Measurement of protein backbone 13CO and 15N relaxation dispersion at high resolution

Beyond traditional magnetic resonance processing with artificial intelligence

Smart signal processing approaches using Artificial Intelligence are gaining momentum in NMR applications. In this study, we demonstrate that AI offers new opportunities beyond tasks addressed by traditional techniques. We developed and trained artificial neural networks to solve three problems that until now were deemed "impossible": quadrature detection using only Echo (or Anti-Echo) modulation from the traditional Echo/Anti-Echo scheme; accessing uncertainty of signal intensity at each point in a spectrum processed by any given method; and defining a reference-free score for quantitative access of NMR spectrum quality. Our findings highlight the potential of AI techniques to revolutionize NMR processing and analysis.

Rapid measurement of heteronuclear transverse relaxation rates using non-uniformly sampled R1ρ accordion experiments

Multidimensional, heteronuclear NMR relaxation methods are used extensively to characterize the dynamics of biological macromolecules. Acquisition of relaxation datasets on proteins typically requires significant measurement time, often several days. Accordion spectroscopy offers a powerful means to shorten relaxation rate measurements by encoding the "relaxation dimension" into the indirect evolution period in multidimensional experiments. Time savings can also be achieved by non-uniform sampling (NUS) of multidimensional NMR data, which is used increasingly to improve spectral resolution or increase sensitivity per unit time. However, NUS is not commonly implemented in relaxation experiments, because most reconstruction algorithms are inherently nonlinear, leading to problems when estimating signal intensities, relaxation rate constants and their error bounds. We have previously shown how to avoid these shortcomings by combining accordion spectroscopy with NUS, followed by data reconstruction using sparse exponential mode analysis, thereby achieving a dramatic decrease in the total length of longitudinal relaxation experiments. Here, we present the corresponding transverse relaxation experiment, taking into account the special considerations required for its successful implementation in the framework of the accordion-NUS approach. We attain the highest possible precision in the relaxation rate constants by optimizing the NUS scheme with respect to the Cramér-Rao lower bound of the variance of the estimated parameter, given the total number of sampling points and the spectrum-specific signal characteristics. The resulting accordion-NUS R 1 ρ relaxation experiment achieves comparable precision in the parameter estimates compared to conventional CPMG (Carr-Purcell-Meiboom-Gill) R 2 or spin-lock R 1 ρ experiments while saving an order of magnitude in experiment time.

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.

15N CPMG Relaxation Dispersion for the Investigation of Protein Conformational Dynamics on the µs-ms Timescale

Protein conformational dynamics play fundamental roles in regulation of enzymatic catalysis, ligand binding, allostery, and signaling, which are important biological processes. Understanding how the balance between structure and dynamics governs biological function is a new frontier in modern structural biology and has ignited several technical and methodological developments. Among these, CPMG relaxation dispersion solution NMR methods provide unique, atomic-resolution information on the structure, kinetics, and thermodynamics of protein conformational equilibria occurring on the µs-ms timescale. Here, the study presents detailed protocols for acquisition and analysis of a ¹⁵N relaxation dispersion experiment. As an example, the pipeline for the analysis of the µs-ms dynamics in the C-terminal domain of bacteria Enzyme I is shown.

Software for reconstruction of nonuniformly sampled NMR data

Nonuniform sampling (NUS) of multidimensional NMR experiments is a powerful tool to obtain high-resolution spectra with less instrument time. With NUS, only a subset of the points needed for conventional Fourier transformation is recorded, and sophisticated algorithms are needed to reconstruct the missing data points. During the last decade, several software packages implementing the reconstruction algorithms have emerged and been refined and now result in spectra of almost similar quality as spectra from conventionally recorded and processed data. However, from the number of literature references to the reconstruction methods, many more multidimensional NMR spectra could presumably be recorded with NUS. To help researchers considering to start using NUS for their NMR experiments, we here review 13 different reconstruction methods found in five software packages (CambridgeCS, hmsIST, MddNMR, NESTA-NMR, and SMILE). We have compared how the methods run with the provided example scripts for reconstructing a nonuniform sampled three-dimensional ¹⁵ N-NOESY-HSQC at sampling densities from 5% to 50%. Overall, the spectra are all of similar quality above 20% sampling density. Thus, without any particular knowledge about the details of the reconstruction algorithms, significant reduction in the experiment time can be achieved. Below 20% sampling density, the intensities of particular weak peaks start being affected. MddNMR's IST with virtual echo and the SMILE algorithms still reproduced the spectra with the highest accuracy of peak intensities.

Signaling Mechanism of Phytochromes in Solution

Phytochrome proteins guide the red/far-red photoresponse of plants, fungi, and bacteria. Crystal structures suggest that the mechanism of signal transduction from the chromophore to the output domains involves refolding of the so-called PHY tongue. It is currently not clear how the two other notable structural features of the phytochrome superfamily, the so-called helical spine and a knot in the peptide chain, are involved in photoconversion. Here, we present solution NMR data of the complete photosensory core module from Deinococcus radiodurans. Photoswitching between the resting and the active states induces changes in amide chemical shifts, residual dipolar couplings, and relaxation dynamics. All observables indicate a photoinduced structural change in the knot region and lower part of the helical spine. This implies that a conformational signal is transduced from the chromophore to the helical spine through the PAS and GAF domains. The discovered pathway underpins functional studies of plant phytochromes and may explain photosensing by phytochromes under biological conditions.

A CEST NMR experiment to obtain glycine 1Hα chemical shifts in 'invisible' minor states of proteins

Chemical exchange saturation transfer (CEST) experiments are routinely used to study protein conformational exchange between a 'visible' major state and 'invisible' minor states because they can detect minor states with lifetimes varying from ~ 3 to ~ 100 ms populated to just ~ 0.5%. Consequently several ¹H, ¹⁵N and ¹³C CEST experiments have been developed to study exchange and obtain minor state chemical shifts at almost all backbone and sidechain sites in proteins. Conspicuously missing from this extensive set of CEST experiments is a ¹H CEST experiment to study exchange at glycine (Gly) ¹H^α sites as the existing ¹H CEST experiments that have been designed to study dynamics in amide ¹H-¹⁵N spin systems and methyl ¹³CH₃ groups with three equivalent protons while suppressing ¹H-¹H NOE induced dips are not suitable for studying exchange in methylene ¹³CH₂ groups with inequivalent protons. Here a Gly ¹H^α CEST experiment to obtain the minor state Gly ¹H^α chemical shifts is presented. The utility of this experiment is demonstrated on the L99A cavity mutant of T4 Lysozyme (T4L L99A) that undergoes conformational exchange between two compact conformers. The CEST derived minor state Gly ¹H^α chemical shifts of T4L L99A are in agreement with those obtained previously using CPMG techniques. The experimental strategy presented here can also be used to obtain methylene proton minor state chemical shifts from protein sidechain and nucleic acid backbone sites.

Boosting the resolution of low-field 15 N relaxation experiments on intrinsically disordered proteins with triple-resonance NMR

Improving our understanding of nanosecond motions in disordered proteins requires the enhanced sampling of the spectral density function obtained from relaxation at low magnetic fields. High-resolution relaxometry and two-field NMR measurements of relaxation have, so far, only been based on the recording of one- or two-dimensional spectra, which provide insufficient resolution for challenging disordered proteins. Here, we introduce a 3D-HNCO-based two-field NMR experiment for measurements of protein backbone15 N amide longitudinal relaxation rates. The experiment provides accurate longitudinal relaxation rates at low field (0.33 T in our case) preserving the resolution and sensitivity typical for high-field NMR spectroscopy. Radiofrequency pulses applied on six different radiofrequency channels are used to manipulate the spin system at both fields. The experiment was demonstrated on the C-terminal domain ofδ subunit of RNA polymerase from Bacillus subtilis, a protein with highly repetitive amino-acid sequence and very low dispersion of backbone chemical shifts.

Amino-acid selective isotope labeling enables simultaneous overlapping signal decomposition and information extraction from NMR spectra

Signal overlapping is a major bottleneck for protein NMR analysis. We propose a new method, stable-isotope-assisted parameter extraction (SiPex), to resolve overlapping signals by a combination of amino-acid selective isotope labeling (AASIL) and tensor decomposition. The basic idea of Sipex is that overlapping signals can be decomposed with the help of intensity patterns derived from quantitative fractional AASIL, which also provides amino-acid information. In SiPex, spectra for protein characterization, such as ¹⁵N relaxation measurements, are assembled with those for amino-acid information to form a four-order tensor, where the intensity patterns from AASIL contribute to high decomposition performance even if the signals share similar chemical shift values or characterization profiles, such as relaxation curves. The loading vectors of each decomposed component, corresponding to an amide group, represent both the amino-acid and relaxation information. This information link provides an alternative protein analysis method that does not require "assignments" in a general sense; i.e., chemical shift determinations, since the amino-acid information for some of the residues allows unambiguous assignment according to the dual selective labeling. SiPex can also decompose signals in time-domain raw data without Fourier transform, even in non-uniformly sampled data without spectral reconstruction. These features of SiPex should expand biological NMR applications by overcoming their overlapping and assignment problems.

Fast time-resolved NMR with non-uniform sampling

NMR spectroscopy is a versatile tool for studying time-dependent processes: chemical reactions, phase transitions or macromolecular structure changes. However, time-resolved NMR is usually based on the simplest among available techniques - one-dimensional spectra serving as "snapshots" of the studied process. One of the reasons is that multidimensional experiments are very time-expensive due to costly sampling of evolution time space. In this review we summarize efforts to alleviate the problem of limited applicability of multidimensional NMR in time-resolved studies. We focus on techniques based on sparse or non-uniform sampling (NUS), which lead to experimental time reduction by omitting a significant part of the data during measurement and reconstructing it mathematically, adopting certain assumptions about the spectrum. NUS spectra are faster to acquire than conventional ones and thus better suited to the role of "snapshots", but still suffer from non-stationarity of the signal i.e. amplitude and frequency variations within a dataset. We discuss in detail how these instabilities affect the spectra, and what are the optimal ways of sampling the non-stationary FID signal. Finally, we discuss related areas of NMR where serial experiments are exploited and how they can benefit from the same NUS-based approaches.

Rapid NMR Relaxation Measurements Using Optimal Nonuniform Sampling of Multidimensional Accordion Data Analyzed by a Sparse Reconstruction Method

Nonuniform sampling (NUS) of multidimensional NMR data offers significant time savings while improving spectral resolution or increasing sensitivity per unit time. However, NUS has not been widely used for quantitative analysis because of the nonlinearity of most methods used to model NUS data, which leads to problems in estimating signal intensities, relaxation rate constants, and their error bounds. Here, we present an approach that avoids these limitations by combining accordion spectroscopy and NUS in the indirect dimensions of multidimensional spectra and then applying sparse exponential mode analysis, which is well suited for analyzing accordion-type relaxation data in a NUS context. By evaluating the Cramér-Rao lower bound of the variances of the estimated relaxation rate constants, we achieve a robust benchmark for the underlying reconstruction model. Furthermore, we design NUS schemes optimized with respect to the information theoretical lower bound of the error in the parameters of interest, given a specified number of sampling points. The accordion-NUS method compares favorably with conventional relaxation experiments in that it produces identical results, within error, while shortening the length of the experiment by an order of magnitude. Thus, our approach enables rapid acquisition of NMR relaxation data for optimized use of spectrometer time or accurate measurements on samples of limited lifetime.

Characterization of Internal Protein Dynamics and Conformational Entropy by NMR Relaxation

Recent studies suggest that the fast timescale motion of methyl-bearing side chains may play an important role in mediating protein activity. These motions have been shown to encapsulate the residual conformational entropy of the folded state that can potentially contribute to the energetics of protein function. Here, we provide an overview of how to characterize these motions using nuclear magnetic resonance (NMR) spin relaxation methods. The strengths and limitations of several techniques are highlighted in order to assist with experimental design. Particular emphasis is placed on the practical aspects of sample preparation, data collection, data fitting, and statistical analysis. Additionally, discussion of the recently refined "entropy meter" is presented and its use in converting NMR observables to conformational entropy is illustrated. Taken together, these methods should yield new insights into the complex interplay between structure and dynamics in protein function.