A novel technique for measuring solute diffusivities in entrapment matrices used in immobilization

A novel technique has been developed for measuring effective solute diffusivities in entrapment matrices used for cell immobilization. In this technique radiotracers were used to measure effective diffusivities and equilibrium partition coefficients of the solute between the liquid and solid matrix. Ca-alginate was used in this study, because it is one of the most commonly employed matrices for the immobilization of microbial, plant and mammalian cells. The experimental apparatus consisted of a single spherical Ca-alginate bead which was attached to a rotating rod and immersed in water containing C(14)-glucose. The rotational speed of the spherical bead was controlled and resulted in excellent mixing, and negligible external film mass transfer resistance, which allowed the measurement of true effective solute diffusivity within the solid matrix. The rates of C(14)-glucose diffusion within the Ca-alginate sphere were measured using a scintillation spectrometer. A mathematical model of unsteady-state diffusion in a sphere was used with appropriate boundary conditions, and the effective diffusivity of glucose was found from the best fit of the experimental data using a computer regression analysis method. Using 2% (w/v) Ca-alginate beads in this new radiotracer technique the effective diffusivity and partition coefficient of glucose were found to be 6.62 x 10(-10) m(2)/s and 0.98, respectively. The accuracy, advantages, and simplicity of this new method for diffusivity measurements are also compared to other existing methods.     

Biodegradation of coumaphos, chlorferon, and diethylthiophosphate using bacteria immobilized in Ca-alginate gel beads

Calcium-alginate immobilized cell systems were developed for the detoxification and biodegradation of coumaphos, an organophosphate insecticide, and its hydrolysis products, chlorferon and diethlythiophosphate (DETP). Optimum bead loadings for bioreactor operation were found to be 200 g-beads/L for chlorferon degradation and 300 g-beads/L for DETP degradation. Using waste cattle dip (UCD) solution as substrate, the degradation rate for an immobilized consortium of chlorferon-degrading bacteria was five times greater than that for freely suspended cells, and hydrolysis of coumaphos by immobilized OPH(+)Escherichia coli was 2.5 times greater. The enhanced degradation of immobilized cells was due primarily to protection of the cells from inhibitory substances present in the UCD solution. In addition, physiological changes of the cells caused by Ca-alginate immobilization may have contributed to increased reaction rates. Degradation rates for repeated operations increased for successive batches indicating that cells became better adapted to the reaction conditions over time.     

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 glucose and ethanol effective diffusion coefficients in Ca-alginate gel.

Glucose and ethanol diffusion coefficients in 2% Ca-alginate gel were measured using the experimental technique based on solute diffusion into or out of gel beads in a well-stirred solution. The aim of the study was to make the measurements under typical conditions found in alcoholic fermentations, such as the concentrations of glucose (100 g l-1) and ethanol (50 g l-1), the simultaneous counter-diffusion of glucose and ethanol, and the presence of cells in the gel beads at a level of 10(9) cells g-1 of beads. Previously, an evaluation of the error associated with the methodology used indicated how the experimental procedure would minimize the error. The individual measurement of glucose and ethanol coefficients in 2% Ca-alginate with no cells gave values of 5.1 and 9.6 x 10(-6) cm2 s-1, respectively, which are lower than those in water. When the effect of counter-diffusion was investigated, both coefficients decreased: glucose by 14% and ethanol by 28%. When cells were incorporated into the beads, only the ethanol coefficient decreased significantly, while the glucose coefficient apparently increased its value to 6.9 10(-6) cm2 s-1.     

Oxygen diffusivity in gel beads containing viable cells

This article proposes a simple steady-state method for measuring the effective diffusion coefficient of oxygen (D(e)) in gel beads entrapping viable cells. We applied this method to the measurement of D(e) in Ca- and Ba-alginate gel beads entrapping Saccharomyces cerevisiae and Pseudomonas ovalis. The diffusivity of oxygen through gel beads containing viable cells was measured within an accuracy of +/-7% and found not to be influenced by cell density (0-30 g/L gel), cell type, and cell viability in gel beads. The oxygen diffusivity in the Ca-alginate gel beads was superior to that of the Ba-alginate gel beads, and the D(e) in the Ca-alginate gel beads nearly equalled the molecular diffusion coefficient in the liquid containing the gel beads. The oxygen concentration profile in a single Ca-alginate gel bead was calculated and compared to the distribution of mycelia of Aspergillus awamori grown in that gel bead. This procedure indicated that the oxygen concentration profile is useful for the estimation of the thickness of the cell layer in a gel bead. Numerical investigation revealed that high effectiveness factors, greater than 0.8, could be obtained using microgel beads with a radius of 0.25 mm.     

Diffusion and partitioning of proteins in charged agarose gels.

The effects of electrostatic interactions on the diffusion and equilibrium partitioning of fluorescein-labeled proteins in charged gels were examined using fluorescence recovery after photobleaching and gel chromatography, respectively. Measurements were made with BSA, ovalbumin, and lactalbumin in SP-Sepharose (6% sulfated agarose), in phosphate buffers at pH 7 and ionic strengths ranging from 0.01 to 1.0 M. Diffusivities in individual gel beads (D) and in the adjacent bulk solution (D infinity) were determined from the spatial Fourier transform of the digitized two-dimensional fluorescence recovery images. Equilibrium partition coefficients (phi) were measured by recirculating protein solutions through a gel chromatography column until equilibrium was reached, and using a mass balance. Diffusion in the gel beads was hindered noticeably, with D/D infinity = 0.4-0.5 in each case. There were no effects of ionic strength on BSA diffusivities, but with the smaller proteins (ovalbumin and lactalbumin) D infinity increased slightly and D decreased at the lowest ionic strength. In contrast to the modest changes in diffusivity, there were marked effects of ionic strength on the partition coefficients of these proteins. We conclude that for diffusion of globular proteins through gel membranes of like charge, electrostatic effects on the effective diffusivity (Deff = phi D) are likely to result primarily from variations in phi with only small contributions from the intramembrane diffusivity.     

Characterisation of small molecules diffusion in hydrogel-membrane liquid-core capsules

The overall diffusion coefficients for several low molecular weight solutes, such as glucose, fructose, sucrose, lactose, and vitamin B(12) have been determined in Ca-alginate membrane liquid-core capsules using the unsteady-state method following the release of solutes from the capsules to a well-stirred solution of limited volume. The diffusion coefficients obtained for saccharides were 5-20% lower than the corresponding diffusivity in water while for vitamin B(12) about 50% that of water. The diffusion coefficients of the investigated capsules were not influenced by the change in alginate concentration in the capsule membrane from 0.5 to 1.0%. Lower diffusivities and higher deviations from the diffusivity in water were obtained for higher molecular weight solutes.     

Diffusion characteristics of substrates in Ca-alginate gel beads

The diffusion characteristics of several substrates of varying molecular sizes into and from Ca-alginate gel beads in well-stirred solutions were investigated. The values of the diffusion coefficient (D) of substrates such as glucose, L-tryptophan, and alpha-lactoalbumin [with molecular weight (MW) less than 2 x 10(4)] into and from the gel beads agreed with those in the water system. Their substrates could diffuse freely into and from the gel beads without disturbance by the pores in the gel beads. The diffusion of their substrates into and from the gel beads was also not disturbed by increasing the Ca-alginate concentration in the beads and the CaCl(2) concentration used in the gel preparation. In the case of higher molecular weight substances such as albumin (MW = 6.9 x 10(4)), gamma-globulin (MW = 1.54 x 10(5)) and fibrinogen (MW = 3.41 x 10(5)), the diffusion behaviors of the substrates into and from the gel beads were very different. No diffusion of their substrates into the gel beads from solutions was observed, and only albumin was partly absorbed on the surface of the gel beads. The values of D of their substrates from the gel beads into their solutions were smaller than their values in the water system, but all their substrates could diffuse from the gel beads. The diffusion of high molecular weight substrates was limited more strongly by the increase of Ca-alginate concentration in the gel beads than by the increase of the CaCl(2) concentration used in the gel preparation. Using these results, the capacity of Ca-alginate gel as a matrix of immobilization was discussed.     

Counter-diffusion of lactose and lactic acid in kappa-carrageenan/locust bean gum gel beads with or without entrapped lactic acid bacteria.

The effective diffusion coefficient (De) and equilibrium partition factor (Kp) for lactose and lactic acid in k-carrageenan (2.75% w/w)/locust bean gum (0.25% w/w) (LBG) gel beads (1.5-2.0 mm diameter), with or without entrapped Lactobacillus casei subsp. casei (L. casei), were determined at 40 degrees C. Results were obtained from transient concentration changes in well-stirred solutions of finite volume in which the beads were suspended. Mathematical models of unsteady-state diffusion into and/or from a sphere and appropriate boundary conditions were used to calculate effective diffusion coefficients of lactose and lactic acid from the best fit of the experimental solute concentration changes. The effective diffusivities of lactose and lactic acid were 5.73 x 10(-10) and 9.96 x 10(-10) m2 s-1, respectively. Furthermore, lactic acid was found to modify gel structure since lactose diffusion characteristics (De and Kp) differed significantly from an earlier study and in the literature. In gel beads heavily colonized with L. casei, the effective diffusion coefficients of lactose and lactic acid were respectively 17% and 24% lower than for cell-free beads. Partition coefficients also confirmed the obstruction effect due to the cells, and decreased from 0.89 to 0.79, and from 0.98 to 0.87, for lactose and lactic acid, respectively. External mass transfer was estimated by an unsteady-state model in infinite volume using the Biot number. The effect of external mass transfer resistance on De results and the data reported in the literature are discussed.     

Biodegradation of chlorferon and diethylthiophosphate by consortia enriched from waste cattle dip solution

Chlorferon and diethylthiophosphate (DETP) are the hydrolysis products of coumaphos, an organophosphate pesticide. In this research, two consortia of bacterial cultures, one responsible for degrading chlorferon and the other for degrading DETP, were selectively enriched from waste cattle dip solution. The enriched cultures were used as inocula to grow biomass for biodegradation studies. For chlorferon degradation, the optimum biomass concentration was found to be 80g/L, and pH 7.5 was selected as the optimal operating pH. Chlorferon degradation was characterized by substrate inhibition kinetics with parameter values estimated to be V(m)=0.062+/-0.011mg/(g-biomass)h, K(m)=21+/-7mg/L, and K(Si)=118+/-45mg/L. For DETP degradation, the optimum biomass concentration was found to be 60g/L, and the optimum pH was in the range of 7.5-8. DETP degradation was characterized by Michaelis-Menten kinetics with parameter values estimated to be V(m)=1.52+/-0.10mg/(g-biomass)h and K(m)=610+/-106mg/L.     

Diffusivity of oxygen into carriers entrapping whole cells

The effective diffusivity of oxygen, D(e), in Ca-alginate and PVA-SbQ gels was measured using a two-chamber vessel with a membrane between the two chambers. The effect of cell density, C(c), on D(e) in Ca-alginate gels was studied. The effective diffusivity of oxygen decreased with increasing cell density, to C(c) = 170 kg dry cells/m(3) gel. The dependency of D(e) on cell density was discussed in terms of a random-pore model. The model correlated well with experimental data, i.e., kD(e)/D(0) = 0.86(1 - 1.47 x 10(-3) C(c))(2). Here, k is the partition coefficient, and D(0) is diffusivity in water.     

Kluyveromyces lactis cells entrapped in Ca-alginate beads for the continuous production of a heterologous glucoamylase

Viable cells of Kluyveromyces lactis, transformed with the glucoamylase gene from Arxula adeninivorans, were entrapped in beads of Ca-alginate and employed on a lab scale in a continuous stirred and a fluidised bed reactor (FBR), both fed with a rich medium (YEP) containing lactose as carbon source. Experiments with freely suspended cells in batch and chemostat had demonstrated that glucoamylase production was favoured in the presence of lactose and YEP medium. Employing controlled-sized beads having a 2.13 mm diameter, specific glucoamylase productivity was higher in the stirred reactor (CSTR) than in the FBR; in the latter a higher volumetric productivity was achieved, due to the lower void degree. The performance of the immobilised cell systems, in terms of specific glucoamylase productivity, was strongly affected by mass transfer limitations occurring throughout the gel due to the high molecular weight of the product. In the perspective to improve and scale-up the immobilised cell system proposed, a mathematical model, which takes into account substrate transfer limitations throughout the gel, has been developed. The effective lactose diffusivity was related to the bead reactive efficiency by means of the Thiele modulus. The regression of the model parameters on the experimental data of substrate consumption obtained both in the CSTR and in the FBR allowed to estimate lactose diffusivity and the kinetic parameters of the immobilised yeast.     

Extraction of polyphenols from white distilled grape pomace: optimization and modelling

Both ethanolic and aqueous extraction were carried out in a laboratory-scale vertical extractor to obtain polyphenols from distilled grape pomace of Vitis vinifera var. "Albari?o". An experimental design was performed to analyse the effects of flow (2 ml/min and 4 ml/min) and temperature (40 degrees C and 50 degrees C). Yields of polyphenolics from aqueous extraction were much higher (up to 30-fold) than those of ethanolic extraction, in contrast with previous results obtained by us from batch extraction of different grape varieties. Polyphenols extraction was modelled by application of second Fick's law to spherical particles of 0.5 mm diameter, so obtaining the effective diffusion coefficient as parameter. The mass transfer coefficients were also estimated, giving as result that the external mass transfer resistance was negligible. Correlation coefficients ranged 0.989-0.9999. Effective diffusivity values in water extraction assays were between 0.6x10(-11) m(2)/s and 2.1x10(-11) m(2)/s. Using ethanol as solvent, the effective diffusivity was lower, between 0.1x10(-11) m(2)/s and 0.76x10(-11) m(2)/s.     

Diffusion in cell‐free and cell immobilising κ‐carrageenan gel beads with and without chemical reaction

Diffusion into and from κ‐carrageenan gel beads was studied, both in the absence and presence of bacterial cells, both with and without biochemical reaction. The solutes were indole, L ‐serine, and L ‐tryptophan. The reaction was that of indole and L ‐serine to give L ‐tryptophan. Established theory concerning diffusion of a single solute in cell‐free gels was found to describe well the effect of the gel on diffusivity. Simultaneous diffusion of the three solutes resulted in lower diffusivities than those for individual solutes, suggesting the need to use multicomponent diffusion theory. The effect of cells on diffusion could only be accounted for by models assuming permeable cells. Diffusion with chemical reaction was reasonably well described by an effectiveness factor calculated using an effective diffusivity estimated from diffusion data without reaction. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 63: 625–631, 1999.     

The effective diffusion coefficient and the distribution constant for small molecules in calcium-alginate gel beads

The effective diffusion coefficient, D(e), and the distribution constant, K(i), for selected mono- and disaccharides and organic acids were determined in homogeneous calcium-alginate gel with and without entrapped bacteria. Results were obtained from transient concentration changes in well-stirred solutions of limited volume, in which the gel beads were suspended. The effective diffusioncoefficients and the distribution constants were estimated by fitting mathematical model predictions to the experimental data using a nonlinear model fitting program (MODFIT). Both single solute diffusion and multiple solute diffusion were performed. A small positive effect was obtained onthe values of D(e) for the system of multiple solute diffusion; however, the values of K(i) were not significantly influenced. For the nine solutes tested, D(e) for 2% Ca-alginate gel beads was found to be approximately 85% of the diffusivity measured in water. The effects on D(e) and K(i), for lactose and lactic acid were determined for variations of alginate concentration, pH, temperature, and biomass content in the beads. D(e) decreased linearly for both lactose and lactic acid with increasing cell concentration in the Ca-alginate gel. K(i), was constant for both lactose and lactic acid with increasing cell concentration. D(e) was significantly lower at pH 4.5 than at pH 5.5 and 6.5 for both lactose and lactic acid. Furthermore, D(e) seemed to decrease with increased alginate concentration in the range of 1% to 4%. The diffusion rate increased with increasing temperature, and the activation energy for the diffusion process for both lactose and lactic acid was constant in the temperature range tested. (c) 1995 John Wiley & Sons Inc.     

Diffusion of sucrose and yohimbine in calcium alginate gel beads with or without entrapped plant cells

The diffusion characteristics of sucrose, a nutrient, and yohimbine, a secondary metabolite, in alginate gel beads, with or without entrapped periwinkle (Catharanthus roseus) or apple (Malus domestica) cells, were investigated. Effective diffusivities of both solutes in the gel beads were determined by two different methods from transient concentration changes in well-stirred solutions where the beads were suspended. The linear plot method developed in this work is easy to use and requires no data from the initial periods of diffusion experiments. It was found that while the cell-free beads provided only minor diffusional resistance to both solutes, the effective diffusivities of both solutes decreased significantly with the presence of cells in the beads and the amount of reduction was proportional to the amount of cell loading. Further, the effective diffusivity of sucrose appeared to be slightly larger than that of yohimbine under identical conditions. It was also observed that permeabilization of apple cells with dimethyl sulfoxide (DMSO) led to an increase in effective diffusivity with the effect being more significant for yohimbine.     

Diffusion of (de)acylated antibiotic A40926 in alginate and carrageenan beads with or without cells and/or soybean meal

Effective diffusion coefficients (D(e)) of antibiotic A40926 and its deacylated derivative were determined in Ca-alginate (2% wt/wt) and kappa-carrageenan (2.6% wt/wt) gel beads with or without immobilized Actinoplanes teichomyceticus cells and/or soybean meal (SBM). The method used was based on transient concentration changes in a well-stirred antibiotic solution in which gel beads, initially free of solute, were suspended. Unsteady-state diffusion in a sphere was applied and D(e) determined from the best fit of experimental data. A40926 showed markedly different diffusion characteristics than its deacylated derivative. Diffusivity of deacyl-A40926 in alginate or carrageenan gel beads was six to seven times that of A40926. Large differences in partition coefficients (Kp) were also found. In case of beads without additions, A40926, in contrast to deacyl-A40926, strongly partitioned to the liquid phase. Introduction of SBM and/or mycelium in the gel beads decreased the effective diffusivity of deacyl-A40926, but increased its partitioning to the solid phase. Our findings indicate that a relatively moderate structural change of a lipoglycopeptide molecule could lead to a major change in its diffusion/partition characteristics.     

Diffusion of acetophenone and phenethyl alcohol in the calcium-alginate-bakers' yeast-hexane system

The intrabead diffusion coefficients of acetophenone and phenethyl alcohol were measured at 30 degrees C in the triphasic immobilized yeast-water-hexane system. Saccharomyces cerevisiae cells were deactivated with hydrochloric acid and entrapped in calcium-alginate beads. Measurements of dry cell loss during deactivation, shrinkage of the beads during deactivation and the final porosity of the beads were made for various cell loadings. Final concentrations of wet cells in the beads ranged from approximately 0.25 to 0.30 g/mL. Mass transfer in the hexane phase, external to the beads, was eliminated experimentally. The estimated error of 5% to 10% in the diffusion coefficients is within the experimental error associated with the bead method. The effect of significant sampling volumes on the diffusivities was estimated theoretically and accounted for experimentally. The intrabead concentration of acetophenone and phenethyl alcohol was 150 to 800 ppm. The deactivated cells were shown to be impervious to acetophenone so that the measured diffusivities are extracellular parameters. The cell volume fraction in the beads ranged from 0.70 to 0.90, significantly higher than previously reported data. The effective diffusion coefficients conform to the random pore model. No diffusional interaction between acetophenone and phenethyl alcohol was observed. The addition of 2 vol% ethanol or methanol slightly increased the diffusivities. The thermodynamic partition coefficients were measured in the bead-free water-organic system and found to be an order of magnitude lower than the values calculated from the analysis of the diffusion data for the organic-bead system, suggesting that bead-free equilibrium data cannot be used in triphasic systems. (c) 1994 John Wiley & Sons, Inc.     

Measurement of local diffusion coefficients in biofilms by microinjection and confocal microscopy

A new technique for the determination of local diffusion coefficients in biofilms is described. It is based on the microinjection of fluorescent dyes and quantitative analysis of the subsequent plume formation using confocal laser microscopy. The diffusion coefficients of fluorescein (MW 332), TRITC-IgG (MW 150000) and phycoerythrin (MW 240000) were measured in the cell clusters and interstitial voids of a heterogeneous biofilm. The diffusivities measured in the voids were close to the theoretical values in water. Fluorescein had the same diffusivity in cell clusters, voids, and sterile medium. TRITC-IgG did not diffuse in cell clusters, presumably due to binding to the cell cluster matrix. After treatment of the biofilm with bovine serum albumin, binding capacity decreased and the diffusion coefficient could be measured. The diffusivity of phycoerythrin in cell clusters was impeded by 41%, compared to interstitial voids. From the diffusion data of phycoerythrin it was further calculated that the cell cluster matrix had the characteristics of a gel with 0.6 nm thick fibers and pore diameters of 80 nm. (c) 1997 John Wiley & Sons, Inc.     

Biosorption of Cr (VI) with Trichoderma viride immobilized fungal biomass and cell free Ca-alginate beads

Ability of Cr (VI) biosorption with immobilized Trichoderma viride biomass and cell free Ca-alginate beads was studied in the present study. Biosorption efficiency in the powdered fungal biomass entrapped in polymeric matric of calcium alginate compared with cell free calcium alginate beads. Effect of pH, initial metal ion concentration, time and biomass dose on the Cr (VI) removal by immobilized and cell free Ca-alginate beads were also determined. Biosorption of Cr (VI) was pH dependent and the maximum adsorption was observed at pH 2.0. The adsorption equilibrium was reached in 90 min. The maximum adsorption capacity of 16.075 mgg(-1) was observed at dose 0.2 mg in 100 ml of Cr (VI) solution. The high value of kinetics rate constant Kad (3.73 x 10(-2)) with immobilized fungal biomass and (3.75 x 10(-2)) with cell free Ca- alginate beads showed that the sorption of Cr (VI) ions on immobilized biomass and cell free Ca-alginate beads followed pseudo first order kinetics. The experimental results were fitted satisfactory to the Langmuir and Freundlich isotherm models. The hydroxyl (-OH) and amino (-NH) functional groups were responsible in biosorption of Cr (VI) with fungal biomass spp. Trichoderma viride analysed using Fourier Transform Infrared (FTIR) Spectrometer.