Periodic trends and hidden dynamics of magnetic properties in three series of triazacyclononane lanthanide complexes

In three structurally related series of nine-coordinate lanthanide(iii) complexes, solution NMR studies and DFT/CASSCF calculations have provided key information on the magnetic susceptibility anisotropy.

14N overtone NMR under MAS: Signal enhancement using cross-polarization methods

Polarization transfer methods are widely adopted for the purpose of correlating different nuclear species as well as to achieve signal enhancement. Polarization transfer from ¹H to the ¹⁴N overtone transition (Δm = 2) can be achieved using cross polarization methods under magic-angle spinning conditions, where spin locks of the order of several milliseconds can be obtained on common bio-solids (α-glycine and N-acetylvaline). Signal enhancement factors up to 4.4 per scan, can be achieved under favorable conditions, despite MHz-sized quadrupolar interaction. Moreover, we present a detailed theoretical treatment and accurate numerical simulations which are in excellent agreement the unusual experimental matching conditions observed for cross-polarization to ¹⁴N overtone.

Feedback control optimisation of ESR experiments

Numerically optimised microwave pulses are used to increase excitation efficiency and modulation depth in electron spin resonance experiments performed on a spectrometer equipped with an arbitrary waveform generator. The optimisation procedure is sample-specific and reminiscent of the magnet shimming process used in the early days of nuclear magnetic resonance - an objective function (for example, echo integral in a spin echo experiment) is defined and optimised numerically as a function of the pulse waveform vector using noise-resilient gradient-free methods. We found that the resulting shaped microwave pulses achieve higher excitation bandwidth and better echo modulation depth than the pulse shapes used as the initial guess. Although the method is theoretically less sophisticated than simulation based quantum optimal control techniques, it has the advantage of being free of the linear response approximation; rapid electron spin relaxation also means that the optimisation takes only a few seconds. This makes the procedure fast, convenient, and easy to use. An important application of this method is at the final stage of the implementation of theoretically designed pulse shapes: compensation of pulse distortions introduced by the instrument. The performance is illustrated using spin echo and out-of-phase electron spin echo envelope modulation experiments. Interface code between Bruker SpinJet arbitrary waveform generator and Matlab is included in versions 2.2 and later of the Spinach library.

Transmembrane Exchange of Fluorosugars: Characterization of Red Cell GLUT1 Kinetics Using 19F NMR

We have developed a new approach, to our knowledge, to quantify the equilibrium exchange kinetics of carrier-mediated transmembrane transport of fluorinated substrates. The method is based on adapted kinetic theory that describes the concentration dependence of the transmembrane exchange rates of two competing, simultaneously transported species. Using the new approach, we quantified the kinetics of membrane transport of both anomers of three monofluorinated glucose analogs in human erythrocytes (red blood cells) using ¹⁹F NMR exchange spectroscopy. An inosine-based glucose-free medium was shown to promote survival and stable metabolism of red blood cells over the duration of the experiments (several hours). Earlier NMR studies only yielded the apparent rate constants and transmembrane fluxes of the anomeric species, whereas we could categorize the two anomers in terms of the catalytic activity (specificity constants) of the glucose transport protein GLUT1 toward them. Differences in the membrane permeability of the three glucose analogs were qualitatively interpreted in terms of local perturbations in the bonding of substrates to key amino acid residues in the active site of GLUT1. The methodology of this work will be applicable to studies of other carrier-mediated membrane transport processes, especially those with competition between simultaneously transported species. The GLUT1-specific results can be applied to the design of probes of glucose transport or inhibitors of glucose metabolism in cells, including those exhibiting the Warburg effect.

Deep neural network processing of DEER data

The established model-free methods for the processing of two-electron dipolar spectroscopy data [DEER (double electron-electron resonance), PELDOR (pulsed electron double resonance), DQ-EPR (double-quantum electron paramagnetic resonance), RIDME (relaxation-induced dipolar modulation enhancement), etc.] use regularized fitting. In this communication, we describe an attempt to process DEER data using artificial neural networks trained on large databases of simulated data. Accuracy and reliability of neural network outputs from real experimental data were found to be unexpectedly high. The networks are also able to reject exchange interactions and to return a measure of uncertainty in the resulting distance distributions. This paper describes the design of the training databases, discusses the training process, and rationalizes the observed performance. Neural networks produced in this work are incorporated as options into Spinach and DeerAnalysis packages.

Lanthanide-induced relaxation anisotropy

Lanthanide ions accelerate nuclear spin relaxation by two primary mechanisms: dipolar and Curie. Both are commonly assumed to depend on the length of the lanthanide-nucleus vector, but not on its direction. Here we show experimentally that this is wrong - careful proton relaxation data analysis in a series of isostructural lanthanide complexes (Ln = Tb, Dy, Ho, Er, Tm, Yb) reveals angular dependence in both Curie and dipolar relaxation. The reasons are: (a) that magnetic susceptibility anisotropy can be of the same order of magnitude as the isotropic part (contradicting the unstated assumption in Guéron's theory of the Curie relaxation process), and (b) that zero-field splitting can be much stronger than the electron Zeeman interaction (Bloembergen's original theory of the lanthanide-induced dipolar relaxation process makes the opposite assumption). These factors go beyond the well researched cross-correlation effects; they alter the relaxation theory treatment and make strong angular dependencies appear in the nuclear spin relaxation rates. Those dependencies are impossible to ignore - this is now demonstrated both theoretically and experimentally, and suggests that a major revision is needed of the way lanthanide-induced relaxation data are used in structural biology.

Measuring Spin Relaxation Rates Using Satellite Exchange NMR Spectroscopy

An approach to the indirect measurement of nuclear spin relaxation rates of low-magnetogyric ratio (γ) nuclei using the process of satellite exchange is described. The method does not require the observation of, or even the ability to provide radio-frequency pulses to, the low-γ nucleus, but requires this to be scalar coupled to an NMR observable nucleus, such as ³¹ P or ¹ H, making it especially attractive for the study of diamagnetic transition metals. In situations where spin relaxation is dominated by chemical shift anisotropy (CSA), the determination of the longitudinal spin relaxation time constant (T₁ ) of the metal becomes possible, as illustrated for ¹⁹⁵ Pt and ^107/109 Ag.

Indirect detection of 10B (I = 3) overtone NMR at very fast magic angle spinning

The application of overtone nuclear magnetic resonance (OT NMR) to symmetric spin transitions of integer quadrupolar nuclei is of considerable interest since this transition is immune to the first-order quadrupolar interaction, thus resulting in narrow NMR lines. Owing to its roles in nature and its high natural abundance, ¹⁴N (I = 1) OT NMR has been explored, in which the indirect and/or direct acquisitions of ¹⁴N OT were experimentally demonstrated. However, other than ¹⁴N nucleus, no OT NMR observation of other integer quadrupolar nuclei has been reported in the literature. In this work, we extend the application of OT NMR to another integer quadrupolar nucleus, namely ¹⁰B (I = 3). However, this is not straightforward owing to the unfavorable characteristics of ¹⁰B isotope. Here, for the first time, we present the selective acquisition of ¹⁰B central (-1 ↔ +1) OT NMR via detection of ¹H nuclei on perborate monohydrate sample. Numerical calculations are in a good agreement with the experimental results. Both show that the optimal sensitivity is achieved when the carrier frequency is applied at the second OT spinning sideband, i.e. an offset of twice of the spinning frequency from the center band.

1H line width dependence on MAS speed in solid state NMR - Comparison of experiment and simulation

Recent developments in magic angle spinning (MAS) technology permit spinning frequencies of ≥100 kHz. We examine the effect of such fast MAS rates upon nuclear magnetic resonance proton line widths in the multi-spin system of β-Asp-Ala crystal. We perform powder pattern simulations employing Fokker-Plank approach with periodic boundary conditions and ¹H-chemical shift tensors calculated using the bond polarization theory. The theoretical predictions mirror well the experimental results. Both approaches demonstrate that homogeneous broadening has a linear-quadratic dependency on the inverse of the MAS spinning frequency and that, at the faster end of the spinning frequencies, the residual spectral line broadening becomes dominated by chemical shift distributions and susceptibility effects even for crystalline systems.

Large-scale NMR simulations in liquid state: A tutorial

Liquid state nuclear magnetic resonance is the only class of magnetic resonance experiments for which the simulation problem is solved comprehensively for spin systems of any size. This paper contains a practical walkthrough for one of the many available simulation packages - Spinach. Its unique feature is polynomial complexity scaling: the ability to simulate large spin systems quantum mechanically and with accurate account of relaxation, diffusion, chemical processes, and hydrodynamics. This paper is a gentle introduction written with a PhD student in mind.

Minimising conformational bias in fluoroprolines through vicinal difluorination

Monofluorination at the proline 4-position results in conformational effects, which is exploited for a range of applications. However, this conformational distortion is a hindrance when the natural proline conformation is important. Here we introduce (3S,4R)-3,4-difluoroproline, in which the individual fluorine atoms instil opposite conformational effects, as a suitable probe for fluorine NMR studies.

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.

Model-free extraction of spin label position distributions from pseudocontact shift data

Not a point, but a cloud: advanced PCS data analysis using 3D probability density reconstruction provides more information.

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.

Spatially encoded 2D and 3D diffusion-ordered NMR spectroscopy

The separation of 2D spectra of components in mixtures is accelerated with spatial encoding.

Measurement of 14N quadrupole couplings in biomolecular solids using indirect-detection 14N solid-state NMR with DNP

Insights into protein structure through the determination of ¹⁴N quadrupolar interactions using magic-angle spinning dynamic nuclear polarization NMR.

Efficient simulation of ultrafast magnetic resonance experiments

We present a convenient and powerful simulation formalism for ultrafast NMR spectroscopy. The formalism is based on the Fokker–Planck equation that supports systems with complicated combinations of classical spatial dynamics and quantum mechanical spin dynamics.

Quantifying the exchange coupling in linear copper porphyrin oligomers

The unique combination of EPR, DFT and novel large-scale simulation methods provides information on exchange coupling between metal centers in molecular wires.

Using Paramagnetism to Slow Down Nuclear Relaxation in Protein NMR

Paramagnetic metal ions accelerate nuclear spin relaxation; this effect is widely used for distance measurement and called paramagnetic relaxation enhancement (PRE). Theoretical predictions established that, under special circumstances, it is also possible to achieve a reduction in nuclear relaxation rates (negative PRE). This situation would occur if the mechanism of nuclear relaxation in the diamagnetic state is counterbalanced by a paramagnetic relaxation mechanism caused by the metal ion. Here we report the first experimental evidence for such a cross-correlation effect. Using a uniformly ¹⁵N-labeled mutant of calbindin D_9k loaded with either Tm³⁺ or Tb³⁺, reduced R₁ and R₂ relaxation rates of backbone ¹⁵N spins were observed compared with the diamagnetic reference (the same protein loaded with Y³⁺). The effect arises from the compensation of the chemical shift anisotropy tensor by the anisotropic dipolar shielding generated by the unpaired electron spin.