Solution structure of the ESCRT-I complex by small-angle X-ray scattering, EPR, and FRET spectroscopy

Bouřa, Evžen; Różycki, Bartosz; Herrick, Dawn Z.; Chung, Hoi Sung; Večeř, Jaroslav; Eaton, William A.; Cafiso, David S.; Hummer, Gerhard; Hurley, James H.

doi:10.1073/pnas.1101763108

Cited by 106 publications

(125 citation statements)

References 35 publications

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“…We note that for θ = 1, this distribution is identical to the Bayesian posterior of single-copy refinement in Eqs. (2)(3)(4). This procedure is closely related to the maximumentropy method.…”

Section: B Bayesian Ensemble Refinement In Probability Density Spacementioning

confidence: 99%

Bayesian ensemble refinement by replica simulations and reweighting

Hummer

Köfinger

2015

The Journal of Chemical Physics

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225

394

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We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation.Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraint should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" (BioEn) method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of singlemolecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

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Section: B Bayesian Ensemble Refinement In Probability Density Spacementioning

confidence: 99%

Bayesian ensemble refinement by replica simulations and reweighting

Hummer

Köfinger

2015

The Journal of Chemical Physics

Self Cite

225

394

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“…In integrative modelling, the approximation of the local environment can be iteratively improved [33]. Rotamer library-based predictions are a computationally inexpensive approach for testing many models in ensemble refinement [34] and for simulating PDS data from MD trajectories of unlabelled biomolecules with the Python package RotamerConvolveMD [35].…”

Section: From Distance Distributions To Modelsmentioning

confidence: 99%

The contribution of modern EPR to structural biology

Jeschke

2018

Emerging Topics in Life Sciences

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133

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Electron paramagnetic resonance (EPR) spectroscopy combined with site-directed spin labelling is applicable to biomolecules and their complexes irrespective of system size and in a broad range of environments. Neither short-range nor long-range order is required to obtain structural restraints on accessibility of sites to water or oxygen, on secondary structure, and on distances between sites. Many of the experiments characterize a static ensemble obtained by shock-freezing. Compared with characterizing the dynamic ensemble at ambient temperature, analysis is simplified and information loss due to overlapping timescales of measurement and system dynamics is avoided. The necessity for labelling leads to sparse restraint sets that require integration with data from other methodologies for building models. The double electron-electron resonance experiment provides distance distributions in the nanometre range that carry information not only on the mean conformation but also on the width of the native ensemble. The distribution widths are often inconsistent with Anfinsen's concept that a sequence encodes a single native conformation defined at atomic resolution under physiological conditions.

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“…Obtaining as detailed as possible a picture of the disordered ensemble would ideally combine information from all of these experiments, if available. This can be done most comprehensively via an explicit ensemble description of the disordered state, either by reweighting of an existing molecular simulation [2][3][4][12][13][14][15][16][17] , or by performing an ensemble structural refinement with a very large number of replicas of the system [18][19][20][21][22][23] . However, a simpler approach is frequently useful.…”

Section: Introductionmentioning

confidence: 99%

Inferring Properties of Disordered Chains From FRET Transfer Efficiencies

Zheng

Zerze

Borgia

et al. 2018

Biophysical Journal

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Förster resonance energy transfer (FRET) is a powerful tool for elucidating both structural and dynamic properties of unfolded or disordered biomolecules, especially in single-molecule experiments. However, the key observables, namely, the mean transfer efficiency and fluorescence lifetimes of the donor and acceptor chromophores, are averaged over a broad distribution of donor-acceptor distances. The inferred average properties of the ensemble therefore depend on the form of the model distribution chosen to describe the distance, as has been widely recognized. In addition, while the distribution for one type of polymer model may be appropriate for a chain under a given set of physico-chemical conditions, it may not be suitable for the same chain in a different environment so that even an apparently consistent application of the same model over all conditions may distort the apparent changes in chain dimensions with variation of temperature or solution composition. Here, we present an alternative and straightforward approach to determining ensemble properties from FRET data, in which the polymer scaling exponent is allowed to vary with solution conditions. In its simplest form, it requires either the mean FRET efficiency or fluorescence lifetime information. In order to test the accuracy of the method, we have utilized both synthetic FRET data from implicit and explicit solvent simulations for 30 different protein sequences, and experimental single-molecule FRET data for an intrinsically disordered and a denatured protein. In all cases, we find that the inferred radii of gyration are within 10% of the true values, thus providing higher accuracy than simpler polymer models. In addition, the scaling exponents obtained by our procedure are in good agreement with those determined directly from the molecular ensemble. Our approach can in principle be generalized to treating other ensemble-averaged functions of intramolecular distances from experimental data. Förster resonance energy transfer (FRET) is a powerful tool for elucidating both structural and dynamic properties of unfolded or disordered biomolecules, especially in single-molecule experiments. However, the key observables, namely the mean transfer efficiency and fluorescence lifetimes of the donor and acceptor chromophores, are averaged over a broad distribution of donor-acceptor distances. The inferred average properties of the ensemble therefore depend on the form of the model distribution chosen to describe the distance, as has been widely recognized. In addition, while the distribution for one type of polymer model may be appropriate for a chain under a given set of physico-chemical conditions, it may not be suitable for the same chain in a different environment, so that even an apparently consistent application of the same model over all conditions may distort the apparent changes in chain dimensions with variation of temperature or solution composition. Here, we present an alternative and straightforward approach to determining ensemble proper...

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Solution structure of the ESCRT-I complex by small-angle X-ray scattering, EPR, and FRET spectroscopy

Cited by 106 publications

References 35 publications

Bayesian ensemble refinement by replica simulations and reweighting

Bayesian ensemble refinement by replica simulations and reweighting

The contribution of modern EPR to structural biology

Inferring Properties of Disordered Chains From FRET Transfer Efficiencies

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