Macromolecular NMR spectroscopy for the non-spectroscopist

NMR spectroscopy is a powerful tool for studying the structure, function and dynamics of biological macromolecules. However, non-spectroscopists often find NMR theory daunting and data interpretation nontrivial. As the first of two back-to-back reviews on NMR spectroscopy aimed at non-spectroscopists, the present review first provides an introduction to the basics of macromolecular NMR spectroscopy, including a discussion of typical sample requirements and what information can be obtained from simple NMR experiments. We then review the use of NMR spectroscopy for determining the 3D structures of macromolecules and examine how to judge the quality of NMR-derived structures.     

Macromolecular NMR spectroscopy for the non-spectroscopist: beyond macromolecular solution structure determination

A strength of NMR spectroscopy is its ability to monitor, on an atomic level, molecular changes and interactions. In this review, which is intended for non-spectroscopist, we describe major uses of NMR in protein science beyond solution structure determination. After first touching on how NMR can be used to quickly determine whether a mutation induces structural perturbations in a protein, we describe the unparalleled ability of NMR to monitor binding interactions over a wide range of affinities, molecular masses and solution conditions. We discuss the use of NMR to measure the dynamics of proteins at the atomic level and over a wide range of timescales. Finally, we outline new and expanding areas such as macromolecular structure determination in multicomponent systems, as well as in the solid state and in vivo.     

Macromolecular crowding in biological systems: hydrodynamics and NMR methods

Most biologically relevant environments involve highly concentrated macromolecular solutions and most biological processes involve macromolecules that diffuse and interact with other macromolecules. Macromolecular crowding is a general phenomenon that strongly affects the transport properties of macromolecules (rotational and translational diffusion) as well as the position of their equilibria. NMR methods can provide information on molecular interactions, as well as on translational and rotational diffusion. In fact, rotational diffusion, through its determinant role in NMR relaxation, places a practical limit on the systems that can be studied by NMR. While in dilute solutions of non-aggregating macromolecules this limit is set by macromolecular size, in crowded solutions excluded volume effects can have a strong effect on the observed diffusion rates. Hydrodynamic theory offers some insight into the magnitude of crowding effects on NMR observable parameters.     

Structure-based protein NMR assignments using native structural ensembles

An important step in NMR protein structure determination is the assignment of resonances and NOEs to corresponding nuclei. Structure-based assignment (SBA) uses a model structure ("template") for the target protein to expedite this process. Nuclear vector replacement (NVR) is an SBA framework that combines multiple sources of NMR data (chemical shifts, RDCs, sparse NOEs, amide exchange rates, TOCSY) and has high accuracy when the template is close to the target protein's structure (less than 2 A backbone RMSD). However, a close template may not always be available. We extend the circle of convergence of NVR for distant templates by using an ensemble of structures. This ensemble corresponds to the low-frequency perturbations of the given template and is obtained using normal mode analysis (NMA). Our algorithm assigns resonances and sparse NOEs using each of the structures in the ensemble separately, and aggregates the results using a voting scheme based on maximum bipartite matching. Experimental results on human ubiquitin, using four distant template structures show an increase in the assignment accuracy. Our algorithm also improves the robustness of NVR with respect to structural noise. We provide a confidence measure for each assignment using the percentage of the structures that agree on that assignment. We use this measure to assign a subset of the peaks with even higher accuracy. We further validate our algorithm on data for two additional proteins with NVR. We then show the general applicability of our approach by applying our NMA ensemble-based voting scheme to another SBA tool, MARS. For three test proteins with corresponding templates, including the 370-residue maltose binding protein, we increase the number of reliable assignments made by MARS. Finally, we show that our voting scheme is sound and optimal, by proving that it is a maximum likelihood estimator of the correct assignments.     

Characterizing RNA ensembles from NMR data with kinematic models

Functional mechanisms of biomolecules often manifest themselves precisely in transient conformational substates. Researchers have long sought to structurally characterize dynamic processes in non-coding RNA, combining experimental data with computer algorithms. However, adequate exploration of conformational space for these highly dynamic molecules, starting from static crystal structures, remains challenging. Here, we report a new conformational sampling procedure, KGSrna, which can efficiently probe the native ensemble of RNA molecules in solution. We found that KGSrna ensembles accurately represent the conformational landscapes of 3D RNA encoded by NMR proton chemical shifts. KGSrna resolves motionally averaged NMR data into structural contributions; when coupled with residual dipolar coupling data, a KGSrna ensemble revealed a previously uncharacterized transient excited state of the HIV-1 trans-activation response element stem–loop. Ensemble-based interpretations of averaged data can aid in formulating and testing dynamic, motion-based hypotheses of functional mechanisms in RNAs with broad implications for RNA engineering and therapeutic intervention.     

Reweighted atomic densities to represent ensembles of NMR structures

A reweighted atomic probability density is introduced as a means of representing ensembles of NMR structures in a simple, concise and informative manner. This density is shown to give a better visual representation of molecular structure information than an unweighted density, and should provide a useful interactive graphics tool during the course of iterative NMR structure refinement. The approach is illustrated using several examples.     

Principal components analysis of protein structure ensembles calculated using NMR data

One important problem when calculating structures of biomolecules from NMR data is distinguishing converged structures from outlier structures. This paper describes how Principal Components Analysis (PCA) has the potential to classify calculated structures automatically, according to correlated structural variation across the population. PCA analysis has the additional advantage that it highlights regions of proteins which are varying across the population. To apply PCA, protein structures have to be reduced in complexity and this paper describes two different representations of protein structures which achieve this. The calculated structures of a 28 amino acid peptide are used to demonstrate the methods. The two different representations of protein structure are shown to give equivalent results, and correct results are obtained even though the ensemble of structures used as an example contains two different protein conformations. The PCA analysis also correctly identifies the structural differences between the two conformations.     

Characterization of conformational and dynamic properties of natively unfolded human and mouse alpha-synuclein ensembles by NMR: implication for aggregation

Conversion of human α-synuclein (aS) from the free soluble state to the insoluble fibrillar state has been implicated in the etiology of Parkinson's disease. Human aS is highly homologous in amino acid sequence to mouse aS, which contains seven substitutions including the A53T that has been linked to familial Parkinson's disease, and including five substitutions in the C-terminal region. It has been shown that the rate of fibrillation is highly dependent on the exact sequence of the protein, and mouse aS is reported to aggregate more rapidly than human aS in vitro. Nuclear magnetic resonance experiments of mouse and human aS at supercooled temperatures (263 K) are used to understand the effect of sequence on conformational fluctuations in the disordered ensembles and to relate these to differences in propensities to aggregate. We show that both aS are natively unfolded at low temperature with different propensities to secondary structure, backbone dynamics and long-range contacts across the protein. Mouse aS exhibits a higher propensity to helical conformation around the C-terminal substitutions as well as the loss of transient long-range contacts from the C- to the N-terminal end and hydrophobic central regions of the protein relative to human aS. Lack of back-folding from the C-terminal end of mouse aS exposes the N-terminal region, which is shown, by ¹⁵N relaxation experiments, to be very restricted in mobility relative to human aS. We propose that the restricted mobility in the N-terminal region may arise from transient interchain interactions, suggesting that the N-terminal KTK(E/Q)GV repeats may serve as initiation sites for aggregation in mouse aS. These transient interchain interactions coupled with a non-Aβ amyloid component (NAC) region that is both more exposed and has a higher propensity to β structure may accelerate the rate of fibril formation of aS.     

Wavelet transform analysis of NMR structure ensembles to reveal internal fluctuations of enzymes

Internal motions and flexibility are essential for biological functions in proteins. To assess the internal fluctuations and conformational flexibility of proteins, reliable computational methods are needed. In this study, wavelet transformation was used to filter out the noise and facilitate investigating the internal positional fluctuations of enzymes within nuclear magnetic resonance (NMR) structure ensembles. Moreover, potential active sites were identified by combining with positional fluctuation score, sequence conservation, and solvent accessible surface area. Among the total 107 catalytic residues in 44 examined enzymes, 69 residues were identified correctly. Our results suggest that wavelet transform analysis of structure ensemble is applicable to extract essential fluctuation information of proteins; furthermore, analysis of positional fluctuations is helpful for the identification of catalytic residues.     

Conformer selection and induced fit in flexible backbone protein-protein docking using computational and NMR ensembles

Accommodating backbone flexibility continues to be the most difficult challenge in computational docking of protein-protein complexes. Towards that end, we simulate four distinct biophysical models of protein binding in RosettaDock, a multiscale Monte-Carlo-based algorithm that uses a quasi-kinetic search process to emulate the diffusional encounter of two proteins and to identify low-energy complexes. The four binding models are as follows: (1) key-lock (KL) model, using rigid-backbone docking; (2) conformer selection (CS) model, using a novel ensemble docking algorithm; (3) induced fit (IF) model, using energy-gradient-based backbone minimization; and (4) combined conformer selection/induced fit (CS/IF) model. Backbone flexibility was limited to the smaller partner of the complex, structural ensembles were generated using Rosetta refinement methods, and docking consisted of local perturbations around the complexed conformation using unbound component crystal structures for a set of 21 target complexes. The lowest-energy structure contained > 30% of the native residue-residue contacts for 9, 13, 13, and 14 targets for KL, CS, IF, and CS/IF docking, respectively. When applied to 15 targets using nuclear magnetic resonance ensembles of the smaller protein, the lowest-energy structure recovered at least 30% native residue contacts in 3, 8, 4, and 8 targets for KL, CS, IF, and CS/IF docking, respectively. CS/IF docking of the nuclear magnetic resonance ensemble performed equally well or better than KL docking with the unbound crystal structure in 10 of 15 cases. The marked success of CS and CS/IF docking shows that ensemble docking can be a versatile and effective method for accommodating conformational plasticity in docking and serves as a demonstration for the CS theory—that binding-competent conformers exist in the unbound ensemble and can be selected based on their favorable binding energies.     

Survival ensembles

We propose a unified and flexible framework for ensemble learning in the presence of censoring. For right-censored data, we introduce a random forest algorithm and a generic gradient boosting algorithm for the construction of prognostic and diagnostic models. The methodology is utilized for predicting the survival time of patients suffering from acute myeloid leukemia based on clinical and genetic covariates. Furthermore, we compare the diagnostic capabilities of the proposed censored data random forest and boosting methods, applied to the recurrence-free survival time of node-positive breast cancer patients, with previously published findings.     

Constructing ensembles for intrinsically disordered proteins

The relatively flat energy landscapes associated with intrinsically disordered proteins makes modeling these systems especially problematic. A comprehensive model for these proteins requires one to build an ensemble consisting of a finite collection of structures, and their corresponding relative stabilities, which adequately capture the range of accessible states of the protein. In this regard, methods that use computational techniques to interpret experimental data in terms of such ensembles are an essential part of the modeling process. In this review, we critically assess the advantages and limitations of current techniques and discuss new methods for the validation of these ensembles.     

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example, showed that the geometry-based FRODA occasionally sampled the pathway space of force field-based DIMS MD. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.     

Macromolecular technologies: applications and improvements

A report on the Association of Biomolecular Resource Facilities (ABRF) meeting, San Diego, USA, 24-27 February, 2001.