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.

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 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.

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.

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.

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.

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.

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.

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.

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 19F 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 19F relaxation properties, and we exploit the latter in elucidating binding kinetics to the SH3 (Src homology 3) domain.

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 Cγ-Cδ 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 Cß and Cα 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.