Analysis of Velocity Autocorrelation Functions from Molecular Dynamics Simulations of a Small Peptide by the Generalized Langevin Equation with a Power-Law Kernel.

Internal motions play an essential role in the biological functions of proteins and have been the subject of numerous theoretical and spectroscopic studies. Such complex environments are associated with anomalous diffusion where, in contrast to the classical Brownian motion, the relevant correlation functions have power law decays with time. In this work, we investigate the presence of long memory stochastic processes through the analysis of atomic velocity autocorrelation functions. Analytical expressions of the velocity autocorrelation function spectrum obtained through a Mori-Zwanzig projection approach were shown to be compatible with molecular dynamics simulations of a small helical peptide (8-polyalanine).

Intrinsic Flexibility beyond the Highly Ordered DNA Tetrahedron: An Integrative Spectroscopic and Molecular Dynamics Approach.

Since the introduction of DNA-based architectures, in the past decade, DNA tetrahedrons have aroused great interest. Applications of such nanostructures require structural control, especially in the perspective of their possible functionalities. In this work, an integrated approach for structural characterization of a tetrahedron structure is proposed with a focus on the fundamental biophysical aspects driving the assembly process. To address such an issue, spin-labeled DNA sequences are chemically synthesized, self-assembled, and then analyzed by Continuous-Wave (CW) and pulsed Electron Paramagnetic Resonance (EPR) spectroscopy. Interspin distance measurements based on PELDOR/DEER techniques combined with molecular dynamics (MD) thus revealed unexpected dynamic heterogeneity and flexibility of the assembled structures. The observation of flexibility in these ordered 3D structures demonstrates the sensitivity of this approach and its effectiveness in accessing the main dynamic and structural features with unprecedented resolution.

Quantitative analysis of cross-talk in partly deuterated samples of nuclear spins hyperpolarized by dynamic nuclear polarization (DNP) in the thermal mixing regime.

Dynamical nuclear polarization (DNP) is a powerful method that allows one to polarize virtually any spin-bearing nucleus by transferring electron polarization by microwave irradiation of the electron Zeeman transitions. Under certain conditions, the DNP process can be described in thermodynamical terms using the thermal mixing (TM) model. Different nuclear species can exchange energy indirectly through their interactions with the electron spins and reach a common spin temperature. Such "cross-talk" effects can occur between proton (H) and deuterium (D) nuclei in de- and re-polarization experiments. In this work, we investigate such effects experimentally, using either protonated or deuterated TEMPOL radicals as polarizing agents. An analysis of these experiments based on Provotorov's equations allows one to extract the relevant kinetic parameters, such as the rates of energy transfer between the different reservoirs, and the heat capacity of the non-Zeeman (NZ) electron reservoir, while the heat capacities of the proton and deuterium reservoirs can be estimated based on their usual expressions. These parameters allow one to make predictions of the behaviour of heteronuclei such as carbon-13 or phosphorous-31, provided that their heat capacities are negligible. Finally, we present an experimental study of the dependence of Provotorov's kinetic parameters on the TEMPOL concentration and on the H/D ratio, thus providing insight into the nature of "hidden" spins that are not observable directly because of their proximity to the radicals.

Dipolar field effects in a solid-state NMR maser pumped by dynamic nuclear polarization.

We report the observations and the analysis of a pulsed solid state sustained maser generated by proton spins hyperpolarized by Dynamic Nuclear Polarization (DNP) at cryogenic temperatures. Similar unconventional behaviour was observed recently [Weber et al., Phys. Chem. Chem. Phys., 2019, 21, 21278-21286], with induction decays exhibiting multiple asymmetric maser pulses for short time (100 ms) and persistent for tens of second, when the spins are polarized negatively. We present new evidence of such DNP NMR masers, and shed light on previously observed but unexplained features of these masers through simulations of the non-linear spin dynamics using the Bloch-Maxwell-Provotrov (BMP) equations for radiation damping and DNP, and taking into account the (distant) dipolar field.

A Toolbox for Glutamine Use in Dissolution Dynamic Nuclear Polarization: from Enzymatic Reaction Monitoring to the Study of Cellular Metabolic Pathways and Imaging.

Glutamine is under scrutiny regarding its metabolic deregulation linked to energetic reprogramming in cancer cells. Many analytical techniques have been used to better understand the impact of the metabolism of amino acids on biological processes, however only a few are suited to work with complex samples. Here, we report the use of a general dissolution dynamic nuclear polarization (D-DNP) formulation using an unexpensive radical as a multipurpose tool to study glutamine, with insights from enzymatic modelling to complex metabolic networks and fast imaging. First, hyperpolarized [5-13 C] glutamine is used as molecular probe to study the kinetic action of two enzymes: L-asparaginase that has been used as an anti-metabolic treatment for cancer, and glutaminase. These results are also compared with those acquired with another hyperpolarized amino acid, [1,4-13 C] asparagine. Second, we explored the use of hyperpolarized (HP) substrates to probe metabolic pathways by monitoring metabolic profiles arising from hyperpolarized glutamine in E. coli extracts. Finally, a highly concentrated sample formulation is proposed for the purpose of fast imaging applications. We think that this approach can be extended to formulate other amino acids as well as other metabolites and provide complementary insights into the analysis of metabolic networks.

Inversion of Hyperpolarized 13C NMR Signals through Cross-Correlated Cross-Relaxation in Dissolution DNP Experiments.

Dissolution dynamic nuclear polarization (DDNP) is a versatile tool to boost signal amplitudes in solution-state nuclear magnetic resonance (NMR) spectroscopy. For DDNP, nuclei are spin-hyperpolarized "ex situ" in a dedicated DNP device and then transferred to an NMR spectrometer for detection. Dramatic signal enhancements can be achieved, enabling shorter acquisition times, real-time monitoring of fast reactions, and reduced sample concentrations. Here, we show how the sample transfer in DDNP experiments can affect NMR spectra through cross-correlated cross-relaxation (CCR), especially in the case of low-field passages. Such processes can selectively invert signals of 13C spins in proton-carrying moieties. For their investigations, we use schemes for simultaneous or "parallel" detection of hyperpolarized 1H and 13C nuclei. We find that 1H → 13C CCR can invert signals of 13C spins if the proton polarization is close to 100%. We deduce that low-field passage in a DDNP experiment, a common occurrence due to the introduction of so-called "ultra-shielded" magnets, accelerates these effects due to field-dependent paramagnetic relaxation enhancements that can influence CCR. The reported effects are demonstrated for various molecules, laboratory layouts, and DDNP systems. As coupled 13C-1H spin systems are ubiquitous, we expect similar effects to be observed in various DDNP experiments. This might be exploited for selective spectroscopic labeling of hydrocarbons.

Spin relaxation: is there anything new under the Sun?

Spin relaxation has been at the core of many studies since the early days of nuclear magnetic resonance (NMR) and the underlying theory worked out by its founding fathers. This Bloch-Redfield-Abraham relaxation theory has been recently reinvestigated () in the perspective of Lindblad theory of quantum Markovian master equations in order to account for situations where the widely used semi-classical relaxation theory breaks down. In this article, we review the conventional approach of quantum mechanical theory of NMR relaxation and show that, under the usual assumptions, it is equivalent to the Lindblad formulation. We also comment on the debate on semi-classical versus quantum versions of spectral density functions involved in relaxation.

Effects of Microwave Gating on Nuclear Spin Echoes in Dynamic Nuclear Polarization.

Dipolar or quadrupolar echoes allow one to observe undistorted powder patterns, in contrast to simple Fourier transformations of free induction decays (FIDs). In this work, the buildup of proton polarization due to dynamic nuclear polarization (DNP) is monitored by observing echoes rather than FIDs. When the microwave irradiation is interrupted during the buildup of DNP, the electrons relax back to their Boltzmann distribution at high fields (B0 = 6.7 T) and low temperatures 1.2 < Tsample < 4.0 K, so that dipolar flip-flop-flip terms involving two electrons and one proton become largely ineffective as a mechanism of proton decoherence. This leads to a prolongation of the nuclear coherence lifetime T2'(1H). The increase in T2'(1H) leads to transient surges of the amplitudes of spin echoes. Conversely, transient slumps of spin echoes are observed when the microwave irradiation is switched back on, due to a shortening of nuclear coherence lifetimes.

Natural abundance oxygen-17 solid-state NMR of metal organic frameworks enhanced by dynamic nuclear polarization.

The 17O resonances of zirconium-oxo clusters that can be found in porous Zr carboxylate metal-organic frameworks (MOFs) have been investigated by magic-angle spinning (MAS) NMR spectroscopy enhanced by dynamic nuclear polarization (DNP). High-resolution 17O spectra at 0.037% natural abundance could be obtained in 48 hours, thanks to DNP enhancement of the 1H polarization by factors ε(1H) = Swith/Swithout = 28, followed by 1H → 17O cross-polarization, allowing a saving in experimental time by a factor of ca. 800. The distinct 17O sites from the oxo-clusters can be resolved at 18.8 T. Their assignment is supported by density functional theory (DFT) calculations of chemical shifts and quadrupolar parameters. Protonation of 17O sites seems to be leading to large characteristic shifts. Hence, natural abundance 17O NMR spectra of diamagnetic MOFs can thus be used to probe and characterize the local environment of different 17O sites on an atomic scale.

Assessing the Onset of Calcium Phosphate Nucleation by Hyperpolarized Real-Time NMR.

We report an experimental approach for high-resolution real-time monitoring of transiently formed species occurring during the onset of precipitation of ionic solids from solution. This is made possible by real-time nuclear magnetic resonance (NMR) monitoring using dissolution dynamic nuclear polarization (D-DNP) to amplify signals of functional intermediates and is supported by turbidimetry, cryogenic electron microscopy, and solid-state NMR measurements. D-DNP can provide drastic signal improvements in NMR signal amplitudes, permitting dramatic reductions in acquisition times and thereby enabling us to probe fast interaction kinetics such as those underlying formation of prenucleation species (PNS) that precede solid-liquid phase separation. This experimental strategy allows for investigation of the formation of calcium phosphate (CaP)-based minerals by 31P NMR-a process of substantial industrial, geological, and biological interest. Thus far, many aspects of the mechanisms of CaP nucleation remain unclear due to the absence of experimental methods capable of accessing such processes on sufficiently short time scales. The approach reported here aims to address this by an improved characterization of the initial steps of CaP precipitation, permitting detection of PNS by NMR and determination of their formation rates, exchange dynamics, and sizes. Using D-DNP monitoring, we find that under our conditions (i) in the first 2 s after preparation of oversaturated calcium phosphate solutions, PNS with a hydrodynamic radius of Rh ≈ 1 nm is formed and (ii) following this rapid initial formation, the entire crystallization processes proceed on considerably longer time scales, requiring >20 s to form the final crystal phase.

A DNP-hyperpolarized solid-state water NMR MASER: observation and qualitative analysis.

We present observations of an NMR MASER (microwave amplification by stimulated emission of radiation) of hyperpolarized 1H nuclei by dynamic nuclear polarization (DNP) at 1.2 K and in a magnetic field of 6.7 T. The sustained maser pulses originate from the interplay between radiation damping (RD) due to the large 1H magnetization, and the remagnetization to a negative value by the DNP process. NMR signals lasting for several tens of seconds are thus observed on an ensemble of dipolar-coupled nuclear spins. Magnetization dynamics are analyzed in terms of the combined Bloch-Maxwell and Provotorov (BMP) equations for RD and DNP. Insight into the long time evolution of the magnetization is provided by a theoretical analysis of this nonlinear dynamical system, and by fitting the NMR signal to a simplified version of the BMP equations.

Transport of hyperpolarized samples in dissolution-DNP experiments.

Dissolution dynamic nuclear polarization (D-DNP) experiments rely on the transfer of a sample between two high-field magnets. During this transfer, samples might experience passage through regions where the stray fields of the magnets are very weak, can approach zero, and even change their sign. This can lead to unexpected spectral features in spin systems that undergo transitions from weak- to strong-coupling regimes and vice versa, much like in field cycling nuclear magnetic resonance experiments. We herein demonstrate that the spectral features observed in D-DNP experiments can be rationalized, provided the time-dependence of the spin Hamiltonian upon field cycling is sufficiently adiabatic. Under such conditions, a passage through a weak static field can lead to the emergence of a long-lived state (LLS) based on an imbalance between the populations of singlet and triplet states in pairs of nuclei that are strongly coupled during the passage through low field. The LLS entails the appearance of anti-phase multiplet components upon transfer to a high-field magnet for observation of NMR signals.

Stochastic modeling of macromolecules in solution. II. Spectral densities.

In Paper I [Polimeno et al., J. Chem. Phys. 150, 184107 (2019)], we proposed a general approach for interpreting relaxation properties of a macromolecule in solution, derived from an atomistic description. A simple scheme (the semiflexible Brownian, SFB, model) has been defined for the case of limited internal flexibility, but retaining full coupling with external degrees of freedom, inclusion of all of the momenta, and dissipation. Here we discuss the application of the SFB model to the practical evaluation of orientation spectral densities, based on two complementary computational treatments.

Stochastic modeling of macromolecules in solution. I. Relaxation processes.

A framework for the stochastic description of relaxation processes in flexible macromolecules, including dissipative effects, is introduced from an atomistic point of view. Projection-operator techniques are employed to obtain multidimensional Fokker-Planck operators governing the relaxation of internal coordinates and global degrees of freedom and depending upon parameters fully recoverable from classic force fields (energetics) and continuum models (friction tensors). A hierarchy of approaches of different complexity is proposed in this unified context, aimed primarily at the interpretation of magnetic resonance relaxation experiments. In particular, a model based on a harmonic internal Hamiltonian is discussed as a test case.

Targeting the Pentose Phosphate Pathway: Characterization of a New 6PGL Inhibitor.

Human African trypanosomiasis, or sleeping sickness, is a lethal disease caused by the protozoan parasite Trypanosoma brucei. However, although many efforts have been made to understand the biochemistry of this parasite, drug development has led to treatments that are of limited efficiency and of great toxicity. To develop new drugs, new targets must be identified, and among the several metabolic processes of trypanosomes that have been proposed as drug targets, carbohydrate metabolism (glycolysis and the pentose phosphate pathway (PPP)) appears as a promising one. As far as the PPP is concerned, a limited number of studies are related to the glucose-6-phosphate dehydrogenase. In this work, we have focused on the activity of the second PPP enzyme (6-phospho-gluconolactonase (6PGL)) that transforms 6-phosphogluconolactone into 6-phosphogluconic acid. A lactam analog of the natural substrate has been synthesized, and binding of the ligand to 6PGL has been investigated by NMR titration. The ability of this ligand to inhibit 6PGL has also been demonstrated using ultraviolet experiments, and protein-inhibitor interactions have been investigated through docking calculations and molecular dynamics simulations. In addition, a marginal inhibition of the third enzyme of the PPP (6-phosphogluconate dehydrogenase) was also demonstrated. Our results thus open new prospects for targeting T. brucei.

Relaxation of long-lived modes in NMR of deuterated methyl groups.

Long-lived imbalances of spin state populations can circumvent fast quadrupolar relaxation by reducing effective longitudinal relaxation rates by about an order of magnitude. This opens new avenues for the study of dynamic processes in deuterated molecules. Here we present an analysis of the relaxation properties of deuterated methyl groups CD3. The number of coupled equations that describe cross-relaxation between the 27 symmetry-adapted spin states of a D3 system can be reduced to only 2 non-trivial "lumped modes" by (i) taking the sums of the populations of all states that equilibrate rapidly within each irreducible representation of the symmetry group, and (ii) by combining populations that have similar relaxation rates although they belong to different irreducible representations. The quadrupolar relaxation rates of the spin state imbalances in CD3 groups are determined not by the correlation time of overall tumbling of the molecule, but by the frequency of jumps of methyl groups about their three-fold symmetry axis. We access these states via dissolution dynamic nuclear polarization (D-DNP), a method that allows one to populate the desired long-lived states at cryogenic temperatures and their subsequent detection at ambient temperatures after rapid dissolution. Experimental examples of DMSO-d6 and ethanol-d6 demonstrate that long-lived deuterium spin states are indeed accessible and that their lifetimes can be determined. Our analysis of the system via "lumped" modes allows us to visualize different possible spin-state populations of symmetry A, B, or E. Thus, we identify a long-lived spin state involving all three deuterons in a CD3 group as an A/E imbalance that can be populated through DNP at low temperatures.

Sample Ripening through Nanophase Separation Influences the Performance of Dynamic Nuclear Polarization.

Mixtures of water and glycerol provide popular matrices for low-temperature spectroscopy of vitrified samples. However, they involve counterintuitive physicochemical properties, such as spontaneous nanoscopic phase separations (NPS) in solutions that appear macroscopically homogeneous. We demonstrate that such phenomena can substantially influence the efficiency of dynamic nuclear polarization (DNP) by factors up to 20 % by causing fluctuations in local concentrations of polarization agents (radicals). Thus, a spontaneous NPS of water/glycerol mixtures that takes place on time scales on the order of 30-60 min results in a confinement of polarization agents in nanoscopic water-rich vesicles, which in return affects the DNP. Such effects were found for three common polarization agents, TEMPOL, AMUPol and Trityl.

Rates of Chemical Reactions Embedded in a Metabolic Network by Dissolution Dynamic Nuclear Polarisation NMR.

The isomerisation of 6-phosphogluconolactones and their hydrolyses into 6-phosphogluconic acid form a non enzymatic side cycle of the pentose-phosphate pathway (PPP) in cells. Dissolution dynamic nuclear polarisation can be used for determining the kinetic rates of the involved transformations in real time. It is found that the hydrolysis of both lactones is significantly slower than the isomerisation process, thereby shedding new light onto this subtle chemical process.