A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo

Schütte, Ch.; Fischer, Alexander; Huisinga, Wilhelm; Deuflhard, Peter

doi:10.1006/jcph.1999.6231

Cited by 362 publications

(489 citation statements)

References 39 publications

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“…Recent years have seen the advance of Markov state models (MSM) as lowdimensional models for metastable dynamical behaviour of molecular systems [23][24][25][26][27]. Recently the interest in MSMs has increased a lot, for it had been demonstrated that MSMs can be constructed even for very high dimensional systems [25].…”

Section: Markov State Modelsmentioning

confidence: 99%

Optimal control of molecular dynamics using Markov state models

2012

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A numerical scheme for solving high-dimensional stochastic control problems on an infinite time horizon that appear relevant in the context of molecular dynamics is outlined. The scheme rests on the interpretation of the corresponding Hamilton-Jacobi-Bellman equation as a nonlinear eigenvalue problem that, using a logarithmic transformation, can be recast as a linear eigenvalue problem, for which the principal eigenvalue and its eigenfunction are sought. The latter can be computed e ciently by approximating the underlying stochastic process with a coarse-grained Markov state model for the dominant metastable sets. We illustrate our method with two numerical examples, one of which involves the task of maximizing the population of ↵-helices in an ensemble of small biomolecules (Alanine dipeptide), and discuss the relation to the large deviation principle of Donsker and Varadhan.

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Section: Markov State Modelsmentioning

confidence: 99%

Optimal control of molecular dynamics using Markov state models

2012

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“…DS2: Data are derived from recently published simulations on the intrinsically disordered peptide Aβ [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] . 39 The trajectory contained 7.5x10 5 snapshots saved at an interval of 20 ps, and the same 144, partially redundant internal distances that DS1 was originally derived from were extracted at each frame (D = 144).…”

Section: Ds1mentioning

confidence: 99%

“…39 The trajectory contained 7.5x10 5 snapshots saved at an interval of 20 ps, and the same 144, partially redundant internal distances that DS1 was originally derived from were extracted at each frame (D = 144). For the data in Table 1, backbone (φ/ψ/ω) dihedral angles of residues 14-24 of the peptide (D = 66), their sine/cosine terms (D = 66), the respective terms weighted by inertial masses (see equation 6), or the Cartesian coordinates of backbone nitrogen and oxygen atoms of residues [14][15][16][17][18][19][20][21][22][23][24] (D = 66) were also extracted.…”

Section: Ds1mentioning

confidence: 99%

“…10,11 The use of geometric clustering to identify fine-grained mesostates a constituting a conformational space network at equilibrium is a very powerful technique as these networks in principle are able to represent both thermodynamics and kinetics of the system in detail. [12][13][14][15][16] Computing these networks requires that simulation data are sampled frequently enough to resolve transitions of interest between those mesostates that exchange most rapidly. This is linked to the chosen resolution of mesostates.…”

Section: Introductionmentioning

confidence: 99%

“…The literature offers similar, kinetic (re)grouping techniques that operate on fine-grained mesostate networks obtained from structural clustering. 16,19,28 In clustering, the issue of dimensionality deserves particular attention since very frequently molecular simulation data are represented in fairly high-dimensional spaces (D ≈ 100 -1000). The so-called "curse of dimensionality" 29 is a colloquialism for the fact that high-dimensional spaces generally lead to low data density (sparsity) due to exponential growth of the available space.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Construction of Mesostate Networks from Molecular Dynamics Trajectories

Vitalis

Caflisch

2012

J. Chem. Theory Comput.

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The coarse-graining of data from molecular simulations yields conformational space networks that may be used for predicting the system's long time scale behavior, to discover structural pathways connecting free energy basins in the system, or simply to represent accessible phase space regions of interest and their connectivities in a two-dimensional plot. In this contribution, we present a tree-based algorithm to partition conformations of biomolecules into sets of similar microstates, i.e., to coarse-grain trajectory data into mesostates. On account of utilizing an architecture similar to that of established tree-based algorithms, the proposed scheme operates in near-linear time with data set size. We derive expressions needed for the fast evaluation of mesostate properties and distances when employing typical choices for measures of similarity between microstates. Using both a pedagogically useful and a realword application, the algorithm is shown to be robust with respect to tree height, which in addition to mesostate threshold size is the main adjustable parameter. It is demonstrated that the derived mesostate networks can preserve information regarding the free energy basins and barriers by which the system is characterized. ABSTRACTThe coarse-graining of data from molecular simulations yields conformational space networks that may be used for predicting the system's long timescale behavior, to discover structural pathways connecting free energy basins in the system, or simply to represent accessible phase space regions of interest and their connectivities in a two-dimensional plot. In this contribution, we present a tree-based algorithm to partition conformations of biomolecules into sets of similar microstates, i.e., to coarse-grain trajectory data into mesostates. On account of utilizing an architecture similar to that of established tree-based algorithms, the proposed scheme operates in near-linear time with dataset size. We derive expressions needed for the fast evaluation of mesostate properties and distances when employing typical choices for measures of similarity between microstates. Using both a pedagogically useful and a real-word application, the algorithm is shown to be robust with respect to tree height, which in addition to mesostate threshold size is the main adjustable parameter. It is demonstrated that the derived mesostate networks can preserve information regarding the free energy basins and barriers the system is characterized by.2

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From simulation data to conformational ensembles: Structure and dynamics-based methods

et al. 1999

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Statistical methods for analyzing large data sets of molecular configurations within the chemical concept of molecular conformations are described. The strategies are based on dependencies between configurations of a molecular ensemble; the article concentrates on dependencies induced by (a) correlations between the molecular degrees of freedom, (b) geometrical similarities of configurations, and (c) dynamical relations between subsets of configurations. The statistical technique realizing aspect (a) is based on an approach suggested by Amadei et al. (Proteins 1993, 17). It allows identification of essential degrees of freedom of a molecular system, and is extended to determine single configurations as representatives for the crucial features related to these essential degrees of freedom. Aspects (b) and (c) are based on statistical cluster methods. They lead to a decomposition of the available simulation data into conformational ensembles or subsets, with the property that all configurations in one of these subsets share a common chemical property. In contrast to the restriction to single representative conformations, conformational ensembles include information about, for examples, structural flexibility or dynamical connectivity. The conceptual similarities and differences of the three approaches are discussed in detail, and are illustrated by application to simulation data originating from a hybrid Monte Carlo sampling of a triribonucleotide.© 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1760–1774, 1999

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A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo

Cited by 362 publications

References 39 publications

Optimal control of molecular dynamics using Markov state models

Optimal control of molecular dynamics using Markov state models

Efficient Construction of Mesostate Networks from Molecular Dynamics Trajectories

From simulation data to conformational ensembles: Structure and dynamics-based methods

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