Rapid convergence of optimal control in NMR using numerically-constructed toggling frames

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.

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

The ability to measure nuclear magnetic resonance (NMR) spectra with a large sample volume is crucial for concentration-limited biological samples to attain adequate signal-to-noise (S/N) ratio. The possibility to measure with a 5-mm cryoprobe is currently absent at the 1.2-GHz NMR instruments due to the exceedingly high radio frequency power demands, which is four times compared to 600-MHz instruments. Here, we overcome the high-power demands by designing optimal control (OC) pulses with up to 20 times lower power requirements than currently necessary at a 1.2-GHz spectrometer. We show that multidimensional biomolecular NMR experiments constructed using these OC pulses can bestow improvement in the S/N ratio of up to 26%. With the expected power limitations of a 5-mm cryoprobe, we observe an enhancement in the S/N ratio of more than 240% using our OC sequences. This motivates the development of a cryoprobe with a larger volume than the current 3-mm cryoprobes.

Robust Strategy for Hit-to-Lead Discovery: NMR for SAR

Establishing robust structure-activity relationships (SARs) is key to successful drug discovery campaigns, yet it often remains elusive due to screening and hit validation artifacts (false positives and false negatives), which frequently result in unproductive downstream expenditures of time and resources. To address this issue, we developed an integrative biophysics-driven strategy that expedites hit-to-lead discovery, mitigates false positives/negatives and common hit validation errors, and provides a robust approach to obtaining accurate binding and affinity measurements. The advantage of this method is that it vastly improves the clarity and reproducibility for affinity-driven SAR by monitoring and eliminating confounding factors. We demonstrate the ease at which high-quality micromolar binders can be generated from the initial millimolar fragment screening hits against an "undruggable" protein target, HRas.

High-fidelity control of spin ensemble dynamics via artificial intelligence: from quantum computing to NMR spectroscopy and imaging

High-fidelity control of spin ensemble dynamics is essential for many research areas, spanning from quantum computing and radio-frequency (RF) engineering to NMR spectroscopy and imaging. However, attaining robust and high-fidelity spin operations remains an unmet challenge. Using an evolutionary algorithm and artificial intelligence (AI), we designed new RF pulses with customizable spatial or temporal field inhomogeneity compensation. Compared with the standard RF shapes, the new AI-generated pulses show superior performance for bandwidth, robustness, and tolerance to field imperfections. As a benchmark, we constructed a spin entanglement operator for the weakly coupled two-spin-1/2 system of ¹³CHCl₃, achieving high-fidelity transformations under multiple inhomogeneity sources. We then generated band-selective and ultra-broadband RF pulses typical of biomolecular NMR spectroscopy. When implemented in multipulse NMR experiments, the AI-generated pulses significantly increased the sensitivity of medium-size and large protein spectra relative to standard pulse sequences. Finally, we applied the new pulses to typical imaging experiments, showing a remarkable tolerance to changes in the RF field. These AI-generated RF pulses can be directly implemented in quantum information, NMR spectroscopy of biomolecules, magnetic resonance imaging techniques for in vivo and materials sciences.

Optimization of phase dispersion enables broadband excitation without homonuclear coupling artifacts

In NMR spectroscopy, many specialized shaped pulses are available for broadband excitation, beyond the bandwidth of conventional high-powered hard pulses. These shaped pulses typically have long duration. However, long-duration pulses are unsuitable for spectra containing significant homonuclear couplings, such as polyfluorinated compounds in 19F NMR. J-coupling evolution during the excitation pulse leads to spectral artifacts and incorrect peak integrals. Here, we report an approach to optimal control pulse design which significantly reduces the pulse length required to excite large bandwidths of chemical shift frequencies. The target state phase is not chosen beforehand but is instead only constrained to be linearly dependent on offset frequency. The first-order phase of the target state is then treated as a free-variable, to be optimized at the same time as the RF waveform itself. The resulting spectra are easily phased using standard NMR processing software. We observe that the required pulse length is significantly shorter than for currently available in-phase excitation schemes. Spectral artifacts from homonuclear couplings are avoided. We also demonstrate that pure in-phase excitation can be obtained over the same bandwidth by appending two inversion pulses, at the expense of increased overall duration.

Nearest-neighbor NMR spectroscopy: categorizing spectral peaks by their adjacent nuclei

Methyl-NMR enables atomic-resolution studies of structure and dynamics of large proteins in solution. However, resonance assignment remains challenging. The problem is to combine existing structural informational with sparse distance restraints and search for the most compatible assignment among the permutations. Prior classification of peaks as either from isoleucine, leucine, or valine reduces the search space by many orders of magnitude. However, this is hindered by overlapped leucine and valine frequencies. In contrast, the nearest-neighbor nuclei, coupled to the methyl carbons, resonate in distinct frequency bands. Here, we develop a framework to imprint additional information about passively coupled resonances onto the observed peaks. This depends on simultaneously orchestrating closely spaced bands of resonances along different magnetization trajectories, using principles from control theory. For methyl-NMR, the method is implemented as a modification to the standard fingerprint spectrum (the 2D-HMQC). The amino acid type is immediately apparent in the fingerprint spectrum. There is no additional relaxation loss or an increase in experimental time. The method is validated on biologically relevant proteins. The idea of generating new spectral information using passive, adjacent resonances is applicable to other contexts in NMR spectroscopy.

The precious fluorine on the ring: fluorine NMR for biological systems

The fluorine-19 nucleus was recognized early to harbor exceptional properties for NMR spectroscopy. With 100% natural abundance, a high gyromagnetic ratio (83% sensitivity compared to 1H), a chemical shift that is extremely sensitive to its surroundings and near total absence in biological systems, it was destined to become a favored NMR probe, decorating small and large molecules. However, after early excitement, where uptake of fluorinated aromatic amino acids was explored in a series of animal studies, 19F-NMR lost popularity, especially in large molecular weight systems, due to chemical shift anisotropy (CSA) induced line broadening at high magnetic fields. Recently, two orthogonal approaches, (i) CF3 labeling and (ii) aromatic 19F-13C labeling leveraging the TROSY (Transverse Relaxation Optimized Spectroscopy) effect have been successfully applied to study large biomolecular systems. In this perspective, we will discuss the fascinating early work with fluorinated aromatic amino acids, which reveals the enormous potential of these non-natural amino acids in biological NMR and the potential of 19F-NMR to characterize protein and nucleic acid structure, function and dynamics in the light of recent developments. Finally, we explore how fluorine NMR might be exploited to implement small molecule or fragment screens that resemble physiological conditions and discuss the opportunity to follow the fate of small molecules in living cells.

Comprehensive and High-Throughput Exploration of Chemical Space Using Broadband 19 F NMR-Based Screening

Fragment-based lead discovery has become a fundamental approach to identify ligands that efficiently interact with disease-relevant targets. Among the numerous screening techniques, fluorine-detected NMR has gained popularity owing to its high sensitivity, robustness, and ease of use. To effectively explore chemical space, a universal NMR experiment, a rationally designed fragment library, and a sample composition optimized for a maximal number of compounds and minimal measurement time are required. Here, we introduce a comprehensive method that enabled the efficient assembly of a high-quality and diverse library containing nearly 4000 fragments and screening for target-specific binders within days. At the core of the approach is a novel broadband relaxation-edited NMR experiment that covers the entire chemical shift range of drug-like ¹⁹ F motifs in a single measurement. Our approach facilitates the identification of diverse binders and the fast ligandability assessment of new targets.

Recent developments in the use of fluorine NMR in synthesis and characterisation

A review of developments in fluorine NMR of relevance to synthesis, characterisation and industrial applications of small organic molecules. Developments considered include those in spectrometer technology, computational methods and pulse sequences. The review of 80 references outlines applications in areas of identification, quantitation, mixture analysis, reaction monitoring, environmental studies and fragment-based drug design.

Optimal control theory enables homonuclear decoupling without Bloch-Siegert shifts in NMR spectroscopy

The Bloch-Siegert shift is a phenomenon in NMR spectroscopy and atomic physics in which the observed resonance frequency is changed by the presence of an off-resonance applied field. In NMR, it occurs especially in the context of homonuclear decoupling. Here we develop a practical method for homonuclear decoupling that avoids inducing Bloch-Siegert shifts. This approach enables accurate observation of the resonance frequencies of decoupled nuclear spins. We apply this method to increase the resolution of the HNCA experiment. We also observe a doubling in sensitivity for a 30 kDa protein. We demonstrate the use of band-selective Cβ decoupling to produce amino acid-specific line shapes, which are valuable for assigning resonances to the protein sequence. Finally, we assign the backbone of a 30 kDa protein, Human Carbonic Anhydrase II, using only HNCA experiments acquired with band-selective decoupling schemes, and instrument time of one week.