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

Machine Learning-Enhanced Quantum Chemistry-Assisted Refinement of the Active Site Structure of Metalloproteins

Understanding the fine structural details of inhibitor binding at the active site of metalloenzymes can have a profound impact on the rational drug design targeted to this broad class of biomolecules. Structural techniques such as NMR, cryo-EM, and X-ray crystallography can provide bond lengths and angles, but the uncertainties in these measurements can be as large as the range of values that have been observed for these quantities in all the published structures. This uncertainty is far too large to allow for reliable calculations at the quantum chemical (QC) levels for developing precise structure-activity relationships or for improving the energetic considerations in protein-inhibitor studies. Therefore, the need arises to rely upon computational methods to refine the active site structures well beyond the resolution obtained with routine application of structural methods. In a recent paper, we have shown that it is possible to refine the active site of cobalt(II)-substituted MMP12, a metalloprotein that is a relevant drug target, by matching to the experimental pseudocontact shifts (PCS) those calculated using multireference ab initio QC methods. The computational cost of this methodology becomes a significant bottleneck when the starting structure is not sufficiently close to the final one, which is often the case with biomolecular structures. To tackle this problem, we have developed an approach based on a neural network (NN) and a support vector regression (SVR) and applied it to the refinement of the active site structure of oxalate-inhibited human carbonic anhydrase 2 (hCAII), another prototypical metalloprotein target. The refined structure gives a remarkably good agreement between the QC-calculated and the experimental PCS. This study not only contributes to the knowledge of CAII but also demonstrates the utility of combining machine learning (ML) algorithms with QC calculations, offering a promising avenue for investigating other drug targets and complex biological systems in general.

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.

Elucidating the concentration-dependent effects of thiocyanate binding to carbonic anhydrase

Many proteins naturally carry metal centers, with a large share of them being in the active sites of several enzymes. Paramagnetic effects are a powerful source of structural information and, therefore, if the native metal is paramagnetic, or it can be functionally substituted with a paramagnetic one, paramagnetic effects can be used to study the metal sites, as well as the overall structure of the protein. One notable example is cobalt(II) substitution for zinc(II) in carbonic anhydrase. In this manuscript we investigate the effects of sodium thiocyanate on the chemical environment of the metal ion of the human carbonic anhydrase II. The electron paramagnetic resonance (EPR) titration of the cobalt(II) protein with thiocyanate shows that the EPR spectrum changes from A-type to C-type on passing from 1:1 to 1:1000-fold ligand excess. This indicates the occurrence of a change in the electronic structure, which may reflect a sizable change in the metal coordination environment in turn caused by a modification of the frozen solvent glass. However, paramagnetic nuclear magnetic resonance (NMR) data indicate that the metal coordination cage remains unperturbed even in 1:1000-fold ligand excess. This result proves that the C-type EPR spectrum observed at large ligand concentration should be ascribed to the low temperature at which EPR measurements are performed, which impacts on the structure of the protein when it is destabilized by a high concentration of a chaotropic agent.

Ligand-Capped Cobalt(II) Multiplies the Value of the Double-Histidine Motif for PCS NMR Studies

In structural studies by NMR, pseudocontact shifts (PCSs) provide both angular and distance information. For proteins, incorporation of a di-histidine (diHis) motif, coordinated to Co2+, has emerged as an important tool to measure PCS. Here, we show that using different Co(II)-chelating ligands, such as nitrilotriacetic acid (NTA) and iminodiacetic acid (IDA), resolves the isosurface ambiguity of Co2+-diHis and yields orthogonal PCS data sets with different Δχ-tensors for the same diHis-bearing protein. Importantly, such capping ligands effectively eliminate undesired intermolecular interactions, which can be detrimental to PCS studies. Devising and employing ligand-capping strategies afford versatile and powerful means to obtain multiple orthogonal PCS data sets, significantly extending the use of the diHis motif for structural studies by NMR.

Solid-state NMR methods for the characterization of bioconjugations and protein-material interactions

Protein solid-state NMR has evolved dramatically over the last two decades, with the development of new hardware and sample preparation methodologies. This technique is now ripe for complex applications, among which one can count bioconjugation, protein chemistry and functional biomaterials. In this review, we provide our account on this aspect of protein solid-state NMR.

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.

Theoretical analysis of the long-distance limit of NMR chemical shieldings

After some years of controversy, it was recently demonstrated how to obtain the correct long-distance limit [point-dipole approximation (PDA)] of pseudo-contact nuclear magnetic resonance chemical shifts from rigorous first-principles quantum mechanics [Lang et al., J. Phys. Chem. Lett. 11, 8735 (2020)]. This result confirmed the classical Kurland-McGarvey theory. In the present contribution, we elaborate on these results. In particular, we provide a detailed derivation of the PDA both from the Van den Heuvel-Soncini equation for the chemical shielding tensor and from a spin Hamiltonian approximation. Furthermore, we discuss in detail the PDA within the approximate density functional theory and Hartree-Fock theories. In our previous work, we assumed a relatively crude effective nuclear charge approximation for the spin-orbit coupling operator. Here, we overcome this assumption by demonstrating that the derivation is also possible within the fully relativistic Dirac equation and even without the assumption of a specific form for the Hamiltonian. Crucial ingredients for the general derivation are a Hamiltonian that respects gauge invariance, the multipolar gauge, and functional derivatives of the Hamiltonian, where it is possible to identify the first functional derivative with the electron number current density operator. The present work forms an important foundation for future extensions of the Kurland-McGarvey theory beyond the PDA, including induced magnetic quadrupole and higher moments to describe the magnetic hyperfine field.

Paramagnetic relaxation enhancement NMR as a tool to probe guest binding and exchange in metallohosts

Paramagnetic metallohost systems can bind guest molecules and find application as biomimetic catalysts. Due to the presence of the paramagnetic metal center, rigorous characterization of these systems by NMR spectroscopy can be very difficult. We report here that metallohost-guest systems can be studied by using the paramagnetic relaxation enhancement (PRE) effect. Manganese(III) porphyrin cage compounds are shown through their PRE to thread and bind viologen guests, including a polymeric one. The binding constants and dethreading activation parameters are lower than those of the metal-free porphyrin cage compounds, which is proposed to be a result of charge repulsion of the trivalent metal center and dicationic viologen guest. The threading rate of the manganese(III) porphyrin cage onto the polymer is more than 10 times faster than that of the non-metallated one, which is ascribed to initial binding of the cage to the polymer chain prior to threading, and to an entron effect.

Paramagnetic metallohost systems are difficult to characterize. Here the authors report that the paramagnetic relaxation enhancement effect can be used to prove by nuclear magnetic resonance experiments that Mn(III) porphyrin cage compounds can bind and thread low molecular weight and polymeric guests.

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.

Observability of Paramagnetic NMR Signals at over 10 000 ppm Chemical Shifts

We report an experimental observation of 31 P NMR resonances shifted by over 10 000 ppm (meaning percent range, and a new record for solutions), and similar 1 H chemical shifts, in an intermediate-spin square planar ferrous complex [tBu (PNP)Fe-H], where PNP is a carbazole-based pincer ligand. Using a combination of electronic structure theory, nuclear magnetic resonance, magnetometry, and terahertz electron paramagnetic resonance, the influence of magnetic anisotropy and zero-field splitting on the paramagnetic shift and relaxation enhancement is investigated. Detailed spin dynamics simulations indicate that, even with relatively slow electron spin relaxation (T1 ≈10-11  s), it remains possible to observe NMR signals of directly metal-bonded atoms because pronounced rhombicity in the electron zero-field splitting reduces nuclear paramagnetic relaxation enhancement.