Optimal control pulses for the 1.2-GHz (28.2-T) NMR spectrometers

Instrumental distortions in quantum optimal control

Quantum optimal control methods, such as gradient ascent pulse engineering (GRAPE), are used for precise manipulation of quantum states. Many of those methods were pioneered in magnetic resonance spectroscopy, where instrumental distortions are often negligible. However, that is not the case elsewhere: the usual jumble of cables, resonators, modulators, splitters, amplifiers, and filters can and would distort control signals. Those distortions may be non-linear; their inverse functions may be ill-defined and unstable; they may even vary from one day to the next and across the sample. Here we introduce the response-aware gradient ascent pulse engineering framework, which accounts for any cascade of differentiable distortions within the GRAPE optimization loop, does not require filter function inversion, and produces control sequences that are resilient to user-specified distortion cascades with user-specified parameter ensembles. The framework is implemented into the optimal control module supplied with versions 2.10 and later of the open-source Spinach library; the user needs to provide function handles returning the actions by the distortions and, optionally, parameter ensembles for those actions.

Optimized 13C Relaxation-Filtered Nuclear Magnetic Resonance: Harnessing Optimal Control Pulses and Ultra-High Magnetic Fields for Metalloprotein Structural Elucidation

Ultra-high magnetic fields and high-sensitivity cryoprobes permit the achievement of a high S/N ratio in 13C detection experiments, thus making a 13C superWEFT (Super water eliminated Fourier transform) experiment feasible. 13C signals that are not visible using 1H observed heteronuclear experiments, nor with established 2D 13C direct detection experiments, become easily observable when a 13C relaxation-based filter is used. Within this frame, optimal control pulses (OC pulses) have been, for the first time, applied to paramagnetic systems. Although the duration of OC pulses competes with relaxation, their application to paramagnetic signals has been successfully tested. OC pulses are much more efficient with respect to the phase- and amplitude-modulated ones routinely used at lower fields while providing bandwidth excitation profiles that are sufficient to meet the need to cover up to an 80 ppm spectral region. On the other hand, when paramagnetic relaxation is shorter than the duration of OC pulses, the use of hard, rectangular pulses is, at the present state of the art, the best approach to minimize the loss of signal intensity.

WPR-Net: A Deep Learning Protocol for Highly Accelerated NMR Spectroscopy with Faithful Weak Peak Reconstruction

Multidimensional NMR spectroscopy contains a large amount of molecular-level species and structure information, which is of great significance in various disciplines; however, it is unfortunately limited by lengthy acquisition times. Undersampling signals accompanied by spectral reconstruction provide a powerful and efficient way to accelerate its implementation. However, the accurate reconstruction of weak peaks remains a crucial issue to compromise the reconstruction performance. In this work, we introduce a deep learning architecture for highly accelerated NMR spectroscopy along with the reliable reconstruction of weak peaks. This deep learning protocol allows one to eliminate undersampled artifacts and reconstruct high-quality multidimensional NMR spectroscopy signals, even under the conditions of highly sparse sampling density or in the presence of severe noise. Therefore, this study provides a powerful tool for fast multidimensional NMR spectroscopy and presents meaningful application prospects toward broader chemical and biological applications.

Optimal control-based nuclear spin cross-polarization in the presence of complicating anisotropic interactions

Cross-polarization is an indispensable part of solid state nuclear magnetic resonance spectroscopy to enhance sensitivity and extract structural information. However, the presence of certain anisotropic interactions, including chemical shift anisotropy and quadrupolar coupling, makes the inter-nuclear spin correlation experiments challenging. This impedes characterization of numerous materials and pharmaceutical compounds containing isotopes, such as 19F with large chemical shift anisotropy and 6/7Li, 23Na, 27Al, etc., with quadrupolar coupling. To address this problem, we introduce a new optimal control simulation-generated pulse sequence for Optimal Polarization Transfer In the presence of Anisotropic Nuclear Spin interactions (OPTIANS). Numerical simulations show high efficiency and robustness against experimental imperfections under a broad range of anisotropic interaction strengths for 19F-7Li, 19F-23Na, 19F-27Al, and 19F-13C polarization transfers. The polarization transfer curves show transient oscillations, which make the pulse sequence a quantitative method for dipolar coupling measurements. Experiments on a multi-metal fluoride system validate the predictions of the simulations by showing efficient PT in three spin pairs at varying experimental conditions. Remarkably, this method shows 50% better 19F-7Li PT efficiency at 14.1 T compared to the ramped cross-polarization experiment. The underlying polarization transfer mechanism is analyzed using the Fourier transform of the polarization transfer curves revealing that this optimal control method utilizes the chemical shift anisotropy and quadrupolar coupling to facilitate robust and efficient cross-polarization.

Optimal control: From sensitivity improvement to alternative pulse-sequence design in solid-state NMR

Exciting developments in new experimental methods for multidimensional solid-state NMR spectroscopy have recently been achieved using optimal-control theory. These results, in turn, have triggered the development of new pulse sequences based on traditional analytical theories. This trend article summarises the key steps leading to these advancements. It also describes additional applications of optimal control beyond structural biology and envisions similar progress in the NMR of solid materials. Despite attractive features of optimal-control pulse sequences demonstrated in the proof-of-concept studies, their experimental utilization remains sparse, probably due to the lack of awareness among experimentalists. We hope this mini-review helps to spread optimal-control methods into routine experimental workflows. Furthermore, we offer a personal outlook on how numerical optimisations could in general enhance the experimental capabilities of solid-state NMR in the near future, with optimal control serving as a pioneer exploring new possibilities.

Deep learning enabled ultra-high quality NMR chemical shift resolved spectra

High quality chemical shift resolved spectra have long been pursued in nuclear magnetic resonance (NMR). In order to obtain chemical shift information with high resolution and sensitivity, a neural network named spin echo to obtain chemical shifts network (SE2CSNet) is developed to process the NMR data acquired by the spin echo pulse sequence. Through detecting the change of phase in the spin echo spectra, SE2CSNet can accurately detect the chemical shift position of spectral signals. The results show that the network can discern the chemical shift even when spectral signals overlap, but without strong coupling and chunking artifacts. In addition, this method can process the sample with low S/N (signal to noise ratio), and recover weak signals even hidden in noise, leading to ultra-high quality chemical shift resolved spectra. It is envisioned that the proposed methodology will find wide applications in many fields.

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.

Sensitivity-enhanced NMR 15N R1 and R1ρ relaxation experiments for the investigation of intrinsically disordered proteins at high magnetic fields

NMR relaxation experiments provide residue-specific insights into the structural dynamics of proteins. Here, we present an optimized set of sensitivity-enhanced 15N R1 and R1ρ relaxation experiments applicable to fully protonated proteins. The NMR pulse sequences are conceptually similar to the set of TROSY-based sequences and their HSQC counterpart (Lakomek et al., J. Biomol. NMR 2012). Instead of the TROSY read-out scheme, a sensitivity-enhanced HSQC read-out scheme is used, with improved and easier optimized water suppression. The presented pulse sequences are applied on the cytoplasmic domain of the SNARE protein Synpatobrevin-2 (Syb-2), which is intrinsically disordered in its monomeric pre-fusion state. A two-fold increase in the obtained signal-to-noise ratio is observed for this intrinsically disordered protein, therefore offering a four-fold reduction of measurement time compared to the TROSY-detected version. The inter-scan recovery delay can be shortened to two seconds. Pulse sequences were tested at 600 MHz and 1200 MHz 1H Larmor frequency, thus applicable over a wide magnetic field range. A comparison between protonated and deuterated protein samples reveals high agreement, indicating that reliable 15N R1 and R1ρ rate constants can be extracted for fully protonated and deuterated samples. The presented pulse sequences will benefit not only for IDPs but also for an entire range of low and medium-sized proteins.