Bleaney’s long-standing theory of magnetic anisotropy has been employed with some success for many decades to explain paramagnetic NMR pseudocontact shifts, and has been the subject of many subsequent approximations. Here, we present a detailed experimental and theoretical investigation accounting for the anomalous solvent dependence of NMR shifts for a series of lanthanide(III) complexes, namely [LnL1] (Ln = Eu, Tb, Dy, Ho, Er, Tm, and Yb; L1: 1,4,7-tris[(6-carboxypyridin-2-yl)methyl]-1,4,7-triazacyclononane), taking into account the effect of subtle ligand flexibility on the electronic structure. We show that the anisotropy of the room temperature magnetic susceptibility tensor, which in turn affects the sign and magnitude of the pseudocontact chemical shift, is extremely sensitive to minimal structural changes in the first coordination sphere of L1. We show that DFT structural optimizations do not give accurate structural models, as assessed by the experimental chemical shifts, and thus we determine a magnetostructural correlation and employ this to evaluate the accurate solution structure for each [LnL1]. This approach allows us to explain the counterintuitive pseudocontact shift behavior, as well as a striking solvent dependence. These results have important consequences for the analysis and design of novel magnetic resonance shift and optical emission probes that are sensitive to the local solution environment and polarity.

A significant problem with paramagnetic tags attached to proteins and nucleic acids is their conformational mobility. Each tag is statistically distributed within a volume between 5 and 10 Angstroms across; structural biology conclusions from NMR and EPR work are necessarily diluted by this uncertainty. The problem is solved in electron spin resonance, but remains open in the other major branch of paramagnetic resonance – pseudocontact shift (PCS) NMR spectroscopy, where structural biologists have so far been reluctantly using the point paramagnetic centre approximation. Here we describe a new method for extracting probability densities of lanthanide tags from PCS data. The method relies on Tikhonov-regularised 3D reconstruction and opens a new window into biomolecular structure and dynamics because it explores a very different range of conditions from those accessible to double electron resonance work on paramagnetic tags: a room-temperature solution rather than a glass at cryogenic temperatures. The method is illustrated using four different Tm3+ DOTA-M8 tagged mutants of human carbonic anhydrase II; the results are in good agreement with rotamer library and DEER data. The wealth of high-quality pseudocontact shift data accumulated by the biological magnetic resonance community over the last 30 years, and so far only processed using point models, could now become a major source of useful information on conformational distributions of paramagnetic tags in biomolecules.

AbstractA detailed analysis of paramagnetic NMR shifts in a series of isostructural lanthanide complexes relavant to PARASHIFT contrast agents reveals unexpected trends in the magnetic susceptibility anisotropy that cannot be explained by the commonly used Bleaney's theory. Ab initio calculations reveal that the primary assumption of Bleaney's theory—that thermal energy is larger than the ligand field splitting—does not hold for the lanthanide complexes in question, and likely for a large fraction of lanthanide complexes in general. This makes the orientation of the magnetic susceptibility tensor differ significantly between complexes of different lanthanides with the same ligand: one of the most popular assumptions about isostructural lanthanide series is wrong.

AbstractA detailed analysis of paramagnetic NMR shifts in a series of isostructural lanthanide complexes relavant to PARASHIFT contrast agents reveals unexpected trends in the magnetic susceptibility anisotropy that cannot be explained by the commonly used Bleaney's theory. Ab initio calculations reveal that the primary assumption of Bleaney's theory—that thermal energy is larger than the ligand field splitting—does not hold for the lanthanide complexes in question, and likely for a large fraction of lanthanide complexes in general. This makes the orientation of the magnetic susceptibility tensor differ significantly between complexes of different lanthanides with the same ligand: one of the most popular assumptions about isostructural lanthanide series is wrong.

Magnetic resonance spectroscopy and imaging experiments in which spatial dynamics (diffusion and flow) closely coexists with chemical and quantum dynamics (spin–spin couplings, exchange, cross-relaxation, etc.) have historically been very hard to simulate – Bloch–Torrey equations do not support complicated spin Hamiltonians, and the Liouville–von Neumann formalism does not support explicit spatial dynamics. In this paper, we formulate and implement a more advanced simulation framework based on the Fokker–Planck equation. The proposed methods can simulate, without significant approximations, any spatio-temporal magnetic resonance experiment, even in situations when spatial motion co-exists intimately with quantum spin dynamics, relaxation and chemical kinetics.

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.

•Liquid state 2D and 3D NMR spectra are simulated for 1000+ spin system of ubiquitin.•All simulations use time domain quantum mechanics in a restricted Liouville space.•Full Redfield relaxation superoperator, including cross-correlations, is computed and used.•Quantitative agreement with experimental data is demonstrated.Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling quantum mechanical simulation methods have not so far been available. In this communication we adapt the restricted state space approximation to protein NMR spectroscopy and illustrate its performance by simulating common 2D and 3D liquid state NMR experiments (including accurate description of relaxation processes using Bloch–Redfield–Wangsness theory) on isotopically enriched human ubiquitin – a protein containing over a thousand nuclear spins forming an irregular polycyclic three-dimensional coupling lattice. The algorithm uses careful tailoring of the density operator space to only include nuclear spin states that are populated to a significant extent. The reduced state space is generated by analysing spin connectivity and decoherence properties: rapidly relaxing states as well as correlations between topologically remote spins are dropped from the basis set.Graphical abstractDownload high-res image (357KB)Download full-size image

Magnetic resonance spectroscopy and imaging experiments in which spatial dynamics (diffusion and flow) closely coexists with chemical and quantum dynamics (spin–spin couplings, exchange, cross-relaxation, etc.) have historically been very hard to simulate – Bloch–Torrey equations do not support complicated spin Hamiltonians, and the Liouville–von Neumann formalism does not support explicit spatial dynamics. In this paper, we formulate and implement a more advanced simulation framework based on the Fokker–Planck equation. The proposed methods can simulate, without significant approximations, any spatio-temporal magnetic resonance experiment, even in situations when spatial motion co-exists intimately with quantum spin dynamics, relaxation and chemical kinetics.

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.