Combining Experiments and Simulations Using the Maximum Entropy Principle

Boomsma, Wouter; Ferkinghoff‐Borg, Jesper; Lindorff‐Larsen, Kresten

doi:10.1371/journal.pcbi.1003406

Cited by 193 publications

(209 citation statements)

References 49 publications

Supporting

Mentioning

209

Contrasting

Order By: Relevance

“…Despite their obvious complementarity, SAXS, NMR, and single-molecule FRET data on unfolded proteins or IDPs have only rarely been directly combined or compared, and concerns have been raised about the validity of the individual methods for correctly quantifying unfolded-state properties (36,37). Here we present a direct comparison of the properties of urea-denatured ubiquitin as quantified from all three methods and enhance the description of the ensemble by the FRET-specific single-molecule, time-dependent, and long-range distance information.…”

mentioning

confidence: 99%

Comprehensive structural and dynamical view of an unfolded protein from the combination of single-molecule FRET, NMR, and SAXS

Aznauryan

Delgado

Soranno

et al. 2016

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

145

167

View full text Add to dashboard Cite

The properties of unfolded proteins are essential both for the mechanisms of protein folding and for the function of the large group of intrinsically disordered proteins. However, the detailed structural and dynamical characterization of these highly dynamic and conformationally heterogeneous ensembles has remained challenging. Here we combine and compare three of the leading techniques for the investigation of unfolded proteins, NMR spectroscopy (NMR), smallangle X-ray scattering (SAXS), and single-molecule Förster resonance energy transfer (FRET), with the goal of quantitatively testing their consistency and complementarity and for obtaining a comprehensive view of the unfolded-state ensemble. Using unfolded ubiquitin as a test case, we find that its average dimensions derived from FRET and from structural ensembles calculated using the program X-PLOR-NIH based on NMR and SAXS restraints agree remarkably well; even the shapes of the underlying intramolecular distance distributions are in good agreement, attesting to the reliability of the approaches. The NMR-based results provide a highly sensitive way of quantifying residual structure in the unfolded state. FRETbased nanosecond fluorescence correlation spectroscopy allows long-range distances and chain dynamics to be probed in a time range inaccessible by NMR. The combined techniques thus provide a way of optimally using the complementarity of the available methods for a quantitative structural and dynamical description of unfolded proteins both at the global and the local level.protein folding | unfolded protein ensemble | Förster resonance energy transfer | nuclear magnetic resonance | small-angle X-ray scattering P roteins exist as ensembles of interconverting conformations.Obviously, unfolded polypeptide chains, such as chemically or physically denatured proteins and intrinsically disordered proteins (IDPs), can access extremely large numbers of conformations (1). A comprehensive description of their structural and dynamical behavior is a prerequisite for understanding protein folding (2-4) and the function of IDPs in health and disease (5, 6). Due to the very large number of conformational degrees of freedom of the unfolded polypeptide ensemble, it is of utmost importance to obtain as many independent experimental parameters as possible for a quantitative description of its behavior. Three experimental methods have been particularly informative in this respect: NMR spectroscopy (2, 5, 7-9), small angle X-ray scattering (SAXS) (10, 11), and single-molecule Förster resonance energy transfer spectroscopy (single-molecule FRET) (12, 13).NMR in solution provides very rich local structural and dynamical information at virtually any atom site with the exception of oxygen. Distance and angular information can be obtained from nuclear Overhauser enhancements (14), three-bond scalar couplings (15), paramagnetic relaxation enhancements (PREs) (16), pseudo contact shifts (17), residual dipolar couplings (RDCs) (8, 18), chemical shifts (19), and hydrogen bond scalar ...

show abstract

mentioning

confidence: 99%

Comprehensive structural and dynamical view of an unfolded protein from the combination of single-molecule FRET, NMR, and SAXS

Aznauryan

Delgado

Soranno

et al. 2016

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

145

167

View full text Add to dashboard Cite

show abstract

“…21 EDS is the part of a growing body of work where molecular models are minimally modified to match experimental data, thus arriving at a unique synthesis of experimental data with the underlying physics, while allowing the latter to be less than perfect (i.e., approximate). [22][23][24][25] The present work is the first to incorporate experimental data by a minimal bias method into AIMD simulation, and specifically via the EDS approach.…”

mentioning

confidence: 99%

Communication: Improved ab initio molecular dynamics by minimally biasing with experimental data

White

Knight

Hocky

et al. 2017

The Journal of Chemical Physics

View full text Add to dashboard Cite

Accounting for electrons and nuclei simultaneously is a powerful capability of ab initio molecular dynamics (AIMD). However, AIMD is often unable to accurately reproduce properties of systems such as water due to inaccuracies in the underlying electronic density functionals. This shortcoming is often addressed by added empirical corrections and/or increasing the simulation temperature. We present here a maximum-entropy approach to directly incorporate limited experimental data via a minimal bias. Biased AIMD simulations of water and an excess proton in water are shown to give significantly improved properties both for observables which were biased to match experimental data and for unbiased observables. This approach also yields new physical insight into inaccuracies in the underlying density functional theory as utilized in the unbiased AIMD.

show abstract

“…From the initial emphasis on the determination of the native structures of proteins, the focus is increasingly shifting toward generating conformational ensembles representing their conformational fluctuations (2)(3)(4). In this context, problems with overfitting are systematically addressed (5), and in general efforts are made to implement the structural restraints as conservatively as possible, for instance by using the maximum entropy principle (6)(7)(8)(9). The field is also seeing increasingly sophisticated modeling approaches, often based on Bayesian statistics, for dealing rigorously with the problem of updating prior information (e.g., the force field) in the light of observed data (10)(11)(12).…”

mentioning

confidence: 99%

Equilibrium simulations of proteins using molecular fragment replacement and NMR chemical shifts

Boomsma

Tian

Frellsen

et al. 2014

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

Self Cite

View full text Add to dashboard Cite

Methods of protein structure determination based on NMR chemical shifts are becoming increasingly common. The most widely used approaches adopt the molecular fragment replacement strategy, in which structural fragments are repeatedly reassembled into different complete conformations in molecular simulations. Although these approaches are effective in generating individual structures consistent with the chemical shift data, they do not enable the sampling of the conformational space of proteins with correct statistical weights. Here, we present a method of molecular fragment replacement that makes it possible to perform equilibrium simulations of proteins, and hence to determine their free energy landscapes. This strategy is based on the encoding of the chemical shift information in a probabilistic model in Markov chain Monte Carlo simulations. First, we demonstrate that with this approach it is possible to fold proteins to their native states starting from extended structures. Second, we show that the method satisfies the detailed balance condition and hence it can be used to carry out an equilibrium sampling from the Boltzmann distribution corresponding to the force field used in the simulations. Third, by comparing the results of simulations carried out with and without chemical shift restraints we describe quantitatively the effects that these restraints have on the free energy landscapes of proteins. Taken together, these results demonstrate that the molecular fragment replacement strategy can be used in combination with chemical shift information to characterize not only the native structures of proteins but also their conformational fluctuations.

show abstract

Combining Experiments and Simulations Using the Maximum Entropy Principle

Cited by 193 publications

References 49 publications

Comprehensive structural and dynamical view of an unfolded protein from the combination of single-molecule FRET, NMR, and SAXS

Comprehensive structural and dynamical view of an unfolded protein from the combination of single-molecule FRET, NMR, and SAXS

Communication: Improved ab initio molecular dynamics by minimally biasing with experimental data

Equilibrium simulations of proteins using molecular fragment replacement and NMR chemical shifts

Contact Info

Product

Resources

About