A partial differential equation for pseudocontact shift

It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density. The equation enables straightforward PCS prediction and analysis in systems with delocalized unpaired electrons, particularly for the nuclei located in their immediate vicinity. It is also shown that the probability density of the unpaired electron may be extracted, using a regularization procedure, from PCS data

Solution Structure of Oxidized Horse Heart Cytochrome c

The solution structure of oxidized horse heart cytochrome c was obtained at pH 7.0 in 100 mM phosphate buffer from 2278 NOEs and 241 pseudocontact shift constraints. The final structure was refined through restrained energy minimization. A 35-member family, with RMSD values with respect to the average structure of 0.70 ± 0.11 Å and 1.21 ± 0.14 Å for the backbone and all heavy atoms, respectively, and with an average penalty function of 130 ± 4.0 kJ/mol and 84 ± 3.7 kJ/mol for NOE and pseudocontact shift constraints, respectively (corresponding to a target function of 0.9 Å^2 and 0.2 Å^2), was obtained. The solution structure is somewhat different from that recently reported (Qi et al., 1996) and appears to be similar to the X-ray structure of the same oxidation state (Bushnell et al., 1990). A noticeable difference is a rotation of 17 ± 8° of the imidazole plane between solid and solution structure. Detailed and accurate structural determinations are important within the frame of the current debate of the structural rearrangements occurring upon oxidation or reduction. From the obtained magnetic susceptibility tensor a separation of the hyperfine shifts into their contact and pseudocontact contributions is derived and compared to that of the analogous isoenzyme from S. cerevisiae and to previous results

Dissecting the theories of lanthanide magnetic resonance

The NMR relaxation and chemical shift behaviour of isostructural series of macrocyclic lanthanide(III) complexes has been investigated. The 1H, 31P and 19F longitudinal relaxation rates of multiple series of lanthanide(III) complexes (Tb, Dy, Ho, Er, Tm, Yb) have been measured in solution at five magnetic field strengths in the range 4.7 to 16.5 Tesla. The electronic relaxation time, T1e, is a function of both the lanthanide(III) ion and the local ligand field. Analysis of the field-dependent nuclear relaxation rates, based on Solomon-Bloembergen Morgan theory, describing the paramagnetic enhancement of the nuclear relaxation rates, has allowed reliable estimates of the electronic relaxation times, T1e. It has been shown that in systems of high symmetry, the electronic relaxation times are directly proportional to the ligand field and that in some cases changing the ligand field can have a greater effect on the nuclear relaxation rates than lanthanide selection. The chemical shift data for the series of lanthanide(III) complexes were analysed. The pseudocontact shift of lanthanide(III) complexes is described by Bleaney’s theory of magnetic anisotropy. Most of the assumptions in this theory were shown to be questionable. In particular for systems in low symmetry significant deivations between the experimental chemical shifts and those predicted by theory were found. The low symmetry systems exhibit crystal field splittings of the same order of magnitude as the spin-orbit coupling. The possibility of a mixing of the electronic energy levels of the lanthanide(III) ion has to be considered. The effect of the coordination environment on the magnetic susceptibility was investigated using a variety of methods. Significant deviation (10 – 20%) from the theoretical values was observed in systems of low symmetry. These investigations show that paramagnetic relaxation enhancements and magnetic susceptibility are dependent on the ligand field. Applying this knowledge allows the design of more efficient paramagnetic probes, as needed in PARASHIFT magnetic resonance

Pseudocontact shifts from mobile spin labels

This paper presents a detailed analysis of the pseudocontact shift (PCS) field induced by a mobile spin label that is viewed as a probability density distribution with an associated effective magnetic susceptibility anisotropy. It is demonstrated that non-spherically symmetric density can lead to significant deviations from the commonly used point dipole approximation for the PCS. Analytical and numerical solutions are presented for the general partial differential equation that describes the non-point case. It is also demonstrated that it is possible, with some reasonable approximations, to reconstruct paramagnetic centre probability distributions from the experimental PCS data

Aggregation of Rare Earth Coordination Complexes in Solution Studied by Paramagnetic and DOSY NMR

The degree of aggregation of neutral, 9‐coordinate rare earth coordination complexes has been shown to affect their ligand field, as revealed by diffusion‐ordered NMR spectroscopy (DOSY‐NMR) measurements on Y(III) complexes, paramagnetic NMR analyses of Yb and Tb analogues and emission spectral studies with the EuIII systems. In non‐polar media a lipophilic tris‐isopropyl complex, [Ln.L2] tends to aggregate in chloroform and dichloromethane giving rise to oligomers, whereas in acetic and trifluoroacetic acid the more polar parent complex, [Ln.L1], also aggregates, profoundly affecting the pseudocontact shift and the form of the Eu emission spectrum. Such behaviour has important implications in the design of responsive spectral probes

Design and applications of lanthanide chelating tags for pseudocontact shift NMR spectroscopy with biomacromolecules

In this review, lanthanide chelating tags and their applications to pseudocontact shift NMR spectroscopy as well as analysis of residual dipolar couplings are covered. A complete overview is presented of DOTA-derived and non-DOTA-derived lanthanide chelating tags, critical points in the design of lanthanide chelating tags as appropriate linker moieties, their stability under reductive conditions, e.g., for in-cell applications, the magnitude of the anisotropy transferred from the lanthanide chelating tag to the biomacromolecule under investigation and structural properties, as well as conformational bias of the lanthanide chelating tags are discussed. Furthermore, all DOTA-derived lanthanide chelating tags used for PCS NMR spectroscopy published to date are displayed in tabular form, including their anisotropy parameters, with all employed lanthanide ions, C; B; -Ln distances and tagging reaction conditions, i.e., the stoichiometry of lanthanide chelating tags, pH, buffer composition, temperature and reaction time. Additionally, applications of lanthanide chelating tags for pseudocontact shifts and residual dipolar couplings that have been reported for proteins, protein-protein and protein-ligand complexes, carbohydrates, carbohydrate-protein complexes, nucleic acids and nucleic acid-protein complexes are presented and critically reviewed. The vast and impressive range of applications of lanthanide chelating tags to structural investigations of biomacromolecules in solution clearly illustrates the significance of this particular field of research. The extension of the repertoire of lanthanide chelating tags from proteins to nucleic acids holds great promise for the determination of valuable structural parameters and further developments in characterizing intermolecular interactions

Exquisite sensitivity of the ligand field to solvation and donor polarisability in coordinatively saturated lanthanide complexes

Crystallographic, emission and NMR studies of a series of C3-symmetric, nine-coordinate substituted pyridyl triazacyclononane Yb(III) and Eu(III) complexes reveal the impact of local solvation and ligand dipolar polarisability on ligand field strength, leading to dramatic variations in pseudocontact NMR shifts and emission spectral profiles, giving new guidance for responsive NMR and spectral probe design