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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Ariskina K, Galliéro G, Obliger A. Confined fluid dynamics in a viscoelastic, amorphous, and microporous medium: Study of a kerogen by molecular simulations and the generalized Langevin equation. J Chem Phys 2024; 161:124901. [PMID: 39319658 DOI: 10.1063/5.0225299] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2024] [Accepted: 09/10/2024] [Indexed: 09/26/2024] Open
Abstract
We combine the use of molecular dynamics simulations and the generalized Langevin equation to study the diffusion of a fluid adsorbed within kerogen, the main organic phase of shales. As a class of microporous and amorphous materials that can exhibit significant adsorption-induced swelling, the dynamics of the kerogen's microstructure is expected to play an important role in the confined fluid dynamics. This role is investigated by conducting all-atom simulations with or without solid dynamics. Whenever the dynamics coupling between the fluid and solid is accounted for, we show that the fluid dynamics displays some qualitative differences compared to bulk fluids, which can be modulated by the amount of adsorbed fluid owing to adsorption-induced swelling. We highlight that working with the memory kernel, the central time correlation function of the generalized Langevin equation, allows the fingerprint of the dynamics of the solid to appear on that of the fluid. Interestingly, we observe that the memory kernels of fluid diffusion in kerogen qualitatively behave as those of tagged particles in supercooled liquids. We emphasize the importance of reproducing the velocity-force correlation function to validate the memory kernel numerically obtained as confinement enhances the numerical instabilities. This route is interesting as it opens the way for modeling the impact of fluid concentration on the diffusion coefficient in such ultra-confining cases.
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Affiliation(s)
- Kristina Ariskina
- Laboratoire des Fluides Complexes et leurs Réservoirs, University of Pau and Pays de l'Adour - E2S - TOTAL - CNRS, UMR 5150, 64000 Pau, France
| | - Guillaume Galliéro
- Laboratoire des Fluides Complexes et leurs Réservoirs, University of Pau and Pays de l'Adour - E2S - TOTAL - CNRS, UMR 5150, 64000 Pau, France
| | - Amaël Obliger
- Institut des Sciences Moléculaires, University of Bordeaux - Bordeaux INP - CNRS, UMR 5255, F-33400 Talence, France
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3
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Te Vrugt M, Topp L, Wittkowski R, Heuer A. Microscopic derivation of the thin film equation using the Mori-Zwanzig formalism. J Chem Phys 2024; 161:094904. [PMID: 39225531 DOI: 10.1063/5.0217535] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2024] [Accepted: 07/19/2024] [Indexed: 09/04/2024] Open
Abstract
The hydrodynamics of thin films is typically described using macroscopic models whose connection to the microscopic particle dynamics is a subject of ongoing research. Existing methods based on density functional theory provide a good description of static thin films but are not sufficient for understanding nonequilibrium dynamics. In this work, we present a microscopic derivation of the thin film equation using the Mori-Zwanzig projection operator formalism. This method allows to directly obtain the correct gradient dynamics structure along with microscopic expressions for mobility and free energy. Our results are verified against molecular dynamics simulations for both simple fluids and polymers.
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Affiliation(s)
- Michael Te Vrugt
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Leon Topp
- Institute of Physical Chemistry, Universität Münster, 48149 Münster, Germany
| | - Raphael Wittkowski
- Institute of Theoretical Physics, Center for Soft Nanoscience, Universität Münster, 48149 Münster, Germany
| | - Andreas Heuer
- Institute of Physical Chemistry, Universität Münster, 48149 Münster, Germany
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4
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Postnikov EB, Sokolov IM. Generalized Langevin subdiffusion in channels: The bath always wins. Phys Rev E 2024; 110:034104. [PMID: 39425319 DOI: 10.1103/physreve.110.034104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2024] [Accepted: 08/12/2024] [Indexed: 10/21/2024]
Abstract
We consider subdiffusive motion, modeled by the generalized Langevin equation in an equilibrium setting, of tracer particles in channels of indefinite length in the x direction: the channels of varying width and the channels with sinusoidally meandering midline. The subdiffusion in the x direction is not affected by constraints put by the channel. This is especially astonishing for meandering channels whose centerline might be quite long. The same behavior is seen in a holonomic model of a bead on a sinusoidal and meandering wire, where some analytic insights are possible.
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5
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Ge P, Zhang Z, Lei H. Data-Driven Learning of the Generalized Langevin Equation with State-Dependent Memory. PHYSICAL REVIEW LETTERS 2024; 133:077301. [PMID: 39213577 DOI: 10.1103/physrevlett.133.077301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2023] [Revised: 02/27/2024] [Accepted: 07/12/2024] [Indexed: 09/04/2024]
Abstract
We present a data-driven method to learn stochastic reduced models of complex systems that retain a state-dependent memory beyond the standard generalized Langevin equation with a homogeneous kernel. The constructed model naturally encodes the heterogeneous energy dissipation by jointly learning a set of state features and the non-Markovian coupling among the features. Numerical results demonstrate the limitation of the standard generalized Langevin equation and the essential role of the broadly overlooked state-dependency nature in predicting molecule kinetics related to conformation relaxation and transition.
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Affiliation(s)
| | | | - Huan Lei
- Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, USA
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6
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Klippenstein V, Wolf N, van der Vegt NFA. A Gauss-Newton method for iterative optimization of memory kernels for generalized Langevin thermostats in coarse-grained molecular dynamics simulations. J Chem Phys 2024; 160:204115. [PMID: 38804493 DOI: 10.1063/5.0203832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Accepted: 05/08/2024] [Indexed: 05/29/2024] Open
Abstract
In molecular dynamics simulations, dynamically consistent coarse-grained (CG) models commonly use stochastic thermostats to model friction and fluctuations that are lost in a CG description. While Markovian, i.e., time-local, formulations of such thermostats allow for an accurate representation of diffusivities/long-time dynamics, a correct description of the dynamics on all time scales generally requires non-Markovian, i.e., non-time-local, thermostats. These thermostats typically take the form of a Generalized Langevin Equation (GLE) determined by a memory kernel. In this work, we use a Markovian embedded formulation of a position-independent GLE thermostat acting independently on each CG degree of freedom. Extracting the memory kernel of this CG model from atomistic reference data requires several approximations. Therefore, this task is best understood as an inverse problem. While our recently proposed approximate Newton scheme allows for the iterative optimization of memory kernels (IOMK), Markovian embedding remained potentially error-prone and computationally expensive. In this work, we present an IOMK-Gauss-Newton scheme (IOMK-GN) based on IOMK that allows for the direct parameterization of a Markovian embedded model.
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Affiliation(s)
- Viktor Klippenstein
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
| | - Niklas Wolf
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
| | - Nico F A van der Vegt
- Department of Chemistry, Technical University of Darmstadt, 64287 Darmstadt, Germany
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7
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Bag S, Meinel MK, Müller-Plathe F. Synthetic Force-Field Database for Training Machine Learning Models to Predict Mobility-Preserving Coarse-Grained Molecular-Simulation Potentials. J Chem Theory Comput 2024; 20:3046-3060. [PMID: 38593205 DOI: 10.1021/acs.jctc.4c00242] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2024]
Abstract
Balancing accuracy and efficiency is a common problem in molecular simulation. This tradeoff is evident in coarse-grained molecular dynamics simulation, which prioritizes efficiency, and all-atom molecular simulation, which prioritizes accuracy. Despite continuous efforts, creating a coarse-grained model that accurately captures both the system's structure and dynamics remains elusive. In this article, we present a data-driven approach for constructing coarse-grained models that aim to describe both the structure and dynamics of the system equally well. While the development of machine learning models is well-received in the scientific community, the significance of dataset creation for these models is often overlooked. However, data-driven approaches cannot progress without a robust dataset. To address this, we construct a database of synthetic coarse-grained potentials generated from unphysical all-atom models. A neural network is trained with the generated database to predict the coarse-grained potentials of real liquids. We evaluate their quality by calculating the combined loss of structural and dynamical accuracy upon coarse-graining. When we compare our machine learning-based coarse-grained potential with the one from iterative Boltzmann inversion, the machine learning prediction turns out better for all eight hydrocarbon liquids we studied. As all-atom surfaces turn more nonspherical, both ways of coarse-graining degrade. Still, the neural network outperforms iterative Boltzmann inversion in constructing good quality coarse-grained models for such cases. The synthetic database and the developed machine learning models are freely available to the community, and we believe that our approach will generate interest in efficiently deriving accurate coarse-grained models for liquids.
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Affiliation(s)
- Saientan Bag
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Peter-Grünberg-Str. 8, 64287 Darmstadt, Germany
| | - Melissa K Meinel
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Peter-Grünberg-Str. 8, 64287 Darmstadt, Germany
| | - Florian Müller-Plathe
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Peter-Grünberg-Str. 8, 64287 Darmstadt, Germany
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8
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Wiśniewski M, Łuczka J, Spiechowicz J. Effective mass approach to memory in non-Markovian systems. Phys Rev E 2024; 109:044116. [PMID: 38755811 DOI: 10.1103/physreve.109.044116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Accepted: 03/14/2024] [Indexed: 05/18/2024]
Abstract
Recent pioneering experiments on non-Markovian dynamics done, e.g., for active matter have demonstrated that our theoretical understanding of this challenging yet hot topic is rather incomplete and there is a wealth of phenomena still awaiting discovery. It is related to the fact that typically for simplification the Markovian approximation is employed and as a consequence the memory is neglected. Therefore, methods allowing to study memory effects are extremely valuable. We demonstrate that a non-Markovian system described by the Generalized Langevin Equation (GLE) for a Brownian particle of mass M can be approximated by the memoryless Langevin equation in which the memory effects are correctly reproduced solely via the effective mass M^{*} of the Brownian particle which is determined only by the form of the memory kernel. Our work lays the foundation for an impactful approach which allows one to readily study memory-related corrections to Markovian dynamics.
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Affiliation(s)
- M Wiśniewski
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Łuczka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Spiechowicz
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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9
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Silvano N, Barci DG. Emergent gauge symmetry in active Brownian matter. Phys Rev E 2024; 109:044605. [PMID: 38755850 DOI: 10.1103/physreve.109.044605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 04/04/2024] [Indexed: 05/18/2024]
Abstract
We investigate a two-dimensional system of interacting active Brownian particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the hydrodynamic regime with a constant density stationary state. Our findings reveal that, within a small density fluctuations regime, an emergent U(1) gauge symmetry arises, originated from the conservation of fluid vorticity. Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of "electric charge density" aligns with the local vorticity of the original fluid. We study in detail the case of a microscopic local two-body interaction. We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a nonlocal Frank free energy for a nematic fluid. We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (Pe) and the diffusion interaction constant (k_{d}).
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Affiliation(s)
- Nathan Silvano
- Center for Advanced Systems Understanding, Untermarkt 20, 02826 Görlitz, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany
- Departamento de Física Teórica, 20270-004 Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil
| | - Daniel G Barci
- Departamento de Física Teórica, 20270-004 Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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10
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Hsu T, Sadigh B, Bulatov V, Zhou F. Score Dynamics: Scaling Molecular Dynamics with Picoseconds Time Steps via Conditional Diffusion Model. J Chem Theory Comput 2024; 20:2335-2348. [PMID: 38489243 DOI: 10.1021/acs.jctc.3c01361] [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
We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular dynamics (MD) simulations. SD is centered around scores or derivatives of the transition log-probability with respect to the dynamical degrees of freedom. The latter play the same role as force fields in MD but are used in denoising diffusion probability models to generate discrete transitions of the dynamical variables in an SD time step, which can be orders of magnitude larger than a typical MD time step. In this work, we construct graph neural network-based SD models of realistic molecular systems that are evolved with 10 ps timesteps. We demonstrate the efficacy of SD with case studies of the alanine dipeptide and short alkanes in aqueous solution. Both equilibrium predictions derived from the stationary distributions of the conditional probability and kinetic predictions for the transition rates and transition paths are in good agreement with MD. Our current SD implementation is about 2 orders of magnitude faster than the MD counterpart for the systems studied in this work. Open challenges and possible future remedies to improve SD are also discussed.
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Affiliation(s)
- Tim Hsu
- Lawrence Livermore National Laboratory, Livermore, California 94551, United States
| | - Babak Sadigh
- Lawrence Livermore National Laboratory, Livermore, California 94551, United States
| | - Vasily Bulatov
- Lawrence Livermore National Laboratory, Livermore, California 94551, United States
| | - Fei Zhou
- Lawrence Livermore National Laboratory, Livermore, California 94551, United States
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11
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Zhang XZ, Shi R, Lu ZY, Qian HJ. Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties. JACS AU 2024; 4:1018-1030. [PMID: 38559727 PMCID: PMC10976574 DOI: 10.1021/jacsau.3c00756] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Revised: 02/23/2024] [Accepted: 02/28/2024] [Indexed: 04/04/2024]
Abstract
The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.
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Affiliation(s)
| | | | - Zhong-Yuan Lu
- State Key Laboratory of Supramolecular
Structure and Materials, Institute of Theoretical Chemistry, College
of Chemistry, Jilin University, Changchun 130021, China
| | - Hu-Jun Qian
- State Key Laboratory of Supramolecular
Structure and Materials, Institute of Theoretical Chemistry, College
of Chemistry, Jilin University, Changchun 130021, China
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12
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Shea J, Jung G, Schmid F. Force renormalization for probes immersed in an active bath. SOFT MATTER 2024; 20:1767-1785. [PMID: 38305056 DOI: 10.1039/d3sm01387a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/03/2024]
Abstract
Langevin equations or generalized Langevin equations (GLEs) are popular models for describing the motion of a particle in a fluid medium in an effective manner. Here we examine particles immersed in an inherently nonequilibrium fluid, i.e., an active bath, which are subject to an external force. Specifically, we consider two types of forces that are highly relevant for microrheological studies: A harmonic, trapping force and a constant, "drag" force. We study such systems by molecular simulations and use the simulation data to extract an effective GLE description. We find that within this description, in an active bath, the external force in the GLE is not equal to the physical external force, but rather a renormalized external force, which can be significantly smaller. The effect cannot be attributed to the mere temperature renormalization, which is also observed.
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Affiliation(s)
- Jeanine Shea
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.
| | - Gerhard Jung
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany.
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13
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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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14
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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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15
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Cammarata MDM, Contin MD, Negri RM, Factorovich MH. Diffusion Coefficients of Variable-Size Amphiphilic Additives in a Glass-Forming Polyethylene Matrix. J Phys Chem B 2024; 128:312-328. [PMID: 38146058 DOI: 10.1021/acs.jpcb.3c04904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2023]
Abstract
Diffusion of additives in polymers is an important issue in the plastics industry since migratory-type molecules are widely used to tune the properties of polymeric composites. Predicting the diffusional behavior of new additives can minimize the need for repetitive experiments. This work presents molecular dynamics simulations at the microsecond time scale and uses the MARTINI force field to estimate self-diffusion coefficients, D, of six monounsaturated amides and their analogs carboxylic acids in polyethylene matrices (PE, MW = 5600 Da). The results are strongly influenced by the glass-forming properties of the PE matrix, which we characterize by three distinct temperatures. The metastability region (T < 325 K), the glass transition temperature (Tg = 256-260 K), and the end of the transition (T ≅ 200 K). Self-diffusion mechanisms are inferred from the results of the dependence of D on the molecular mass of the additive, observing a Rouse-like behavior at high temperatures and deviations from it within the metastability region of the matrix. Interestingly, D values are nonsensitive to the nature of the considered polar head for additives of similar size. The temperature-dependent behavior of D follows, at fixed additive size, a linear Arrhenius pattern at high temperatures and a super Arrhenius trend at lower temperatures, which is well represented with a power law equation as predicted by the Mode Coupling Theory (MCT). We offer a conceptual explanation for the observed super-Arrhenius behavior. This explanation draws on Truhlar and Kohen's interpretation of the available energies at both the initial and the transition states along the diffusion pathway. The matrix's mobility significantly affects solute self-diffusion, yielding equal activation enthalpies for the Arrhenius region or the same power law parameters for the super-Arrhenius regime. Finally, we establish a one-to-one time-equivalence of the self-diffusion processes between CG and all-atom systems for the largest additives and the PE matrix in the high-temperature regime.
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Affiliation(s)
- María Del Mar Cammarata
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
| | - Mario D Contin
- Departamento de Ciencias Química, Catedra de Química Analítica. Facultad de Farmacia y Bioquímica, Universidad de Buenos Aires, Junín 954, Buenos Aires C1113AAD, Argentina
| | - R Martín Negri
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
| | - Matias H Factorovich
- Departamento de Química Inorgánica, Analítica y Química Física/INQUIMAE, Facultad de Ciencias y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, Buenos Aires C1428EHA, Argentina
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16
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Lyu L, Lei H. Construction of Coarse-Grained Molecular Dynamics with Many-Body Non-Markovian Memory. PHYSICAL REVIEW LETTERS 2023; 131:177301. [PMID: 37955502 DOI: 10.1103/physrevlett.131.177301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Accepted: 09/19/2023] [Indexed: 11/14/2023]
Abstract
We introduce a machine-learning-based coarse-grained molecular dynamics model that faithfully retains the many-body nature of the intermolecular dissipative interactions. Unlike the common empirical coarse-grained models, the present model is constructed based on the Mori-Zwanzig formalism and naturally inherits the heterogeneous state-dependent memory term rather than matching the mean-field metrics such as the velocity autocorrelation function. Numerical results show that preserving the many-body nature of the memory term is crucial for predicting the collective transport and diffusion processes, where empirical forms generally show limitations.
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Affiliation(s)
- Liyao Lyu
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Huan Lei
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, USA
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17
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Taylor PA, Stevens MJ. Explicit solvent machine-learned coarse-grained model of sodium polystyrene sulfonate to capture polymer structure and dynamics. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:97. [PMID: 37831216 DOI: 10.1140/epje/s10189-023-00355-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Accepted: 09/26/2023] [Indexed: 10/14/2023]
Abstract
Strongly charged polyelectrolytes (PEs) demonstrate complex solution behavior as a function of chain length, concentrations, and ionic strength. The viscosity behavior is important to understand and is a core quantity for many applications, but aspects remain a challenge. Molecular dynamics simulations using implicit solvent coarse-grained (CG) models successfully reproduce structure, but are often inappropriate for calculating viscosities. To address the need for CG models which reproduce viscoelastic properties of one of the most studied PEs, sodium polystyrene sulfonate (NaPSS), we report our recent efforts in using Bayesian optimization to develop CG models of NaPSS which capture both polymer structure and dynamics in aqueous solutions with explicit solvent. We demonstrate that our explicit solvent CG NaPSS model with the ML-BOP water model [Chan et al. Nat Commun 10, 379 (2019)] quantitatively reproduces NaPSS chain statistics and solution structure. The new explicit solvent CG model is benchmarked against diffusivities from atomistic simulations and experimental specific viscosities for short chains. We also show that our Bayesian-optimized CG model is transferable to larger chain lengths across a range of concentrations. Overall, this work provides a machine-learned model to probe the structural, dynamic, and rheological properties of polyelectrolytes such as NaPSS and aids in the design of novel, strongly charged polymers with tunable structural and viscoelastic properties.
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Affiliation(s)
- Phillip A Taylor
- Sandia National Laboratories, Center for Integrated Nanotechnologies, Albuquerque, NM, 87123, USA
| | - Mark J Stevens
- Sandia National Laboratories, Center for Integrated Nanotechnologies, Albuquerque, NM, 87123, USA.
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18
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Wand T, Heßler M, Kamps O. Memory Effects, Multiple Time Scales and Local Stability in Langevin Models of the S&P500 Market Correlation. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1257. [PMID: 37761556 PMCID: PMC10529658 DOI: 10.3390/e25091257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2023] [Revised: 08/16/2023] [Accepted: 08/22/2023] [Indexed: 09/29/2023]
Abstract
The analysis of market correlations is crucial for optimal portfolio selection of correlated assets, but their memory effects have often been neglected. In this work, we analyse the mean market correlation of the S&P500, which corresponds to the main market mode in principle component analysis. We fit a generalised Langevin equation (GLE) to the data whose memory kernel implies that there is a significant memory effect in the market correlation ranging back at least three trading weeks. The memory kernel improves the forecasting accuracy of the GLE compared to models without memory and hence, such a memory effect has to be taken into account for optimal portfolio selection to minimise risk or for predicting future correlations. Moreover, a Bayesian resilience estimation provides further evidence for non-Markovianity in the data and suggests the existence of a hidden slow time scale that operates on much slower times than the observed daily market data. Assuming that such a slow time scale exists, our work supports previous research on the existence of locally stable market states.
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Affiliation(s)
- Tobias Wand
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany;
- Center for Nonlinear Science Münster, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany;
| | - Martin Heßler
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany;
- Center for Nonlinear Science Münster, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany;
| | - Oliver Kamps
- Center for Nonlinear Science Münster, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany;
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19
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Gilbert BR, Thornburg ZR, Brier TA, Stevens JA, Grünewald F, Stone JE, Marrink SJ, Luthey-Schulten Z. Dynamics of chromosome organization in a minimal bacterial cell. Front Cell Dev Biol 2023; 11:1214962. [PMID: 37621774 PMCID: PMC10445541 DOI: 10.3389/fcell.2023.1214962] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2023] [Accepted: 07/10/2023] [Indexed: 08/26/2023] Open
Abstract
Computational models of cells cannot be considered complete unless they include the most fundamental process of life, the replication and inheritance of genetic material. By creating a computational framework to model systems of replicating bacterial chromosomes as polymers at 10 bp resolution with Brownian dynamics, we investigate changes in chromosome organization during replication and extend the applicability of an existing whole-cell model (WCM) for a genetically minimal bacterium, JCVI-syn3A, to the entire cell-cycle. To achieve cell-scale chromosome structures that are realistic, we model the chromosome as a self-avoiding homopolymer with bending and torsional stiffnesses that capture the essential mechanical properties of dsDNA in Syn3A. In addition, the conformations of the circular DNA must avoid overlapping with ribosomes identitied in cryo-electron tomograms. While Syn3A lacks the complex regulatory systems known to orchestrate chromosome segregation in other bacteria, its minimized genome retains essential loop-extruding structural maintenance of chromosomes (SMC) protein complexes (SMC-scpAB) and topoisomerases. Through implementing the effects of these proteins in our simulations of replicating chromosomes, we find that they alone are sufficient for simultaneous chromosome segregation across all generations within nested theta structures. This supports previous studies suggesting loop-extrusion serves as a near-universal mechanism for chromosome organization within bacterial and eukaryotic cells. Furthermore, we analyze ribosome diffusion under the influence of the chromosome and calculate in silico chromosome contact maps that capture inter-daughter interactions. Finally, we present a methodology to map the polymer model of the chromosome to a Martini coarse-grained representation to prepare molecular dynamics models of entire Syn3A cells, which serves as an ultimate means of validation for cell states predicted by the WCM.
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Affiliation(s)
- Benjamin R. Gilbert
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, United States
| | - Zane R. Thornburg
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, United States
| | - Troy A. Brier
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, United States
| | - Jan A. Stevens
- Molecular Dynamics Group, Groningen Biomolecular Sciences and Biotechnology Institute, University of Groningen, Groningen, Netherlands
| | - Fabian Grünewald
- Molecular Dynamics Group, Groningen Biomolecular Sciences and Biotechnology Institute, University of Groningen, Groningen, Netherlands
| | - John E. Stone
- NVIDIA Corporation, Santa Clara, CA, United States
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL, United States
| | - Siewert J. Marrink
- Molecular Dynamics Group, Groningen Biomolecular Sciences and Biotechnology Institute, University of Groningen, Groningen, Netherlands
| | - Zaida Luthey-Schulten
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, United States
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL, United States
- NSF Center for the Physics of Living Cells, Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, United States
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20
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Sokhan VP, Seaton MA, Todorov IT. Phase behaviour of coarse-grained fluids. SOFT MATTER 2023. [PMID: 37470164 DOI: 10.1039/d3sm00835e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/21/2023]
Abstract
Soft condensed matter structures often challenge us with complex many-body phenomena governed by collective modes spanning wide spatial and temporal domains. In order to successfully tackle such problems, mesoscopic coarse-grained (CG) statistical models are being developed, providing a dramatic reduction in computational complexity. CG models provide an intermediate step in the complex statistical framework of linking the thermodynamics of condensed phases with the properties of their constituent atoms and molecules. These allow us to offload part of the problem to the CG model itself and reformulate the remainder in terms of reduced CG phase space. However, such exchange of pawns to chess pieces, or 'Hamiltonian renormalization', is a radical step and the thermodynamics of the primary atomic and CG models could be quite distinct. Here, we present a comprehensive study of the phase diagram including binodal and interfacial properties of a dissipative particle dynamics (DPD) model, extended to include finite-range attraction to support the liquid-gas equilibrium. Despite the similarities with the atomic model potentials, its phase envelope is markedly different featuring several anomalies such as an unusually broad liquid range, change in concavity of the liquid coexistence branch with variation of the model parameters, volume contraction on fusion, temperature of maximum density in the liquid phase and negative thermal expansion in the solid phase. These results provide new insight into the connection between simple potential models and complex emergent condensed matter phenomena.
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Affiliation(s)
- V P Sokhan
- Scientific Computing Department, Science and Technology Facilities Council, STFC Daresbury Laboratory, Sci-Tech Daresbury, Keckwick Lane, Daresbury, Cheshire WA4 4AD, UK.
| | - M A Seaton
- Scientific Computing Department, Science and Technology Facilities Council, STFC Daresbury Laboratory, Sci-Tech Daresbury, Keckwick Lane, Daresbury, Cheshire WA4 4AD, UK.
| | - I T Todorov
- Scientific Computing Department, Science and Technology Facilities Council, STFC Daresbury Laboratory, Sci-Tech Daresbury, Keckwick Lane, Daresbury, Cheshire WA4 4AD, UK.
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21
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Liwo A, Pyrka M, Czaplewski C, Peng X, Niemi AJ. Long-Time Dynamics of Selected Molecular-Motor Components Using a Physics-Based Coarse-Grained Approach. Biomolecules 2023; 13:941. [PMID: 37371521 PMCID: PMC10296118 DOI: 10.3390/biom13060941] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Revised: 05/26/2023] [Accepted: 05/30/2023] [Indexed: 06/29/2023] Open
Abstract
Molecular motors are essential for the movement and transportation of macromolecules in living organisms. Among them, rotatory motors are particularly efficient. In this study, we investigated the long-term dynamics of the designed left-handed alpha/alpha toroid (PDB: 4YY2), the RBM2 flagellum protein ring from Salmonella (PDB: 6SD5), and the V-type Na+-ATPase rotor in Enterococcus hirae (PDB: 2BL2) using microcanonical and canonical molecular dynamics simulations with the coarse-grained UNRES force field, including a lipid-membrane model, on a millisecond laboratory time scale. Our results demonstrate that rotational motion can occur with zero total angular momentum in the microcanonical regime and that thermal motions can be converted into net rotation in the canonical regime, as previously observed in simulations of smaller cyclic molecules. For 6SD5 and 2BL2, net rotation (with a ratcheting pattern) occurring only about the pivot of the respective system was observed in canonical simulations. The extent and direction of the rotation depended on the initial conditions. This result suggests that rotatory molecular motors can convert thermal oscillations into net rotational motion. The energy from ATP hydrolysis is required probably to set the direction and extent of rotation. Our findings highlight the importance of molecular-motor structures in facilitating movement and transportation within living organisms.
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Affiliation(s)
- Adam Liwo
- Faculty of Chemistry, University of Gdańsk, Fahrenheit Union of Universities, Wita Stwosza 63, 80-308 Gdańsk, Poland; (M.P.); (C.C.)
| | - Maciej Pyrka
- Faculty of Chemistry, University of Gdańsk, Fahrenheit Union of Universities, Wita Stwosza 63, 80-308 Gdańsk, Poland; (M.P.); (C.C.)
- Department of Physics and Biophysics, University of Warmia and Mazury, ul. Oczapowskiego 4, 10-719 Olsztyn, Poland
| | - Cezary Czaplewski
- Faculty of Chemistry, University of Gdańsk, Fahrenheit Union of Universities, Wita Stwosza 63, 80-308 Gdańsk, Poland; (M.P.); (C.C.)
| | - Xubiao Peng
- Center for Quantum Technology Research, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China;
| | - Antti J. Niemi
- Nordita, Stockholm University and Uppsala University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden;
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22
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Scalfi L, Vitali D, Kiefer H, Netz RR. Frequency-dependent hydrodynamic finite size correction in molecular simulations reveals the long-time hydrodynamic tail. J Chem Phys 2023; 158:2890455. [PMID: 37184000 DOI: 10.1063/5.0151406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 04/07/2023] [Indexed: 05/16/2023] Open
Abstract
Finite-size effects are challenging in molecular dynamics simulations because they have significant effects on computed static and dynamic properties, in particular diffusion constants, friction coefficients, and time- or frequency-dependent response functions. We investigate the influence of periodic boundary conditions on the velocity autocorrelation function and the frequency-dependent friction of a particle in a fluid, and show that the long-time behavior (starting at the picosecond timescale) is significantly affected. We develop an analytical correction allowing us to subtract the periodic boundary condition effects. By this, we unmask the power-law long-time tails of the memory kernel and the velocity autocorrelation function in liquid water and a Lennard-Jones fluid from simulations with rather small box sizes.
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Affiliation(s)
- Laura Scalfi
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Domenico Vitali
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Henrik Kiefer
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
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23
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Dominic AJ, Cao S, Montoya-Castillo A, Huang X. Memory Unlocks the Future of Biomolecular Dynamics: Transformative Tools to Uncover Physical Insights Accurately and Efficiently. J Am Chem Soc 2023; 145:9916-9927. [PMID: 37104720 DOI: 10.1021/jacs.3c01095] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/29/2023]
Abstract
Conformational changes underpin function and encode complex biomolecular mechanisms. Gaining atomic-level detail of how such changes occur has the potential to reveal these mechanisms and is of critical importance in identifying drug targets, facilitating rational drug design, and enabling bioengineering applications. While the past two decades have brought Markov state model techniques to the point where practitioners can regularly use them to glimpse the long-time dynamics of slow conformations in complex systems, many systems are still beyond their reach. In this Perspective, we discuss how including memory (i.e., non-Markovian effects) can reduce the computational cost to predict the long-time dynamics in these complex systems by orders of magnitude and with greater accuracy and resolution than state-of-the-art Markov state models. We illustrate how memory lies at the heart of successful and promising techniques, ranging from the Fokker-Planck and generalized Langevin equations to deep-learning recurrent neural networks and generalized master equations. We delineate how these techniques work, identify insights that they can offer in biomolecular systems, and discuss their advantages and disadvantages in practical settings. We show how generalized master equations can enable the investigation of, for example, the gate-opening process in RNA polymerase II and demonstrate how our recent advances tame the deleterious influence of statistical underconvergence of the molecular dynamics simulations used to parameterize these techniques. This represents a significant leap forward that will enable our memory-based techniques to interrogate systems that are currently beyond the reach of even the best Markov state models. We conclude by discussing some current challenges and future prospects for how exploiting memory will open the door to many exciting opportunities.
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Affiliation(s)
- Anthony J Dominic
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Siqin Cao
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | | | - Xuhui Huang
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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24
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de Las Heras D, Zimmermann T, Sammüller F, Hermann S, Schmidt M. Perspective: How to overcome dynamical density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:271501. [PMID: 37023762 DOI: 10.1088/1361-648x/accb33] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2023] [Accepted: 04/06/2023] [Indexed: 06/19/2023]
Abstract
We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and practical challenges that lie ahead, we discuss and exemplify the limitations of dynamical density functional theory (DDFT). Instead of the implied adiabatic sequence of equilibrium states that this approach provides as a makeshift for the true time evolution, we posit that the pending theoretical tasks lie in developing a systematic understanding of the dynamical functional relationships that govern the genuine nonequilibrium physics. While static density functional theory gives a comprehensive account of the equilibrium properties of many-body systems, we argue that power functional theory is the only present contender to shed similar insights into nonequilibrium dynamics, including the recognition and implementation of exact sum rules that result from the Noether theorem. As a demonstration of the power functional point of view, we consider an idealized steady sedimentation flow of the three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from the mean motion to the internal force field. The trained model is capable of both predicting and designing the steady state dynamics universally for various target density modulations. This demonstrates the significant potential of using such techniques in nonequilibrium many-body physics and overcomes both the conceptual constraints of DDFT as well as the limited availability of its analytical functional approximations.
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Affiliation(s)
- Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Toni Zimmermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
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25
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Klippenstein V, van der Vegt NFA. Bottom-Up Informed and Iteratively Optimized Coarse-Grained Non-Markovian Water Models with Accurate Dynamics. J Chem Theory Comput 2023; 19:1099-1110. [PMID: 36745567 PMCID: PMC9979609 DOI: 10.1021/acs.jctc.2c00871] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Molecular dynamics (MD) simulations based on coarse-grained (CG) particle models of molecular liquids generally predict accelerated dynamics and misrepresent the time scales for molecular vibrations and diffusive motions. The parametrization of Generalized Langevin Equation (GLE) thermostats based on the microscopic dynamics of the fine-grained model provides a promising route to address this issue, in conjunction with the conservative interactions of the CG model obtained with standard coarse graining methods, such as iterative Boltzmann inversion, force matching, or relative entropy minimization. We report the application of a recently introduced bottom-up dynamic coarse graining method, based on the Mori-Zwanzig formalism, which provides accurate estimates of isotropic GLE memory kernels for several CG models of liquid water. We demonstrate that, with an additional iterative optimization of the memory kernels (IOMK) for the CG water models based on a practical iterative optimization technique, the velocity autocorrelation function of liquid water can be represented very accurately within a few iterations. By considering the distinct Van Hove function, we demonstrate that, with the presented methods, an accurate representation of structural relaxation can be achieved. We consider several distinct CG potentials to study how the choice of the CG potential affects the performance of bottom-up informed and iteratively optimized models.
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26
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Sieradzan AK, Sans-Duñó J, Lubecka EA, Czaplewski C, Lipska AG, Leszczyński H, Ocetkiewicz KM, Proficz J, Czarnul P, Krawczyk H, Liwo A. Optimization of parallel implementation of UNRES package for coarse-grained simulations to treat large proteins. J Comput Chem 2023; 44:602-625. [PMID: 36378078 DOI: 10.1002/jcc.27026] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Revised: 09/19/2022] [Accepted: 10/17/2022] [Indexed: 11/16/2022]
Abstract
We report major algorithmic improvements of the UNRES package for physics-based coarse-grained simulations of proteins. These include (i) introduction of interaction lists to optimize computations, (ii) transforming the inertia matrix to a pentadiagonal form to reduce computing and memory requirements, (iii) removing explicit angles and dihedral angles from energy expressions and recoding the most time-consuming energy/force terms to minimize the number of operations and to improve numerical stability, (iv) using OpenMP to parallelize those sections of the code for which distributed-memory parallelization involves unfavorable computing/communication time ratio, and (v) careful memory management to minimize simultaneous access of distant memory sections. The new code enables us to run molecular dynamics simulations of protein systems with size exceeding 100,000 amino-acid residues, reaching over 1 ns/day (1 μs/day in all-atom timescale) with 24 cores for proteins of this size. Parallel performance of the code and comparison of its performance with that of AMBER, GROMACS and MARTINI 3 is presented.
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Affiliation(s)
- Adam K Sieradzan
- Faculty of Chemistry, University of Gdańsk, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland.,Centre of Informatics Tri-city Academic Supercomputer and Network (CI TASK), Gdańsk University of Technology, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland
| | - Jordi Sans-Duñó
- Department of Chemistry, University of Lleida, Lleida, Spain
| | - Emilia A Lubecka
- Faculty of Electronics, Telecommunication and Informatics, Gdańsk University of Technology, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland
| | - Cezary Czaplewski
- Faculty of Chemistry, University of Gdańsk, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland.,Centre of Informatics Tri-city Academic Supercomputer and Network (CI TASK), Gdańsk University of Technology, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland
| | - Agnieszka G Lipska
- Faculty of Chemistry, University of Gdańsk, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland.,Centre of Informatics Tri-city Academic Supercomputer and Network (CI TASK), Gdańsk University of Technology, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland
| | - Henryk Leszczyński
- Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland
| | - Krzysztof M Ocetkiewicz
- Centre of Informatics Tri-city Academic Supercomputer and Network (CI TASK), Gdańsk University of Technology, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland
| | - Jerzy Proficz
- Centre of Informatics Tri-city Academic Supercomputer and Network (CI TASK), Gdańsk University of Technology, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland
| | - Paweł Czarnul
- Faculty of Electronics, Telecommunication and Informatics, Gdańsk University of Technology, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland
| | - Henryk Krawczyk
- Centre of Informatics Tri-city Academic Supercomputer and Network (CI TASK), Gdańsk University of Technology, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland.,Faculty of Electronics, Telecommunication and Informatics, Gdańsk University of Technology, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland
| | - Adam Liwo
- Faculty of Chemistry, University of Gdańsk, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland.,Centre of Informatics Tri-city Academic Supercomputer and Network (CI TASK), Gdańsk University of Technology, Fahrenheit Union of Universities in Gdańsk, Gdańsk, Poland
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27
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Jin J, Schweizer KS, Voth GA. Understanding dynamics in coarse-grained models. II. Coarse-grained diffusion modeled using hard sphere theory. J Chem Phys 2023; 158:034104. [PMID: 36681632 DOI: 10.1063/5.0116300] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of the scaling relationship was not possible due to the semi-empirical nature. In this second paper, an analytical excess entropy scaling relation is derived for bottom-up CG systems. At the single-site CG resolution, effective hard sphere systems are constructed that yield near-identical dynamical properties as the target CG systems by taking advantage of how hard sphere dynamics and excess entropy can be analytically expressed in terms of the liquid packing fraction. Inspired by classical equilibrium perturbation theories and recent advances in constructing hard sphere models for predicting activated dynamics of supercooled liquids, we propose a new approach for understanding the diffusion of molecular liquids in the normal regime using hard sphere reference fluids. The proposed "fluctuation matching" is designed to have the same amplitude of long wavelength density fluctuations (dimensionless compressibility) as the CG system. Utilizing the Enskog theory to derive an expression for hard sphere diffusion coefficients, a bridge between the CG dynamics and excess entropy is then established. The CG diffusion coefficient can be roughly estimated using various equations of the state, and an accurate prediction of accelerated CG dynamics at different temperatures is also possible in advance of running any CG simulation. By introducing another layer of coarsening, these findings provide a more rigorous method to assess excess entropy scaling and understand the accelerated CG dynamics of molecular fluids.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Kenneth S Schweizer
- Department of Material Science, Department of Chemistry, Department of Chemical and Biomolecular Engineering, and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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28
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Jin J, Schweizer KS, Voth GA. Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship. J Chem Phys 2023; 158:034103. [PMID: 36681649 DOI: 10.1063/5.0116299] [Citation(s) in RCA: 15] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Kenneth S Schweizer
- Department of Material Science, Department of Chemistry, Department of Chemical and Biomolecular Engineering, and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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29
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She Z, Ge P, Lei H. Data-driven construction of stochastic reduced dynamics encoded with non-Markovian features. J Chem Phys 2023; 158:034102. [PMID: 36681628 DOI: 10.1063/5.0130033] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale separations, where the reduced dynamics generally exhibits pronounced memory and non-white noise terms. We propose a data-driven approach to learn the reduced model of multi-dimensional resolved variables that faithfully retains the non-Markovian dynamics. Different from the common approaches based on the direct construction of the memory function, the present approach seeks a set of non-Markovian features that encode the history of the resolved variables and establishes a joint learning of the extended Markovian dynamics in terms of both the resolved variables and these features. The training is based on matching the evolution of the correlation functions of the extended variables that can be directly obtained from the ones of the resolved variables. The constructed model essentially approximates the multi-dimensional generalized Langevin equation and ensures numerical stability without empirical treatment. We demonstrate the effectiveness of the method by constructing the reduced models of molecular systems in terms of both one-dimensional and four-dimensional resolved variables.
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Affiliation(s)
- Zhiyuan She
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Pei Ge
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Huan Lei
- Department of Computational Mathematics, Science and Engineering and Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, USA
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30
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Brünig F, Daldrop JO, Netz RR. Pair-Reaction Dynamics in Water: Competition of Memory, Potential Shape, and Inertial Effects. J Phys Chem B 2022; 126:10295-10304. [PMID: 36473702 PMCID: PMC9761671 DOI: 10.1021/acs.jpcb.2c05923] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Revised: 11/11/2022] [Indexed: 12/12/2022]
Abstract
When described by a one-dimensional reaction coordinate, pair-reaction rates in a solvent depend, in addition to the potential barrier height and the friction coefficient, on the potential shape, the effective mass, and the friction relaxation spectrum, but a rate theory that accurately accounts for all of these effects does not exist. After a review of classical reaction-rate theories, we show how to extract all parameters of the generalized Langevin equation (GLE) and, in particular, the friction memory function from molecular dynamics (MD) simulations of two prototypical pair reactions in water, the dissociation of NaCl and of two methane molecules. The memory exhibits multiple time scales and, for NaCl, pronounced oscillatory components. Simulations of the GLE by Markovian embedding techniques accurately reproduce the pair-reaction kinetics from MD simulations without any fitting parameters, which confirms the accuracy of the approximative form of the GLE and of the parameter extraction techniques. By modification of the GLE parameters, we investigate the relative importance of memory, mass, and potential shape effects. Neglect of memory slows down NaCl and methane dissociation by roughly a factor of 2; neglect of mass accelerates reactions by a similar factor, and the harmonic approximation of the potential shape gives rise to slight acceleration. This partial error cancellation explains why Kramers' theory, which neglects memory effects and treats the potential shape in harmonic approximation, describes reaction rates better than more sophisticated theories. In essence, all three effects, friction memory, inertia, and the potential shape nonharmonicity, are important to quantitatively describe pair-reaction kinetics in water.
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Affiliation(s)
- Florian
N. Brünig
- Fachbereich Physik, Freie Universität
Berlin, Arnimallee 14, 14195Berlin, Germany
| | - Jan O. Daldrop
- Fachbereich Physik, Freie Universität
Berlin, Arnimallee 14, 14195Berlin, Germany
| | - Roland R. Netz
- Fachbereich Physik, Freie Universität
Berlin, Arnimallee 14, 14195Berlin, Germany
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31
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Te Vrugt M, Wittkowski R. Perspective: New directions in dynamical density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:041501. [PMID: 35917827 DOI: 10.1088/1361-648x/ac8633] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2022] [Accepted: 08/01/2022] [Indexed: 06/15/2023]
Abstract
Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.
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Affiliation(s)
- Michael Te Vrugt
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
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32
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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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33
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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: 84] [Impact Index Per Article: 42.0] [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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34
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Shea J, Jung G, Schmid F. Passive probe particle in an active bath: can we tell it is out of equilibrium? SOFT MATTER 2022; 18:6965-6973. [PMID: 36069290 DOI: 10.1039/d2sm00905f] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We study a passive probe immersed in a fluid of active particles. Despite the system's non-equilibrium nature, the trajectory of the probe does not exhibit non-equilibrium signatures: its velocity distribution remains Gaussian, the second fluctuation dissipation theorem is not fundamentally violated, and the motion does not indicate breaking of time reversal symmetry. To tell that the probe is out of equilibrium requires examination of its behavior in tandem with that of the active fluid: the kinetic temperature of the probe does not equilibrate to that of the surrounding active particles. As a strategy to diagnose non-equilibrium from probe trajectories alone, we propose to examine their response to a small perturbation which reveals a non-equilibrium signature through a violation of the first fluctuation dissipation theorem.
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Affiliation(s)
- Jeanine Shea
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany.
| | - Gerhard Jung
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany.
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35
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Klippenstein V, van der Vegt N. Cross-Correlation Corrected Friction in Generalized Langevin Models: Application to the continuous Asakura-Oosawa Model. J Chem Phys 2022; 157:044103. [DOI: 10.1063/5.0093056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In a previous study we proposed a method to parameterize isotropic, configuration independent, non-Markovian generalized Langevin thermostats to achieve dynamic consistency in coarse-grained models. In the current study, by applying the same strategy, we develop coarse-grained implicit solvent models for the continuous Asakura-Oosawa model, which under certain conditions allows to develop very accurate coarse-grained potentials. By developing coarse-grained models for different reference systems with varying parameters, we test the broader applicability of the proposed procedure and demonstrate the relevance of accurate coarse-grained potentials in bottom-up derived dissipative models. We study how different system parameters affect the dynamic representability of the coarse-grained models. In particular we find that the quality of the coarse-grained potential is crucial to correctly model the backscattering effect due to collisions on the coarse-grained scale. In the dynamics of colloid suspensions the hydrodynamic interactions affect the long-time scale dynamics by solvent mediated momentum transfer. These interactions are not explicitly modeled in the presented coarse-grained models, which poses some limitations to the proposed coarse-graining scheme. The Asakura-Oosawa model allows a tuning of system parameters, to gain an improved understanding of these limitations. We also propose three new iterative optimization schemes to fine tune the generalized Langevin thermostat to exactly match the reference velocity-autocorrelation function.
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Affiliation(s)
| | - Nico van der Vegt
- Chemistry, Technische Universität Darmstadt Fachbereich Chemie, Germany
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36
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Vroylandt H, Monmarché P. Position-dependent memory kernel in generalized Langevin equations: Theory and numerical estimation. J Chem Phys 2022; 156:244105. [DOI: 10.1063/5.0094566] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Generalized Langevin equations with non-linear forces and position-dependent linear friction memory kernels, such as commonly used to describe the effective dynamics of coarse-grained variables in molecular dynamics, are rigorously derived within the Mori–Zwanzig formalism. A fluctuation–dissipation theorem relating the properties of the noise to the memory kernel is shown. The derivation also yields Volterra-type equations for the kernel, which can be used for a numerical parametrization of the model from all-atom simulations.
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Affiliation(s)
- Hadrien Vroylandt
- Sorbonne Université, Institut des Sciences du Calcul et des Données, ISCD, F-75005 Paris, France
| | - Pierre Monmarché
- Sorbonne Université, Laboratoire Jacques-Louis Lions, LJLL, F-75005 Paris, France
- Sorbonne Université, Laboratoire de Chimie Théorique, LCT, F-75005 Paris, France
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37
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Meinel MK, Müller-Plathe F. Roughness Volumes: An Improved RoughMob Concept for Predicting the Increase of Molecular Mobility upon Coarse-Graining. J Phys Chem B 2022; 126:3737-3747. [PMID: 35559647 DOI: 10.1021/acs.jpcb.2c00944] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The reduced number of degrees of freedom in a coarse-grained molecular model compared to its parent atomistic model not only makes it possible to simulate larger systems for longer time scales but also results in an artificial mobility increase. The RoughMob method [Meinel, M. K. and Müller-Plathe, F. J. Chem. Theory Comput. 2020, 16, 1411.] linked the acceleration factor of the dynamics to the loss of geometric information upon coarse-graining. Our hypothesis is that coarse-graining a multiatom molecule or group into a single spherical bead smooths the molecular surface and, thus, leads to reduced intermolecular friction. A key parameter is the molecular roughness difference, which is calculated via a numerical comparison of the molecular surfaces of both the atomistic and coarse-grained models. Augmenting the RoughMob method, we add the concept of the region where the roughness acts. This information is contained in four so-called roughness volumes. For 17 systems of homogeneous hydrocarbon fluids, simple one-bead coarse-grained models are derived by the structure-based iterative Boltzmann inversion. They include 13 different homogeneous aliphatic and aromatic molecules and two different mapping schemes. We present a simple way to correlate the roughness volumes to the acceleration factor. The resulting relation is able to a priori predict the acceleration factors for an extended size and shape range of hydrocarbon molecules, with different mapping schemes and different densities.
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Affiliation(s)
- Melissa K Meinel
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Strasse 8, D-64287 Darmstadt, Germany
| | - Florian Müller-Plathe
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Strasse 8, D-64287 Darmstadt, Germany
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38
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Ayaz C, Scalfi L, Dalton BA, Netz RR. Generalized Langevin equation with a nonlinear potential of mean force and nonlinear memory friction from a hybrid projection scheme. Phys Rev E 2022; 105:054138. [PMID: 35706310 DOI: 10.1103/physreve.105.054138] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 04/12/2022] [Indexed: 06/15/2023]
Abstract
We introduce a hybrid projection scheme that combines linear Mori projection and conditional Zwanzig projection techniques and use it to derive a generalized Langevin equation (GLE) for a general interacting many-body system. The resulting GLE includes (i) explicitly the potential of mean force (PMF) that describes the equilibrium distribution of the system in the chosen space of reaction coordinates, (ii) a random force term that explicitly depends on the initial state of the system, and (iii) a memory friction contribution that splits into two parts: a part that is linear in the past reaction-coordinate velocity and a part that is in general nonlinear in the past reaction coordinates but does not depend on velocities. Our hybrid scheme thus combines all desirable properties of the Zwanzig and Mori projection schemes. The nonlinear memory friction contribution is shown to be related to correlations between the reaction-coordinate velocity and the random force. We present a numerical method to compute all parameters of our GLE, in particular the nonlinear memory friction function and the random force distribution, from a trajectory in reaction coordinate space. We apply our method on the dihedral-angle dynamics of a butane molecule in water obtained from atomistic molecular dynamics simulations. For this example, we demonstrate that nonlinear memory friction is present and that the random force exhibits significant non-Gaussian corrections. We also present the derivation of the GLE for multidimensional reaction coordinates that are general functions of all positions in the phase-space of the underlying many-body system; this corresponds to a systematic coarse-graining procedure that preserves not only the correct equilibrium behavior but also the correct dynamics of the coarse-grained system.
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Affiliation(s)
- Cihan Ayaz
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Laura Scalfi
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Benjamin A Dalton
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
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39
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Ahuja VR, van der Gucht J, Briels W. Large Scale Hydrodynamically Coupled Brownian Dynamics Simulations of Polymer Solutions Flowing through Porous Media. Polymers (Basel) 2022; 14:polym14071422. [PMID: 35406296 PMCID: PMC9003297 DOI: 10.3390/polym14071422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Revised: 03/19/2022] [Accepted: 03/25/2022] [Indexed: 11/20/2022] Open
Abstract
Large scale simulations of polymer flow through porous media provide an important tool for solving problems in enhanced oil recovery, polymer processing and biological applications. In order to include the effects of a wide range of velocity and density fluctuations, we base our work on a coarse-grain particle-based model consisting of polymers following Brownian dynamics coupled to a background fluid flow through momentum conserving interactions. The polymers are represented as Finitely Extensible Non-Linear Elastic (FENE) dumbbells with interactions including slowly decaying transient forces to properly describe dynamic effects of the eliminated degrees of freedom. Model porous media are constructed from arrays of parallel solid beams with circular or square cross-sections, arranged periodically in the plane perpendicular to their axis. No-slip boundary conditions at the solid–fluid interfaces are imposed through interactions with artificial particles embedded within the solid part of the system. We compare the results of our simulations with those of standard Smoothed Particle Hydrodynamics simulations for Newtonian flow through the same porous media. We observe that in all cases the concentration of polymers at steady state is not uniform even though we start the simulations with a uniform polymer concentration, which is indicative of shear-induced cross-flow migration. Furthermore, we see the characteristic flattening of the velocity profile experimentally observed for shear-thinning polymer solutions flowing through channels as opposed to the parabolic Poiseuille flow profile for Newtonian fluids.
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Affiliation(s)
- Vishal Raju Ahuja
- Shell India Markets Private Limited, Shell Technology Centre Bangalore, Plot No 7, Bangalore Hardware Park, Devanahalli Industrial Park, Mahadeva Kodigehalli, Bengaluru 562149, Karnataka, India
- Correspondence: (V.R.A.); (W.B.)
| | - Jasper van der Gucht
- Physical Chemistry and Soft Matter, Wageningen University, Building 124, Stippeneng 4, 6708 WE Wageningen, The Netherlands;
| | - Wim Briels
- Computational Chemical Physics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Forschungszentrum Jülich, IBI 4, D-52425 Jülich, Germany
- Correspondence: (V.R.A.); (W.B.)
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40
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Vroylandt H, Goudenège L, Monmarché P, Pietrucci F, Rotenberg B. Likelihood-based non-Markovian models from molecular dynamics. Proc Natl Acad Sci U S A 2022; 119:e2117586119. [PMID: 35320038 PMCID: PMC9060509 DOI: 10.1073/pnas.2117586119] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Accepted: 02/16/2022] [Indexed: 01/09/2023] Open
Abstract
SignificanceThe analysis of complex systems with many degrees of freedom generally involves the definition of low-dimensional collective variables more amenable to physical understanding. Their dynamics can be modeled by generalized Langevin equations, whose coefficients have to be estimated from simulations of the initial high-dimensional system. These equations feature a memory kernel describing the mutual influence of the low-dimensional variables and their environment. We introduce and implement an approach where the generalized Langevin equation is designed to maximize the statistical likelihood of the observed data. This provides an efficient way to generate reduced models to study dynamical properties of complex processes such as chemical reactions in solution, conformational changes in biomolecules, or phase transitions in condensed matter systems.
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Affiliation(s)
- Hadrien Vroylandt
- Institut des Sciences du Calcul et des Données, Sorbonne Université, F-75005 Paris, France
| | - Ludovic Goudenège
- CNRS, FR 3487, Fédération de Mathématiques de CentraleSupélec, CentraleSupélec, Université Paris-Saclay, 91190 Gif-sur-Yvette, France
| | - Pierre Monmarché
- Laboratoire Jacques-Louis Lions, Sorbonne Université, F-75005 Paris, France
- Laboratoire de Chimie Théorique, Sorbonne Université, F-75005 Paris, France
| | - Fabio Pietrucci
- Muséum National d’Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, F-75005 Paris, France
| | - Benjamin Rotenberg
- Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, Sorbonne Université, CNRS, F-75005 Paris, France
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41
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Jung G. Non-Markovian systems out of equilibrium: exact results for two routes of coarse graining. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:204004. [PMID: 35180708 DOI: 10.1088/1361-648x/ac56a7] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Accepted: 02/18/2022] [Indexed: 06/14/2023]
Abstract
Generalized Langevin equations (GLEs) can be systematically derived via dimensional reduction from high-dimensional microscopic systems. For linear models the derivation can either be based on projection operator techniques such as the Mori-Zwanzig (MZ) formalism or by 'integrating out' the bath degrees of freedom. Based on exact analytical results we show that both routes can lead to fundamentally different GLEs and that the origin of these differences is based inherently on the non-equilibrium nature of the microscopic stochastic model. The most important conceptional difference between the two routes is that the MZ result intrinsically fulfills the generalized second fluctuation-dissipation theorem while the integration result can lead to its violation. We supplement our theoretical findings with numerical and simulation results for two popular non-equilibrium systems: time-delayed feedback control and the active Ornstein-Uhlenbeck process.
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Affiliation(s)
- Gerhard Jung
- Department of Chemical Engineering, Kyoto University, Japan
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
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42
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Schmid F. Editorial: Multiscale simulation methods for soft matter systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:160401. [PMID: 35179129 DOI: 10.1088/1361-648x/ac5071] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 01/31/2022] [Indexed: 06/14/2023]
Affiliation(s)
- Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
- Max-Planck Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany
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43
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Te Vrugt M, Hossenfelder S, Wittkowski R. Mori-Zwanzig Formalism for General Relativity: A New Approach to the Averaging Problem. PHYSICAL REVIEW LETTERS 2021; 127:231101. [PMID: 34936793 DOI: 10.1103/physrevlett.127.231101] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2021] [Accepted: 10/20/2021] [Indexed: 06/14/2023]
Abstract
Cosmology relies on a coarse-grained description of the universe, assumed to be valid on large length scales. However, the nonlinearity of general relativity makes coarse graining extremely difficult. We here address this problem by extending the Mori-Zwanzig projection operator formalism, a highly successful coarse-graining method from statistical mechanics, towards general relativity. Using the Buchert equations, we derive a new dynamic equation for the Hubble parameter which captures the effects of averaging through a memory function. This gives an empirical prediction for the cosmic jerk.
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Affiliation(s)
- Michael Te Vrugt
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany
| | - Sabine Hossenfelder
- Frankfurt Institute for Advanced Studies, D-60438 Frankfurt am Main, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany
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44
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Liwo A, Czaplewski C, Sieradzan AK, Lipska AG, Samsonov SA, Murarka RK. Theory and Practice of Coarse-Grained Molecular Dynamics of Biologically Important Systems. Biomolecules 2021; 11:1347. [PMID: 34572559 PMCID: PMC8465211 DOI: 10.3390/biom11091347] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Revised: 09/03/2021] [Accepted: 09/09/2021] [Indexed: 12/16/2022] Open
Abstract
Molecular dynamics with coarse-grained models is nowadays extensively used to simulate biomolecular systems at large time and size scales, compared to those accessible to all-atom molecular dynamics. In this review article, we describe the physical basis of coarse-grained molecular dynamics, the coarse-grained force fields, the equations of motion and the respective numerical integration algorithms, and selected practical applications of coarse-grained molecular dynamics. We demonstrate that the motion of coarse-grained sites is governed by the potential of mean force and the friction and stochastic forces, resulting from integrating out the secondary degrees of freedom. Consequently, Langevin dynamics is a natural means of describing the motion of a system at the coarse-grained level and the potential of mean force is the physical basis of the coarse-grained force fields. Moreover, the choice of coarse-grained variables and the fact that coarse-grained sites often do not have spherical symmetry implies a non-diagonal inertia tensor. We describe selected coarse-grained models used in molecular dynamics simulations, including the most popular MARTINI model developed by Marrink's group and the UNICORN model of biological macromolecules developed in our laboratory. We conclude by discussing examples of the application of coarse-grained molecular dynamics to study biologically important processes.
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Affiliation(s)
- Adam Liwo
- Faculty of Chemistry, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland; (C.C.); (A.K.S.); (A.G.L.); (S.A.S.)
| | - Cezary Czaplewski
- Faculty of Chemistry, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland; (C.C.); (A.K.S.); (A.G.L.); (S.A.S.)
| | - Adam K. Sieradzan
- Faculty of Chemistry, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland; (C.C.); (A.K.S.); (A.G.L.); (S.A.S.)
| | - Agnieszka G. Lipska
- Faculty of Chemistry, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland; (C.C.); (A.K.S.); (A.G.L.); (S.A.S.)
| | - Sergey A. Samsonov
- Faculty of Chemistry, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland; (C.C.); (A.K.S.); (A.G.L.); (S.A.S.)
| | - Rajesh K. Murarka
- Department of Chemistry, Indian Institute of Science Education and Research Bhopal, Bhopal Bypass Road, Bhopal 462066, MP, India;
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Klippenstein V, van der Vegt NFA. Cross-correlation corrected friction in (generalized) Langevin models. J Chem Phys 2021; 154:191102. [PMID: 34240903 DOI: 10.1063/5.0049324] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a route for parameterizing isotropic (generalized) Langevin [(G)LE] thermostats with the aim to correct the dynamics of coarse-grained (CG) models with pairwise conservative interactions. The approach is based on the Mori-Zwanzig formalism and derives the memory kernels from Q-projected time correlation functions. Bottom-up informed (GLE and LE) thermostats for a CG star-polymer melt are investigated, and it is demonstrated that the inclusion of memory in the CG simulation leads to predictions of polymer diffusion in quantitative agreement with fine-grained simulations. Interestingly, memory effects are observed in the diffusive regime. We demonstrate that previously neglected cross-correlations between the "irrelevant" and the CG degree of freedom are important and lie at the origin of shortcomings in previous CG simulations.
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Affiliation(s)
- Viktor Klippenstein
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, 64287 Darmstadt, Germany
| | - Nico F A van der Vegt
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, 64287 Darmstadt, Germany
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