Gelation conditions and transport properties of hollow calcium alginate capsules

The diameter, membrane thickness, and compression intensity of hollow Ca-alginate capsules were measured at different gelation conditions, such as the reactant concentration, dropping velocity, and gelation time. The optimum operation conditions for preparing capsules were determined at 100 g/L CaCl(2), 10 g/L sodium alginate (Na-alginate), a dropping velocity of 150 droplets/min, and a gelation time of 10 min. Diffusion of some saccharide and amino acid from bulk solution into capsules was investigated, and the diffusion coefficients were calculated by the developed mathematical model. All the tested substances can diffuse easily into the capsules. The combined diffusion coefficients of the capsule D(m) are 92-99% as large as their diffusion coefficients in pure water, while the diffusion coefficients in the capsule membrane D(1) are 60-95% as large as those. By employing polyethylene glycol (PEG) and bovine serum albumin (fraction V) (BSA(V)), the molecular weight cut-off of the capsule was determined. For linear macromolecules, hollow Ca-alginate capsules have a molecular weight cut-off of 4000. No diffusion of BSA(V) into the capsules was observed.     

Diffusion of sucrose and dextran through agar gel membranes

Mass transfer limitations severely impede the performance of bioreactions involving large molecules by gel-entrapped microorganisms. This paper describes a quantitative investigation of such diffusional limitations in agar gel membranes. Sucrose and commercial dextran fractions with (weight-average) molecular weights ranging from 10,000 to 2,000,000 Da were used as standard diffusants. For all tested solutes but sucrose, the values of the agar/water partition coefficients highlighted steric hindrance at the entrance of the membrane pores. The effective diffusivity of sucrose in agar was similar to that in water. All dextran fractions, however, displayed restricted diffusion in the agar membranes. Their effective diffusivities were a decreasing function of the agar content of the gel membrane (0.5, 1.0, or 1.5% w/v). The effective diffusivity in a given membrane decreased as the molecular weight of the diffusing molecule increased. T500 (ucbar|M_w = 470,000 Da) and ucbar|M_w = 1,950,000 Da) fractions were unable to diffuse through 1.0 or 1.5% agar membranes. The diffusion data did not agree with the classical (Renkin) model for a hard sphere diffusing through a cylindrical pore. These results are discussed in terms of gel and diffusant characteristics.     

Transport characterization of hydrogel matrices for cell encapsulation

Current membrane-based bioartificial organs consist of three basic components: (1) a synthetic membrane, (2) cells that secrete the product of interest, and (3) an encapsulated matrix material. Alginate and agarose have been widely used to encapsulate cells for artificial organ applications. It is important to understand the degree of transport resistance imparted by these matrices in cell encapsulation to determine if adequate nutrient and product fluxes can be obtained. For artificial organs in xenogeneic applications, it may also be important to determine the extent of immunoprotection offered by the matrix material. In this study, diffusion coefficients were measured for relevant solutes [ranging in size from oxygen to immunoglobulin G (IgG)] into and out of agarose and alginate gels. Alginate gels were produced by an extrusion/ionic crosslinking process using calcium while agarose gels were thermally gelled. The effect of varying crosslinking condition, polymer concentration, and direction of diffusion on transport was investigated. In general, 2-4% agarose gels offered little transport resistance for solutes up to 150 kD, while 1.5-3% alginate gels offered significant transport resistance for solutes in the molecular weight range 44-155 kD-lowering their diffusion rates from 10- to 100-fold as compared to their diffusion in water. Doubling the alginate concentration had a more significant effect on hindering diffusion of larger molecular weight species than did doubling the agarose concentration. Average pore diameters of approximately 170 and 147 A for 1.5 and 3% alginate gels, respectively, and 480 and 360 A for 2 and 4% agarose gels, respectively, were estimated using a semiempirical correlation based on diffusional transport of different-size solutes. The method developed for measuring diffusion in these gels is highly reproducible and useful for gels crosslinked in the cylindrical geometry, relevant for studying transport through matrices used in cell immobilization in the hollow fiber configuration. (c) 1996 John Wiley & Sons, Inc.     

Distribution and diffusion of solutes in articular cartilage

An experimental study was made on the distribution of solutes between articular cartilage and external solution, and on their diffusivity in cartilage. The solutes were classed as small ions, small uncharged molecules, and uncharged molecules of increasing size ranging from glucose to hemoglobin. The distribution of sodium and chloride ions obeys the Donnan equilibrium when cartilage is equilibrated in physiological saline solution. However, in cartilage immersed in dilute solution the concentration of chloride ions is higher than predicted. This is probably due to the presence in cartilage of some microscopic regions depleted of mucopolysaccharide in which the Donnan exclusion does not operate. The molal distribution coefficients of small uncharged molecules like urea are close to unity, which indicates that all water in cartilage seems to behave as solvent water. For larger molecules the distribution as well as the diffusion coefficients decrease with increase in molecular weight and are very sensitive to variations in fixed charge density. The results have been interpreted on the basis of the “steric exclusion” principle. The largest molecules which can penetrate into cartilage are of the size of the hemoglobin molecule.     

NMR imaging of the diffusion of water at 37 degrees C into Poly(2-hydroxyethyl methacrylate) containing aspirin or vitamin B(12)

The ingress of water into poly(2-hydroxyethyl methacrylate), PHEMA, loaded with either one of two model drugs, vitamin B(12) or aspirin, was studied at 37 degrees C using three-dimensional NMR imaging. PHEMA was loaded with 5 and 10 wt % of the drugs. From the imaging profiles, it was observed that incorporation of vitamin B(12) into PHEMA resulted in enhanced crack formation on sorption of water and the crack healing behind the diffusion front was slower than for PHEMA without added drug. This was accounted for by the anti-plasticization of PHEMA by vitamin B(12). Crack formation was inhibited in the PHEMA-aspirin systems because of the plasticizing effect of the aspirin on the PHEMA matrix. All of the polymers were found to absorb water according to an underlying Fickian diffusion mechanism. For PHEMA loaded with 5 wt % of aspirin or vitamin B(12), the best values of the water diffusion coefficients were both found to be 1.3 +/- 0.1 x 10(-11) m(2) s(-1) at 37 degrees C, while the values for the polymer loaded with 10 wt % of the drugs were slightly higher, 1.5 +/- 0.1 x 10(-11) m(2) s(-1).     

Use of holographic laser interferometry to study the diffusion of polymers in gels

The aim of this study was to demonstrate the potential for holographic interferometry to be used for diffusion studies of large molecules in gels. The diffusion and partitioning of BSA (67,000 g/mol) and pullulans (5,900-112,000 g/mol) in agarose gel were investigated. The gel diffusion coefficients obtained for BSA were higher when distilled water was used as a solvent compared to those obtained with 0.1 M NaCl as the solvent. Furthermore, the gel diffusion coefficient increased with increasing BSA concentration. The same trend was found for liquid BSA diffusion coefficients obtained by DLS. BSA partition coefficients obtained at different agarose gel concentrations (2-6%, w/w) decreased slightly with increasing gel concentration. However, all BSA gel diffusion coefficients measured were significantly lower than those in pure solvent and they decreased with increasing agarose concentration. The gel diffusion coefficients obtained for pullulans decreased with increasing pullulan molecular weight. The same effect from increased molecular weight was seen in the liquid diffusion coefficients measured by DLS. The pullulan partition coefficients obtained decreased with increasing molecular weight. However, pullulans with a larger Stokes' radius than BSA had partition coefficients that were higher or approximately the same as BSA. This implied that the pullulan molecules were more flexible than the BSA molecules. The results obtained for BSA in this study agreed well with other experimental studies. In addition, the magnitude of the relative standard deviation was acceptable and in the same range as for many other methods. The results thereby obtained showed that holographic interferometry is a suitable method for studying diffusion of macromolecules in gels.     

Apparent Diffusivity and Taylor Dispersion of Water and Solutes in Capillary Beds

A physical theory explaining the anisotropic dispersion of water and solutes in biological tissues is introduced based on the phenomena of Taylor dispersion, in which highly diffusive solutes cycle between flowing and stagnant regions in the tissue, enhancing dispersion in the direction of microvascular flow. An effective diffusion equation is derived, for which the coefficient of dispersion in the axial direction (direction of capillary orientation) depends on the molecular diffusion coefficient, tissue perfusion, and vessel density. This analysis provides a homogenization that represents three-dimensional transport in capillary beds as an effectively one-dimensional phenomenon. The derived dispersion equation may be used to simulate the transport of solutes in tissues, such as in pharmacokinetic modeling. In addition, the analysis provides a physically based hypothesis for explaining dispersion anisotropy observed in diffusion-weighted imaging (DWI) and diffusion-tensor magnetic resonance imaging (DTMRI) and suggests the means of obtaining quantitative functional information on capillary vessel density from measurements of dispersion coefficients. It is shown that a failure to account for flow-mediated dispersion in vascular tissues may lead to misinterpretations of imaging data and significant overestimates of directional bias in molecular diffusivity in biological tissues. Measurement of the ratio of axial to transverse diffusivity may be combined with an independent measurement of perfusion to provide an estimate of capillary vessel density in the tissue.     

Characterization of sugar diffusion coefficients in alginate membranes

The diffusivity of several monosaccharides and disaccharides in calcium alginate gels was determined using a specially designed diaphragm cell. The diffusion coefficients of the tested sugars are 4 to 18% smaller in alginate gel than in water and, with the exception of fructose, this difference increases with increasing sugar molecular weight. Also the position of the carbonyl group seems to be determined in the value of the diffusion coefficient - ketoses have lower diffusion coefficients than aldoses.     

Preparation of comb-type N-isopropylacrylamide hydrogel beads and their application for size-selective separation media

A series of the comb-type poly(N-isopropylacrylamide) (NIPAM) gel beads were prepared by inverse suspension polymerization techniques. The comb-type NIPAM gel beads exhibited large volume change at 30 degrees C, and their deswelling rate, defined as the time required for half-shrinking, was 10 times faster than that of the normal-type NIPAM gel beads. The gel beads were utilized to concentrate dilute aqueous solutions of albumin, gamma-globulin, and vitamin B(12). The separation efficiencies of albumin and gamma -globulin with the comb-type NIPAM gel were 80% and 85%, respectively. Whereas those with normal-type NIPAM gel were 55% and 60%, respectively. The incorporation of grafted chains into gel makes the effective mesh size smaller. Therefore it induces the additional obstruction effects between the solutes and network and excludes the high molecular weight solutes. After they have extracted water, their rapid deswelling property makes the gel regenerate effectively by warming to release the absorbed water.     

Diffusion in kappa-carrageenan gel beads

Using a well-mixed and temperature-led vessel, the diffusion characteristics of various solutes into spherical kappa-carrageenan gel beads were experimentally investigated. The diffusion coefficient of glucose was markedly affected by the glucose concentration and the operating temperature. In all cases the diffusivity obtained was noticeably smaller than that of glucose in pure water. The experimental data also indicated an inverse relationship between the diffusivity and the polymer concentration used in the gel preparation. As well, the glucose diffusivity was affected by the presence of other solutes in the glucose solution. Electrolytes such as ammonium sulfate, KCl, and CaCl(2) were observed to enhance the diffusion coefficient. On the other hand, the addition of arginine or bovine serum albumin had an adverse effect on the diffusivity. No diffusion of albumin into the gel beads was observed, and such a solute created a significant mass transfer resistance during the diffusion process.     

Diffusion of Small Solutes in the Lateral Intercellular Spaces of MDCK Cell Epithelium Grown on Permeable Supports

The diffusion coefficients of four solutes ranging in molecular weight from 238 to 10,000 in the lateral intercellular spaces (LIS) of cultured kidney cells (MDCK) grown on permeable supports were determined from the spread of fluorescence produced after the release of caged compounds by a pulse from a UV laser. Two types of experiments were performed: measurement of the rate of change of fluorescence after releasing a caged fluorophore, and measurement of the change in fluorescence of a relatively static fluorescent dye produced by the diffusion of an uncaged ligand for the dye. Fluorescence intensity was determined by photon-counting the outputs of a multichannel photomultiplier tube. Diffusion coefficients were determined in free solution as well as in the LIS of MDCK cells grown on permeable supports and the hindrance factor, θ, determined from the ratio of the free solution diffusivity to that in the LIS. The hindrance factors for 3000-MW dextran, 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS, MW 524) and N-2-hydroxyethylpiperazine-N′-2-ethanesulfonic acid (HEPES, MW 238) were not significantly different from 1. The diffusion of 10,000-MW dextran was substantially reduced in the LIS with a θ of 5.6 ± 0.3. Enzymatic digestion by neuraminidase of the sialic acid residues of the glycosylation groups in the LIS increased the diffusivity of the 10,000-MW dextran 1.8-fold indicating hindrance by the glycocalyx. We conclude that small solutes, such as Na⁺ and Cl⁻, would not be significantly restricted in their diffusion in the LIS and that solute concentration gradients could not develop along the LIS under physiologic conditions. Received: 7 October 1999     

A review of experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms

Experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms are reviewed. Effective diffusive permeabilities, the parameter appropriate to the analysis of reaction-diffusion interactions, depend on solute type and biofilm density. Three categories of solute physical chemistry with distinct diffusive properties were distinguished by the present analysis. In order of descending mean relative effective diffusive permeability (De/Daq) these were inorganic anions or cations (0.56), nonpolar solutes with molecular weights of 44 or less (0.43), and organic solutes of molecular weight greater than 44 (0.29). Effective diffusive permeabilities decrease sharply with increasing biomass volume fraction suggesting a serial resistance model of diffusion in biofilms as proposed by Hinson and Kocher (1996). A conceptual model of biofilm structure is proposed in which each cell is surrounded by a restricted permeability envelope. Effective diffusion coefficients, which are appropriate to the analysis of transient penetration of nonreactive solutes, are generally similar to effective diffusive permeabilities in biofilms of similar composition. In three studies that examine diffusion of very large molecular weight solutes (>5000) in biofilms, the average ratio of the relative effective diffusion coefficient of the large solute to the relative effective diffusion coefficient of either sucrose or fluorescein was 0.64, 0.61, and 0.36. It is proposed that large solutes are effectively excluded from microbial cells, that small solutes partition into and diffuse within cells, and that ionic solutes are excluded from cells but exhibit increased diffusive permeability (but decreased effective diffusion coefficients) due to sorption to the biofilm matrix.     

PEG molecular weight and lateral diffusion of PEG-ylated lipids in magnetically aligned bicelles

Lateral diffusion coefficients of PEG-ylated lipids with three different molecular weight PEG groups (1000, 2000 and 5000) were measured in magnetically-aligned bicelles using the stimulated echo (STE) pulsed field gradient (PEG) (1)H nuclear magnetic resonance (NMR) method. At concentrations below the PEG "mushroom-to-brush" transition, all three PEG-ylated lipids exhibited unrestricted lateral diffusion, with lateral diffusion coefficients comparable to those of corresponding non-PEG-ylated lipids and independent of PEG molecular weight. At concentrations above this transition, lateral diffusion slowed progressively with increasing concentration of PEG-ylated lipid as a result of surface crowding. As well, the lateral diffusion coefficients exhibited a pronounced decrease with increasing PEG group molecular weight and a diffusion-time dependence indicative of obstructed diffusion. We conclude that, while lateral diffusion of PEG-ylated lipids within lipid bilayers is determined primarily by the hydrophobic anchoring group, when crowding at the lipid bilayer surface becomes significant, the size of the extra-membranous domain, in this case the PEG group, can influence lateral diffusion, leading to decreased diffusivity with increasing size and producing obstructed diffusion at high crowding. These findings imply that similar considerations will pertain to lateral diffusion of membrane proteins with large extra-membranous domains.     

Molecular modeling and simulation of Mycobacterium tuberculosis cell wall permeability

The low permeability of the mycobacterial cell wall is thought to contribute to the intrinsic drug resistance of mycobacteria. In this study, the permeability of the Mycobacterium tuberculosis cell wall is studied by computer simulation. Thirteen known drugs with diverse chemical structures were modeled as solutes undergoing transport across a model for the M. tuberculosis cell wall. The properties of the solute-membrane complexes were investigated by means of molecular dynamics simulation, especially the diffusion coefficients of the solute molecules inside the cell wall. The molecular shape of the solute was found to be an important factor for permeation through the M. tuberculosis cell wall. Predominant lateral diffusion within, as opposed to transverse diffusion across, the membrane/cell wall system was observed for some solutes. The extent of lateral diffusion relative to transverse diffusion of a solute within a biological cell membrane may be an important finding with respect to absorption distribution, metabolism, elimination, and toxicity properties of drug candidates. Molecular similarity measures among the solutes were computed, and the results suggest that compounds having high molecular similarity will display similar transport behavior in a common membrane/cell wall environment. In addition, the diffusion coefficients of the solute molecules across the M. tuberculosis cell wall model were compared to those across the monolayers of dipalmitoylphosphatidylethanolamine and dimyristoylphosphatidylcholine, are two common phospholipids in bacterial and animal membranes. The differences among these three groups of diffusion coefficients were observed and analyzed.     

Diffusion coefficients of glucose and ethanol in cell-free and cell-occupied calcium alginate membranes

The diffusivities of glucose and ethanol in cell-free and cell-occupied membranes of calcium alginate were measured in a diffusion cell. The lag time analysis was used. Diffusivities decreased with increasing alginate concentration and were comparable with those in water for a 2% alginate membrane. Glucose and ethanol concentrations had no effect on the respective diffusion coefficients. The ratio of ethanol diffusivity to glucose diffusivity in 2 and 4% alginate agreed closely with the inverse ratio of the hydrodynamic raii for the two molecules in water, indicating that the hydrodynamic theory of diffusion in liquids may be applicable to diffusion in dilute alginate gels. Also, the presence of 20% dead yeast cells had no effect on the diffusivities. The data reported can be used to study reaction and diffusion in immobilized cell reactors and cell physiology under immobilized conditions.     

PEG molecular weight and lateral diffusion of PEG-ylated lipids in magnetically aligned bicelles

Lateral diffusion coefficients of PEG-ylated lipids with three different molecular weight PEG groups (1000, 2000 and 5000) were measured in magnetically-aligned bicelles using the stimulated echo (STE) pulsed field gradient (PEG) ¹H nuclear magnetic resonance (NMR) method. At concentrations below the PEG “mushroom-to-brush” transition, all three PEG-ylated lipids exhibited unrestricted lateral diffusion, with lateral diffusion coefficients comparable to those of corresponding non-PEG-ylated lipids and independent of PEG molecular weight. At concentrations above this transition, lateral diffusion slowed progressively with increasing concentration of PEG-ylated lipid as a result of surface crowding. As well, the lateral diffusion coefficients exhibited a pronounced decrease with increasing PEG group molecular weight and a diffusion-time dependence indicative of obstructed diffusion. We conclude that, while lateral diffusion of PEG-ylated lipids within lipid bilayers is determined primarily by the hydrophobic anchoring group, when crowding at the lipid bilayer surface becomes significant, the size of the extra-membranous domain, in this case the PEG group, can influence lateral diffusion, leading to decreased diffusivity with increasing size and producing obstructed diffusion at high crowding. These findings imply that similar considerations will pertain to lateral diffusion of membrane proteins with large extra-membranous domains.     

Permeability of composite chondrocyte-culture-millipore membranes to solutes of varying size and shape.

A model connective-tissue system was developed that is amenable to the determination of permeability coefficients of diffusing solutes. The system involves the culture of 13-day chick-embryo chondrocytes on a Millipore filter (HA:0.45 micron pore size) to form what is, in effect, a confluent, extremely thin cartilage slice of uniform thickness. These cultured chondrocyte membranes were used to measure the steady-state flux of radioactively labelled low-molecular-weight solutes and micro-ions. Similarly, the permeability coefficients of either radioactively labelled or enzymically active proteins across the membranes were determined. The membrane was found to have no marked effects on the diffusional behaviour of low-molecular-weight non-electrolytes (water, proline, ribose, glucose, sorbitol, raffinose). For micro-ions (Na+, SO42-, Cl-, glutamate, glucuronate,), the diffusive behaviour was found to be markedly affected by the ionic strength of the solvent used in a manner which was consistent with a Donnan distribution resulting from the immobilized proteoglycans. Globular proteins permeated the membrane at rates which decreased as the molecular size of the diffusing solute increased. The apparent diffusion rates of fibrinogen and of collagen through the membranes were greater than would be expected on the basis of their diffusion coefficients in free solution. Reasons for this behaviour are discussed.     

A method for the determination of diffusion coefficients for small molecules in aqueous solution

A method is described for determining the diffusion coefficients of small solutes in limited volumes (approximately equal to 4-9 ml) of fluid. Diffusion is measured in a three-chamber diffusion cell across a central unstirred compartment. Compartments are separated by nitrocellulose membranes. The instantaneous concentration gradient and the instantaneous flux of solute into the dilute end compartment are derived from changes in the concentration of solute in the two stirred end compartments through time. The diffusion coefficient is calculated from the slope of the least-squares regression line relating the magnitude of the instantaneous solute flux to that of the instantaneous concentration gradient. The apparatus is calibrated with a solute of known diffusivity (KCl). Diffusion coefficients thus determined in water at 25 degrees C for CaCl2 (7.54 X 10(-6) cm2.s-1), Na2-ATP (7.01 X 10(-6) cm2.s-1), 2-deoxyglucose (5.31 X 10(-6) cm2.s-1), and D-Na-lactate (5.62 X 10(-6) cm2.s-1) differed by an average of 3.7% from literature values. The method described results in accurate estimates of diffusion coefficients by a simple and relatively rapid procedure.     

Diffusion of lactose in kappa-carrageenan/locust bean gum gel beads with or without entrapped growing lactic acid bacteria

Effective diffusion coefficients (De) of lactose in kappa-carrageenan (2.75% wt/wt)/locust bean gum (0.25% wt/wt) (LBG) gel beads (1.5-2.0-mm diameter)with or without entrapped lactic acid bacteria (LAB) were determined at 40 degrees C. The effects of lactose concentration, bacteria strain (Streptococcus salivarius subsp. thermophilus and Lactobacillus casei subsp. casei) and cell content at various steps of the fermentation process (after immobilization, pre-incubation of the beads and successive fermentations) were measured on De as a first step for process modelling. Results were obtained from transiend concentration changes n well-stirred lactose solutions in which the beads were suspended. A mathematical model of unsteady-state diffusion in a sphere was used, and De was obtained from the best fit of the experimental data. Diffusivity of lactose in cell-tree beads was significantly lower than in pure water mainly because of the obstruction effect of the polymer chains and the hydration region. Furthermore, effective diffusivity and equilibrium partition factor were independent of lactose concentration in the range from 12.5 to 50 g/L. No significant difference was found for De (effective diffusivity) and Kp (partition) coefficients between beads entrapping S. thermophilus (approximately 5 x 10(9) CFU/mL) and cell-free beads. On the other hand higher cell counts obtained with L. casei (close to 1.8 x 10(11) CFU/mL) increased mass transfer resistance resulting in lower effective diffusivities and Kp. Finally, the effects of the type of bacteria and their distribution in the beads on the diffusivity were also discussed.     

Determination of diffusion coefficients in a solution by the transport of a solute through porous membranes

The possibility of determining the coefficients of diffusion in solution by the transport of solutes through porous polymeric membrane was studied. Reliable and reproducible results can be obtained by using nucleoporous filters with cylindrical pores. The method enables the selective determining of the diffusion coefficients of solutes being in complex mixtures, which is of special interest for biochemical research. The possibilities of the method are illustrated on the pattern of some globular proteins, polyethylene glycols and proteolytic enzymes.