Size Sensitivity of Metabolite Diffusion in Macromolecular Crowds.

Metabolites play crucial roles in cellular processes, yet their diffusion in the densely packed interiors of cells remains poorly understood, compounded by conflicting reports in existing studies. Here, we employ pulsed-gradient stimulated-echo NMR and Brownian/Stokesian dynamics simulations to elucidate the behavior of nano- and subnanometer-sized tracers in crowded environments. Using Ficoll as a crowder, we observe a linear decrease in tracer diffusivity with increasing occupied volume fraction, persisting─somewhat surprisingly─up to volume fractions of 30-40%. While simulations suggest a linear correlation between diffusivity slowdown and particle size, experimental findings hint at a more intricate relationship, possibly influenced by Ficoll's porosity. Simulations and numerical calculations of tracer diffusivity in the E. coli cytoplasm show a nonlinear yet monotonic diffusion slowdown with particle size. We discuss our results in the context of nanoviscosity and discrepancies with existing studies.

Magnetstein: An Open-Source Tool for Quantitative NMR Mixture Analysis Robust to Low Resolution, Distorted Lineshapes, and Peak Shifts.

1H NMR spectroscopy is a powerful tool for analyzing mixtures including determining the concentrations of individual components. When signals from multiple compounds overlap, this task requires computational solutions. They are typically based on peak-picking and the comparison of obtained peak lists with libraries of individual components. This can fail if peaks are not sufficiently resolved or when peak positions differ between the library and the mixture. In this paper, we present Magnetstein, a quantification algorithm rooted in the optimal transport theory that makes it robust to unexpected frequency shifts and overlapping signals. Thanks to this, Magnetstein can quantitatively analyze difficult spectra with the estimation trueness an order of magnitude higher than that of commercial tools. Furthermore, the method is easier to use than other approaches, having only two parameters with default values applicable to a broad range of experiments and requiring little to no preprocessing of the spectra.

A pH-enhanced resolution in benchtop NMR spectroscopy.

NMR spectroscopy is one of the most potent methods in analytical chemistry. NMR titration experiments are particularly useful since they measure molecular binding affinities and other concentration-dependent effects. These experiments, however, require a long series of measurements. An alternative to these serial measurements has recently been presented, exploiting a pH (or generally - a concentration) gradient along the NMR tube. The proposed experiment, although efficient, was based on the sensitivity- and hardware-demanding chemical shift imaging (CSI) method. Thus, it is practically limited to high-resolution NMR spectrometers. This paper proposes modifying and adapting the approach to the popular and cost-efficient benchtop NMR machines. Instead of CSI, we use a device that shifts the NMR tube vertically to measure the spectra of different sample volumes, which have different pH values due to the established gradient along the tube. We demonstrate the potential of the method on the test samples of L-tyrosine and 2,6-lutidine, and two real samples from the food industry - an infant formula and an energy drink. The proposed method boosts spectral resolution and allows for the sampling of a broader range of pH values when compared to the original approach.

Supporting the assignment of NMR spectra with variable-temperature experiments.

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful tools in analytical chemistry. An important step in the analysis of NMR data is the assignment of resonance frequencies to the corresponding atoms in the molecule being investigated. The traditional approach considers the spectrum's characteristic parameters: chemical shift values, internuclear couplings, and peak intensities. In this paper, we show how to support the process of assigning a series of spectra of similar organic compounds by using temperature coefficients, that is, the rates of change in chemical shift values associated with given changes in temperature.

Non-uniform sampling of similar NMR spectra and its application to studies of the interaction between alpha-synuclein and liposomes.

The accelerated acquisition of multidimensional NMR spectra using sparse non-uniform sampling (NUS) has been widely adopted in recent years. The key concept in NUS is that a major part of the data is omitted during measurement, and then reconstructed using, for example, compressed sensing (CS) methods. CS requires spectra to be compressible, that is, they should contain relatively few "significant" points. The more compressible the spectrum, the fewer experimental NUS points needed in order for it to be accurately reconstructed. In this paper we show that the CS processing of similar spectra can be enhanced by reconstructing only the differences between them. Accurate reconstruction can be obtained at lower sampling levels as the difference is sparser than the spectrum itself. In many situations this method is superior to "conventional" compressed sensing. We exemplify the concept of "difference CS" with one such case-the study of alpha-synuclein binding to liposomes and its dependence on temperature. To obtain information on temperature-dependent transitions between different states, we need to acquire several dozen spectra at various temperatures, with and without the presence of liposomes. Our detailed investigation reveals that changes in the binding modes of the alpha-synuclein ensemble are not only temperature-dependent but also show non-linear behavior in their transitions. Our proposed CS processing approach dramatically reduces the number of NUS points required and thus significantly shortens the experimental time.

Linear discriminant analysis reveals hidden patterns in NMR chemical shifts of intrinsically disordered proteins.

NMR spectroscopy is key in the study of intrinsically disordered proteins (IDPs). Yet, even the first step in such an analysis-the assignment of observed resonances to particular nuclei-is often problematic due to low peak dispersion in the spectra of IDPs. We show that the assignment process can be aided by finding "hidden" chemical shift patterns specific to the amino acid residue types. We find such patterns in the training data from the Biological Magnetic Resonance Bank using linear discriminant analysis, and then use them to classify spin systems in an α-synuclein sample prepared by us. We describe two situations in which the procedure can greatly facilitate the analysis of NMR spectra. The first involves the mapping of spin systems chains onto the protein sequence, which is part of the assignment procedure-a prerequisite for any NMR-based protein analysis. In the second, the method supports assignment transfer between similar samples. We conducted experiments to demonstrate these cases, and both times the majority of spin systems could be unambiguously assigned to the correct residue types.

The assignment of 11 B and 1 H resonances in the post-reaction mixture from the dry synthesis of Li(BH3 NH2 BH2 NH2 BH3 ).

We report a detailed 1 H NMR and 11 B NMR study of as synthesised Li ( BH 3 NH 2 BH 2 NH 2 BH 3 ) obtained in a novel dry-synthesis method. A combination of 1D and 2D single- and triple-quantum techniques was used for the assignment of all observed signals. Minor side-products and reactants were detected in the product: NH 3 BH 3 , Li ( NH 2 BH 3 ) , Li ( BH 4 ) , and two yet unknown salts containing 7-membered chain anions: ( BH 3 NH 2 BH 2 NH 2 BH 2 NH 2 BH 3 ) - and ( BH ( NH 2 BH 3 ) 3 ) - . We believe the assignment provided within this study might be helpful when analysing the mixtures containing numerous ammonia borane derivatives, which often give overlapping signals that are hard to distinguish.

Enhanced Nuclear Magnetic Resonance Spectroscopy with Isotropic Mixing as a Pseudodimension.

Chemical analysis based on liquid-state nuclear magnetic resonance spectroscopy exploits numerous observables, mainly chemical shifts, relaxation rates, and internuclear coupling constants. Regarding the latter, the efficiencies of internuclear coherence transfers may be encoded in spectral peak intensities. The dependencies of these intensities on the experimental parameter that influences the transfer, for example, mixing time, are an important source of structural information. Yet, they are costly to measure and difficult to analyze. Here, we show that peak intensity build-up curves in two-dimensional total correlation spectroscopy (2D TOCSY) experiments may be quickly measured by employing nonuniform sampling and that their analysis can be effective if supported by quantum mechanical calculations. Thus, such curves can be used to form a new, third pseudodimension of the TOCSY spectrum. Similarly to the other two frequency dimensions, this one also resolves ambiguities and provides characteristic information. We show how the approach supports the analysis of a fragment of protein Tau Repeat-4 domain. Yet, its potential applications are far broader, including the analysis of complex mixtures or other polymers.

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.

Temperature as an Extra Dimension in Multidimensional Protein NMR Spectroscopy.

NMR spectroscopy is a particularly informative method for studying protein structures and dynamics in solution; however, it is also one of the most time-consuming. Modern approaches to biomolecular NMR spectroscopy are based on lengthy multidimensional experiments, the duration of which grows exponentially with the number of dimensions. The experimental time may even be several days in the case of 3D and 4D spectra. Moreover, the experiment often has to be repeated under several different conditions, for example, to measure the temperature-dependent effects in a spectrum (temperature coefficients (TCs)). Herein, a new approach that involves joint sampling of indirect evolution times and temperature is proposed. This allows TCs to be measured through 3D spectra in even less time than that needed to acquire a single spectrum by using the conventional approach. Two signal processing methods that are complementary, in terms of sensitivity and resolution, 1) dividing data into overlapping subsets followed by compressed sensing reconstruction, and 2) treating the complete data set with a variant of the Radon transform, are proposed. The temperature-swept 3D HNCO spectra of two intrinsically disordered proteins, osteopontin and CD44 cytoplasmic tail, show that this new approach makes it possible to determine TCs and their non-linearities effectively. Non-linearities, which indicate the presence of a compact state, are particularly interesting. The complete package of data acquisition and processing software for this new approach are provided.

Restriction of S-adenosylmethionine conformational freedom by knotted protein binding sites.

S-adenosylmethionine (SAM) is one of the most important enzyme substrates. It is vital for the function of various proteins, including large group of methyltransferases (MTs). Intriguingly, some bacterial and eukaryotic MTs, while catalysing the same reaction, possess significantly different topologies, with the former being a knotted one. Here, we conducted a comprehensive analysis of SAM conformational space and factors that affect its vastness. We investigated SAM in two forms: free in water (via NMR studies and explicit solvent simulations) and bound to proteins (based on all data available in the PDB and on all-atom molecular dynamics simulations in water). We identified structural descriptors-angles which show the major differences in SAM conformation between unknotted and knotted methyltransferases. Moreover, we report that this is caused mainly by a characteristic for knotted MTs compact binding site formed by the knot and the presence of adenine-binding loop. Additionally, we elucidate conformational restrictions imposed on SAM molecules by other protein groups in comparison to conformational space in water.

Benefits of time-resolved nonuniform sampling in reaction monitoring: The case of aza-Michael addition of benzylamine and acrylamide.

Monitoring of chemical reactions is best carried out using methods that sample the test object at a rate greater than the time scale of the processes taking place. The recently proposed time-resolved nonuniform sampling (TR-NUS) method allows the use of two-dimensional (2D) nuclear magnetic resonance (NMR) spectra for this purpose and provides a time resolution equivalent to that achievable using one-dimensional spectra. Herein, we show that TR-NUS acquired data eliminates 2D spectral line disturbances and enables more accurate signal integration and kinetics conclusions. The considerations are exemplified with a seemingly simple aza-Michael reaction of benzylamine and acrylamide. Surprisingly, the product identification is possible only using 2D spectra, although credible monitoring requires TR-NUS.

A novel high-dimensional NMR experiment for resolving protein backbone dihedral angle ambiguities.

Intrinsically disordered proteins (IDPs) are challenging established structural biology perception and urge a reassessment of the conventional understanding of the subtle interplay between protein structure and dynamics. Due to their importance in eukaryotic life and central role in protein interaction networks, IDP research is a fascinating and highly relevant research area in which NMR spectroscopy is destined to be a key player. The flexible nature of IDPs, as a result of the sampling of a vast conformational space, however, poses a tremendous scientific challenge, both technically and theoretically. Pronounced signal averaging results in narrow signal dispersion and requires higher dimensionality NMR techniques. Moreover, a fundamental problem in the structural characterization of IDPs is the definition of the conformational ensemble sampled by the polypeptide chain in solution, where often the interpretation relies on the concept of 'residual structure' or 'conformational preference'. An important source of structural information is information-rich NMR experiments that probe protein backbone dihedral angles in a unique manner. Cross-correlated relaxation experiments have proven to fulfil this task as they provide unique information about protein backbones, particularly in IDPs. Here we present a novel cross-correlation experiment that utilizes non-uniform sampling detection schemes to resolve protein backbone dihedral ambiguities in IDPs. The sensitivity of this novel technique is illustrated with an application to the prototypical IDP [Formula: see text]-Synculein for which unexpected deviations from random-coil-like behaviour could be observed.

Blue-Shift Hydrogen Bonds in Silyltriptycene Derivatives: Antibonding σ* Orbitals of the Si-C Bond as Effective Acceptors of Electron Density.

Triptycene derivatives are widely utilized in different fields of chemistry and materials sciences. Their physicochemical properties, often of pivotal importance for the rational design of triptycene-based functional materials, are influenced by noncovalent interactions between substituents mounted on the triptycene skeleton. Herein, a unique interaction between electron-rich substituents in the peri position and the silyl group located on the bridgehead sp3 -carbon is discussed on the example of 1,4-dichloro-9-(p-methoxyphenyl)-silyltriptycene (TRPCl) which exists in solution in the form of two rotamers differing by dispositions, syn or anti, of the Si-CPh (the CPh atom is from the p-methoxyphenyl group) bond against the peri-Cl atom. For the first time, substantial differences between the Si-CPh bonds in these two dispositions are identified, based on indirect experimental and direct theoretical evidence. For these two orientations, the experimental 1 J(Si,CPh ) values differ by as much as 10 percent. The differences are explained in terms of effective electron density transfer from the peri-Cl atom to the antibonding σ* orbitals of the Si-X bonds (X=H, CPh ) oriented anti to that atom. The electronic effects are revealed by an NBO analysis. Connections of these observations with the notion of blue-shifting hydrogen bonds are discussed.

Enhancing benchtop NMR spectroscopy by means of sample shifting.

Benchtop NMR spectrometers have become widely available over the last decade. They are now used successfully in various branches of chemistry. Their popularity continues to grow due to their low price and almost zero running costs. However, benchtop spectrometers suffer from low resolution and sensitivity compared to the high-field spectrometers used in NMR labs for several decades. In this article we present a solution for boosting the sensitivity of benchtop NMR spectrometers in a multi-scan experiment and improving their capabilities in quantitative measurement. Our solution involves the synchronized shifting of a sample to preserve its high nuclear polarization during the measurement. We performed several experiments using different samples to confirm this improved performance: an 1H NMR experiment for 4,4-dimethoxy-2-butanone, and 13C NMR experiments for benzyl salicylate, the liquid pharmaceutical product Acerin (skin solution), and a mixture of m-anisaldehyde and (R)-(+)-limonene.

Enhancing Compression Level for More Efficient Compressed Sensing and Other Lessons from NMR Spectroscopy.

Modern nuclear magnetic resonance spectroscopy (NMR) is based on two- and higher-dimensional experiments that allow the solving of molecular structures, i.e., determine the relative positions of single atoms very precisely. However, rich chemical information comes at the price of long data acquisition times (up to several days). This problem can be alleviated by compressed sensing (CS)-a method that revolutionized many fields of technology. It is known that CS performs the most efficiently when measured objects feature a high level of compressibility, which in the case of NMR signal means that its frequency domain representation (spectrum) has a low number of significant points. However, many NMR spectroscopists are not aware of the fact that various well-known signal acquisition procedures enhance compressibility and thus should be used prior to CS reconstruction. In this study, we discuss such procedures and show to what extent they are complementary to CS approaches. We believe that the survey will be useful not only for NMR spectroscopists but also to inspire the broader signal processing community.

Non-Stationary Complementary Non-Uniform Sampling (NOSCO NUS) for Fast Acquisition of Serial 2D NMR Titration Data.

NMR spectroscopy offers unique benefits for ligand binding studies on isotopically labelled target proteins. These benefits include atomic resolution, direct distinction of binding sites and modes, a lowest detectable affinity limit, and function independent setup. Yet, retracing protein signal assignments from apo to holo states to derive exact dissociation constants and chemical shift perturbation amplitudes (for ligand docking and structure-based optimization) requires lengthy titration series of 2D heteronuclear correlation spectra at variable ligand concentration that may exceed the protein's lifetime and available spectrometer time. We present a novel method to overcome this critical limitation, based on non-stationary complementary non-uniform sampling (NOSCO NUS) combined with a robust particle swarm optimization algorithm. We illustrate its potential in two challenging studies with very distinct protein sizes and binding affinities, showing that NOSCO NUS can reduce measurement times by an order of magnitude to make such highly informative NMR titration studies more broadly feasible.

Nonstationary Two-Dimensional Nuclear Magnetic Resonance: A Method for Studying Reaction Mechanisms in Situ.

Nuclear magnetic resonance spectroscopy (NMR) is a versatile tool of chemical analysis allowing one to determine structures of molecules with atomic resolution. Particularly informative are two-dimensional (2D) experiments that directly identify atoms coupled by chemical bonds or a through-space interaction. Thus, NMR could potentially be powerful tool to study reactions in situ and explain their mechanisms. Unfortunately, 2D NMR is very time-consuming and thus often cannot serve as a "snapshot" technique for in situ reaction monitoring. Particularly difficult is the case of spectra, in which resonance frequencies vary in the course of reaction. This leads to resolution and sensitivity loss, often hindering the detection of transient products. In this paper we introduce a novel approach to correct such nonstationary 2D NMR signals and raise the detection limits over 10 times. We demonstrate success of its application for studying the mechanism of the reaction of AgSO4-induced synthesis of diphenylmethane-type compounds. Several reactions occur in the studied mixture of benzene and toluene, all with rather low yield and leading to compounds with similar chemical shifts. Nevertheless, with the use of a proposed 2D NMR approach we were able to describe complex mechanisms of diphenylmethane formation involving AgSO4-induced toluene deprotonation and formation of benzyl carbocation, followed by nucleophilic attacks.

Quick temperature-sweep pure-shift NMR: the case of solvent effects in atorvastatin.

Pure-shift NMR experiments provide highly resolved spectra, which could be perfect for precise monitoring of chemical shift variations under different conditions, such as temperature or concentration. However, their sensitivity is relatively low and signal sampling is time-consuming, which leads to long experimental times, making such serial acquisition problematic. In this paper we present a new method of NMR spectroscopy which improves the speed and sensitivity of serial pseudo-two-dimensional pure-shift experiments. The example of variable-temperature study of atorvastatin reveals the potential of the method in verifying the theoretical predictions of solvent-dependent spectral effects.

TReNDS-Software for reaction monitoring with time-resolved non-uniform sampling.

NMR spectroscopy, used routinely for structure elucidation, has also become a widely applied tool for process and reaction monitoring. However, the most informative of NMR methods-correlation experiments-are often useless in this kind of applications. The traditional sampling of a multidimensional FID is usually time-consuming, and thus, the reaction-monitoring toolbox was practically limited to 1D experiments (with rare exceptions, e.g., single-scan or fast-sampling experiments). Recently, the technique of time-resolved non-uniform sampling (TR-NUS) has been proposed, which allows to use standard multidimensional pulse sequences preserving the temporal resolution close to that achievable in 1D experiments. However, the method existed only as a prototype and did not allow on-the-fly processing during the reaction. In this paper, we introduce TReNDS: free, user-friendly software kit for acquisition and processing of TR-NUS data. The program works on Bruker, Agilent, and Magritek spectrometers, allowing to carry out up to four experiments with interleaved TR-NUS. The performance of the program is demonstrated on the example of enzymatic hydrolysis of sucrose.