1
|
Izvekov S, Kroonblawd MP, Larentzos JP, Brennan JK, Rice BM. Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB). J Phys Chem B 2024. [PMID: 38489758 DOI: 10.1021/acs.jpcb.3c07078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/17/2024]
Abstract
The MSCG/FM (multiscale coarse-graining via force-matching) approach is an efficient supervised machine learning method to develop microscopically informed coarse-grained (CG) models. We present a theory based on the principle of maximum entropy (PME) enveloping the existing MSCG/FM approaches. This theory views the MSCG/FM method as a special case of matching the thermodynamic forces from the extended ensemble described by the set of thermodynamic (relevant) system coordinates. This set may include CG coordinates, the stress tensor, applied external fields, and so forth, and may be characterized by nonequilibrium conditions. Following the presentation of the theory, we discuss the consistent matching of both bonded and nonbonded interactions. The proposed PME formulation is used as a starting point to extend the MSCG/FM method to the constant strain ensemble, which together with the explicit matching of the bonded forces is better suited for coarse-graining anisotropic media at a submolecular resolution. The theory is demonstrated by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a well-known insensitive molecular energetic material, which exhibits highly anisotropic mechanical properties.
Collapse
Affiliation(s)
- Sergei Izvekov
- U.S. Army DEVCOM Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
| | - Matthew P Kroonblawd
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - James P Larentzos
- U.S. Army DEVCOM Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
| | - John K Brennan
- U.S. Army DEVCOM Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
| | - Betsy M Rice
- U.S. Army DEVCOM Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
| |
Collapse
|
2
|
Izvekov S, Rice BM. Hierarchical Machine Learning of Low-Resolution Coarse-Grained Free Energy Potentials. J Chem Theory Comput 2023. [PMID: 37256918 DOI: 10.1021/acs.jctc.3c00128] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
A force-matching-based method for supervised machine learning (ML) of coarse-grained (CG) free energy (FE) potentials─known as multiscale coarse-graining via force-matching (MSCG/FM)─is an efficient method to develop microscopically informed CG models that are thermodynamically and statistically equivalent to the reference microscopic models. For low-resolution models, when the coarse-graining is at supramolecular scales, objective-oriented clustering of nonbonded particles is required and the reduced description becomes a function of the clustering algorithm. In the present work, we explore the dependence of the ML of the CG Helmholtz FE potential on the clustering algorithm. We consider coarse-graining based on partitional (k-means, leading to Voronoi diagram) and hierarchical agglomerative (bottom-up) clustering algorithms common in unsupervised ML and develop theory connecting the MSCG/FM learned CG Helmholtz potential and the clustering statistics. By combining the agglomerative clustering and the MSCG/FM learning in a recursive manner, we propose an efficient ML methodology to develop the fine-to-low resolution hierarchies of the CG models. The methodology does not suffer from degrading accuracy or increased computational cost to construct larger hierarchies and as such does not impose an upper size limitation of the CG particles resulting from the extended hierarchies. The utility of the methodology is demonstrated by obtaining the bottom-up agglomerative hierarchy for liquid nitromethane from all-atom molecular dynamics (MD) simulations. For agglomerative hierarchies, we prove the existence of renormalization group transformations that indicate self-similarity and allow for learning the low-resolution MSCG/FM potentials at low computational cost by rescaling and renormalizing the certain finer-resolution members of the hierarchy. The hierarchies of the CG models can be used to carry out simulations under constant-pressure conditions.
Collapse
Affiliation(s)
- Sergei Izvekov
- U.S. Army DEVCOM Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
| | - Betsy M Rice
- U.S. Army DEVCOM Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States
| |
Collapse
|
3
|
Inverse Boltzmann Iterative Multi-Scale Molecular Dynamics Study between Carbon Nanotubes and Amino Acids. MOLECULES (BASEL, SWITZERLAND) 2022; 27:molecules27092785. [PMID: 35566140 PMCID: PMC9104776 DOI: 10.3390/molecules27092785] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Revised: 04/23/2022] [Accepted: 04/26/2022] [Indexed: 11/17/2022]
Abstract
Our work uses Iterative Boltzmann Inversion (IBI) to study the coarse-grained interaction between 20 amino acids and the representative carbon nanotube CNT55L3. IBI is a multi-scale simulation method that has attracted the attention of many researchers in recent years. It can effectively modify the coarse-grained model derived from the Potential of Mean Force (PMF). IBI is based on the distribution result obtained by All-Atom molecular dynamics simulation; that is, the target distribution function and the PMF potential energy are extracted, and then, the initial potential energy extracted by the PMF is used to perform simulation iterations using IBI. Our research results have been through more than 100 iterations, and finally, the distribution obtained by coarse-grained molecular simulation (CGMD) can effectively overlap with the results of all-atom molecular dynamics simulation (AAMD). In addition, our work lays the foundation for the study of force fields for the simulation of the coarse-graining of super-large proteins and other important nanoparticles.
Collapse
|
4
|
Vaiwala R, Ayappa KG. A generic force field for simulating native protein structures using dissipative particle dynamics. SOFT MATTER 2021; 17:9772-9785. [PMID: 34651150 DOI: 10.1039/d1sm01194d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
A coarse-grained force field for molecular dynamics simulations of the native structures of proteins in a dissipative particle dynamics (DPD) framework is developed. The parameters for bonded interactions are derived by mapping the bonds and angles for 20 amino acids onto target distributions obtained from fully atomistic simulations in explicit solvent. A dual-basin potential is introduced for stabilizing backbone angles, to cover a wide spectrum of protein secondary structures. The backbone dihedral potential enables folding of the protein from an unfolded initial state to the folded native structure. The proposed force field is validated by evaluating the structural properties of several model peptides and proteins including the SARS-CoV-2 fusion peptide, consisting of α-helices, β-sheets, loops and turns. Detailed comparisons with fully atomistic simulations are carried out to assess the ability of the proposed force field to stabilize the different secondary structures present in proteins. The compact conformations of the native states were evident from the radius of gyration and the high intensity peaks of the root mean square deviation histograms, which were found to be within 0.4 nm. The Ramachandran-like energy landscape on the phase space of backbone angles (θ) and dihedrals (ϕ) effectively captured the conformational phase space of α-helices at ∼(ϕ = 50°,θ = 90°) and β-strands at ∼(ϕ = ±180°,θ = 90-120°). Furthermore, the residue-residue native contacts were also well reproduced by the proposed DPD model. The applicability of the model to multidomain complexes was assessed using lysozyme and a large α-helical bacterial pore-forming toxin, cytolysin A. Our study illustrates that the proposed force field is generic, and can potentially be extended for efficient in silico investigations of membrane bound polypeptides and proteins using DPD simulations.
Collapse
Affiliation(s)
- Rakesh Vaiwala
- Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India.
| | - K Ganapathy Ayappa
- Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India.
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India
| |
Collapse
|
5
|
Aggregation Behavior of Model Asphaltenes Revealed from Large-Scale Coarse-Grained Molecular Simulations. J Phys Chem B 2019; 123:2380-2396. [PMID: 30735393 DOI: 10.1021/acs.jpcb.8b12295] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Fully atomistic simulations of models of asphaltenes in simple solvents have allowed the study of trends in aggregation phenomena to understand the underlying role played by molecular structure. The detail included at this scale of molecular modeling is, however, at odds with the required spatial and temporal resolution needed to fully understand asphaltene aggregation. The computational cost required to explore the relevant scales can be reduced by employing coarse-grained (CG) models, which consist of lumping a few atoms into a single segment that is characterized by effective interactions. In this work, CG force fields developed via the statistical associating fluid theory (SAFT-γ) [ Müller , E. A. ; Jackson , G. Annu. Rev. Chem. Biomol. Eng. 5 , 2014 , 405 - 427 ] equation of state (EoS) provide a reliable pathway to link the molecular description with macroscopic thermophysical data. A recent modification of the SAFT-VR EoS [ Müller , E. A. ; Mejía , A. Langmuir 33 , 2017 , 11518 - 11529 ], which allows for the parameterization of homonuclear rings, is selected as the starting point to develop CG models for polycyclic aromatic hydrocarbons. The new aromatic-core models, along with others published for simpler organic molecules, are adopted for the construction of asphaltene models by combining different chemical moieties in a group-contribution fashion. We apply the procedure to two previously reported asphaltene models and perform molecular dynamics simulations to validate the coarse-grained representation against benchmark systems of 27 asphaltenes in a pure solvent (toluene or heptane) described in a fully atomistic fashion. An excellent match between both levels of description is observed for the cluster size, radii of gyration, and relative-shape-anisotropy-factor distributions. We exploit the advantages of the CG representation by simulating systems containing up to 2000 asphaltene molecules in an explicit solvent investigating the effect of asphaltene concentration, solvent composition, and temperature on aggregation. By studying large systems facilitated by the use of CG models, we observe stable continuous distributions of molecular aggregates at conditions away from the two-phase precipitation point. As a further example application, a widely accepted interpretation of cluster-size distributions in asphaltenic systems is challenged by performing system-size tests, reversibility checks, and a time-dependence analysis. The proposed coarse-graining procedure is seen to be general and predictive and, hence, can be applied to other asphaltenic molecular structures.
Collapse
|
6
|
Chu JW, Yang H. Identifying the structural and kinetic elements in protein large-amplitude conformational motions. INT REV PHYS CHEM 2017. [DOI: 10.1080/0144235x.2017.1283885] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
|
7
|
Izvekov S. Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit. Phys Rev E 2017; 95:013303. [PMID: 28208451 DOI: 10.1103/physreve.95.013303] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Indexed: 04/29/2023]
Abstract
We derive alternative Markov approximations for the projected (stochastic) force and memory function in the coarse-grained (CG) generalized Langevin equation, which describes the time evolution of the center-of-mass coordinates of clusters of particles in the microscopic ensemble. This is done with the aid of the Mori-Zwanzig projection operator method based on the recently introduced projection operator [S. Izvekov, J. Chem. Phys. 138, 134106 (2013)10.1063/1.4795091]. The derivation exploits the "generalized additive fluctuating force" representation to which the projected force reduces in the adopted projection operator formalism. For the projected force, we present a first-order time expansion which correctly extends the static fluctuating force ansatz with the terms necessary to maintain the required orthogonality of the projected dynamics in the Markov limit to the space of CG phase variables. The approximant of the memory function correctly accounts for the momentum dependence in the lowest (second) order and indicates that such a dependence may be important in the CG dynamics approaching the Markov limit. In the case of CG dynamics with a weak dependence of the memory effects on the particle momenta, the expression for the memory function presented in this work is applicable to non-Markov systems. The approximations are formulated in a propagator-free form allowing their efficient evaluation from the microscopic data sampled by standard molecular dynamics simulations. A numerical application is presented for a molecular liquid (nitromethane). With our formalism we do not observe the "plateau-value problem" if the friction tensors for dissipative particle dynamics (DPD) are computed using the Green-Kubo relation. Our formalism provides a consistent bottom-up route for hierarchical parametrization of DPD models from atomistic simulations.
Collapse
Affiliation(s)
- Sergei Izvekov
- Weapons and Materials Research Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, Maryland 21005, USA
| |
Collapse
|
8
|
Moore JD, Barnes BC, Izvekov S, Lísal M, Sellers MS, Taylor DE, Brennan JK. A coarse-grain force field for RDX: Density dependent and energy conserving. J Chem Phys 2016; 144:104501. [DOI: 10.1063/1.4942520] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Joshua D. Moore
- Energetic Materials Science Branch, RDRL-WML-B, US Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005-5066, USA
| | - Brian C. Barnes
- Energetic Materials Science Branch, RDRL-WML-B, US Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005-5066, USA
| | - Sergei Izvekov
- Energetic Materials Science Branch, RDRL-WML-B, US Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005-5066, USA
| | - Martin Lísal
- Laboratory of Aerosols Chemistry and Physics, Institute of Chemical Process Fundamentals of the Czech Academy of Sciences, v. v. i., 165 02 Prague 6-Suchdol, Czech Republic
- Department of Physics, Institute of Science, J. E. Purkinje University, 400 96 Ústí n. Lab., Czech Republic
| | - Michael S. Sellers
- Energetic Materials Science Branch, RDRL-WML-B, US Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005-5066, USA
| | - DeCarlos E. Taylor
- Energetic Materials Science Branch, RDRL-WML-B, US Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005-5066, USA
| | - John K. Brennan
- Energetic Materials Science Branch, RDRL-WML-B, US Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005-5066, USA
| |
Collapse
|
9
|
Ramakrishnan N, Radhakrishnan R. Phenomenology based multiscale models as tools to understand cell membrane and organelle morphologies. ACTA ACUST UNITED AC 2015; 22:129-175. [PMID: 27087801 DOI: 10.1016/bs.adplan.2015.06.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
An intriguing question in cell biology is "how do cells regulate their shape?" It is commonly believed that the observed cellular morphologies are a result of the complex interaction among the lipid molecules (constituting the cell membrane), and with a number of other macromolecules, such as proteins. It is also believed that the common biophysical processes essential for the functioning of a cell also play an important role in cellular morphogenesis. At the cellular scale-where typical dimensions are in the order of micrometers-the effects arising from the molecular scale can either be modeled as equilibrium or non-equilibrium processes. In this chapter, we discuss the dynamically triangulated Monte Carlo technique to model and simulate membrane morphologies at the cellular scale, which in turn can be used to investigate several questions related to shape regulation in cells. In particular, we focus on two specific problems within the framework of isotropic and anisotropic elasticity theories: namely, (i) the origin of complex, physiologically relevant, membrane shapes due to the interaction of the membrane with curvature remodeling proteins, and (ii) the genesis of steady state cellular shapes due to the action of non-equilibrium forces that are generated by the fission and fusion of transport vesicles and by the binding and unbinding of proteins from the parent membrane.
Collapse
Affiliation(s)
- N Ramakrishnan
- Department of Chemical and Biomolecular Engineering, Department of Bioengineering, Department of Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, PA-19104
| | - Ravi Radhakrishnan
- Department of Chemical and Biomolecular Engineering, Department of Bioengineering, Department of Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, PA-19104
| |
Collapse
|
10
|
Zhao S, Liu Y, Chen X, Lu Y, Liu H, Hu Y. Unified Framework of Multiscale Density Functional Theories and Its Recent Applications. MESOSCALE MODELING IN CHEMICAL ENGINEERING PART II 2015. [DOI: 10.1016/bs.ache.2015.10.001] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
|
11
|
Izvekov S, Rice BM. Multi-scale coarse-graining of non-conservative interactions in molecular liquids. J Chem Phys 2014; 140:104104. [DOI: 10.1063/1.4866142] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
12
|
Feig M, Sugita Y. Reaching new levels of realism in modeling biological macromolecules in cellular environments. J Mol Graph Model 2013; 45:144-56. [PMID: 24036504 DOI: 10.1016/j.jmgm.2013.08.017] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2013] [Revised: 08/14/2013] [Accepted: 08/19/2013] [Indexed: 12/21/2022]
Abstract
An increasing number of studies are aimed at modeling cellular environments in a comprehensive and realistic fashion. A major challenge in these efforts is how to bridge spatial and temporal scales over many orders of magnitude. Furthermore, there are additional challenges in integrating different aspects ranging from questions about biomolecular stability in crowded environments to the description of reactive processes on cellular scales. In this review, recent studies with models of biomolecules in cellular environments at different levels of detail are discussed in terms of their strengths and weaknesses. In particular, atomistic models, implicit representations of cellular environments, coarse-grained and spheroidal models of biomolecules, as well as the inclusion of reactive processes via reaction-diffusion models are described. Furthermore, strategies for integrating the different models into a comprehensive description of cellular environments are discussed.
Collapse
Affiliation(s)
- Michael Feig
- Department of Biochemistry & Molecular Biology and Department of Chemistry, Michigan State University, 603 Wilson Road, BCH 218, East Lansing, MI 48824, United States; RIKEN Quantitative Biology Center, International Medical Device Alliance (IMDA) 6F, 1-6-5 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan.
| | | |
Collapse
|
13
|
Izvekov S. Microscopic derivation of particle-based coarse-grained dynamics. J Chem Phys 2013; 138:134106. [DOI: 10.1063/1.4795091] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
|
14
|
|
15
|
Abstract
The Martini force field is a coarse-grained force field suited for molecular dynamics simulations of biomolecular systems. The force field has been parameterized in a systematic way, based on the reproduction of partitioning free energies between polar and apolar phases of a large number of chemical compounds. In this chapter the methodology underlying the force field is presented together with details of its parameterization and limitations. Then currently available topologies are described with a short overview of the key elements of their parameterization. These include the new polarizable Martini water model. A set of three selected ongoing studies using the Martini force field is presented. Finally the latest lines of development are discussed.
Collapse
|
16
|
de Jong DH, Singh G, Bennett WFD, Arnarez C, Wassenaar TA, Schäfer LV, Periole X, Tieleman DP, Marrink SJ. Improved Parameters for the Martini Coarse-Grained Protein Force Field. J Chem Theory Comput 2012; 9:687-97. [DOI: 10.1021/ct300646g] [Citation(s) in RCA: 922] [Impact Index Per Article: 76.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Djurre H. de Jong
- Groningen Biomolecular Sciences
and Biotechnology Institute and Zernike Institute for Advanced Materials,
University of Groningen, Nijenborgh 7, 9747 AG Groningen, The Netherlands
| | - Gurpreet Singh
- Department of Biological Sciences
and Institute for Biocomplexity and Informatics, University of Calgary,
2500 University Dr. NW, Calgary, AB, Canada, T2N 1N4
| | - W. F. Drew Bennett
- Department of Biological Sciences
and Institute for Biocomplexity and Informatics, University of Calgary,
2500 University Dr. NW, Calgary, AB, Canada, T2N 1N4
| | - Clement Arnarez
- Groningen Biomolecular Sciences
and Biotechnology Institute and Zernike Institute for Advanced Materials,
University of Groningen, Nijenborgh 7, 9747 AG Groningen, The Netherlands
| | - Tsjerk A. Wassenaar
- Groningen Biomolecular Sciences
and Biotechnology Institute and Zernike Institute for Advanced Materials,
University of Groningen, Nijenborgh 7, 9747 AG Groningen, The Netherlands
| | - Lars V. Schäfer
- Groningen Biomolecular Sciences
and Biotechnology Institute and Zernike Institute for Advanced Materials,
University of Groningen, Nijenborgh 7, 9747 AG Groningen, The Netherlands
| | - Xavier Periole
- Groningen Biomolecular Sciences
and Biotechnology Institute and Zernike Institute for Advanced Materials,
University of Groningen, Nijenborgh 7, 9747 AG Groningen, The Netherlands
| | - D. Peter Tieleman
- Department of Biological Sciences
and Institute for Biocomplexity and Informatics, University of Calgary,
2500 University Dr. NW, Calgary, AB, Canada, T2N 1N4
| | - Siewert J. Marrink
- Groningen Biomolecular Sciences
and Biotechnology Institute and Zernike Institute for Advanced Materials,
University of Groningen, Nijenborgh 7, 9747 AG Groningen, The Netherlands
| |
Collapse
|
17
|
Izvekov S, Rice BM. Free-energy based pair-additive potentials for bulk Ni-Al systems: Application to study Ni-Al reactive alloying. J Chem Phys 2012; 137:094704. [DOI: 10.1063/1.4747546] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
18
|
Sala J, Guàrdia E, Martí J, Spångberg D, Masia M. Fitting properties from density functional theory based molecular dynamics simulations to parameterize a rigid water force field. J Chem Phys 2012; 136:054103. [DOI: 10.1063/1.3679402] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
|
19
|
Joshi H, Singharoy A, Sereda YV, Cheluvaraja SC, Ortoleva PJ. Multiscale simulation of microbe structure and dynamics. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2011; 107:200-17. [PMID: 21802438 PMCID: PMC3383072 DOI: 10.1016/j.pbiomolbio.2011.07.006] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2011] [Accepted: 07/01/2011] [Indexed: 10/18/2022]
Abstract
A multiscale mathematical and computational approach is developed that captures the hierarchical organization of a microbe. It is found that a natural perspective for understanding a microbe is in terms of a hierarchy of variables at various levels of resolution. This hierarchy starts with the N -atom description and terminates with order parameters characterizing a whole microbe. This conceptual framework is used to guide the analysis of the Liouville equation for the probability density of the positions and momenta of the N atoms constituting the microbe and its environment. Using multiscale mathematical techniques, we derive equations for the co-evolution of the order parameters and the probability density of the N-atom state. This approach yields a rigorous way to transfer information between variables on different space-time scales. It elucidates the interplay between equilibrium and far-from-equilibrium processes underlying microbial behavior. It also provides framework for using coarse-grained nanocharacterization data to guide microbial simulation. It enables a methodical search for free-energy minimizing structures, many of which are typically supported by the set of macromolecules and membranes constituting a given microbe. This suite of capabilities provides a natural framework for arriving at a fundamental understanding of microbial behavior, the analysis of nanocharacterization data, and the computer-aided design of nanostructures for biotechnical and medical purposes. Selected features of the methodology are demonstrated using our multiscale bionanosystem simulator DeductiveMultiscaleSimulator. Systems used to demonstrate the approach are structural transitions in the cowpea chlorotic mosaic virus, RNA of satellite tobacco mosaic virus, virus-like particles related to human papillomavirus, and iron-binding protein lactoferrin.
Collapse
Affiliation(s)
- Harshad Joshi
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, IN 47405 U. S. A
| | - Abhishek Singharoy
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, IN 47405 U. S. A
| | - Yuriy V. Sereda
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, IN 47405 U. S. A
| | - Srinath C. Cheluvaraja
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, IN 47405 U. S. A
| | - Peter J. Ortoleva
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, IN 47405 U. S. A
| |
Collapse
|
20
|
Kowalczyk P, Gauden PA, Ciach A. Optimization of Coarse-Grained Interaction Potential: Inside Inherent Limitations of Coarse-Graining Methods. J Phys Chem B 2011; 115:6985-94. [DOI: 10.1021/jp2019999] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Piotr Kowalczyk
- Nanochemistry Research Institute, Department of Chemistry, Curtin University of Technology, P.O. Box U1987, Perth, 6845 Western Australia, Australia
| | - Piotr A. Gauden
- Department of Chemistry, Physicochemistry of Carbon Materials Research Group, N. Copernicus University, Gagarin St. 7, 87-100 Torun, Poland
| | - Alina Ciach
- Institute of Physical Chemistry, Polish Academy of Science, Kasprzaka Street 44/52, 01-224 Warsaw, Poland
| |
Collapse
|
21
|
Woodcock HL, Miller BT, Hodoscek M, Okur A, Larkin JD, Ponder JW, Brooks BR. MSCALE: A General Utility for Multiscale Modeling. J Chem Theory Comput 2011; 7:1208-1219. [PMID: 21691425 DOI: 10.1021/ct100738h] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
The combination of theoretical models of macromolecules that exist at different spatial and temporal scales has become increasingly important for addressing complex biochemical problems. This work describes the extension of concurrent multiscale approaches, introduces a general framework for carrying out calculations, and describes its implementation into the CHARMM macromolecular modeling package. This functionality, termed MSCALE, generalizes both the additive and subtractive multiscale scheme (e.g. QM/MM ONIOM-type), and extends its support to classical force fields, coarse grained modeling (e.g. ENM, GNM, etc.), and a mixture of them all. The MSCALE scheme is completely parallelized with each subsystem running as an independent, but connected calculation. One of the most attractive features of MSCALE is the relative ease of implementation using the standard MPI communication protocol. This allows external access to the framework and facilitates the combination of functionality previously isolated in separate programs. This new facility is fully integrated with free energy perturbation methods, Hessian based methods, and the use of periodicity and symmetry, which allows the calculation of accurate pressures. We demonstrate the utility of this new technique with four examples; (1) subtractive QM/MM and QM/QM calculations; (2) multi-force field alchemical free energy perturbation; (3) integration with the SANDER module of AMBER and the TINKER package to gain access to potentials not available in CHARMM; and (4) mixed resolution (i.e. coarse grain / all-atom) normal mode analysis. The potential of this new tool is clearly established and in conclusion an interesting mathematical problem is highlighted and future improvements are proposed.
Collapse
Affiliation(s)
- H Lee Woodcock
- Department of Chemistry, University of South Florida, 4202 E. Fowler Ave., CHE205, Tampa, FL 33620-5250
| | | | | | | | | | | | | |
Collapse
|
22
|
Frustration, specific sequence dependence, and nonlinearity in large-amplitude fluctuations of allosteric proteins. Proc Natl Acad Sci U S A 2011; 108:3504-9. [PMID: 21307307 DOI: 10.1073/pnas.1018983108] [Citation(s) in RCA: 119] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Proteins have often evolved sequences so as to acquire the ability for regulation via allosteric conformational change. Here we investigate how allosteric dynamics is designed through sequences with nonlinear interaction features. First, for 71 allosteric proteins of which two, open and closed, structures are available, a statistical survey of interactions using an all-atom model with effective solvation shows that those residue contact interactions specific to one of the two states are significantly weaker than are the contact interactions shared by the two states. This interaction feature indicates there is underlying sequence design to facilitate conformational change. Second, based on the energy landscape theory, we implement these interaction features into a new atomic-interaction-based coarse-grained model via a multiscale simulation protocol (AICG). The AICG model outperforms standard coarse-grained models for predictions of the native-state mean fluctuations and of the conformational change direction. Third, using the new model for adenylate kinase, we show that intrinsic fluctuations in one state contain rare and large-amplitude motions nearly reaching the other state. Such large-amplitude motions are realized partly by sequence specificity and partly by the nonlinear nature of contact interactions, leading to cracking. Both features enhance conformational transition rates.
Collapse
|
23
|
Merchant BA, Madura JD. A Review of Coarse-Grained Molecular Dynamics Techniques to Access Extended Spatial and Temporal Scales in Biomolecular Simulations. ANNUAL REPORTS IN COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1016/b978-0-444-53835-2.00003-1] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
|
24
|
Li W, Takada S. Characterizing protein energy landscape by self-learning multiscale simulations: application to a designed β-hairpin. Biophys J 2010; 99:3029-37. [PMID: 21044601 PMCID: PMC2965946 DOI: 10.1016/j.bpj.2010.08.041] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2010] [Revised: 08/17/2010] [Accepted: 08/18/2010] [Indexed: 11/29/2022] Open
Abstract
Characterizing the energy landscape of proteins at atomic resolution is still a very challenging problem, since it simultaneously requires high accuracy in estimating specific interactions and high efficiency in conformational sampling. Here, for these two requirements to meet, we extended the self-learning multiscale simulation (SLMS) method developed recently and applied it to the designed β-hairpin CLN025. The SLMS integrates all-atom and coarse-grained (CG) models in an iterative way such that the conformational sampling is performed by the CG model, the AA energy is used to calibrate the energy landscape, and the CG model is improved by the calibrated energy landscape. We extended the SLMS in two aspects, use of the energy decomposition for self-learning of the CG potential and a two-bead/residue CG model. The results show that the self-learning greatly improved the CG potential, and with the derived CG potential, the β-hairpin CLN025 robustly folded to the native structure. The self-learning iteration progressively enhanced the context dependence in the CG potential and increased the energy gap between the native and the denatured states of the CG model, leading to a funnel-like energy landscape. By using the SLMS method, without prior knowledge of the native structure but with the help of the AA energy, we can obtain a tailor-made CG potential specific to the target protein. The method can be useful for de novo structure prediction as well.
Collapse
Affiliation(s)
- Wenfei Li
- Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto, Japan, and CREST, Japan Science and Technology Agency, Kawaguchi, Japan
- Department of Physics, Nanjing University, Nanjing, China
| | - Shoji Takada
- Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto, Japan, and CREST, Japan Science and Technology Agency, Kawaguchi, Japan
| |
Collapse
|
25
|
Izvekov S, Chung PW, Rice BM. The multiscale coarse-graining method: Assessing its accuracy and introducing density dependent coarse-grain potentials. J Chem Phys 2010; 133:064109. [DOI: 10.1063/1.3464776] [Citation(s) in RCA: 76] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
26
|
Li W, Yoshii H, Hori N, Kameda T, Takada S. Multiscale methods for protein folding simulations. Methods 2010; 52:106-14. [PMID: 20434561 DOI: 10.1016/j.ymeth.2010.04.014] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2010] [Revised: 03/26/2010] [Accepted: 04/23/2010] [Indexed: 10/19/2022] Open
Abstract
Inherently hierarchic nature of proteins makes multiscale computational methods especially useful in the studies of folding and other functional dynamics. With the multiscale strategies, one can achieve improved accuracy and efficiency by coupling the atomistic and the coarse grained simulations. Depending on the problems studied, very different implementation protocols can be used to realize the multiscale idea. Here, we give detailed introductions to the currently used multiscale protocols, together with some recent applications to the protein folding simulations in our group. The advantages and weakness, as well as the application scopes of these multiscale protocols are discussed. The directions for the future developments are also proposed.
Collapse
Affiliation(s)
- Wenfei Li
- Department of Biophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | | | | | | | | |
Collapse
|
27
|
Abstract
The activity within a living cell is based on a complex network of interactions among biomolecules, exchanging information and energy through biochemical processes. These events occur on different scales, from the nano- to the macroscale, spanning about 10 orders of magnitude in the space domain and 15 orders of magnitude in the time domain. Consequently, many different modeling techniques, each proper for a particular time or space scale, are commonly used. In addition, a single process often spans more than a single time or space scale. Thus, the necessity arises for combining the modeling techniques in multiscale approaches. In this Account, I first review the different modeling methods for bio-systems, from quantum mechanics to the coarse-grained and continuum-like descriptions, passing through the atomistic force field simulations. Special attention is devoted to their combination in different possible multiscale approaches and to the questions and problems related to their coherent matching in the space and time domains. These aspects are often considered secondary, but in fact, they have primary relevance when the aim is the coherent and complete description of bioprocesses. Subsequently, applications are illustrated by means of two paradigmatic examples: (i) the green fluorescent protein (GFP) family and (ii) the proteins involved in the human immunodeficiency virus (HIV) replication cycle. The GFPs are currently one of the most frequently used markers for monitoring protein trafficking within living cells; nanobiotechnology and cell biology strongly rely on their use in fluorescence microscopy techniques. A detailed knowledge of the actions of the virus-specific enzymes of HIV (specifically HIV protease and integrase) is necessary to study novel therapeutic strategies against this disease. Thus, the insight accumulated over years of intense study is an excellent framework for this Account. The foremost relevance of these two biomolecular systems was recently confirmed by the assignment of two of the Nobel prizes in 2008: in chemistry for the discovery of GFP and in medicine for the discovery of HIV. Accordingly, these proteins were studied with essentially all of the available modeling techniques, making them ideal examples for studying the details of multiscale approaches in protein modeling.
Collapse
Affiliation(s)
- Valentina Tozzini
- NEST CNR-INFM, and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
| |
Collapse
|
28
|
Stamati H, Clementi C, Kavraki LE. Application of nonlinear dimensionality reduction to characterize the conformational landscape of small peptides. Proteins 2010; 78:223-35. [PMID: 19731366 PMCID: PMC2795065 DOI: 10.1002/prot.22526] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
The automatic classification of the wealth of molecular configurations gathered in simulation in the form of a few coordinates that help to explain the main states and transitions of the system is a recurring problem in computational molecular biophysics. We use the recently proposed ScIMAP algorithm to automatically extract motion parameters from simulation data. The procedure uses only molecular shape similarity and topology information inferred directly from the simulated conformations, and is not biased by a priori known information. The automatically recovered coordinates prove as excellent reaction coordinates for the molecules studied and can be used to identify stable states and transitions, and as a basis to build free-energy surfaces. The coordinates provide a better description of the free energy landscape when compared with coordinates computed using principal components analysis, the most popular linear dimensionality reduction technique. The method is first validated on the analysis of the dynamics of an all-atom model of alanine dipeptide, where it successfully recover all previously known metastable states. When applied to characterize the simulated folding of a coarse-grained model of beta-hairpin, in addition to the folded and unfolded states, two symmetric misfolding crossings of the hairpin strands are observed, together with the most likely transitions from one to the other.
Collapse
Affiliation(s)
- Hernán Stamati
- Department of Computer Science, Rice University, Houston, Texas, 77005
| | - Cecilia Clementi
- Department of Chemistry Rice University, Houston, Texas, 77005
- Structural and Computational Biology and Molecular Biophysics, Baylor College of Medicine, Houston, Texas, 77030
| | - Lydia E. Kavraki
- Department of Computer Science, Rice University, Houston, Texas, 77005
- Structural and Computational Biology and Molecular Biophysics, Baylor College of Medicine, Houston, Texas, 77030
- Department of Bioengineering Rice University, Houston, Texas, 77005
| |
Collapse
|
29
|
Zhang J, King CA, Dalby K, Ren P. Conformational preference of ChaK1 binding peptides: a molecular dynamics study. PMC BIOPHYSICS 2010; 3:2. [PMID: 20180991 PMCID: PMC2831825 DOI: 10.1186/1757-5036-3-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/13/2009] [Accepted: 01/21/2010] [Indexed: 11/10/2022]
Abstract
TRPM7/ChaK1 is a recently discovered atypical protein kinase that has been suggested to selectively phosphorylate the substrate residues located in α-helices. However, the actual structure of kinase-substrate complex has not been determined experimentally and the recognition mechanism remains unknown. In this work we explored possible kinase-substrate binding modes and the likelihood of an α-helix docking interaction, within a kinase active site, using molecular modeling. Specifically kinase ChaK1 and its two peptide substrates were examined; one was an 11-residue segment from the N-terminal domain of annexin-1, a putative endogenous substrate for ChaK1, and the other was an engineered 16-mer peptide substrate determined via peptide library screening. Simulated annealing (SA), replica-exchange molecular dynamics (REMD) and steered molecular dynamics (SMD) simulations were performed on the two peptide substrates and the ChaK1-substrate complex in solution. The simulations indicate that the two substrate peptides are unlikely to bind and react with the ChaK1 kinase in a stable α-helical conformation overall. The key structural elements, sequence motifs, and amino acid residues in the ChaK1 and their possible functions involved in the substrate recognition are discussed. PACS Codes: 87.15.A-
Collapse
Affiliation(s)
- Jiajing Zhang
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712, USA.
| | | | | | | |
Collapse
|
30
|
Gkeka P, Sarkisov L. Interactions of Phospholipid Bilayers with Several Classes of Amphiphilic α-Helical Peptides: Insights from Coarse-Grained Molecular Dynamics Simulations. J Phys Chem B 2009; 114:826-39. [DOI: 10.1021/jp908320b] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- Paraskevi Gkeka
- Institute for Materials and Processes, School of Engineering, University of Edinburgh, Edinburgh, U.K
| | - Lev Sarkisov
- Institute for Materials and Processes, School of Engineering, University of Edinburgh, Edinburgh, U.K
| |
Collapse
|
31
|
Ayton GS, Voth GA. Multiscale simulation of protein mediated membrane remodeling. Semin Cell Dev Biol 2009; 21:357-62. [PMID: 19922811 DOI: 10.1016/j.semcdb.2009.11.011] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2009] [Accepted: 11/09/2009] [Indexed: 11/29/2022]
Abstract
Proteins interacting with membranes can result in substantial membrane deformations and curvatures. This effect is known in its broadest terms as membrane remodeling. This review article will survey current multiscale simulation methodologies that have been employed to examine protein mediated membrane remodeling.
Collapse
Affiliation(s)
- Gary S Ayton
- Center for Biophysical Modeling and Simulation and Department of Chemistry, University of Utah, Salt Lake City, UT 84112-0850, USA
| | | |
Collapse
|
32
|
Kowalczyk P, Gauden PA, Ciach A. Role of Short-Range Directional Interactions in Coarse-Graining of Protic/Aprotic Liquids. J Phys Chem B 2009; 113:12988-98. [DOI: 10.1021/jp9038368] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Affiliation(s)
- Piotr Kowalczyk
- Applied Physics, RMIT University, GPO Box 2476 V, Victoria 3001, Australia, Department of Chemistry, Physicochemistry of Carbon Materials Research Group, N. Copernicus University, Gagarin St. 7, 87-100 Torun, Poland, and Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka Street 44/52, 01-224 Warsaw, Poland
| | - Piotr A. Gauden
- Applied Physics, RMIT University, GPO Box 2476 V, Victoria 3001, Australia, Department of Chemistry, Physicochemistry of Carbon Materials Research Group, N. Copernicus University, Gagarin St. 7, 87-100 Torun, Poland, and Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka Street 44/52, 01-224 Warsaw, Poland
| | - Alina Ciach
- Applied Physics, RMIT University, GPO Box 2476 V, Victoria 3001, Australia, Department of Chemistry, Physicochemistry of Carbon Materials Research Group, N. Copernicus University, Gagarin St. 7, 87-100 Torun, Poland, and Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka Street 44/52, 01-224 Warsaw, Poland
| |
Collapse
|
33
|
Affiliation(s)
- Stefan Balaz
- Department of Pharmaceutical Sciences, College of Pharmacy, North Dakota State University, Fargo, North Dakota 58105, USA.
| |
Collapse
|
34
|
Abstract
The multiscale coarse-graining (MS-CG) approach developed in our previous work is extended here to model solvent-free lipid bilayers. The water (solvent) molecules are completely integrated out of the coarse-grained (CG) effective force field. The MS-CG potential, a sum of pairwise central terms, accurately approximates the many-body potential of mean force in the coarse-grained coordinates. It thus incorporates both energetic and entropic contributions. To improve the stability and elastic properties of the MS-CG simulated bilayer, an additional constraint was adopted: the partial virial associated with CG bilayer sites was matched to its corresponding atomistic value for each configuration of the system. The resulting solvent-free MS-CG model reproduces a liquid-state lipid bilayer with accurate structural and elastic properties. Finally, the solvent-free MS-CG model is used to simulate a very large, flat bilayer and two liposome geometries, demonstrating its greatly enhanced computational efficiency.
Collapse
Affiliation(s)
- Sergei Izvekov
- Department of Chemistry and Center for Biophysical Modeling and Simulation, University of Utah, Salt Lake City, 84112-0850, USA
| | | |
Collapse
|
35
|
van der Kamp MW, Shaw KE, Woods CJ, Mulholland AJ. Biomolecular simulation and modelling: status, progress and prospects. J R Soc Interface 2008; 5 Suppl 3:S173-90. [PMID: 18611844 PMCID: PMC2706107 DOI: 10.1098/rsif.2008.0105.focus] [Citation(s) in RCA: 65] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2008] [Revised: 06/05/2008] [Accepted: 06/06/2008] [Indexed: 11/12/2022] Open
Abstract
Molecular simulation is increasingly demonstrating its practical value in the investigation of biological systems. Computational modelling of biomolecular systems is an exciting and rapidly developing area, which is expanding significantly in scope. A range of simulation methods has been developed that can be applied to study a wide variety of problems in structural biology and at the interfaces between physics, chemistry and biology. Here, we give an overview of methods and some recent developments in atomistic biomolecular simulation. Some recent applications and theoretical developments are highlighted.
Collapse
Affiliation(s)
| | | | | | - Adrian J. Mulholland
- Centre for Computational Chemistry, School of Chemistry, University of BristolBristol BS8 1TS, UK
| |
Collapse
|
36
|
Marrink SJ, de Vries AH, Tieleman DP. Lipids on the move: simulations of membrane pores, domains, stalks and curves. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2008; 1788:149-68. [PMID: 19013128 DOI: 10.1016/j.bbamem.2008.10.006] [Citation(s) in RCA: 369] [Impact Index Per Article: 23.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2008] [Revised: 10/13/2008] [Accepted: 10/14/2008] [Indexed: 11/16/2022]
Abstract
In this review we describe the state-of-the-art of computer simulation studies of lipid membranes. We focus on collective lipid-lipid and lipid-protein interactions that trigger deformations of the natural lamellar membrane state, showing that many important biological processes including self-aggregation of membrane components into domains, the formation of non-lamellar phases, and membrane poration and curving, are now amenable to detailed simulation studies.
Collapse
Affiliation(s)
- Siewert J Marrink
- Groningen Biomolecular Sciences and Biotechnology Institute, University of Groningen, Groningen, The Netherlands.
| | | | | |
Collapse
|
37
|
Noid WG, Chu JW, Ayton GS, Krishna V, Izvekov S, Voth GA, Das A, Andersen HC. The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models. J Chem Phys 2008; 128:244114. [PMID: 18601324 PMCID: PMC2671183 DOI: 10.1063/1.2938860] [Citation(s) in RCA: 528] [Impact Index Per Article: 33.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2008] [Accepted: 05/13/2008] [Indexed: 01/16/2023] Open
Abstract
Coarse-grained (CG) models provide a computationally efficient method for rapidly investigating the long time- and length-scale processes that play a critical role in many important biological and soft matter processes. Recently, Izvekov and Voth introduced a new multiscale coarse-graining (MS-CG) method [J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] for determining the effective interactions between CG sites using information from simulations of atomically detailed models. The present work develops a formal statistical mechanical framework for the MS-CG method and demonstrates that the variational principle underlying the method may, in principle, be employed to determine the many-body potential of mean force (PMF) that governs the equilibrium distribution of positions of the CG sites for the MS-CG models. A CG model that employs such a PMF as a "potential energy function" will generate an equilibrium probability distribution of CG sites that is consistent with the atomically detailed model from which the PMF is derived. Consequently, the MS-CG method provides a formal multiscale bridge rigorously connecting the equilibrium ensembles generated with atomistic and CG models. The variational principle also suggests a class of practical algorithms for calculating approximations to this many-body PMF that are optimal. These algorithms use computer simulation data from the atomically detailed model. Finally, important generalizations of the MS-CG method are introduced for treating systems with rigid intramolecular constraints and for developing CG models whose equilibrium momentum distribution is consistent with that of an atomically detailed model.
Collapse
Affiliation(s)
- W G Noid
- Center for Biophysical Modeling and Simulation and Department of Chemistry, University of Utah, Salt Lake City, Utah 84112-0850, USA
| | | | | | | | | | | | | | | |
Collapse
|
38
|
Noid WG, Liu P, Wang Y, Chu JW, Ayton GS, Izvekov S, Andersen HC, Voth GA. The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models. J Chem Phys 2008; 128:244115. [PMID: 18601325 PMCID: PMC2671180 DOI: 10.1063/1.2938857] [Citation(s) in RCA: 271] [Impact Index Per Article: 16.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2008] [Accepted: 05/13/2008] [Indexed: 01/19/2023] Open
Abstract
The multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potential are introduced and if the equilibrium distribution of the atomistic model has been adequately sampled, then the MS-CG variational principle determines the exact many-body potential of mean force (PMF) governing the equilibrium distribution of CG sites generated by the atomistic model. In practice, though, CG force fields are not completely flexible, but only include particular types of interactions between CG sites, e.g., nonbonded forces between pairs of sites. If the CG force field depends linearly on the force field parameters, then the vector valued functions that relate the CG forces to these parameters determine a set of basis vectors that span a vector subspace of CG force fields. The companion paper introduced a distance metric for the vector space of CG force fields and proved that the MS-CG variational principle determines the CG force force field that is within that vector subspace and that is closest to the force field determined by the many-body PMF. The present paper applies the MS-CG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this many-body PMF. Linear systems of equations for these CG force field parameters are derived and analyzed in terms of equilibrium structural correlation functions. Numerical calculations for a one-site CG model of methanol and a molecular CG model of the EMIM(+)NO(3) (-) ionic liquid are provided to illustrate the method.
Collapse
Affiliation(s)
- W G Noid
- Center for Biophysical Modeling and Simulation and Department of Chemistry, University of Utah, Salt Lake City, Utah 84112-0850, USA
| | | | | | | | | | | | | | | |
Collapse
|
39
|
Golubkov PA, Wu JC, Ren P. A transferable coarse-grained model for hydrogen-bonding liquids. Phys Chem Chem Phys 2008; 10:2050-7. [PMID: 18688358 DOI: 10.1039/b715841f] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present here a recent development of a generalized coarse-grained model for use in molecular simulations. In this model, interactions between coarse-grained particles consist of both van der Waals and explicit electrostatic components. As a result, the coarse-grained model offers the transferability that is lacked by most current effective-potential based approaches. The previous center-of-mass framework (P. A. Golubkov and P. Ren, J. Chem. Phys., 2006, 125, 64103) is generalized here to include arbitrary off-center interaction sites for both Gay-Berne and multipoles. The new model has been applied to molecular dynamic simulations of neat methanol liquid. By placing a single point multipole at the oxygen atom rather than at the center of mass of methanol, there is a significant improvement in the ability to capture hydrogen-bonding. The critical issue of transferability of the coarse-grained model is verified on methanol-water mixtures, using parameters derived from neat liquids without any modification. The mixture density and internal energy from coarse-grained molecular dynamics simulations show good agreement with experimental measurements, on a par with what has been obtained from more detailed atomic models. By mapping the dynamics trajectory from the coarse-grained simulation into the all-atom counterpart, we are able to investigate atomic-level structure and interaction. Atomic radial distribution functions of neat methanol, neat water and mixtures compare favorably to experimental measurements. Furthermore, hydrogen-bonded 6- and 7-molecule chains of water and methanol observed in the mixture are in agreement with previous atomic simulations.
Collapse
Affiliation(s)
- Pavel A Golubkov
- Department of Biomedical Engineering, University of Texas at Austin, Austin, TX 78712, USA
| | | | | |
Collapse
|