Multiscale Modelling in Molecular Dynamics: Biomolecular Conformations as Metastable States

Meerbach, Eike; Dittmer, Evelyn; Horenko, Illia; Schütte, Ch.

doi:10.1007/3-540-35273-2_14

Cited by 11 publications

(11 citation statements)

References 22 publications

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“…More precisely, we study the rate at which trajectories of two coupled 1D-maps synchronise up to some difference ε in the limit ε → 0. Finally, in section 5, we indicate relations among between formula and approaches to metastability in molecular dynamics [19], in oceanic structures [11], and with the Shannon capacity of constrained binary codes [15].…”

Section: Introductionmentioning

confidence: 99%

Rare Events, Escape Rates and Quasistationarity: Some Exact Formulae

2009

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Section: Introductionmentioning

confidence: 99%

Rare Events, Escape Rates and Quasistationarity: Some Exact Formulae

2009

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“…Metastable systems are studied in relation to phenomena ranging from molecular [MDHS06] to oceanic [FPET07] dynamics. Typical trajectories of such a system remain in one of its almost invariant (metastable or quasi-stationary) components for a relatively long period of time, but eventually switch to a different component and repeat this behavior.…”

Section: Introductionmentioning

confidence: 99%

Approximating invariant densities of metastable systems

González-Tokman¹,

Hunt²,

Wright³

2010

Ergod. Th. Dynam. Sys.

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We consider a piecewise smooth expanding map on an interval which has two invariant subsets of positive Lebesgue measure and exactly two ergodic absolutely continuous invariant probability measures (ACIMs). When this system is perturbed slightly to make the invariant sets merge, we describe how the unique ACIM of the perturbed map can be approximated by a convex combination of the two initial ergodic ACIMs. The result is generalized to the case of finitely many invariant components.

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“…In recent years, there has been widespread interest in multiscale methods for enhanced sampling [15][16][17][18] and such methods likely offer the best approach to bridging the timescale gap. We observe that work on enhanced numerical schemes for molecular dynamics remains essential as it plays a crucial underpinning role in all the enhanced sampling approaches.…”

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confidence: 99%

Robust and efficient configurational molecular sampling via Langevin dynamics

Leimkuhler

Matthews

2013

The Journal of Chemical Physics

173

236

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A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian motions in some combination. The Baker-Campbell-Hausdorff expansion is used to study sampling accuracy following recent work by the authors, which allows determination of the stepsize-dependent bias in configurational averaging. For harmonic oscillators, configurational averaging is exact for certain schemes, which may result in improved performance in the modelling of biomolecules where bond stretches play a prominent role. For general systems, an optimal method can be identified that has very low bias compared to alternatives. In simulations of the alanine dipeptide reported here (both solvated and unsolvated), higher accuracy is obtained without loss of computational efficiency, while allowing large timestep, and with no impairment of the conformational exploration rate (the effective diffusion rate observed in simulation).The optimal scheme is a uniformly better performing algorithm for molecular sampling, with overall efficiency improvements of 25% or more in practical timestep size achievable in vacuum, and with reductions in the error of configurational averages of a factor of ten or more attainable in solvated simulations at large timestep.

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Multiscale Modelling in Molecular Dynamics: Biomolecular Conformations as Metastable States

Cited by 11 publications

References 22 publications

Rare Events, Escape Rates and Quasistationarity: Some Exact Formulae

Rare Events, Escape Rates and Quasistationarity: Some Exact Formulae

Approximating invariant densities of metastable systems

Robust and efficient configurational molecular sampling via Langevin dynamics

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