Coarse-graining molecular dynamics: stochastic models with non-Gaussian force distributions

Erban, Radek

doi:10.1007/s00285-019-01433-5

Cited by 8 publications

(13 citation statements)

References 53 publications

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“…This reveals that it is possible to efficiently manipulate such properties and characteristics for larger size RNA nanotubes, which are practically important for drug delivery and other biomedical applications of these structures. The developed models could be further generalized to account for more complex multiscale interactions, integrating our developed methodology with predictive, dynamic, and stochastic coarse-grained approaches [11,[57][58][59][60][61][62]. This would allow us to better face challenges of a vast separation of spatial and temporal scales between processes happening at the atomic and cellular levels and to provide a route for more efficient integrations of atomistic and molecular information into larger-scale models.…”

Section: Discussionmentioning

confidence: 99%

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

2020

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In order to describe the physical properties of large time scale biological systems, coarse-grained models play an increasingly important role. In this paper we develop Coarse-Grained (CG) models for RNA nanotubes and then, by using Molecular Dynamics (MD) simulation, we study their physical properties. Our exemplifications include RNA nanotubes of 40 nm long, equivalent to 10 RNA nanorings connected in series. The developed methodology is based on a coarse-grained representation of RNA nanotubes, where each coarse bead represents a group of atoms. By decreasing computation cost, this allows us to make computations feasible for realistic structures of interest. In particular, for the developed coarse-grained models with three bead approximations, we calculate the histograms for the bond angles and the dihedral angles. From the dihedral angle histograms, we analyze the characteristics of the links used to build the nanotubes. Furthermore, we also calculate the bead distances along the chains of RNA strands in the nanoclusters. The variations in these features with the size of the nanotube are discussed in detail. Finally, we present the results on the calculation of the root mean square deviations for a developed RNA nanotube to demonstrate the equilibration of the systems for drug delivery and other biomedical applications such as medical imaging and tissue engineering.

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Section: Discussionmentioning

confidence: 99%

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

2020

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“…By utilising the far field integral approximation (14), we arrive at f 0 (L) ∼ (b 0 + L), where b 0 = b 0 (c) is a constant term that depends on cutoff parameter c. With this, our leading order approximation of the k-th standardised moment, α 0 k , obeys…”

Section: B Far-field Integral Approximationmentioning

confidence: 99%

“…., (2) a) Electronic mail: utterson@maths.ox.ac.uk b) Electronic mail: erban@maths.ox.ac.uk and the second moment F 2 1 would be sufficient to parametrize the force distribution. However, the force distributions in simple liquids have been reported to deviate from Gaussian distribution [12][13][14] . Thus our analysis will also tell us how non-Gaussian the force distribution is.…”

Section: Introductionmentioning

confidence: 99%

On standardised moments of force distribution in simple liquids

Utterson,

Erban

2021

Preprint

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The force distribution of a tagged atom in a Lennard-Jones fluid in the canonical ensemble is studied with a focus on its dependence on inherent physical parameters: number density (n) and temperature (T ). Utilising structural information from molecular dynamics simulations of the Lennard-Jones fluid, explicit analytical expressions for the dependence of standardised force moments on n and T are derived. Leading order behaviour of standardised moments of the force distribution are obtained in the limiting cases of small density (n → 0) and low temperature (T → 0), while the variations in the standardised moments are probed for general n and T using molecular dynamics simulations. Clustering effects are seen in molecular dynamics simulations and their effect on these standardised moments is discussed.

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“…For example, comprehensive models for climate change prediction or molecular dynamics simulations involve stochastic components (e.g. [4,30,58,60,77,78,90]) to mimic the effects of unresolved dynamics, while reduced-order models typically involve stochastic noise terms (e.g. [15,21,49,57,72].…”

Section: Introductionmentioning

confidence: 99%

Time-periodic measures, random periodic orbits, and the linear response for dissipative non-autonomous stochastic differential equations

Branicki

Uda

2021

Res Math Sci

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We consider a class of dissipative stochastic differential equations (SDE’s) with time-periodic coefficients in finite dimension, and the response of time-asymptotic probability measures induced by such SDE’s to sufficiently regular, small perturbations of the underlying dynamics. Understanding such a response provides a systematic way to study changes of statistical observables in response to perturbations, and it is often very useful for sensitivity analysis, uncertainty quantification, and improving probabilistic predictions of nonlinear dynamical systems, especially in high dimensions. Here, we are concerned with the linear response to small perturbations in the case when the time-asymptotic probability measures are time-periodic. First, we establish sufficient conditions for the existence of stable random time-periodic orbits generated by the underlying SDE. Ergodicity of time-periodic probability measures supported on these random periodic orbits is subsequently discussed. Then, we derive the so-called fluctuation–dissipation relations which allow to describe the linear response of statistical observables to small perturbations away from the time-periodic ergodic regime in a manner which only exploits the unperturbed dynamics. The results are formulated in an abstract setting, but they apply to problems ranging from aspects of climate modelling, to molecular dynamics, to the study of approximation capacity of neural networks and robustness of their estimates.

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Coarse-graining molecular dynamics: stochastic models with non-Gaussian force distributions

Cited by 8 publications

References 53 publications

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

On standardised moments of force distribution in simple liquids

Time-periodic measures, random periodic orbits, and the linear response for dissipative non-autonomous stochastic differential equations

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