Accurate Solution Structures of Proteins from X-ray Data and a Minimal Set of NMR Data: Calmodulin−Peptide Complexes As Examples

Computational Mutagenesis of Antibody Fragments: Disentangling Side Chains from ΔΔG Predictions

The development of highly potent antibodies and antibody fragments as binding agents holds significant implications in fields such as biosensing and biotherapeutics. Their binding strength is intricately linked to the arrangement and composition of residues at the binding interface. Computational techniques offer a robust means to predict the three-dimensional structure of these complexes and to assess the affinity changes resulting from mutations. Given the interdependence of structure and affinity prediction, our objective here is to disentangle their roles. We aim to evaluate independently six side-chain reconstruction methods and ten binding affinity estimation techniques. This evaluation was pivotal in predicting affinity alterations due to single mutations, a key step in computational affinity maturation protocols. Our analysis focuses on a data set comprising 27 distinct antibody/hen egg white lysozyme complexes, each with crystal structures and experimentally determined binding affinities. Using six different side-chain reconstruction methods, we transformed each structure into its corresponding mutant via in silico single-point mutations. Subsequently, these structures undergo minimization and molecular dynamics simulation. We therefore estimate ΔΔG values based on the original crystal structure, its energy-minimized form, and the ensuing molecular dynamics trajectories. Our research underscores the critical importance of selecting reliable side-chain reconstruction methods and conducting thorough molecular dynamics simulations to accurately predict the impact of mutations. In summary, our study demonstrates that the integration of conformational sampling and scoring is a potent approach to precisely characterizing mutation processes in single-point mutagenesis protocols and crucial for computational antibody design.

Structural Evolution of Paramagnetic Lanthanide Compounds in Solution Compared to Time- and Ensemble-Average Structures

Anisotropy in the magnetic susceptibility strongly influences the paramagnetic shifts seen in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) experiments. A previous study on a series of C3-symmetric prototype MRI contrast agents showed that their magnetic anisotropy was highly sensitive to changes in molecular geometry and concluded that changes in the average angle between the lanthanide-oxygen (Ln-O) bonds and the molecular C3 axis due to solvent interactions had a significant impact on the magnetic anisotropy and, consequently, the paramagnetic shift. However, this study, like many others, was predicated on an idealized C3-symmetric structural model, which may not be representative of the dynamic structure in solution at the single-molecule level. Here, we address this by using ab initio molecular dynamics simulations to simulate how the molecular geometry, in particular the angles between the Ln-O bonds and the pseudo-C3 axis, evolves over time in the solution, mimicking typical experimental conditions. We observe large-amplitude oscillations in the O-Ln-C̃3 angles, and complete active space self-consistent field spin-orbit calculations show that this leads to similarly large oscillations in the pseudocontact (dipolar) paramagnetic NMR shifts. The time-averaged shifts show good agreement with experimental measurements, while the large fluctuations suggest that an idealized structure provides an incomplete description of the solution dynamics. Our observations have significant implications for modeling the electronic and nuclear relaxation times in this and other systems where the magnetic susceptibility is exquisitely sensitive to the molecular structure.

The evolution of paramagnetic NMR as a tool in structural biology

Paramagnetic NMR data contain extremely accurate long-range information on metalloprotein structures and, when used in the frame of integrative structural biology approaches, they allow for the retrieval of structural details to a resolution that is not achievable using other techniques. Paramagnetic data thus represent an extremely powerful tool to refine protein models in solution, especially when coupled to X-ray or cryoelectron microscopy data, to monitor the formation of complexes and determine the relative arrangements of their components, and to highlight the presence of conformational heterogeneity. More recently, theoretical and computational advancements in quantum chemical calculations of paramagnetic NMR observables are progressively opening new routes in structural biology, because they allow for the determination of the structure within the coordination sphere of the metal center, thus acting as a loupe on sites that are difficult to observe but very important for protein function.

DEER experiments reveal fundamental differences between calmodulin complexes with IQ and MARCKS peptides in solution

Calmodulin (CaM) is a calcium-binding protein that regulates the function of many proteins by indirectly conferring Ca²⁺ sensitivity, and it undergoes a large conformational change on partners' binding. We compared the solution binding mode of the target peptides MARCKS and IQ by double electron-electron resonance (DEER) distance measurements and paramagnetic NMR. We combined nitroxide and Gd(III) spin labels, including specific substitution of one of the Ca²⁺ ions in the CaM mutant N60D by a Gd(III) ion. The binding of MARCKS to holo-CaM resulted neither in a closed conformation nor in a unique relative orientation between the two CaM domains, in contrast with the crystal structure. Binding of IQ to holo-CaM did generate a closed conformation. Using elastic network modeling and 12 distance restraints obtained from multiple holo-CaM/IQ DEER data, we derived a model of the solution structure, which is in reasonable agreement with the crystal structure.

Characterizing conformational ensembles of multi-domain proteins using anisotropic paramagnetic NMR restraints

It has been over two decades since paramagnetic NMR started to form part of the essential techniques for structural analysis of proteins under physiological conditions. Paramagnetic NMR has significantly expanded our understanding of the inherent flexibility of proteins, in particular, those that are formed by combinations of two or more domains. Here, we present a brief overview of techniques to characterize conformational ensembles of such multi-domain proteins using paramagnetic NMR restraints produced through anisotropic metals, with a focus on the basics of anisotropic paramagnetic effects, the general procedures of conformational ensemble reconstruction, and some representative reweighting approaches.

Pseudocontact Shifts in Biomolecular NMR Spectroscopy

Paramagnetic centers in biomolecules, such as specific metal ions that are bound to a protein, affect the nuclei in their surrounding in various ways. One of these effects is the pseudocontact shift (PCS), which leads to strong chemical shift perturbations of nuclear spins, with a remarkably long range of 50 Å and beyond. The PCS in solution NMR is an effect originating from the anisotropic part of the dipole-dipole interaction between the magnetic momentum of unpaired electrons and nuclear spins. The PCS contains spatial information that can be exploited in multiple ways to characterize structure, function, and dynamics of biomacromolecules. It can be used to refine structures, magnify effects of dynamics, help resonance assignments, allows for an intermolecular positioning system, and gives structural information in sensitivity-limited situations where all other methods fail. Here, we review applications of the PCS in biomolecular solution NMR spectroscopy, starting from early works on natural metalloproteins, following the development of non-natural tags to chelate and attach lanthanoid ions to any biomolecular target to advanced applications on large biomolecular complexes and inside living cells. We thus hope to not only highlight past applications but also shed light on the tremendous potential the PCS has in structural biology.

A Free-Energy Landscape Analysis of Calmodulin Obtained from an NMR Data-Utilized Multi-Scale Divide-and-Conquer Molecular Dynamics Simulation

Calmodulin (CaM) is a multifunctional calcium-binding protein, which regulates a variety of biochemical processes. CaM acts through its conformational changes and complex formation with its target enzymes. CaM consists of two globular domains (N-lobe and C-lobe) linked by an extended linker region. Upon calcium binding, the N-lobe and C-lobe undergo local conformational changes, followed by a major conformational change of the entire CaM to wrap the target enzyme. However, the regulation mechanisms, such as allosteric interactions, which regulate the large structural changes, are still unclear. In order to investigate the series of structural changes, the free-energy landscape of CaM was obtained by multi-scale divide-and-conquer molecular dynamics (MSDC-MD). The resultant free-energy landscape (FEL) shows that the Ca²⁺ bound CaM (holo-CaM) would take an experimentally famous elongated structure, which can be formed in the early stage of structural change, by breaking the inter-domain interactions. The FEL also shows that important interactions complete the structural change from the elongated structure to the ring-like structure. In addition, the FEL might give a guiding principle to predict mutational sites in CaM. In this study, it was demonstrated that the movement process of macroscopic variables on the FEL may be diffusive to some extent, and then, the MSDC-MD is suitable to the parallel computation.

Advances in NMR Spectroscopy of Weakly Aligned Biomolecular Systems

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.

Allosteric Switching of Calmodulin in a Mycobacterium smegmatis porin A (MspA) Nanopore-Trap

Recent developments concerning large protein nanopores suggest a new approach to structure profiling of native folded proteins. In this work, the large vestibule of Mycobacterium smegmatis porin A (MspA) and calmodulin (CaM), a Ca²⁺ -binding protein, were used in the direct observation of the protein structure. Three conformers, including the Ca²⁺ -free, Ca²⁺ -bound, and target peptide-bound states of CaM, were unambiguously distinguished. A disease related mutant, CaM D129G was also discriminated by MspA, revealing how a single amino acid replacement can interfere with the Ca²⁺ -binding capacity of the whole protein. The binding capacity and aggregation effect of CaM induced by different ions (Mg²⁺ /Sr²⁺ /Ba²⁺ /Ca²⁺ /Pb²⁺ /Tb³⁺ ) were also investigated and the stability of MspA in extreme conditions was evaluated. This work demonstrates the most systematic single-molecule investigation of different allosteric conformers of CaM, acknowledging the high sensing resolution offered by the MspA nanopore trap.

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.

Molecular insights on CALX-CBD12 interdomain dynamics from MD simulations, RDCs, and SAXS

Na⁺/Ca²⁺ exchangers (NCXs) are secondary active transporters that couple the translocation of Na⁺ with the transport of Ca²⁺ in the opposite direction. The exchanger is an essential Ca²⁺ extrusion mechanism in excitable cells. It consists of a transmembrane domain and a large intracellular loop that contains two Ca²⁺-binding domains, CBD1 and CBD2. The two CBDs are adjacent to each other and form a two-domain Ca²⁺ sensor called CBD12. Binding of intracellular Ca²⁺ to CBD12 activates the NCX but inhibits the NCX of Drosophila, CALX. NMR spectroscopy and SAXS studies showed that CALX and NCX CBD12 constructs display significant interdomain flexibility in the apo state but assume rigid interdomain arrangements in the Ca²⁺-bound state. However, detailed structure information on CBD12 in the apo state is missing. Structural characterization of proteins formed by two or more domains connected by flexible linkers is notoriously challenging and requires the combination of orthogonal information from multiple sources. As an attempt to characterize the conformational ensemble of CALX-CBD12 in the apo state, we applied molecular dynamics (MD) simulations, NMR (¹H-¹⁵N residual dipolar couplings), and small-angle x-ray scattering (SAXS) data in a combined strategy to select an ensemble of conformations in agreement with the experimental data. This joint approach demonstrated that CALX-CBD12 preferentially samples closed conformations, whereas the wide-open interdomain arrangement characteristic of the Ca²⁺-bound state is less frequently sampled. These results are consistent with the view that Ca²⁺ binding shifts the CBD12 conformational ensemble toward extended conformers, which could be a key step in the NCXs' allosteric regulation mechanism. This strategy, combining MD with NMR and SAXS, provides a powerful approach to select ensembles of conformations that could be applied to other flexible multidomain systems.

Conformational Space Sampled by Domain Reorientation of Linear Diubiquitin Reflected in Its Binding Mode for Target Proteins

Linear polyubiquitin chains regulate diverse signaling proteins, in which the chains adopt various conformations to recognize different target proteins. Thus, the structural plasticity of the chains plays an important role in controlling the binding events. Herein, paramagnetic NMR spectroscopy is employed to explore the conformational space sampled by linear diubiquitin, a minimal unit of linear polyubiquitin, in its free state. Rigorous analysis of the data suggests that, regarding the relative positions of the ubiquitin units, particular regions of conformational space are preferentially sampled by the molecule. By combining these results with further data collected for charge-reversal derivatives of linear diubiquitin, structural insights into the factors underlying the binding events of linear diubiquitin are obtained.

A High-Resolution View of the Coordination Environment in a Paramagnetic Metalloprotein from its Magnetic Properties

Metalloproteins constitute a significant fraction of the proteome of all organisms and their characterization is critical for both basic sciences and biomedical applications. A large portion of metalloproteins bind paramagnetic metal ions, and paramagnetic NMR spectroscopy has been widely used in their structural characterization. However, the signals of nuclei in the immediate vicinity of the metal center are often broadened beyond detection. In this work, we show that it is possible to determine the coordination environment of the paramagnetic metal in the protein at a resolution inaccessible to other techniques. Taking the structure of a diamagnetic analogue as a starting point, a geometry optimization is carried out by fitting the pseudocontact shifts obtained from first principles quantum chemical calculations to the experimental ones.

Characterization of lanthanoid-binding proteins using NMR spectroscopy

The variety of magnetic properties exhibited by paramagnetic lanthanoids provides outstanding information in NMR-based structural biology and therefore can be a very useful tool for characterizing lanthanoid-binding proteins. Because of their dependence on the relative positions of the protein nuclei and of the lanthanoid ion, the paramagnetic restraints (PCS, PRDC and PRE) provide information on structure and dynamics of proteins. In this Chapter, we cover the use of lanthanoids in structural biology including protein sample preparation, NMR experiments and data interpretation.

De novo designed coiled coils as scaffolds for lanthanides, including novel imaging agents with a twist

The design of artificial miniature lanthanide proteins, provide an opportunity to access new functional metalloproteins as well as insight into native lanthanide biochemistry.

Paramagnetic NMR in drug discovery

The presence of an unpaired electron in paramagnetic molecules generates significant effects in NMR spectra, which can be exploited to provide restraints complementary to those used in standard structure-calculation protocols. NMR already occupies a central position in drug discovery for its use in fragment screening, structural biology and validation of ligand-target interactions. Paramagnetic restraints provide unique opportunities, for example, for more sensitive screening to identify weaker-binding fragments. A key application of paramagnetic NMR in drug discovery, however, is to provide new structural restraints in cases where crystallography proves intractable. This is particularly important at early stages in drug-discovery programs where crystal structures of weakly-binding fragments are difficult to obtain and crystallization artefacts are probable, but structural information about ligand poses is crucial to guide medicinal chemistry. Numerous applications show the value of paramagnetic restraints to filter computational docking poses and to generate interaction models. Paramagnetic relaxation enhancements (PREs) generate a distance-dependent effect, while pseudo-contact shift (PCS) restraints provide both distance and angular information. Here, we review strategies for introducing paramagnetic centers and discuss examples that illustrate the utility of paramagnetic restraints in drug discovery. Combined with standard approaches, such as chemical shift perturbation and NOE-derived distance information, paramagnetic NMR promises a valuable source of information for many challenging drug-discovery programs.

On the complementarity of X-ray and NMR data

X-ray crystallography and NMR contain complementary information for the structural characterization of biological macromolecules. X-ray diffraction is primarily sensitive to the overall shape of the molecule, whereas NMR is mostly sensitive to the atomic detail. Their combination can therefore provide a stronger justification for the resulting structure. For their combination we have recently proposed REFMAC-NMR, which relies on primary data from both techniques for joint refinement. This possibility raises the compelling question of how far the complementarity can be extended. In this paper, we describe an integrative approach to the refinement with NMR data of four X-ray structures of hen-egg-white lysozyme, solved at atomic resolution in four different crystal forms, and we demonstrate that the outcome critically depends on the crystal form itself, reflecting the sensitivity of NMR to fine details.

Magnetic susceptibility and paramagnetism-based NMR

The magnetic interactions between the nuclear magnetic moment and the magnetic moment of unpaired electron(s) depend on the structure and dynamics of the molecules where the paramagnetic center is located and of their partners. The long-range nature of the magnetic interactions is thus a reporter of invaluable information for structural biology studies, when other techniques often do not provide enough data for the atomic-level characterization of the system. This precious information explains the flourishing of paramagnetism-assisted NMR studies in recent years. Many paramagnetic effects are related to the magnetic susceptibility of the paramagnetic metal. Although these effects have been known for more than half a century, different theoretical models and new approaches have been proposed in the last decade. In this review, we have summarized the consequences for NMR spectroscopy of magnetic interactions between nuclear and electron magnetic moments, and thus of the presence of a magnetic susceptibility due to metals, and we do so using a unified notation.

Integrative Protein Modeling in RosettaNMR from Sparse Paramagnetic Restraints

Computational methods to predict protein structure from nuclear magnetic resonance (NMR) restraints that only require assignment of backbone signals, hold great potential to study larger proteins. Ideally, computational methods designed to work with sparse data need to add atomic detail that is missing in the experimental restraints. We introduce a comprehensive framework into the Rosetta suite that uses NMR restraints derived from paramagnetic labeling. Specifically, RosettaNMR incorporates pseudocontact shifts, residual dipolar couplings, and paramagnetic relaxation enhancements. It continues to use backbone chemical shifts and nuclear Overhauser effect distance restraints. We assess RosettaNMR for protein structure prediction by folding 28 monomeric proteins and 8 homo-oligomeric proteins. Furthermore, the general applicability of RosettaNMR is demonstrated on two protein-protein and three protein-ligand docking examples. Paramagnetic restraints generated more accurate models for 85% of the benchmark proteins and, when combined with chemical shifts, sampled high-accuracy models (≤2Å) in 50% of the cases.

Integrative Approaches in Structural Biology: A More Complete Picture from the Combination of Individual Techniques

With the recent technological and computational advancements, structural biology has begun to tackle more and more difficult questions, including complex biochemical pathways and transient interactions among macromolecules. This has demonstrated that, to approach the complexity of biology, one single technique is largely insufficient and unable to yield thorough answers, whereas integrated approaches have been more and more adopted with successful results. Traditional structural techniques (X-ray crystallography and Nuclear Magnetic Resonance (NMR)) and the emerging ones (cryo-electron microscopy (cryo-EM), Small Angle X-ray Scattering (SAXS)), together with molecular modeling, have pros and cons which very nicely complement one another. In this review, three examples of synergistic approaches chosen from our previous research will be revisited. The first shows how the joint use of both solution and solid-state NMR (SSNMR), X-ray crystallography, and cryo-EM is crucial to elucidate the structure of polyethylene glycol (PEG)ylated asparaginase, which would not be obtainable through any of the techniques taken alone. The second deals with the integrated use of NMR, X-ray crystallography, and SAXS in order to elucidate the catalytic mechanism of an enzyme that is based on the flexibility of the enzyme itself. The third one shows how it is possible to put together experimental data from X-ray crystallography and NMR restraints in order to refine a protein model in order to obtain a structure which simultaneously satisfies both experimental datasets and is therefore closer to the ‘real structure’.

How Do Nuclei Couple to the Magnetic Moment of a Paramagnetic Center? A New Theory at the Gauntlet of the Experiments

The recent derivation, based on pure quantum chemistry (QC) first-principles, of the pseudocontact shifts (PCSs) caused by a paramagnetic metal center on far away nuclei has cast doubts on the validity of the semiempirical (SE) theory, predicting PCSs to arise from the metal magnetic susceptibility anisotropy. The SE theory has been used and applied countless times, especially in the last 2 decades, to obtain structural information on proteins containing paramagnetic metal ions. We show here that the QC and SE predictions can be directly tested against experiments, provided a suitable macromolecular system is used. The SE approach yields a good prediction of the experimental PCSs while the QC one does not. It appears that the classic theory is able to grasp satisfactorily the underlying physics.

Joint X-ray/NMR structure refinement of multidomain/multisubunit systems

Data integration in structural biology has become a paradigm for the characterization of biomolecular systems, and it is now accepted that combining different techniques can fill the gaps in each other's blind spots. In this frame, one of the combinations, which we have implemented in REFMAC-NMR, is residual dipolar couplings from NMR together with experimental data from X-ray diffraction. The first are exquisitely sensitive to the local details but does not give any information about overall shape, whereas the latter encodes more the information about the overall shape but at the same time tends to miss the local details even at the highest resolutions. Once crystals are obtained, it is often rather easy to obtain a complete X-ray dataset, however it is time-consuming to obtain an exhaustive NMR dataset. Here, we discuss the effect of including a-priori knowledge on the properties of the system to reduce the number of experimental data needed to obtain a more complete picture. We thus introduce a set of new features of REFMAC-NMR that allow for improved handling of RDC data for multidomain proteins and multisubunit biomolecular complexes, and encompasses the use of pseudo-contact shifts as an additional source of NMR-based information. The new feature may either help in improving the refinement, or assist in spotting differences between the crystal and the solution data. We show three different examples where NMR and X-ray data can be reconciled to a unique structural model without invoking mobility.

Pseudocontact shifts and paramagnetic susceptibility in semiempirical and quantum chemistry theories

Pseudocontact shifts are traditionally described as a function of the anisotropy of the paramagnetic susceptibility tensor, according to the semiempirical theory mainly developed by Kurland and McGarvey [J. Magn. Reson. 2, 286-301 (1970)]. The paramagnetic susceptibility tensor is required to be symmetric. Applying point-dipole approximation to the quantum chemistry theory of hyperfine shift, pseudocontact shifts are found to scale with a non-symmetric tensor that differs by a factor g^T/g_e from the paramagnetic susceptibility tensor derived within the semiempirical framework. We analyze the foundations of the Kurland-McGarvey pseudocontact shift expression and recall that it is inherently based on the Russell-Saunders (LS) coupling approximation for the spin-orbit coupling. We show that the difference between the semiempirical and quantum chemistry pseudocontact shift expressions arises directly from the different treatment of the orbital contribution to the hyperfine coupling.

Localization of ligands within human carbonic anhydrase II using 19F pseudocontact shift analysis

Unraveling the native structure of protein-ligand complexes in solution enables rational drug design. We report here the use of ¹⁹F pseudocontact shift (PCS) NMR as a method to determine fluorine positions of high affinity ligands bound within the drug target human carbonic anhydrase II with high accuracy. Three different ligands were localized within the protein by analysis of the obtained PCS from simple one-dimensional ¹⁹F spectra with an accuracy of up to 0.8 Å. In order to validate the PCS, four to five independent magnetic susceptibility tensors induced by lanthanide chelating tags bound site-specifically to single cysteine mutants were refined. Least-squares minimization and a Monte-Carlo approach allowed the assessment of experimental errors on the intersection of the corresponding four to five PCS isosurfaces. By defining an angle score that reflects the relative isosurface orientation for different tensor combinations, it was established that the ligand can be localized accurately using only three tensors, if the isosurfaces are close to orthogonal. For two out of three ligands, the determined position closely matched the X-ray coordinates. Our results for the third ligand suggest, in accordance with previously reported ab initio calculations, a rotated position for the difluorophenyl substituent, enabling a favorable interaction with Phe-131. The lanthanide-fluorine distance varied between 22 and 38 Å and induced ¹⁹F PCS ranged from 0.078 to 0.409 ppm, averaging to 0.213 ppm. Accordingly, even longer metal-fluorine distances will lead to meaningful PCS, rendering the investigation of protein-ligand complexes significantly larger than 30 kDa feasible.

The theory of frame ordering: observing motions in calmodulin complexes

Large scale functional motions of molecules are studied experimentally using numerous molecular and biophysics techniques, the data from which are subsequently interpreted using diverse models of Brownian molecular dynamics. To unify all rotational physics techniques and motional models, the frame order tensor - a universal statistical mechanics theory based on the rotational ordering of rigid body frames - is herein formulated. The frame ordering is the fundamental physics that governs how motions modulate rotational molecular physics and it defines the properties and maximum information content encoded in the observable physics. Using the tensor to link residual dipolar couplings and pseudo-contact shifts, two distinct information-rich and atomic-level biophysical measurements from the field of nuclear magnetic resonance spectroscopy, to a number of basic mechanical joint models, a highly dynamic state of calmodulin (CaM) bound to a target peptide in a tightly closed conformation was observed. Intra- and inter-domain motions reveal the CaM complex to be entropically primed for peptide release.

Paramagnetic NMR in solution and the solid state

The field of paramagnetic NMR has expanded considerably in recent years. This review addresses both the theoretical description of paramagnetic NMR, and the way in which it is currently practised. We provide a review of the theory of the NMR parameters of systems in both solution and the solid state. Here we unify the different languages used by the NMR, EPR, quantum chemistry/DFT, and magnetism communities to provide a comprehensive and coherent theoretical description. We cover the theory of the paramagnetic shift and shift anisotropy in solution both in the traditional formalism in terms of the magnetic susceptibility tensor, and using a more modern formalism employing the relevant EPR parameters, such as are used in first-principles calculations. In addition we examine the theory first in the simple non-relativistic picture, and then in the presence of spin-orbit coupling. These ideas are then extended to a description of the paramagnetic shift in periodic solids, where it is necessary to include the bulk magnetic properties, such as magnetic ordering at low temperatures. The description of the paramagnetic shift is completed by describing the current understanding of such shifts due to lanthanide and actinide ions. We then examine the paramagnetic relaxation enhancement, using a simple model employing a phenomenological picture of the electronic relaxation, and again using a more complex state-of-the-art theory which incorporates electronic relaxation explicitly. An additional important consideration in the solid state is the impact of bulk magnetic susceptibility effects on the form of the spectrum, where we include some ideas from the field of classical electrodynamics. We then continue by describing in detail the solution and solid-state NMR methods that have been deployed in the study of paramagnetic systems in chemistry, biology, and the materials sciences. Finally we describe a number of case studies in paramagnetic NMR that have been specifically chosen to highlight how the theory in part one, and the methods in part two, can be used in practice. The systems chosen include small organometallic complexes in solution, solid battery electrode materials, metalloproteins in both solution and the solid state, systems containing lanthanide ions, and multi-component materials used in pharmaceutical controlled-release formulations that have been doped with paramagnetic species to measure the component domain sizes.

Arginine Side-Chain Hydrogen Exchange: Quantifying Arginine Side-Chain Interactions in Solution

The rate with which labile backbone hydrogen atoms in proteins exchange with the solvent has long been used to probe protein interactions in aqueous solutions. Arginine, an essential amino acid found in many interaction interfaces, is capable of an impressive range of interactions via its guanidinium group. The hydrogen exchange rate of the guanidinium hydrogens therefore becomes an important measure to quantify side-chain interactions. Herein we present an NMR method to quantify the hydrogen exchange rates of arginine side-chain 1 Hϵ protons and thus present a method to gauge the strength of arginine side-chain interactions. The method employs 13 C-detection and the one-bond deuterium isotope shift observed for 15 Nϵ to generate two exchanging species in 1 H2 O/2 H2 O mixtures. An application to the protein T4 Lysozyme is shown, where protection factors calculated from the obtained exchange rates correlate well with the interactions observed in the crystal structure. The methodology presented provides an important step towards characterising interactions of arginine side-chains in enzymes, in phase separation, and in protein interaction interfaces in general.

Assessing protein conformational landscapes: integration of DEER data in Maximum Occurrence analysis

The properties of the conformational landscape of a biomolecule are of capital importance to understand its function. It is widely accepted that a statistical ensemble is far more representative than a single structure, especially for proteins with disordered regions. While experimental data provide the most important handle on the conformational variability that the system is experiencing, they usually report on either time or ensemble averages. Since the available conformations largely outnumber the (independent) available experimental data, the latter can be equally well reproduced by a variety of ensembles. We have proposed the Maximum Occurrence (MaxOcc) approach to provide an upper bound of the statistical weight of each conformation. This method is expected to converge towards the true statistical weights by increasing the number of independent experimental datasets. In this paper we explore the ability of DEER (Double Electron Electron Resonance) data, which report on the distance distribution between two spin labels attached to a biomolecule, to restrain the MaxOcc values and its complementarity to previously introduced experimental techniques such as NMR and Small-Angle X-ray Scattering. We here present the case of Ca2+ bound calmodulin (CaM) as a test case and show that DEER data impose a sizeable reduction of the conformational space described by high MaxOcc conformations.

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.

Coordination to lanthanide ions distorts binding site conformation in calmodulin

The Ca²⁺-sensing protein calmodulin (CaM) is a popular model of biological ion binding since it is both experimentally tractable and essential to survival in all eukaryotic cells. CaM modulates hundreds of target proteins and is sensitive to complex patterns of Ca²⁺ exposure, indicating that it functions as a sophisticated dynamic transducer rather than a simple on/off switch. Many details of this transduction function are not well understood. Fourier transform infrared (FTIR) spectroscopy, ultrafast 2D infrared (2D IR) spectroscopy, and electronic structure calculations were used to probe interactions between bound metal ions (Ca²⁺ and several trivalent lanthanide ions) and the carboxylate groups in CaM's EF-hand ion-coordinating sites. Since Tb³⁺ is commonly used as a luminescent Ca²⁺ analog in studies of protein-ion binding, it is important to characterize distinctions between the coordination of Ca²⁺ and the lanthanides in CaM. Although functional assays indicate that Tb³⁺ fully activates many Ca²⁺-dependent proteins, our FTIR spectra indicate that Tb³⁺, La³⁺, and Lu³⁺ disrupt the bidentate coordination geometry characteristic of the CaM binding sites' strongly conserved position 12 glutamate residue. The 2D IR spectra indicate that, relative to the Ca²⁺-bound form, lanthanide-bound CaM exhibits greater conformational flexibility and larger structural fluctuations within its binding sites. Time-dependent 2D IR lineshapes indicate that binding sites in Ca²⁺-CaM occupy well-defined configurations, whereas binding sites in lanthanide-bound-CaM are more disordered. Overall, the results show that binding to lanthanide ions significantly alters the conformation and dynamics of CaM's binding sites.

Paramagnetic NMR as a new tool in structural biology

NMR (nuclear magnetic resonance) investigation through the exploitation of paramagnetic effects is passing from an approach limited to few specialists in the field to a generally applicable method that must be considered, especially for the characterization of systems hardly affordable with other techniques. This is mostly due to the fact that paramagnetic data are long range in nature, thus providing information for the structural and dynamic characterization of complex biomolecular architectures in their native environment. On the other hand, this information usually needs to be complemented by data from other sources. Integration of paramagnetic NMR with other techniques, and the development of protocols for a joint analysis of all available data, is fundamental for achieving a comprehensive characterization of complex biological systems. We describe here a few examples of the new possibilities offered by paramagnetic data used in integrated structural approaches.

Long-range paramagnetic NMR data can provide a closer look on metal coordination in metalloproteins

Paramagnetic NMR data can be profitably incorporated in structural refinement protocols of metalloproteins or metal-substituted proteins, mostly as distance or angle restraints. However, they could in principle provide much more information, because the magnetic susceptibility of a paramagnetic metal ion is largely determined by its coordination sphere. This information can in turn be used to evaluate changes occurring in the coordination sphere of the metal when ligands (e.g.: inhibitors) are bound to the protein. This gives an experimental handle on the molecular structure in the vicinity of the metal which falls in the so-called blind sphere. The magnetic susceptibility anisotropy tensors of cobalt(II) and nickel(II) ions bound to human carbonic anhydrase II in free and inhibited forms have been determined. The change of the magnetic susceptibility anisotropy is directly linked to the binding mode of different ligands in the active site of the enzyme. Indication about the metal coordination sphere in the presence of an inhibitor in pharmaceutically relevant proteins could be important in the design of selective drugs with a structure-based approach.

Conformational landscape mapping the difference between N-lobes and C-lobes of calmodulin

Calmodulin is a calcium binding protein that consists of four EF-hand domains. The two EF-lobes of calmodulin, called the N-lobe and the C-lobe, arose from duplication and fusion of a precursor EF-hand. The amino acid sequences and the structures of the N-lobe and of the C-lobe are quite similar to each other. The N-lobe and the C-lobe, however, have subtle differences in structure and function. We analyzed the helix positions of calmodulin lobes by the alignment with the pseudo-two fold axis of the EF-lobe. We made a map of conformational landscape of helix positions. The four states of the EF-lobe appeared on two lines in the landscape; these two lines show the trajectory of opening and closing of the EF-lobe. For the N-lobe of calmodulin, the calcium bound form and the apo-forms are on the lower line. The two apo-forms of the C-lobe of calmodulin, with target and without target, are on the upper line. The calcium bound form of the C-lobe is on the lower line. The rearrangement of helix interaction between two the EF-hands is necessary for calcium binding in the C-lobe. The hydrophobic packing in the apo-form of the N-lobe is similar to the packing of the N- and C-lobes of the calcium bound form. However, the packing of C-lobe side chains in the apo-form is different from these other three structures. Our detailed analysis should serve as an example that can be applied to other proteins that undergo changes in conformation upon binding effectors.

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.

The structure and function of Mycobacterium tuberculosis MazF-mt6 toxin provide insights into conserved features of MazF endonucleases

Toxin-antitoxin systems are ubiquitous in prokaryotic and archaeal genomes and regulate growth in response to stress. Escherichia coli contains at least 36 putative toxin-antitoxin gene pairs, and some pathogens such as Mycobacterium tuberculosis have over 90 toxin-antitoxin operons. E. coli MazF cleaves free mRNA after encountering stress, and nine M. tuberculosis MazF family members cleave mRNA, tRNA, or rRNA. Moreover, M. tuberculosis MazF-mt6 cleaves 23S rRNA Helix 70 to inhibit protein synthesis. The overall tertiary folds of these MazFs are predicted to be similar, and therefore, it is unclear how they recognize structurally distinct RNAs. Here we report the 2.7-Å X-ray crystal structure of MazF-mt6. MazF-mt6 adopts a PemK-like fold but lacks an elongated β1-β2 linker, a region that typically acts as a gate to direct RNA or antitoxin binding. In the absence of an elongated β1-β2 linker, MazF-mt6 is unable to transition between open and closed states, suggesting that the regulation of RNA or antitoxin selection may be distinct from other canonical MazFs. Additionally, a shortened β1-β2 linker allows for the formation of a deep, solvent-accessible, active-site pocket, which may allow recognition of specific, structured RNAs like Helix 70. Structure-based mutagenesis and bacterial growth assays demonstrate that MazF-mt6 residues Asp-10, Arg-13, and Thr-36 are critical for RNase activity and likely catalyze the proton-relay mechanism for RNA cleavage. These results provide further critical insights into how MazF secondary structural elements adapt to recognize diverse RNA substrates.

Modeling Protein Excited-state Structures from "Over-length" Chemical Cross-links

Chemical cross-linking coupled with mass spectroscopy (CXMS) provides proximity information for the cross-linked residues and is used increasingly for modeling protein structures. However, experimentally identified cross-links are sometimes incompatible with the known structure of a protein, as the distance calculated between the cross-linked residues far exceeds the maximum length of the cross-linker. The discrepancies may persist even after eliminating potentially false cross-links and excluding intermolecular ones. Thus the "over-length" cross-links may arise from alternative excited-state conformation of the protein. Here we present a method and associated software DynaXL for visualizing the ensemble structures of multidomain proteins based on intramolecular cross-links identified by mass spectrometry with high confidence. Representing the cross-linkers and cross-linking reactions explicitly, we show that the protein excited-state structure can be modeled with as few as two over-length cross-links. We demonstrate the generality of our method with three systems: calmodulin, enzyme I, and glutamine-binding protein, and we show that these proteins alternate between different conformations for interacting with other proteins and ligands. Taken together, the over-length chemical cross-links contain valuable information about protein dynamics, and our findings here illustrate the relationship between dynamic domain movement and protein function.

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.

Improved Accuracy from Joint X-ray and NMR Refinement of a Protein-RNA Complex Structure

Integrated experimental approaches play an increasingly important role in structural biology, taking advantage of the complementary information provided by different techniques. In particular, the combination of NMR data with X-ray diffraction patterns may provide accurate and precise information about local conformations not available from average-resolution X-ray structures alone. Here, we refined the structure of a ternary protein-protein-RNA complex comprising three domains, Sxl and Unr, bound to a single-stranded region derived in the msl2 mRNA. The joint X-ray and NMR refinement reveals that-despite the poor quality of the fit found for the original structural model-the NMR data can be largely accommodated within the uncertainty in the atom positioning (structural noise) from the primary X-ray data and that the overall domain arrangements and binding interfaces are preserved on passing from the crystalline state to the solution. The refinement highlights local conformational differences, which provide additional information on specific features of the structure. For example, conformational dynamics and heterogeneity observed at the interface between the CSD1 and the Sxl protein components in the ternary complex are revealed by the combination of NMR and crystallographic data. The joint refinement protocol offers unique opportunities to detect structural differences arising from various experimental conditions and reveals static or dynamic differences in the conformation of the biomolecule between the solution and the crystals.

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.

Delicate conformational balance of the redox enzyme cytochrome P450cam

The energy landscapes of proteins are highly complex and can be influenced by changes in physical and chemical conditions under which the protein is studied. The redox enzyme cytochrome P450cam undergoes a multistep catalytic cycle wherein two electrons are transferred to the heme group and the enzyme visits several conformational states. Using paramagnetic NMR spectroscopy with a lanthanoid tag, we show that the enzyme bound to its redox partner, putidaredoxin, is in a closed state at ambient temperature in solution. This result contrasts with recent crystal structures of the complex, which suggest that the enzyme opens up when bound to its partner. The closed state supports a model of catalysis in which the substrate is locked in the active site pocket and the enzyme acts as an insulator for the reactive intermediates of the reaction.

FANTEN: a new web-based interface for the analysis of magnetic anisotropy-induced NMR data

Pseudocontact shifts (PCSs) and residual dipolar couplings (RDCs) arising from the presence of paramagnetic metal ions in proteins as well as RDCs due to partial orientation induced by external orienting media are nowadays routinely measured as a part of the NMR characterization of biologically relevant systems. PCSs and RDCs are becoming more and more popular as restraints (1) to determine and/or refine protein structures in solution, (2) to monitor the extent of conformational heterogeneity in systems composed of rigid domains which can reorient with respect to one another, and (3) to obtain structural information in protein-protein complexes. The use of both PCSs and RDCs proceeds through the determination of the anisotropy tensors which are at the origin of these NMR observables. A new user-friendly web tool, called FANTEN (Finding ANisotropy TENsors), has been developed for the determination of the anisotropy tensors related to PCSs and RDCs and has been made freely available through the WeNMR ( http://fanten-enmr.cerm.unifi.it:8080 ) gateway. The program has many new features not available in other existing programs, among which the possibility of a joint analysis of several sets of PCS and RDC data and the possibility to perform rigid body minimizations.

Insights into domain-domain motions in proteins and RNA from solution NMR

Many multidomain proteins and ribonucleic acids consist of domains that autonomously fold and that are linked together by flexible junctions. This architectural design allows domains to sample a wide range of positions with respect to one another, yet do so in a way that retains structural specificity, since the number of sampled conformations remains extremely small compared to the total conformations that would be sampled if the domains were connected by an infinitely long linker. This “tuned” flexibility in interdomain conformation is in turn used in many biochemical processes.

There is great interest in characterizing the dynamic properties of multidomain systems, and moving beyond conventional descriptions in terms of static structures, toward the characterization of population-weighted ensembles describing a distribution of many conformations sampled in solution. There is also great interest in understanding the design principles and underlying physical and chemical interactions that specify the nature of interdomain flexibility. NMR spectroscopy is one of the most powerful techniques for characterizing motions in complex biomolecules and has contributed greatly toward our basic understanding of dynamics in proteins and nucleic acids and its role in folding, recognition, and signaling.

Here, we review methods that have been developed in our laboratories to address these challenges. Our approaches are based on the ability of one domain of the molecule to self-align in a magnetic field, or to dominate the overall orientation of the molecule, so that the conformational freedom of other domains can be assessed by their degree of alignment induced by the aligned part. In turn, this self-alignment ability can be intrinsic or can be caused by tagging appropriate constructs to the molecule of interest. In general, self-alignment is due to magnetic susceptibility anisotropy. Nucleic acids with elongated helices have this feature, as well as several paramagnetic metal centers that can be found in, or attached to, a protein domain.