Estimation of Water Diffusion Coefficients in Freeze-Concentrated Matrices of Sugar Solutions Using Molecular Dynamics: Correlation Between Estimated Diffusion Coefficients and Measured Ice-Crystal Recrystallization Rates

The diffusion coefficient of the water component in a freeze-concentrated matrix is a useful parameter for predicting and controlling the recrystallization rate of ice crystals in sugar solutions relevant to frozen desserts. Herein, application of molecular dynamics (MD) for estimating the water diffusion coefficient in a freeze-concentrated matrix of sugar solutions is described. Diffusion coefficients evaluated using MD with the optimized potentials for liquid simulations all atom force field and water models of three types (simple point charge, simple point charge extended, and transferable intermolecular potential-4 point) show a good positive linear relation with measured values, indicating that the MD methods used in this study are useful for predicting differences in water diffusion coefficients in a sugar freeze-concentrated matrix. Furthermore, similarly to measured values, the estimated diffusion coefficients show a good positive correlation with recrystallization rates of ice crystals, which suggests that MD is useful to predict differences in recrystallization rates of ice crystals in frozen sugar solutions.     

Recrystallization of Ice Crystals in Trehalose Solution at Isothermal Condition

An isothermal ice recrystallization behavior in trehalose solution was investigated. The isothermal recrystallization rate constants of ice crystals in trehalose solution were obtained at ?5 °C, ?7 °C, and ?10 °C. Then the results were compared to those of a sucrose solution used as a control sample. Simultaneous estimation of water mobility in the freeze-concentrated matrix was conducted by ¹H spin–spin relaxation time T₂ to investigate mechanisms causing the different ice crystal recrystallization behaviors of sucrose and trehalose. At lower temperatures, lower recrystallization rates were obtained for both trehalose and sucrose solutions. The ice crystallization rate constants in trahalose solution tended to be smaller than those in sucrose solution at the same temperature. Although different ice contents (less than 3.6%) were observed between trehalose and sucrose solutions at the same temperature, the recrystallization behaviors of ice crystals were not markedly different. The ¹H spin–spin relaxation time T₂ of water components in a freeze-concentrated matrix for trehalose solution was shorter than in a sucrose solution at the same temperature. Results show that the water mobility of trehalose solutions in freeze-concentrated matrix was less than that of sucrose solutions, which was suggested as the reason for retarded ice crystal growth in a trehalose solution. Results of this study suggest that the replacement of sucrose with trehalose will not negatively affect deterioration caused by ice crystal recrystallization in frozen foods and cryobiological materials.     

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 polymers in cartilage as studied by pulsed field gradient NMR

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) was used to investigate the self-diffusion behaviour of polymers in cartilage. Polyethylene glycol and dextran with different molecular weights and in different concentrations were used as model compounds to mimic the diffusion behaviour of metabolites of cartilage. The polymer self-diffusion depends extremely on the observation time: The short-time self-diffusion coefficients (diffusion time Delta approximately 15 ms) are subjected to a rather non-specific obstruction effect that depends mainly on the molecular weights of the applied polymers as well as on the water content of the cartilage. The observed self-diffusion coefficients decrease with increasing molecular weights of the polymers and with a decreasing water content of the cartilage. In contrast, the long-time self-diffusion coefficients of the polymers in cartilage (diffusion time Delta approximately 600 ms) reflect the structural properties of the tissue. Measurements at different water contents, different molecular weights of the polymers and varying observation times suggest that primarily the collagenous network of cartilage but also the entanglements of the polymer chains themselves are responsible for the observed restricted diffusion. Additionally, anomalous restricted diffusion was shown to occur already in concentrated polymer solutions.     

Lateral diffusion of cholesterol and dimyristoylphosphatidylcholine in a lipid bilayer measured by pulsed field gradient NMR spectroscopy

The pulsed field gradient NMR method for measuring self-diffusion has been used for a direct determination of the lateral diffusion coefficient of cholesterol, fluorine labeled at the 6-position, for an oriented lamellar liquid-crystalline phase of dimyristoylphosphatidylcholine (DMPC)/cholesterol/water. It is found that the diffusion coefficients of DMPC and cholesterol are equal over a large temperature interval. The apparent energy of activation for the diffusion process (58 kJ/mol) is about the same as for a lamellar phase of DMPC/water, whereas the phospholipid lateral diffusion coefficient is approximately four times smaller in the presence of cholesterol.     

Temperature dependence of water self-diffusion through lipid bilayers assessed by NMR

The temperature dependence of the coefficient of water self-diffusion across plane-parallel multib-ilayers of dioleoylphosphatidylcholine oriented on a glass support was studied in the 20–60°C range by pulsed field gradient NMR. The coefficient for transbilayer diffusion of water proved almost four orders of magnitude smaller than for bulk water, and 10 times smaller than that for lateral diffusion of lipid under the same conditions. The temperature dependence obeyed the Arrhenius law with apparent activation energy of 41 kJ/mol, much higher than that for bulk water (18 kJ/mol). The experimental data were analyzed using the “dissolution-diffusion” model, by simulating water passage through membrane channels, and by examining water exchange in states with different modes of translational mobility, including pore channels and bilayer defects. Each approach could take into account the role of bilayer permeability and assess the apparent activation energy for water diffusion in the hydrophobic part of the bilayer, which proved close to the value for bulk water. Estimates were obtained for water diffusion coefficients in the system, coefficients of bilayer permeability for water, and the influence of bilayer defects on the lateral and transverse diffusion coefficients.     

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.     

An NMR study of the temperature dependence of the coefficient of water self-diffusion through lipid bilayer membranes

The temperature dependence of the coefficient of water self-diffusion through plane-parallel lipid multilayers of the phospholipid dioleoylphosphatidylcholine oriented on a glass support has been studied in the temperature range of 20-60 degrees C by the method of NMR with magnetic field pulse gradient. The values of the coefficients of transbilayer water diffusion are by four orders of magnitude less than for bulky water and ten times less than the coefficients of lateral diffusion of the lipid under the same conditions. The temperature dependence of the coefficient of water diffusion is described by the Arrhenius law with an apparent activation energy of about 41 kJ/mol, which far exceeds the activation energy for the diffusion of bulky water (18 kJ/mol). The experimental data were analyzed using a "dissolving-diffusion" model, by simulating the passage of water through membrane channels, and by analyzing the exchange of water molecules in states with different modes of translation mobility, including pore channels and bilayer "defects". Each of the approaches used made it possible to take the significance of bilayer permeability for the apparent energy of activation of water diffusion into account and estimate the energies of activation of water diffusion in the hydrophobic moiety of the bilayer, which were found to be close to the values for bulky water. The coefficients of water diffusion in the system under examination and the coefficients of permeation of water through the bilayer were estimated, and the effect of bilayer "defects" on the coefficients of water diffusion along and across bilayers was studied.     

The self-diffusion of water in Artemia cysts

The self-diffusion coefficient of water molecules has been measured by nuclear magnetic resonance in cysts of Artemia over a wide range of hydration. Compared to the value for bulk water, the diffusion coefficient is reduced by a factor of 7 at the highest hydration and by approximately 100 at the lowest hydration. The results are used to evaluate various models that have been proposed to account for the reduction of water self-diffusion coefficients in complex systems.     

Permeability of lysozyme tetragonal crystals to water

Diffusion of water within cross-linked tetragonal crystals of hen egg-white lysozyme has been measured and simulated on a computer using the X-ray structure of water-filled channels within the crystal lattice. Relative to the self-diffusion coefficient of bulk water molecules, the experimental diffusion coefficient of water within the crystal was found to be 13 times reduced in the (001) crystallographic plane and 5 times reduced in the [001] direction. Comparison of the experimental and computer simulated diffusion coefficients shows that steric limitations for water diffusion are mostly responsible for this reduction of the water diffusion in the crystal, with the self-diffusion coefficient of intracrystalline water reduced by no more than 30–40% as compared to that of bulk 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.     

The molecular basis of the solution properties of hyaluronan investigated by confocal fluorescence recovery after photobleaching.

Hyaluronan (HA) is a highly hydrated polyanion, which is a network-forming and space-filling component in the extracellular matrix of animal tissues. Confocal fluorescence recovery after photobleaching (confocal-FRAP) was used to investigate intramolecular hydrogen bonding and electrostatic interactions in hyaluronan solutions. Self and tracer lateral diffusion coefficients within hyaluronan solutions were measured over a wide range of concentrations (c), with varying electrolyte and at neutral and alkaline pH. The free diffusion coefficient of fluoresceinamine-labeled HA of 500 kDa in PBS was 7.9 x 10(-8) cm(2) s(-1) and of 830 kDa HA was 5.6 x 10(-8) cm(2) s(-1). Reductions in self- and tracer-diffusion with c followed a stretched exponential model. Electrolyte-induced polyanion coil contraction and destiffening resulted in a 2.8-fold increase in self-diffusion between 0 and 100 mM NaCl. Disruption of hydrogen bonds by strong alkali (0.5 M NaOH) resulted in further larger increases in self- and tracer-diffusion coefficients, consistent with a more dynamic and permeable network. Concentrated hyaluronan solution properties were attributed to hydrodynamic and entanglement interactions between domains. There was no evidence of chain-chain associations. At physiological electrolyte concentration and pH, the greatest contribution to the intrinsic stiffness of hyaluronan appeared to be due to hydrogen bonds between adjacent saccharides.     

Calorimetric study of crystal growth of ice in hydrated methemoglobin and of redistribution of the water clusters formed on melting the ice.

Calorimetric studies of the melting patterns of ice in hydrated methemoglobin powders containing between 0.43 and 0.58 (g water)/(g protein), and of their dependence on annealing at subzero temperatures and on isothermal treatment at ambient temperature are reported. Cooling rates were varied between approximately 1500 and 5 K min-1 and heating rate was 30 K min-1. Recrystallization of ice during annealing is observed at T > 228 K. The melting patterns of annealed samples are characteristically different from those of unannealed samples by the shifting of the melting temperature of the recrystallized ice fraction to higher temperatures toward the value of "bulk" ice. The "large" ice crystals formed during recrystallization melt on heating into "large" clusters of water whose redistribution and apparent equilibration is followed as a function of time and/or temperature by comparison with melting endotherms. We have also studied the effect of cooling rate on the melting pattern of ice with a methemoglobin sample containing 0.50 (g water)/(g protein), and we surmise that for this hydration cooling at rates of > or = approximately 150 K min-1 preserves on the whole the distribution of water molecules present at ambient temperature.     

Application of a thermodynamic model to the prediction of phase separations in freeze-concentrated formulations for protein lyophilization

Many of the compounds considered for use in pharmaceutical formulations demonstrate incompatibilities with other components at high enough concentrations, including pairs of polymers, polymers and salts, or even proteins in combination with polymers, salts, or other proteins. Freeze concentration can force solutions into a region where incompatibilities between solutes will manifest as the formation of multiple phases. Such phase separation complicates questions of the stability of the formulation as well as labile components, such as proteins. Yet, phase separation events are difficult to identify by common formulation screening methods. In this report, we use the osmotic virial expansion model of Edmond and Ogston (1) to describe phase-separating behavior of ternary aqueous polymer solutions. Second osmotic virial coefficients of polyethylene glycol 3350 (PEG) and dextran T500 were measured by light scattering. Assuming an equilibrium between ice and water in the freeze-concentrated solution, a degree of freeze concentration can be estimated, which, when combined with the phase separation spinodal, describes a "phase separation envelope" in which phase separation tendencies can be expected in the frozen solution. The phase separation envelope is bounded at low temperatures by the glass transition temperature of the freeze-concentrated solution. Scanning electron microscopic images and infrared spectroscopy of protein structure are provided as experimental evidence of the phase separation envelope in a freeze-dried system of PEG, dextran, and hemoglobin.     

Ice Recrystallization Behavior of Corn Starch/Sucrose Solutions: Effects of Addition of Corn Starch and Antifreeze Protein III

Knowledge of the behavior of corn starch during frozen storage is necessary to understand more complex systems. In the present study, ice recrystallization in corn starch (0.3% and 3%, w/w)/sucrose (40%, w/w) solution was investigated at −10 °C based on the theory of Ostwald ripening. The addition of corn starch to the sucrose solution increased the ice recrystallization (IR) rate constant. To explore the mechanism causing higher IR rate constant, fluorescence microscopy was used to analyze the distribution of corn starch molecules. Fluorescence micrograph showed corn starch distributed homogenously in the freeze-concentrated phase. Ice crystal size distribution assessment showed that at the same average radius, the addition of corn starch increased the standard deviation of ice crystal size distribution. The findings revealed that the addition of corn starch widened the distribution of ice crystal size, which may be the mechanism causing higher IR rate constant. To inhibit the ice recrystallization process, antifreeze protein type III (AFP III) was added to sucrose solutions with and without corn starch. In the presence of corn starch, 0.01-mg/mL AFP III was enough to significantly reduce the IR rate. Conversely, the samples without corn starch did not show a significant reduction in IR rate constant at the same AFP III concentration. The outcomes revealed that corn starch enhanced the activity of AFP III. The results of this study showed that corn starch increased the IR rate constant, and AFP III supplemented with corn starch was synergistically more efficient in retarding IR rate constant.

     

Heterogeneous diffusion in aerobic granular sludge

Aerobic granular sludge (AGS) technology allows simultaneous nitrogen, phosphorus, and carbon removal in compact wastewater treatment processes. To operate, design, and model AGS reactors, it is essential to properly understand the diffusive transport within the granules. In this study, diffusive mass transfer within full-scale and lab-scale AGS was characterized with nuclear magnetic resonance (NMR) methods. Self-diffusion coefficients of water inside the granules were determined with pulsed-field gradient NMR, while the granule structure was visualized with NMR imaging. A reaction-diffusion granule-scale model was set up to evaluate the impact of heterogeneous diffusion on granule performance. The self-diffusion coefficient of water in AGS was ∼70% of the self-diffusion coefficient of free water. There was no significant difference between self-diffusion in AGS from full-scale treatment plants and from lab-scale reactors. The results of the model showed that diffusional heterogeneity did not lead to a major change of flux into the granule (<1%). This study shows that differences between granular sludges and heterogeneity within granules have little impact on the kinetic properties of AGS. Thus, a relatively simple approach is sufficient to describe mass transport by diffusion into the granules.     

High resolution q-space imaging studies of water in elastin

We report on the direct measurement of the molecular diffusion coefficients of water confined to purified bovine nuchal ligament elastin by high resolution q-space NMR imaging. The experimental data indicate that water trapped within an elastin fiber has two distinguishable molecular diffusion coefficients. The component with the slowest mobility has a diffusion coefficient on the order of 10(-6) cm(2)/s that varies inversely with the diffusion time and is seen to reduce near 37 degrees C. The component with higher mobility has a diffusion coefficient reminiscent of free water but is observed to also behave similarly at 37 degrees C. From our experimental data we extract the surface-to-volume ratio of pores within elastin and associated changes as a function of temperature.     

Peptide self-association in aqueous trifluoroethanol monitored by pulsed field gradient NMR diffusion measurements

Defining the self-association state of a molecule in solution can be an important step in NMR-based structure determination. This is particularly true of peptides, where there can be a relatively small number of long-range interactions and misinterpretation of an intermolecular NOE as an intramolecular contact can have a dramatic influence on the final calculated structure. In this paper, we have investigated the use of translational self-diffusion coefficient measurements to detect self-association in aqueous trifluoroethanol of three peptides which are analogues of the C-terminal region of human neuropeptide Y. Experimentally measured diffusion coefficients were extrapolated to D⁰, the limiting value as the peptide concentration approaches zero, and then converted to D_20,w, the diffusion coefficient after correction for temperature and the viscosity of the solvent. A decrease in D_20,w of about 16% was found for all three peptides in aqueous TFE (30% by volume) compared with water, which is in reasonable agreement with the expected decrease upon dimerisation, the presence of which was indicated by sedimentation equilibrium measurements. Apparent molecular masses of these peptides in both solutions were also calculated from their diffusion coefficients and similar results were obtained. Several potential internal standards, including acetone, acetonitrile, dimethylsulfoxide and dioxane, were assessed as monitors of solution viscosity over a range of trifluoroethanol concentrations. Compared with independent measurements of viscosity, acetonitrile was the most accurate standard among these four. The practical limitations of a quantitative assessment of peptide self-association from translational diffusion coefficients measured by PFGNMR, including the calculation of apparent molecular mass, are also discussed.     

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).     

Solubility and diffusion of nitrogen in maltodextrin/protein tablets

The gas transport properties of compacted tablets consisting of an amorphous mixture of maltodextrin and sodium caseinate were studied by dissolving nitrogen gas in the tablets and then determining the gas release over time as a function of temperature and water activity. Gas was dissolved in the tablet matrix by heating the tablets under pressure, generally to temperatures above the glass transition temperature of the matrix, holding them at these conditions for a specified time and then rapidly cooling them while maintaining the external pressure. The solubility of nitrogen was found to be largely determined by the free volume of the matrix, which in turn can be influenced to some degree by thermal and pressure treatments during gas loading. At the levels of free volume studied, the dissolved nitrogen is densely packed in the free volume, the packing density being virtually independent of the externally applied pressure. Release of gas from the tablets at temperatures below the glass transition temperature is generally well described by Fickian diffusion. The effective diffusion coefficient of gas release is strongly dependent on the microstructure and porosity of the tablet matrix, and an approximate model describing the relationship between tablet structure and rate of gas release is formulated. The model is in semiquantitative agreement with the rates of gas diffusion obtained for tablets and dense granules. Owing to the structural heterogeneity and variability of the tablets and the history-dependent properties of the tablet matrix, the effective diffusion coefficients of gas release from the tablets showed a relatively large spread. The temperature dependence of diffusional release follows an Arrhenius relation below the glass transition temperature. This allows the prediction of the nitrogen retention in the tablets as function of time, temperature and pressure.