Quantitative Analysis of 2D EXSY NMR Spectra of Strongly Coupled Spin Systems in Transmembrane Exchange

Solute translocation by membrane transport proteins is a vital biological process that can be tracked, on the sub-second timescale, using nuclear magnetic resonance (NMR). Fluorinated substrate analogues facilitate such studies because of high sensitivity of 19 F NMR and absence of background signals. Accurate extraction of translocation rate constants requires precise quantification of NMR signal intensities. This becomes complicated in the presence of J-couplings, cross-correlations, and nuclear Overhauser effects (NOE) that alter signal integrals through mechanisms unrelated to translocation. Geminal difluorinated motifs introduce strong and hard-to-quantify contributions from non-exchange effects, the nuanced nature of which makes them hard to integrate into data analysis methodologies. With analytical expressions not being available, numerical least squares fitting of theoretical models to 2D spectra emerges as the preferred quantification approach. For large spin systems with simultaneous coherent evolution, cross-relaxation, cross-correlation, conformational exchange, and membrane translocation between compartments with different viscosities, the only available simulation framework is Spinach. In this study, we demonstrate GLUT-1 dependent membrane transport of two model sugars featuring CF2 and CF2 CF2 fluorination motifs, with precise determination of translocation rate constants enabled by numerical fitting of 2D EXSY spectra. For spin systems and kinetic networks of this complexity, this was not previously tractable.

Simulation and design of shaped pulses beyond the piecewise-constant approximation

Response functions of resonant circuits create ringing artefacts if their input changes rapidly. When physical limits of electromagnetic spectroscopies are explored, this creates two types of problems. Firstly, simulation: the system must be propagated accurately through every response transient, this may be computationally expensive. Secondly, optimal control: circuit response must be taken into account; it may be advantageous to design pulses that are resilient to such distortions. At the root of both problems is the popular piecewise-constant approximation for control sequences in the rotating frame; in magnetic resonance it has persisted since the earliest days and has become entrenched in the commercially available hardware. In this paper, we report an implementation and benchmarks of recent Lie-group methods that can efficiently simulate and optimise smooth control sequences.

Toroidal optical transitions in hydrogen-like atoms

It is commonly believed that electromagnetic spectra of atoms and molecules can be fully described by interactions involving electric and magnetic multipoles. However, it has recently become clear that interactions between light and matter also involve toroidal multipoles-toroidal absorption lines have been observed in electromagnetic metamaterials. Here, we show that a previously unexplored type of spectroscopy of the hitherto largely neglected toroidal dipolar interaction becomes feasible if, apart from the classical r × r × p toroidal dipole density term responsible for the toroidal transitions in metamaterials, the spin-dependent r × σ term (which only occurs in relativistic quantum mechanics) is taken into account. Toroidal dipole operators are odd under parity and time-reversal symmetries; toroidal dipole transitions can therefore be distinguished from electric multipole and magnetic dipole transitions.

The ABC transporter MsbA adopts the wide inward-open conformation in E. coli cells

Membrane proteins are currently investigated after detergent extraction from native cellular membranes and reconstitution into artificial liposomes or nanodiscs, thereby removing them from their physiological environment. However, to truly understand the biophysical properties of membrane proteins in a physiological environment, they must be investigated within living cells. Here, we used a spin-labeled nanobody to interrogate the conformational cycle of the ABC transporter MsbA by double electron-electron resonance. Unexpectedly, the wide inward-open conformation of MsbA, commonly considered a nonphysiological state, was found to be prominently populated in Escherichia coli cells. Molecular dynamics simulations revealed that extensive lateral portal opening is essential to provide access of its large natural substrate core lipid A to the binding cavity. Our work paves the way to investigate the conformational landscape of membrane proteins in cells.

Neural networks in pulsed dipolar spectroscopy: A practical guide

This is a methodological guide to the use of deep neural networks in the processing of pulsed dipolar spectroscopy (PDS) data encountered in structural biology, organic photovoltaics, photosynthesis research, and other domains featuring long-lived radical pairs and paramagnetic metal ions. PDS uses distance dependence of magnetic dipolar interactions; measuring a single well-defined distance is straightforward, but extracting distance distributions is a hard and mathematically ill-posed problem requiring careful regularisation and background fitting. Neural networks do this exceptionally well, but their "robust black box" reputation hides the complexity of their design and training - particularly when the training dataset is effectively infinite. The objective of this paper is to give insight into training against simulated databases, to discuss network architecture choices, to describe options for handling DEER (double electron-electron resonance) and RIDME (relaxation-induced dipolar modulation enhancement) experiments, and to provide a practical data processing flowchart.

J-Driven dynamic nuclear polarization for sensitizing high field solution state NMR

Dynamic nuclear polarization (DNP) is widely used to enhance solid state nuclear magnetic resonance (NMR) sensitivity. Its efficiency as a generic signal-enhancing approach for liquid state NMR, however, decays rapidly with magnetic field B₀, unless mediated by scalar interactions arising only in exceptional cases. This has prevented a more widespread use of DNP in structural and dynamical solution NMR analyses. This study introduces a potential solution to this problem, relying on biradicals with exchange couplings J_ex of the order of the electron Larmor frequency ω_E. Numerical and analytical calculations show that in such J_ex ≈ ±ω_E cases a phenomenon akin to that occurring in chemically induced DNP (CIDNP) happens, leading to different relaxation rates for the biradical singlet and triplet states which are hyperfine-coupled to the nuclear α or β states. Microwave irradiation can then generate a transient nuclear polarization build-up with high efficiency, at all magnetic fields that are relevant in contemporary NMR, and for all rotational diffusion correlation times that occur in small- and medium-sized molecules in conventional solvents.

Heteronuclear transfers from labile protons in biomolecular NMR: Cross polarization, revisited

INEPT- and HMQC-based pulse sequences are widely used to transfer polarization between heteronuclei, particularly in biomolecular spectroscopy: they are easy to setup and involve low power deposition. Still, these short-pulse polarization transfers schemes are challenged by fast solvent chemical exchange. An alternative to improve these heteronuclear transfers is J-driven cross polarization (J-CP), which transfers polarization by spin-locking the coupled spins under Hartmann-Hahn conditions. J-CP provides certain immunity against chemical exchange and other T₂-like relaxation effects, a behavior that is here examined in depth by both Liouville-space numerical and analytical derivations describing the transfer efficiency. While superior to INEPT-based transfers, fast exchange may also slow down these J-CP transfers, hurting their efficiency. This study therefore explores the potential of repeated projective operations to improve ¹H→¹⁵N and ¹H→¹⁵N→¹³C J-CP transfers in the presence of fast solvent chemical exchanges. It is found that while repeating J-CP provides little ¹H→¹⁵N transfer advantages over a prolonged CP, multiple contacts that keep both the water and the labile protons effectively spin-locked can improve ¹H→¹⁵N→¹³C transfers in the presence of chemical exchange. The ensuing Looped, Concatenated Cross Polarization (L-CCP) compensates for single J-CP losses by relying on the ¹³C's longer lifetimes, leading to a kind of "algorithmic cooling" that can provide high polarization for the ¹⁵N as well as carbonyl and alpha ¹³Cs. This can facilitate certain experiments, as demonstrated with triple resonance experiments on intrinsically disordered proteins involving labile, chemically exchanging protons.

Optimal control gradient precision trade-offs: Application to fast generation of DeepControl libraries for MRI

We have recently demonstrated supervised deep learning methods for rapid generation of radiofrequency pulses in magnetic resonance imaging (https://doi.org/10.1002/mrm.27740, https://doi.org/10.1002/mrm.28667). Unlike the previous iterative optimization approaches, deep learning methods generate a pulse using a fixed number of floating-point operations - this is important in MRI, where patient-specific pulses preferably must be produced in real time. However, deep learning requires vast training libraries, which must be generated using the traditional methods, e.g., iterative quantum optimal control methods. Those methods are usually variations of gradient descent, and the calculation of the gradient of the performance metric with respect to the pulse waveform can be the most numerically intensive step. In this communication, we explore various ways in which the calculation of gradients in quantum optimal control theory may be accelerated. Four optimization avenues are explored: truncated commutator series expansions at zeroth and first order, a novel midpoint truncation scheme at first order, and the exact complex-step method. For the spin systems relevant to MRI, the first-order midpoint truncation is found to be sufficiently accurate, but also significantly faster than the machine precision gradient. This makes the generation of training databases for the machine learning methods considerably more realistic.

Fluorine NMR study of proline-rich sequences using fluoroprolines

Proline homopolymer motifs are found in many proteins; their peculiar conformational and dynamic properties are often directly involved in those proteins' functions. However, the dynamics of proline homopolymers is hard to study by NMR due to a lack of amide protons and small chemical shift dispersion. Exploiting the spectroscopic properties of fluorinated prolines opens interesting perspectives to address these issues. Fluorinated prolines are already widely used in protein structure engineering - they introduce conformational and dynamical biases - but their use as 19 F NMR reporters of proline conformation has not yet been explored. In this work, we look at model peptides where Cγ -fluorinated prolines with opposite configurations of the chiral Cγ centre have been introduced at two positions in distinct polyproline segments. By looking at the effects of swapping these (4R )-fluoroproline and (4S )-fluoroproline within the polyproline segments, we were able to separate the intrinsic conformational properties of the polyproline sequence from the conformational alterations instilled by fluorination. We assess the fluoroproline 19 F relaxation properties, and we exploit the latter in elucidating binding kinetics to the SH3 (Src homology 3) domain.

Benchmark Test and Guidelines for DEER/PELDOR Experiments on Nitroxide-Labeled Biomolecules

Distance distribution information obtained by pulsed dipolar EPR spectroscopy provides an important contribution to many studies in structural biology. Increasingly, such information is used in integrative structural modeling, where it delivers unique restraints on the width of conformational ensembles. In order to ensure reliability of the structural models and of biological conclusions, we herein define quality standards for sample preparation and characterization, for measurements of distributed dipole-dipole couplings between paramagnetic labels, for conversion of the primary time-domain data into distance distributions, for interpreting these distributions, and for reporting results. These guidelines are substantiated by a multi-laboratory benchmark study and by analysis of data sets with known distance distribution ground truth. The study and the guidelines focus on proteins labeled with nitroxides and on double electron-electron resonance (DEER aka PELDOR) measurements and provide suggestions on how to proceed analogously in other cases.

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.

High-field solution state DNP using cross-correlations

At the magnetic fields of common NMR instruments, electron Zeeman frequencies are too high for efficient electron-nuclear dipolar cross-relaxation to occur in solution. The rate of that process fades with the electron Zeeman frequency as ω^-2 - in the absence of isotropic hyperfine couplings, liquid state dynamic nuclear polarisation (DNP) in high-field magnets is therefore impractical. However, contact coupling and dipolar cross-relaxation are not the only mechanisms that can move electron magnetisation to nuclei in liquids: multiple cross-correlated (CC) relaxation processes also exist, involving various combinations of interaction tensor anisotropies. The rates of some of those processes have more favourable high-field behaviour than dipolar cross-relaxation, but due to the difficulty of their numerical - and particularly analytical - treatment, they remain largely uncharted. In this communication, we report analytical evaluation of every rotationally driven relaxation process in liquid state for 1e1n and 2e1n spin systems, as well as numerical optimisations of the steady-state DNP with respect to spin Hamiltonian parameters. A previously unreported cross-correlated DNP (CCDNP) mechanism was identified for the 2e1n system, involving multiple relaxation interference effects and inter-electron exchange coupling. Using simulations, we found realistic spin Hamiltonian parameters that yield stronger nuclear polarisation at high magnetic fields than dipolar cross-relaxation.

Using molecular dynamics trajectories to predict nuclear spin relaxation behaviour in large spin systems

Molecular dynamics (MD) trajectories provide useful insights into molecular structure and dynamics. However, questions persist about the quantitative accuracy of those insights. Experimental NMR spin relaxation rates can be used as tests, but only if relaxation superoperators can be efficiently computed from MD trajectories - no mean feat for the quantum Liouville space formalism where matrix dimensions quadruple with each added spin 1/2. Here we report a module for the Spinach software framework that computes Bloch-Redfield-Wangsness relaxation superoperators (including non-secular terms and cross-correlations) from MD trajectories. Predicted initial slopes of nuclear Overhauser effects for sucrose trajectories using advanced water models and a force field optimised for glycans are within 25% of experimental values.

Strategies for 1 H-Detected Dynamic Nuclear Polarization Magic-Angle Spinning NMR Spectroscopy

Combining dynamic nuclear polarization with proton detection significantly enhances the sensitivity of magic-angle spinning NMR spectroscopy. Herein, the feasibility of proton-detected experiments with slow (10 kHz) magic angle spinning was demonstrated. The improvement in sensitivity permits the acquisition of indirectly detected 14 N NMR spectra allowing biomolecular structures to be characterized without recourse to isotope labelling. This provides a new tool for the structural characterization of environmental and medical samples, in which isotope labelling is frequently intractable.

How the Ligand Field in Lanthanide Coordination Complexes Determines Magnetic Susceptibility Anisotropy, Paramagnetic NMR Shift, and Relaxation Behavior

Complexes of lanthanide(III) ions are being actively studied because of their unique ground and excited state properties and the associated optical and magnetic behavior. In particular, they are used as emissive probes in optical spectroscopy and microscopy and as contrast agents in magnetic resonance imaging (MRI). However, the design of new complexes with specific optical and magnetic properties requires a thorough understanding of the correlation between molecular structure and electric and magnetic susceptibilities, as well as their anisotropies. The traditional Judd-Ofelt-Mason theory has failed to offer useful guidelines for systematic design of emissive lanthanide optical probes. Similarly, Bleaney's theory of magnetic anisotropy and its modifications fail to provide accurate detail that permits new paramagnetic shift reagents to be designed rather than discovered.A key determinant of optical and magnetic behavior in f-element compounds is the ligand field, often considered as an electrostatic field at the lanthanide created by the ligands. The resulting energy level splitting is a sensitive function of several factors: the nature and polarizability of the whole ligand and its donor atoms; the geometric details of the coordination polyhedron; the presence and extent of solvent interactions; specific hydrogen bonding effects on donor atoms and the degree of supramolecular order in the system. The relative importance of these factors can vary widely for different lanthanide ions and ligands. For nuclear magnetic properties, it is both the ligand field splitting and the magnetic susceptibility tensor, notably its anisotropy, that determine paramagnetic shifts and nuclear relaxation enhancement.We review the factors that control the ligand field in lanthanide complexes and link these to aspects of their utility in magnetic resonance and optical emission spectroscopy and imaging. We examine recent progress in this area particularly in the theory of paramagnetic chemical shift and relaxation enhancement, where some long-neglected effects of zero-field splitting, magnetic susceptibility anisotropy, and spatial distribution of lanthanide tags have been accommodated in an elegant way.

Coherence transfer delay optimisation in PSYCOSY experiments

PSYCOSY is an f1 broadband homonuclear decoupled version of the COSY nuclear magnetic resonance pulse sequence. Here, we investigate by a combination of experimental measurements, spatially distributed spin dynamics simulations, and analytical predictions the coherence evolution delay necessary in PSYCOSY experiments to ensure intensity discrimination in favour of the correlations typically arising from short range (ⁿ J, n ≤ 3) ¹ H-¹ H couplings and show that, in general, a coherence evolution delay of around 35 ms is optimum.

Combining Molecular and Spin Dynamics Simulations with Solid-State NMR: A Case Study of Amphiphilic Lysine-Leucine Repeat Peptide Aggregates

Interpreting dynamics in solid-state molecular systems requires characterization of the potentially heterogeneous environmental contexts of molecules. In particular, the analysis of solid-state nuclear magnetic resonance (ssNMR) data to elucidate molecular dynamics (MD) involves modeling the restriction to overall tumbling by neighbors, as well as the concentrations of water and buffer. In this exploration of the factors that influence motion, we utilize atomistic MD trajectories of peptide aggregates with varying hydration to mimic an amorphous solid-state environment and predict ssNMR relaxation rates. We also account for spin diffusion in multiply spin-labeled (up to 19 nuclei) residues, with several models of dipolar-coupling networks. The framework serves as a general approach to determine essential spin couplings affecting relaxation, benchmark MD force fields, and reveal the hydration dependence of dynamics in a crowded environment. We demonstrate the methodology on a previously characterized amphiphilic 14-residue lysine-leucine repeat peptide, LKα14 (Ac-LKKLLKLLKKLLKL-c), which has an α-helical secondary structure and putatively forms leucine-burying tetramers in the solid state. We measure the R₁ relaxation rates of uniformly ¹³C-labeled and site-specific ²H-labeled leucines in the hydrophobic core of LKα14 at multiple hydration levels. Studies of 9 and 18 tetramer bundles reveal the following: (a) for the incoherent component of ¹³C relaxation, the nearest-neighbor spin interactions dominate, while the ¹H-¹H interactions have minimal impact; (b) the AMBER ff14SB dihedral barriers for the leucine C_γ-C_δ bond ("methyl rotation barriers") must be lowered by a factor of 0.7 to better match the ²H data; (c) proton-driven spin diffusion explains some of the discrepancy between experimental and simulated rates for the C_β and C_α nuclei; and (d) ¹³C relaxation rates are mostly underestimated in the MD simulations at all hydrations, and the discrepancies identify likely motions missing in the 50 ns MD trajectories.

Defeating the Matrix

These are personal recollections and musings, written for the 50th Anniversary of the Journal of Magnetic Resonance. They are distilled from twenty years of writing simulation code, and filtered through hindsight and sarcastic intransigence. To me, the biggest recent achievements of the magnetic resonance community in the field of theory and simulation have been the successful war on the exponential scaling, the powerful and general simulation software, and the return to elegant notation. It appears that our future will be defined by computers. Three aspects are pertinent: simulation as the experiment is designed, optimal control as the experiment proceeds, and machine learning at the data processing stage.

Quantum mechanical MRI simulations: Solving the matrix dimension problem

We propose a solution to the matrix dimension problem in quantum mechanical simulations of MRI (magnetic resonance imaging) experiments on complex molecules. This problem is very old; it arises when Kronecker products of spin operators and spatial dynamics generators are taken-the resulting matrices are far too large for any current or future computer. However, spin and spatial operators individually have manageable dimensions, and we note here that the action by their Kronecker products on any vector may be computed without opening those products. This eliminates large matrices from the simulation process. MRI simulations for coupled spin systems of complex metabolites in three dimensions with diffusion, flow, chemical kinetics, and quantum mechanical treatment of spin relaxation are now possible. The methods described in this paper are implemented in versions 2.4 and later of the Spinach library.

Aromatic 19F-13C TROSY: a background-free approach to probe biomolecular structure, function, and dynamics

Atomic-level information about the structure and dynamics of biomolecules is critical for an understanding of their function. Nuclear magnetic resonance (NMR) spectroscopy provides unique insights into the dynamic nature of biomolecules and their interactions, capturing transient conformers and their features. However, relaxation-induced line broadening and signal overlap make it challenging to apply NMR spectroscopy to large biological systems. Here we took advantage of the high sensitivity and broad chemical shift range of 19F nuclei and leveraged the remarkable relaxation properties of the aromatic 19F-13C spin pair to disperse 19F resonances in a two-dimensional transverse relaxation-optimized spectroscopy spectrum. We demonstrate the application of 19F-13C transverse relaxation-optimized spectroscopy to investigate proteins and nucleic acids. This experiment expands the scope of 19F NMR in the study of the structure, dynamics, and function of large and complex biological systems and provides a powerful background-free NMR probe.

Quantitative analysis of 14N quadrupolar coupling using 1H detected 14N solid-state NMR

Magic-angle spinning solid-state NMR is increasingly utilized to study the naturally abundant, spin-1 nucleus 14N, providing insights into the structure and dynamics of biological and organic molecules. In particular, the characterisation of 14N sites using indirect detection has proven useful for complex molecules, where the 'spy' nucleus provides enhanced sensitivity and resolution. Here we exploit the sensitivity of proton detection, to indirectly characterise 14N sites using a moderate rf field to generate coherence between the 1H and 14N at moderate and fast-magic-angle spinning frequencies. Efficient numerical simulations have been developed that have allowed us to quantitatively analyse the resulting 14N lineshapes to determine both the size and asymmetry of the quadrupolar interaction. Exploiting only naturally occurring abundant isotopes will aid the analysis of materials with the need to resort to isotope labelling, whilst providing additional insights into the structure and dynamics that the characterisation of the quadrupolar interaction affords.

Synthesis and Conformational Properties of 3,4-Difluoro-l-prolines

Fluorinated proline derivatives have found diverse applications in areas ranging from medicinal chemistry over structural biochemistry to organocatalysis. Depending on the stereochemistry of monofluorination at the proline 3- or 4-position, different effects on the conformational properties of proline (ring pucker, cis/ trans isomerization) are introduced. With fluorination at both 3- and 4-positions, matching or mismatching effects can occur depending on the relative stereochemistry. Here we report, in full, the syntheses and conformational properties of three out of the four possible 3,4-difluoro-l-proline diastereoisomers. The yet unreported conformational properties are described for (3 S,4 S)- and (3 R,4 R)-difluoro-l-proline, which are shown to bias ring pucker and cis/ trans ratios on the same order of magnitude as their respective monofluorinated progenitors, although with significantly faster amide cis/ trans isomerization rates. The reported analogues thus expand the scope of available fluorinated proline analogues as tools to tailor proline's distinct conformational and dynamical properties, allowing for the interrogation of its role in, for instance, protein stability or folding.

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.

Fokker-Planck formalism in magnetic resonance simulations

This paper presents an overview of the Fokker-Planck formalism for non-biological magnetic resonance simulations, describes its existing applications and proposes some novel ones. The most attractive feature of Fokker-Planck theory compared to the commonly used Liouville - von Neumann equation is that, for all relevant types of spatial dynamics (spinning, diffusion, stationary flow, etc.), the corresponding Fokker-Planck Hamiltonian is time-independent. Many difficult NMR, EPR and MRI simulation problems (multiple rotation NMR, ultrafast NMR, gradient-based zero-quantum filters, diffusion and flow NMR, off-resonance soft microwave pulses in EPR, spin-spin coupling effects in MRI, etc.) are simplified significantly in Fokker-Planck space. The paper also summarises the author's experiences with writing and using the corresponding modules of the Spinach library - the methods described below have enabled a large variety of simulations previously considered too complicated for routine practical use.