The MUMO (minimal under-restraining minimal over-restraining) method for the determination of native state ensembles of proteins

Patterns in Protein Flexibility: A Comparison of NMR "Ensembles", MD Trajectories, and Crystallographic B-Factors

Proteins are molecular machines requiring flexibility to function. Crystallographic B-factors and Molecular Dynamics (MD) simulations both provide insights into protein flexibility on an atomic scale. Nuclear Magnetic Resonance (NMR) lacks a universally accepted analog of the B-factor. However, a lack of convergence in atomic coordinates in an NMR-based structure calculation also suggests atomic mobility. This paper describes a pattern in the coordinate uncertainties of backbone heavy atoms in NMR-derived structural “ensembles” first noted in the development of FindCore2 (previously called Expanded FindCore: DA Snyder, J Grullon, YJ Huang, R Tejero, GT Montelione, Proteins: Structure, Function, and Bioinformatics 82 (S2), 219–230) and demonstrates that this pattern exists in coordinate variances across MD trajectories but not in crystallographic B-factors. This either suggests that MD trajectories and NMR “ensembles” capture motional behavior of peptide bond units not captured by B-factors or indicates a deficiency common to force fields used in both NMR and MD calculations.

Ensemble-Based Analysis of the Dynamic Allostery in the PSD-95 PDZ3 Domain in Relation to the General Variability of PDZ Structures

PDZ domains are abundant interaction hubs found in a number of different proteins and they exhibit characteristic differences in their structure and ligand specificity. Their internal dynamics have been proposed to contribute to their biological activity via changes in conformational entropy upon ligand binding and allosteric modulation. Here we investigate dynamic structural ensembles of PDZ3 of the postsynaptic protein PSD-95, calculated based on previously published backbone and side-chain S2 order parameters. We show that there are distinct but interdependent structural rearrangements in PDZ3 upon ligand binding and the presence of the intramolecular allosteric modulator helix α3. We have also compared these rearrangements in PDZ1-2 of PSD-95 and the conformational diversity of an extended set of PDZ domains available in the PDB database. We conclude that although the opening-closing rearrangement, occurring upon ligand binding, is likely a general feature for all PDZ domains, the conformer redistribution upon ligand binding along this mode is domain-dependent. Our findings suggest that the structural and functional diversity of PDZ domains is accompanied by a diversity of internal motional modes and their interdependence.

Protein Motional Details Revealed by Complementary Structural Biology Techniques

Proteins depend on defined molecular plasticity for their functionality. How to comprehensively capture dynamics correctly is of ubiquitous biological importance. Approaches commonly used to probe protein dynamics include model-free elucidation of site-specific motion by NMR relaxation, molecular dynamics (MD)-based approaches, and capturing the substates within a dynamic ensemble by recent eNOE-based multiple-structure approaches. Even though MD is sometimes combined with ensemble-averaged NMR restraints, these approaches have largely been developed and used individually. Owing to the different underlying concepts and practical requirements, it has remained unclear how they compare, and how they cross-validate and complement each other. Here, we extract and compare the differential information contents of MD simulations, NMR relaxation measurements, and eNOE-based multi-state structures for the SH3 domain of chicken α-spectrin. The data show that a validated, consistent, and detailed picture is feasible both for timescales and actual conformational states sampled in the dynamic ensemble. This includes the biologically important side-chain plasticity, for which experimentally cross-validated assessment is a significant challenge.

Evaluation and Selection of Dynamic Protein Structural Ensembles with CoNSEnsX. Methods Mol Biol 2020;2112:241-254. [PMID: 32006289 DOI: 10.1007/978-1-0716-0270-6_16] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Understanding protein function at atomistic detail is not possible without accounting for the internal dynamics of these molecules. Ensemble-based models are based on the premise that single conformers cannot account for all experimental observations on the given molecule. Rather, a suitable set of structures, representing the internal dynamics of the protein at a given timescale, are necessary to achieve correspondence to measurements. CoNSEnsX⁺ is a service specifically designed for the investigation of such ensembles for compliance with NMR-derived parameters. In contrast to common structure evaluation tools, all parameters are treated as an average over the ensemble, if are not themselves an ensemble property like order parameters. CoNSEnsX⁺ is also capable of selecting a sub-ensemble with increased correspondence to a set of user-defined experimental parameters. CoNSEnsX⁺ is available as a web server at http://consensx.itk.ppke.hu , and the full Python source code is available on GitHub.

Enhancing NMR derived ensembles with kinetics on multiple timescales

Nuclear magnetic resonance (NMR) has the unique advantage of elucidating the structure and dynamics of biomolecules in solution at physiological temperatures, where they are in constant movement on timescales from picoseconds to milliseconds. Such motions have been shown to be critical for enzyme catalysis, allosteric regulation, and molecular recognition. With NMR being particularly sensitive to these timescales, detailed information about the kinetics can be acquired. However, nearly all methods of NMR-based biomolecular structure determination neglect kinetics, which introduces a large approximation to the underlying physics, limiting both structural resolution and the ability to accurately determine molecular flexibility. Here we present the Kinetic Ensemble approach that uses a hierarchy of interconversion rates between a set of ensemble members to rigorously calculate Nuclear Overhauser Effect (NOE) intensities. It can be used to simultaneously refine both temporal and structural coordinates. By generalizing ideas from the extended model free approach, the method can analyze the amplitudes and kinetics of motions anywhere along the backbone or side chains. Furthermore, analysis of a large set of crystal structures suggests that NOE data contains a surprising amount of high-resolution information that is better modeled using our approach. The Kinetic Ensemble approach provides the means to unify numerous types of experiments under a single quantitative framework and more fully characterize and exploit kinetically distinct protein states. While we apply the approach here to the protein ubiquitin and cross validate it with previously derived datasets, the approach can be applied to any protein for which NOE data is available.

Determination of a Structural Ensemble Representing the Dynamics of a G-Quadruplex DNA

It is increasingly recognized that the structures and dynamics of G-quadruplex DNA molecules are dictated by their sequences and greatly affected by environmental factors. The core guanine tetrads (G-tetrads) coordinate cations and display a strong conformational rigidity compared with that of the connecting loops. Although long loops linking the G-tetrads are typically disfavored, when present, they provide a striking illustration of the dynamics of short, single-stranded DNA regions. In addition to their role in determining the stability of the G-quadruplex state, these loops are also interesting as potential drug targets. To characterize accurately the dynamics of this DNA state, we apply here the principles of structural ensemble determination developed in the past two decades for protein molecules to DNA molecules. We thus perform extensive molecular dynamics simulations restrained with nuclear magnetic resonance residual dipolar couplings to determine a structural ensemble of the human CEB25 minisatellite G-quadruplex, which contains a connecting loop of nine nucleotides. This structural ensemble displays a wide set of arrangements for the loop and a compact, well-defined G-quadruplex core. Our results show the importance of stacking interactions in the loop and strengthen the ability of the closing base pairs to confer a large thermodynamic stability to the G-quadruplex structure.

RNA Dynamics by NMR Spectroscopy

An ever-increasing number of functional RNAs require a mechanistic understanding. RNA function relies on changes in its structure, so-called dynamics. To reveal dynamic processes and higher energy structures, new NMR methods have been developed to elucidate these dynamics in RNA with atomic resolution. In this Review, we provide an introduction to dynamics novices and an overview of methods that access most dynamic timescales, from picoseconds to hours. Examples are provided as well as insight into theory, data acquisition and analysis for these different methods. Using this broad spectrum of methodology, unprecedented detail and invisible structures have been obtained and are reviewed here. RNA, though often more complicated and therefore neglected, also provides a great system to study structural changes, as these RNA structural changes are more easily defined-Lego like-than in proteins, hence the numerous revelations of RNA excited states.

Ligand-dependent intra- and interdomain motions in the PDZ12 tandem regulate binding interfaces in postsynaptic density protein-95

The postsynaptic density protein-95 (PSD-95) regulates synaptic plasticity through interactions mediated by its peptide-binding PDZ domains. The two N-terminal PDZ domains of PSD-95 form an autonomous structural unit, and their interdomain orientation and dynamics depend on ligand binding. To understand the mechanistic details of the effect of ligand binding, we generated conformational ensembles using available experimentally determined nuclear Overhauser effect interatomic distances and S² order parameters. In our approach, the fast dynamics of the two domains is treated independently. We find that intradomain structural changes induced by ligand binding modulate the probability of the occurrence of specific domain-domain orientations. Our results suggest that the β2-β3 loop in the PDZ domains is a key regulatory region, which influences both intradomain motions and supramodular rearrangement.

Bayesian-Maximum-Entropy Reweighting of IDP Ensembles Based on NMR Chemical Shifts

Bayesian and Maximum Entropy approaches allow for a statistically sound and systematic fitting of experimental and computational data. Unfortunately, assessing the relative confidence in these two types of data remains difficult as several steps add unknown error. Here we propose the use of a validation-set method to determine the balance, and thus the amount of fitting. We apply the method to synthetic NMR chemical shift data of an intrinsically disordered protein. We show that the method gives consistent results even when other methods to assess the amount of fitting cannot be applied. Finally, we also describe how the errors in the chemical shift predictor can lead to an incorrect fitting and how using secondary chemical shifts could alleviate this problem.

Different modes of barrel opening suggest a complex pathway of ligand binding in human gastrotropin

Gastrotropin, the intracellular carrier of bile salts in the small intestine, binds two ligand molecules simultaneously in its internal cavity. The molecular rearrangements required for ligand entry are not yet fully clear. To improve our understanding of the binding process we combined molecular dynamics simulations with previously published structural and dynamic NMR parameters. The resulting ensembles reveal two distinct modes of barrel opening with one corresponding to the transition between the apo and holo states, whereas the other affecting different protein regions in both ligation states. Comparison of the calculated structures with NMR-derived parameters reporting on slow conformational exchange processes suggests that the protein undergoes partial unfolding along a path related to the second mode of the identified barrel opening motion.

Mapping Local Conformational Landscapes of Proteins in Solution

The ability of proteins to adopt multiple conformational states is essential to their function, and elucidating the details of such diversity under physiological conditions has been a major challenge. Here we present a generalized method for mapping protein population landscapes by NMR spectroscopy. Experimental NOESY spectra are directly compared with a set of expectation spectra back-calculated across an arbitrary conformational space. Signal decomposition of the experimental spectrum then directly yields the relative populations of local conformational microstates. In this way, averaged descriptions of conformation can be eliminated. As the method quantitatively compares experimental and expectation spectra, it inherently delivers an R factor expressing how well structural models explain the input data. We demonstrate that our method extracts sufficient information from a single 3D NOESY experiment to perform initial model building, refinement, and validation, thus offering a complete de novo structure determination protocol.

eNORA2 Exact NOE Analysis Program

We have recently developed an NMR protocol to extract exact distances between nuclei in proteins from an exact interpretation of NOESY buildup intensities (eNOEs). This enabled us to calculate multistate structural ensembles that exhibit realistic spatial sampling and long-range correlations. Our initial studies were laborious and required a deep understanding of the underlying spin dynamics. Here, we present a MatLab package that integrates all data processing steps required to convert intensities of assigned peaks in NOESY series into upper and lower distance limits for structure calculation. Those steps include organization of the data in object format, extraction of autorelaxation and cross-relaxation rate constants by fitting of diagonal peak decays and cross peak buildups, validation of the data, correction for spin diffusion, graphical display of the results, and generation of distance limits in CYANA compatible format. The analysis may be carried out using a full relaxation matrix or a simplified "divide and conquer" approach that allows for partial deuteration of protons. As the program does not require expertise beyond that of standard resonance assignment/structure calculation, it is suitable for experts and nonexperts alike.

Fine-tuning the extent and dynamics of binding cleft opening as a potential general regulatory mechanism in parvulin-type peptidyl prolyl isomerases

Parvulins or rotamases form a distinct group within peptidyl prolyl cis-trans isomerases. Their exact mode of action as well as the role of conserved residues in the family are still not unambiguously resolved. Using backbone S² order parameters and NOEs as restraints, we have generated dynamic structural ensembles of three distinct parvulins, SaPrsA, TbPin1 and CsPinA. The resulting ensembles are in good agreement with the experimental data but reveal important differences between the three enzymes. The largest difference can be attributed to the extent of the opening of the substrate binding cleft, along which motional mode the three molecules occupy distinct regions. Comparison with a wide range of other available parvulin structures highlights structural divergence along the bottom of the binding cleft acting as a hinge during the opening-closing motion. In the prototype WW-domain containing parvulin, Pin1, this region is also important in forming contacts with the WW domain known to modulate enzymatic activity of the catalytic domain. We hypothesize that modulation of the extent and dynamics of the identified ‘breathing motion’ might be one of the factors responsible for functional differences in the distinct parvulin subfamilies.

The Exact NOE as an Alternative in Ensemble Structure Determination

The structure-function paradigm is increasingly replaced by the structure-dynamics-function paradigm. All protein activity is steered by the interplay between enthalpy and entropy. Conformational dynamics serves as a proxy of conformational entropy. Therefore, it is essential to study not only the average conformation but also the spatial sampling of a protein on all timescales. To this purpose, we have established a protocol for determining multiple-state ensembles of proteins based on exact nuclear Overhauser effects (eNOEs). We have recently extended our previously reported eNOE data set for the protein GB3 by a very large set of backbone and side-chain residual dipolar couplings and three-bond J couplings. Here, we demonstrate that at least four structural states are required to represent the complete data set by dissecting the contributions to the CYANA target function, which quantifies restraint violations in structure calculation. We present a four-state ensemble of GB3, which largely preserves the characteristics obtained from eNOEs only. Due to the abundance of the input data, the ensemble and χ(1) angles in particular are well suited for cross-validation of the input data and comparison to x-ray structures. Principal component analysis is used to automatically identify and validate relevant states of the ensembles. Overall, our findings suggest that eNOEs are a valuable alternative to traditional NMR probes in spatial elucidation of proteins.

Predicting protein dynamics from structural ensembles

The biological properties of proteins are uniquely determined by their structure and dynamics. A protein in solution populates a structural ensemble of metastable configurations around the global fold. From overall rotation to local fluctuations, the dynamics of proteins can cover several orders of magnitude in time scales. We propose a simulation-free coarse-grained approach which utilizes knowledge of the important metastable folded states of the protein to predict the protein dynamics. This approach is based upon the Langevin Equation for Protein Dynamics (LE4PD), a Langevin formalism in the coordinates of the protein backbone. The linear modes of this Langevin formalism organize the fluctuations of the protein, so that more extended dynamical cooperativity relates to increasing energy barriers to mode diffusion. The accuracy of the LE4PD is verified by analyzing the predicted dynamics across a set of seven different proteins for which both relaxation data and NMR solution structures are available. Using experimental NMR conformers as the input structural ensembles, LE4PD predicts quantitatively accurate results, with correlation coefficient ρ = 0.93 to NMR backbone relaxation measurements for the seven proteins. The NMR solution structure derived ensemble and predicted dynamical relaxation is compared with molecular dynamics simulation-derived structural ensembles and LE4PD predictions and is consistent in the time scale of the simulations. The use of the experimental NMR conformers frees the approach from computationally demanding simulations.

Finding Our Way in the Dark Proteome

The traditional structure-function paradigm has provided significant insights for well-folded proteins in which structures can be easily and rapidly revealed by X-ray crystallography beamlines. However, approximately one-third of the human proteome is comprised of intrinsically disordered proteins and regions (IDPs/IDRs) that do not adopt a dominant well-folded structure, and therefore remain "unseen" by traditional structural biology methods. This Perspective considers the challenges raised by the "Dark Proteome", in which determining the diverse conformational substates of IDPs in their free states, in encounter complexes of bound states, and in complexes retaining significant disorder requires an unprecedented level of integration of multiple and complementary solution-based experiments that are analyzed with state-of-the art molecular simulation, Bayesian probabilistic models, and high-throughput computation. We envision how these diverse experimental and computational tools can work together through formation of a "computational beamline" that will allow key functional features to be identified in IDP structural ensembles.

Characterization of the conformational fluctuations in the Josephin domain of ataxin-3

As for a variety of other molecular recognition processes, conformational fluctuations play an important role in the cleavage of polyubiquitin chains by the Josephin domain of ataxin-3. The interaction between Josephin and ubiquitin appears to be mediated by the motions of α-helical hairpin that is unusual among deubiquitinating enzymes. Here, we characterized the conformational fluctuations of the helical hairpin by incorporating NMR measurements as replica-averaged restraints in molecular dynamics simulations, and by validating the results by small-angle x-ray scattering measurements. This approach allowed us to define the extent of the helical hairpin motions and suggest a role of such motions in the recognition of ubiquitin.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Solid-State NMR-Restrained Ensemble Dynamics of a Membrane Protein in Explicit Membranes

Solid-state NMR has been used to determine the structures of membrane proteins in native-like lipid bilayer environments. Most structure calculations based on solid-state NMR observables are performed using simulated annealing with restrained molecular dynamics and an energy function, where all nonbonded interactions are represented by a single, purely repulsive term with no contributions from van der Waals attractive, electrostatic, or solvation energy. To our knowledge, this is the first application of an ensemble dynamics technique performed in explicit membranes that uses experimental solid-state NMR observables to obtain the refined structure of a membrane protein together with information about its dynamics and its interactions with lipids. Using the membrane-bound form of the fd coat protein as a model membrane protein and its experimental solid-state NMR data, we performed restrained ensemble dynamics simulations with different ensemble sizes in explicit membranes. For comparison, a molecular dynamics simulation of fd coat protein was also performed without any restraints. The average orientation of each protein helix is similar to a structure determined by traditional single-conformer approaches. However, their variations are limited in the resulting ensemble of structures with one or two replicas, as they are under the strong influence of solid-state NMR restraints. Although highly consistent with all solid-state NMR observables, the ensembles of more than two replicas show larger orientational variations similar to those observed in the molecular dynamics simulation without restraints. In particular, in these explicit membrane simulations, Lys(40), residing at the C-terminal side of the transmembrane helix, is observed to cause local membrane curvature. Therefore, compared to traditional single-conformer approaches in implicit environments, solid-state NMR restrained ensemble simulations in explicit membranes readily characterize not only protein dynamics but also protein-lipid interactions in detail.

NMR Order Parameter Determination from Long Molecular Dynamics Trajectories for Objective Comparison with Experiment

Functional protein motions covering a wide range of time scales can be studied, among other techniques, by NMR and by molecular dynamics (MD) computer simulations. MD simulations of proteins now routinely extend into the hundreds of nanoseconds time scale range exceeding the overall tumbling correlation times of proteins in solution by several orders of magnitude. This provides a unique opportunity to rigorously validate these simulations by quantitative comparison with model-free order parameters derived from NMR relaxation experiments. However, presently there is no consensus on how such a comparison is best done. We address here how this can be accomplished in a way that is both efficient and objective. For this purpose, we analyze (15)N R1 and R2 and heteronuclear {(1)H}-(15)N NOE NMR relaxation parameters computed from 500 ns MD trajectories of 10 different protein systems using the model-free analysis. The resulting model-free S(2) order parameters are then used as targets for S(2) values computed directly from the trajectories by the iRED method by either averaging over blocks of variable lengths or by using exponentially weighted snapshots (wiRED). We find that the iRED results are capable of reproducing the target S(2) values with high accuracy provided that the averaging window is chosen 5 times the length of the overall tumbling correlation time. These results provide useful guidelines for the derivation of NMR order parameters from MD for a meaningful comparison with their experimental counterparts.

Ensembles of a small number of conformations with relative populations

In our previous work, we proposed a new way to represent protein native states, using ensembles of a small number of conformations with relative Populations, or ESP in short. Using Ubiquitin as an example, we showed that using a small number of conformations could greatly reduce the potential of overfitting and assigning relative populations to protein ensembles could significantly improve their quality. To demonstrate that ESP indeed is an excellent alternative to represent protein native states, in this work we compare the quality of two ESP ensembles of Ubiquitin with several well-known regular ensembles or average structure representations. Extensive amount of significant experimental data are employed to achieve a thorough assessment. Our results demonstrate that ESP ensembles, though much smaller in size comparing to regular ensembles, perform equally or even better sometimes in all four different types of experimental data used in the assessment, namely, the residual dipolar couplings, residual chemical shift anisotropy, hydrogen exchange rates, and solution scattering profiles. This work further underlines the significance of having relative populations in describing the native states.

ENCORE: Software for Quantitative Ensemble Comparison

There is increasing evidence that protein dynamics and conformational changes can play an important role in modulating biological function. As a result, experimental and computational methods are being developed, often synergistically, to study the dynamical heterogeneity of a protein or other macromolecules in solution. Thus, methods such as molecular dynamics simulations or ensemble refinement approaches have provided conformational ensembles that can be used to understand protein function and biophysics. These developments have in turn created a need for algorithms and software that can be used to compare structural ensembles in the same way as the root-mean-square-deviation is often used to compare static structures. Although a few such approaches have been proposed, these can be difficult to implement efficiently, hindering a broader applications and further developments. Here, we present an easily accessible software toolkit, called ENCORE, which can be used to compare conformational ensembles generated either from simulations alone or synergistically with experiments. ENCORE implements three previously described methods for ensemble comparison, that each can be used to quantify the similarity between conformational ensembles by estimating the overlap between the probability distributions that underlie them. We demonstrate the kinds of insights that can be obtained by providing examples of three typical use-cases: comparing ensembles generated with different molecular force fields, assessing convergence in molecular simulations, and calculating differences and similarities in structural ensembles refined with various sources of experimental data. We also demonstrate efficient computational scaling for typical analyses, and robustness against both the size and sampling of the ensembles. ENCORE is freely available and extendable, integrates with the established MDAnalysis software package, reads ensemble data in many common formats, and can work with large trajectory files.

Unveiling Inherent Degeneracies in Determining Population-Weighted Ensembles of Interdomain Orientational Distributions Using NMR Residual Dipolar Couplings: Application to RNA Helix Junction Helix Motifs

A growing number of studies employ time-averaged experimental data to determine dynamic ensembles of biomolecules. While it is well-known that different ensembles can satisfy experimental data to within error, the extent and nature of these degeneracies, and their impact on the accuracy of the ensemble determination remains poorly understood. Here, we use simulations and a recently introduced metric for assessing ensemble similarity to explore degeneracies in determining ensembles using NMR residual dipolar couplings (RDCs) with specific application to A-form helices in RNA. Various target ensembles were constructed representing different domain-domain orientational distributions that are confined to a topologically restricted (<10%) conformational space. Five independent sets of ensemble averaged RDCs were then computed for each target ensemble and a "sample and select" scheme used to identify degenerate ensembles that satisfy RDCs to within experimental uncertainty. We find that ensembles with different ensemble sizes and that can differ significantly from the target ensemble (by as much as ∑Ω ∼ 0.4 where ∑Ω varies between 0 and 1 for maximum and minimum ensemble similarity, respectively) can satisfy the ensemble averaged RDCs. These deviations increase with the number of unique conformers and breadth of the target distribution, and result in significant uncertainty in determining conformational entropy (as large as 5 kcal/mol at T = 298 K). Nevertheless, the RDC-degenerate ensembles are biased toward populated regions of the target ensemble, and capture other essential features of the distribution, including the shape. Our results identify ensemble size as a major source of uncertainty in determining ensembles and suggest that NMR interactions such as RDCs and spin relaxation, on their own, do not carry the necessary information needed to determine conformational entropy at a useful level of precision. The framework introduced here provides a general approach for exploring degeneracies in ensemble determination for different types of experimental data.

Structural Impact of Tau Phosphorylation at Threonine 231

Phosphorylation of the microtubule-associated protein Tau influences the assembly and stabilization of microtubules and is deregulated in several neurodegenerative diseases. The high flexibility of Tau, however, has prevented an atomic-level description of its phosphorylation-induced structural changes. Employing an extensive set of distance and orientational restraints together with a novel ensemble calculation approach, we determined conformational ensembles of Tau fragments in the non-phosphorylated state and, when phosphorylated at T231/S235 or T231/S235/S237/S238, four important sites of phosphorylation in Alzheimer disease. Comparison of the molecular ensembles showed that phosphorylation of the regulatory T231 does not perturb the backbone conformation of the proximal microtubule-binding (225)KVAVVR(230) motif. Instead, phosphorylated T231 selectively engages in a salt bridge with R230 that can compete with the formation of intermolecular salt bridges to tubulin. Our study provides an ensemble description which will be useful for the analysis of conformational transitions in Tau and other intrinsically disordered proteins.

Molecular dynamics study of naturally existing cavity couplings in proteins

Couplings between protein sub-structures are a common property of protein dynamics. Some of these couplings are especially interesting since they relate to function and its regulation. In this article we have studied the case of cavity couplings because cavities can host functional sites, allosteric sites, and are the locus of interactions with the cell milieu. We have divided this problem into two parts. In the first part, we have explored the presence of cavity couplings in the natural dynamics of 75 proteins, using 20 ns molecular dynamics simulations. For each of these proteins, we have obtained two trajectories around their native state. After applying a stringent filtering procedure, we found significant cavity correlations in 60% of the proteins. We analyze and discuss the structure origins of these correlations, including neighbourhood, cavity distance, etc. In the second part of our study, we have used longer simulations (≥100 ns) from the MoDEL project, to obtain a broader view of cavity couplings, particularly about their dependence on time. Using moving window computations we explored the fluctuations of cavity couplings along time, finding that these couplings could fluctuate substantially during the trajectory, reaching in several cases correlations above 0.25/0.5. In summary, we describe the structural origin and the variations with time of cavity couplings. We complete our work with a brief discussion of the biological implications of these results.

A relationship between the transient structure in the monomeric state and the aggregation propensities of α-synuclein and β-synuclein

α-Synuclein is an intrinsically disordered protein whose aggregation is implicated in Parkinson's disease. A second member of the synuclein family, β-synuclein, shares significant sequence similarity with α-synuclein but is much more resistant to aggregation. β-Synuclein is missing an 11-residue stretch in the central non-β-amyloid component region that forms the core of α-synuclein amyloid fibrils, yet insertion of these residues into β-synuclein to produce the βSHC construct does not markedly increase the aggregation propensity. To investigate the structural basis of these different behaviors, quantitative nuclear magnetic resonance data, in the form of paramagnetic relaxation enhancement-derived interatomic distances, are combined with molecular dynamics simulations to generate ensembles of structures representative of the solution states of α-synuclein, β-synuclein, and βSHC. Comparison of these ensembles reveals that the differing aggregation propensities of α-synuclein and β-synuclein are associated with differences in the degree of residual structure in the C-terminus coupled to the shorter separation between the N- and C-termini in β-synuclein and βSHC, making protective intramolecular contacts more likely.

Bayesian energy landscape tilting: towards concordant models of molecular ensembles

Predicting biological structure has remained challenging for systems such as disordered proteins that take on myriad conformations. Hybrid simulation/experiment strategies have been undermined by difficulties in evaluating errors from computational model inaccuracies and data uncertainties. Building on recent proposals from maximum entropy theory and nonequilibrium thermodynamics, we address these issues through a Bayesian energy landscape tilting (BELT) scheme for computing Bayesian hyperensembles over conformational ensembles. BELT uses Markov chain Monte Carlo to directly sample maximum-entropy conformational ensembles consistent with a set of input experimental observables. To test this framework, we apply BELT to model trialanine, starting from disagreeing simulations with the force fields ff96, ff99, ff99sbnmr-ildn, CHARMM27, and OPLS-AA. BELT incorporation of limited chemical shift and (3)J measurements gives convergent values of the peptide's α, β, and PPII conformational populations in all cases. As a test of predictive power, all five BELT hyperensembles recover set-aside measurements not used in the fitting and report accurate errors, even when starting from highly inaccurate simulations. BELT's principled framework thus enables practical predictions for complex biomolecular systems from discordant simulations and sparse data.

Time-averaged order parameter restraints in molecular dynamics simulations

A method is described that allows experimental S(2) order parameters to be enforced as a time-averaged quantity in molecular dynamics simulations. The two parameters that characterize time-averaged restraining, the memory relaxation time and the weight of the restraining potential energy term in the potential energy function used in the simulation, are systematically investigated based on two model systems, a vector with one end restrained in space and a pentapeptide. For the latter it is shown that the backbone N-H order parameter of individual residues can be enforced such that the spatial fluctuations of quantities depending on atomic coordinates are not significantly perturbed. The applicability to realistic systems is illustrated for the B3 domain of protein G in aqueous solution.

Biophysical highlights from 54 years of macromolecular crystallography

The United Nations has declared 2014 the International Year of Crystallography, and in commemoration, this review features a selection of 54 notable macromolecular crystal structures that have illuminated the field of biophysics in the 54 years since the first excitement of the myoglobin and hemoglobin structures in 1960. Chronological by publication of the earliest solved structure, each illustrated entry briefly describes key concepts or methods new at the time and key later work leveraged by knowledge of the three-dimensional atomic structure.

The expanded FindCore method for identification of a core atom set for assessment of protein structure prediction

Maximizing the scientific impact of NMR-based structure determination requires robust and statistically sound methods for assessing the precision of NMR-derived structures. In particular, a method to define a core atom set for calculating superimpositions and validating structure predictions is critical to the use of NMR-derived structures as targets in the CASP competition. FindCore (Snyder and Montelione, Proteins 2005;59:673-686) is a superimposition independent method for identifying a core atom set and partitioning that set into domains. However, as FindCore optimizes superimposition by sensitively excluding not-well-defined atoms, the FindCore core may not comprise all atoms suitable for use in certain applications of NMR structures, including the CASP assessment process. Adapting the FindCore approach to assess predicted models against experimental NMR structures in CASP10 required modification of the FindCore method. This paper describes conventions and a standard protocol to calculate an "Expanded FindCore" atom set suitable for validation and application in biological and biophysical contexts. A key application of the Expanded FindCore method is to identify a core set of atoms in the experimental NMR structure for which it makes sense to validate predicted protein structure models. We demonstrate the application of this Expanded FindCore method in characterizing well-defined regions of 18 NMR-derived CASP10 target structures. The Expanded FindCore protocol defines "expanded core atom sets" that match an expert's intuition of which parts of the structure are sufficiently well defined to use in assessing CASP model predictions. We also illustrate the impact of this analysis on the CASP GDT assessment scores.

A tensor-free method for the structural and dynamical refinement of proteins using residual dipolar couplings

Residual dipolar couplings (RDCs) are parameters measured in nuclear magnetic resonance spectroscopy that can provide exquisitely detailed information about the structure and dynamics of biological macromolecules. We describe here a method of using RDCs for the structural and dynamical refinement of proteins that is based on the observation that the RDC between two atomic nuclei depends directly on the angle ϑ between the internuclear vector and the external magnetic field. For every pair of nuclei for which an RDC is available experimentally, we introduce a structural restraint to minimize the deviation from the value of the angle ϑ derived from the measured RDC and that calculated in the refinement protocol. As each restraint involves only the calculation of the angle ϑ of the corresponding internuclear vector, the method does not require the definition of an overall alignment tensor to describe the preferred orientation of the protein with respect to the alignment medium. Application to the case of ubiquitin demonstrates that this method enables an accurate refinement of the structure and dynamics of this protein to be obtained.

The nuclear Overhauser effect from a quantitative perspective

The nuclear Overhauser enhancement or effect (NOE) is the most important measure in liquid-state NMR with macromolecules. Thus, the NOE is the subject of numerous reviews and books. Here, the NOE is revisited in light of our recently introduced measurements of exact nuclear Overhauser enhancements (eNOEs), which enabled the determination of multiple-state 3D protein structures. This review encompasses all relevant facets from the theoretical considerations to the use of eNOEs in multiple-state structure calculation. Important aspects include a detailed presentation of the relaxation theory relevant for the nuclear Overhauser effect, the estimation of the correction for spin diffusion, the experimental determination of the eNOEs, the conversion of eNOE rates into distances and validation of their quality, the distance-restraint classification and the protocols for calculation of structures and ensembles.

NMR-based simulation studies of Pf1 coat protein in explicit membranes

As time- and ensemble-averaged measures, NMR observables contain information about both protein structure and dynamics. This work represents a computational study to extract such information for membrane proteins from orientation-dependent NMR observables: solid-state NMR chemical shift anisotropy and dipolar coupling, and solution NMR residual dipolar coupling. We have performed NMR-restrained molecular dynamics simulations to refine the structure of the membrane-bound form of Pf1 coat protein in explicit lipid bilayers using the recently measured chemical shift anisotropy, dipolar coupling, and residual dipolar coupling data. From the simulations, we have characterized detailed protein-lipid interactions and explored the dynamics. All simulations are stable and the NMR restraints are well satisfied. The C-terminal transmembrane (TM) domain of Pf1 finds its optimal position in the membrane quickly (within 6 ns), illustrating efficient solvation of TM domains in explicit bilayer environments. Such rapid convergence also leads to well-converged interaction patterns between the TM helix and the membrane, which clearly show the interactions of interfacial membrane-anchoring residues with the lipids. For the N-terminal periplasmic helix of Pf1, we identify a stable, albeit dynamic, helix orientation parallel to the membrane surface that satisfies the amphiphatic nature of the helix in an explicit lipid bilayer. Such detailed information cannot be obtained solely from NMR observables. Therefore, the present simulations illustrate the usefulness of NMR-restrained MD refinement of membrane protein structure in explicit membranes.

Improved cross validation of a static ubiquitin structure derived from high precision residual dipolar couplings measured in a drug-based liquid crystalline phase

The antibiotic squalamine forms a lyotropic liquid crystal at very low concentrations in water (0.3-3.5% w/v), which remains stable over a wide range of temperature (1-40 °C) and pH (4-8). Squalamine is positively charged, and comparison of the alignment of ubiquitin relative to 36 previously reported alignment conditions shows that it differs substantially from most of these, but is closest to liquid crystalline cetyl pyridinium bromide. High precision residual dipolar couplings (RDCs) measured for the backbone (1)H-(15)N, (15)N-(13)C', (1)H(α)-(13)C(α), and (13)C'-(13)C(α) one-bond interactions in the squalamine medium fit well to the static structural model previously derived from NMR data. Inclusion into the structure refinement procedure of these RDCs, together with (1)H-(15)N and (1)H(α)-(13)C(α) RDCs newly measured in Pf1, results in improved agreement between alignment-induced changes in (13)C' chemical shift, (3)JHNHα values, and (13)C(α)-(13)C(β) RDCs and corresponding values predicted by the structure, thereby validating the high quality of the single-conformer structural model. This result indicates that fitting of a single model to experimental data provides a better description of the average conformation than does averaging over previously reported NMR-derived ensemble representations. The latter can capture dynamic aspects of a protein, thus making the two representations valuable complements to one another.

Enhancing the quality of protein conformation ensembles with relative populations

The function and dynamics of many proteins are best understood not from a single structure but from an ensemble. A high quality ensemble is necessary for accurately delineating protein dynamics. However, conformations in an ensemble are generally given equal weights. Few attempts were made to assign relative populations to the conformations, mainly due to the lack of right experimental data. Here we propose a method for assigning relative populations to ensembles using experimental residue dipolar couplings (RDC) as constraints, and show that relative populations can significantly enhance an ensemble's ability in representing the native states and dynamics. The method works by identifying conformation states within an ensemble and assigning appropriate relative populations to them. Each of these conformation states is represented by a sub-ensemble consisting of a subset of the conformations. Application to the ubiquitin X-ray ensemble clearly identifies two key conformation states, with relative populations in excellent agreement with previous work. We then apply the method to a reprotonated ERNST ensemble that is enhanced with a switched conformation, and show that as a result of population reweighting, not only the reproduction of RDCs is significantly improved, but common conformational features (particularly the dihedral angle distributions of ϕ 53 and ψ 52) also emerge for both the X-ray ensemble and the reprotonated ERNST ensemble.

Combining experiments and simulations using the maximum entropy principle

A key component of computational biology is to compare the results of computer modelling with experimental measurements. Despite substantial progress in the models and algorithms used in many areas of computational biology, such comparisons sometimes reveal that the computations are not in quantitative agreement with experimental data. The principle of maximum entropy is a general procedure for constructing probability distributions in the light of new data, making it a natural tool in cases when an initial model provides results that are at odds with experiments. The number of maximum entropy applications in our field has grown steadily in recent years, in areas as diverse as sequence analysis, structural modelling, and neurobiology. In this Perspectives article, we give a broad introduction to the method, in an attempt to encourage its further adoption. The general procedure is explained in the context of a simple example, after which we proceed with a real-world application in the field of molecular simulations, where the maximum entropy procedure has recently provided new insight. Given the limited accuracy of force fields, macromolecular simulations sometimes produce results that are at not in complete and quantitative accordance with experiments. A common solution to this problem is to explicitly ensure agreement between the two by perturbing the potential energy function towards the experimental data. So far, a general consensus for how such perturbations should be implemented has been lacking. Three very recent papers have explored this problem using the maximum entropy approach, providing both new theoretical and practical insights to the problem. We highlight each of these contributions in turn and conclude with a discussion on remaining challenges.

Determination of the individual roles of the linker residues in the interdomain motions of calmodulin using NMR chemical shifts

Many protein molecules are formed by two or more domains whose structures and dynamics are closely related to their biological functions. It is thus important to develop methods to determine the structural properties of these multidomain proteins. Here, we characterize the interdomain motions in the calcium-bound state of calmodulin (Ca(2+)-CaM) using NMR chemical shifts as replica-averaged structural restraints in molecular dynamics simulations. We find that the conformational fluctuations of the interdomain linker, which are largely responsible for the overall interdomain motions of CaM, can be well described by exploiting the information provided by chemical shifts. We thus identify 10 residues in the interdomain linker region that change their conformations upon substrate binding. Five of these residues (Met76, Lys77, Thr79, Asp80 and Ser81) are highly flexible and cover the range of conformations observed in the substrate-bound state, while the remaining five (Arg74, Lys75, Asp78, Glu82 and Glu83) are much more rigid and do not populate conformations typical of the substrate-bound form. The ensemble of conformations representing the Ca(2+)-CaM state obtained in this study is in good agreement with residual dipolar coupling, paramagnetic resonance enhancement, small-angle X-ray scattering and fluorescence resonance energy transfer measurements, which were not used as restraints in the calculations. These results provide initial evidence that chemical shifts can be used to characterize the conformational fluctuations of multidomain proteins.

Comparison of structure determination methods for intrinsically disordered amyloid-β peptides

Intrinsically disordered proteins (IDPs) represent a new frontier in structural biology since the primary characteristic of IDPs is that structures need to be characterized as diverse ensembles of conformational substates. We compare two general but very different ways of combining NMR spectroscopy with theoretical methods to derive structural ensembles for the disease IDPs amyloid-β 1-40 and amyloid-β 1-42, which are associated with Alzheimer's Disease. We analyze the performance of de novo molecular dynamics and knowledge-based approaches for generating structural ensembles by assessing their ability to reproduce a range of NMR experimental observables. In addition to the comparison of computational methods, we also evaluate the relative value of different types of NMR data for refining or validating the IDP structural ensembles for these important disease peptides.

A method of determining RNA conformational ensembles using structure-based calculations of residual dipolar couplings

We describe a method of determining the conformational fluctuations of RNA based on the incorporation of nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) as replica-averaged structural restraints in molecular dynamics simulations. In this approach, the alignment tensor required to calculate the RDCs corresponding to a given conformation is estimated from its shape, and multiple replicas of the RNA molecule are simulated simultaneously to reproduce in silico the ensemble-averaging procedure performed in the NMR measurements. We provide initial evidence that with this approach it is possible to determine accurately structural ensembles representing the conformational fluctuations of RNA by applying the reference ensemble test to the trans-activation response element of the human immunodeficiency virus type 1.

Application of the maximum entropy principle to determine ensembles of intrinsically disordered proteins from residual dipolar couplings

We present a method based on the maximum entropy principle that can re-weight an ensemble of protein structures based on data from residual dipolar couplings (RDCs).

Protein structure validation and refinement using amide proton chemical shifts derived from quantum mechanics

We present the ProCS method for the rapid and accurate prediction of protein backbone amide proton chemical shifts--sensitive probes of the geometry of key hydrogen bonds that determine protein structure. ProCS is parameterized against quantum mechanical (QM) calculations and reproduces high level QM results obtained for a small protein with an RMSD of 0.25 ppm (r = 0.94). ProCS is interfaced with the PHAISTOS protein simulation program and is used to infer statistical protein ensembles that reflect experimentally measured amide proton chemical shift values. Such chemical shift-based structural refinements, starting from high-resolution X-ray structures of Protein G, ubiquitin, and SMN Tudor Domain, result in average chemical shifts, hydrogen bond geometries, and trans-hydrogen bond ((h3)J(NC')) spin-spin coupling constants that are in excellent agreement with experiment. We show that the structural sensitivity of the QM-based amide proton chemical shift predictions is needed to obtain this agreement. The ProCS method thus offers a powerful new tool for refining the structures of hydrogen bonding networks to high accuracy with many potential applications such as protein flexibility in ligand binding.

Advances in the determination of nucleic acid conformational ensembles

Conformational changes in nucleic acids play a key role in the way genetic information is stored, transferred, and processed in living cells. Here, we describe new approaches that employ a broad range of experimental data, including NMR-derived chemical shifts and residual dipolar couplings, small-angle X-ray scattering, and computational approaches such as molecular dynamics simulations to determine ensembles of DNA and RNA at atomic resolution. We review the complementary information that can be obtained from diverse sets of data and the various methods that have been developed to combine these data with computational methods to construct ensembles and assess their uncertainty. We conclude by surveying RNA and DNA ensembles determined using these methods, highlighting the unique physical and functional insights obtained so far.

Ensemble-based interpretations of NMR structural data to describe protein internal dynamics

NMR spectroscopy is the leading technique to characterize protein internal dynamics at the atomic level and on multiple time scales. However, the structural interpretation of the observables obtained by various measurements is not always straightforward and in many cases dynamics-related parameters are only used to “decorate” static structural models without offering explicit description of conformational heterogeneity. To overcome such limitations, several computational techniques have been developed to generate ensemble-based representations of protein structure and dynamics with the use of NMR-derived data. An important common aspect of the methods is that NMR observables and derived parameters are interpreted as properties of the ensemble instead of individual conformers. The resulting ensembles reflect the experimentally determined internal mobility of proteins at a given time scale and can be used to understand the role of internal motions in biological processes at atomic detail. In this review we provide an overview of the calculation methods currently available and examples of biological insights obtained by the ensemble-based models of the proteins investigated.

Molecular dynamics simulations with replica-averaged structural restraints generate structural ensembles according to the maximum entropy principle

In order to characterise the dynamics of proteins, a well-established method is to incorporate experimental parameters as replica-averaged structural restraints into molecular dynamics simulations. Here, we justify this approach in the case of interproton distance information provided by nuclear Overhauser effects by showing that it generates ensembles of conformations according to the maximum entropy principle. These results indicate that the use of replica-averaged structural restraints in molecular dynamics simulations, given a force field and a set of experimental data, can provide an accurate approximation of the unknown Boltzmann distribution of a system.

On the statistical equivalence of restrained-ensemble simulations with the maximum entropy method

An issue of general interest in computer simulations is to incorporate information from experiments into a structural model. An important caveat in pursuing this goal is to avoid corrupting the resulting model with spurious and arbitrary biases. While the problem of biasing thermodynamic ensembles can be formulated rigorously using the maximum entropy method introduced by Jaynes, the approach can be cumbersome in practical applications with the need to determine multiple unknown coefficients iteratively. A popular alternative strategy to incorporate the information from experiments is to rely on restrained-ensemble molecular dynamics simulations. However, the fundamental validity of this computational strategy remains in question. Here, it is demonstrated that the statistical distribution produced by restrained-ensemble simulations is formally consistent with the maximum entropy method of Jaynes. This clarifies the underlying conditions under which restrained-ensemble simulations will yield results that are consistent with the maximum entropy method.