JF, Bereau T. Coarse-grained conformational surface hopping: Methodology and transferability. J Chem Phys 2020; 153:214110. [DOI: 10.1063/5.0031249] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
- Van ’t Hoff Institute for Molecular Sciences and Informatics Institute, University of Amsterdam, Amsterdam 1098 XH, The Netherlands
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24
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Jin J, Yu A, Voth GA. Temperature and Phase Transferable Bottom-up Coarse-Grained Models. J Chem Theory Comput 2020; 16:6823-6842. [PMID: 32975948 DOI: 10.1021/acs.jctc.0c00832] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
Despite the high fidelity of bottom-up coarse-grained (CG) approaches to recapitulate the structural correlations in atomistic simulations, the general use of bottom-up CG methods is limited because of the nontransferable nature of these CG models under different thermodynamic conditions. Because bottom-up CG potentials usually correspond to configuration-dependent free energies of the system, recent studies have focused on adjusting enthalpic or entropic contributions to account for issues with transferability. However, these approaches can require a manual adjustment of the CG interaction a priori and are usually limited to constant volume ensembles. To overcome these limitations, we construct temperature and phase transferable CG models under constant pressure by developing the ultra-coarse-graining (UCG) methodology in the mean-field limit. In the mean-field ansatz, an embedded semi-global order parameter recapitulates global changes to the system by automatically adjusting the effective CG interactions, thus bridging free energy decompositions with UCG theory. The method presented is designed to faithfully capture structural correlations under different thermodynamic conditions, using a single UCG model. Specifically, we test the applicability of the developed theory in three distinct cases: (1) different temperatures at constant pressure in liquids, (2) different temperatures across thermodynamic phases, and (3) liquid/vapor interfaces. We demonstrate that the systematic construction of both temperature and phase transferable bottom-up CG models is possible using this generalized UCG theory. Based on our findings, this approach significantly extends the transferability and applicability of the bottom-up CG theory and method.
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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 Avenue, Chicago, Illinois 60637, United States
| | - Alvin Yu
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 S. Ellis Avenue, Chicago, Illinois 60637, United States
| | - 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 Avenue, Chicago, Illinois 60637, United States
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25
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Sherman ZM, Howard MP, Lindquist BA, Jadrich RB, Truskett TM. Inverse methods for design of soft materials. J Chem Phys 2020; 152:140902. [DOI: 10.1063/1.5145177] [Citation(s) in RCA: 42] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Affiliation(s)
- Zachary M. Sherman
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
| | - Michael P. Howard
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
| | - Beth A. Lindquist
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Ryan B. Jadrich
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Thomas M. Truskett
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
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26
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Abstract
Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for an ML revolution and have already been profoundly affected by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into ML structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation.
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Affiliation(s)
- Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany; .,Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany.,Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA;
| | - Alexandre Tkatchenko
- Physics and Materials Science Research Unit, University of Luxembourg, 1511 Luxembourg, Luxembourg;
| | - Klaus-Robert Müller
- Department of Computer Science, Technical University Berlin, 10587 Berlin, Germany; .,Max-Planck-Institut für Informatik, 66123 Saarbrücken, Germany.,Department of Brain and Cognitive Engineering, Korea University, Seoul 136-713, South Korea
| | - Cecilia Clementi
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany; .,Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA; .,Department of Physics, Rice University, Houston, Texas 77005, USA
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27
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Liwo A, Czaplewski C. Extension of the force-matching method to coarse-grained models with axially symmetric sites to produce transferable force fields: Application to the UNRES model of proteins. J Chem Phys 2020; 152:054902. [DOI: 10.1063/1.5138991] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Affiliation(s)
- Adam Liwo
- Faculty of Chemistry, University of Gdańsk, ul. Wita-Stwosza 63, 80-308 Gdańsk, Poland
- School of Computational Sciences, Korea Institute for Advanced Study, 87 Hoegiro, Dongdaemun-gu, 130-722 Seoul, South Korea
| | - Cezary Czaplewski
- Faculty of Chemistry, University of Gdańsk, ul. Wita-Stwosza 63, 80-308 Gdańsk, Poland
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28
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Lebold KM, Noid WG. Dual-potential approach for coarse-grained implicit solvent models with accurate, internally consistent energetics and predictive transferability. J Chem Phys 2019; 151:164113. [PMID: 31675902 DOI: 10.1063/1.5125246] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
The dual-potential approach promises coarse-grained (CG) models that accurately reproduce both structural and energetic properties, while simultaneously providing predictive estimates for the temperature-dependence of the effective CG potentials. In this work, we examine the dual-potential approach for implicit solvent CG models that reflect large entropic effects from the eliminated solvent. Specifically, we construct implicit solvent models at various resolutions, R, by retaining a fraction 0.10 ≤ R ≤ 0.95 of the molecules from a simple fluid of Lennard-Jones spheres. We consider the dual-potential approach in both the constant volume and constant pressure ensembles across a relatively wide range of temperatures. We approximate the many-body potential of mean force for the remaining solutes with pair and volume potentials, which we determine via multiscale coarse-graining and self-consistent pressure-matching, respectively. Interestingly, with increasing temperature, the pair potentials appear increasingly attractive, while the volume potentials become increasingly repulsive. The dual-potential approach not only reproduces the atomic energetics but also quite accurately predicts this temperature-dependence. We also derive an exact relationship between the thermodynamic specific heat of an atomic model and the energetic fluctuations that are observable at the CG resolution. With this generalized fluctuation relationship, the approximate CG models quite accurately reproduce the thermodynamic specific heat of the underlying atomic model.
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Affiliation(s)
- Kathryn M Lebold
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
| | - W G Noid
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
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29
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Jin J, Pak AJ, Voth GA. Understanding Missing Entropy in Coarse-Grained Systems: Addressing Issues of Representability and Transferability. J Phys Chem Lett 2019; 10:4549-4557. [PMID: 31319036 PMCID: PMC6782054 DOI: 10.1021/acs.jpclett.9b01228] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Coarse-grained (CG) models facilitate efficient simulation of complex systems by integrating out the atomic, or fine-grained (FG), degrees of freedom. Systematically derived CG models from FG simulations often attempt to approximate the CG potential of mean force (PMF), an inherently multidimensional and many-body quantity, using additive pairwise contributions. However, they currently lack fundamental principles that enable their extensible use across different thermodynamic state points, i.e., transferability. In this work, we investigate the explicit energy-entropy decomposition of the CG PMF as a means to construct transferable CG models. In particular, despite its high-dimensional nature, we find for liquid systems that the entropic component to the CG PMF can similarly be represented using additive pairwise contributions, which we show is highly coupled to the CG configurational entropy. This approach formally connects the missing entropy that is lost due to the CG representation, i.e., translational, rotational, and vibrational modes associated with the missing degrees of freedom, to the CG entropy. By design, the present framework imparts transferable CG interactions across different temperatures due to the explicit definition of an additive entropic contribution. Furthermore, we demonstrate that transferability across composition state points, such as between bulk liquids and their mixtures, is also achieved by designing combining rules to approximate cross-interactions from bulk CG PMFs. Using the predicted CG model for liquid mixtures, structural correlations of the fitted CG model were found to corroborate a high-fidelity combining rule. Our findings elucidate the physical nature and compact representation of CG entropy and suggest a new approach for overcoming the transferability problem. We expect that this approach will further extend the current view of CG modeling into predictive multiscale modeling.
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30
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Sanyal T, Mittal J, Shell MS. A hybrid, bottom-up, structurally accurate, Go¯-like coarse-grained protein model. J Chem Phys 2019; 151:044111. [PMID: 31370551 PMCID: PMC6663515 DOI: 10.1063/1.5108761] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Accepted: 06/24/2019] [Indexed: 12/21/2022] Open
Abstract
Coarse-grained (CG) protein models in the structural biology literature have improved over the years from being simple tools to understand general folding and aggregation driving forces to capturing detailed structures achieved by actual folding sequences. Here, we ask whether such models can be developed systematically from recent advances in bottom-up coarse-graining methods without relying on bioinformatic data (e.g., protein data bank statistics). We use relative entropy coarse-graining to develop a hybrid CG but Go¯-like CG peptide model, hypothesizing that the landscape of proteinlike folds is encoded by the backbone interactions, while the sidechain interactions define which of these structures globally minimizes the free energy in a unique native fold. To construct a model capable of capturing varied secondary structures, we use a new extended ensemble relative entropy method to coarse-grain based on multiple reference atomistic simulations of short polypeptides with varied α and β character. Subsequently, we assess the CG model as a putative protein backbone forcefield by combining it with sidechain interactions based on native contacts but not incorporating native distances explicitly, unlike standard Go¯ models. We test the model's ability to fold a range of proteins and find that it achieves high accuracy (∼2 Å root mean square deviation resolution for both short sequences and large globular proteins), suggesting the strong role that backbone conformational preferences play in defining the fold landscape. This model can be systematically extended to non-natural amino acids and nonprotein polymers and sets the stage for extensions to non-Go¯ models with sequence-specific sidechain interactions.
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Affiliation(s)
- Tanmoy Sanyal
- Department of Chemical Engineering, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - Jeetain Mittal
- Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, USA
| | - M. Scott Shell
- Department of Chemical Engineering, University of California Santa Barbara, Santa Barbara, California 93106, USA
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31
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Wang J, Olsson S, Wehmeyer C, Pérez A, Charron NE, de Fabritiis G, Noé F, Clementi C. Machine Learning of Coarse-Grained Molecular Dynamics Force Fields. ACS CENTRAL SCIENCE 2019; 5:755-767. [PMID: 31139712 PMCID: PMC6535777 DOI: 10.1021/acscentsci.8b00913] [Citation(s) in RCA: 199] [Impact Index Per Article: 39.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2018] [Indexed: 05/17/2023]
Abstract
Atomistic or ab initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper, we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select and compare the performance of different models. We introduce CGnets, a deep learning approach, that learns coarse-grained free energy functions and can be trained by a force-matching scheme. CGnets maintain all physically relevant invariances and allow one to incorporate prior physics knowledge to avoid sampling of unphysical structures. We show that CGnets can capture all-atom explicit-solvent free energy surfaces with models using only a few coarse-grained beads and no solvent, while classical coarse-graining methods fail to capture crucial features of the free energy surface. Thus, CGnets are able to capture multibody terms that emerge from the dimensionality reduction.
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Affiliation(s)
- Jiang Wang
- Center
for Theoretical Biological Physics, Rice
University, Houston, Texas 77005, United States
- Department
of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Simon Olsson
- Department
of Mathematics and Computer Science, Freie
Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Christoph Wehmeyer
- Department
of Mathematics and Computer Science, Freie
Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Adrià Pérez
- Computational
Science Laboratory, Universitat Pompeu Fabra, PRBB, C/Dr Aiguader 88, 08003 Barcelona, Spain
| | - Nicholas E. Charron
- Center
for Theoretical Biological Physics, Rice
University, Houston, Texas 77005, United States
- Department
of Physics, Rice University, Houston, Texas 77005, United States
| | - Gianni de Fabritiis
- Computational
Science Laboratory, Universitat Pompeu Fabra, PRBB, C/Dr Aiguader 88, 08003 Barcelona, Spain
- Institucio
Catalana de Recerca i Estudis Avanats (ICREA), Passeig Lluis Companys 23, 08010 Barcelona, Spain
| | - Frank Noé
- Center
for Theoretical Biological Physics, Rice
University, Houston, Texas 77005, United States
- Department
of Chemistry, Rice University, Houston, Texas 77005, United States
- Department
of Mathematics and Computer Science, Freie
Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Cecilia Clementi
- Center
for Theoretical Biological Physics, Rice
University, Houston, Texas 77005, United States
- Department
of Chemistry, Rice University, Houston, Texas 77005, United States
- Department
of Mathematics and Computer Science, Freie
Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- Department
of Physics, Rice University, Houston, Texas 77005, United States
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32
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Rosenberger D, van der Vegt NFA. Relative entropy indicates an ideal concentration for structure-based coarse graining of binary mixtures. Phys Rev E 2019; 99:053308. [PMID: 31212527 DOI: 10.1103/physreve.99.053308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2019] [Indexed: 06/09/2023]
Abstract
Many methodological approaches have been proposed to improve systematic or bottom-up coarse-graining techniques to enhance the representability and transferability of the derived interaction potentials. Transferability describes the ability of a coarse-grained (CG) model to be predictive, i.e., to describe a system at state points different from those chosen for parametrization. Whereas the representability characterizes the accuracy of a CG model to reproduce target properties of the underlying reference or fine-grained model at a given state point. In this article, we shift the focus away from methodological aspects and rather raise the question whether we can overcome the disadvantages of a given method in terms of representability and transferability by systematically selecting the state point at which the CG model gets parametrized. We answer this question by applying the inverse Monte Carlo (IMC) approach-a structure-based coarse-graining method-to derive effective interactions for binary mixtures of simple Lennard-Jones (LJ) particles, which are different in size. For such simple systems we indeed can identify a concentration where the derived potentials show the best performance in terms of structural representability and transferability. This specific concentration is identified by computing the relative entropy which quantifies the information loss between different IMC models and the reference LJ model at varying mixture compositions. Further, we show that an IMC model for mixtures of n-hexane and n-perfluorohexane shows the same trend in transferability as the IMC models for the LJ system. All derived models are more transferable in the direction of increasing concentration of the larger-sized compound.
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Affiliation(s)
- David Rosenberger
- Eduard Zintl Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Darmstadt, 64287, Germany
| | - Nico F A van der Vegt
- Eduard Zintl Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Darmstadt, 64287, Germany
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33
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Rosenberger D, Sanyal T, Shell MS, van der Vegt NFA. Transferability of Local Density-Assisted Implicit Solvation Models for Homogeneous Fluid Mixtures. J Chem Theory Comput 2019; 15:2881-2895. [PMID: 30995034 DOI: 10.1021/acs.jctc.8b01170] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The application of bottom-up coarse grained (CG) models to study the equilibrium mixing behavior of liquids is rather challenging, since these models can be significantly influenced by the density or the concentration of the state chosen during parametrization. This dependency leads to low transferability in density/concentration space and has been one of the major limitations in bottom-up coarse graining. Recent approaches proposed to tackle this shortcoming range from the addition of thermodynamic constraints, to an extended ensemble parametrization, to the addition of supplementary terms to the system's Hamiltonian. To study fluid phase equilibria with bottom-up CG models, the application of local density (LD) potentials appears to be a promising approach, as shown in previous work by Sanyal and Shell [T. Sanyal, M. S. Shell, J. Phys. Chem. B, 2018, 122, 5678]. Here, we want to further explore this method and test its ability to model a system which contains structural inhomogeneities only on the molecular scale, namely, solutions of methanol and water. We find that a water-water LD potential improves the transferability of an implicit-methanol CG model toward high water concentration. Conversely, a methanol-methanol LD potential does not significantly improve the transferability of an implicit-water CG model toward high methanol concentration. These differences appear due to the presence of cooperative interactions in water at high concentrations that the LD potentials can capture. In addition, we compare two different approaches to derive our CG models, namely, relative entropy optimization and the Inverse Monte Carlo method, and formally demonstrate under which analytical and numerical assumptions these two methods yield equivalent results.
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Affiliation(s)
- David Rosenberger
- Eduard Zintl Institut für Anorganische und Physikalische Chemie , Technische Universität Darmstadt , Darmstadt , Germany
| | - Tanmoy Sanyal
- Department of Chemical Engineering , University of California Santa Barbara , Santa Barbara , California 93106 , United States
| | - M Scott Shell
- Department of Chemical Engineering , University of California Santa Barbara , Santa Barbara , California 93106 , United States
| | - Nico F A van der Vegt
- Eduard Zintl Institut für Anorganische und Physikalische Chemie , Technische Universität Darmstadt , Darmstadt , Germany
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34
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Abstract
The necessity for accurate and computationally efficient representations of water in atomistic simulations that can span biologically relevant timescales has born the necessity of coarse-grained (CG) modeling. Despite numerous advances, CG water models rely mostly on a-priori specified assumptions. How these assumptions affect the model accuracy, efficiency, and in particular transferability, has not been systematically investigated. Here we propose a data driven comparison and selection for CG water models through a Hierarchical Bayesian framework. We examine CG water models that differ in their level of coarse-graining, structure, and number of interaction sites. We find that the importance of electrostatic interactions for the physical system under consideration is a dominant criterion for the model selection. Multi-site models are favored, unless the effects of water in electrostatic screening are not relevant, in which case the single site model is preferred due to its computational savings. The charge distribution is found to play an important role in the multi-site model’s accuracy while the flexibility of the bonds/angles may only slightly improve the models. Furthermore, we find significant variations in the computational cost of these models. We present a data informed rationale for the selection of CG water models and provide guidance for future water model designs.
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35
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Deichmann G, van der Vegt NFA. Conditional Reversible Work Coarse-Grained Models with Explicit Electrostatics—An Application to Butylmethylimidazolium Ionic Liquids. J Chem Theory Comput 2019; 15:1187-1198. [DOI: 10.1021/acs.jctc.8b00881] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Gregor Deichmann
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
| | - Nico F. A. van der Vegt
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
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36
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Lebold KM, Noid WG. Systematic study of temperature and density variations in effective potentials for coarse-grained models of molecular liquids. J Chem Phys 2019; 150:014104. [DOI: 10.1063/1.5050509] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Kathryn M. Lebold
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
| | - W. G. Noid
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
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37
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Potter TD, Tasche J, Wilson MR. Assessing the transferability of common top-down and bottom-up coarse-grained molecular models for molecular mixtures. Phys Chem Chem Phys 2019; 21:1912-1927. [DOI: 10.1039/c8cp05889j] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Assessing the performance of top-down and bottom-up coarse-graining approaches.
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Affiliation(s)
| | - Jos Tasche
- Department of Chemistry
- Durham University
- Lower Mountjoy
- Durham
- UK
| | - Mark R. Wilson
- Department of Chemistry
- Durham University
- Lower Mountjoy
- Durham
- UK
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38
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Webb MA, Delannoy JY, de Pablo JJ. Graph-Based Approach to Systematic Molecular Coarse-Graining. J Chem Theory Comput 2018; 15:1199-1208. [PMID: 30557028 DOI: 10.1021/acs.jctc.8b00920] [Citation(s) in RCA: 46] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A novel methodology is introduced here to generate coarse-grained (CG) representations of molecular models for simulations. The proposed strategy relies on basic graph-theoretic principles and is referred to as graph-based coarse-graining (GBCG). It treats a given system as a molecular graph and derives a corresponding CG representation by using edge contractions to combine nodes in the graph, which correspond to atoms in the molecule, into CG sites. A key element of this methodology is that the nodes are combined according to well-defined protocols that rank-order nodes based on the underlying chemical connectivity. By iteratively performing these operations, successively coarser representations of the original atomic system can be produced to yield a systematic set of CG mappings with hierarchical resolution in an automated fashion. These capabilities are demonstrated in the context of several test systems, including toluene, pentadecane, a polysaccharide dimer, and a rhodopsin protein. In these examples, GBCG yields multiple, intuitive structures that naturally preserve the chemical topology of the system. Importantly, these representations are rendered from algorithmic implementation rather than an arbitrary ansatz, which, until now, has been the conventional approach for defining CG mapping schemes. Overall, the results presented here indicate that GBCG is efficient, robust, and unambiguous in its application, making it a valuable tool for future CG modeling.
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Affiliation(s)
- Michael A Webb
- Institute for Molecular Engineering , University of Chicago , Chicago , Illinois 60637 , United States
| | - Jean-Yves Delannoy
- Simulation, Modeling and Artificial Intelligence team , Solvay , Bristol , Pennsylvania 19007 , United States
| | - Juan J de Pablo
- Institute for Molecular Engineering , University of Chicago , Chicago , Illinois 60637 , United States.,Institute for Molecular Engineering and Materials Science Division , Argonne National Laboratory , Lemont , Illinois 60439 , United States
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39
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Deichmann G, Dallavalle M, Rosenberger D, van der Vegt NFA. Phase Equilibria Modeling with Systematically Coarse-Grained Models—A Comparative Study on State Point Transferability. J Phys Chem B 2018; 123:504-515. [DOI: 10.1021/acs.jpcb.8b07320] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Affiliation(s)
- Gregor Deichmann
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
| | - Marco Dallavalle
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
| | - David Rosenberger
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
| | - Nico F. A. van der Vegt
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
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40
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Scherer C, Andrienko D. Understanding three-body contributions to coarse-grained force fields. Phys Chem Chem Phys 2018; 20:22387-22394. [PMID: 30129962 DOI: 10.1039/c8cp00746b] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Coarse-graining is a systematic reduction of the number of degrees of freedom used to describe a system of interest. Coarse-graining can be thought of as a projection on the coarse-grained degrees of freedom and is therefore dependent on the number and type of basis functions used to represent the coarse-grained force field. We show that many-body extensions of the coarse-grained force field can result in substantial changes of the two-body interactions, making them much more attractive at short distances. This interplay can be alleviated by first parametrizing the two-body potential and then fitting the additional three-body contribution to the residual forces. The approach is illustrated on liquid water where three-body interactions are essential to reproduce the structural properties, and liquid methanol where two-body interactions are sufficient to reproduce the main structural features of the atomistic system. Furthermore, we demonstrate that the structural and thermodynamic accuracy of the coarse-grained models can be controlled by varying the magnitude of the three-body interactions. Our findings motivate basis set extensions which separate the many-body contributions of different order.
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Affiliation(s)
- Christoph Scherer
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
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41
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Moradzadeh A, Motevaselian MH, Mashayak SY, Aluru NR. Coarse-Grained Force Field for Imidazolium-Based Ionic Liquids. J Chem Theory Comput 2018; 14:3252-3261. [DOI: 10.1021/acs.jctc.7b01293] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Alireza Moradzadeh
- Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Mohammad H. Motevaselian
- Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Sikandar Y. Mashayak
- Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Narayana R. Aluru
- Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
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42
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43
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Rosenberger D, van der Vegt NFA. Addressing the temperature transferability of structure based coarse graining models. Phys Chem Chem Phys 2018; 20:6617-6628. [DOI: 10.1039/c7cp08246k] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a novel idea to improve the temperature transferability of structure based coarse graining models.
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Affiliation(s)
- David Rosenberger
- Technische Universität Darmstadt, Eduard-Zintl-Institut für Anorganische und Physikalische Chemie
- Darmstadt
- Germany
| | - Nico F. A. van der Vegt
- Technische Universität Darmstadt, Eduard-Zintl-Institut für Anorganische und Physikalische Chemie
- Darmstadt
- Germany
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44
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Dunn NJH, Lebold KM, DeLyser MR, Rudzinski JF, Noid W. BOCS: Bottom-up Open-source Coarse-graining Software. J Phys Chem B 2017; 122:3363-3377. [DOI: 10.1021/acs.jpcb.7b09993] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Affiliation(s)
- Nicholas J. H. Dunn
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Kathryn M. Lebold
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Michael R. DeLyser
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Joseph F. Rudzinski
- 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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45
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Deichmann G, van der Vegt NFA. Conditional Reversible Work Coarse-Grained Models of Molecular Liquids with Coulomb Electrostatics – A Proof of Concept Study on Weakly Polar Organic Molecules. J Chem Theory Comput 2017; 13:6158-6166. [DOI: 10.1021/acs.jctc.7b00611] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gregor Deichmann
- Eduard-Zintl-Institut für
Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
| | - Nico F. A. van der Vegt
- Eduard-Zintl-Institut für
Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
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46
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Zavadlav J, Bevc S, Praprotnik M. Adaptive resolution simulations of biomolecular systems. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2017; 46:821-835. [PMID: 28905203 DOI: 10.1007/s00249-017-1248-0] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2017] [Revised: 06/12/2017] [Accepted: 08/15/2017] [Indexed: 10/18/2022]
Abstract
In this review article, we discuss and analyze some recently developed hybrid atomistic-mesoscopic solvent models for multiscale biomolecular simulations. We focus on the biomolecular applications of the adaptive resolution scheme (AdResS), which allows solvent molecules to change their resolution back and forth between atomistic and coarse-grained representations according to their positions in the system. First, we discuss coupling of atomistic and coarse-grained models of salt solution using a 1-to-1 molecular mapping-i.e., one coarse-grained bead represents one water molecule-for development of a multiscale salt solution model. In order to make use of coarse-grained molecular models that are compatible with the MARTINI force field, one has to resort to a supramolecular mapping, in particular to a 4-to-1 mapping, where four water molecules are represented with one coarse-grained bead. To this end, bundled atomistic water models are employed, i.e., the relative movement of water molecules that are mapped to the same coarse-grained bead is restricted by employing harmonic springs. Supramolecular coupling has recently also been extended to polarizable coarse-grained water models with explicit charges. Since these coarse-grained models consist of several interaction sites, orientational degrees of freedom of the atomistic and coarse-grained representations are coupled via a harmonic energy penalty term. The latter aligns the dipole moments of both representations. The reviewed multiscale solvent models are ready to be used in biomolecular simulations, as illustrated in a few examples.
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Affiliation(s)
- Julija Zavadlav
- Department of Molecular Modeling, National Institute of Chemistry, Hajdrihova 19, 1001, Ljubljana, Slovenia.,Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia.,Chair of Computational Science, ETH Zurich, Clausiusstrasse 33, 8092, Zurich, Switzerland
| | - Staš Bevc
- Department of Molecular Modeling, National Institute of Chemistry, Hajdrihova 19, 1001, Ljubljana, Slovenia
| | - Matej Praprotnik
- Department of Molecular Modeling, National Institute of Chemistry, Hajdrihova 19, 1001, Ljubljana, Slovenia. .,Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia.
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47
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Rudzinski JF, Lu K, Milner ST, Maranas JK, Noid WG. Extended Ensemble Approach to Transferable Potentials for Low-Resolution Coarse-Grained Models of Ionomers. J Chem Theory Comput 2017; 13:2185-2201. [DOI: 10.1021/acs.jctc.6b01160] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Joseph F. Rudzinski
- Department
of Chemistry and ‡Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Keran Lu
- Department
of Chemistry and ‡Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Scott T. Milner
- Department
of Chemistry and ‡Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Janna K. Maranas
- Department
of Chemistry and ‡Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - William G. Noid
- Department
of Chemistry and ‡Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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48
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Sanyal T, Shell MS. Coarse-grained models using local-density potentials optimized with the relative entropy: Application to implicit solvation. J Chem Phys 2017; 145:034109. [PMID: 27448876 DOI: 10.1063/1.4958629] [Citation(s) in RCA: 73] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
Bottom-up multiscale techniques are frequently used to develop coarse-grained (CG) models for simulations at extended length and time scales but are often limited by a compromise between computational efficiency and accuracy. The conventional approach to CG nonbonded interactions uses pair potentials which, while computationally efficient, can neglect the inherently multibody contributions of the local environment of a site to its energy, due to degrees of freedom that were coarse-grained out. This effect often causes the CG potential to depend strongly on the overall system density, composition, or other properties, which limits its transferability to states other than the one at which it was parameterized. Here, we propose to incorporate multibody effects into CG potentials through additional nonbonded terms, beyond pair interactions, that depend in a mean-field manner on local densities of different atomic species. This approach is analogous to embedded atom and bond-order models that seek to capture multibody electronic effects in metallic systems. We show that the relative entropy coarse-graining framework offers a systematic route to parameterizing such local density potentials. We then characterize this approach in the development of implicit solvation strategies for interactions between model hydrophobes in an aqueous environment.
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Affiliation(s)
- Tanmoy Sanyal
- Department of Chemical Engineering, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - M Scott Shell
- Department of Chemical Engineering, University of California Santa Barbara, Santa Barbara, California 93106, USA
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49
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Gooneie A, Schuschnigg S, Holzer C. A Review of Multiscale Computational Methods in Polymeric Materials. Polymers (Basel) 2017; 9:E16. [PMID: 30970697 PMCID: PMC6432151 DOI: 10.3390/polym9010016] [Citation(s) in RCA: 86] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Revised: 12/07/2016] [Accepted: 12/22/2016] [Indexed: 11/17/2022] Open
Abstract
Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.
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Affiliation(s)
- Ali Gooneie
- Chair of Polymer Processing, Montanuniversitaet Leoben, Otto Gloeckel-Strasse 2, 8700 Leoben, Austria.
| | - Stephan Schuschnigg
- Chair of Polymer Processing, Montanuniversitaet Leoben, Otto Gloeckel-Strasse 2, 8700 Leoben, Austria.
| | - Clemens Holzer
- Chair of Polymer Processing, Montanuniversitaet Leoben, Otto Gloeckel-Strasse 2, 8700 Leoben, Austria.
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50
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Dunn NJH, Foley TT, Noid WG. Van der Waals Perspective on Coarse-Graining: Progress toward Solving Representability and Transferability Problems. Acc Chem Res 2016; 49:2832-2840. [PMID: 27993007 DOI: 10.1021/acs.accounts.6b00498] [Citation(s) in RCA: 71] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Low-resolution coarse-grained (CG) models provide the necessary efficiency for simulating phenomena that are inaccessible to more detailed models. However, in order to realize their considerable promise, CG models must accurately describe the relevant physical forces and provide useful predictions. By formally integrating out the unnecessary details from an all-atom (AA) model, "bottom-up" approaches can, at least in principle, quantitatively reproduce the structural and thermodynamic properties of the AA model that are observable at the CG resolution. In practice, though, bottom-up approaches only approximate this "exact coarse-graining" procedure. The resulting models typically reproduce the intermolecular structure of AA models at a single thermodynamic state point but often describe other state points less accurately and, moreover, tend to provide a poor description of thermodynamic properties. These two limitations have been coined the "transferability" and "representability" problems, respectively. Perhaps, the simplest and most commonly discussed manifestation of the representability problem regards the tendency of structure-based CG models to dramatically overestimate the pressure. Furthermore, when these models are adjusted to reproduce the pressure, they provide a poor description of the compressibility. More generally, it is sometimes suggested that CG models are fundamentally incapable of reproducing both structural and thermodynamic properties. After all, there is no such thing as a "free lunch"; any significant gain in computational efficiency should come at the cost of significant model limitations. At least in the case of structural and thermodynamic properties, though, we optimistically propose that this may be a false dichotomy. Accordingly, we have recently re-examined the "exact coarse-graining" procedure and investigated the intrinsic consequences of representing an AA model in reduced resolution. These studies clarify the origin and inter-relationship of representability and transferability problems. Both arise as consequences of transferring thermodynamic information from the high resolution configuration space and encoding this information into the many-body potential of mean force (PMF), that is, the potential that emerges from an exact coarse-graining procedure. At least in principle, both representability and transferability problems can be resolved by properly addressing this thermodynamic information. In particular, we have demonstrated that "pressure-matching" provides a practical and rigorous means for addressing the density dependence of the PMF. The resulting bottom-up models accurately reproduce the structure, equilibrium density, compressibility, and pressure equation of state for AA models of molecular liquids. Additionally, we have extended this approach to develop transferable potentials that provide similar accuracy for heptane-toluene mixtures. Moreover, these potentials provide predictive accuracy for modeling concentrations that were not considered in their parametrization. More generally, this work suggests a "van der Waals" perspective on coarse-graining, in which conventional structure-based methods accurately describe the configuration dependence of the PMF, while independent variational principles infer the thermodynamic information that is necessary to resolve representability and transferability problems.
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Affiliation(s)
- Nicholas J. H. Dunn
- Department
of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Thomas T. Foley
- Department
of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - William G. Noid
- Department
of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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