1
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Zhu Y, Zhao X, Xiang C, Liu X, Li J. Evaluation of Essential Dynamics and Fixed-Length Coarse Graining for Multidomain Proteins. J Phys Chem B 2024; 128:5147-5156. [PMID: 38758598 DOI: 10.1021/acs.jpcb.3c08198] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/19/2024]
Abstract
For multiscale modeling of biomolecules, reliable coarse-grained (CG) models can offer great potential to simulate larger temporal and spatial scales than traditional all-atom (AA) models. In this study, we explore the essential dynamics coarse graining (EDCG) and fixed-length coarse graining (FLCG) approaches for constructing highly coarse-grained models for multidomain proteins (MDPs), with 1 to 10 amino acid residues per CG site. In the studies of 13 MDPs, our data indicate that both EDCG and FLCG can preserve the protein dynamics of MDPs. FLCG, which restricts an equal number of residues in each CG site, represents an excellent approximation to EDCG and a straightforward approach for coarse-graining MDPs. Furthermore, FLCG is tested with a class B G-protein-coupled receptor protein, and the agreement with prior experiments suggests its general application to various MDPs in different environments or conditions. Finally, we demonstrate another application of FLCG through progressive backmapping, showcasing the ability to recover from lower-resolution CG models (6 residues/CG site) to higher-resolution ones (1 residue/CG site). These promising outcomes underscore the broad applicability of FLCG to construct highly or ultra-coarse-grained models of complex biomolecules for multiscale simulations.
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Affiliation(s)
- Yu Zhu
- Borch Department of Medicinal Chemistry and Molecular Pharmacology, Purdue University, West Lafayette, Indiana 47907, United States
| | - Xiaochuan Zhao
- Department of Chemistry, University of Vermont, Burlington, Vermont 05405, United States
| | - Chijian Xiang
- Department of Horticulture & Landscape Architecture, Purdue University, West Lafayette, Indiana 47907, United States
| | - Xianshi Liu
- Borch Department of Medicinal Chemistry and Molecular Pharmacology, Purdue University, West Lafayette, Indiana 47907, United States
| | - Jianing Li
- Borch Department of Medicinal Chemistry and Molecular Pharmacology, Purdue University, West Lafayette, Indiana 47907, United States
- Department of Chemistry, University of Vermont, Burlington, Vermont 05405, United States
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2
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Peng Y, Pak AJ, Durumeric AEP, Sahrmann PG, Mani S, Jin J, Loose TD, Beiter J, Voth GA. OpenMSCG: A Software Tool for Bottom-Up Coarse-Graining. J Phys Chem B 2023; 127:8537-8550. [PMID: 37791670 PMCID: PMC10577682 DOI: 10.1021/acs.jpcb.3c04473] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Revised: 09/05/2023] [Indexed: 10/05/2023]
Abstract
The "bottom-up" approach to coarse-graining, for building accurate and efficient computational models to simulate large-scale and complex phenomena and processes, is an important approach in computational chemistry, biophysics, and materials science. As one example, the Multiscale Coarse-Graining (MS-CG) approach to developing CG models can be rigorously derived using statistical mechanics applied to fine-grained, i.e., all-atom simulation data for a given system. Under a number of circumstances, a systematic procedure, such as MS-CG modeling, is particularly valuable. Here, we present the development of the OpenMSCG software, a modularized open-source software that provides a collection of successful and widely applied bottom-up CG methods, including Boltzmann Inversion (BI), Force-Matching (FM), Ultra-Coarse-Graining (UCG), Relative Entropy Minimization (REM), Essential Dynamics Coarse-Graining (EDCG), and Heterogeneous Elastic Network Modeling (HeteroENM). OpenMSCG is a high-performance and comprehensive toolset that can be used to derive CG models from large-scale fine-grained simulation data in file formats from common molecular dynamics (MD) software packages, such as GROMACS, LAMMPS, and NAMD. OpenMSCG is modularized in the Python programming framework, which allows users to create and customize modeling "recipes" for reproducible results, thus greatly improving the reliability, reproducibility, and sharing of bottom-up CG models and their applications.
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Affiliation(s)
- Yuxing Peng
- NVIDIA
Corporation, 2788 San Tomas Expressway, Santa Clara, California 95051, United States
| | - Alexander J. Pak
- Department
of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States
| | | | - Patrick G. Sahrmann
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, James Franck
Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
| | - Sriramvignesh Mani
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, James Franck
Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
| | - Jaehyeok Jin
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, James Franck
Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
| | - Timothy D. Loose
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, James Franck
Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
| | - Jeriann Beiter
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, James Franck
Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
| | - Gregory A. Voth
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, James Franck
Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
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3
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Zha J, Xia F. Developing Hybrid All-Atom and Ultra-Coarse-Grained Models to Investigate Taxol-Binding and Dynein Interactions on Microtubules. J Chem Theory Comput 2023; 19:5621-5632. [PMID: 37489636 DOI: 10.1021/acs.jctc.3c00275] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/26/2023]
Abstract
Simulating the conformations and functions of biological macromolecules by using all-atom (AA) models is a challenging task due to expensive computational costs. One possible strategy to solve this problem is to develop hybrid all-atom and ultra-coarse-grained (AA/UCG) models of the biological macromolecules. In the AA/UCG scheme, the interest regions are described by AA models, while the other regions are described in the UCG representation. In this study, we develop the hybrid AA/UCG models and apply them to investigate the conformational changes of microtubule-bound tubulins. The simulation results of the hybrid models elucidated the mechanism of why the taxol molecules selectively bound microtubules but not tubulin dimers. In addition, we also explore the interactions of the microtubules and dyneins. Our study shows that the hybrid AA/UCG model has great application potential in studying the function of complex biological systems.
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Affiliation(s)
- Jinyin Zha
- School of Chemistry and Molecular Engineering, NYU-ECNU Center for Computational Chemistry at NYU Shanghai, East China Normal University, Shanghai 200062, China
- Medicinal Chemistry and Bioinformatics Center, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China
| | - Fei Xia
- School of Chemistry and Molecular Engineering, NYU-ECNU Center for Computational Chemistry at NYU Shanghai, East China Normal University, Shanghai 200062, China
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4
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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: 79] [Impact Index Per Article: 39.5] [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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5
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Lubecka EA, Liwo A. A coarse-grained approach to NMR-data-assisted modeling of protein structures. J Comput Chem 2022; 43:2047-2059. [PMID: 36134668 DOI: 10.1002/jcc.27003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Revised: 08/03/2022] [Accepted: 09/05/2022] [Indexed: 11/06/2022]
Abstract
The ESCASA algorithm for analytical estimation of proton positions from coarse-grained geometry developed in our recent work has been implemented in modeling protein structures with the highly coarse-grained UNRES model of polypeptide chains (two sites per residue) and nuclear magnetic resonance (NMR) data. A penalty function with the shape of intersecting gorges was applied to treat ambiguous distance restraints, which automatically selects consistent restraints. Hamiltonian replica exchange molecular dynamics was used to carry out the conformational search. The method was tested with both unambiguous and ambiguous restraints producing good-quality models with GDT_TS from 7.4 units higher to 14.4 units lower than those obtained with the CYANA or MELD software for protein-structure determination from NMR data at the all-atom resolution. The method can thus be applied in modeling the structures of flexible proteins, for which extensive conformational search enabled by coarse-graining is more important than high modeling accuracy.
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Affiliation(s)
- Emilia A Lubecka
- Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, Gdańsk, Poland
| | - Adam Liwo
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland
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6
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Markutsya S, Haley A, Gordon MS. Coarse-Grained Water Model Development for Accurate Dynamics and Structure Prediction. ACS OMEGA 2022; 7:25898-25904. [PMID: 35910114 PMCID: PMC9330847 DOI: 10.1021/acsomega.2c03857] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
Several coarse-graining (CG) methods have been combined to develop a CG model of water capable of the accurate prediction of structure and dynamics properties. The multiscale coarse-graining (MS-CG) method based on force matching and the PDF-based coarse-graining method were used for accurate dynamics prediction. The iterative Boltzmann inversion (IBI) method was added for accurate structure representation. The approach is applied to bulk water, and the results show close reproduction of the CG structure when compared with the reference atomistic data. The combination of MS-CG and IBI methods facilitates the development of CG force fields at different temperatures based on a single MS-CG coarse-graining procedure. The dynamic properties of the CG water model closely match those obtained from the reference atomistic system. The general application of this approach to any existing coarse-graining methods is discussed.
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Affiliation(s)
- Sergiy Markutsya
- Department
of Mechanical Engineering, University of
Kentucky, Paducah, Kentucky 42001, United States
| | - Austin Haley
- Department
of Mechanical Engineering, University of
Kentucky, Paducah, Kentucky 42001, United States
| | - Mark S. Gordon
- Department
of Chemistry and Ames Laboratory, Iowa State
University, Ames, Iowa 50011, United States
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7
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Dhamankar S, Webb MA. Chemically specific coarse‐graining of polymers: Methods and prospects. JOURNAL OF POLYMER SCIENCE 2021. [DOI: 10.1002/pol.20210555] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Satyen Dhamankar
- Department of Chemical and Biological Engineering Princeton University Princeton New Jersey USA
| | - Michael A. Webb
- Department of Chemical and Biological Engineering Princeton University Princeton New Jersey USA
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8
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Pretti E, Shell MS. A microcanonical approach to temperature-transferable coarse-grained models using the relative entropy. J Chem Phys 2021; 155:094102. [PMID: 34496595 DOI: 10.1063/5.0057104] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Bottom-up coarse-graining methods provide systematic tools for creating simplified models of molecular systems. However, coarse-grained (CG) models produced with such methods frequently fail to accurately reproduce all thermodynamic properties of the reference atomistic systems they seek to model and, moreover, can fail in even more significant ways when used at thermodynamic state points different from the reference conditions. These related problems of representability and transferability limit the usefulness of CG models, especially those of strongly state-dependent systems. In this work, we present a new strategy for creating temperature-transferable CG models using a single reference system and temperature. The approach is based on two complementary concepts. First, we switch to a microcanonical basis for formulating CG models, focusing on effective entropy functions rather than energy functions. This allows CG models to naturally represent information about underlying atomistic energy fluctuations, which would otherwise be lost. Such information not only reproduces energy distributions of the reference model but also successfully predicts the correct temperature dependence of the CG interactions, enabling temperature transferability. Second, we show that relative entropy minimization provides a direct and systematic approach to parameterize such classes of temperature-transferable CG models. We calibrate the approach initially using idealized model systems and then demonstrate its ability to create temperature-transferable CG models for several complex molecular liquids.
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Affiliation(s)
- Evan Pretti
- Department of Chemical Engineering, Engineering II Building, University of California, Santa Barbara, Santa Barbara, California 93106-5080, USA
| | - M Scott Shell
- Department of Chemical Engineering, Engineering II Building, University of California, Santa Barbara, Santa Barbara, California 93106-5080, USA
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9
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Kim S, Voth GA. Physical Characterization of Triolein and Implications for Its Role in Lipid Droplet Biogenesis. J Phys Chem B 2021; 125:6874-6888. [PMID: 34139844 DOI: 10.1021/acs.jpcb.1c03559] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Lipid droplets (LDs) are neutral lipid-storing organelles surrounded by a phospholipid (PL) monolayer. At present, how LDs are formed in the endoplasmic reticulum (ER) bilayer is poorly understood. In this study, we present a revised all-atom (AA) triolein (TG) model, the main constituent of the LD core, and characterize its properties in a bilayer membrane to demonstrate the implications of its behavior in LD biogenesis. In bilayer simulations, TG resides at the surface, adopting PL-like conformations (denoted in this work as SURF-TG). Free energy sampling simulation results estimate the barrier for TG relocating from the bilayer surface to the bilayer center to be ∼2 kcal/mol in the absence of an oil lens. SURF-TG is able to modulate membrane properties by increasing PL ordering, decreasing bending modulus, and creating local negative curvature. The other neutral lipid, dioleoyl-glycerol (DAG), also reduces the membrane bending modulus and populates negative curvature regions. A phenomenological coarse-grained (CG) model is also developed to observe larger-scale SURF-TG-mediated membrane deformation. CG simulations confirm that TG nucleates between the bilayer leaflets at a critical concentration when SURF-TG is evenly distributed. However, when one monolayer contains more SURF-TG, the membrane bends toward the other leaflet, followed by TG nucleation if a concentration is higher than the critical threshold. The central conclusion of this study is that SURF-TG is a negative curvature inducer, as well as a membrane modulator. To this end, a model is proposed in which the accumulation of SURF-TG in the luminal leaflet bends the ER bilayer toward the cytosolic side, followed by TG nucleation.
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Affiliation(s)
- Siyoung Kim
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
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10
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Giulini M, Rigoli M, Mattiotti G, Menichetti R, Tarenzi T, Fiorentini R, Potestio R. From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules. Front Mol Biosci 2021; 8:676976. [PMID: 34164432 PMCID: PMC8215203 DOI: 10.3389/fmolb.2021.676976] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2021] [Accepted: 05/06/2021] [Indexed: 12/18/2022] Open
Abstract
The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.
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Affiliation(s)
- Marco Giulini
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Marta Rigoli
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Giovanni Mattiotti
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Roberto Menichetti
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Thomas Tarenzi
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Raffaele Fiorentini
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Raffaello Potestio
- Physics Department, University of Trento, Trento, Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
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11
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Cao X, Tian P. "Dividing and Conquering" and "Caching" in Molecular Modeling. Int J Mol Sci 2021; 22:5053. [PMID: 34068835 PMCID: PMC8126232 DOI: 10.3390/ijms22095053] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Revised: 04/26/2021] [Accepted: 04/27/2021] [Indexed: 11/17/2022] Open
Abstract
Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, most important methodological advancements in more than half century of molecular modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but results are not transferable. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science. This framework is based on a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.
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Affiliation(s)
- Xiaoyong Cao
- School of Life Sciences, Jilin University, Changchun 130012, China;
| | - Pu Tian
- School of Life Sciences, Jilin University, Changchun 130012, China;
- School of Artificial Intelligence, Jilin University, Changchun 130012, China
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12
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Rudzinski JF, Kloth S, Wörner S, Pal T, Kremer K, Bereau T, Vogel M. Dynamical properties across different coarse-grained models for ionic liquids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:224001. [PMID: 33592598 DOI: 10.1088/1361-648x/abe6e1] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2020] [Accepted: 02/16/2021] [Indexed: 06/12/2023]
Abstract
Room-temperature ionic liquids (RTILs) stand out among molecular liquids for their rich physicochemical characteristics, including structural and dynamic heterogeneity. The significance of electrostatic interactions in RTILs results in long characteristic length- and timescales, and has motivated the development of a number of coarse-grained (CG) simulation models. In this study, we aim to better understand the connection between certain CG parameterization strategies and the dynamical properties and transferability of the resulting models. We systematically compare five CG models: a model largely parameterized from experimental thermodynamic observables; a refinement of this model to increase its structural accuracy; and three models that reproduce a given set of structural distribution functions by construction, with varying intramolecular parameterizations and reference temperatures. All five CG models display limited structural transferability over temperature, and also result in various effective dynamical speedup factors, relative to a reference atomistic model. On the other hand, the structure-based CG models tend to result in more consistent cation-anion relative diffusion than the thermodynamic-based models, for a single thermodynamic state point. By linking short- and long-timescale dynamical behaviors, we demonstrate that the varying dynamical properties of the different CG models can be largely collapsed onto a single curve, which provides evidence for a route to constructing dynamically-consistent CG models of RTILs.
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Affiliation(s)
| | - Sebastian Kloth
- Institute of Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
| | - Svenja Wörner
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | - Tamisra Pal
- Institute of Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
| | - Kurt Kremer
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
- Van 't Hoff Institute for Molecular Sciences and Informatics Institute, University of Amsterdam, Amsterdam 1098 XH, The Netherlands
| | - Michael Vogel
- Institute of Condensed Matter Physics, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
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13
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Baul U, Dzubiella J. Structure and dynamics of responsive colloids with dynamical polydispersity. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:174002. [PMID: 33443239 DOI: 10.1088/1361-648x/abdbaa] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 12/31/2020] [Indexed: 06/12/2023]
Abstract
Dynamical polydispersity in single-particle properties, for example a fluctuating particle size, shape, charge density, etc, is intrinsic to responsive colloids (RCs), such as biomacromolecules or microgels, but is typically not resolved in coarse-grained mesoscale simulations. Here, we present Brownian dynamics simulations of suspensions of RCs modeling soft hydrogel colloids, for which the size of the individual particles is an explicitly resolved (Gaussian) degree of freedom and dynamically responds to the local interacting environment. We calculate the liquid structure, emergent size distributions, long-time diffusion, and property (size) relaxation kinetics for a wide range of densities and intrinsic property relaxation times in the canonical ensemble. Comparison to interesting reference cases, such as conventional polydisperse suspensions with a frozen parent distribution, or conventional monodisperse systems interacting with an effective pair potential for one fixed size, shows a significant spread in the structure and dynamics. The differences, most apparent in the high density regimes, are due to many-body correlations and the dynamical coupling between property and translation in RC systems, not explicitly accounted for in the conventional treatments. In particular, the translational diffusion in the RC systems is surprisingly close to the free (single RC) diffusion, mainly due to a cancellation of crowding and size compression effects. We show that an effective monodisperse pair potential can be constructed that describes the many-body correlations reasonably well by convoluting the RC pair potential with the density-dependent emergent size distributions and using a mean effective diffusion constant.
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Affiliation(s)
- Upayan Baul
- Applied Theoretical Physics-Computational Physics, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
| | - Joachim Dzubiella
- Applied Theoretical Physics-Computational Physics, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
- Cluster of Excellence livMatS @ FIT - Freiburg Center for Interactive Materials and Bioinspired Technologies, Albert-Ludwigs-Universität Freiburg, D-79110 Freiburg, Germany
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14
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Yu A, Pak AJ, He P, Monje-Galvan V, Casalino L, Gaieb Z, Dommer AC, Amaro RE, Voth GA. A multiscale coarse-grained model of the SARS-CoV-2 virion. Biophys J 2021; 120:1097-1104. [PMID: 33253634 PMCID: PMC7695975 DOI: 10.1016/j.bpj.2020.10.048] [Citation(s) in RCA: 101] [Impact Index Per Article: 33.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2020] [Revised: 10/27/2020] [Accepted: 10/30/2020] [Indexed: 01/01/2023] Open
Abstract
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative agent of the COVID-19 pandemic. Computer simulations of complete viral particles can provide theoretical insights into large-scale viral processes including assembly, budding, egress, entry, and fusion. Detailed atomistic simulations are constrained to shorter timescales and require billion-atom simulations for these processes. Here, we report the current status and ongoing development of a largely "bottom-up" coarse-grained (CG) model of the SARS-CoV-2 virion. Data from a combination of cryo-electron microscopy (cryo-EM), x-ray crystallography, and computational predictions were used to build molecular models of structural SARS-CoV-2 proteins, which were then assembled into a complete virion model. We describe how CG molecular interactions can be derived from all-atom simulations, how viral behavior difficult to capture in atomistic simulations can be incorporated into the CG models, and how the CG models can be iteratively improved as new data become publicly available. Our initial CG model and the detailed methods presented are intended to serve as a resource for researchers working on COVID-19 who are interested in performing multiscale simulations of the SARS-CoV-2 virion.
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Affiliation(s)
- Alvin Yu
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics and James Franck Institute, The University of Chicago, Chicago, Illinois
| | - 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
| | - Peng He
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics and James Franck Institute, The University of Chicago, Chicago, Illinois
| | - Viviana Monje-Galvan
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics and James Franck Institute, The University of Chicago, Chicago, Illinois
| | - Lorenzo Casalino
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California
| | - Zied Gaieb
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California
| | - Abigail C Dommer
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California
| | - Rommie E Amaro
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California
| | - 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.
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15
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Mani S, Katkar HH, Voth GA. Compressive and Tensile Deformations Alter ATP Hydrolysis and Phosphate Release Rates in Actin Filaments. J Chem Theory Comput 2021; 17:1900-1913. [PMID: 33596075 DOI: 10.1021/acs.jctc.0c01186] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Actin filament networks in eukaryotic cells are constantly remodeled through nucleotide state controlled interactions with actin binding proteins, leading to macroscopic structures such as bundled filaments, branched filaments, and so on. The nucleotide (ATP) hydrolysis, phosphate release, and polymerization/depolymerization reactions that lead to the formation of these structures are correlated with the conformational fluctuations of the actin subunits at the molecular scale. The resulting structures generate and experience varying levels of force and impart cells with several functionalities such as their ability to move, divide, transport cargo, etc. Models that explicitly connect the structure to reactions are essential to elucidate a fundamental level of understanding of these processes. In this regard, a bottom-up Ultra-Coarse-Grained (UCG) model of actin filaments that can simulate ATP hydrolysis, inorganic phosphate release (Pi), and depolymerization reactions is presented in this work. In this model, actin subunits are represented using coarse-grained particles that evolve in time and undergo reactions depending on the conformations sampled. The reactions are represented through state transitions, with each state represented by a unique effective coarse-grained potential. Effects of compressive and tensile strains on the rates of reactions are then analyzed. Compressive strains tend to unflatten the actin subunits, reduce the rate of ATP hydrolysis, and increase the Pi release rate. On the other hand, tensile strain flattens subunits, increases the rate of ATP hydrolysis, and decrease the Pi release rate. Incorporating these predictions into a Markov State Model highlighted that strains alter the steady-state distribution of subunits with ADPPi and ADP nucleotide, thus identifying possible additional factors underlying the cooperative binding of regulatory proteins to actin filaments.
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Affiliation(s)
- Sriramvignesh Mani
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
| | - Harshwardhan H Katkar
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
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16
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Zha J, Zhang Y, Xia K, Gräter F, Xia F. Coarse-Grained Simulation of Mechanical Properties of Single Microtubules With Micrometer Length. Front Mol Biosci 2021; 7:632122. [PMID: 33659274 PMCID: PMC7917235 DOI: 10.3389/fmolb.2020.632122] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2020] [Accepted: 12/30/2020] [Indexed: 01/03/2023] Open
Abstract
Microtubules are one of the most important components in the cytoskeleton and play a vital role in maintaining the shape and function of cells. Because single microtubules are some micrometers long, it is difficult to simulate such a large system using an all-atom model. In this work, we use the newly developed convolutional and K-means coarse-graining (CK-CG) method to establish an ultra-coarse-grained (UCG) model of a single microtubule, on the basis of the low electron microscopy density data of microtubules. We discuss the rationale of the micro-coarse-grained microtubule models of different resolutions and explore microtubule models up to 12-micron length. We use the devised microtubule model to quantify mechanical properties of microtubules of different lengths. Our model allows mesoscopic simulations of micrometer-level biomaterials and can be further used to study important biological processes related to microtubule function.
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Affiliation(s)
- Jinyin Zha
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, China
| | - Yuwei Zhang
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, China
| | - Kelin Xia
- Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore.,School of Biological Sciences, Nanyang Technological University, Singapore, Singapore
| | - Frauke Gräter
- Interdisciplinary Centre for Scientific Computing (IWR), Heidelberg University, Heidelberg, Germany.,Heidelberg Institute for Theoretical Studies (HITS), Schloβ-Wolfsbrunnenweg 35, Heidelberg, Germany.,Max Planck School Matter to Life, Jahnstraβe 29, Heidelberg, Germany
| | - Fei Xia
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, China.,Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai, China
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17
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Jin J, Han Y, Pak AJ, Voth GA. A new one-site coarse-grained model for water: Bottom-up many-body projected water (BUMPer). I. General theory and model. J Chem Phys 2021; 154:044104. [PMID: 33514116 PMCID: PMC7826168 DOI: 10.1063/5.0026651] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Accepted: 12/14/2020] [Indexed: 12/26/2022] Open
Abstract
Water is undoubtedly one of the most important molecules for a variety of chemical and physical systems, and constructing precise yet effective coarse-grained (CG) water models has been a high priority for computer simulations. To recapitulate important local correlations in the CG water model, explicit higher-order interactions are often included. However, the advantages of coarse-graining may then be offset by the larger computational cost in the model parameterization and simulation execution. To leverage both the computational efficiency of the CG simulation and the inclusion of higher-order interactions, we propose a new statistical mechanical theory that effectively projects many-body interactions onto pairwise basis sets. The many-body projection theory presented in this work shares similar physics from liquid state theory, providing an efficient approach to account for higher-order interactions within the reduced model. We apply this theory to project the widely used Stillinger-Weber three-body interaction onto a pairwise (two-body) interaction for water. Based on the projected interaction with the correct long-range behavior, we denote the new CG water model as the Bottom-Up Many-Body Projected Water (BUMPer) model, where the resultant CG interaction corresponds to a prior model, the iteratively force-matched model. Unlike other pairwise CG models, BUMPer provides high-fidelity recapitulation of pair correlation functions and three-body distributions, as well as N-body correlation functions. BUMPer extensively improves upon the existing bottom-up CG water models by extending the accuracy and applicability of such models while maintaining a reduced computational cost.
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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
| | - Yining Han
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - 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, 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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18
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Rudzinski JF, Bereau T. Coarse-grained conformational surface hopping: Methodology and transferability. J Chem Phys 2020; 153:214110. [DOI: 10.1063/5.0031249] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
- Van ’t Hoff Institute for Molecular Sciences and Informatics Institute, University of Amsterdam, Amsterdam 1098 XH, The Netherlands
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19
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Jin J, Yu A, Voth GA. Temperature and Phase Transferable Bottom-up Coarse-Grained Models. J Chem Theory Comput 2020; 16:6823-6842. [PMID: 32975948 DOI: 10.1021/acs.jctc.0c00832] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
Despite the high fidelity of bottom-up coarse-grained (CG) approaches to recapitulate the structural correlations in atomistic simulations, the general use of bottom-up CG methods is limited because of the nontransferable nature of these CG models under different thermodynamic conditions. Because bottom-up CG potentials usually correspond to configuration-dependent free energies of the system, recent studies have focused on adjusting enthalpic or entropic contributions to account for issues with transferability. However, these approaches can require a manual adjustment of the CG interaction a priori and are usually limited to constant volume ensembles. To overcome these limitations, we construct temperature and phase transferable CG models under constant pressure by developing the ultra-coarse-graining (UCG) methodology in the mean-field limit. In the mean-field ansatz, an embedded semi-global order parameter recapitulates global changes to the system by automatically adjusting the effective CG interactions, thus bridging free energy decompositions with UCG theory. The method presented is designed to faithfully capture structural correlations under different thermodynamic conditions, using a single UCG model. Specifically, we test the applicability of the developed theory in three distinct cases: (1) different temperatures at constant pressure in liquids, (2) different temperatures across thermodynamic phases, and (3) liquid/vapor interfaces. We demonstrate that the systematic construction of both temperature and phase transferable bottom-up CG models is possible using this generalized UCG theory. Based on our findings, this approach significantly extends the transferability and applicability of the bottom-up CG theory and method.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 S. Ellis Avenue, Chicago, Illinois 60637, United States
| | - Alvin Yu
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 S. Ellis Avenue, Chicago, Illinois 60637, United States
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 S. Ellis Avenue, Chicago, Illinois 60637, United States
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20
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Yu A, Pak AJ, He P, Monje-Galvan V, Casalino L, Gaieb Z, Dommer AC, Amaro RE, Voth GA. A Multiscale Coarse-grained Model of the SARS-CoV-2 Virion. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2020. [PMID: 33024966 DOI: 10.1101/2020.10.02.323915] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative agent of the COVID-19 pandemic. Computer simulations of complete viral particles can provide theoretical insights into large-scale viral processes including assembly, budding, egress, entry, and fusion. Detailed atomistic simulations, however, are constrained to shorter timescales and require billion-atom simulations for these processes. Here, we report the current status and on-going development of a largely "bottom-up" coarse-grained (CG) model of the SARS-CoV-2 virion. Structural data from a combination of cryo-electron microscopy (cryo-EM), x-ray crystallography, and computational predictions were used to build molecular models of structural SARS-CoV-2 proteins, which were then assembled into a complete virion model. We describe how CG molecular interactions can be derived from all-atom simulations, how viral behavior difficult to capture in atomistic simulations can be incorporated into the CG models, and how the CG models can be iteratively improved as new data becomes publicly available. Our initial CG model and the detailed methods presented are intended to serve as a resource for researchers working on COVID-19 who are interested in performing multiscale simulations of the SARS-CoV-2 virion. Significance Statement This study reports the construction of a molecular model for the SARS-CoV-2 virion and details our multiscale approach towards model refinement. The resulting model and methods can be applied to and enable the simulation of SARS-CoV-2 virions.
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21
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Zhang Y, Cao Z, Zhang JZ, Xia F. Double-Well Ultra-Coarse-Grained Model to Describe Protein Conformational Transitions. J Chem Theory Comput 2020; 16:6678-6689. [PMID: 32926616 DOI: 10.1021/acs.jctc.0c00551] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The double-well model is usually used to describe the conformational transition between two states of a protein. Since conformational changes usually occur within a relatively large time scale, coarse-grained models are often used to accelerate the dynamic process due to their inexpensive computational cost. In this work, we develop a double-well ultra-coarse-grained (DW-UCG) model to describe the conformational transitions of the adenylate kinase, glutamine-binding protein, and lactoferrin. The coarse-grained simulation results show that the DW-UCG model of adenylate kinase captures the crucial intermediate states in the LID-closing and NMP-closing pathways, reflecting the key secondary structural changes in the conformational transition. A comparison of the different DW-UCG models of adenylate kinase indicates that an appropriate choice of bead resolution could generate the free energy landscape that is comparable to that from the residue-based model. The coarse-grained simulations for the glutamine-binding protein and lactoferrin also demonstrate that the DW-UCG model is valid in reproducing the correct two-state behavior for their functional study, which indicates the potential application of the DW-UCG model in investigating the mechanism of conformational changes of large proteins.
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Affiliation(s)
- Yuwei Zhang
- State Key Laboratory of Physical Chemistry of Solid Surfaces and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, College of Chemistry and Chemistry Engineering, Xiamen University, Xiamen 361005, China.,School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China
| | - Zexing Cao
- State Key Laboratory of Physical Chemistry of Solid Surfaces and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, College of Chemistry and Chemistry Engineering, Xiamen University, Xiamen 361005, China
| | - John Zenghui Zhang
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China.,Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
| | - Fei Xia
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China.,Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
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22
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Mani S, Cosgrove DJ, Voth GA. Anisotropic Motions of Fibrils Dictated by Their Orientations in the Lamella: A Coarse-Grained Model of a Plant Cell Wall. J Phys Chem B 2020; 124:3527-3539. [DOI: 10.1021/acs.jpcb.0c01697] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Sriramvignesh Mani
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
| | - Daniel J. Cosgrove
- Department of Biology and Center for Lignocellulose Structure and Formation, Pennsylvania State University, University Park, State College, Pennsylvania 16801, United States
| | - Gregory A. Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
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23
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24
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Liwo A, Czaplewski C, Sieradzan AK, Lubecka EA, Lipska AG, Golon Ł, Karczyńska A, Krupa P, Mozolewska MA, Makowski M, Ganzynkowicz R, Giełdoń A, Maciejczyk M. Scale-consistent approach to the derivation of coarse-grained force fields for simulating structure, dynamics, and thermodynamics of biopolymers. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2020; 170:73-122. [PMID: 32145953 DOI: 10.1016/bs.pmbts.2019.12.004] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
In this chapter the scale-consistent approach to the derivation of coarse-grained force fields developed in our laboratory is presented, in which the effective energy function originates from the potential of mean force of the system under consideration and embeds atomistically detailed interactions in the resulting energy terms through use of Kubo's cluster-cumulant expansion, appropriate selection of the major degrees of freedom to be averaged out in the derivation of analytical approximations to the energy terms, and appropriate expression of the interaction energies at the all-atom level in these degrees of freedom. Our approach enables the developers to find correct functional forms of the effective coarse-grained energy terms, without having to import them from all-atom force fields or deriving them on a heuristic basis. In particular, the energy terms derived in such a way exhibit correct dependence on coarse-grained geometry, in particular on site orientation. Moreover, analytical formulas for the multibody (correlation) terms, which appear to be crucial for coarse-grained modeling of many of the regular structures such as, e.g., protein α-helices and β-sheets, can be derived in a systematic way. Implementation of the developed theory to the UNIfied COarse-gRaiNed (UNICORN) model of biological macromolecules, which consists of the UNRES (for proteins), NARES-2P (for nucleic acids), and SUGRES-1P (for polysaccharides) components, and is being developed in our laboratory is described. Successful applications of UNICORN to the prediction of protein structure, simulating the folding and stability of proteins and nucleic acids, and solving biological problems are discussed.
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Affiliation(s)
- Adam Liwo
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland; School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Republic of Korea.
| | | | - Adam K Sieradzan
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland; School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Republic of Korea
| | - Emilia A Lubecka
- Institute of Informatics, Faculty of Mathematics, Physics, and Informatics, University of Gdańsk, Gdańsk, Poland
| | | | - Łukasz Golon
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland
| | | | - Paweł Krupa
- Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
| | | | | | | | - Artur Giełdoń
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland
| | - Maciej Maciejczyk
- Department of Physics and Biophysics, Faculty of Food Science, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland
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25
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Das A, Limmer DT. Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations. J Chem Phys 2019; 151:244123. [DOI: 10.1063/1.5128956] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Affiliation(s)
- Avishek Das
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Kavli Energy NanoScience Institute, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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26
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Wu Z, Zhang Y, Zhang JZ, Xia K, Xia F. Determining Optimal Coarse-Grained Representation for Biomolecules Using Internal Cluster Validation Indexes. J Comput Chem 2019; 41:14-20. [PMID: 31568566 DOI: 10.1002/jcc.26070] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2019] [Revised: 08/15/2019] [Accepted: 08/27/2019] [Indexed: 12/30/2022]
Abstract
The development of ultracoarse-grained models for large biomolecules needs to derive the optimal number of coarse-grained (CG) sites to represent the targets. In this work, we propose to use the statistical internal cluster validation indexes to determine the optimal number of CG sites that are optimized based on the essential dynamics coarse-graining method. The calculated curves of Calinski-Harabasz and Silhouette Coefficient indexes exhibit the extrema corresponding to the similar CG numbers. The calculated ratios of the optimal CG numbers to the residue numbers of fine-grained models are in the range from 4 to 2. The comparison of the stability of index results indicates that Calinski-Harabasz index is the better choice to determine the optimal CG representation in coarse-graining. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Zhenliang Wu
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, 200062, China
| | - Yuwei Zhang
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, 200062, China
| | - John Zenghui Zhang
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, 200062, China.,NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai, 200062, China
| | - Kelin Xia
- Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore.,School of Biological Sciences, Nanyang Technological University, 637371, Singapore
| | - Fei Xia
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, 200062, China.,NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai, 200062, China
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27
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Abstract
Most current molecular dynamics simulation and analysis methods rely on the idea that the molecular system can be represented by a single global state (e.g., a Markov state in a Markov state model [MSM]). In this approach, molecules can be extensively sampled and analyzed when they only possess a few metastable states, such as small- to medium-sized proteins. However, this approach breaks down in frustrated systems and in large protein assemblies, where the number of global metastable states may grow exponentially with the system size. To address this problem, we here introduce dynamic graphical models (DGMs) that describe molecules as assemblies of coupled subsystems, akin to how spins interact in the Ising model. The change of each subsystem state is only governed by the states of itself and its neighbors. DGMs require fewer parameters than MSMs or other global state models; in particular, we do not need to observe all global system configurations to characterize them. Therefore, DGMs can predict previously unobserved molecular configurations. As a proof of concept, we demonstrate that DGMs can faithfully describe molecular thermodynamics and kinetics and predict previously unobserved metastable states for Ising models and protein simulations.
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Affiliation(s)
- Simon Olsson
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany;
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany;
- Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, TX 77005
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28
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Zhang Y, Xia K, Cao Z, Gräter F, Xia F. A new method for the construction of coarse-grained models of large biomolecules from low-resolution cryo-electron microscopy data. Phys Chem Chem Phys 2019; 21:9720-9727. [PMID: 31025999 DOI: 10.1039/c9cp01370a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
The rapid development of cryo-electron microscopy (cryo-EM) has led to the generation of significant low-resolution electron density data of biomolecules. However, the atomistic details of huge biomolecules usually cannot be obtained because it is very difficult to construct all-atom models for MD simulations. Thus, it is still a challenge to make use of the rich low-resolution cryo-EM data for computer simulation and functional study. In this study, we proposed a new method called Convolutional and K-means Coarse-Graining (CK-CG) for the efficient coarse-graining of large biological systems. Using the CK-CG method, we could directly map the cryo-EM data into coarse-grained (CG) beads. Furthermore, the CG beads were parameterized with an empirical harmonic potential to construct a new CG model. We subjected the CK-CG models of the fibrillar protein assemblies F-actin and collagen to external forces in pulling dynamic simulations to assess their mechanical response. The agreement between the estimated tensile stiffness between CG models and experiments demonstrates the validity of the CK-CG method. Thus, our method provides a practical strategy for the direct construction of a structural model from low-resolution data for biological function studies.
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Affiliation(s)
- Yuwei Zhang
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China.
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29
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Marrink SJ, Corradi V, Souza PC, Ingólfsson HI, Tieleman DP, Sansom MS. Computational Modeling of Realistic Cell Membranes. Chem Rev 2019; 119:6184-6226. [PMID: 30623647 PMCID: PMC6509646 DOI: 10.1021/acs.chemrev.8b00460] [Citation(s) in RCA: 422] [Impact Index Per Article: 84.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2018] [Indexed: 12/15/2022]
Abstract
Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.
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Affiliation(s)
- Siewert J. Marrink
- Groningen
Biomolecular Sciences and Biotechnology Institute & Zernike Institute
for Advanced Materials, University of Groningen, Nijenborgh 7, 9747 AG Groningen, The Netherlands
| | - Valentina Corradi
- Centre
for Molecular Simulation and Department of Biological Sciences, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Paulo C.T. Souza
- Groningen
Biomolecular Sciences and Biotechnology Institute & Zernike Institute
for Advanced Materials, University of Groningen, Nijenborgh 7, 9747 AG Groningen, The Netherlands
| | - Helgi I. Ingólfsson
- Biosciences
and Biotechnology Division, Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States
| | - D. Peter Tieleman
- Centre
for Molecular Simulation and Department of Biological Sciences, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Mark S.P. Sansom
- Department
of Biochemistry, University of Oxford, South Parks Road, Oxford OX1 3QU, U.K.
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30
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Pak A, Dannenhoffer-Lafage T, Madsen JJ, Voth GA. Systematic Coarse-Grained Lipid Force Fields with Semiexplicit Solvation via Virtual Sites. J Chem Theory Comput 2019; 15:2087-2100. [PMID: 30702887 PMCID: PMC6416712 DOI: 10.1021/acs.jctc.8b01033] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2018] [Indexed: 12/15/2022]
Abstract
Despite the central role of lipids in many biophysical functions, the molecular mechanisms that dictate macroscopic lipid behavior remain elusive to both experimental and computational approaches. As such, there has been much interest in the development of low-resolution, implicit-solvent coarse-grained (CG) models to dynamically simulate biologically relevant spatiotemporal scales with molecular fidelity. However, in the absence of solvent, a key challenge for CG models is to faithfully emulate solvent-mediated forces, which include both hydrophilic and hydrophobic interactions that drive lipid aggregation and self-assembly. In this work, we provide a new methodological framework to incorporate semiexplicit solvent effects through the use of virtual CG particles, which represent structural features of the solvent-lipid interface. To do so, we leverage two systematic coarse-graining approaches, multiscale coarse-graining (MS-CG) and relative entropy minimization (REM), in a hybrid fashion to construct our virtual-site CG (VCG) models. As a proof-of-concept, we focus our efforts on two lipid species, 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC) and 1,2-dipalmitoyl- sn-glycero-3-phosphocholine (DPPC), which adopt a liquid-disordered and gel phase, respectively, at room temperature. Through our analysis, we also present, to our knowledge, the first direct comparison between the MS-CG and REM methods for a complex biomolecule and highlight each of their strengths and weaknesses. We further demonstrate that VCG models recapitulate the rich biophysics of lipids, which enable self-assembly, morphological diversity, and multiple phases. Our findings suggest that the VCG framework is a powerful approach for investigation into macromolecular biophysics.
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Affiliation(s)
- Alexander
J. Pak
- Department of Chemistry, The
University of Chicago, Chicago, Illinois 60637, United States
| | | | - Jesper J. Madsen
- Department of Chemistry, The
University of Chicago, Chicago, Illinois 60637, United States
| | - Gregory A. Voth
- Department of Chemistry, The
University of Chicago, Chicago, Illinois 60637, United States
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31
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Bidone TC, Polley A, Jin J, Driscoll T, Iwamoto DV, Calderwood DA, Schwartz MA, Voth GA. Coarse-Grained Simulation of Full-Length Integrin Activation. Biophys J 2019; 116:1000-1010. [PMID: 30851876 DOI: 10.1016/j.bpj.2019.02.011] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Revised: 12/25/2018] [Accepted: 02/13/2019] [Indexed: 01/01/2023] Open
Abstract
Integrin conformational dynamics are critical to their receptor and signaling functions in many cellular processes, including spreading, adhesion, and migration. However, assessing integrin conformations is both experimentally and computationally challenging because of limitations in resolution and dynamic sampling. Thus, structural changes that underlie transitions between conformations are largely unknown. Here, focusing on integrin αvβ3, we developed a modified form of the coarse-grained heterogeneous elastic network model (hENM), which allows sampling conformations at the onset of activation by formally separating local fluctuations from global motions. Both local fluctuations and global motions are extracted from all-atom molecular dynamics simulations of the full-length αvβ3 bent integrin conformer, but whereas the former are incorporated in the hENM as effective harmonic interactions between groups of residues, the latter emerge by systematically identifying and treating weak interactions between long-distance domains with flexible and anharmonic connections. The new hENM model allows integrins and single-point mutant integrins to explore various conformational states, including the initiation of separation between α- and β-subunit cytoplasmic regions, headpiece extension, and legs opening.
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Affiliation(s)
- Tamara C Bidone
- Department of Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois
| | - Anirban Polley
- Department of Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois
| | - Jaehyeok Jin
- Department of Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois
| | - Tristan Driscoll
- Yale Cardiovascular Research Center and Department of Internal Medicine (Section of Cardiovascular Medicine), Yale School of Medicine, New Haven, Connecticut
| | | | - David A Calderwood
- Department of Pharmacology, New Haven, Connecticut; Department of Cell Biology, Yale University, New Haven, Connecticut
| | - Martin A Schwartz
- Departments of Cell Biology and Biomedical Engineering, Yale University, New Haven, Connecticut; Yale Cardiovascular Research Center and Department of Internal Medicine (Section of Cardiovascular Medicine), Yale School of Medicine, New Haven, Connecticut
| | - Gregory A Voth
- Department of Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois.
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32
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Deichmann G, van der Vegt NFA. Conditional Reversible Work Coarse-Grained Models with Explicit Electrostatics—An Application to Butylmethylimidazolium Ionic Liquids. J Chem Theory Comput 2019; 15:1187-1198. [DOI: 10.1021/acs.jctc.8b00881] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Gregor Deichmann
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
| | - Nico F. A. van der Vegt
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
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33
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Bereau T, Rudzinski JF. Accurate Structure-Based Coarse Graining Leads to Consistent Barrier-Crossing Dynamics. PHYSICAL REVIEW LETTERS 2018; 121:256002. [PMID: 30608819 DOI: 10.1103/physrevlett.121.256002] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2018] [Revised: 11/09/2018] [Indexed: 06/09/2023]
Abstract
Structure-based coarse graining of molecular systems offers a systematic route to reproduce the many-body potential of mean force. Unfortunately, common strategies are inherently limited by the molecular mechanics force field employed. Here, we extend the concept of multisurface dynamics, initially developed to describe electronic transitions in chemical reactions, to accurately sample the conformational ensemble of a classical system in equilibrium. In analogy to describing different electronic configurations, a surface-hopping scheme couples distinct conformational basins beyond the additivity of the Hamiltonian. The incorporation of more surfaces leads systematically toward improved cross-correlations. The resulting models naturally achieve consistent long-time dynamics for systems governed by barrier-crossing events.
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Affiliation(s)
- Tristan Bereau
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
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34
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Aydin F, Katkar HH, Voth GA. Multiscale simulation of actin filaments and actin-associated proteins. Biophys Rev 2018; 10:1521-1535. [PMID: 30382557 PMCID: PMC6297090 DOI: 10.1007/s12551-018-0474-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2018] [Accepted: 10/21/2018] [Indexed: 02/04/2023] Open
Abstract
Actin is an important cytoskeletal protein that serves as a building block to form filament networks that span across the cell. These networks are orchestrated by a myriad of other cytoskeletal entities including the unbranched filament-forming protein formin and branched network-forming protein complex Arp2/3. Computational models have been able to provide insights into many important structural transitions that are involved in forming these networks, and into the nature of interactions essential for actin filament formation and for regulating the behavior of actin-associated proteins. In this review, we summarize a subset of such models that focus on the atomistic features and those that can integrate atomistic features into a larger picture in a multiscale fashion.
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Affiliation(s)
- Fikret Aydin
- Department of Chemistry, Institute of Biophysical Dynamics, and James Frank Institute, University of Chicago, Chicago, IL, USA
| | - Harshwardhan H Katkar
- Department of Chemistry, Institute of Biophysical Dynamics, and James Frank Institute, University of Chicago, Chicago, IL, USA
| | - Gregory A Voth
- Department of Chemistry, Institute of Biophysical Dynamics, and James Frank Institute, University of Chicago, Chicago, IL, USA.
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35
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Advances in coarse-grained modeling of macromolecular complexes. Curr Opin Struct Biol 2018; 52:119-126. [PMID: 30508766 DOI: 10.1016/j.sbi.2018.11.005] [Citation(s) in RCA: 83] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2018] [Revised: 11/05/2018] [Accepted: 11/17/2018] [Indexed: 01/12/2023]
Abstract
Recent progress in coarse-grained (CG) molecular modeling and simulation has facilitated an influx of computational studies on biological macromolecules and their complexes. Given the large separation of length-scales and time-scales that dictate macromolecular biophysics, CG modeling and simulation are well-suited to bridge the microscopic and mesoscopic or macroscopic details observed from all-atom molecular simulations and experiments, respectively. In this review, we first summarize recent innovations in the development of CG models, which broadly include structure-based, knowledge-based, and dynamics-based approaches. We then discuss recent applications of different classes of CG models to explore various macromolecular complexes. Finally, we conclude with an outlook for the future in this ever-growing field of biomolecular modeling.
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36
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Jin J, Han Y, Voth GA. Ultra-Coarse-Grained Liquid State Models with Implicit Hydrogen Bonding. J Chem Theory Comput 2018; 14:6159-6174. [PMID: 30354110 DOI: 10.1021/acs.jctc.8b00812] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Coarse-graining (CG) methodologies have been widely used to extend the time and length scales of computer simulations by averaging over the atomistic details beneath the resolution of the CG models. Despite the efficiency of CG models, important configurational information during a given process may be lost at the CG resolution. One example of this is the topology of the hydrogen bonding network in the liquid state. When the functional group that participates in hydrogen bonding (e.g., -OH in methanol) is coarse-grained into one CG site, the effective interactions of the resultant CG model are usually derived from an averaged overall trajectory and, thus, do not take into account the hydrogen bonding interactions and topologies that are present at the all-atom resolution. In order to overcome this challenge, the present study develops new ultra-coarse-grained (UCG) models that include internal states within the CG sites that participate in hydrogen bonding, where each state represents a specific configuration such as the hydrogen bonding donor or acceptor. Internal states of the UCG beads are modeled to remain in quasi-equilibrium, and the degree of mixing is controlled by utilizing the effective local density of the UCG sites. In particular, we consider two groups of UCG models with different types of hydrogen bonding motifs: chain-like and ring-like. Using five different liquid systems that contain the same fundamental functional groups as biomolecules, we demonstrate the ability of the UCG models to reproduce the structural properties that originate from the configurations beneath the resolution of the UCG model. This proposed approach can also be applied to other liquids with such specific and directional interactions, or even to complex biomolecular systems in which hydrogen bonding is critical.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics , The University of Chicago , Chicago , Illinois 60637 , United States
| | - Yining Han
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics , The University of Chicago , Chicago , Illinois 60637 , United States
| | - Gregory A Voth
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics , The University of Chicago , Chicago , Illinois 60637 , United States
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37
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Katkar HH, Davtyan A, Durumeric AEP, Hocky GM, Schramm AC, De La Cruz EM, Voth GA. Insights into the Cooperative Nature of ATP Hydrolysis in Actin Filaments. Biophys J 2018; 115:1589-1602. [PMID: 30249402 PMCID: PMC6260209 DOI: 10.1016/j.bpj.2018.08.034] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2018] [Revised: 08/21/2018] [Accepted: 08/22/2018] [Indexed: 12/11/2022] Open
Abstract
Actin filaments continually assemble and disassemble within a cell. Assembled filaments "age" as a bound nucleotide ATP within each actin subunit quickly hydrolyzes followed by a slower release of the phosphate Pi, leaving behind a bound ADP. This subtle change in nucleotide state of actin subunits affects filament rigidity as well as its interactions with binding partners. We present here a systematic multiscale ultra-coarse-graining approach that provides a computationally efficient way to simulate a long actin filament undergoing ATP hydrolysis and phosphate-release reactions while systematically taking into account available atomistic details. The slower conformational changes and their dependence on the chemical reactions are simulated with the ultra-coarse-graining model by assigning internal states to the coarse-grained sites. Each state is represented by a unique potential surface of a local heterogeneous elastic network. Internal states undergo stochastic transitions that are coupled to conformations of the underlying molecular system. The model reproduces mechanical properties of the filament and allows us to study whether conformational fluctuations in actin subunits produce cooperative filament aging. We find that the nucleotide states of neighboring subunits modulate the reaction kinetics, implying cooperativity in ATP hydrolysis and Pi release. We further systematically coarse grain the system into a Markov state model that incorporates assembly and disassembly, facilitating a direct comparison with previously published models. We find that cooperativity in ATP hydrolysis and Pi release significantly affects the filament growth dynamics only near the critical G-actin concentration, whereas far from it, both cooperative and random mechanisms show similar growth dynamics. In contrast, filament composition in terms of the bound nucleotide distribution varies significantly at all monomer concentrations studied. These results provide new insights, to our knowledge, into the cooperative nature of ATP hydrolysis and Pi release and the implications it has for actin filament properties, providing novel predictions for future experimental studies.
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Affiliation(s)
- Harshwardhan H Katkar
- Department of Chemistry, Institute for Biophysical Dynamics and James Frank Institute, University of Chicago, Chicago, Illinois
| | - Aram Davtyan
- Department of Chemistry, Institute for Biophysical Dynamics and James Frank Institute, University of Chicago, Chicago, Illinois
| | - Aleksander E P Durumeric
- Department of Chemistry, Institute for Biophysical Dynamics and James Frank Institute, University of Chicago, Chicago, Illinois
| | - Glen M Hocky
- Department of Chemistry, Institute for Biophysical Dynamics and James Frank Institute, University of Chicago, Chicago, Illinois
| | - Anthony C Schramm
- Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut
| | - Enrique M De La Cruz
- Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut
| | - Gregory A Voth
- Department of Chemistry, Institute for Biophysical Dynamics and James Frank Institute, University of Chicago, Chicago, Illinois.
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38
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39
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Wagoner JA, Pande VS. Communication: Adaptive boundaries in multiscale simulations. J Chem Phys 2018; 148:141104. [PMID: 29655340 DOI: 10.1063/1.5025826] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Combined-resolution simulations are an effective way to study molecular properties across a range of length and time scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size and/or shape) as the simulation progresses. The number of degrees of freedom required to accurately represent even a simple molecular process can vary by several orders of magnitude throughout the course of a simulation, and adaptive boundaries react to these changes to include an appropriate but not excessive amount of detail. Here, we derive the Hamiltonian and distribution function for such a molecular simulation. We also design an algorithm that can efficiently sample the boundary as a new coordinate of the system. We apply this framework to a mixed explicit/continuum simulation of a peptide in solvent. We use this example to discuss the conditions necessary for a successful implementation of adaptive boundaries that is both efficient and accurate in reproducing molecular properties.
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Affiliation(s)
- Jason A Wagoner
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
| | - Vijay S Pande
- Department of Chemistry, Department of Structural Biology, and Department of Computer Science, Stanford University, Stanford, California 94305, USA
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40
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Wagner JW, Dannenhoffer-Lafage T, Jin J, Voth GA. Extending the range and physical accuracy of coarse-grained models: Order parameter dependent interactions. J Chem Phys 2018; 147:044113. [PMID: 28764380 DOI: 10.1063/1.4995946] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Order parameters (i.e., collective variables) are often used to describe the behavior of systems as they capture different features of the free energy surface. Yet, most coarse-grained (CG) models only employ two- or three-body non-bonded interactions between the CG particles. In situations where these interactions are insufficient for the CG model to reproduce the structural distributions of the underlying fine-grained (FG) model, additional interactions must be included. In this paper, we introduce an approach to expand the basis sets available in the multiscale coarse-graining (MS-CG) methodology by including order parameters. Then, we investigate the ability of an additive local order parameter (e.g., density) and an additive global order parameter (i.e., distance from a hard wall) to improve the description of CG models in interfacial systems. Specifically, we study methanol liquid-vapor coexistence, acetonitrile liquid-vapor coexistence, and acetonitrile liquid confined by hard-wall plates, all using single site CG models. We find that the use of order parameters dramatically improves the reproduction of structural properties of interfacial CG systems relative to the FG reference as compared with pairwise CG interactions alone.
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Affiliation(s)
- Jacob W Wagner
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Thomas Dannenhoffer-Lafage
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Jaehyeok Jin
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Gregory A Voth
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
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41
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Jin J, Voth GA. Ultra-Coarse-Grained Models Allow for an Accurate and Transferable Treatment of Interfacial Systems. J Chem Theory Comput 2018; 14:2180-2197. [PMID: 29481754 DOI: 10.1021/acs.jctc.7b01173] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
Interfacial systems are fundamentally important in many processes. However, constructing coarse-grained (CG) models for such systems is a significant challenge due to their inhomogeneous nature. This problem is made worse due to the generally nontransferable nature of the interactions in CG models across different phases. In this paper, we address these challenges by systematically constructing ultra-coarse-grained (UCG) models for interfaces, in which the CG sites are allowed to have internal states. We find that a multiscale coarse-grained (MS-CG) representation of a single CG site model fails to identify the directionality of a molecule and is unable to reproduce the correct phase coexistence for aspherical molecules. In contrast with conventional MS-CG models, the UCG methodology allows chemical and environmental changes to be captured by modulating the interactions between internal states. In this work, we design the internal states to depend on local particle density to distinguish different phases in liquid/vapor or liquid/liquid interfaces. These UCG models are able to capture phase coexistence and recapitulate structures, notably at state points in which the MS-CG method yields poor results. Interestingly, effective pairwise forces and potentials from the UCG models are almost identical to those of the bulk liquids that correspond to each phase, indicating that the UCG approach can provide transferable interactions. This approach is expected to be applicable to other systems that exhibit phase coexistence and also to complex macromolecular systems by modulating interactions based on local density or other order parameters to unravel the complex nature underlying heterogeneous system boundaries.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry , James Franck Institute, and Institute for Biophysical Dynamics The University of Chicago , Chicago , Illinois 60637 , United States
| | - Gregory A Voth
- Department of Chemistry , James Franck Institute, and Institute for Biophysical Dynamics The University of Chicago , Chicago , Illinois 60637 , United States
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42
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Sinitskiy AV, Voth GA. Quantum mechanics/coarse-grained molecular mechanics (QM/CG-MM). J Chem Phys 2018; 148:014102. [DOI: 10.1063/1.5006810] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Anton V. Sinitskiy
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Gregory A. Voth
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA
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43
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Chen YL, Habeck M. Data-driven coarse graining of large biomolecular structures. PLoS One 2017; 12:e0183057. [PMID: 28817608 PMCID: PMC5560709 DOI: 10.1371/journal.pone.0183057] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2017] [Accepted: 07/29/2017] [Indexed: 11/18/2022] Open
Abstract
Advances in experimental and computational techniques allow us to study the structure and dynamics of large biomolecular assemblies at increasingly higher resolution. However, with increasing structural detail it can be challenging to unravel the mechanism underlying the function of molecular machines. One reason is that atomistic simulations become computationally prohibitive. Moreover it is difficult to rationalize the functional mechanism of systems composed of tens of thousands to millions of atoms by following each atom’s movements. Coarse graining (CG) allows us to understand biological structures from a hierarchical perspective and to gradually zoom into the adequate level of structural detail. This article introduces a Bayesian approach for coarse graining biomolecular structures. We develop a probabilistic model that aims to represent the shape of an experimental structure as a cloud of bead particles. The particles interact via a pairwise potential whose parameters are estimated along with the bead positions and the CG mapping between atoms and beads. Our model can also be applied to density maps obtained by cryo-electron microscopy. We illustrate our approach on various test systems.
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Affiliation(s)
- Yi-Ling Chen
- Statistical Inverse Problems in Biophysics, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
- Department of NMR based Structural Biology, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
| | - Michael Habeck
- Statistical Inverse Problems in Biophysics, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
- Felix Bernstein Institute for Mathematical Statistics in the Biosciences, Georg August University Göttingen, Goldschmidtstrasse 7, 37077 Göttingen, Germany
- * E-mail:
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44
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Zhang Y, Cao Z, Xia F. Construction of ultra-coarse-grained model of protein with a Gō-like potential. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.05.039] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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45
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Voth GA. A Multiscale Description of Biomolecular Active Matter: The Chemistry Underlying Many Life Processes. Acc Chem Res 2017; 50:594-598. [PMID: 28945406 DOI: 10.1021/acs.accounts.6b00572] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
This Commentary will describe the goal of developing and implementing novel, powerful, and integrated multiscale computer simulation methodology capable of accessing the large length and long time scales inherent in the behavior of biomolecular, multiprotein "active matter" complexes within the context of cellular biology. Examples include those involved in the actin-based cytoskeleton and its mechanochemistry. The primary objective is to connect detailed molecular and chemical properties with the key mesoscopic features manifest at the scales of cellular biology through a transformative theoretical and computer simulation approach, based on real physical and chemical interactions. This multiscale computational work would also make critical contact with rapidly developing experimental techniques such as super-resolution optical imaging, single molecule spectroscopy, and cryo-electron tomography, which are providing remarkable insight into the internal mesoscale self-organization and dynamics of cells.
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Affiliation(s)
- Gregory A. Voth
- Department of Chemistry,
James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637, United States
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46
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Sevink GJA, Schmid F, Kawakatsu T, Milano G. Combining cell-based hydrodynamics with hybrid particle-field simulations: efficient and realistic simulation of structuring dynamics. SOFT MATTER 2017; 13:1594-1623. [PMID: 28128838 DOI: 10.1039/c6sm02252a] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We have extended an existing hybrid MD-SCF simulation technique that employs a coarsening step to enhance the computational efficiency of evaluating non-bonded particle interactions. This technique is conceptually equivalent to the single chain in mean-field (SCMF) method in polymer physics, in the sense that non-bonded interactions are derived from the non-ideal chemical potential in self-consistent field (SCF) theory, after a particle-to-field projection. In contrast to SCMF, however, MD-SCF evolves particle coordinates by the usual Newton's equation of motion. Since collisions are seriously affected by the softening of non-bonded interactions that originates from their evaluation at the coarser continuum level, we have devised a way to reinsert the effect of collisions on the structural evolution. Merging MD-SCF with multi-particle collision dynamics (MPCD), we mimic particle collisions at the level of computational cells and at the same time properly account for the momentum transfer that is important for a realistic system evolution. The resulting hybrid MD-SCF/MPCD method was validated for a particular coarse-grained model of phospholipids in aqueous solution, against reference full-particle simulations and the original MD-SCF model. We additionally implemented and tested an alternative and more isotropic finite difference gradient. Our results show that efficiency is improved by merging MD-SCF with MPCD, as properly accounting for hydrodynamic interactions considerably speeds up the phase separation dynamics, with negligible additional computational costs compared to efficient MD-SCF. This new method enables realistic simulations of large-scale systems that are needed to investigate the applications of self-assembled structures of lipids in nanotechnologies.
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Affiliation(s)
- G J A Sevink
- Leiden Institute of Chemistry, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands.
| | - F Schmid
- Institut for Physik, Johannes Gutenberg Univeristat Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - T Kawakatsu
- Department of Physics, Tohoku University, Aoba, Aoba-ku, Sendai 980-8578, Japan
| | - G Milano
- Dipartimento di Chimica e Biologia, Universit degli Studi di Salerno, via Ponte don Melillo, Fisciano, Italy
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47
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Dama JF, Jin J, Voth GA. The Theory of Ultra-Coarse-Graining. 3. Coarse-Grained Sites with Rapid Local Equilibrium of Internal States. J Chem Theory Comput 2017; 13:1010-1022. [PMID: 28112956 DOI: 10.1021/acs.jctc.6b01081] [Citation(s) in RCA: 44] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
When viewed through a coarse-grained lens, important molecular and biophysical systems can appear to undergo discrete, switch-like state changes in addition to more continuous configurational motions. One of our recent papers described a theory for bottom-up coarse-graining of the equilibrium statistics of models with such behavior, called ultra-coarse-grained (UCG) models, and a follow up paper described an implementation when the states of the coarse-grained sites or "beads" change rarely. However, not all systems with this discrete behavior fall under that special limit. This article develops the general UCG theory for the opposite limit, that is, where the internal states of the CG particles or beads adjust rapidly so as to always remain effectively at quasi-equilibrium no matter what the positions of the coarse-grained particles. This rapid local equilibrium allows ultra-coarse-graining to mix standard coarse-grained force fields by using local order parameters to control the degree of mixing, which adds an environmental dependence and many-body effects to the coarse-grained model while requiring minimal new coding. This article first presents the definition of such UCG force fields as well as their fitting procedures from atomistic-scale data, and then it presents three examples of UCG simulations with an approach that we call UCG with rapid local equilibrium (UCG-RLE). We then present an application of UCG-RLE using the full bottom-up methodology to coarse-grain and simulate cooperative hydrophobic association of neopentane in methanol solvent. UCG-RLE force matching does a superior job of matching solute-solute correlation functions and solute cluster size distributions compared to the more standard force-matched models not having coarse-grained sites with discrete internal states.
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Affiliation(s)
- James F Dama
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago , Chicago, Illinois 60637, United States
| | - Jaehyeok Jin
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago , Chicago, Illinois 60637, United States
| | - Gregory A Voth
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago , Chicago, Illinois 60637, United States
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Madsen J, Sinitskiy AV, Li J, Voth GA. Highly Coarse-Grained Representations of Transmembrane Proteins. J Chem Theory Comput 2017; 13:935-944. [PMID: 28043122 PMCID: PMC5312841 DOI: 10.1021/acs.jctc.6b01076] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2016] [Indexed: 01/04/2023]
Abstract
Numerous biomolecules and biomolecular complexes, including transmembrane proteins (TMPs), are symmetric or at least have approximate symmetries. Highly coarse-grained models of such biomolecules, aiming at capturing the essential structural and dynamical properties on resolution levels coarser than the residue scale, must preserve the underlying symmetry. However, making these models obey the correct physics is in general not straightforward, especially at the highly coarse-grained resolution where multiple (∼3-30 in the current study) amino acid residues are represented by a single coarse-grained site. In this paper, we propose a simple and fast method of coarse-graining TMPs obeying this condition. The procedure involves partitioning transmembrane domains into contiguous segments of equal length along the primary sequence. For the coarsest (lowest-resolution) mappings, it turns out to be most important to satisfy the symmetry in a coarse-grained model. As the resolution is increased to capture more detail, however, it becomes gradually more important to match modular repeats in the secondary structure (such as helix-loop repeats) instead. A set of eight TMPs of various complexity, functionality, structural topology, and internal symmetry, representing different classes of TMPs (ion channels, transporters, receptors, adhesion, and invasion proteins), has been examined. The present approach can be generalized to other systems possessing exact or approximate symmetry, allowing for reliable and fast creation of multiscale, highly coarse-grained mappings of large biomolecular assemblies.
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Affiliation(s)
| | | | | | - Gregory A. Voth
- Department of Chemistry,
Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
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Kmiecik S, Gront D, Kolinski M, Wieteska L, Dawid AE, Kolinski A. Coarse-Grained Protein Models and Their Applications. Chem Rev 2016; 116:7898-936. [DOI: 10.1021/acs.chemrev.6b00163] [Citation(s) in RCA: 555] [Impact Index Per Article: 69.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Sebastian Kmiecik
- Faculty
of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Dominik Gront
- Faculty
of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michal Kolinski
- Bioinformatics
Laboratory, Mossakowski Medical Research Center of the Polish Academy of Sciences, Pawinskiego 5, 02-106 Warsaw, Poland
| | - Lukasz Wieteska
- Faculty
of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
- Department
of Medical Biochemistry, Medical University of Lodz, Mazowiecka 6/8, 92-215 Lodz, Poland
| | | | - Andrzej Kolinski
- Faculty
of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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50
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Hocky GM, Baker JL, Bradley MJ, Sinitskiy AV, De La Cruz EM, Voth GA. Cations Stiffen Actin Filaments by Adhering a Key Structural Element to Adjacent Subunits. J Phys Chem B 2016; 120:4558-67. [PMID: 27146246 PMCID: PMC4959277 DOI: 10.1021/acs.jpcb.6b02741] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
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Ions
regulate the assembly and mechanical properties of actin filaments.
Recent work using structural bioinformatics and site-specific mutagenesis
favors the existence of two discrete and specific divalent cation
binding sites on actin filaments, positioned in the long axis between
actin subunits. Cation binding at one site drives polymerization,
while the other modulates filament stiffness and plays a role in filament
severing by the regulatory protein, cofilin. Existing structural methods
have not been able to resolve filament-associated cations, and so
in this work we turn to molecular dynamics simulations to suggest
a candidate binding pocket geometry for each site and to elucidate
the mechanism by which occupancy of the “stiffness site”
affects filament mechanical properties. Incorporating a magnesium
ion in the “polymerization site” does not seem to require
any large-scale change to an actin subunit’s conformation.
Binding of a magnesium ion in the “stiffness site” adheres
the actin DNase-binding loop (D-loop) to its long-axis neighbor, which
increases the filament torsional stiffness and bending persistence
length. Our analysis shows that bound D-loops occupy a smaller region
of accessible conformational space. Cation occupancy buries key conserved
residues of the D-loop, restricting accessibility to regulatory proteins
and enzymes that target these amino acids.
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Affiliation(s)
- Glen M Hocky
- Department of Chemistry, James Franck Institute, Institute for Biophysical Dynamics, and Computation Institute, The University of Chicago , Chicago, Illinois 60637, United States
| | - Joseph L Baker
- Department of Chemistry, The College of New Jersey , Ewing Township, New Jersey 08628, United States
| | - Michael J Bradley
- Molecular Biophysics and Biochemistry, Yale University , New Haven, Connecticut 06520, United States
| | - Anton V Sinitskiy
- Department of Chemistry, James Franck Institute, Institute for Biophysical Dynamics, and Computation Institute, The University of Chicago , Chicago, Illinois 60637, United States
| | - Enrique M De La Cruz
- Molecular Biophysics and Biochemistry, Yale University , New Haven, Connecticut 06520, United States
| | - Gregory A Voth
- Department of Chemistry, James Franck Institute, Institute for Biophysical Dynamics, and Computation Institute, The University of Chicago , Chicago, Illinois 60637, United States
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