Peptide Conformational Equilibria Computed via a Single-Stage Shifting Protocol

Ytreberg, F. Marty; Zuckerman, Daniel M.

doi:10.1021/jp0510692

Cited by 15 publications

(19 citation statements)

References 57 publications

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“…Such a situation was indeed observed for transitions between low-energy configurations of Lennard-Jones clusters [41], which could be sampled successfully only with non-equilibrium path sampling, but not with other approaches. Compared to standard methods, fast switching algorithms appeared on the scene only recently, such that substantial improvements and new developments are to be expected [13,21,57,[73][74][75][76][77][78]. It is worth noting that fast switching ideas have not only been applied to the calculation of free energies, but have also been combined with existing sampling methods to enhance the efficiency of the simulation.…”

Section: Discussionmentioning

confidence: 99%

Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics

Dellago

Hummer

2013

Entropy

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As shown by Jarzynski, free energy differences between equilibrium states can be expressed in terms of the statistics of work carried out on a system during non-equilibrium transformations. This exact result, as well as the related Crooks fluctuation theorem, provide the basis for the computation of free energy differences from fast switching molecular dynamics simulations, in which an external parameter is changed at a finite rate, driving the system away from equilibrium. In this article, we first briefly review the Jarzynski identity and the Crooks fluctuation theorem and then survey various algorithms building on these relations. We pay particular attention to the statistical efficiency of these methods and discuss practical issues arising in their implementation and the analysis of the results.

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Section: Discussionmentioning

confidence: 99%

Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics

Dellago

Hummer

2013

Entropy

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“…This ratio cannot be estimated without sampling within both states – or effectively doing so 38, 39. Note that this argument does not assume that sampling is performed dynamically.…”

Section: Overall Sampling Quality In Simulationsmentioning

confidence: 99%

Chapter 2 Quantifying Uncertainty and Sampling Quality in Biomolecular Simulations

Grossfield

Zuckerman

2009

Annual Reports in Computational Chemistry

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289

356

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Growing computing capacity and algorithmic advances have facilitated the study of increasingly large biomolecular systems at longer timescales. However, with these larger, more complex systems come questions about the quality of sampling and statistical convergence. What size systems can be sampled fully? If a system is not fully sampled, can certain “fast variables” be considered well-converged? How can one determine the statistical significance of observed results? The present review describes statistical tools and the underlying physical ideas necessary to address these questions. Basic definitions and ready-to-use analyses are provided, along with explicit recommendations. Such statistical analyses are of paramount importance in establishing the reliability of simulation data in any given study.

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“…Note that our strategy, as shown here, is an example of an end-point free energy difference method, because no path connecting alpha and beta is needed (e.g., refs. [15][16][17][18][19][20][21]. Fig.…”

Section: Resultsmentioning

confidence: 99%

“…To provide a proof of principle for our reweighting approach, we will determine free energy differences ( F), between states for various test systems (15)(16)(17)(18)(19)(20)(21).…”

Section: Background and Theorymentioning

confidence: 99%

A black-box re-weighting analysis can correct flawed simulation data

Ytreberg

Zuckerman

2008

Proc. Natl. Acad. Sci. U.S.A.

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There is a great need for improved statistical sampling in a range of physical, chemical, and biological systems. Even simulations based on correct algorithms suffer from statistical error, which can be substantial or even dominant when slow processes are involved. Further, in key biomolecular applications, such as the determination of protein structures from NMR data, non-Boltzmann-distributed ensembles are generated. We therefore have developed the "blackbox" strategy for reweighting a set of configurations generated by arbitrary means to produce an ensemble distributed according to any target distribution. In contrast to previous algorithmic efforts, the black-box approach exploits the configuration-space density observed in a simulation, rather than assuming a desired distribution has been generated. Successful implementations of the strategy, which reduce both statistical error and bias, are developed for a one-dimensional system, and a 50-atom peptide, for which the correct 250-to-1 population ratio is recovered from a heavily biased ensemble.canonical sampling | free energy | non-Boltzmann | molecular simulation E nsemble averages over configurations are fundamental to the analysis of finite-temperature systems of physical, chemical, and biological interest, as well as to any statistically defined system. Yet it is well appreciated that estimates of such averages based on computer simulations can suffer from both systematic and statistical error (1, 2). We therefore ask: Given a set of previously generated configurations of uncertain quality, what is the best way to estimate ensemble averages? Our proposed answer, the "black-box reweighting" (BBRW) strategy described below, appears promising in its ability to overcome both types of error in some systems.Statistical error is a ubiquitous problem of underappreciated practical importance. Every algorithm known to the authors, including sophisticated methods (3-5), relies on repeated visits to a state (a subset of configuration space) to generate statistical reliability or precision in the population estimate for that state. If we define the simulation-and-system-specific correlation time t corr as the time required to visit all important states at least once, then statistical precision requires a long total simulation time, t sim t corr . Standard square-root-of-duration arguments (1, 2) suggest that a simulation retains a fractional imprecision of √ t corr /t sim (on a unit scale). Below, we show that BBRW dramatically cuts statistical error, avoiding the slow square-root behavior.Systematic bias is typical in some systems of great practical importance-such as full-sized proteins-where, to date, it is not clear that any atomically detailed simulation has come close to reaching t corr . Indeed, surprisingly lengthy simulations are required to obtain statistical ensembles for small peptides (6). Nevertheless, biased non-Boltzmann distributed sets of atomically detailed protein structures are regularly generated, e.g., for NMR structure determination (7) and i...

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Peptide Conformational Equilibria Computed via a Single-Stage Shifting Protocol

Cited by 15 publications

References 57 publications

Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics

Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics

Chapter 2 Quantifying Uncertainty and Sampling Quality in Biomolecular Simulations

A black-box re-weighting analysis can correct flawed simulation data

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