Product inhibition of immobilized Escherichia coli arising from mass transfer limitation

Mass transfer-limited removal of metabolic products led to product-inhibited growth of Escherichia coli that was immobilized in a model system. Comparison of the growth kinetics of immobilized and free-living cells revealed no further physiological differences between cells in these two modes of existence beyond those manifested in the local concentrations of substrate and product. Bacteria were retained on a microporous membrane in a dense, planar aggregate and were grown anaerobically on a glucose-based minimal medium. Radioisotope labeling of the immobilized cell mass with 35S was used to determine growth kinetic parameters. Growth rates in the immobilized cell layer were measured by an autoradiographic technique which allowed comparison of the size of the growing region with the rate of cell convection caused by growth. Immobilized cell growth rates and growth yields ranged from near maximal (0.56 h-1 and 39 g of dry cell weight/mol of glucose, respectively) to substantially reduced (0.15 h-1 and 15 g/mol). The depression of these kinetic parameters was attributed to product inhibition arising from mass transfer-limited removal of acidic waste products from the cell mass. A simple one-dimensional reaction-diffusion model, which incorporated data on the product-inhibited growth kinetics of free-living cells collected in a product-limited chemostat, satisfactorily predicted product inhibition of immobilized cell growth.     

Cell mass synthesis and degradation by immobilized Escherichia coli

Escherichia coli K-12 cells were grown in a confined volume using microporous hollow fiber membranes. The local cell concentrations in the reactors were above 400 g dry mass/L, in excess of the predicted limit based on the specific volume of free cells determined by tracer exclusion. Cell mass synthesis and degradation rates in these reactors were measured using radioisotope labeling with (35)S. Net accumulation of cell material persisted at these high cell densities. The rates of substrate uptake and cell growth were predicted from the theory of reaction and diffusion assuming that kinetics of cell metabolism are identical for free-living and immobilized cells. This theory was tested by comparison of overall rates and by the size of the region in which cell growth occurred, measured by autoradiography. A yield coefficient of 4 +/- 1 mol sulfur/mol glucose was measured, in agreement with the value determined for free-living cells in similar conditions. Cell growth occurs in a thin layer (10-30 mum), at a rate similar to the growth rate for free cells. Volume expansion by the cells as a consequence of proliferation induces convection of cell mass out of the growth region into a region of the reactor filled with starving cells, which then accumulate in the reactor. The combination of mass-balance and spatial distribution measurements made possible by the use of radioisotope labeling enables a direct test for mass transfer limitations, the determination of the intrinsic cell kinetics, and noninvasive measurements of cell growth in immobilized cell reactors.     

Comparison of substrate utilization and growth kinetics between immobilized and suspended Pseudomonas cells

A methodology is described for measurement if immobilized and suspended cell growth and substrate utilization kinetics parameters. Substrate utilization and growth kinetics were compared between immobilized and suspended cells for toluene degrading Pseudomonas strains K3-2 and 2,4-dichlorophenoxyacetic acid (2,4-D) degrading strain DBO131(pR0101), respectively. Kinetic parameters were estimated using nonlinear parameter estimation methods and compared between the immobilized and suspended Pseudomonas cells to determine the effect of immobilization on cellular growth and substrate utilization. Factors influencing the experimental design included calculated oxygen flux rates, primary carbon substrate flux rates, and shear stresses on the immobilize cell. Statistical interpretation of the cellular reaction rate parameters indicates that only the growth kinetics of the toluene system were significantly altered upon immobilization. Substrate utilization kinetics remained unchanged upon immobilization. The substrate growth associated half-saturation constant (K(g)) for the toluene system increased by 30-fold and the maximum specific growth rate (mu(max)) decreased by 2-fold upon immobilization. Implication of these results for experimental determination of cellular kinetic parameters and for immobilization cell bioreactors design are discussed. (c) 1993 John Wiley & Sons, Inc.     

Urea hydrolysis by immobilized urease in a fixed-bed reactor: analysis and kinetic parameter estimation

Urea hydrolysis by urease immobilized onto ion exchange resins in a fixed-bed reactor has been studied. A modified Michaelis-Menten rate expression is used to describe the pH-dependent, substrate- and product-inhibited kinetics. Ionic equilibria of product and buffer species are included to account for pH changes generated by reaction. An isothermal, heterogeneous plug-flow reactor model has been developed. An effectiveness factor is used to describe the reaction-diffusion process within the particle phase. The procedure for covalent immobilization of urease onto macroporous cation exchangers is described. Urea conversion data are used to estimate kinetic parameters by a simplex optimization method. The best-fitted parameters are then used to predict the outlet conversions and pH values for systems with various inlet pH values, inlet urea and ammonia concentrations, buffers, particle sizes, and spacetimes. Very good agreement is obtained between experimental data and model predictions. This immobilized urease system exhibits quite different kinetic behavior from soluble urease because the pH near the enzyme active sites is different from that of the pore fluid. This effect results in a shift of the optimal pH value of the V(max) (pH) curve from 6.6 (soluble urease) to ca. 7.6 in dialysate solution, and ca. pH 8.0 in 20mM phosphate buffer. The reactor model is especially useful for estimating intrinsic kinetic parameters of immobilized enzymes and for designing urea removal columns.     

Kinetic studies of phenol degradation by Rhodococcus sp. P1 I. Batch cultivation

Rhodococcus sp. P1 utilizes phenol as the sole carbon and energy source via the beta-ketoadipate pathway. In batch cultivation, concentrations up to 2.8 g.l-1 phenol were degraded. The highest values for the specific growth rate of 0.32 h-1 were obtained at concentrations near 0.25 g.l-1. At higher concentrations, substrate inhibition was observed, characterized by increases in lag phase and decreasing growth rates. A mathematical expression was proposed to fit the kinetic pattern of phenol inhibition on the specific growth rate mu: [formula: see text] Nomenclature: K- Exponent of the inhibition function, Ks- Monod saturation constant, g.l-1, KI- Inhibition constant, g.l-1, S- Substrate concentration in culture broth, g.l-1, So- Initial substrate concentration, g.l-1, Y- Yield constant, g cell dry mass.g substrate-1, mu- Specific growth rate, h-1, mu max- Maximum growth rate, h-1.     

Modeling of immobilized cell columns for bioconversion and wastewater treatment

Immobilized cells are widely used in bioconversions to produce biological products as well as in wastewater treatment such as solvent removal from wastewater streams. In this work, a rate model is proposed to simulate this kind of process in an axial-flow fixed-bed column packed with porous particles containing immobilized cells. The transient model considered various mass transfer mechanisms including axial dispersion, interfacial film mass transfer, and intraparticle diffusion. Cell death in the immobilized cell system was also considered. Effects of various parameters such as kinetic constants and mass transfer parameters were studied. Operational situations such as feed fluctuation flow rate increase and two columns in series were also investigated. The model can be used to study the behavior and characteristics of immobilized cell columns in order to perform scale-up predictions of effluent profiles and for the purpose of process optimization.     

The effect of temperature and pH on ethanol production by free and immobilized cells of Kluyveromyces marxianus grown on Jerusalem artichoke extract

The effect of temperature and pH on the kinetics of ethanol production by free and calcium alginate immobilized cells of Kluyveromyces marxianus grown on Jerusalem artichoke extract was investigated. With the free cells, the ethanol and biomass yields were relatively constant over the temperature range 25-35 degrees C, but dropped sharply beyond 35 degrees C. Other kinetic parameters, specific growth rate, specific ethanol production rate, and specific total sugar uptake rate were maximum at 35 degrees C. However, with the immobilized cells, ethanol yield remained almost constant in the temperature range 25-45 degrees C, and the specific ethanol production rate and specific total sugar uptake rate attained their maximum values at 40 degrees C. For the pH range between 3 and 7, the free-cell optimum for growth and product formation was found to be ca. pH 5. At this pH, the specific growth rate was 0.35 h(-1) and specific ethanol production rate was 2.83 g/g/h. At values higher or lower than pH 5, a sharp decrease in specific ethanol production rate as well as specific growth rate was observed. In comparison, the immobilized cells showed a broad optimum pH profile. The best ethanol production rates were observed between pH 4 and 6.     

Kinetics of microbial growth on pentachlorophenol

Batch and fed-batch experiments were conducted to examine the kinetics of pentachlorophenol utilization by an enrichment culture of pentachlorophenol-degrading bacteria. The Haldane modification of the Monod equation was found to describe the relationship between the specific growth rate and substrate concentration. Analysis of the kinetic parameters indicated that the maximum specific growth rate and yield coefficients are low, with values of 0.074 h-1 and 0.136 g/g, respectively. The Monod constant (Ks) was estimated to be 60 micrograms/liter, indicating a high affinity of the microorganisms for the substrate. However, high concentrations (KI = 1,375 micrograms/liter) were shown to be inhibitory for metabolism and growth. These kinetic parameters can be used to define the optimal conditions for the removal of pentachlorophenol in biological treatment systems.     

Kinetics of microbial growth on pentachlorophenol.

Batch and fed-batch experiments were conducted to examine the kinetics of pentachlorophenol utilization by an enrichment culture of pentachlorophenol-degrading bacteria. The Haldane modification of the Monod equation was found to describe the relationship between the specific growth rate and substrate concentration. Analysis of the kinetic parameters indicated that the maximum specific growth rate and yield coefficients are low, with values of 0.074 h-1 and 0.136 g/g, respectively. The Monod constant (Ks) was estimated to be 60 micrograms/liter, indicating a high affinity of the microorganisms for the substrate. However, high concentrations (KI = 1,375 micrograms/liter) were shown to be inhibitory for metabolism and growth. These kinetic parameters can be used to define the optimal conditions for the removal of pentachlorophenol in biological treatment systems.     

Growth and removal of nitrogen and phosphorus by free-living and chitosan-immobilized cells of the marine cyanobacterium Synechococcus elongatus

This study investigated the growth rate of chitosan-immobilized cells of the marine cyanobacterium Synechococcus elongatus and its potential application in the removal of nitrogen and phosphorus for wastewater treatment. Immobilized cell cultures had a lag phase of growth due to the immobilization method, and their growth rate was similar to that of free-living cell cultures. Ammonia removal was higher in free cells (54%) than in immobilized cells (29%), but nitrate removal was similar in immobilized (38%) and free cells (44%); phosphorus removal was more efficient in free cells (88%) than in immobilized cells (77%). Chlorophyll a and protein content were higher in immobilized cells. Our study demonstrates that S. elongatus immobilized into chitosan capsules can remove nutrients and is able to maintain a growth rate comparable to that of free cells in culture.     

A simple kinetic model for the hydrolysis of α-d-glucans using glucoamylase immobilized on titanium (IV) activated porous silica

A simple kinetic model which describes the hydrolysis of α-d-glucans by immobilized glucoamylase (exo-1,4-d-glucosidase, EC 3.2.1.3) is reported. The hydrolysis of starch, amylose, amylopectin, maltose and 40DE starch hydrolysates using glucoamylase immobilized on alkylamine derivatives of titanium(IV) activated porous silica are described by a kinetic model based on Langmuir-Hinshelwood kinetics. This model involves enzyme kinetics with or without product inhibition and reverse reactions as well as mass transfer and diffusion effects in immobilized enzyme reactors. The results of other authors are also interpreted by the model developed in this article.     

Cell growth patterns in immobilization matrices

Within an immobilized cell matrix, mass transfer limitations on substrate delivery or product removal can often lead to a wide range of local chemical environments. As immobilized living cell populations actively grow and adapt to their surroundings, these mass transfer effects often lead to strong, time-dependent spatial variations in substrate concentration and biomass densities and growth rates. This review focuses on the methods that have been devised, both experimentally and theoretically, to study the non-uniform growth patterns that arise in the mass transfer limited environment of an immobilization matrix, with particular attention being paid to cell growth in polysaccharide gels.     

Determination of the intrinsic fermentation kinetics of Saccharomyces cerevisiae cells immobilized in Ca-alginate beads and observations on their growth

Continuous fermentation experiments in a well-stirred fermentor with Saccharomyces cerevisiae cells immobilized in Ca-alginate beads of small diameter (approx. 1 mm) have been performed in order to discover their intrinsic fermentation kinetics, and compare them to the fermentation kinetics for free cells, by fitting both sets of results to the same model. The results show similar kinetic parameters for free and immobilized cells. The changes in cell concentration inside the beads and microscopical observations of transverse sections throughout the experiments, allowed discernment of two different scenarios of cell growth inside the beads: low cell density and fully developed growth. Correspondence to: F. Gòdia     

Physiology and metabolic fluxes of wild-type and riboflavin-producing Bacillus subtilis.

Continuous cultivation in a glucose-limited chemostat was used to determine the growth parameters of wild-type Bacillus subtilis and of a recombinant, riboflavin-producing strain. Maintenance coefficients of 0.45 and 0.66 mmol of glucose g-1 h-1 were determined for the wild-type and recombinant strains, respectively. However, the maximum molar growth yield of 82 to 85 g (cell dry weight)/mol of glucose was found to be almost identical in both strains. A nonlinear relationship between the specific riboflavin production rate and the dilution rate was observed, revealing a coupling of product formation and growth under strict substrate-limited conditions. Most prominently, riboflavin formation completely ceased at specific growth rates below 0.15 h-1. For molecular characterization of B. subtilis, the total amino acid composition of the wild type was experimentally determined and the complete building block requirements for biomass formation were derived. In particular, the murein sacculus was found to constitute approximately 9% of B. subtilis biomass, three- to fivefold more than in Escherichia coli. Estimation of intracellular metabolic fluxes by a refined mass balance approach revealed a substantial, growth rate-dependent flux through the oxidative branch of the pentose phosphate pathway. Furthermore, this flux is indicated to be increased in the strain engineered for riboflavin formation. Glucose catabolism at low growth rates with reduced biomass yields was supported mainly by the tricarboxylic acid cycle.     

Evaluation of intrinsic immobilized kinetics in hollow fiber reactor systems.

Immobilized cell and enzyme hollow fiber reactors have been developed for a variety of biochemical and biomedical applications. Reported mathematical models for predicting substrate conversion in these reactors have been limited in accuracy because of the use of free-solution kinetic parameters. This paper describes a method for determining the intrinsic kinetics of enzymes immobilized in hollow fiber reactor systems using a mathematical model for diffusion and reaction in porous media and an optimization procedure to fit intrinsic kinetic parameters to experimental data. Two enzymes, a thermophilic beta-galactosidase that exhibits product inhibition and L-lysine alpha-oxidase, were used in the analysis. The intrinsic kinetic parameters show that immobilization enhanced the activity of the beta-galactosidase while decreasing the activity of L-lysine alpha-oxidase. Both immobilized enzymes had higher Km values than did the soluble enzyme, indicating less affinity for the substrate. These results are used to illustrate the significant improvement in the ability to predict substrate conversion in hollow fiber reactors.     

Substrate and product inhibition kinetics in succinic acid production by Actinobacillus succinogenes

The inhibition of substrate and products on the growth of Actinobacillus succinogenes in fermentation using glucose as the major carbon source was studied. A. succinogenes tolerated up to 143 g/L glucose and cell growth was completely inhibited with glucose concentration over 158 g/L. Significant decrease in succinic acid yield and prolonged lag phase were observed with glucose concentration above 100 g/L. Among the end-products investigated, formate was found to have the most inhibitory effect on succinic acid fermentation. The critical concentrations of acetate, ethanol, formate, pyruvate and succinate were 46, 42, 16, 74, 104 g/L, respectively. A growth kinetic model considering both substrate and product inhibition is proposed, which adequately simulates batch fermentation kinetics using both semi-defined and wheat-derived media. The model accurately describes the inhibitory kinetics caused by both externally added chemicals and the same chemicals produced during fermentation. This paper provides key insights into the improvement of succinic acid production and the modelling of inhibition kinetics.     

An immobilized cell reactor with simultaneous product separation. II. Experimental reactor performance

The simultaneous separation of volatile fermentation products from product-inhibited fermentations can greatly increase the productivity of a bioreactor by reducing the product concentration in the bioreactor, as well as concentrating the product in an output stream free of cells, substrate, or other feed impurities. The Immobilized Cell Reactor-Separator (ICRS) consists of two column reactors: a cocurrent gas-liquid "enricher" followed by a countercurrent "stripper" The columns are four-phase tubular reactors consisting of (1) an inert gas phase, (2) the liquid fermentation broth, (3) the solid column internal packing, and (4) the immobilized biological catalyst or cells. The application of the ICRS to the ethanol-from-whey-lactose fermentation system has been investigated. Operation in the liquid continuous or bubble flow regime allows a high liquid holdup in the reactor and consequent long and controllable liquid residence time but results in a high gas phase pressure drop over the length of the reactor and low gas flow rates. Operation in the gas continuous regime gives high gas flow rates and low pressure drop but also results in short liquid residence time and incomplete column wetting at low liquid loading rates using conventional gas-liquid column packings. Using cells absorbed to conventional ceramic column packing (0.25-in. Intalox saddles), it was found that a good reaction could be obtained in the liquid continuous mode, but little separation, while in the gas continuous mode there was little reaction but good separation. Using cells sorbed to an absorbant matrix allowed operation in the gas continuous regime with a liquid holdup of up to 30% of the total reactor volume. Good reaction rates and product separation were obtained using this matrix. High reaction rates were obtained due to high density cell loading in the reactor. A dry cell density of up to 92 g/L reactor was obtained in the enricher. The enricher ethanol productivity ranged from 50 to 160 g/L h while the stripper productivity varied from 0 to 32 g/L h at different feed rates and concentrations. A separation efficiency of as high as 98% was obtained from the system.     

Effectiveness factors for substrate and product inhibition

The transformation technique of Na and Na (Math. Biosci., 6 , 25, 1970) is extended to convert boundary-value problems involving the steady-state diffusion equation for spherical immobilized enzyme particles exhibiting substrate and product inhibition to initial-value problems. This allows a study of the influence of external mass transfer resistances on the effectiveness factors. It also considerably reduces the number of calculations required to investigate the effect of changes in the kinetic parameters on the overall rate of reaction. The existence of multiple steady states for substrate inhibition kinetics in spherical catalyst particles is illustrated and a criterion for uniqueness of steady states is developed. Effectiveness factors for competitive and noncompetitive product inhibition increase with increasing value of the Sherwood number for the substrate and increasing value of the ratio of substrate to product effective diffusivities within the particle.