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.

Conformational Analysis of 1,3-Difluorinated Alkanes.

Fluorine substitution can have a profound impact on molecular conformation. Here, we present a detailed conformational analysis of how the 1,3-difluoropropylene motif (-CHF-CH2-CHF-) determines the conformational profiles of 1,3-difluoropropane, anti- and syn-2,4-difluoropentane, and anti- and syn-3,5-difluoroheptane. It is shown that the 1,3-difluoropropylene motif strongly influences alkane chain conformation, with a significant dependence on the polarity of the medium. The conformational effect of 1,3-fluorination is magnified upon chain extension, which contrasts with vicinal difluorination. Experimental evidence was obtained from NMR analysis, where polynomial complexity scaling simulation algorithms were necessary to enable J-coupling extraction from the strong second-order spectra, particularly for the large 16-spin systems of the difluorinated heptanes. These results improve our understanding of the conformational control toolkit for aliphatic chains, yield simple rules for conformation population analysis, and demonstrate quantum mechanical time-domain NMR simulations for liquid state systems with large numbers of strongly coupled spins.

Neural network interpretation using descrambler groups.

The lack of interpretability and trust is a much-criticized feature of deep neural networks. In fully connected nets, the signaling between inner layers is scrambled because backpropagation training does not require perceptrons to be arranged in any particular order. The result is a black box; this problem is particularly severe in scientific computing and digital signal processing (DSP), where neural nets perform abstract mathematical transformations that do not reduce to features or concepts. We present here a group-theoretical procedure that attempts to bring inner-layer signaling into a human-readable form, the assumption being that this form exists and has identifiable and quantifiable features-for example, smoothness or locality. We applied the proposed method to DEERNet (a DSP network used in electron spin resonance) and managed to descramble it. We found considerable internal sophistication: the network spontaneously invents a bandpass filter, a notch filter, a frequency axis rescaling transformation, frequency-division multiplexing, group embedding, spectral filtering regularization, and a map from harmonic functions into Chebyshev polynomials-in 10 min of unattended training from a random initial guess.

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.

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 Jex of the order of the electron Larmor frequency ωE. Numerical and analytical calculations show that in such Jex ≈ ±ωE 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 ß 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Separating the coherence transfer from chemical shift evolution in high-resolution pure shift COSY NMR.

Recent developments in data sampling and processing techniques have made it possible to acquire 2-dimensional NMR spectra of small molecules at digital resolutions in both dimensions approaching the intrinsic limitations of the equipment and sample on a realistic timescale. These developments offer the possibility of enormously increased effective resolution (peak dispersion) and the ability to effectively study samples where peak overlap was previously a limiting factor. Examples of such spectra have been produced for a number of 2-dimensional techniques including TOCSY and HSQC. In this paper, we investigate some of the problems in applying such techniques to COSY spectra and suggest a modification to the classic experiment that alleviates some of these problems.

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.

Rationalization of Anomalous Pseudocontact Shifts and Their Solvent Dependence in a Series of C3-Symmetric Lanthanide Complexes.

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.

Heterometallic Zn3 Ln3 Ensembles Containing (µ6 -CO3 ) Ligand and Triangular Disposition of Ln3+ ions: Analysis of Single-Molecule Toroic (SMT) and Single-Molecule Magnet (SMM) Behavior.

Two new heterometallic Zn3 Ln3 (Ln3+ =Dy, Tb) complexes, with a double triangular topology of the metal ions, have been assembled from the polytopic Mannich base ligand 6,6'-{[2-(dimethylamino)ethylazanediyl]bis(methylene)}bis(2-methoxy-4-methylphenol) (H2 L) with the aid of an in situ generated carbonate ligand from atmospheric CO2 fixation. Theoretical calculations indicate axial ground states for the Ln3+ ions in these complexes, with their local magnetic moments being almost coplanar and tangential to the Ln3+ atoms that define the equilateral triangle. Therefore, they can be considered as single-molecule toroics (SMTs) with almost zero total magnetic moment. Micro-SQUID measurements on the Dy3+ counterpart show hysteresis loops below 3 K that have an S-shape, with large coercive fields opening upon cooling. This behavior is typical of a single molecule magnet (SMM) with very slow zero-field relaxation. At around ±0.35 T, the loops have a broad step, which is due to a direct relaxation process and corresponds to an acceleration of the relaxation of the magnetization, also observed at this magnetic field from ac susceptibility measurements. Simulations suggest that the broad step corresponds to two level avoidance of crossing points where the spin chiral Kramers doublet meets excited states of the coupled manifold, whose position is defined by exchange and dipole interactions. The Tb3+ counterpart does not exhibit SMM behavior, which is due to the fact that the degeneracy of the ground state of the exchange coupled system is lifted at zero field, thus favoring quantum tunneling of magnetization (QTM).

PARASHIFT Probes: Solution NMR and X-ray Structural Studies of Macrocyclic Ytterbium and Yttrium Complexes.

Ytterbium and yttrium complexes of octadentate ligands based on 1,4,7,10-tetraazacyclododecane with a coordinated pyridyl group and either tricarboxylate (L1) or triphosphinate (L2) donors form twisted-square-antiprismatic structures. The former crystallizes in the centrosymmetric group P21/c, with the two molecules related by an inversion center, whereas the latter was found as an unusual kryptoracemate in the chiral space group P21. Pure shift NMR and EXSY spectroscopy allowed the dynamic exchange between the (RRR)-Δ-(δδδδ) and (RRR)-Λ-(λλλλ) TSAP diastereomers of the [Y.L2] complex to be detected. The rate-limiting step in the exchange between Δ and Λ isomers involves cooperative ligand arm rotation, which is much faster for [Ln.L1] than for [Ln.L2]. Detailed analysis of NOESY, COSY, HSQC, and HMBC spectra confirms that the major conformer in solution is (RRR)-Λ-(λλλλ), consistent with crystal structure analysis and DFT calculations. The magnetic susceptibility tensors for [Yb.L1] and [Yb.L2], obtained from a full pseudocontact chemical shift analysis, are very different, in agreement with a CASSCF calculation. The remarkably different pseudocontact shift behavior is explained by the change in the orientation of the pseudocontact shift field, as defined by the Euler angles of the susceptibility tensor.