Contribution of rotational diffusion to pulsed field gradient diffusion measurements

NMR diffusion experiments employing pulsed field gradients are well established as sensitive probes of the displacement of individual nuclear spins in a sample. Conventionally such measurements are used as a measure of translational diffusion, but here we demonstrate that under certain conditions rotational motion will contribute very significantly to the experimental data. This situation occurs when at least one spatial dimension of the species under study exceeds the root mean square displacement associated with translational diffusion, and leads to anomalously large apparent diffusion coefficients when conventional analytical procedures are employed. We show that in such a situation the effective diffusion coefficient is a function of the duration of the diffusion delay used, and that this dependence provides a means of characterizing the dimensions of the species under investigation.     

Restricted diffusion in silica particles measured by pulsed field gradient NMR

The restricted diffusion coefficient of water through porous silica is measured by pulsed field gradient (PFG) NMR as a function of loading in order to develop a model for self-diffusion at full pore filling in sol-gel-made porous silica particles. This model describes the pore or intraparticle diffusion coefficient as a function of particle porosity, tortuosity, and the steric hindrance applied on the molecules by the pore space. The particle morphology is characterized by nitrogen adsorption and an appropriate tortuosity model is chosen in comparison with literature data. To characterize the material, NMR relaxation and diffusion studies at different degrees of pore filling were carried out in relation to the silica/water adsorption isotherm.     

Lateral diffusion studied by pulsed field gradient NMR on oriented lipid membranes

This mini-review focuses on the utilization of pulsed magnetic field gradients to measure diffusional motion in systems of macroscopically oriented lipid bilayers. The NMR diffusion technique is proposed to have appreciable potential for future biophysical investigations in the field of membrane biology. Topics such as transport of molecules both across and in the plane of the membrane can be successfully studied, and the formation of lipid domains and their intrinsic dynamics can also be scrutinized. First, a short introduction to the NMR technique is given together with a brief discussion on methods of obtaining a good bilayer orientation. Then, a number of recent results on biophysical/biological membrane systems of great interest is presented, in which some unique conclusions on so-called 'raft membranes' are reached. It is shown for systems with large two-phase areas of liquid disordered and liquid ordered phases that lipid lateral diffusion is faster in the former phase and has a smaller apparent activation energy. Further, on the time-scale of the experiments (50-250 ms), exchange between the two phases is fast in the phospholipid-cholesterol-water ternary system, whereas it is slow in the sphingomyelin-dioleoylphosphatidylcholine-cholesterol-water quaternary system.     

Slow diffusion of macromolecular assemblies by a new pulsed field gradient NMR method

The translational diffusion coefficient of an integral membrane protein/surfactant complex has been measured using a novel pulsed field gradient NMR method. In this new approach, the information about the localization of the molecules is temporarily stored in the form of longitudinal magnetization of isotopes with long spin-lattice relaxation times. This allows one to increase the duration of the diffusion interval by about 1 order of magnitude. Unlike standard proton NMR methods using pulsed field gradients and stimulated echoes, the new method can be applied to macromolecular assemblies with diffusion coefficients well below 10(-10) m(2) s(-1), corresponding to masses in excess of 25 kDa in aqueous solution at room temperature. The method was illustrated by application to a water-soluble complex of tOmpA, the hydrophobic transmembrane domain of bacterial outer membrane protein A, with the detergent octyl-tetraoxyethylene (C(8)E(4); overall mass of complex approximately 45 kDa). The diffusion coefficient was found to be D = (4.99 +/- 0.07) x 10(-11) m(2) s(-1), consistent with measurements by size exclusion chromatography and by ultracentrifugation. The method has also been applied to a solution of recombinant human tRNA(3)(Lys), which has a molecular mass of 24 kDa, and the diffusion coefficient D = (1.05 +/- 0.015) x 10(-10) m(2) s(-1).     

Translational diffusion of macromolecular assemblies measured using transverse-relaxation-optimized pulsed field gradient NMR

In structural biology, pulsed field gradient (PFG) NMR spectroscopy for the characterization of size and hydrodynamic parameters of macromolecular solutes has the advantage over other techniques that the measurements can be recorded with identical solution conditions as used for NMR structure determination or for crystallization trials. This paper describes two transverse-relaxation-optimized (TRO) (15)N-filtered PFG stimulated-echo (STE) experiments for studies of macromolecular translational diffusion in solution, (1)H-TRO-STE and (15)N-TRO-STE, which include CRINEPT and TROSY elements. Measurements with mixed micelles of the Escherichia coli outer membrane protein X (OmpX) and the detergent Fos-10 were used for a systematic comparison of (1)H-TRO-STE and (15)N-TRO-STE with conventional (15)N-filtered STE experimental schemes. The results provide an extended platform for evaluating the NMR experiments available for diffusion measurements in structural biology projects involving molecular particles with different size ranges. An initial application of the (15)N-TRO-STE experiment with very long diffusion delays showed that the tedradecamer structure of the 800 kDa Thermus thermophilus chaperonin GroEL is preserved in aqueous solution over the temperature range 25-60 °C.     

Transport properties in ionic liquids and ionic liquid mixtures: the challenges of NMR pulsed field gradient diffusion measurements

Pulsed field gradient NMR is a powerful method for the measurement of diffusion coefficients in liquids and solids and has begun to attract much attention in the ionic liquids field. However, aspects of the methodology as traditionally applied to solutions may not be uniformly applicable in these more viscous and chemically complex systems. In this paper we present data which shows that the Pulsed Gradient Spin Echo (PGSE) method in particular suffers from intrinsic internal gradients and can produce apparent diffusion coefficients which vary by as much as 20% for different 1H nuclei within a given molecule--an obvious anomaly. In contrast, we show that the Pulsed Gradient Stimulated Echo method does not suffer from this problem to the same extent and produces self-consistent data to a high degree of accuracy (better than 1%). This level of significance has allowed the detection, in this work, of subtle mixing effects in [C(3)mpyr][NTf(2)] and [C(4)mpyr][NTf(2)] mixtures.     

A pulsed field gradient NMR diffusion investigation of enkephalin peptide-sodium dodecyl sulfate micelle association

Pulsed field gradient NMR (PFG-NMR) diffusion experiments were used to investigate the binding of leucine and methionine enkephalin peptides to anionic sodium dodecyl sulfate (SDS) micelles. The study was undertaken to investigate the mechanism of interaction between enkephalin peptides and SDS micelles and to determine if NMR-derived association constants, K(eq), can predict the elution order in electrokinetic chromatography (EKC). In EKC, peptides are separated on the basis of their interactions with micelles. The Leu-enkephalin peptide-micelle association constant increased from 130 +/- 8 to 1459 +/- 57 and 1744 +/- 64 M(-1), respectively, when an Arg or Lys was added to the C-terminus. The association constant of Leu-enkephalinamide was approximately equal to that of Leu-enkephalin-Arg. Substitution of Phe4 with a Trp or Gly2 with an Ala in the Leu-enkephalin peptides also increased the micelle binding affinity. These results confirm that the interaction of Leu-enkephalin peptides with SDS micelles is largely electrostatic and that the non-polar amino acid side chains interact with the hydrophobic micelle core. The peptide-micelle association constants for the cationic Met-enkephalin peptides were also greater than their zwitterionic counterparts. For example, the Met-enkephalin K(eq) value was 162 +/- 9 M(-1), while the association constants for Met-enkephalin-Arg, Met-enkephalin-Lys, and Met-enkephalinamide were, respectively, 674 +/- 31, 426 +/- 23, and 453 +/- 27 M(-1). In both Met-enkephalin and Met-enkephalinamide, replacing Gly2 with an Ala did not significantly increase the association constant. These results confirm that with the Met-enkephalin peptides, there was little or no interaction of the amino acid side chains with the micelle core. For both the Leu-enkephalin and Met-enkephalin peptides, the association constants were consistent with EKC results, in that the peptides with smaller K(eq) values were found to elute before those with larger association constants.     

Study of protonic diffusion in hydrogen uranyl phosphate using a pulsed field gradient NMR method

The diffusion of ¹H in the fast protonic conductor H(UO₂PO₄) · 4H₂O has been investigated as a function of temperature by employing pulsed field gradient NMR measurements. In the light of the present diffusion results and published conductivity observations on the same compound, it is likely that protonic diffusion and conductivity in this material occur by the same mechanism. Possible mechanistic processes for the proton motion in this material which are consistent with the activation energy for protonic diffusion found in this study are briefly discussed.     

Influence of local chain dynamics on diffusion of gases in polymers as determined by pulsed field gradient NMR

Diffusion of gases in polymers below the glass transition temperature, T_g, is strongly modulated by local chain dynamics. For this reason, an analysis of pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements considering the viscoelastic behavior of polymers is proposed. Carbon‐13 PFG NMR measurements of [¹³C]O₂ diffusion in polymer films at 298 K are performed. Data obtained in polymers with T_g above (polycarbonate) and below (polyethylene) the temperature set for diffusion measurements are analyzed with a stretched exponential. The results show that the distribution of diffusion coefficients in amorphous phases below T_g is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below T_g requires long diffusion times, which suggests fluctuations of local chain density on a macroscopic scale may occur. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 231–235, 2010     

Heterogeneity of polyelectrolyte diffusion in polyelectrolyte-protein coacervates: a 1H pulsed field gradient NMR study

Proton pulsed field gradient (PFG) NMR was used to study the diffusion of poly(diallyldimethylammonium chloride) (PDADMAC) in coacervates formed from this polycation and the protein bovine serum albumin (BSA). Application of high (up to 30 T/m) magnetic field gradients in PFG NMR measurements allowed probing the diffusion of PDADMAC on a length scale of displacements as small as 100 nm in coacervates formed at different pH's and ionic strengths, i.e., conditions of varying protein-polycation interaction energy. Studies were carried out for a broad range of diffusion times and corresponding values of the mean square displacements. Several ensembles of PDADMAC polycations with different diffusivities were observed in the measured range of diffusion times. The existence of these ensembles and the pattern of their changes with increasing diffusion time support the hypothesis about the microscopic heterogeneity of PDADMAC-BSA coacervates and also provide evidence for the dynamic disintegration and reformation of dense domains.     

A new selective population transfer experiment using a double pulsed field gradient spin-echo

A new pulse sequence is proposed for the determination of scalar coupling correlation in small- and medium-sized organic compounds. The method uses a combination of the double pulsed field gradient spin-echo (DPFGSE) and the selective population transfer (SPT) techniques and is shown to be useful in the analysis of complex spectra with many overlapped signals. The usefulness of this method in the structural elucidation of natural substances is demonstrated using strychnine and digitoxin as examples.     

A pulsed field gradient NMR study of diffusion in semicrystalline polymers: self-diffusion of alkanes in polyethylenes

By means of the pulsed field gradient NMR technique the self-diffusion of six alkanes (from n-butane to n-pentadecane) in three low density polyethylenes and one high density polyethylene differently thermally treated was examined. The concentration dependence could be described very satisfactorily with the free volume theory in the form of Fujita (Adv. Polymer Sci. 3(1961) 1). The parameter B of the diffusants and the fractional free volumef ₂ of the polyethylenes were determined from the experimental data. The fractional free volumesf ₂ show a strong dependence on the type of polyethylene, the main influence results from the different content of CH₃ groups or short chain branches. The diffusion coefficient extrapolated to zero diffusant concentration is proportional to the eighth power of the amorphous content. This strong dependence shows that the free volumes of the amorphous parts of the polyethylenes are intimately connected with crystallinity, both determined by the different degrees of short chain branching. The pre-exponential factor in the free volume expression decreases with increasing amorphous content of the polyethylenes and increases with increasing length of the diffusants. It was found that the spherulite boundaries in the polyethylenes do not act as diffusion barriers.     

Molecular motion and ion diffusion in choline chloride based deep eutectic solvents studied by 1H pulsed field gradient NMR spectroscopy

Deep Eutectic Solvents (DESs) are a novel class of solvents with potential industrial applications in separation processes, chemical reactions, metal recovery and metal finishing processes such as electrodeposition and electropolishing. Macroscopic physical properties such as viscosity, conductivity, eutectic composition and surface tension are already available for several DESs, but the microscopic transport properties for this class of compounds are not well understood and the literature lacks experimental data that could give a better insight into the understanding of such properties. This paper presents the first pulsed field gradient nuclear magnetic resonance (PFG-NMR) study of DESs. Several choline chloride based DESs were chosen as experimental samples, each of them with a different associated hydrogen bond donor. The molecular equilibrium self-diffusion coefficient of both the choline cation and hydrogen bond donor was probed using a standard stimulated echo PFG-NMR pulse sequence. It is shown that the increasing temperature leads to a weaker interaction between the choline cation and the correspondent hydrogen bond donor. The self-diffusion coefficients of the samples obey an Arrhenius law temperature-dependence, with values of self-diffusivity in the range of [10(-10)-10(-13) m(2) s(-1)]. In addition, the results also highlight that the molecular structure of the hydrogen bond donor can greatly affect the mobility of the whole system. While for ethaline, glyceline and reline the choline cation diffuses slower than the associated hydrogen bond donor, reflecting the trend of molecular size and molecular weight, the opposite behaviour is observed for maline, in which the hydrogen bond donor, i.e. malonic acid, diffuses slower than the choline cation, with self-diffusion coefficients values of the order of 10(-13) m(2) s(-1) at room temperature, which are remarkably low values for a liquid. This is believed to be due to the formation of extensive dimer chains between malonic acid molecules, which restricts the mobility of the whole system at low temperature (<30 °C), with malonic acid and choline chloride having almost identical diffusivity values. Diffusion and viscosity data were combined together to gain insights into the diffusion mechanism, which was found to be the same as for ionic liquids with discrete anions.     

Multi-dimensional pulsed field gradient magic angle spinning NMR experiments on membranes

The benefits of gradient techniques in the study of lipid membranes are demonstrated on a sample of 1-palmitoyl-2-oleoyl-sn-glycero-3 phosphocholine (POPC) liposomes embedded with ibuprofen. Most techniques from gradient NMR spectroscopy on solution samples are directly applicable to membrane samples subjected to magic angle spinning (MAS). Gradient-enhanced homo- and heteronuclear chemical shift correlation techniques were used to make resonance assignments. Gradient NOESY experiments provide insight into the location and dynamics of lipids, ibuprofen and water. Application of gradients not only reduces experiment time but also the t(1) noise in the multi-dimensional spectra. Diffusion measurements with pulsed field gradients characterize lateral movements of lipid and drug molecules in membranes. The theoretical framework for data analysis of MAS diffusion experiments on randomly oriented multilamellar liposomes is presented.     

Diffusion of molecules confined in semipenetrable nanoscale carriers probed by pulsed field gradient NMR

Diffusion of three low-molecular-weight compounds cyclohexane (CX), benzene (BZ), and chloroform (CL) preferentially confined in the cores of nanoscale carriers was probed by pulsed field gradient (PFG) NMR methods. The carriers were monolayer micelles of sodium dodecyl sulfate (SDS), bilayer micelles of poly(hexyl methacrylate)-block-(acrylic acid) (M2), and trilayer micelles of poly(2-ethylhexyl methacrylate)-block-(methyl methacrylate)-block-(acrylic acid) (M3) in D(2)O at 300 K. Although the radius of the confinement space was 10(-)(8) m or lower, the course of the PFG signal attenuation in pulsed gradient spin-echo or stimulated echo experiments under varied diffusion time corresponds to apparently unrestricted diffusion, which is slowed down compared to that of the compound dissolved in D(2)O. Analysis using approximate relations reveals that the response of the system to PFG NMR consists of three independent components, namely (i) diffusion of the carrier as a whole, (ii) hindered escape of a confined molecule and its diffusion in the medium, and (iii) diffusion of the molecules dissolved in the medium. If process ii is fast enough, exchange of the compound between the carrier and the medium includes the influence of iii as a component of a monoexponential PFG decay; otherwise, two sets of signals are observed with different diffusion responses, or biexponential PFG is observed. According to the results of this study, the only barrier of the diffusion of the inspected compounds CX, BZ, and CL out of their confinement in the carriers SDS or M2 is a thermodynamic one, that is, the resistance of the saturated solution to accept surplus molecules of the solute. In a three-layer micelle M3, the additional polymer sheet around the confinement area forms an additional diffusion barrier for CX, however. The study shows that PFG NMR, though unable to observe directly restricted diffusion on the nanoscale, can be useful in studying systems designed, for example, for a controlled release of low-molecular-weight substances.     

Microscopic anisotropy revealed by NMR double pulsed field gradient experiments with arbitrary timing parameters

We consider a general double pulsed field gradient experiment with arbitrary experimental parameters and calculate an exact expression for the NMR signal attenuation from restricted geometries, which is valid at long wavelengths, i.e., when the product of the gyromagnetic ratio of the spins, the pulsed gradients' duration, and their magnitude is small compared to the reciprocal of the pore size. It is possible to observe microscopic anisotropy within the pore space induced by the boundaries of the pore, which can be used to differentiate restricted from free or multicompartmental diffusion and to estimate a characteristic pore dimension in the former case. Explicit solutions for diffusion taking place between parallel plates as well as in cylindrical and spherical pores are provided. In coherently packed cylindrical pores, it is possible to measure simultaneously the cylinders' orientation and diameter using small gradient strengths. The presence of orientational heterogeneity of cylinders is addressed, and a scheme for differentiating microscopic from ensemble anisotropy is proposed.     

Application of the thermal frequency response method and of pulsed field gradient NMR to study water diffusion in zeolite NaX

The thermal frequency response and pulsed field gradient NMR methods are applied in a comparative study of water diffusion in zeolite NaX under non-equilibrium and equilibrium conditions. The obtained results are found to be in satisfactory agreement with each other, indicating that by applying the thermal frequency response method, complications due to uncontrolled water adsorption at the chamber walls inherent in conventional frequency response measurements may be circumvented.     

Diffusion of PEG confined between lamellae of negatively magnetically aligned bicelles: pulsed field gradient 1H NMR measurements

The diffusion of various molecular weight poly(ethyleneglycol)s (PEG) confined between the lamellae of magnetically aligned bicelles has been measured using stimulated echo (STE) pulsed field gradient (PFG) 1H nuclear magnetic resonance (NMR) spectroscopy. Bicelles were formulated to contain dimyristoylphosphatidylcholine (DMPC), dimyristoylphosphatidylglycerol (DMPG), and dihexanoylphosphatidylcholine (DHPC) in the proportion DMPG/DMPC = 0.05 and q = (DMPC + DMPG)/DHPC = 4.5. PEG diffusion within the interlamellar spaces between such bicelles was found to be unrestricted over diffusion distances of tens of microns. Two confinement regimes could be differentiated according to the dependence of the reduced PEG diffusivity D/D0, where D0 is the unconfined PEG diffusion coefficient, on the relative confinement Rh/H, where Rh is the unperturbed hydration radius of the particular PEG and H approximately 60 A is the separation between apposing lamellae of the magnetically aligned bicelles. In the regime Rh/H < 0.4, the reduced PEG diffusivity was altered only in proportion to the viscosity increase associated with the bicelle dispersion relative to bulk solution. In the regime Rh/H > 0.4, the reduced PEG diffusivity scaled as (Rh/H)-2/3, in agreement with scaling theories for confined polymers.     

How to compare diffusion processes assessed by single-particle tracking and pulsed field gradient nuclear magnetic resonance

Heterogeneous diffusion processes occur in many different fields such as transport in living cells or diffusion in porous media. A characterization of the transport parameters of such processes can be achieved by ensemble-based methods, such as pulsed field gradient nuclear magnetic resonance (PFG NMR), or by trajectory-based methods obtained from single-particle tracking (SPT) experiments. In this paper, we study the general relationship between both methods and its application to heterogeneous systems. We derive analytical expressions for the distribution of diffusivities from SPT and further relate it to NMR spin-echo diffusion attenuation functions. To exemplify the applicability of this approach, we employ a well-established two-region exchange model, which has widely been used in the context of PFG NMR studies of multiphase systems subjected to interphase molecular exchange processes. This type of systems, which can also describe a layered liquid with layer-dependent self-diffusion coefficients, has also recently gained attention in SPT experiments. We reformulate the results of the two-region exchange model in terms of SPT-observables and compare its predictions to that obtained using the exact transformation which we derived.