Distribution Of Correlation Times Research Articles

Robust Algorithms for the Analysis of Fast-Field-Cycling Nuclear Magnetic Resonance Dispersion Curves

Fast-Field-Cycling (FFC) Nuclear Magnetic Resonance (NMR) relaxometry is a powerful, non-destructive magnetic resonance technique that enables, among other things, the investigation of slow molecular dynamics at low magnetic field intensities. FFC-NMR relaxometry measurements provide insight into molecular motion across various timescales within a single experiment. This study focuses on a model-free approach, representing the NMRD profile R1 as a linear combination of Lorentzian functions, thereby addressing the challenges of fitting data within an ill-conditioned linear least-squares framework. Tackling this problem, we present a comprehensive review and experimental validation of three regularization approaches to implement the model-free approach to analyzing NMRD profiles. These include (1) MF-UPen, utilizing locally adapted L2 regularization; (2) MF-L1, based on L1 penalties; and (3) a hybrid approach combining locally adapted L2 and global L1 penalties. Each method’s regularization parameters are determined automatically according to the Balancing and Uniform Penalty principles. Our contributions include the implementation and experimental validation of the MF-UPen and MF-MUPen algorithms, and the development of a “dispersion analysis” technique to assess the existence range of the estimated parameters. The objective of this work is to delineate the variance in fit quality and correlation time distribution yielded by each algorithm, thus broadening the set of software tools for the analysis of sample structures in FFC-NMR studies. The findings underline the efficacy and applicability of these algorithms in the analysis of NMRD profiles from samples representing different potential scenarios.

Water dynamics in solutions of linear poly (N-isopropyl acrylamide) studied by 2H NMR field-cycling relaxometry

We use 2H nuclear magnetic resonance to study the dynamics of deuterated water in a solution of linear poly (N-isopropyl acrylamide) (pNIPAM, 4 wt%) across its coil-to-globule transition at a lower critical solubility temperature (LCST) around 32°C. In agreement with previous studies, we find that the 2H spin-lattice (T1) and, in particular, spin-spin (T2) relaxation times abruptly decrease when heating through the LCST, indicating that the polymer collapse causes an emergence of a water fraction with strongly reduced mobility. To quantify the dynamics of this slow water fraction, we exploit the fact that 2H field-cycling relaxometry allows us to measure the spectral density of the water reorientation in a broad frequency range. We find that the slow water fraction is characterised by a broad logarithmic Gaussian distribution of correlation times (σLG = 2.3), which is centred about τLG ≈ 10–9 s near the LCST. Hence, the common assumption of a Debye spectral density does not apply. We argue that a minor water fraction, which is located inside the pNIPAM globules and shows dynamics governed by the disordered polymer matrix, accompanies a major water fraction with bulk-like dynamics above the LCST. The former fraction amounts to about 0.4 water molecules per NIPAM monomer. Several findings indicate fast exchange between these bound and free water fractions on the T1 and T2 time scales.

Analytical Framework to Understand the Origins of Methyl Side-Chain Dynamics in Protein Assemblies.

Side-chain motions play an important role in understanding protein structure, dynamics, protein-protein, and protein-ligand interactions. However, our understanding of protein side-chain dynamics is currently limited by the lack of analytical tools. Here, we present a novel analytical framework employing experimental nuclear magnetic resonance (NMR) relaxation measurements at atomic resolution combined with molecular dynamics (MD) simulation to characterize with a high level of detail the methyl side-chain dynamics in insoluble protein assemblies, using amyloid fibrils formed by the prion HET-s. We use MD simulation to interpret experimental results, where rotameric hops, including methyl group rotation and χ1/χ2 rotations, cannot be completely described with a single correlation time but rather sample a broad distribution of correlation times, resulting from continuously changing local structure in the fibril. Backbone motion similarly samples a broad range of correlation times, from ∼100 ps to μs, although resulting from mostly different dynamic processes; nonetheless, we find that the backbone is not fully decoupled from the side-chain motion, where changes in side-chain dynamics influence backbone motion and vice versa. While the complexity of side-chain motion in protein assemblies makes it very challenging to obtain perfect agreement between experiment and simulation, our analytical framework improves the interpretation of experimental dynamics measurements for complex protein assemblies.

Molecular insights into nuclear-magnetic-resonance properties of NaCl solution confined within calcite nanopores

Nuclear magnetic resonance (NMR) relaxation time is an important petrophysical property probing fluid dynamics within pores and providing valuable information to understand solid–fluid interactions and ion-related effects. In this study, we investigate NMR and diffusion properties of confined sodium chloride (NaCl) solutions within calcite nanopores via molecular dynamics (MD) simulations. Density profiles, self-diffusion coefficients, and NMR relaxation times were analyzed as a function of pore size, pore geometry, and NaCl concentration. MD results indicate that the presence of NaCl hinders water movement, resulting in reduced self-diffusion coefficients and relaxation times of water. Nevertheless, the influence of NaCl on water mobility is less than the effects caused by confinement and geometry. Strength of oscillations in water and ion density profiles increases when the slit pore size is reduced to 1 nm, suggesting that water-calcite interactions near pore surfaces are stronger in smaller pore sizes. Analysis of dipole–dipole correlation functions and probability distribution of correlation times shows that ions in aqueous solution have an impact on both intra- and intermolecular interactions. A comprehensive comparison of NMR relaxation times of water in both slit and spherical nanopores reveals that spherical models provide a more accurate representation of the confinement effect induced by pore networks within tight rocks. These findings provide a novel quantitative understanding of the impact of confinement, pore geometry, and ion concentration on the translational and rotational dynamics of confined fluids in calcite nanopores.

The intriguing molecular dynamics of Cer[EOS] in rigid skin barrier lipid layers requires improvement of the model

Omega-O-acyl ceramides such as 32-linoleoyloxydotriacontanoyl sphingosine (Cer[EOS]) are essential components of the lipid skin barrier, which protects our body from excessive water loss and the penetration of unwanted substances. These ceramides drive the lipid assembly to epidermal-specific long periodicity phase (LPP), structurally much different than conventional lipid bilayers. Here, we synthesized Cer[EOS] with selectively deuterated segments of the ultralong N-acyl chain or deuterated or 13C-labeled linoleic acid and studied their molecular behavior in a skin lipid model. Solid-state 2H NMR data revealed surprising molecular dynamics for the ultralong N-acyl chain of Cer[EOS] with increased isotropic motion toward the isotropic ester-bound linoleate. The sphingosine moiety of Cer[EOS] is also highly mobile at skin temperature, in stark contrast to the other LPP components, N-lignoceroyl sphingosine acyl, lignoceric acid, and cholesterol, which are predominantly rigid. The dynamics of the linoleic chain is quantitatively described by distributions of correlation times and using dynamic detector analysis. These NMR results along with neutron diffraction data suggest an LPP structure with alternating fluid (sphingosine chain-rich), rigid (acyl chain-rich), isotropic (linoleate-rich), rigid (acyl-chain rich), and fluid layers (sphingosine chain-rich). Such an arrangement of the skin barrier lipids with rigid layers separated with two different dynamic “fillings” i) agrees well with ultrastructural data, ii) satisfies the need for simultaneous rigidity (to ensure low permeability) and fluidity (to ensure elasticity, accommodate enzymes, or antimicrobial peptides), and iii) offers a straightforward way to remodel the lamellar body lipids into the final lipid barrier.

Liquid mean residence time (MRT) in rotating packed bed (RPB) by empirical correlation and residence time distribution (RTD) method using computational fluid dynamics (CFD) simulation

Rotating packed bed (RPB) belongs to a HIGee technology, a process intensification device that can provide better mass transfer rate due to the generation of hyper-gravity under the influence of centrifugal force. While determining the efficiency of the RPB, the MRT of the liquid plays a vital role. The MRT of the RPB is very small and can be tuned in accordance with the mass transfer rate of the solvent to achieve the required outlet concentration of the absorbed gas. There exist two methods, i.e., empirical correlation and the residence time distribution (RTD) method. The applicability of both methods still needs to be investigated for better prediction of MRT in RPB. The current study compares the MRT of the two of the most widely employed techniques, i.e., MRT by empirical correlation and the RTD approach using the Computational Fluid Dynamics (CFD). The difference between the MRT by both methods lies between 30-38%. The results show that the RTD better predicts the MRT in the RPB as compared to the Burns empirical correlation.

Revealing heterogeneity in correlation times of EGFP encapsulated in complex coacervate core micelles by analysis of fluorescence anisotropies

Encapsulation of enhanced green fluorescent protein (EGFP) in complex coacervate core micelles (C3Ms) can be established by mixing EGFP with diblock polymers at equal charge ratio. It has previously been shown that this encapsulation system is highly dynamic, implying existence of different populations; GFP free in solution or complexed with polymers (small complexes) and EGFP encapsulated in C3Ms. We performed time resolved fluorescence anisotropy experiments to determine the relative populations of EGFP encapsulated in C3Ms using three different fluorescence anisotropy decay analysis methods. First, Maximum Entropy Method (MEM) data analysis was employed for five different EGFP concentrations in C3Ms that were mixed with dark fluorescent proteins (10, 20, 30, 40 and 50% EGFP, respectively). In all cases, correlation-time distributions between 0.1 and 100 ns (on a logarithmic timescale) are clearly visible showing bimodal distribution. The distribution between 0.1 and 2.0 ns is due to homo-FRET between EGFP molecules packed in micelles and the distribution between 8 and 30 ns coincides with the correlation-time distribution of free EGFP in solution. The fraction of homo-FRET distribution linearly increases with increase of relative micellar EGFP concentrations. These MEM results were corroborated by two different analysis methods: global population analysis of all five fluorescence anisotropy decays arising from EGFP in micelles together with the one of free EGFP (direct analysis of anisotropies) and global associative population analysis of anisotropies by fitting parallel and perpendicular fluorescence decay components. In contrast to global analyses approaches, the MEM method directly reveals distributions of correlation times without any prior information about the sample. However, global associative analysis of anisotropies by fitting parallel and perpendicular fluorescence decay components is the only method that allows to estimate accurately fractions of free fluorophores in solution and encapsulated fluorophores.

Molecular motion of imidazolium cations and phase transitions in (ImH)2KCo(CN)6 with double perovskite structure

Temperature dependence of 1H nuclear magnetic resonance spin–lattice relaxation time T1 of (ImH)2KCo(CN)6, ImH+: imidazolium cation, is reported. The asymmetric T1 minimum observed in intermediate-temperature phase between 198 and 112 K is analyzed assuming the Cole-Davidson distribution of correlation time. Temperature dependences of 14N nuclear quadrupole resonance frequencies and spin–lattice relaxation times are also reported. The phase transitions at 198 and 112 K are shown to be of second and first order, respectively. The 14N relaxation is shown to be governed by the electric field gradient fluctuation due to the in-plane reorientational motion of the imidazolium cations.

Oxygen NMR of high-density and low-density amorphous ice.

Using oxygen-17 as a nuclear probe, spin relaxometry was applied to study the high-density and low-density states of amorphous ice, covering temperatures below and somewhat above their glass transitions. These findings are put in perspective with results from deuteron nuclear magnetic resonance and with calculations based on dielectrically detected correlation times. This comparison reveals the presence of a wide distribution of correlation times. Furthermore, oxygen-17 central-transition echo spectra were recorded for wide ranges of temperature and pulse spacing. The spectra cannot be described by a single set of quadrupolar parameters, suggesting a distribution of H-O-H opening angles that is broader for high-density than for low-density amorphous ice. Simulations of the pulse separation dependent spin-echo spectra for various scenarios demonstrate that a small-step frequency diffusion process, assigned to the presence of homonuclear oxygen-oxygen interactions, determines the shape evolution of the pulse-separation-dependent spectra.

Transport and Diffusion Enhancement in Experimentally Realized Non-Gaussian Correlated Ratchets.

Living cells are known to generate non-Gaussian active fluctuations significantly larger than thermal fluctuations owing to various active processes. Understanding the effect of these active fluctuations on various physicochemical processes, such as the transport of molecular motors, is a fundamental problem in nonequilibrium physics. Therefore, we experimentally and numerically studied an active Brownian ratchet comprising a colloidal particle in an optically generated asymmetric periodic potential driven by non-Gaussian noise having finite-amplitude active bursts, each arriving at random and decaying exponentially. We find that the particle velocity is maximum for relatively sparse bursts with finite correlation time and non-Gaussian distribution. These occasional kicks, which produce Brownian yet non-Gaussian diffusion, are more efficient for transport and diffusion enhancement of the particle than the incessant kicks of active Ornstein-Uhlenbeck noise.

Model-Free or Not?

Relaxation in nuclear magnetic resonance is a powerful method for obtaining spatially resolved, timescale-specific dynamics information about molecular systems. However, dynamics in biomolecular systems are generally too complex to be fully characterized based on NMR data alone. This is a familiar problem, addressed by the Lipari-Szabo model-free analysis, a method that captures the full information content of NMR relaxation data in case all internal motion of a molecule in solution is sufficiently fast. We investigate model-free analysis, as well as several other approaches, and find that model-free, spectral density mapping, LeMaster’s approach, and our detector analysis form a class of analysis methods, for which behavior of the fitted parameters has a well-defined relationship to the distribution of correlation times of motion, independent of the specific form of that distribution. In a sense, they are all “model-free.” Of these methods, only detectors are generally applicable to solid-state NMR relaxation data. We further discuss how detectors may be used for comparison of experimental data to data extracted from molecular dynamics simulation, and how simulation may be used to extract details of the dynamics that are not accessible via NMR, where detector analysis can be used to connect those details to experiments. We expect that combined methodology can eventually provide enough insight into complex dynamics to provide highly accurate models of motion, thus lending deeper insight into the nature of biomolecular dynamics.

Study of used marine oils by the photon correlation spectroscopy method

In this paper, we investigate the possibility of using the method of photon correlation spectroscopy for diagnostics of marine engines based on used engine oil in order to improve efficiency and safety of operation of sea vessels. The study used the dynamic light scattering (DLS) method to measure correlation functions and then to obtain distributions of correlation times, diffusion coefficients and particle sizes. To invert the Laplace transform, a method based on standard deviation minimization and regularization (RILT) was used, modified to find the distribution of correlation times. It has been found that the distributions of the hydrodynamic radii of the particles for fresh and used oils differ significantly. By the nature of the distribution of large particles, it has been found that the level of aggregation or micelle formation of the polymer of the viscosity modifier decreases in waste oils. It is shown that the dynamic light scattering method makes it possible to obtain parameters suitable for analyzing the state of engine oil and for obtaining diagnostic data on the state of the engine for used oil.

NMR 1H-1H Dipole Relaxation in Fluids: Relaxation of Individual 1H-1H Pairs versus Relaxation of Molecular Modes.

The intramolecular 1H NMR dipole-dipole relaxation of molecular fluids has traditionally been interpreted within the Bloembergen-Purcell-Pound (BPP) theory of NMR intramolecular relaxation. The BPP theory draws upon Debye's theory for describing the rotational diffusion of the 1H-1H pair and predicts a monoexponential decay of the 1H-1H dipole-dipole autocorrelation function between distinct spin pairs. Using molecular dynamics (MD) simulations, we show that for both n-heptane and water this is not the case. In particular, the autocorrelation function of individual 1H-1H intramolecular pairs itself evinces a rich stretched-exponential behavior, implying a distribution in rotational correlation times. However, for the high-symmetry molecule neopentane, the individual 1H-1H intramolecular pairs do conform to the BPP description, suggesting an important role of molecular symmetry in aiding agreement with the BPP model. The intermolecular autocorrelation functions for n-heptane, water, and neopentane also do not admit a monoexponential behavior of individual 1H-1H intermolecular pairs at distinct initial separations. We suggest expanding the autocorrelation function in terms of modes, provisionally termed molecular modes, that do have an exponential relaxation behavior. With care, the resulting Fredholm integral equation of the first kind can be inverted to recover the probability distribution of the molecular modes. The advantages and limitations of this approach are noted.

Heterogeneous Polymer Dynamics Explored Using Static 1H NMR Spectra.

NMR spectroscopy continues to provide important molecular level details of dynamics in different polymer materials, ranging from rubbers to highly crosslinked composites. It has been argued that thermoset polymers containing dynamic and chemical heterogeneities can be fully cured at temperatures well below the final glass transition temperature (Tg). In this paper, we described the use of static solid-state 1H NMR spectroscopy to measure the activation of different chain dynamics as a function of temperature. Near Tg, increasing polymer segmental chain fluctuations lead to dynamic averaging of the local homonuclear proton-proton (1H-1H) dipolar couplings, as reflected in the reduction of the NMR line shape second moment (M2) when motions are faster than the magnitude of the dipolar coupling. In general, for polymer systems, distributions in the dynamic correlation times are commonly expected. To help identify the limitations and pitfalls of M2 analyses, the impact of activation energy or, equivalently, correlation time distributions, on the analysis of 1H NMR M2 temperature variations is explored. It is shown by using normalized reference curves that the distributions in dynamic activation energies can be measured from the M2 temperature behavior. An example of the M2 analysis for a series of thermosetting polymers with systematically varied dynamic heterogeneity is presented and discussed.

Elucidating the 1H NMR Relaxation Mechanism in Polydisperse Polymers and Bitumen Using Measurements, MD Simulations, and Models.

The mechanism behind the 1H nuclear magnetic resonance (NMR) frequency dependence of T1 and the viscosity dependence of T2 for polydisperse polymers and bitumen remains elusive. We elucidate the matter through NMR relaxation measurements of polydisperse polymers over an extended range of frequencies (f0 = 0.01-400 MHz) and viscosities (η = 385-102 000 cP) using T1 and T2 in static fields, T1 field-cycling relaxometry, and T1ρ in the rotating frame. We account for the anomalous behavior of the log-mean relaxation times T1LM ∝ f0 and T2LM ∝ (η/T)-1/2 with a phenomenological model of 1H-1H dipole-dipole relaxation, which includes a distribution in molecular correlation times and internal motions of the nonrigid polymer branches. We show that the model also accounts for the anomalous T1LM and T2LM in previously reported bitumen measurements. We find that molecular dynamics (MD) simulations of the T1 ∝ f0 dispersion and T2 of similar polymers simulated over a range of viscosities (η = 1-1000 cP) are in good agreement with measurements and the model. The T1 ∝ f0 dispersion at high viscosities agrees with previously reported MD simulations of heptane confined in a polymer matrix, which suggests a common NMR relaxation mechanism between viscous polydisperse fluids and fluids under nanoconfinement, without the need to invoke paramagnetism.

The dynamics of the plastically crystalline phase of cyanoadamantane revisited by NMR line shape analysis and field-cycling relaxometry.

The dynamics of cyanoadamantane (CN-ADA) in its plastically crystalline phase encompasses three processes: overall tumbling of the rigid molecule, rotation around the molecular symmetry axis, and vacancy diffusion. This makes CN-ADA a prototypical case to be studied by field-cycling as well as by conventional NMR relaxometry. Data are collected from 430 K down to about 4 K and frequencies in the range of 10 kHz-56 MHz are covered. The overall tumbling is interpreted as a cooperative jump process preceding along the orthogonal axis of the cubic lattice and exhibiting a temperature independent non-Lorentzian spectral density. Consequently, a master curve is constructed, which yields model-independent correlation times, which agree well with those reported in the literature. It can be interpolated by a Cole-Davidson function with a width parameter βCD = 0.83. The uniaxial rotation persisting in the glassy crystal (T < Tg = 170 K) is governed by a broad distribution of activation energies, g(E). In this case, the standard master curve construction applied for the overall tumbling, for example, fails, as the actually probed distribution of correlation times G(ln τ) strongly changes with temperature. We suggest a scaling method that generally applies for the case that a relaxation process is determined by a distribution of thermally activated processes. Frequency as well as temperature dependence of the relaxation rate can be used to reconstruct g(E). In addition, g(E) is extracted from the proton line-shape, which was measured down to 4 K. Vacancy diffusion governs the relaxation dispersion at highest temperatures; yet, a quantitative analysis is not possible due to instrumental limitations.

Local and global dynamics of the viscous ion conductors 2Ca(NO3)2-3KNO3 and 2Ca(NO3)2-3RbNO3 probed by 87Rb nuclear magnetic resonance and shear rheology.

The microscopic and macroscopic dynamics of calcium alkali nitrate melts are studied in their supercooled regime by means of shear rheology and nuclear magnetic resonance (NMR). The structural relaxation is probed using shear rheology to access the viscoelastic flow as well as using physical aging experiments. By exploiting the strongly quadrupole-perturbed 87Rb nucleus, the local dynamics is probed on the milliseconds to nanoseconds range using various NMR methods involving central-transition stimulated-echo techniques, line shape analyses, spin relaxations, and second-order dynamic shift effects. The time scales monitored via the local Rb probe are in harmony with the electrical conductivity relaxation times. The low-temperature NMR line shapes agree excellently with those predicted by the Czjzek model. The temperature dependent second-order dynamic frequency shift is described using the imaginary part of the spectral density. It is demonstrated how the latter quantity can be generalized to include effects of correlation time distributions.

Analysis of NMR Spin-Relaxation Data Using an Inverse Gaussian Distribution Function

Spin relaxation in solution-state NMR spectroscopy is a powerful approach to explore the conformational dynamics of biological macromolecules. Probability distribution functions for overall or internal correlation times have been used previously to model spectral density functions central to spin-relaxation theory. Applications to biological macromolecules rely on transverse relaxation rate constants, and when studying nanosecond timescale motions, sampling at ultralow frequencies is often necessary. Consequently, appropriate distribution functions necessitate spectral density functions that are accurate and convergent as frequencies approach zero. In this work, the inverse Gaussian probability distribution function is derived from general properties of spectral density functions at low and high frequencies for macromolecules in solution, using the principle of maximal entropy. This normalized distribution function is first used to calculate the correlation function, followed by the spectral density function. The resulting model-free spectral density functions are finite at a frequency of zero and can be used to describe distributions of either overall or internal correlation times using the model-free ansatz. To validate the approach, 15N spin-relaxation data for the bZip transcription factor domain of the Saccharomyces cerevisiae protein GCN4, in the absence of cognate DNA, were analyzed using the inverse Gaussian probability distribution for intramolecular correlation times. The results extend previous models for the conformational dynamics of the intrinsically disordered, DNA-binding region of the bZip transcription factor domain.

Nature of magnetism in thiol-capped gold nanoparticles investigated with Muon spin rotation

Muon spin rotation/relaxation measurements show clear evidence for magnetism in 2.2 nm gold nanoparticles capped with butanethiol. At low temperatures (1.8 K), there is significant spin relaxation which decreases as a function of both the applied longitudinal magnetic field and increasing temperature. The results indicate that there are spatially inhomogeneous electronic moments that fluctuate with a wide distribution of correlation times. Possible explanations are discussed.

Revealing Local Dynamics of the Protonic Conductor CsH(PO3H) by Solid-State NMR Spectroscopy and First-Principles Calculations

A joint study incorporating multinuclear solid-state NMR spectroscopy and first-principles calculations has been performed to investigate the local structure and dynamics of the protonic conductor CsH(PO3H) in the paraelectric phase. The existence of the superprotonic phase (>137 °C) is clearly confirmed by NMR, in good agreement with the literature. The variable-temperature 1H, 2H, and 31P NMR data further reveal a distribution of motional correlation times, with isotropic rotation of the phosphite ion being observed below the superprotonic phase transition for a small but gradually increasing subset of anions. This isotropic rotation is associated with fast local protonic motion, with the distribution of correlation times being tentatively assigned to internal defects or surface adsorbed H2O. The phosphite ion dynamics of the majority slower subset of phosphite ions is quantified through analysis of variable-temperature 17O spectra recorded from 34 to 150 °C, by considering a model for the pseudo C3 rot...