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Sereda YV, Ortoleva PJ. Temporally Coarse-Grained All-Atom Molecular Dynamics Achieved via Stochastic Padé Approximants. J Phys Chem B 2020; 124:1392-1410. [PMID: 31958947 DOI: 10.1021/acs.jpcb.9b10735] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A Padé approximant scheme for realizing the discrete-time evolution of the state of a many-atom system is introduced. This temporal coarse-graining scheme accounts for the underlying Newtonian physics and avoids the need for construction of spatially coarse-grained variables. Newtonian physics is incorporated through short molecular dynamics simulations at the beginning of each of the large coarse-grained timesteps. The balance between stochastic and coherent dynamics expressed by many-atom systems is captured via incorporation of the Ito formula into a Padé approximant for the time dependence of individual atom positions over large timesteps. Since the time for a many-atom system to express a characteristic ensemble of atomic velocity fluctuations is typically short relative to the characteristic time of large-scale atomic displacements, a computationally efficient and accurate temporal coarse-graining of the atom-resolved Newtonian dynamics is formulated, denoted all-atom Padé-Ito molecular dynamics (APIMD). Evolution of the system over a time step much longer than that required for standard molecular dynamics (MD) is achieved via incorporation of information from the short MD simulations into a Padé approximant extrapolation in time. The extrapolated atomic configuration is subjected to energy minimization and, when needed, thermal equilibration so as to avoid occasional unphysical close encounters deriving from the Padé approximant extrapolation and to represent configurations appropriate for the temperature of interest. APIMD is implemented and tested via comparison with traditional MD simulations of five phenomena: (1) pertussis toxin subunit deformation, (2) structural transition in a T = 1 capsid-like structure of HPV16 L1 protein, (3) coalescence of argon nanodroplets, and structural transitions in dialanine in (4) vacuum, and (5) water. Accuracy of APIMD is demonstrated using semimicroscopic descriptors (rmsd, radius of gyration, residue-residue contact maps, and densities) and the free energy. Significant computational acceleration relative to traditional molecular dynamics is illustrated.
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Affiliation(s)
- Yuriy V Sereda
- Department of Chemistry Indiana University Bloomington , Indiana 47405 , United States
| | - Peter J Ortoleva
- Department of Chemistry Indiana University Bloomington , Indiana 47405 , United States
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2
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Abstract
Classical molecular dynamics modeling of whole viruses or their capsids in explicit water is discussed, and known examples from the literature are analyzed. Only works on all-atom modeling in explicit water are included. Physical chemistry of the whole system is the focus, which includes the structure and dynamics of the biomolecules as well as water and ion behavior in and around the virus particle. It was demonstrated that in most investigations molecular phenomena that currently can not be studied experimentally are successfully reproduced and explained by the simulations. These include, for example, transport and distribution of ions inside viruses that ultimately connected to their stability, the hydrodynamic pressure in the capsid related to viruses' elastic properties, the role of metal ions in virus swelling, and others. Current and future tendencies in the development of all-atom virus simulations are outlined.
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Affiliation(s)
- Elvira Tarasova
- Department of Mathematics , Aston University , Birmingham B4 7ET , U.K
- Laboratory for Computational Molecular Design , RIKEN Center for Biosystems Dynamics (BDR) , Building B, 6-2-4 Furuedai , Suita , Osaka 565-0874 , Japan
- Immanuel Kant Baltic Federal University , A. Nevskogo str. 14 , Kaliningrad 236041 , Russian Federation
| | - Dmitry Nerukh
- Department of Mathematics , Aston University , Birmingham B4 7ET , U.K
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3
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Chen Y, Roux B. Enhanced Sampling of an Atomic Model with Hybrid Nonequilibrium Molecular Dynamics-Monte Carlo Simulations Guided by a Coarse-Grained Model. J Chem Theory Comput 2016; 11:3572-83. [PMID: 26574442 PMCID: PMC4894282 DOI: 10.1021/acs.jctc.5b00372] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
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Molecular
dynamics (MD) trajectories based on a classical equation
of motion provide a straightforward, albeit somewhat inefficient approach,
to explore and sample the configurational space of a complex molecular
system. While a broad range of techniques can be used to accelerate
and enhance the sampling efficiency of classical simulations, only
algorithms that are consistent with the Boltzmann equilibrium distribution
yield a proper statistical mechanical computational framework. Here,
a multiscale hybrid algorithm relying simultaneously on all-atom fine-grained
(FG) and coarse-grained (CG) representations of a system is designed
to improve sampling efficiency by combining the strength of nonequilibrium
molecular dynamics (neMD) and Metropolis Monte Carlo (MC). This CG-guided
hybrid neMD-MC algorithm comprises six steps: (1) a FG configuration
of an atomic system is dynamically propagated for some period of time
using equilibrium MD; (2) the resulting FG configuration is mapped
onto a simplified CG model; (3) the CG model is propagated for a brief
time interval to yield a new CG configuration; (4) the resulting CG
configuration is used as a target to guide the evolution of the FG
system; (5) the FG configuration (from step 1) is driven via a nonequilibrium
MD (neMD) simulation toward the CG target; (6) the resulting FG configuration
at the end of the neMD trajectory is then accepted or rejected according
to a Metropolis criterion before returning to step 1. A symmetric
two-ends momentum reversal prescription is used for the neMD trajectories
of the FG system to guarantee that the CG-guided hybrid neMD-MC algorithm
obeys microscopic detailed balance and rigorously yields the equilibrium
Boltzmann distribution. The enhanced sampling achieved with the method
is illustrated with a model system with hindered diffusion and explicit-solvent
peptide simulations. Illustrative tests indicate that the method can
yield a speedup of about 80 times for the model system and up to 21
times for polyalanine and (AAQAA)3 in water.
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Affiliation(s)
- Yunjie Chen
- Department of Chemistry, and ‡Department of Biochemistry and Molecular Biology, University of Chicago , Chicago, Illinois 60637, United States
| | - Benoît Roux
- Department of Chemistry, and ‡Department of Biochemistry and Molecular Biology, University of Chicago , Chicago, Illinois 60637, United States
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4
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Abi Mansour A, Ortoleva PJ. Implicit Time Integration for Multiscale Molecular Dynamics Using Transcendental Padé Approximants. J Chem Theory Comput 2016; 12:1965-71. [PMID: 26845510 DOI: 10.1021/acs.jctc.5b01232] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Molecular dynamics systems evolve through the interplay of collective and localized disturbances. As a practical consequence, there is a restriction on the time step imposed by the broad spectrum of time scales involved. To resolve this restriction, multiscale factorization was introduced for molecular dynamics as a method that exploits the separation of time scales by coevolving the coarse-grained and atom-resolved states via Trotter factorization. Developing a stable time-marching scheme for this coevolution, however, is challenging because the coarse-grained dynamical equations depend on the microstate; therefore, these equations cannot be expressed in closed form. The objective of this paper is to develop an implicit time integration scheme for multiscale simulation of large systems over long periods of time and with high accuracy. The scheme uses Padé approximants to account for both the stochastic and deterministic features of the coarse-grained dynamics. The method is demonstrated for a protein either undergoing a conformational change or migrating under the influence of an external force. The method shows promise in accelerating multiscale molecular dynamics without a loss of atomic precision or the need to conjecture the form of coarse-grained governing equations.
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Affiliation(s)
- Andrew Abi Mansour
- Department of Chemistry and Center for Theoretical and Computational Nanoscience, Indiana University , Bloomington, Indiana 47405, United States
| | - Peter J Ortoleva
- Department of Chemistry and Center for Theoretical and Computational Nanoscience, Indiana University , Bloomington, Indiana 47405, United States
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5
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Mansour AA, Sereda YV, Yang J, Ortoleva PJ. Prospective on multiscale simulation of virus-like particles: Application to computer-aided vaccine design. Vaccine 2015; 33:5890-6. [DOI: 10.1016/j.vaccine.2015.05.099] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2015] [Revised: 05/25/2015] [Accepted: 05/28/2015] [Indexed: 10/23/2022]
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6
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Yang J, Singharoy A, Sereda Y, Ortoleva P. Quasiequivalence of multiscale coevolution and ensemble MD simulations: A demonstration with lactoferrin. Chem Phys Lett 2014. [DOI: 10.1016/j.cplett.2014.10.020] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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7
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Sereda YV, Espinosa-Duran JM, Ortoleva PJ. Energy transfer between a nanosystem and its host fluid: a multiscale factorization approach. J Chem Phys 2014; 140:074102. [PMID: 24559333 DOI: 10.1063/1.4864200] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Energy transfer between a macromolecule or supramolecular assembly and a host medium is considered from the perspective of Newton's equations and Lie-Trotter factorization. The development starts by demonstrating that the energy of the molecule evolves slowly relative to the time scale of atomic collisions-vibrations. The energy is envisioned to be a coarse-grained variable that coevolves with the rapidly fluctuating atomistic degrees of freedom. Lie-Trotter factorization is shown to be a natural framework for expressing this coevolution. A mathematical formalism and workflow for efficient multiscale simulation of energy transfer is presented. Lactoferrin and human papilloma virus capsid-like structure are used for validation.
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Affiliation(s)
- Yuriy V Sereda
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, 800 E. Kirkwood Ave, Bloomington, Indiana 47405, USA
| | - John M Espinosa-Duran
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, 800 E. Kirkwood Ave, Bloomington, Indiana 47405, USA
| | - Peter J Ortoleva
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, 800 E. Kirkwood Ave, Bloomington, Indiana 47405, USA
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8
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Abi Mansour A, Ortoleva PJ. Multiscale Factorization Method for Simulating Mesoscopic Systems with Atomic Precision. J Chem Theory Comput 2014; 10:518-523. [PMID: 24803852 PMCID: PMC3985745 DOI: 10.1021/ct400615a] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2013] [Indexed: 01/05/2023]
Abstract
Mesoscopic N-atom systems derive their structural and dynamical properties from processes coupled across multiple scales in space and time. A multiscale method for simulating these systems in the friction dominated regime from the underlying N-atom formulation is presented. The method integrates notions of multiscale analysis, Trotter factorization, and a hypothesis that the momenta conjugate to coarse-grained variables constitute a stationary process on the time scale of coarse-grained dynamics. The method is demonstrated for lactoferrin, nudaurelia capensis omega virus, and human papillomavirus to assess its accuracy.
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Affiliation(s)
- Andrew Abi Mansour
- Department of Chemistry, Indiana
University, Bloomington, Indiana 47405, United
States
| | - Peter J. Ortoleva
- Department of Chemistry, Indiana
University, Bloomington, Indiana 47405, United
States
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9
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Zhao S, Xue J, Kang W. Ion selection of charge-modified large nanopores in a graphene sheet. J Chem Phys 2013; 139:114702. [DOI: 10.1063/1.4821161] [Citation(s) in RCA: 81] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
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10
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Ortoleva P, Singharoy A, Pankavich S. Hierarchical Multiscale Modeling of Macromolecules and their Assemblies. SOFT MATTER 2013; 9:4319-4335. [PMID: 23671457 PMCID: PMC3650908 DOI: 10.1039/c3sm50176k] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Soft materials (e.g., enveloped viruses, liposomes, membranes and supercooled liquids) simultaneously deform or display collective behaviors, while undergoing atomic scale vibrations and collisions. While the multiple space-time character of such systems often makes traditional molecular dynamics simulation impractical, a multiscale approach has been presented that allows for long-time simulation with atomic detail based on the co-evolution of slowly-varying order parameters (OPs) with the quasi-equilibrium probability density of atomic configurations. However, this approach breaks down when the structural change is extreme, or when nearest-neighbor connectivity of atoms is not maintained. In the current study, a self-consistent approach is presented wherein OPs and a reference structure co-evolve slowly to yield long-time simulation for dynamical soft-matter phenomena such as structural transitions and self-assembly. The development begins with the Liouville equation for N classical atoms and an ansatz on the form of the associated N-atom probability density. Multiscale techniques are used to derive Langevin equations for the coupled OP-configurational dynamics. The net result is a set of equations for the coupled stochastic dynamics of the OPs and centers of mass of the subsystems that constitute a soft material body. The theory is based on an all-atom methodology and an interatomic force field, and therefore enables calibration-free simulations of soft matter, such as macromolecular assemblies.
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Affiliation(s)
- P Ortoleva
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, IN 47405
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11
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Sereda YV, Ortoleva PJ. Variational methods for time-dependent classical many-particle systems. PHYSICA A 2013; 392:628-638. [PMID: 23459064 PMCID: PMC3580877 DOI: 10.1016/j.physa.2012.10.005] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
A variational method for the classical Liouville equation is introduced that facilitates the development of theories for non-equilibrium classical systems. The method is based on the introduction of a complex-valued auxiliary quantity Ψ that is related to the classical position-momentum probability density ρ via ρ = Ψ*Ψ. A functional of Ψ is developed whose extrema imply that ρ satisfies the Liouville equation. Multiscale methods are used to develop trial functions to be optimized by the variational principle. The present variational principle with multiscale trial functions can capture both the microscopic and the coarse-grained descriptions, thereby yielding theories that account for the two way exchange of information across multiple scales in space and time. Equations of the Smoluchowski form for the coarse-grained state probability density are obtained. Constraints on the initial state of the N-particle probability density for which the aforementioned equation is closed and conserves probability are presented. The methodology has applicability to a wide range of systems including macromolecular assemblies, ionic liquids, and nanoparticles.
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Affiliation(s)
- Yuriy V. Sereda
- Department of Chemistry, Indiana University, 800 E. Kirkwood Ave., Bloomington, Indiana 47405, USA
| | - Peter J. Ortoleva
- Department of Chemistry, Indiana University, 800 E. Kirkwood Ave., Bloomington, Indiana 47405, USA
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12
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Singharoy A, Joshi H, Ortoleva PJ. Multiscale macromolecular simulation: role of evolving ensembles. J Chem Inf Model 2012; 52:2638-49. [PMID: 22978601 DOI: 10.1021/ci3002952] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Multiscale analysis provides an algorithm for the efficient simulation of macromolecular assemblies. This algorithm involves the coevolution of a quasiequilibrium probability density of atomic configurations and the Langevin dynamics of spatial coarse-grained variables denoted order parameters (OPs) characterizing nanoscale system features. In practice, implementation of the probability density involves the generation of constant OP ensembles of atomic configurations. Such ensembles are used to construct thermal forces and diffusion factors that mediate the stochastic OP dynamics. Generation of all-atom ensembles at every Langevin time step is computationally expensive. Here, multiscale computation for macromolecular systems is made more efficient by a method that self-consistently folds in ensembles of all-atom configurations constructed in an earlier step, history, of the Langevin evolution. This procedure accounts for the temporal evolution of these ensembles, accurately providing thermal forces and diffusions. It is shown that efficiency and accuracy of the OP-based simulations is increased via the integration of this historical information. Accuracy improves with the square root of the number of historical timesteps included in the calculation. As a result, CPU usage can be decreased by a factor of 3-8 without loss of accuracy. The algorithm is implemented into our existing force-field based multiscale simulation platform and demonstrated via the structural dynamics of viral capsomers.
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Affiliation(s)
- A Singharoy
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, Indiana 47405, USA
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13
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Sereda YV, Singharoy AB, Jarrold MF, Ortoleva PJ. Discovering free energy basins for macromolecular systems via guided multiscale simulation. J Phys Chem B 2012; 116:8534-44. [PMID: 22423635 PMCID: PMC3408247 DOI: 10.1021/jp2126174] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
An approach for the automated discovery of low free energy states of macromolecular systems is presented. The method does not involve delineating the entire free energy landscape but proceeds in a sequential free energy minimizing state discovery; i.e., it first discovers one low free energy state and then automatically seeks a distinct neighboring one. These states and the associated ensembles of atomistic configurations are characterized by coarse-grained variables capturing the large-scale structure of the system. A key facet of our approach is the identification of such coarse-grained variables. Evolution of these variables is governed by Langevin dynamics driven by thermal-average forces and mediated by diffusivities, both of which are constructed by an ensemble of short molecular dynamics runs. In the present approach, the thermal-average forces are modified to account for the entropy changes following from our knowledge of the free energy basins already discovered. Such forces guide the system away from the known free energy minima, over free energy barriers, and to a new one. The theory is demonstrated for lactoferrin, known to have multiple energy-minimizing structures. The approach is validated using experimental structures and traditional molecular dynamics. The method can be generalized to enable the interpretation of nanocharacterization data (e.g., ion mobility-mass spectrometry, atomic force microscopy, chemical labeling, and nanopore measurements).
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Affiliation(s)
- Yuriy V. Sereda
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, 800 E. Kirkwood Ave, Bloomington, IN 47405
| | - Abhishek B. Singharoy
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, 800 E. Kirkwood Ave, Bloomington, IN 47405
| | - Martin F. Jarrold
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, 800 E. Kirkwood Ave, Bloomington, IN 47405
| | - Peter J. Ortoleva
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, 800 E. Kirkwood Ave, Bloomington, IN 47405
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14
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Singharoy A, Joshi H, Miao Y, Ortoleva PJ. Space warping order parameters and symmetry: application to multiscale simulation of macromolecular assemblies. J Phys Chem B 2012; 116:8423-34. [PMID: 22356532 PMCID: PMC4937887 DOI: 10.1021/jp2119247] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Coarse-grained features of macromolecular assemblies are understood via a set of order parameters (OPs) constructed in terms of their all-atom configuration. OPs are shown to be slowly changing in time and capture the large-scale spatial features of macromolecular assemblies. The relationship of these variables to the classic notion of OPs based on symmetry breaking phase transitions is discussed. OPs based on space warping transformations are analyzed in detail as they naturally provide a connection between overall structure of an assembly and all-atom configuration. These OPs serve as the basis of a multiscale analysis that yields Langevin equations for OP dynamics. In this context, the characteristics of OPs and PCA modes are compared. The OPs enable efficient all-atom multiscale simulations of the dynamics of macromolecular assemblies in response to changes in microenvironmental conditions, as demonstrated on the structural transitions of cowpea chlorotic mottle virus capsid (CCMV) and RNA of the satellite tobacco mosaic virus (STMV).
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Affiliation(s)
- Abhishek Singharoy
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Harshad Joshi
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | | | - Peter J. Ortoleva
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
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15
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Singharoy A, Sereda Y, Ortoleva PJ. Hierarchical Order Parameters for Macromolecular Assembly Simulations I: Construction and Dynamical Properties of Order Parameters. J Chem Theory Comput 2012; 8:1379-1392. [PMID: 22661911 PMCID: PMC3361912 DOI: 10.1021/ct200574x] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
Macromolecular assemblies often display a hierarchical organization of macromolecules or their sub-assemblies. To model this, we have formulated a space warping method that enables capturing overall macromolecular structure and dynamics via a set of coarse-grained order parameters (OPs). This article is the first of two describing the construction and computational implementation of an additional class of OPs that has built into them the hierarchical architecture of macromolecular assemblies. To accomplish this, first, the system is divided into subsystems, each of which is described via a representative set of OPs. Then, a global set of variables is constructed from these subsystem-centered OPs to capture overall system organization. Dynamical properties of the resulting OPs are compared to those of our previous nonhierarchical ones, and implied conceptual and computational advantages are discussed for a 100ns, 2 million atom solvated Human Papillomavirus-like particle simulation. In the second article, the hierarchical OPs are shown to enable a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Langevin equations of stochastic OP dynamics. The latter is demonstrated via a force-field based simulation algorithm that probes key structural transition pathways, simultaneously accounting for all-atom details and overall structure.
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Affiliation(s)
- Abhishek Singharoy
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, IN 47405
| | - Yuriy Sereda
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, IN 47405
| | - Peter J. Ortoleva
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, IN 47405
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Singharoy A, Joshi H, Cheluvaraja S, Miao Y, Brown D, Ortoleva P. Simulating microbial systems: addressing model uncertainty/incompleteness via multiscale and entropy methods. Methods Mol Biol 2012; 881:433-67. [PMID: 22639222 DOI: 10.1007/978-1-61779-827-6_15] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Most systems of interest in the natural and engineering sciences are multiscale in character. Typically available models are incomplete or uncertain. Thus, a probabilistic approach is required. We present a deductive multiscale approach to address such problems, focusing on virus and cell systems to demonstrate the ideas. There is usually an underlying physical model, all factors in which (e.g., particle masses, charges, and force constants) are known. For example, the underlying model can be cast in terms of a collection of N-atoms evolving via Newton's equations. When the number of atoms is 10(6) or more, these physical models cannot be simulated directly. However, one may only be interested in a coarse-grained description, e.g., in terms of molecular populations or overall system size, shape, position, and orientation. The premise of this chapter is that the coarse-grained equations should be derived from the underlying model so that a deductive calibration-free methodology is achieved. We consider a reduction in resolution from a description for the state of N-atoms to one in terms of coarse-grained variables. This implies a degree of uncertainty in the underlying microstates. We present a methodology for modeling microbial systems that integrates equations for coarse-grained variables with a probabilistic description of the underlying fine-scale ones. The implementation of our strategy as a general computational platform (SimEntropics™) for microbial modeling and prospects for developments and applications are discussed.
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Affiliation(s)
- A Singharoy
- Department of Chemistry, Center for Cell and Virus Theory, Indiana University, Bloomington, IN, USA
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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.
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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
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Singharoy A, Cheluvaraja S, Ortoleva P. Order parameters for macromolecules: application to multiscale simulation. J Chem Phys 2011; 134:044104. [PMID: 21280684 DOI: 10.1063/1.3524532] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
Order parameters (OPs) characterizing the nanoscale features of macromolecules are presented. They are generated in a general fashion so that they do not need to be redesigned with each new application. They evolve on time scales much longer than 10(-14) s typical for individual atomic collisions/vibrations. The list of OPs can be automatically increased, and completeness can be determined via a correlation analysis. They serve as the basis of a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Smoluchowski/Langevin equations of stochastic OP dynamics. Such OPs and the multiscale analysis imply computational algorithms that we demonstrate in an application to ribonucleic acid structural dynamics for 50 ns.
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Affiliation(s)
- A Singharoy
- Center for Cell and Virus Theory, Indiana University, Bloomington, Indiana 47405, USA
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Miao Y, Johnson JE, Ortoleva PJ. All-atom multiscale simulation of cowpea chlorotic mottle virus capsid swelling. J Phys Chem B 2010; 114:11181-95. [PMID: 20695471 DOI: 10.1021/jp102314e] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
An all-atom multiscale computational modeling approach, molecular dynamics/order parameter extrapolation (MD/OPX), has recently been developed for simulating large bionanosystems. It accelerates MD simulations and addresses rapid atomistic fluctuations and slowly varying nanoscale dynamics of bionanosystems simultaneously. With modules added to account for water molecules and ions, MD/OPX is applied to simulate the swelling of cowpea chlorotic mottle virus (CCMV) capsid solvated in a host medium in this study. Simulation results show that the N-terminal arms of capsid proteins undergo large deviations from the initial configurations with their length extended quickly during the early stage of capsid swelling. The capsid swelling is a symmetry-breaking process involving local initiation and front propagation. The capsid swelling rate is approximately 0.25 nm/ns (npn) during the early stage of the simulation, and propagation of the structural transition across the capsid is roughly 0.6 npn. The system conditions that affect swelling of the capsid are analyzed. Prospects for creating a phase diagram for CCMV capsid swelling and using predictions to guide experiments are discussed.
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Affiliation(s)
- Yinglong Miao
- Center for Cell and Virus Theory, Department of Chemistry, Indiana University, Bloomington, Indiana 47405, USA
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20
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Jensen F, Palmer DS. Harmonic Vibrational Analysis in Delocalized Internal Coordinates. J Chem Theory Comput 2010; 7:223-30. [DOI: 10.1021/ct100463a] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Frank Jensen
- Department of Chemistry, University of Aarhus, DK-8000 Aarhus, Denmark
| | - David S. Palmer
- Department of Chemistry, University of Aarhus, DK-8000 Aarhus, Denmark
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Pankavich S, Ortoleva P. Multiscaling for systems with a broad continuum of characteristic lengths and times: Structural transitions in nanocomposites. JOURNAL OF MATHEMATICAL PHYSICS 2010; 51:63303. [PMID: 20661319 PMCID: PMC2909304 DOI: 10.1063/1.3420578] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2009] [Accepted: 04/07/2010] [Indexed: 05/29/2023]
Abstract
The multiscale approach to N-body systems is generalized to address the broad continuum of long time and length scales associated with collective behaviors. A technique is developed based on the concept of an uncountable set of time variables and of order parameters (OPs) specifying major features of the system. We adopt this perspective as a natural extension of the commonly used discrete set of time scales and OPs which is practical when only a few, widely separated scales exist. The existence of a gap in the spectrum of time scales for such a system (under quasiequilibrium conditions) is used to introduce a continuous scaling and perform a multiscale analysis of the Liouville equation. A functional-differential Smoluchowski equation is derived for the stochastic dynamics of the continuum of Fourier component OPs. A continuum of spatially nonlocal Langevin equations for the OPs is also derived. The theory is demonstrated via the analysis of structural transitions in a composite material, as occurs for viral capsids and molecular circuits.
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Cheluvaraja S, Ortoleva P. Thermal nanostructure: an order parameter multiscale ensemble approach. J Chem Phys 2010; 132:075102. [PMID: 20170252 DOI: 10.1063/1.3316793] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Deductive all-atom multiscale techniques imply that many nanosystems can be understood in terms of the slow dynamics of order parameters that coevolve with the quasiequilibrium probability density for rapidly fluctuating atomic configurations. The result of this multiscale analysis is a set of stochastic equations for the order parameters whose dynamics is driven by thermal-average forces. We present an efficient algorithm for sampling atomistic configurations in viruses and other supramillion atom nanosystems. This algorithm allows for sampling of a wide range of configurations without creating an excess of high-energy, improbable ones. It is implemented and used to calculate thermal-average forces. These forces are then used to search the free-energy landscape of a nanosystem for deep minima. The methodology is applied to thermal structures of Cowpea chlorotic mottle virus capsid. The method has wide applicability to other nanosystems whose properties are described by the CHARMM or other interatomic force field. Our implementation, denoted SIMNANOWORLD, achieves calibration-free nanosystem modeling. Essential atomic-scale detail is preserved via a quasiequilibrium probability density while overall character is provided via predicted values of order parameters. Applications from virology to the computer-aided design of nanocapsules for delivery of therapeutic agents and of vaccines for nonenveloped viruses are envisioned.
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Affiliation(s)
- S Cheluvaraja
- Department of Chemistry, Center for Cell and Virus Theory, Indiana University, Bloomington, Indiana 47405, USA
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Miao Y, Ortoleva PJ. Viral structural transition mechanisms revealed by multiscale molecular dynamics/order parameter extrapolation simulation. Biopolymers 2010; 93:61-73. [DOI: 10.1002/bip.21299] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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Shreif Z, Pankavich S, Ortoleva P. Liquid-crystal transitions: a first-principles multiscale approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:031703. [PMID: 19905127 DOI: 10.1103/physreve.80.031703] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2009] [Revised: 07/07/2009] [Indexed: 05/28/2023]
Abstract
A rigorous theory of liquid-crystal transitions is developed starting from the Liouville equation. The starting point is an all-atom description and a set of order-parameter field variables that are shown to evolve slowly via Newton's equations. The separation of time scales between that of atomic collision or vibrations and the order-parameter fields enables the derivation of rigorous equations for stochastic order-parameter field dynamics. When the fields provide a measure of the spatial profile of the probability of molecular position, orientation, and internal structure, a theory of liquid-crystal transitions emerges. The theory uses the all-atom/continuum approach developed earlier to obtain a functional generalization of the Smoluchowski equation wherein key atomic details are embedded. The equivalent nonlocal Langevin equations are derived, and the computational aspects are discussed. The theory enables simulations that are much less computationally intensive than molecular dynamics and thus does not require oversimplification of the system's constituent components. The equations obtained do not include factors that require calibration and can thus be applicable to various phase transitions which overcomes the limitations of phenomenological field models. The relation of the theory to phenomenological descriptions of nematic and smectic phase transitions, and the possible existence of other types of transitions involving intermolecular structural parameters are discussed.
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Affiliation(s)
- Z Shreif
- Department of Chemistry, Center for Cell and Virus Theory, Indiana University, Bloomington, Indiana 47405, USA
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Pankavich S, Shreif Z, Miao Y, Ortoleva P. Self-assembly of nanocomponents into composite structures: derivation and simulation of Langevin equations. J Chem Phys 2009; 130:194115. [PMID: 19466829 DOI: 10.1063/1.3134683] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The kinetics of the self-assembly of nanocomponents into a virus, nanocapsule, or other composite structure is analyzed via a multiscale approach. The objective is to achieve predictability and to preserve key atomic-scale features that underlie the formation and stability of the composite structures. We start with an all-atom description, the Liouville equation, and the order parameters characterizing nanoscale features of the system. An equation of Smoluchowski type for the stochastic dynamics of the order parameters is derived from the Liouville equation via a multiscale perturbation technique. The self-assembly of composite structures from nanocomponents with internal atomic structure is analyzed and growth rates are derived. Applications include the assembly of a viral capsid from capsomers, a ribosome from its major subunits, and composite materials from fibers and nanoparticles. Our approach overcomes errors in other coarse-graining methods, which neglect the influence of the nanoscale configuration on the atomistic fluctuations. We account for the effect of order parameters on the statistics of the atomistic fluctuations, which contribute to the entropic and average forces driving order parameter evolution. This approach enables an efficient algorithm for computer simulation of self-assembly, whereas other methods severely limit the timestep due to the separation of diffusional and complexing characteristic times. Given that our approach does not require recalibration with each new application, it provides a way to estimate assembly rates and thereby facilitate the discovery of self-assembly pathways and kinetic dead-end structures.
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Affiliation(s)
- S Pankavich
- Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019, USA.
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Shreif Z, Adhangale P, Cheluvaraja S, Perera R, Kuhn R, Ortoleva P. Enveloped viruses understood via multiscale simulation: computer-aided vaccine design. ACTA ACUST UNITED AC 2008. [DOI: 10.1007/s10820-008-9101-5] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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