Resolution enhancement in NMR spectra by deconvolution with compressed sensing reconstruction

Elimination of homogeneous broadening in 1H solid-state NMR

1H solid-state NMR spectra are plagued by low resolution, necessitating the use of complex pulse sequences or specialized equipment. We introduce a new resolution enhancement method, inspired by super-resolution microscopy, that uses a 2D Hahn-echo experiment to constrain deconvolution. The result is an effective doubling of the MAS frequency.

Post-acquisition correction of NMR spectra distorted by dynamic and static field inhomogeneity of cryogen-free magnets

Post-acquisition correction of NMR spectra is an important part of NMR spectroscopy that enables refined NMR spectra to be obtained, clean from undesirable out-phasing, broadening and noising. We describe analytical and numerical mathematical methods for post-acquisition correction of NMR spectra distorted by static and dynamic magnetic field inhomogeneity caused by imperfections of main superconducting coils and the cold head operation, typical for cryogen-free magnets. For the dynamic inhomogeneity, we apply a variant of the general reference deconvolution method, complemented with our mathematical analysis of spectral parameters. For the static inhomogeneity, we apply the method of a delayed Fourier transform, also supported with our analytical calculations. We verify our approach by correction processing of high-field experimental liquid-state 1H NMR spectra of water and ethanol as well as solid-state 13C MAS NMR spectra of adamantane and obtain good results for both static and dynamic field distortions. This work complements our previous work on instrumental suppression of dynamic distortions caused by the cold head operation. The results presented contribute well to the general field of processing NMR spectra and serve towards a more extensive use of cryogen-free magnets in high-resolution NMR spectroscopy.

Extent of N-Terminus Folding of Semenogelin 1 Cleavage Product Determines Tendency to Amyloid Formation

It is known that four peptide fragments of predominant protein in human semen Semenogelin 1 (SEM1) (SEM1(86-107), SEM1(68-107), SEM1(49-107) and SEM1(45-107)) are involved in fertilization and amyloid formation processes. In this work, the structure and dynamic behavior of SEM1(45-107) and SEM1(49-107) peptides and their N-domains were described. According to ThT fluorescence spectroscopy data, it was shown that the amyloid formation of SEM1(45-107) starts immediately after purification, which is not observed for SEM1(49-107). Seeing that the peptide amino acid sequence of SEM1(45-107) differs from SEM1(49-107) only by the presence of four additional amino acid residues in the N domain, these domains of both peptides were obtained via solid-phase synthesis and the difference in their dynamics and structure was investigated. SEM1(45-67) and SEM1(49-67) showed no principal difference in dynamic behavior in water solution. Furthermore, we obtained mostly disordered structures of SEM1(45-67) and SEM1(49-67). However, SEM1(45-67) contains a helix (E58-K60) and helix-like (S49-Q51) fragments. These helical fragments may rearrange into β-strands during amyloid formation process. Thus, the difference in full-length peptides' (SEM1(45-107) and SEM1(49-107)) amyloid-forming behavior may be explained by the presence of a structured helix at the SEM1(45-107) N-terminus, which contributes to an increased rate of amyloid formation.

Resolution enhancement of NMR by decoupling with the low-rank Hankel model

Nuclear magnetic resonance (NMR) spectroscopy has become a formidable tool for biochemistry and medicine. Although J-coupling carries essential structural information it may also limit the spectral resolution. Homonuclear decoupling remains a challenging problem. In this work, we introduce a new approach that uses a specific coupling value as prior knowledge, and the Hankel property of the exponential NMR signal to achieve broadband heteronuclear decoupling using the low-rank method. Our results on synthetic and realistic HMQC spectra demonstrate that the proposed method not only effectively enhances resolution by decoupling, but also maintains sensitivity and suppresses spectral artefacts. The approach can be combined with non-uniform sampling, which means that the resolution can be further improved without any extra acquisition time.

NMR spectrum reconstruction as a pattern recognition problem

A new deep neural network based on the WaveNet architecture (WNN) is presented, which is designed to grasp specific patterns in the NMR spectra. When trained at a fixed non-uniform sampling (NUS) schedule, the WNN benefits from pattern recognition of the corresponding point spread function (PSF) pattern produced by each spectral peak resulting in the highest quality and robust reconstruction of the NUS spectra as demonstrated in simulations and exemplified in this work on 2D ¹H-¹⁵N correlation spectra of three representative globular proteins with different sizes: Ubiquitin (8.6 kDa), Azurin (14 kDa), and Malt1 (44 kDa). The pattern recognition by WNN is also demonstrated for successful virtual homo-decoupling in a 2D methyl ¹H-¹³C - HMQC spectrum of MALT1. We demonstrate using WNN that prior knowledge about the NUS schedule, which so far was not been fully exploited, can be used for designing new powerful NMR processing techniques that surpass the existing algorithmic methods.

Conformational ensemble of amyloid-forming semenogelin 1 peptide SEM1(68-107) by NMR spectroscopy and MD simulations

SEM1(68-107) is a peptide corresponding to the region of semenogelin 1 protein from 68 to 107 amino acid position. SEM1(68-107) is an abundant component of semen, which participates in HIV infection enhanced by amyloid fibrils forming. To understand the causes influencing amyloid fibril formation, it is necessary to determine the spatial structure of SEM1(68-107). It was shown that the determination of SEM1(68-107) structure is complicated by the non-informative NMR spectra due to the high intramolecular mobility of peptides. The complementary approach based on the geometric restrictions of individual peptide fragments and molecular modeling was used for the determination of the spatial structure of SEM1(68-107). The N- (SEM1(68-85)) and C-terminuses (SEM1(86-107)) of SEM1(68-107) were chosen as two individual peptide fragments. SEM1(68-85) and SEM1(86-107) structures were established with NMR and circular dichroism CD spectroscopies. These regions were used as geometric restraints for the SEM1(68-107) structure modeling. Even though most of the SEM1(68-107) peptide is unstructured, our detailed analysis revealed the following structured elements: N-terminus (70His-84Gln) forms an α-helix, (86Asp-94Thr) and (101Gly-103Ser) regions fold into 3₁₀-helixes. The absence of a SEM1(68-107) rigid conformation leads to instability of these secondary structure regions. The calculated SEM1(68-107) structure is in good agreement with experimental values of hydrodynamic radius and dihedral angles obtained by NMR spectroscopy. This testifies the adequacy of a combined approach based on the use of peptide fragment structures for the molecular modeling formation of full-size peptide spatial structure.

Assignment of IVL-Methyl side chain of the ligand-free monomeric human MALT1 paracaspase-IgL3 domain in solution

Mucosa-associated lymphoid tissue protein 1 (MALT1) plays a key role in adaptive immune responses by modulating specific intracellular signalling pathways that control the development and proliferation of both T and B cells. Dysfunction of these pathways is coupled to the progress of highly aggressive lymphoma as well as to potential development of an array of different immune disorders. In contrast to other signalling mediators, MALT1 is not only activated through the formation of the CBM complex together with the proteins CARMA1 and Bcl10, but also by acting as a protease that cleaves multiple substrates to promote lymphocyte proliferation and survival via the NF-κB signalling pathway. Herein, we present the partial ¹H, ¹³C Ile/Val/Leu-Methyl resonance assignment of the monomeric apo form of the paracaspase-IgL₃ domain of human MALT1. Our results provide a solid ground for future elucidation of both the three-dimensional structure and the dynamics of MALT1, key for adequate development of inhibitors, and a thorough molecular understanding of its function(s).

1H, 13C and 15N resonance assignment of backbone and IVL-methyl side chain of the S135A mutant NS3pro/NS2B protein of Dengue II virus reveals unique secondary structure features in solution

The serotype II Dengue (DENV 2) virus is the most prevalent of all four known serotypes. Herein, we present nearly complete ¹H, ¹⁵N, and ¹³C backbone and ¹H, ¹³C isoleucine, valine, and leucine methyl resonance assignment of the apo S135A catalytically inactive variant of the DENV 2 protease enzyme folded as a tandem formed between the serine protease domain NS3pro and the cofactor NS2B, as well as the secondary structure prediction of this complex based on the assigned chemical shifts using the TALOS-N software. Our results provide a solid ground for future elucidation of the structure and dynamic of the apo NS3pro/NS2B complex, key for adequate development of inhibitors, and a thorough molecular understanding of their function(s).

Clustered sparsity and Poisson-gap sampling

Non-uniform sampling (NUS) is a popular way of reducing the amount of time taken by multidimensional NMR experiments. Among the various non-uniform sampling schemes that exist, the Poisson-gap (PG) schedules are particularly popular, especially when combined with compressed-sensing (CS) reconstruction of missing data points. However, the use of PG is based mainly on practical experience and has not, as yet, been explained in terms of CS theory. Moreover, an apparent contradiction exists between the reported effectiveness of PG and CS theory, which states that a "flat" pseudo-random generator is the best way to generate sampling schedules in order to reconstruct sparse spectra. In this paper we explain how, and in what situations, PG reveals its superior features in NMR spectroscopy. We support our theoretical considerations with simulations and analyses of experimental data from the Biological Magnetic Resonance Bank (BMRB). Our analyses reveal a previously unnoticed feature of many NMR spectra that explains the success of "blue-noise" schedules, such as PG. We call this feature "clustered sparsity". This refers to the fact that the peaks in NMR spectra are not just sparse but often form clusters in the indirect dimension, and PG is particularly suited to deal with such situations. Additionally, we discuss why denser sampling in the initial and final parts of the clustered signal may be useful.

FID-Net: A versatile deep neural network architecture for NMR spectral reconstruction and virtual decoupling

In recent years, the transformative potential of deep neural networks (DNNs) for analysing and interpreting NMR data has clearly been recognised. However, most applications of DNNs in NMR to date either struggle to outperform existing methodologies or are limited in scope to a narrow range of data that closely resemble the data that the network was trained on. These limitations have prevented a widescale uptake of DNNs in NMR. Addressing this, we introduce FID-Net, a deep neural network architecture inspired by WaveNet, for performing analyses on time domain NMR data. We first demonstrate the effectiveness of this architecture in reconstructing non-uniformly sampled (NUS) biomolecular NMR spectra. It is shown that a single network is able to reconstruct a diverse range of 2D NUS spectra that have been obtained with arbitrary sampling schedules, with a range of sweep widths, and a variety of other acquisition parameters. The performance of the trained FID-Net in this case exceeds or matches existing methods currently used for the reconstruction of NUS NMR spectra. Secondly, we present a network based on the FID-Net architecture that can efficiently virtually decouple ¹³C_α-¹³C_β couplings in HNCA protein NMR spectra in a single shot analysis, while at the same time leaving glycine residues unmodulated. The ability for these DNNs to work effectively in a wide range of scenarios, without retraining, paves the way for their widespread usage in analysing NMR data.