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

Cryo-electron Microscopy and Molecular Modeling Methods to Characterize the Dynamics of Tau Bound to Microtubules

The electron microscopy metainference integrative structural biology method enables the combination of cryo-electron microscopy electron density maps with molecular modeling techniques such as molecular dynamics to unveil the atomistic biomolecular structural ensemble and the error in the map data in an efficient manner. Here we illustrate the electron microscopy metainference protocol and analysis used to elucidate the atomistic structural ensemble of the microtubule-associated protein tau bound to microtubules by using state-of-the-art molecular mechanic force field and the electron density map.

Determination of the Structure and Dynamics of the Fuzzy Coat of an Amyloid Fibril of IAPP Using Cryo-Electron Microscopy

In recent years, major advances in cryo-electron microscopy (cryo-EM) have enabled the routine determination of complex biomolecular structures at atomistic resolution. An open challenge for this approach, however, concerns large systems that exhibit continuous dynamics. To address this problem, we developed the metadynamic electron microscopy metainference (MEMMI) method, which incorporates metadynamics, an enhanced conformational sampling approach, into the metainference method of integrative structural biology. MEMMI enables the simultaneous determination of the structure and dynamics of large heterogeneous systems by combining cryo-EM density maps with prior information through molecular dynamics, while at the same time modeling the different sources of error. To illustrate the method, we apply it to elucidate the dynamics of an amyloid fibril of the islet amyloid polypeptide (IAPP). The resulting conformational ensemble provides an accurate description of the structural variability of the disordered region of the amyloid fibril, known as fuzzy coat. The conformational ensemble also reveals that in nearly half of the structural core of this amyloid fibril, the side chains exhibit liquid-like dynamics despite the presence of the highly ordered network backbone of hydrogen bonds characteristic of the cross-β structure of amyloid fibrils.

Experiment-guided molecular simulations define a heterogeneous structural ensemble for the PTPN11 tandem SH2 domains

SHP2 plays an important role in regulating cellular processes, and its pathogenic mutations cause developmental disorders and are linked to cancer. SHP2 is a multidomain protein, comprising two SH2 domains arranged in tandem, a catalytic PTP domain, and a disordered C-terminal tail. SHP2 is activated upon binding two linked phosphopeptides to its SH2 domains, and the peptide orientation and spacing between binding sites are critical for enzymatic activation. For decades, the tandem SH2 has been extensively studied to identify the relative orientation of the two SH2 domains that most effectively binds effectors. So far, neither crystallography nor experiments in solution have provided conclusive results. Using experiment-guided molecular simulations, we determine the heterogeneous structural ensemble of the tandem SH2 in solution in agreement with experimental data from small-angle X-ray scattering and NMR residual dipolar couplings. In the solution ensemble, N-SH2 adopts different orientations and positions relative to C-SH2. We suggest that the intrinsic structural plasticity of the tandem SH2 allows SHP2 to respond to external stimuli and is essential for its functional activity.

NMR-Based Configurational Assignments of Natural Products: How Floating Chirality Distance Geometry Calculations Simplify Gambling with 2N-1 Diastereomers

Using NMR data, the assignment of the correct 3D configuration and conformation to unknown natural products is of pivotal importance in pharmaceutical and medicinal chemistry. In this report, we quantify the probability of configurational assignments to judge the quality of structural elucidations using Bayesian inference in combination with floating-chirality distance geometry simulations. Based on reference-free NOE/ROE data, residual dipolar couplings (RDCs), and residual quadrupolar couplings (RQCs) in various combinations, we demonstrate how the relative configurations of three natural compounds, namely, jatrohemiketal (1), artemisinin (2), and Taxol (3), can be unambiguously established without the necessity to carry out time-consuming DFT-based configurational and conformational analyses. Our results quantitatively describe how reliably molecular geometries can be inferred from experimental NMR data, thereby unequivocally unveiling remaining assignment ambiguities. The methodology presented here will dramatically reduce the risk of incorrect structural assignments based on the overinterpretation of incomplete data and DFT-based structure models in chemistry.

Common sequence motifs of nascent chains engage the ribosome surface and trigger factor

Proteins are produced by ribosomes in the cell, and during this process, can begin to adopt their biologically active forms assisted by molecular chaperones such as trigger factor. This fundamental cellular mechanism is crucial to maintaining a functional proteome and avoiding deleterious misfolding. Here, we study how disordered nascent chains emerge from the ribosome exit tunnel, and find that interactions with the ribosome surface dominate their dynamics in vitro and in vivo. Moreover, we show that the types of amino acids that mediate such interactions are also those that recruit trigger factor. This lays the foundation to describe how nascent chains are handed over from the ribosome surface to chaperones during biosynthesis within the crowded cytosol.

In the cell, the conformations of nascent polypeptide chains during translation are modulated by both the ribosome and its associated molecular chaperone, trigger factor. The specific interactions that underlie these modulations, however, are still not known in detail. Here, we combine protein engineering, in-cell and in vitro NMR spectroscopy, and molecular dynamics simulations to explore how proteins interact with the ribosome during their biosynthesis before folding occurs. Our observations of α-synuclein nascent chains in living Escherichia coli cells reveal that ribosome surface interactions dictate the dynamics of emerging disordered polypeptides in the crowded cytosol. We show that specific basic and aromatic motifs drive such interactions and directly compete with trigger factor binding while biasing the direction of the nascent chain during its exit out of the tunnel. These results reveal a structural basis for the functional role of the ribosome as a scaffold with holdase characteristics and explain how handover of the nascent chain to specific auxiliary proteins occurs among a host of other factors in the cytosol.

NMR-Based Configurational Assignments of Natural Products: Gibbs Sampling and Bayesian Inference Using Floating Chirality Distance Geometry Calculations

Floating chirality restrained distance geometry (fc-rDG) calculations are used to directly evolve structures from NMR data such as NOE-derived intramolecular distances or anisotropic residual dipolar couplings (RDCs). In contrast to evaluating pre-calculated structures against NMR restraints, multiple configurations (diastereomers) and conformations are generated automatically within the experimental limits. In this report, we show that the "unphysical" rDG pseudo energies defined from NMR violations bear statistical significance, which allows assigning probabilities to configurational assignments made that are fully compatible with the method of Bayesian inference. These "diastereomeric differentiabilities" then even become almost independent of the actual values of the force constants used to model the restraints originating from NOE or RDC data.

An Integrative Approach to Determine 3D Protein Structures Using Sparse Paramagnetic NMR Data and Physical Modeling

Paramagnetic nuclear magnetic resonance (NMR) methods have emerged as powerful tools for structure determination of large, sparsely protonated proteins. However traditional applications face several challenges, including a need for large datasets to offset the sparsity of restraints, the difficulty in accounting for the conformational heterogeneity of the spin-label, and noisy experimental data. Here we propose an integrative approach to structure determination combining sparse paramagnetic NMR with physical modelling to infer approximate protein structural ensembles. We use calmodulin in complex with the smooth muscle myosin light chain kinase peptide as a model system. Despite acquiring data from samples labeled only at the backbone amide positions, we are able to produce an ensemble with an average RMSD of ∼2.8 Å from a reference X-ray crystal structure. Our approach requires only backbone chemical shifts and measurements of the paramagnetic relaxation enhancement and residual dipolar couplings that can be obtained from sparsely labeled samples.

DEER-PREdict: Software for efficient calculation of spin-labeling EPR and NMR data from conformational ensembles

Owing to their plasticity, intrinsically disordered and multidomain proteins require descriptions based on multiple conformations, thus calling for techniques and analysis tools that are capable of dealing with conformational ensembles rather than a single protein structure. Here, we introduce DEER-PREdict, a software program to predict Double Electron-Electron Resonance distance distributions as well as Paramagnetic Relaxation Enhancement rates from ensembles of protein conformations. DEER-PREdict uses an established rotamer library approach to describe the paramagnetic probes which are bound covalently to the protein.DEER-PREdict has been designed to operate efficiently on large conformational ensembles, such as those generated by molecular dynamics simulation, to facilitate the validation or refinement of molecular models as well as the interpretation of experimental data. The performance and accuracy of the software is demonstrated with experimentally characterized protein systems: HIV-1 protease, T4 Lysozyme and Acyl-CoA-binding protein. DEER-PREdict is open source (GPLv3) and available at github.com/KULL-Centre/DEERpredict and as a Python PyPI package pypi.org/project/DEERPREdict.

Multi-state recognition pathway of the intrinsically disordered protein kinase inhibitor by protein kinase A

In the nucleus, the spatiotemporal regulation of the catalytic subunit of cAMP-dependent protein kinase A (PKA-C) is orchestrated by an intrinsically disordered protein kinase inhibitor, PKI, which recruits the CRM1/RanGTP nuclear exporting complex. How the PKA-C/PKI complex assembles and recognizes CRM1/RanGTP is not well understood. Using NMR, SAXS, fluorescence, metadynamics, and Markov model analysis, we determined the multi-state recognition pathway for PKI. After a fast binding step in which PKA-C selects PKI's most competent conformations, PKI folds upon binding through a slow conformational rearrangement within the enzyme's binding pocket. The high-affinity and pseudo-substrate regions of PKI become more structured and the transient interactions with the kinase augment the helical content of the nuclear export sequence, which is then poised to recruit the CRM1/RanGTP complex for nuclear translocation. The multistate binding mechanism featured by PKA-C/PKI complex represents a paradigm on how disordered, ancillary proteins (or protein domains) are able to operate multiple functions such as inhibiting the kinase while recruiting other regulatory proteins for nuclear export.

A Practical Guide to the Simultaneous Determination of Protein Structure and Dynamics Using Metainference

Accurate protein structural ensembles can be determined with metainference, a Bayesian inference method that integrates experimental information with prior knowledge of the system and deals with all sources of uncertainty and errors as well as with system heterogeneity. Furthermore, metainference can be implemented using the metadynamics approach, which enables the computational study of complex biological systems requiring extensive conformational sampling. In this chapter, we provide a step-by-step guide to perform and analyse metadynamic metainference simulations using the ISDB module of the open-source PLUMED library, as well as a series of practical tips to avoid common mistakes. Specifically, we will guide the reader in the process of learning how to model the structural ensemble of a small disordered peptide by combining state-of-the-art molecular mechanics force fields with nuclear magnetic resonance data, including chemical shifts, scalar couplings and residual dipolar couplings.

Conformational Investigations in Flexible Molecules Using Orientational NMR Constraints in Combination with 3J-Couplings and NOE Distances

The downscaling of NMR tensorial interactions, such as dipolar couplings, from tens of kilohertz to a few hertz in low-order media is the result of dynamics spanning several orders of magnitudes, including vibrational modes (~ns-fs), whole-molecule reorientation (~ns) and higher barrier internal conformational exchange (<ms). In this work, we propose to employ these dynamically averaged interactions to drive an “alignment-tensor-free” molecular dynamic simulation with orientation constraints (MDOC) in order to efficiently access the conformational space sampled by flexible small molecules such as natural products. Key to this approach is the application of tensorial pseudo-force restraints which simultaneously guide the overall reorientation and conformational fluctuations based on defined memory function over the running trajectory. With the molecular mechanics force-field, which includes bond polarization theory (BPT), and complemented with other available NMR parameters such as NOEs and scalar J-couplings, MDOC efficiently arrives at dynamic ensembles that reproduce the entire NMR dataset with exquisite accuracy and theoretically reveal the systems conformational space and equilibrium. The method as well as its potential towards configurational elucidation is presented on diastereomeric pairs of flexible molecules: a small 1,4-diketone 1 with a single rotatable bond as well as a 24-ring macrolide related to the natural product mandelalide A 2.

Configuration determination by residual dipolar couplings: accessing the full conformational space by molecular dynamics with tensorial constraints

Residual dipolar couplings (RDCs) and other residual anisotropic NMR parameters provide valuable structural information of high quality and quantity, bringing detailed structural models of flexible molecules in solution in reach. The corresponding data interpretation so far is directly or indirectly based on the concept of a molecular alignment tensor, which, however, is ill-defined for flexible molecules. The concept is typically applied to a single or a small set of lowest energy structures, ignoring the effect of vibrational averaging. Here, we introduce an entirely different approach based on time averaged molecular dynamics with dipolar couplings as tensorial orientational restraints that can be used to solve structural problems in molecules of any size without the need of introducing an explicit molecular alignment tensor into the computation. RDC restraints are represented by their full 3D interaction tensor in the laboratory frame, for which pseudo forces are calculated using a secular dipolar Hamiltonian as the target. The resulting rotational averaging of each individual tensorial restraint leads to structural ensembles that best fulfil the experimental data. Using one-bond RDCs, the approach has been implemented in the force field procedures of the program COSMOS and extensively tested. A concise theoretical introduction, including the special treatment of force fields for stable and fast MD simulations, as well as applications regarding configurational analyses of small to medium-sized organic molecules with different degrees of flexibility, is given. The observed results are discussed in detail.

Molecular Dynamics with Orientational Tensorial Constraints: A New Approach to Probe the Torsional Angle Distributions of Small Rotationally Flexible Molecules

The potential of residual dipolar couplings (RDCs) in conformational studies of small molecules is now widely recognized, but current theoretical approaches for their interpretation have several limitations and there is still the need for a general method to probe the torsional angle distributions applicable to any rotationally flexible molecule. Molecular dynamics simulations with RDC-based orientational tensorial constraints (MDOC), implemented in the software COSMOS, are presented here as a conceptually new strategy. For the cases of the fluorinated anti-inflammatory drug diflunisal and the disaccharide cellobiose, we demonstrate that MDOC simulations with one-bond RDCs as tensorial constraints unveil torsion distributions and allow the determination of relative configuration in the presence of rotational flexibility. The independence of the initial structure or any a priori assumption as well as the possibility to combine different experimental constraints represent features, which make the COSMOS software a promising tool for the investigation of torsional angle distributions of flexible molecules, regardless of their size and degree of freedom.

Probing the dynamic stalk region of the ribosome using solution NMR

We describe an NMR approach based on the measurement of residual dipolar couplings (RDCs) to probe the structural and motional properties of the dynamic regions of the ribosome. Alignment of intact 70S ribosomes in filamentous bacteriophage enabled measurement of RDCs in the mobile C-terminal domain (CTD) of the stalk protein bL12. A structural refinement of this domain using the observed RDCs did not show large changes relative to the isolated protein in the absence of the ribosome, and we also found that alignment of the CTD was almost independent of the presence of the core ribosome particle, indicating that the inter-domain linker has significant flexibility. The nature of this linker was subsequently probed in more detail using a paramagnetic alignment strategy, which revealed partial propagation of alignment between neighbouring domains, providing direct experimental validation of a structural ensemble previously derived from SAXS and NMR relaxation measurements. Our results demonstrate the prospect of better characterising dynamical and functional regions of more challenging macromolecular machines and systems, for example ribosome–nascent chain complexes.

Conjugation of NMR and SAXS for flexible and multidomain protein structure determination: From sample preparation to model refinement

Experimental information from small angle X-ray scattering (SAXS) is conjugated with nuclear magnetic resonance (NMR) spectroscopy data for the improvement of protein structure determination, particularly for flexible, multidomain or intrinsically disordered proteins. Individually, each of these techniques presents capabilities and limitations: NMR excels in local information, providing atomic resolution, but is limited by protein size, whereas SAXS yields a global envelope of the protein with lower resolution, but revealing domain positions. Different conjugation methodologies use the complementarity of both techniques' independent constraints to achieve comprehensive protein structure determination and resolve dynamics at a moderate computational expense.

The free energy landscape of the oncogene protein E7 of human papillomavirus type 16 reveals a complex interplay between ordered and disordered regions

When present, structural disorder makes it very challenging to characterise the conformational properties of proteins. This is particularly the case of proteins, such as the oncogene protein E7 of human papillomavirus type 16, which contain both ordered and disordered domains, and that can populate monomeric and oligomeric states under physiological conditions. Nuclear magnetic resonance (NMR) spectroscopy is emerging as a powerful method to study these complex systems, most notably in combination with molecular dynamics simulations. Here we use NMR chemical shifts and residual dipolar couplings as structural restraints in replica-averaged molecular dynamics simulations to determine the free energy landscape of E7. This landscape reveals a complex interplay between a folded but highly dynamical C-terminal domain and a disordered N-terminal domain that forms transient secondary and tertiary structures, as well as an equilibrium between a high-populated (98%) dimeric state and a low-populated (2%) monomeric state. These results provide compelling evidence of the complex conformational heterogeneity associated with the behaviour and interactions of this disordered protein associated with disease.

Characterization of intrinsically disordered proteins and their dynamic complexes: From in vitro to cell-like environments

Over the last two decades, it has become increasingly clear that a large fraction of the human proteome is intrinsically disordered or contains disordered segments of significant length. These intrinsically disordered proteins (IDPs) play important regulatory roles throughout biology, underlining the importance of understanding their conformational behavior and interaction mechanisms at the molecular level. Here we review recent progress in the NMR characterization of the structure and dynamics of IDPs in various functional states and environments. We describe the complementarity of different NMR parameters for quantifying the conformational propensities of IDPs in their isolated and phosphorylated states, and we discuss the challenges associated with obtaining structural models of dynamic protein-protein complexes involving IDPs. In addition, we review recent progress in understanding the conformational behavior of IDPs in cell-like environments such as in the presence of crowding agents, in membrane-less organelles and in the complex environment of the human cell.

The Antibody Light-Chain Linker Regulates Domain Orientation and Amyloidogenicity

The antibody light chain (LC) consists of two domains and is essential for antigen binding in mature immunoglobulins. The two domains are connected by a highly conserved linker that comprises the structurally important Arg108 residue. In antibody light chain (AL) amyloidosis, a severe protein amyloid disease, the LC and its N-terminal variable domain (V_L) convert to fibrils deposited in the tissues causing organ failure. Understanding the factors shaping the architecture of the LC is important for basic science, biotechnology and for deciphering the principles that lead to fibril formation. In this study, we examined the structure and properties of LC variants with a mutated or extended linker. We show that under destabilizing conditions, the linker modulates the amyloidogenicity of the LC. The fibril formation propensity of LC linker variants and their susceptibility to proteolysis directly correlate implying an interplay between the two LC domains. Using NMR and residual dipolar coupling-based simulations, we found that the linker residue Arg108 is a key factor regulating the relative orientation of the V_L and C_L domains, keeping them in a bent and dense, but still flexible conformation. Thus, inter-domain contacts and the relative orientation of V_L and C_L to each other are of major importance for maintaining the structural integrity of the full-length LC.

Treating Biomacromolecular Conformational Variability

The function of a biomacromolecule is related not only to its structure but also to the different conformations that its structural elements can sample. It is therefore important to determine the extent of the structural fluctuations and to identify the states that are actually populated as a result of the rearrangement. However, this accomplishment is undermined by an intrinsic limitation: the amount of experimental data is by and large inferior to the number of the states that a biomacromolecule can actually sample. This means that additional, a priori information must be applied in order to derive the most from the available experimental data but not to run into overinterpretation. In this chapter we will give a summary of the experimental observables that can be used towards the reconstruction of structural ensembles, how the data can be profitably combined and to what extent the data are affected by error; finally we will give an overview of the computational methods that have been developed to model structural ensembles, highlighting their difference and similarities, advantages and disadvantages.

Determination of the conformational states of strychnine in solution using NMR residual dipolar couplings in a tensor-free approach

Small molecules with rotatable bonds can occupy different conformational states in solution as a consequence of their thermal fluctuations. The accurate determination of the structures of such states, as well as of their statistical weights, has been challenging because of the technical difficulties in extracting information from experimental measurements, which are normally averaged over the conformational space available. Here, to achieve this objective, we present an approach based on a recently proposed tensor-free method for incorporating NMR residual dipolar couplings as structural restraints in replica-averaged molecular dynamics simulations. This approach enables the information provided by the experimental data to be used in the spirit of the maximum entropy principle to determine the structural ensembles of small molecules. Furthermore, in order to enhance the sampling of the conformational space we incorporated the metadynamics method in the simulations. We illustrate the method in the case of strychnine, determining the three major conformational states of this small molecule and their associated occupation probabilities.

Structural basis for terminal loop recognition and stimulation of pri-miRNA-18a processing by hnRNP A1

Post-transcriptional mechanisms play a predominant role in the control of microRNA (miRNA) production. Recognition of the terminal loop of precursor miRNAs by RNA-binding proteins (RBPs) influences their processing; however, the mechanistic basis for how levels of individual or subsets of miRNAs are regulated is mostly unexplored. We previously showed that hnRNP A1, an RBP implicated in many aspects of RNA processing, acts as an auxiliary factor that promotes the Microprocessor-mediated processing of pri-mir-18a. Here, by using an integrative structural biology approach, we show that hnRNP A1 forms a 1:1 complex with pri-mir-18a where both RNA recognition motifs (RRMs) bind to cognate RNA sequence motifs in the terminal loop of pri-mir-18a. Terminal loop binding induces an allosteric destabilization of base-pairing in the pri-mir-18a stem that promotes its downstream processing. Our results highlight terminal loop RNA recognition by RBPs as a potential general principle of miRNA biogenesis and regulation.

hnRNP A1 is an auxiliary factor that promotes the Microprocessor-mediated processing of pri-mir-18a, of the oncomiR-1 cluster. Here the authors employ an integrative structural biology approach and provide insights into the molecular mechanism of how hnRNP A1 facilitates pri-mir-18a biogenesis.

Metadynamic metainference: Convergence towards force field independent structural ensembles of a disordered peptide

Metadynamic metainference has been recently introduced as a theoretical framework to determine structural ensembles by combining and weighting their noise multiple sources of experimental data with molecular mechanics force fields and metadynamics simulations. Here we build upon these initial developments to further extend and streamline the computational approach. We also show that metadynamic metainference can actually determine a structural ensemble for a disordered peptide that is essentially independent from the employed force field. We further show that it is possible to use a very computationally efficient implicit solvent force field in the place of very expensive state-of-the-art explicit solvent ones without a significant loss in accuracy.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Xplor-NIH for molecular structure determination from NMR and other data sources

Xplor-NIH is a popular software package for biomolecular structure determination from nuclear magnetic resonance (NMR) and other data sources. Here, some of Xplor-NIH's most useful data-associated energy terms are reviewed, including newer alternative options for using residual dipolar coupling data in structure calculations. Further, we discuss new developments in the implementation of strict symmetry for the calculation of symmetric homo-oligomers, and in the representation of the system as an ensemble of structures to account for motional effects. Finally, the different available force fields are presented, among other Xplor-NIH capabilities.

Methods of probing the interactions between small molecules and disordered proteins

It is generally recognized that a large fraction of the human proteome is made up of proteins that remain disordered in their native states. Despite the fact that such proteins play key biological roles and are involved in many major human diseases, they still represent challenging targets for drug discovery. A major bottleneck for the identification of compounds capable of interacting with these proteins and modulating their disease-promoting behaviour is the development of effective techniques to probe such interactions. The difficulties in carrying out binding measurements have resulted in a poor understanding of the mechanisms underlying these interactions. In order to facilitate further methodological advances, here we review the most commonly used techniques to probe three types of interactions involving small molecules: (1) those that disrupt functional interactions between disordered proteins; (2) those that inhibit the aberrant aggregation of disordered proteins, and (3) those that lead to binding disordered proteins in their monomeric states. In discussing these techniques, we also point out directions for future developments.

Perspectives on paramagnetic NMR from a life sciences infrastructure

The effects arising in NMR spectroscopy because of the presence of unpaired electrons, collectively referred to as "paramagnetic NMR" have attracted increasing attention over the last decades. From the standpoint of the structural and mechanistic biology, paramagnetic NMR provides long range restraints that can be used to assess the accuracy of crystal structures in solution and to improve them by simultaneous refinements through NMR and X-ray data. These restraints also provide information on structure rearrangements and conformational variability in biomolecular systems. Theoretical improvements in quantum chemistry calculations can nowadays allow for accurate calculations of the paramagnetic data from a molecular structural model, thus providing a tool to refine the metal coordination environment by matching the paramagnetic effects observed far away from the metal. Furthermore, the availability of an improved technology (higher fields and faster magic angle spinning) has promoted paramagnetic NMR applications in the fast-growing area of biomolecular solid-state NMR. Major improvements in dynamic nuclear polarization have been recently achieved, especially through the exploitation of the Overhauser effect occurring through the contact-driven relaxation mechanism: the very large enhancement of the ¹³C signal observed in a variety of liquid organic compounds at high fields is expected to open up new perspectives for applications of solution NMR.

Dynamic Descriptions of Highly Flexible Molecules from NMR Dipolar Couplings: Physical Basis and Limitations

Biomolecules that control physiological function by changing their conformation play key roles in biology and remain poorly characterized. NMR dipolar couplings (DCs) depend intrinsically on both molecular shape and structural fluctuations, thereby providing the enticing prospect of tracking these conformational changes at atomic detail. Although this dual dependence has until now severely complicated analysis of DCs from highly dynamic systems, general approaches have recently been proposed that simplify interpretation of experimental DCs, by entirely eliminating molecular alignment from the analysis. Using simple and intuitive simulation of target ensembles, we investigate the impact of such approaches on the resulting descriptions of the conformational energy landscape. We find that ensemble descriptions of highly flexible systems derived from DCs without explicit consideration of the alignment properties of the constituent conformations can be compromised and inaccurate, despite exhibiting high correlation with experimental measurement.

Simultaneous NMR characterisation of multiple minima in the free energy landscape of an RNA UUCG tetraloop

RNA molecules in solution tend to undergo structural fluctuations of relatively large amplitude and to populate a range of different conformations some of which with low populations. It is still very challenging, however, to characterise the structures of these low populated states and to understand their functional roles. In the present study, we address this problem by using NMR residual dipolar couplings (RDCs) as structural restraints in replica-averaged metadynamics (RAM) simulations. By applying this approach to a 14-mer RNA hairpin containing the prototypical UUCG tetraloop motif, we show that it is possible to construct the free energy landscape of this RNA molecule. This free energy landscapes reveals the surprisingly rich dynamics of the UUCG tetraloop and identifies the multiple substates that exist in equilibrium owing to thermal fluctuations. The approach that we present is general and can be applied to the study of the free energy landscapes of other RNA or RNA-protein systems.

A critical assessment of methods to recover information from averaged data

Conformational heterogeneity is key to the function of many biomacromolecules, but only a few groups have tried to characterize it until recently. Now, thanks to the increased throughput of experimental data and the increased computational power, the problem of the characterization of protein structural variability has become more and more popular. Several groups have devoted their efforts in trying to create quantitative, reliable and accurate protocols for extracting such information from averaged data. We analyze here different approaches, discussing strengths and weaknesses of each. All approaches can roughly be clustered into two groups: those satisfying the maximum entropy principle and those recovering ensembles composed of a restricted number of molecular conformations. In the first case, the solution focuses on the features that are common to all the infinite solutions satisfying the experimental data; in the second case, the reconstructed ensemble shows the conformational regions where a large probability can be placed. The upper limits for conformational probabilities (MaxOcc) can also be calculated. We also give an overview of the mainstream experimental observables, with considerations on the assumptions underlying their usage.

Structure of a low-population binding intermediate in protein-RNA recognition

The interaction of the HIV-1 protein transactivator of transcription (Tat) and its cognate transactivation response element (TAR) RNA transactivates viral transcription and represents a paradigm for the widespread occurrence of conformational rearrangements in protein-RNA recognition. Although the structures of free and bound forms of TAR are well characterized, the conformations of the intermediates in the binding process are still unknown. By determining the free energy landscape of the complex using NMR residual dipolar couplings in replica-averaged metadynamics simulations, we observe two low-population intermediates. We then rationally design two mutants, one in the protein and another in the RNA, that weaken specific nonnative interactions that stabilize one of the intermediates. By using surface plasmon resonance, we show that these mutations lower the release rate of Tat, as predicted. These results identify the structure of an intermediate for RNA-protein binding and illustrate a general strategy to achieve this goal with high resolution.

Hybrid Approaches to Structural Characterization of Conformational Ensembles of Complex Macromolecular Systems Combining NMR Residual Dipolar Couplings and Solution X-ray Scattering

Solving structures or structural ensembles of large macromolecular systems in solution poses a challenging problem. While NMR provides structural information at atomic resolution, increased spectral complexity, chemical shift overlap, and short transverse relaxation times (associated with slow tumbling) render application of the usual techniques that have been so successful for medium sized systems (<50 kDa) difficult. Solution X-ray scattering, on the other hand, is not limited by molecular weight but only provides low resolution structural information related to the overall shape and size of the system under investigation. Here we review how combining atomic resolution structures of smaller domains with sparse experimental data afforded by NMR residual dipolar couplings (which yield both orientational and shape information) and solution X-ray scattering data in rigid-body simulated annealing calculations provides a powerful approach for investigating the structural aspects of conformational dynamics in large multidomain proteins. The application of this hybrid methodology is illustrated for the 128 kDa dimer of bacterial Enzyme I which exists in a variety of open and closed states that are sampled at various points in the catalytic cycles, and for the capsid protein of the human immunodeficiency virus.

How to tackle protein structural data from solution and solid state: An integrated approach

Long-range NMR restraints, such as diamagnetic residual dipolar couplings and paramagnetic data, can be used to determine 3D structures of macromolecules. They are also used to monitor, and potentially to improve, the accuracy of a macromolecular structure in solution by validating or "correcting" a crystal model. Since crystal structures suffer from crystal packing forces they may not be accurate models for the macromolecular structures in solution. However, the presence of real differences should be tested for by simultaneous refinement of the structure using both crystal and solution NMR data. To achieve this, the program REFMAC5 from CCP4 was modified to allow the simultaneous use of X-ray crystallographic and paramagnetic NMR data and/or diamagnetic residual dipolar couplings. Inconsistencies between crystal structures and solution NMR data, if any, may be due either to structural rearrangements occurring on passing from the solution to solid state, or to a greater degree of conformational heterogeneity in solution with respect to the crystal. In the case of multidomain proteins, paramagnetic restraints can provide the correct mutual orientations and positions of domains in solution, as well as information on the conformational variability experienced by the macromolecule.

Investigating protein conformational energy landscapes and atomic resolution dynamics from NMR dipolar couplings: a review

Nuclear magnetic resonance spectroscopy is exquisitely sensitive to protein dynamics. In particular inter-nuclear dipolar couplings, that become measurable in solution when the protein is dissolved in a dilute liquid crystalline solution, report on all conformations sampled up to millisecond timescales. As such they provide the opportunity to describe the Boltzmann distribution present in solution at atomic resolution, and thereby to map the conformational energy landscape in unprecedented detail. The development of analytical methods and approaches based on numerical simulation and their application to numerous biologically important systems is presented.

Information content of long-range NMR data for the characterization of conformational heterogeneity

Long-range NMR data, namely residual dipolar couplings (RDCs) from external alignment and paramagnetic data, are becoming increasingly popular for the characterization of conformational heterogeneity of multidomain biomacromolecules and protein complexes. The question addressed here is how much information is contained in these averaged data. We have analyzed and compared the information content of conformationally averaged RDCs caused by steric alignment and of both RDCs and pseudocontact shifts caused by paramagnetic alignment, and found that, despite the substantial differences, they contain a similar amount of information. Furthermore, using several synthetic tests we find that both sets of data are equally good towards recovering the major state(s) in conformational distributions.

Molecular Dynamics of Biomolecules through Direct Analysis of Dipolar Couplings

Residual dipolar couplings (RDCs) are important probes in structural biology, but their analysis is often complicated by the determination of an alignment tensor or its associated assumptions. We here apply the maximum entropy principle to derive a tensor-free formalism which allows for direct, dynamic analysis of RDCs and holds the classic tensor formalism as a special case. Specifically, the framework enables us to robustly analyze data regardless of whether a clear separation of internal and overall dynamics is possible. Such a separation is often difficult in the core subjects of current structural biology, which include multidomain and intrinsically disordered proteins as well as nucleic acids. We demonstrate the method is tractable and self-consistent and generalizes to data sets comprised of observations from multiple different alignment conditions.