Modeling helical proteins using residual dipolar couplings, sparse long-range distance constraints and a simple residue-based force field

The detailed, quantitative characterization of unfolded proteins is a largely unresolved task due to the enormous experimental and theoretical difficulties in describing the highly dimensional space of their conformational ensembles. Recently, residual dipolar coupling (RDC) and paramagnetic relaxation enhancement (PRE) data have provided large numbers of experimental parameters on unfolded states. To obtain a minimal model of the unfolded state according to such data we have developed new modules for the use of steric alignment RDCs and PREs as constraints in ensemble structure calculations by the program XPLOR-NIH. As an example, ensemble calculations were carried out on urea-denatured ubiquitin using a total of 419 previously obtained RDCs and 253 newly determined PREs from eight cysteine mutants coupled to MTSL. The results show that only a small number of about 10 conformers is necessary to fully reproduce the experimental RDCs, PREs and average radius of gyration. C(alpha) contacts determined on a large set (400) of 10-conformer ensembles show significant (10-20%) populations of conformations that are similar to ubiquitin's A-state, i.e. corresponding to an intact native first beta-hairpin and alpha-helix as well as non-native alpha-helical conformations in the C-terminal half. Thus, methanol/acid (A-state) and urea denaturation lead to similar low energy states of the protein ensemble, presumably due to the weakening of the hydrophobic core. Similar contacts are obtained in calculations using solely RDCs or PREs. The sampling statistics of the C(alpha) contacts in the ensembles follow a simple binomial distribution. It follows that the present RDC, PRE, and computational methods allow the statistically significant detection of subconformations in the unfolded ensemble at population levels of a few percent.

Misfolding of the protein alpha-synuclein (aS), which associates with presynaptic vesicles, has been implicated in the molecular chain of events leading to Parkinson's disease. Here, the structure and dynamics of micelle-bound aS are reported. Val3-Val37 and Lys45-Thr92 form curved alpha-helices, connected by a well ordered, extended linker in an unexpected anti-parallel arrangement, followed by another short extended region (Gly93-Lys97), overlapping the recently identified chaperone-mediated autophagy recognition motif and a highly mobile tail (Asp98-Ala140). Helix curvature is significantly less than predicted based on the native micelle shape, indicating a deformation of the micelle by aS. Structural and dynamic parameters show a reduced helical content for Ala30-Val37. A dynamic variation in interhelical distance on the microsecond timescale is complemented by enhanced sub-nanosecond timescale dynamics, particularly in the remarkably glycine-rich segments of the helices. These unusually rich dynamics may serve to mitigate the effect of aS binding on membrane fluidity. The well ordered conformation of the helix-helix connector indicates a defined interaction with lipidic surfaces, suggesting that, when bound to larger diameter synaptic vesicles, it can act as a switch between this structure and a previously proposed uninterrupted helix.

Paramagnetic effects are valuable structural restraints in study of structures, dynamics and interactions of proteins by means of NMR spectroscopy. Site-specific tagging of proteins with paramagnetic ions is generally required to achieve these paramagnetic effects. In this review, we first introduce the concept of paramagnetic effects including paramagnetic relaxation enhancement (PRE), pseudocontact shift (PCS) and residual dipolar couplings (RDCs), which are generally used in biomolecular NMR. Thereafter, strategies of site-specific paramagnetic tagging of proteins are outlined, and the paramagnetic effects are evaluated. On the basis of paramagnetic tagging methods described above, the applications of paramagnetic NMR in characterization of multi-domain protein replacement, 3D structural determination of unstable and low-abundance enzyme intermediate complex in real time condition, and 3D structural determination of proteins in live cells using PCSs are introduced. NMR optimized paramagnetic tags suitable for achieving high spatial resolution of distances determined by double electron-electron resonance (DEER) are reviewed. In the end, the applications of DEER measurement in characterization of protein structures in cells are demonstrated. Paramagnetic NMR and electron paramagnetic resonance (EPR) in characterization of proteins in cells is shown as a powerful technique in structural biology and chemical biology, and the development of biological compatible methods of protein modifications suitable for NMR and EPR applications are in high demand. In summary, paramagnetic tagging proteins are a powerful tool in elucidation of protein structures, dynamics and interactions in chemical and structural biology and it is surely to find wide applications in cells.

As genome-sequencing projects rapidly increase the database of protein sequences, the gap between known sequences and known structures continues to grow exponentially, increasing the demand to accelerate structure determination methods. Residual dipolar couplings (RDCs) are an attractive source of experimental restraints for NMR structure determination, particularly rapid, high-throughput methods, because they yield both local and long-range orientational information and can be easily measured and assigned once the backbone resonances of a protein have been assigned. While very extensive RDC data sets have been used to determine the structure of ubiquitin, it is unclear to what extent such methods will generalize to larger proteins with less complete data sets. Here we incorporate experimental RDC restraints into Rosetta, an ab initio structure prediction method, and demonstrate that the combined algorithm provides a general method for de novo determination of a variety of protein folds from RDC data. Backbone structures for multiple proteins up to approximately 125 residues in length and spanning a range of topological complexities are rapidly and reproducibly generated using data sets that are insufficient in isolation to uniquely determine the protein fold de novo, although ambiguities and errors are observed for proteins with symmetry about an axis of the alignment tensor. The models generated are not high-resolution structures completely defined by experimental data but are sufficiently accurate to accelerate traditional high-resolution NMR structure determination and provide structure-based functional insights.

A major bottleneck in protein structure determination via nuclear magnetic resonance (NMR) is the lengthy and laborious process of assigning resonances and nuclear Overhauser effect (NOE) cross peaks. Recent studies have shown that accurate backbone folds can be determined using sparse NMR data, such as residual dipolar couplings (RDCs) or backbone chemical shifts. This opens a question of whether we can also determine the accurate protein sidechain conformations using sparse or unassigned NMR data. We attack this question by using unassigned nuclear Overhauser effect spectroscopy (NOESY) data, which record the through-space dipolar interactions between protons nearby in 3D space. We propose a Bayesian approach with a Markov random field (MRF) model to integrate the likelihood function derived from observed experimental data, with prior information (i.e., empirical molecular mechanics energies) about the protein structures. We unify the side-chain structure prediction problem with the side-chain structure determination problem using unassigned NMR data, and apply the deterministic dead-end elimination (DEE) and A* search algorithms to provably find the global optimum solution that maximizes the posterior probability. We employ a Hausdorff-based measure to derive the likelihood of a rotamer or a pairwise rotamer interaction from unassigned NOESY data. In addition, we apply a systematic and rigorous approach to estimate the experimental noise in NMR data, which also determines the weighting factor of the data term in the scoring function that is derived from the Bayesian framework. We tested our approach on real NMR data of three proteins, including the FF Domain 2 of human transcription elongation factor CA150 (FF2), the B1 domain of Protein G (GB1), and human ubiquitin. The promising results indicate that our approach can be applied in high-resolution protein structure determination. Since our approach does not require any NOE assignment, it can accelerate the NMR structure determination process.

A metal ion with magnetic anisotropy in a biomolecule exerts strong paramagnetic effects on the nucleus spins of biomolecules in the NMR spectrum. The paramagnetic effects including paramagnetic relaxation enhancement (PRE), pseudocontact shift (PCS) and residual dipolar coupling (RDC) are valuable structural and dynamic restraints of biomolecules, and generation of these paramagnetic effects is a prerequisite. The susceptibility of magnetic anisotropy plays a similar role in the alignment of biomolecules to the commonly used alignment media in an external magnetic field. We summarize the strategies available for generating RDCs in proteins by paramagnetic labeling, selection of paramagnetic ions, and the factors influencing the magnitude of RDCs.

Partial assignments of tunicate βγ-crystallin structure.

We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms-RDC-SOS and RDC-NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramér-Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.

The measurement and application of residual dipolar couplings (RDCs) in solution NMR studies of biological macromolecules has become well established over the past quarter of a century. Numerous methods for generating the requisite anisotropic orientational molecular distribution have been demonstrated, each with its specific strengths and weaknesses. In parallel, an enormous number of pulse schemes have been introduced to measure the many different types of RDCs, ranging from the most widely measured backbone amide 15N-1H RDCs, to 1H-1H RDCs and couplings between low-γ nuclei. Applications of RDCs range from structure validation and refinement to the determination of relative domain orientations, the measurement of backbone and domain motions, and de novo structure determination. Nevertheless, it appears that the power of the RDC methodology remains underutilized. This review aims to highlight the practical aspects of sample preparation and RDC measurement while describing some of the most straightforward applications that take advantage of the exceptionally precise information contained in such data. Some emphasis will be placed on more recent developments that enable the accurate measurement of RDCs in larger systems, which is key to the ongoing shift in focus of biological NMR spectroscopy from structure determination toward gaining improved understanding of how molecular flexibility drives protein function.

Editorial overview: New protein production tools for structural biology

NMR spectroscopy is, next to crystallography, the only method for determination of the high-resolution structure of biomacromolecules such as proteins, nucleic acids, and their complexes. NMR spectroscopy is unique in that it allows the study of the structure and dynamics of these molecules in solution. Until recently, solution structures determined by NMR spectroscopy were mainly based on distance restraints obtained from proton/proton nuclear Overhauser effects (NOEs). Hus et al. have now for the first time demonstrated that the backbone structure of a protein can be determined de novo from residual dipolar couplings (RDCs) without the use of NOE data.[1] This achievement represents a considerable milestone in the rapidly growing applications of residual dipolar couplings for the elucidation of biomolecular structures as outlined below. The main source of structural information from NMR experiments is based on the dipolar coupling between protons. This interaction depends on the internuclear distances and the orientation of the internuclear vector relative to the static magnetic field. The distance and orientation dependence of dipolar couplings has long been used to characterize the structure of molecules by solid-state NMR spectroscopy.[2] However, in solution the dipolar couplings are averaged to zero as a result of the fast random reorientation of the molecule. Nevertheless, the randomly fluctuating magnetic field produced by one nucleus interacts with the spins of nearby nuclei and causes relaxation of their magnetization. This cross-relaxation effect is the basis of the NOE experiments and scales with the distance r between the nuclei ( r 6). In proteins, numerous proton ± proton distances (with an upper limit of 5 ± 6 a) can be measured, which together define the three-dimensional structure. Difficulties arise if the number of experimental proton distances is sparse, as frequently found, for example, between different domains in a protein or in nucleic acids because of the small proton density. As a consequence of the short-range nature of the NOE-derived distance restraints, it is also difficult to accurately define the relative orientation of regions which are far apart from each other in the three-dimensional structure of the molecule.

The calcium- and integrin-binding protein 1 (CIB1) is a ubiquitous Ca(2+)-binding protein and a specific binding partner for the platelet integrin αIIb cytoplasmic domain, which confers the key role of CIB1 in hemostasis. CIB1 is also known to be involved in apoptosis, embryogenesis, and the DNA damage response. In this study, the solution structures of both Ca(2+)-CIB1 and Mg(2+)-CIB1 were determined using solution-state NMR spectroscopy. The methyl groups of Ile, Leu, and Val were selectively protonated to compensate for the loss of protons due to deuteration. The solution structure of Ca(2+)-CIB1 possesses smaller opened EF-hands in its C-domain compared with available crystal structures. Ca(2+)-CIB1 and Mg(2+)-CIB1 have similar structures, but the N-lobe of Mg(2+)-CIB1 is slightly more opened than that of Ca(2+)-CIB1. Additional NMR experiments, such as chemical shift perturbation and methyl group solvent accessibility as measured by a nitroxide surface probe, were carried out to further characterize the structures of Ca(2+)-CIB1 and Mg(2+)-CIB1 as well as their interactions with the integrin αIIb cytoplasmic domain. NMR measurements of backbone amide proton slow motion (microsecond to millisecond) dynamics confirmed that the C-terminal helix of Ca(2+)-CIB1 is displaced upon αIIb binding. The EF-hand III of both Ca(2+)-CIB1 and Mg(2+)-CIB1 was identified to be directly involved in the interaction of CIB1 with αIIb. Together, these data illustrate that CIB1 behaves quite differently from related EF-hand regulatory calcium-binding proteins, such as calmodulin or neuronal calcium sensor proteins.

Recent advances in computational methods like AlphaFold have transformed structural biology, enabling accurate modeling of protein complexes and driving applications in drug discovery and protein engineering. However, predicting the structure of systems involving weak, transient, or dynamic interactions, or of complexes with disordered regions, remains challenging. Nuclear Magnetic Resonance (NMR) spectroscopy offers atomic‐level insights into biomolecular complexes, even in weakly interacting and dynamic systems. Paramagnetic NMR, in particular, provides long‐range structural restraints, easily exceeding distances over 25 Å, making it ideal for studying large protein complexes. Advances in chemical tools for introducing paramagnetic tags into proteins, combined with progress in electron paramagnetic resonance (EPR) spectroscopy, have enhanced the method's utility. This perspective article discusses paramagnetic NMR approaches for analyzing biomolecular complexes in solution and in the solid state, emphasizing quantities like pseudocontact shifts, residual dipolar couplings, and paramagnetic relaxation enhancements. Additionally, dynamic nuclear polarization offers a promising method to amplify NMR signals of large complexes, even in complex environments. The integration of AlphaFold protein structure prediction with paramagnetic NMR holds great potential for advancing our understanding of biomolecular interactions.

The concept of using residual dipolar couplings (RDCs) for the structure determination of organic molecules is applied to the simultaneous assignment of all diastereotopic protons in strychnine. To use this important NMR parameter the molecule has to be aligned in the magnetic field. Here we present a new alignment medium for organic substrates. The optimization of the alignment properties of mixtures of poly-gamma-ethyl-L-glutamate (PELG) and CDCl(3) are described and the alignment properties of PELG at different concentrations are evaluated. A comparison of PELG with poly-gamma-benzyl-L-glutamate (PBLG) shows considerable differences in the magnitude of alignment for strychnine in the two alignment media. PELG induces a lower degree of order and makes the measurement of residual dipolar couplings (RDCs) in strychnine possible. All one-bond C-H RDCs of strychnine in PELG were determined by using 2D heteronuclear single quantum coherence (HSQC) spectroscopy. The strategy for the extraction of RDCs for methylene groups is described in detail. The RDCs and order parameters are used to assign pairs of diastereotopic protons. This methodology can distinguish not only one pair of diastereotopic protons but it can be used to assign all pairs of diastereotopic protons simultaneously. Two different calculation approaches to achieve this task are described in detail.

Chapter 2 - A Review of REDCRAFT: Simultaneous Investigation of Structure and Dynamics of Proteins from RDC Restraints