Curvilinear All-Atom Multiscale (CAM) Theory of Macromolecular Dynamics

Shreif, Z.; Ortoleva, P.

doi:10.1007/s10955-007-9452-4

Cited by 24 publications

(39 citation statements)

References 31 publications

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“…In this way, they capture key pathways for structural transitions and associated energy barriers. Earlier choices for OP-like variables include principal component analysis (PCA) modes to identify collective behaviors in macromolecular systems, [13][14][15] dihedral angles, 16,17 curvilinear coordinates to characterize macromolecular folding and coiling, 18 bead models wherein a peptide or nucleotide is represented by a bead which interacts with others via a phenomenological force, and spatial coarse-grained models. [19][20][21] These approaches suffer from one or more of the following difficulties: (1) characteristic variables are not slowly varying in time; (2) macromolecular twist is not readily accounted for; (3) their internal dynamics, and hence inelasticity of their collisions is neglected; and (4) the forces involved must be calibrated for most new applications.…”

Section: Introductionmentioning

confidence: 99%

Order parameters for macromolecules: Application to multiscale simulation

Singharoy

Cheluvaraja

Ortoleva

2011

The Journal of Chemical Physics

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175

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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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Section: Introductionmentioning

confidence: 99%

Order parameters for macromolecules: Application to multiscale simulation

Singharoy

Cheluvaraja

Ortoleva

2011

The Journal of Chemical Physics

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175

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“…The latter ensembles enable us to construct the average forces and friction coefficients in the equations of stochastic order parameter dynamics. [22][23][24][25][26][27][28][29] The objective of multiscale analysis is to arrive at stochastic equations for a reduced number of variables. Key atomic-scale detail is preserved via the aforementioned probability distribution for atomistic configurations.…”

Section: ͑1͒mentioning

confidence: 99%

Self-assembly of nanocomponents into composite structures: Derivation and simulation of Langevin equations

Pankavich

Shreif

Miao

et al. 2009

The Journal of Chemical Physics

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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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“…These studies start with the Liouville equation and arrive at a Fokker-Planck or Smoluchowski type equation for the stochastic dynamics of a set of slowly evolving variables (order parameters). Of particular relevance to the present study are recent advances [20][21][22][23][24][25][26][27][28][29][30][31] wherein it was shown one could make the hypothesis that the N -atom probability density is a function of the 6N atomic positions and momenta both directly and, via a set of order parameters, indirectly. It was shown that both dependencies could be reconstructed when there is a clear separation of timescales, and that such an assumed dual dependence is not a violation of the number (6N ) of classical degrees of freedom.…”

Section: Construct Atomistic Configurationsmentioning

confidence: 99%

“…By mapping the Liouville problem to a higher dimensional descriptive variable space (i.e. 6N plus the number of variables in − and the function space of the order parameter fields − ), our strategy as suggested by our earlier studies [20][21][22][23][24][25][26][27][28][29][30][31] and examining the multiscale Liouville equation at each order in ε. We hypothesize the lowest order behavior of ρ is slowly varying in time since the phenomena of interest vary on the millisecond or longer, and not the 10 −14 second time scale.…”

Section: Multiscale Integration For Enveloped Virus Modelingmentioning

confidence: 99%

Enveloped viruses understood via multiscale simulation: computer-aided vaccine design

et al. 2008

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Enveloped viruses are viewed as an opportunity to understand how highly organized and functional biosystems can emerge from a collection of millions of chaotically moving atoms. They are an intermediate level of complexity between macromolecules and bacteria. They are a natural system for testing theories of self-assembly and structural transitions, and for demonstrating the derivation of principles of microbiology from laws of molecular physics. As some constitute threats to human health, a computer-aided vaccine and drug design strategy that would follow from a quantitative model would be an important contribution. However, current molecular dynamics simulation approaches are not practical for modeling such systems. Our multiscale approach simultaneously accounts for the outer protein net and inner protein/genomic core, and their less structured membranous material and host fluid. It follows from a rigorous multiscale deductive analysis of laws of molecular physics. Two types of order parameters are introduced: (1) those for structures wherein constituent molecules retain long-lived connectivity (they specify the nanoscale structure as a deformation from a reference configuration) and (2) those for which there is no connectivity but organization is maintained on the average (they are field variables such as mass density or measures of preferred orientation). Rigorous multiscale techniques are used to derive equations for the order parameters dynamics. The equations account for thermal-average forces, diffusion coefficients, and effects of random forces. Statistical properties of the atomic-scale fluctuations and the order parameters are co-evolved. By combining rigorous multiscale techniques and modern supercomputing, systems of extreme complexity can be modeled.

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Curvilinear All-Atom Multiscale (CAM) Theory of Macromolecular Dynamics

Cited by 24 publications

References 31 publications

Order parameters for macromolecules: Application to multiscale simulation

Order parameters for macromolecules: Application to multiscale simulation

Self-assembly of nanocomponents into composite structures: Derivation and simulation of Langevin equations

Enveloped viruses understood via multiscale simulation: computer-aided vaccine design

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