Cation diffusion in cartilage measured by pulsed field gradient NMR

In this study, the pulsed field gradient (PFG) nuclear magnetic resonance (NMR) technique was used for the investigation of (1) concentration and compression effects on cation self-diffusion, and (2) restricted diffusion of cations in cartilage. Since physiologically relevant cations like Na+ are difficult to investigate owing to their very short relaxation times, the cations tetramethylammonium (TMA) and tetraethylammonium (TEA) were employed for diffusion studies in samples of explanted cartilage. Results indicated that the diffusion of monovalent cations shows strong similarities to observations already made in studies of the diffusion of water in cartilage: with increasing compression, i.e. decreasing water content, the diffusion coefficient of the cation decreases concomitantly. The diffusion coefficients also showed a decrease with increasing cation concentrations, basically reflecting the corresponding decrease in the water content. Both results could be explained by the well-established model of Mackie and Meares. This, together with the similarity of the diffusion coefficient D in cartilage relative to free solution (about 50%) for both cations, is consistent with the view that the water content and not the charge is the most important determinant of the intratissue diffusivity of monovalent cations. Diffusion studies with increasing observation times showed strong evidence of restricted diffusion, allowing the estimation of the geometry of barriers within cartilage.     

PFG-NMR measurements of the self-diffusion coefficients of water in equilibrium poly(HEMA-co-THFMA) hydrogels

The self-diffusion coefficients for water in a series of copolymers of 2-hydroxyethyl methacrylate, HEMA, and tetrahydrofurfuryl methacrylate, THFMA, swollen with water to their equilibrium states have been studied at 310 K using PFG-NMR. The self-diffusion coefficients calculated from the Stejskal-Tanner equation, D(obs), for all of the hydrated polymers were found to be dependent on the NMR storage time, as a result of spin exchange between the proton reservoirs of the water and the polymers, reaching an equilibrium plateau value at long storage times. The true values of the diffusion coefficients were calculated from the values of D(obs) in the plateau regions by applying a correction for the fraction of water protons present, obtained from the equilibrium water contents of the gels. The true self-diffusion coefficient for water in polyHEMA obtained at 310 K by this method was 5.5 x 10(-10) m(2)s-1. For the copolymers containing 20% HEMA or more a single value of the self-diffusion coefficient was found, which was somewhat larger than the corresponding values obtained for the macroscopic diffusion coefficient from sorption measurements. For polyTHFMA and copolymers containing less than 20% HEMA, the PFG-NMR stimulated echo attenuation decay curves and the log-attenuation plots were characteristic of the presence of two diffusing water species. The self-diffusion coefficients of water in the equilibrium-hydrated copolymers were found to be dependent on the copolymer composition, decreasing with increasing THFMA content.     

Self-diffusion of water into silk fibers from magnetic field pulse gradient data

Self-diffusion of water was studied in fibers of natural silk (Bombyx mori) with a water content of 0.18 g H2O/g dried material. Self-diffusion measurements were conducted by pulsed gradient of magnetic field (stimulated echo) at diffusion times from 10 to 200 mc. The dependence of experimental diffusion coefficients Dexp = f(delta) (observed decrease when delta increased) was determined to be responsible for the restricted diffusion. A model of planar and regularly spaced permeable barriers to diffusion of water molecules was applied to estimate the barrier spacing a and the permeability constant p. The maximal value of Dexp (at short diffusion time) in B. mori silk fibres was about 0.06 of the value of Dexp in bulk free water. The results obtained are compared to literature data on self-diffusion of water in hydrated biopolymer fibers and are discussed in connection with molecular mobility in natural macromolecular systems with low water content.     

Molecular modeling study of sulfonated SIBS triblock copolymers

An important class of thermoplastic elastomers involves polystyrene and polyisobutylene blocks (SIBS). Sulfonated SIBS Triblock Copolymers (S-SIBS) are of particular interest because of potential applications for fuel cell and textile applications, where breathable, protective clothing is required. We have used multiscale modeling to gain an understanding of the static and dynamic properties of these polymer systems at detailed atomistic levels. Quantum chemistry tools were used to elucidate the bonding of water molecules and sulfonate groups. In addition, molecular dynamics was applied to calculate the polymer density at various levels of sulfonation. The structures of polymer with hydronium ions and also water were studied and the mechanism of water self-diffusion was proposed. It was found that with increase of water content the hydronium ions move further away from sulfonate groups. The self-diffusion coefficients of water were found to reproduce well experimental trends. Two different distributions of sulfonate groups were studied: one blocky and another perfectly dispersed. In the case of the blocky architecture, the water clusters are connected at a lower sulfonation level, leading to increased water diffusion coefficients as compared to the dispersed architecture.     

Immunostimulatory polysaccharides from Chlorella pyrenoidosa. A new galactofuranan. measurement of molecular weight and molecular weight dispersion by DOSY NMR

Fractionation of the hot water extract of Chlorella pyrenoidosa was performed using a combination of ethanol precipitation, size exclusion chromatography, and anion exchange chromatography. One fraction contained a new polysaccharide, and this compound was shown to be a 1-->2-linked beta-d-galactofuranan from its 1D and 2D (1)H and (13)C NMR spectra, with a molecular weight of 15 kDa from DOSY NMR measurements. A number of other fractions were shown to have the same repeating unit as the previously identified arabinogalactan. However, arabinogalactans from different fractions were shown by DOSY NMR to have different molecular weights, which ranged from 27 to 1020 kDa. Agreement with molecular weights measured for some of these fractions by SEC-MALS was very good, further confirming the relationship established by Viel et al. between molecular weights of neutral polysaccharides and self-diffusion coefficients. The smaller molecular weight polysaccharides, the galactofuranan and the 27 and 50 kDa arabinogalactans, were shown to be close to monodisperse by analysis of the distributions of the self-diffusion coefficients for the polymers. The larger arabinogalactans had considerable variation in their molecular weights (188 +/- 109 kDa and 1020 +/- 370 kDa). Only the two larger arabinogalactans showed immunostimulatory activity.     

NMR-investigation of restricted self-diffusion of oil in rape seeds

The self-diffusion of oil and water in rape seeds (Brassica napus L.) was measured with the NMR pulsed field gradient technique. The self-diffusion of oil was found to be completely restricted for diffusion times > 30 ms. The experiments could be explained in terms of the model of diffusion within spherical droplets and a Gaussian mass distribution of the droplet radii. The mean droplet radius was found to be about 0.7 m; this value decreased somewhat with increasing moisture content of the seeds. The experiments could also be explained with a Gaussian number distribution of droplet radii and a fraction of immobile protons in the NMR signal of 5 ... 10%, possibly arising from lipid protons. Though the transverse nuclear magnetic relaxation decay of the oil protons is not a single exponential we observe one uniform diffusive mobility for the oil molecules. The water self-diffusion coefficient at maximum moisture content of about 40% was determined to be 4.2 · 10^-10 m² s^-1 which is typical for swollen polymer-solvent systems at such a concentration. Offprint requests to: P. W. Kuchel     

Combined analysis of diffusion and relaxation behavior of water in apple parenchyma cells

With apple parenchymal cells as an example, we demonstrate the expedience of combined analysis of the relaxation and diffusion of water molecules in plant cells by NMR spectroscopy. At small diffusion times, our approach discerns three relaxation components pertaining to water in the vacuole, cytoplasm, and intercellular space. The corresponding self-diffusion coefficients are determined. At long diffusion times, it is possible to distinguish two components. For the slow-relaxing component (vacuolar water) we observe the mode of restricted diffusion. For the fast-relaxing components, the diffusion coefficient anomalously increases with time.     

Generalized concentration dependence of globular protein self-diffusion coefficients in aqueous solutions.

The self-diffusion coefficients of globular proteins (myoglobin, bovine serum albumin, barstar, lysozyme) in aqueous solutions at different temperatures and pH values are obtained by pulsed-gradient spin-echo NMR, and their concentration dependence is analyzed. The generalized concentration dependence of globular protein self-diffusion coefficients is empirically established, and compared to the concentration dependence of diffusion coefficients of flexible polymers and rigid Brownian particles.     

Dynamics of Small Molecules in a Dense Polymer Matrix: Molecular Dynamics Studies

Abstract

The anomalous diffusion regime appearing in the self-diffusion of small molecules in bulk amorphous polymers has been extensively studied by molecular dynamics simulations. A rather long simulation of duration ～ 10 ^?8 s is performed on a polyethylene-like simple polymer model containing either oxygen molecules or helium atoms as a diffusant. Dynamic properties evaluated for these diffusants are the mean-square displacement, the van Hove self correlation function, and the self part of the density autocorrelation. It is first confirmed that the anomalous diffusion regime appears in a few hundred picoseconds for oxygen molecule, while the Einstein relation adopted beyond this regime results in the self-diffusion coefficient of the order of ～ 10^?5 cm²/s. This anomaly is still observed for helium that diffuses much faster than oxygen. In the anomalous diffusion regime, it is found that the correlation functions for the two diffusants show characteristic features and become essentially the same as time is scaled appropriately. These features allow the estimation of the two characteristic spatial scales which are probably dominated by the microstructure of the polymer matrix, namely, the cage size and the distance between adjacent cages. The time dependence of the mean-square displacements of the two diffusants can be well interpreted by these characteristic spatial scales as time is scaled with the self-diffusion coefficients. It is shown that the anomalous diffusion regime arises from the inhomogeneous microstructure of the polymer matrix.     

Calculation of self-diffusion coefficients of the [BMIM][TFSA]/water system by molecular dynamics simulation

We performed a molecular dynamics simulation to calculate the self-diffusion coefficients of 1-Butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide and water in a water–ionic liquid mixture. We then compared the simulated self-diffusion coefficients of cation, anion and water molecules with experimental data and with simulated data from the literature. Although the simulation overestimated the self-diffusion coefficients of ions, the simulated results qualitatively reproduced the enhancement of the self-diffusion coefficients of water as the water molar fraction increased. We also calculated the radial distribution functions to investigate the solution structure, i.e. the clustering of water molecules. The clustering of water in ionic liquid was found to play an important role in the enhancement of the diffusion of water molecules in the ionic liquid.     

Diffusion of water in the endosperm tissue of wheat grains as studied by pulsed field gradient nuclear magnetic resonance.

Pulsed field gradient nuclear magnetic resonance has been used to measure water self-diffusion coefficients in the endosperm tissue of wheat grains as a function of the tissue water content. A model that confines the water molecules to a randomly oriented array of capillaries with both transverse dimension less than 100 nm has been used to fit the data and give a unique diffusion coefficient at each water content. The diffusion rates vary from 1.8 x 10(-10) m2s-1 at the lowest to 1.2 x 10(-9) m2s-1 at the highest moisture content. This variation can be explained in terms of an increase in water film thickness from approximately 0.5 to approximately 2.5 nm over the moisture range investigated (200-360 mg g-1).     

Hydrolytic Degradation of Poly(3-Hydroxybutyrate) and Its Copolymer with 3-Hydroxyvalerate of Different Molecular Weights in vitro

The hydrolytic degradation of polymer films of poly(3-hydroxybutyrate) of different molecular weights and its copolymers with 3-hydroxyvalerate (9 mol % 3-hydroxyvalerate in the poly(3-hydroxybutyrate) chain) of different molecular weights was studied in model conditions in vitro. The changes in the physicochemical properties of the polymers were investigated using different analytical techniques: viscometry, differential scanning calorimetry, gravimetrical method, and water contact angle measurement for polymers. The data showed that in a period of 6 months the weight of polymer films decreased insignificantly. The molecular weight of the samples was reduced significantly; the largest decline (up to 80% of the initial molecular weight of the polymer) was observed in the high-molecular-weight poly(3-hydroxybutyrate). The surface of all investigated polymers became more hydrophilic. In this work, we focus on a mathematical model that can be used for the analysis of the kinetics of hydrolytic degradation of poly(3-hydroxyaklannoate)s by noncatalytic and autocatalytic hydrolysis mechanisms. It was also shown that the degree of crystallinity of some polymers changes differently during degradation in vitro. Thus, the studied polymers can be used to develop biodegradable medical devices such that they can perform their functions for a long period of time.     

1H-nmr study of water dynamics in hydrated collagen: transverse relaxation-time and diffusion analysis

Water proton transverse relaxation times (T2) and self-diffusion coefficients (D) were measured in randomly oriented hydrated collagen fibers. Three T2 relaxation times were discerned indicating the presence of at least three water fractions in the collagen sample. The D values associated with each water fraction were determined. The diffusion time dependence of D suggests water motion is restricted by macromolecular structure. The experimental results are discussed with reference to the structural properties of hydrated collagen fibers.     

Study of water and oil diffusion in rape seeds with sorption-desorption and NMR techniques.

The sorption and desorption of water in rape seeds was measured. From the sorption isotherm it follows that for water content greater than about 6% the water molecules tend to form clusters. The mutual diffusion coefficient of water into and out of the seeds was determined from the time dependence of sorption and desorption. There is a pronounced hysteresis in the sorption-desorption process, desorption proceeds faster than sorption. The self-diffusion of water (at maximum humidity of the seeds) and oil within the seeds was investigated by the pulsed field gradient NMR. The measurement of oil self-diffusion shows restricted diffusion of the oil within droplets and allows the determination of the droplet radii and their distribution width.     

Analysis of cell growth kinetics and substrate diffusion in a polymer scaffold.

The cultivation of cartilage cells (chondrocytes) in polymer scaffolds leads to implants that may potentially be used to repair damaged joint cartilage or for reconstructive surgery. For this technique to be medically applicable, the physical parameters that govern cell growth in a polymer scaffold must be understood. This understanding of cell behavior under in vitro conditions, where diffusion is the primary mode of transport of nutrients, may aid in the scale-up of the cartilage generation process. A mathematical model of chondrocyte generation and nutrient consumption is developed here to analyze the behavior of cell growth in a biodegradable polymer matrix for a series of different thickness polymers. Recent literature has implied that the diffusion of nutrients is a major factor that limits cell growth (Freed et al., 1994). In the present paper, a mathematical model is developed to directly relate the effects of increasing cell mass in the polymer matrix on the transport of nutrients. Reaction and diffusion of nutrients in the cell-polymer system are described using the fundamental species continuity equations and the volume averaging method. The volume averaging method is utilized to derive a single averaged nutrient continuity equation that includes the effective transport properties. This approach allows for the derivation of effective diffusion and rate coefficients as functions of the cell volume fraction. The cell volume fraction as a function of time is determined by solution of a material balance on cell mass. Growth functions including the Moser, a modified Contois, and an nth-order heterogeneous growth kinetic model are evaluated through a parameter analysis, and the results are compared to experimental data found in the literature. The results indicate that cellular functions in conjunction with mass transfer processes can account partially for the general trends in the cell growth behavior for various thickness polymers. The Contois growth function appeared to describe the data more accurately in terms of the lag period at early times and the long time limits. However, all kinetic growth functions required variations in the kinetic parameters to fully describe the effects of polymer thickness. This result implies that restricted diffusion of nutrients is not the sole factor limiting cell growth when the thickness of the polymer is changed. Therefore, further experimental data and model improvements are needed to accurately describe the cell growth process.     

Lateral diffusion in model membranes is independent of the size of the hydrophobic region of molecules.

We have systematically investigated the probe size and shape dependence of lateral diffusion in model dimyristoyl phosphatidylcholine membranes. Linear hydrophobic polymers, which differ in length by an order of magnitude, were used to explore the effect on the lateral diffusion coefficient of hydrodynamic restrictions in the bilayer interior. The polymers employed are isoprenoid alcohols--citronellol, solanesol, and dolichol. Tracer lateral diffusion coefficients were measured by fluorescence photobleaching recovery. Despite the large difference in lengths, the nitrobenzoxadiazole labelled alcohols all diffuse at the rate of lipid self-diffusion (5.0 x 10(-12) m2 s-1, 29 degrees C) in the liquid crystal phase. Companion measurements in isotropic polymer solution, in gel phase lipid membranes and with nonpolar fluorescent polyaromatic hydrocarbons, show a marked dependence of the lateral diffusion coefficient on the probe molecule size. Our results in the liquid crystal phase are in accord with free area theory which asserts that lateral diffusion in the membrane is restricted by the surface-free area. Probe molecules which are significantly longer than the host phospholipid, seven times longer in the case of dolichol, are still restricted in their lateral motion by the surface properties of the bilayer in the liquid crystal phase. Fluorescence quenching experiments indicate that the nitrobenzoxadiazole label does not reside at the aqueous interface, although it must reside in close proximity according to the diffusion measurements.     

Intracellular diffusion of water

Self-diffusion of cell water has been measured at diffusion times ranging from 0.3 ms to 1.0 s for human red cells, yeast, and brine shrimp using various pulsed gradient NMR methods. Intracellular diffusion coefficients and membrane permeabilities are calculated from these data with the aid of previous theoretical results for regularly spaced permeable planar barriers. The intracellular diffusion coefficients of water range from 1.2 X 10(-6) to 6 X 10(-6) cm2/s for the various samples. Outer-membrane permeabilities to water range from 0.0001 to 0.01 cm/s. The self-diffusion coefficient of lipid in a sample of human breast adipose tissue was found to be 1.5 X 10(-7) cm2/s.     

Activation enthalpy of diffusion for well fractionated dextrans in aqueous solutions

Interdiffusion coefficients have been determined for seven well defined dextran fractions in aqueous solutions at 20, 25, 30 and 35 degrees C. For dextrans with number average molecular weights (Mn) greater than about 20 000, a plot of the apparent activation energy of diffusion (ED) against Mn is given by: ED = 2.763 x 10(-5) Mn + 3.38. Similarly, for weigh molecular weight (Mw): ED = 1.889 x 10(-5) Mw + 3.61. The extrapolated ED values (3.38 and 3.61) are in reasonably good agreement with published data for the activation energy of self-diffusion for water.     

Analysis of diffusion and relaxation behavior of water in apple parenchymal cells

It has been demonstrated by an example of apple parenchymal cells that NMR spectroscopy can be used to analyze the relaxation and diffusion of water molecules in plant cells. With small diffusion times, three relaxation components have been distinguished, which correspond to water in a vacuole, in the cytoplasm, and in intercellular liquid. The coefficient of self-diffusion corresponding to these components have been determined. With large diffusion times, it is possible to distinguish two components. For the slowly relaxing component (which corresponds to water in a vacuole), the regime of restricted diffusion was observed. For a quickly relaxing component, an anomalous increase in the coefficient of self-diffusion with the time of diffusion took place.     

Solvent effects in N-carboxyanhydride (NCA) polymerization initiated by strong base type initiators

The γ-benzyl-L -glutamate N-carboxyanhydride (NCA) polymerization initialed by diisopropylamine was studied in dimethylformamide (DMF)-dioxane mixtures of different compositions. It was found that the shape of the conversion versus time plots and the molecular weights of the polymers depend on the solvent composition. Auto-catalysis is present only when dioxane predominates in the solvent mixtures. Moreover, the molecular weight of the final polymer depends strongly on the precipitation conditions when the polymerization is carried out in DMF.