Long-range Diffusion Coefficient Research Articles

Neutron scattering studies on ionic diffusion behaviors of superionic α-Cu2−δ Se

We present studies on crystal structure and ionic diffusion behaviors of superionic Cu2−δ Se (δ = 0, 0.04, and 0.2) by utilizing neutron powder diffraction and quasi-elastic neutron scattering. In the superionic phase, the structural model with Cu ions occupying the Wyckoff sites of 8c and 32f provides the best description of the structure. As the content of Cu increasing in Cu2−δ Se, the Cu occupancy increases on the 32f site but decreases on the 8c site. Fitting to the quasi-elastic neutron scattering spectra reveals two diffusion modes: the localized diffusion between the 8c and 32f sites and the long-range diffusion between the adjacent 8c sites using the 32f site as a bypass. Between 430 and 650 K, we measured that the compound with more Cu content exhibits a larger long-range diffusion coefficient. Temperature in this range does not affect the long-range diffusion process obviously. Our results suggest the two diffusion modes cooperative and, thus, provide a microscopic understanding of the ionic diffusion of the Cu ions in superionic Cu2−δ Se.

Quasielastic Neutron Scattering and Molecular Dynamics Simulation Study on the Molecular Behaviour of Catechol in Zeolite Beta

The dynamics of catechol in zeolite Beta was studied using quesielastic neutron scattering (QENS) experiments and molecular dynamics simulations at 393 K, to understand the behaviour of phenolic monomers relevant in the catalytic conversion of lignin via metal nanoparticles supported on zeolites. Compared to previous work studying phenol, both methods observe that the presence of the second OH group in catechol can hinder mobility significantly, as explained by stronger hydrogen-bonding interactions between catechol and the Brønsted sites of the zeolite. The instrumental timescale of the QENS experiment allows us to probe rotational motion, and the catechol motions are best fit to an isotropic rotation model with a D^{rot} of 2.9 × 10^{10} s^{-1}. While this D^{rot} is within error of that measured for phenol, the fraction of molecules immobile on the instrumental timescale is found to be significantly higher for catechol. The MD simulations also exhibit this increased in ‘immobility’, showing that the long-range translational diffusion coefficients of catechol are lower than phenol by a factor of 7 in acidic zeolite Beta, and a factor of sim3 in the siliceous material, further illustrating the significance of Brønsted site H-bonding. Upon reproducing QENS observables from our simulations to probe rotational motions, a combination of two isotropic rotations was found to fit the MD-calculated EISF; one corresponds to the free rotation of catechol in the pore system of the zeolite, while the second rotation is used to approximate a restricted and rapid “rattling”, consistent with molecules anchored to the acid sites through their OH groups, the motion of which is too rapid to be observed by experiment.

Effect of Ligand Binding on the Diffusion and Distribution of the G Protein-Coupled Receptor CCR5 in the Cell Membrane

The human immunodeficiency virus (HIV) almost entirely depends on CCR5, a host-encoded chemokine receptor member of the G protein-coupled receptor (GPCR) superfamily, for infection of target cells and hence for transmission from person to person. Inhibiting CCR5 is a viable strategy to prevent viral infection since individuals expressing a truncated version of this protein are perfectly healthy. While native chemokines can display some weak anti-HIV activity, it has been shown that N-terminally-modified analogues of the native CCR5 ligand RANTES/CCL5 are much more potent inhibitors: analogues such as PSC-RANTES, 6P4-RANTES, 5P12-RANTES, and 5P14-RANTES, have potencies in the picomolar range.PSC-RANTES owes its anti-HIV potency to its capacity to induce long-term sequestration of CCR5 inside target cells. This molecule is a strong agonist of CCR5 and activation of the receptor was believed to be required for internalization. While some recombinant chemokines like 6P4-RANTES exhibit a comparable pharmacological profile to PSC-RANTES, others such as 5P12-RANTES and 5P14-RANTES do not, which led us to conclude that anti-HIV potency can be achieved by different mechanisms: 5P12-RANTES is capable of efficiently blocking CCR5 without removing the receptor from the cell surface and without activating it; 5P14-RANTES displays comparable anti-HIV potency while causing only partial internalization in the absence of detectable receptor activation.Because CCR5 needs to be mobile in the cell membrane for HIV infection, we investigated the effect of RANTES analogues on the diffusion dynamics and spatial distribution of CCR5 in the cell membrane, using single-particle tracking and blink microscopy techniques in combination with quantum-dot or small-fluorophore labeled antibodies. We observe confined diffusion, directed diffusion, as well as an immobile fraction of receptors and show how ligand binding affects the short-range and long-range diffusion coefficients.

Two-Dimensional Continuum Percolation Threshold as a Function of the Radius of the Diffusing Particles

Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing diffusion in the presence of immobile obstacles is the percolation threshold, where long-range conducting paths disappear and the long-range diffusion coefficient therefore goes to zero. The thresholds are well-known for point diffusing particles on various lattices or the continuum. But for diffusing particles of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration. For the triangular lattice, the threshold is known to be highly sensitive to the size of the diffusing particle [Saxton, Biophys J 64 (1993) 1053], but lattice calculations give very low resolution. Here high-resolution results are obtained for circular obstacles on the continuum. Random obstacle configurations are generated by Brownian dynamics or Monte Carlo methods, and tested for percolation by examining bond percolation on the Voronoi diagram of the obstacles. The percolation threshold is expressed as the diameter of the largest diffusing particle that can cross a set of obstacles at a prescribed number density. For the simplest case, random overlapping obstacles, the analytical solution is known and the Monte Carlo results agree with it quantitatively. When the obstacles are disks with a 1/r⊥12 repulsion, the percolating diameter is around 10% lower than for overlapping obstacles. Disks with a 1/r⊥6 or 1/r⊥18 repulsion behave similarly. The results are used to find the thresholds for lipids, and for proteins of various diameters. (Supported by NIH grant GM038133)

Determinants of the long-range apparent diffusion coefficient in the human lung: collateral channels or intra-acinar branching?

to the editor: We have given considerable thought to the study by Bartel and colleagues ([1][1]) in an attempt to reconcile their simulation of the long-range apparent diffusion coefficient (LRADC) obtained from hyperpolarized helium-3 experiments in human lungs, with our own simulation using

Percolation Thresholds for Diffusing Particles of Nonzero Radius: Circular Obstacles in the Two-dimensional Continuum

Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing diffusion in the presence of immobile obstacles is the percolation threshold, where long-range connected paths disappear and the long-range diffusion coefficient D goes to zero. To describe obstructed diffusion, it is more accurate to find the threshold directly than to extrapolate a low-density expansion in the obstacle concentration to find the concentration at which D = 0. The thresholds are well-known for point diffusing particles on various lattices or the continuum. But for particles of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration. Earlier results [Saxton, Biophys J 64 (1993) 1053] for the triangular lattice showed a very rapid decrease in the threshold as the radius of the diffusing particle increases, but a lattice model gives very low resolution. The current work finds the percolation threshold for circular obstacles in the two-dimensional continuum as a function of the radius of the diffusing species. The thresholds are obtained by a Monte Carlo method based on the Voronoi diagram for the obstacles. Each Voronoi bond is by definition the path equidistant from the nearest pair of obstacles, so the separation of that pair determines whether a diffusing particle of a given diameter can traverse that bond. For point obstacles, then, one can choose a threshold corresponding to the diameter of the diffusing particle, set the conductivity of all bonds narrower than that diameter to zero and all wider bonds to one, and test for bond percolation on the resulting Voronoi diagram. The results are used to find the thresholds for lipids and for proteins of different diameters. (Supported by NIH grant GM038133)

Persistence of travelling waves in a generalized Fisher equation

Travelling waves of the Fisher equation with arbitrary power of nonlinearity are studied in the presence of long-range diffusion. Using analogy between travelling waves and heteroclinic solutions of corresponding ODEs, we employ the geometric singular perturbation theory to prove the persistence of these waves when the influence of long-range effects is small. When the long-range diffusion coefficient becomes larger, the behaviour of travelling waves can only be studied numerically. In this case we find that starting with some values, solutions of the model lose monotonicity and become oscillatory.

Physical study of dynamics in fully hydrated phospholipid bilayers

We studied the thermotropic phase behavior of a phospholipid membrane bilayer of dimyristoylphosphatidylcholine (DMPC) under excess water conditions. We also investigated the effect induced by the antimicrobial peptide, gramicidin D (GrD), when inserted into the membrane bilayer. Several techniques were used to collect information on different properties and various spatial and temporal regimes, including differential scanning calorimetry, fixed energy window neutron scattering, pulsed-field gradient nuclear magnetic resonance and molecular dynamics simulations. We obtained data on the main phase transition (gel–liquid crystalline) temperature of the bilayer system and on the long-range diffusion coefficient for both phospholipids and hydration water. Moreover, we demonstrated the effect of transition on microscopic molecular mobility, perpendicular and parallel to the membrane plane. The influence of gramicidin on these properties is also discussed.

The Role of Collateral Paths in Long-range Diffusion of 3He in Lungs

The hyperpolarized (3)He long-range diffusion coefficient (LRDC) in lungs is sensitive to changes in lung structure due to emphysema, reflecting the increase in collateral paths resulting from tissue destruction. However, no clear understanding of LRDC in healthy lungs has emerged. Here we compare LRDC measured in healthy lungs with computer simulations of diffusion along the airway tree with no collateral connections. Computer simulations of diffusion of spatially modulated spin magnetization were performed in computer-generated, symmetric-branching models of lungs and compared with existing LRDC measurements in canine and human lungs. The simulations predict LRDC values of order 0.001 cm(2)/sec, approximately 20 times smaller than the measured LRDC. We consider and rule out possible mechanisms for LRDC not included in the simulations: incomplete breath hold, cardiac motion, and passage of dissolved (3)He through airway walls. However, a very low density of small (micron) holes in the airways is shown to account for the observed LRDC. It is proposed that LRDC in healthy lungs is determined by small collateral pathways.

Measuring Collateral Pathways in Health via 3He MRI

IntroductionThere has been recent interest in the use of 3He diffusion MRI because of the close correlations of the imaging measure with tissue morphometry. The long‐range diffusion coefficient (LRDC) has been shown to be a measure of collateral pathways in emphysema, but little is known of the role of collaterals in the LRDC in health. A recent publication attempted to explain the LRDC by simulations within single lung acini, without collateral pathways.MethodsWe measured the LRDC of 3He ex‐vivo in 4 human donor lungs that were rejected for transplantation and in 3 pig lungs, which are known to have greatly reduced collateral ventilation. We also simulated the interacinar diffusion of 3He (at 2‐cm diffusion distances) via the diffusion equation in a strictly branching model of human lung with no collateral pathways. (Airway radii, lengths, and branching angles were taken from detailed, morphometric literature.)ResultsLRDC in pig lungs (0.004 cm2/s) was 4x lower than in the human lungs (0.022 cm2/s), implying that collateral pathways can play a significant role in the measurements. The robustly tested simulations revealed a surprisingly low LRDC (24x lower than the measured value), implying that diffusion via the airway tree alone (no collaterals) cannot account for the measured value in healthy lung. A surprisingly small number of 5‐μ pores is shown to account for the discrepancy.

Role of collateral paths in long-range diffusion in lungs.

The long-range apparent diffusion coefficient (LRADC) of (3)He gas in lungs, measured over times of several seconds and distances of 1-3 cm, probes the connections between the airways. Previous work has shown the LRADC to be small in health and substantially elevated in emphysema, reflecting tissue destruction, which is known to create collateral pathways. To better understand what controls LRADC, we report computer simulations and measurements of (3)He gas diffusion in healthy lungs. The lung is generated with a random algorithm using well-defined rules, yielding a three-dimensional set of nodes or junctions, each connected by airways to one parent node and two daughters; airway dimensions are taken from published values. Spin magnetization in the simulated lung is modulated sinusoidally, and the diffusion equation is solved to 1,000 s. The modulated magnetization decays with a time constant corresponding to an LRADC of approximately 0.001 cm(2)/s, which is smaller by a factor of approximately 20 than the values in healthy lungs measured here and previously in vivo and in explanted lungs. It appears that collateral gas pathways, not present in the simulations, are functional in healthy lungs; they provide additional and more direct routes for long-range motion than the canonical airway tree. This is surprising, inasmuch as collateral ventilation is believed to be physiologically insignificant in healthy lungs. We discuss the effect on LRADC of small collateral connections through airway walls and rule out other possible mechanisms. The role of collateral paths is supported by measurements of smaller LRADC in pigs, where collateral ventilation is known to be smaller.

Non-Brownian Diffusion of Membrane Molecules in Nanopatterned Supported Lipid Bilayers

Molecules associated with the outer surface of living cells exhibit complex, non-Brownian patterns of diffusion. In this report, supported lipid bilayers were patterned with nanoscale barriers to capture key aspects of this anomalous diffusion in a controllable format. First, long-range diffusion coefficients of membrane-associated molecules were significantly reduced by the presence of the barriers, while short-range diffusion was unaffected. Second, this modulation was more pronounced for large molecular complexes than for individual lipids. Surprisingly, the quantitative effect of these barriers on long-range lipid diffusion could be accurately simulated using a simple, continuum-based model of diffusion on a nanostructured surface; we thus describe a metamaterial that captures the properties of the outer membrane of living cells.

Self-Assembly of Solid-Supported Membranes Using a Triggered Fusion of Phospholipid-Enriched Proteoliposomes Prepared from the Inner Mitochondrial Membrane1

A general procedure for the formation ofsolid-supported artificial membranes containing transmembrane proteins is reported. The main objective was to directly use the pool of proteins of the native biomembrane (here the inner membrane from mitochondria of human carcinogenic hepatic cells) and to avoid purification steps with detergent. Proteoliposomes of phospholipid-enriched inner membranes from mitochondria were tethered and fused onto a tailored surface via a streptavidin link. The failure of some preliminary experiments on membrane formation was attributed to strong nonspecific interactions between the solid surface and the protuberant hydrophilic parts of the transmembrane complexes. The correct loading of uniform membranes was performed after optimization of a tailored surface, covered with a grafted short-chain poly(ethylene glycol), so that nonspecific interactions are reduced. Step-by-step assembly of the structure and triggered fusion of the immobilized proteoliposomes were monitored by surface plasmon resonance and fluorescence photobleaching recovery, respectively. The long-range lateral diffusion coefficient (at 22 degrees C) for a fluorescent lipid varies from 2.5 x 10(-8) cm2 s(-1) for a tethered lipid bilayer without protein to 10(-9) cm2 s(-1) for a tethered membrane containing the transmembrane proteins of the respiratory chain at a protein area fraction of about 15%. The decrease in the diffusion coefficient in the tethered membrane with increase in protein area fraction was too pronounced to be fully explained by the theoretical models of obstructed lateral diffusion. Covalent tethering links with the solid are certainly involved in the decrease of the overall lateral mobility of the components in the supported membrane at the highest protein-to-lipid ratios.

Dependence of plastoquinol diffusion on the shape, size, and density of integral thylakoid proteins

The diffusion of plastoquinol in the chloroplast thylakoid membrane is modelled using Monte Carlo techniques. The integral proteins are seen as obstacles to diffusion, and features of percolation theory emerge. Thus, the diffusion coefficient diminishes with increasing distance and there is a critical threshold of protein concentration, above which the long-range diffusion coefficient is zero. The area occupied by proteins in vivo is assessed and appears to be around this threshold, as determined from calculations assuming randomly distributed noninteracting proteins. Slight changes in the protein arrangement lead to pronounced changes in diffusion behaviour under such conditions. Mobility of the proteins increases the protein occupancy threshold, while boundary lipids impermeable to PQ diffusion decrease it. Further, the obstruction of plastoquinone/plastoquinol binding sites in a random arrangement is evaluated.

A Model for Water Motion in Crystals of Lysozyme Based on an Incoherent Quasielastic Neutron-Scattering Study

This paper reports an incoherent quasielastic neutron scattering study of the single particle, diffusive motions of water molecules surrounding a globular protein, the hen egg-white lysozyme. For the first time such an analysis has been done on protein crystals. It can thus be directly related and compared with a recent structural study of the same sample. The measurement temperature ranged from 100 to 300 K, but focus was on the room temperature analysis. The very good agreement between the structural and dynamical studies suggested a model for the dynamics of water in triclinic crystals of lysozyme in the time range ∼330 ps and at 300 K. Herein, the dynamics of all water molecules is affected by the presence of the protein, and the water molecules can be divided into two populations. The first mainly corresponds to the first hydration shell, in which water molecules reorient themselves fivefold to 10-fold slower than in bulk solvent, and diffuse by jumps from hydration site to hydration site. The long-range diffusion coefficient is five to sixfold less than for bulk solvent. The second group corresponds to water molecules further away from the surface of the protein, in a second incomplete hydration layer, confined between hydrated macromolecules. Within the time scale probed they undergo a translational diffusion with a self-diffusion coefficient reduced ∼50-fold compared with bulk solvent. As protein crystals have a highly crowded arrangement close to the packing of macromolecules in cells, our conclusion can be discussed with respect to solvent behavior in intracellular media: as the mobility is highest next to the surface, it suggests that under some crowding conditions, a two-dimensional motion for the transport of metabolites can be dominant.

The existence of more than one jump process of hydrogen in palladium–silver alloys — an NMR study

The hydrogen dynamics in the α-phase of Pd 1− x Ag x H y has been studied by proton nuclear magnetic resonance (NMR) measurements. Jump frequencies of the hydrogen atoms in the metal lattice have been deduced from the dipolar spin-lattice relaxation rates Γ 1d by applying the BPP model. In PdH y , the temperature dependence of Γ 1d is well described by a single jump process for all hydrogen atoms. In contrast, in the palladium–silver alloys Pd 1− x Ag x H y , the Γ 1d data indicate more than one jump process with different activation energies. Two and three processes could be separated for x=0.1 and x=0.3, respectively. In both alloys, the diffusion process with the lowest activation energy ( E a=226 meV) is comparable to that in pure palladium. The jump processes with higher activation energies occur more frequently in Pd 0.7Ag 0.3 than in Pd 0.9Ag 0.1. This indicates higher energy-barriers for jumps between O-sites in silver-rich environments. Direct measurements of the long-range diffusion coefficients D were performed by pulsed-field-gradient (PFG)-NMR at temperatures up to 450 K. For both Pd 1− x Ag x H y samples, D( T) is well represented by a single Arrhenius law with the diffusion parameters D 0=3.0×10 −7 m 2 s −1 and E a=230 meV for x=0.1 and D 0=2.1×10 −7 m 2 s −1 and E a=260 meV for x=0.3. The diffusivities calculated from the jump frequencies of the hydrogen atoms are in good agreement with these PFG results and also with measurements using the time-lag technique.

Structure-dynamics relations in bicontinuous cubic lipid mesophases

We investigated the structural and dynamic properties of water in aqueous dispersions of the monoacylglycerides monoolein and monoelaidin, which exhibit a rich lyotropic mesophase behaviour [1-3]. We present data on the long-range diffusion coefficient of the lipid and the water in their bicontinuous cubic phases at several hydration levels. Using the proton/deuteron selectivity, field-gradient NMR makes the determination of the diffusion coefficients of both, water and lipid molecules, possible. Owing to the mesoscopic structure, effective diffusion coefficients are measured. The water diffusion is drastically slowed down compared to bulk water. In addition, we present a wide-angle neutron scattering study of the water structure in confined cubic geometries. By applying the H/D-substitution technique [4], the structural information could be obtained on the partial structure factor level. Dependent on level of hydration and mean water channel thickness, small, but significant changes of the structure of confined water compared to bulk water are observed.

Electrochemical Measurement of Lateral Diffusion Coefficients of Ubiquinones and Plastoquinones of Various Isoprenoid Chain Lengths Incorporated in Model Bilayers

The long-range diffusion coefficients of isoprenoid quinones in a model of lipid bilayer were determined by a method avoiding fluorescent probe labeling of the molecules. The quinone electron carriers were incorporated in supported dimyristoylphosphatidylcholine layers at physiological molar fractions (<3 mol%). The elaborate bilayer template contained a built-in gold electrode at which the redox molecules solubilized in the bilayer were reduced or oxidized. The lateral diffusion coefficient of a natural quinone like UQ 10 or PQ 9 was 2.0 ± 0.4 × 10 −8 cm 2 s −1 at 30°C, two to three times smaller than the diffusion coefficient of a lipid analog in the same artificial bilayer. The lateral mobilities of the oxidized or reduced forms could be determined separately and were found to be identical in the 4–13 pH range. For a series of isoprenoid quinones, UQ 2 or PQ 2 to UQ 10, the diffusion coefficient exhibited a marked dependence on the length of the isoprenoid chain. The data fit very well the quantitative behavior predicted by a continuum fluid model in which the isoprenoid chains are taken as rigid particles moving in the less viscous part of the bilayer and rubbing against the more viscous layers of lipid heads. The present study supports the concept of a homogeneous pool of quinone located in the less viscous region of the bilayer.

Diffusion in Disordered Structures

A lattice gas model is developed to study the influence of site and saddle point enthalpy disorder on tracer and collective diffusion of particles. This model can be applied to interstitial diffusion as well as substitutional diffusion processes. The short-range and long-range tracer diffusion coefficients are evaluated from Monte Carlo Simulations (MCS) for particle concentrations 0 ≤ c < 1 and compared with Effective Medium Calculations (EMA). The results for short-range diffusion agree rather well to theoretical calculations for any particle concentration and enthalpy disorder. The long-range diffusion coefficient determined by MCS corresponds to results obtained by EMA for low particle and high particle concentrations. The influence of energetical disorder on the tracer correlation factor is investigated for different particle concentrations. In case of low particle concentrations no dependence of the tracer correlation factor on the width of the site enthalpy distribution is found. In contrast, the tracer correlation factor decreases by increasing the width of the distribution of the saddle point enthalpies caused by increasing static correlations. With increasing particle concentrations the tracer correlation factor decreases. A complex interaction between static and dynamic correlations is found in the case of high particle concentrations c → 1. The tracer and the collective diffusion coefficient could be determined as a function of particle concentration as well as the width of the distribution of the site and saddle point enthalpies.

Long-Range Diffusion Coefficients in Two-Dimensional Fluid Media Measured by the Pyrene Excimer Reaction

Diffusion-controlled bimolecular reactions in two-dimensional or quasi two-dimensional space are important in both surface and membrane reaction kinetics. A model reaction that has been extensively used to study the dynamics and structure of phospholipid membranes is the formation of the excimer of pyrene. We present experimental evidence that in multilamellar liposomes of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine, in the fluid phase at temperatures above phase transition, TL, and for a probe/phospholipid ratio of 1:75, or lower, the fluorescence decay of 1-palmitoyl-2-(1-pyrenodecanoyl)-sn-glycero-3-phosphocholine and the time-resolved emission of the excimer follow a kinetic law specific for two-dimensional diffusion-controlled reactions. The parameters obtained from the application of this law to the experimental results, either from steady-state or from time-dependent fluorescence, give diffusion coefficients, e.g., D(25 °C) = 3.1 × 10-8 cm2 s-1 and an activation energy for diffusion, Ea = 35 k...