Mass-transfer limitations for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor

A mathematical model has been developed for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor in which the enzyme-catalyzed reaction (the irreversible uni-uni competitive Michaelis-Menten kinetics is chosen as an example) was coupled with intraparticle diffusion, external mass transfer, and axial dispersion. The effects of mass-transfer limitations, competitive inhibition of substrates, deactivation on the enzyme effective enantioselectivity, and the optical purity and yield of the desired product are examined quantitatively over a wide range of parameters using the orthogonal collocation method. For a first-order reaction, an analytical solution is derived from the mathematical model for slab-, cylindrical-, and spherical-enzyme supports. Based on the analytical solution for the steady-state resolution process, a new concise formulation is presented to predict quantitatively the mass-transfer limitations on enzyme effective enantioselectivity and optical purity and yield of the desired product for a continuous steady-state kinetic resolution process in a fixed-bed reactor.     

A two-step model for the kinetics of BTX degradation and intermediate formation by Pseudomonas putida F1

A two-step model is developed for the aerobic biodegradation of benzene,toluene, and p-xylene (BTX) by Pseudomonas putida F1. The model contains three unique features. First, an initial dioxygenation step transforms BTX into their catechol intermediates, but does not support biomassgrowth. Second, the benzene or toluene intermediates are mineralized, which supports biomass synthesis. Third, BTX exhibit competitive inhibition on each other's transformation, while toluene and benzenenoncompetitively inhibit the mineralization of their catechol intermediate. A suite of batch and chemostat experiments is used to systematically measure the kinetic parameters for the two-step transformations and the substrate interactions.     

Multisubstrate biodegradation kinetics of naphthalene, phenanthrene, and pyrene mixtures.

Biodegradation kinetics of naphthalene, phenanthrene and pyrene were studied in sole-substrate systems, and in binary and ternary mixtures to examine substrate interactions. The experiments were conducted in aerobic batch aqueous systems inoculated with a mixed culture that had been isolated from soils contaminated with polycyclic aromatic hydrocarbons (PAHs). Monod kinetic parameters and yield coefficients for the individual compounds were estimated from substrate depletion and CO(2) evolution rate data in sole-substrate experiments. In all three binary mixture experiments, biodegradation kinetics were comparable to the sole-substrate kinetics. In the ternary mixture, biodegradation of naphthalene was inhibited and the biodegradation rates of phenanthrene and pyrene were enhanced. A multisubstrate form of the Monod kinetic model was found to adequately predict substrate interactions in the binary and ternary mixtures using only the parameters derived from sole-substrate experiments. Numerical simulations of biomass growth kinetics explain the observed range of behaviors in PAH mixtures. In general, the biodegradation rates of the more degradable and abundant compounds are reduced due to competitive inhibition, but enhanced biodegradation of the more recalcitrant PAHs occurs due to simultaneous biomass growth on multiple substrates. In PAH-contaminated environments, substrate interactions may be very large due to additive effects from the large number of compounds present.     

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.     

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.     

Investigations of reaction kinetics for immobilized enzymes--identification of parameters in the presence of diffusion limitation

A method is proposed for identification of kinetic parameters when diffusion of substrates is limiting in reactions catalyzed by immobilized enzymes. This method overcomes conventional sequential procedures, which assume immobilization does not affect the conformation of the enzyme and, thus, consider intrinsic and inherent kinetics to be the same. The coupled equations describing intraparticle mass transport are solved simultaneously using numerical methods and are used for direct estimation of kinetic parameters by fitting modeling results to time-course measurements in a stirred tank reactor. While most traditional procedures were based on Michaelis-Menten kinetics, the method presented here is applicable to more complex kinetic mechanisms involving multiple state variables, such as ping-pong bi-bi. The method is applied to the kinetic resolution of (R/S)-1-methoxy-2-propanol with vinyl acetate catalyzed by Candida antarctica lipase B. A mathematical model is developed consisting of irreversible ping-pong bi-bi kinetics, including competitive inhibition of both enantiomers. The kinetic model, which fits to experimental data over a wide range of both substrates (5-95%) and temperatures (5-56 degrees C), is used for simulations to study typical behavior of immobilized enzyme systems.     

Kinetics of competitive inhibition and cometabolism in the biodegradation of benzene, toluene, and p-xylene by two Pseudomonas isolates

Two Pseudomonas species (designated strains B1 and X1) were isolated from an aerobic pilot-scale fluidized bed reactor treating groundwater containing benzene, toluene, and p-xylene (BTX). Strain B1 grew with benzene and toluene as the sole sources of carbon and energy, and it cometabolized p-xylene in the presence of toluene. Strain X1 grew on toluene and p-xylene, but not benzene. In single substrate experiments, the appearance of biomass lagged the consumption of growth substrates, suggesting that substrate uptake may not be growth-rate limiting for these substrates. Batch tests using paired substrates (BT, TX, or BX) revealed competitive inhibition and cometabolic degradation patterns. Competitive inhibition was modeled by adding a competitive inhibition term to the Monod expression. Cometabolic transformation of nongrowth substrate (p-xylene) by strain B1 was quantified by coupling xylene transformation to consumption of growth substrate (toluene) during growth and to loss of biomass during the decay phase. Coupling was achieved by defining two transformation capacity terms for the cometabolizing culture: one that relates consumption of growth substrate to the consumption of nongrowth substrate, and second that relates consumption of biomass to the consumption of nongrowth substrate. Cometabolism increased decay rates, and the observed yield for strain B1 decreased in the presence of p-xylene. (c) 1993 Wiley & Sons, Inc.     

Continuous production of gibberellic acid in a fixed-bed reactor by immobilized mycelia of Gibberella fujikuroi in calcium alginate beads

Summary The continuous production of gibberellic acid with immobilized mycelia of Gibberella fujikuroi was maintained over a hundred days in a tubular fixed-bed reactor. Free mycelium at the beginning of the storage phase was harvested from G. fujikuroi shake-flask culture and was immobilized by ionotropic gelation in calcium alginate beads.The continuous recycle production system consisted of a fixed-bed reactor, a container in which the culture medium was heated, stirred and aerated, and valves for sample withdrawal or reactant addition during the first 1320 h (55 days). A two-phase continuous extractor was then added for the last 960 hours (40 days). Free and immobilized mycelium shake-flask cultures with the same strain used in the continuous culture system were also realized to compare growth, maintenance and production parameters. The results show about the same gibberellic acid productivity in both free and immobilized mycelium shakeflask cultures: 0.384 and 0.408 mgGA₃·gBiomass^-1 ·day^-1, respectively, whereas in the continuous system the gibberellic acid production is about twice as large for a similar biomass: 0.768 mgGA₃·gBiomass^-1·day^-1. Several factors affecting the overall productivity of the immobilized systems were found to be: the quality and the quantity of mycelia in the biocatalyst beads and the immobilization conditions.     

Advantages of continuous over batch reactors for the kinetic analysis of enzymes inhibited by an unknown substrate impurity

A new experimental technique, employing a continuous stirred-tank reactor, for studying enzyme kinetics in the presence of inhibitor-contaminated substrate is described. The proposed method is simulated mathematically for competitive, uncompetitive, and mixed-type noncompetitive inhibition. The step-by-step experimental procedure is described, as is the necessary data analysis for determining the kinetic parameters. Differences in system response for enzyme inhibition by excess substrate and by an impurity are illustrated, and a stability analysis of the system is performed.     

Design of a large-scale surface-aerated bioreactor for biomass production using a VOC substrate

The design of a large-scale bioreactor for the production of bacterial biomass adapted to the biodegradation of volatile organic compounds was carried out. The bioreactor model used integrated the microbial kinetics and fluid dynamics described by the compartment model approach. The process conditions and kinetic parameters were adopted from the laboratory experimental study of (León, E., Seignez, C., Adler, N., Péringer, P., 1999. Growth inhibition of biomass adapted to the degradation of toluene and xylenes in mixture in a batch reactor with substrates supplied by pulses. Biodegradation 10, 245-250). The performance of the pulsed-batch stirred bioreactor under surface aeration conditions was simulated for different mixing configurations and conditions such as the impeller diameter, number of impellers, stirring speed, and oxygen pressure. The simulations were used for the cost analysis which resulted in the optimal design of the bioreactor.     

Discrimination between rival laccase inhibition models from data sets with one inhibitor concentration using a penalized likelihood analysis and Akaike weights

Laccase from the white-rot fungus Fomes fomentarius was used for the biodegradation of ferulic acid (FA) in the presence of chloride anions. The initial reaction rates of substrate depletion were obtained by reverse-phase HPLC determination of remaining FA since substrate and reaction products have absorption peaks at similar wavelengths. Modelling of time-course data was accomplished by discrimination of the best enzyme inhibition equation from an initial set of seven different models based on Michaelis–Menten kinetics: competitive; uncompetitive; non-competitive; mixed; mixed hyperbolic; mixed parabolic; mixed hyperbolic and parabolic. Corrected Akaike information criterion was used to evaluate the relative merit of each kinetic model in order to rank them and find the more likely one. The discrimination results showed that the models with higher probabilities were the competitive and mixed inhibition types, but Akaike weights supported the selection of competitive inhibition (CI). After optimization by nonlinear regression, laccase kinetic parameters of FA biodegradation in the presence of chloride anions were: V_max?=?0.11?μmol?min^?1?mg^?1, K_m?=?44?μmol?L^?1 and a CI constant K_ic?=?14?mmol?L^?1.     

Packed-Bed Bioreactors Under the Influence of Chemical Modulators

This report considers the behaviour of packed-bed immobilized enzyme reactors operating in the presence of substrate and/or product sequestrators. In some cases, enzyme inhibition by the reaction product and presence of chemical modulators are also considered. For each case, an appropriate analytical model is developed. Using numerical simulations, it is shown that reactor performance is impaired by substrate sequestration. This effect can be partially reversed when competitive sequestration by product or modulator is operational.

In addition, a comparison is made between some of the predicted characteristics of the reactor and experimental data. It reveals the capabilities and limitations of the models employed.     

A study of acetic acid production by immobilized Acetobacter cells: Product inhibition effects

Acetobacter living cells were immobilized by adsorption onto a ceramic support. The effects of acetic acid inhibition have been studied in a fixed-bed pulsed-flow reactor. Provided that sufficient oxygen was available, the concentration of acetic acid was found to be independent of the flow rate. Damped oscillations of acetic acid concentration were observed after step changes in dilution rate. The theoretical model developed from steady-state data was successful in predicting the experimental dynamic behavior of the reactor.     

Packed-Bed Bioreactors Under the Influence of Chemical Modulators

This report considers the behaviour of packed-bed immobilized enzyme reactors operating in the presence of substrate and/or product sequestrators. In some cases, enzyme inhibition by the reaction product and presence of chemical modulators are also considered. For each case, an appropriate analytical model is developed. Using numerical simulations, it is shown that reactor performance is impaired by substrate sequestration. This effect can be partially reversed when competitive sequestration by product or modulator is operational.

In addition, a comparison is made between some of the predicted characteristics of the reactor and experimental data. It reveals the capabilities and limitations of the models employed.     

Kinetics of biodegradation of binary and ternary mixtures of PAHs

The kinetics of biodegradation of mixtures of polycyclic aromatic hydrocarbons (PAHs) by Sphingomonas paucimobilis strain EPA505 were investigated. The investigation focused on three- and four-ring PAHs, specifically 2-methylphenanthrene, fluoranthene, and pyrene. Uptake rates in aerobic batch suspended cultivations were measured for the individual PAHs and their binary and ternary mixtures. It was observed that kinetics were influenced by the mixture composition and the kinetic properties of the components. A material balance equation containing the Monod model was numerically fitted to uptake data to determine extant kinetic parameters for the individual PAHs. Similarly, equations containing kinetic interaction models derived from enzyme kinetics were fitted to the uptake data obtained from experiments with binary and ternary mixtures. The investigation considered the following interaction types: no-interaction (Monod), pure competitive interaction, noncompetitive or mixed-type interaction, uncompetitive inhibition, and nonspecific interaction based on pure competition (SKIP). Model fit was evaluated based on probabilistic and statistical criteria and inferences were reached about underlying interaction mechanisms based on model fit. Mixture kinetics were most adequately simulated by the pure competitive interaction model with mutual substrate exclusivity. This model is fully predictive, relying only on parameters determined in the sole-PAH experiments. It was shown that for low percent inhibition values and with limited data, pure competitive interaction kinetics may not be evident, resembling no-interaction kinetics. This study is a reasonable starting point for understanding and modeling biodegradation of complex PAH mixtures in engineered and natural systems.     

Mathematical modeling of diffusion and reaction in the hydrolysis of vegetable protein in an immobilized enzyme recycle reactor

Experimental investigation is by far the most effective approach for studying the behavior of physical systems. However, an enzymatic solubilization of vegetable protein is a complex combination of intrinsic problems, of which many are not easily adaptable to experimental investigation. Experimental designs to study enzyme vegetable protein reactions yield data which describe the extramembraneous activity of the immobilized enzyme. In a continuous recycle immobilized enzyme reactor, the microenvironment concentration of the substrate or product in the membrane phase, or the concentrations along the reactor axial length in the bulk phase are not discernible to the experimenter. However, the knowledge of such concentration profiles is important in weighing the significance of such factors as intermembrane diffusion, enzyme loading, wet membrane size, and the mode of operation of the reactor. The simulation of mathematical models, which describe the physical system within the constraints imposed, yields information which is vital to the understanding of the process occurring in the reactor. The kinetics and diffusion of an immobilized thermophilic Penicillium duponti enzyme at pH 3.4-3.7 and 50 degrees C was modeled mathematically. The kinetic parameters were evaluated by fitting a model to experimental data using nonlinear regression analysis. Simulation profiles of the effects of reactor geometry, substrate concentration, membrane thickness, and enzyme leading on the hydrolysis rate are presented. From the profiles generated by the mathematical model, the best operational reactor strategy is recommended.     

Biodegradation kinetic constants and sorption coefficients of micropollutants in membrane bioreactors

In order to elucidate the capability of biomass developed in membrane bioreactors (MBR) to degrade and sorb emerging micropollutants, biodegradation (k_biol) and sorption (k_sor) kinetic constants as well as solid–liquid partition coefficients (K_d) of 13 selected pharmaceutical and personal care products (PPCPs) were determined with MBR heterotrophic biomass adding a pulse (100 ppb of each compound) and following the liquid and solid phase concentrations over time. The results obtained were compared to literature data referring to conventional activated sludge (CAS) systems. Two experiments were performed: one in the MBR itself and the second one in a batch reactor with the same type and concentration of biomass as in the MBR. Overall, both biodegradation and sorption coefficients were in the same range as previously reported by other studies in CAS systems, indicating that MBR biomass does not show better capabilities for the biological degradation and/or sorption of PPCPs compared to the biomass developed in CAS reactors. Therefore, the higher PPCPs removal efficiencies found in MBRs are explained by the high biomass concentrations obtained at the long sludge retention times at which this type of reactors are usually operated.     

Enzymatic degradation of low soluble compounds in monophasic water: solvent reactors. Kinetics and modeling of anthracene degradation by MnP

Polycyclic aromatic hydrocarbons (PAHs) are toxic compounds presenting low water solubility and high hydrophobicity, which greatly hampers their natural biodegradation. The enzymatic degradation of a model compound, anthracene, was evaluated in presence of a miscible solvent for an increased solubility. Manganese peroxidase, a ligninolytic enzyme from white-rot fungi, was used as biocatalyst in a medium containing acetone. The kinetic parameters of the enzymatic degradation of anthracene, obtained from fed-batch experiments, were applied to model the operation of a continuous reactor. Kinetics comprised a Michaelis-Menten equation, modified with an autocatalytic term, assumed to the effect of quinones acting as electron carriers, and a logistic function related to enzyme activity. The continuous reactor has been operated for 108 h, attaining a 90% of anthracene degradation, which demonstrated the feasibility of the system for its application in the removal of poorly soluble compounds. The model of this reactor permitted to predict accurately anthracene degradation in different conditions, such as external addition of anthraquinone and different enzymatic activities.     

Evaluation of effective diffusion coefficient and intrinsic kinetic parameters on azo dye biodegradation using PVA-immobilized cell beads

An immobilized mixed culture (Aeromonas hydrophila, Comamonas testosteroni, and Acinetobacter baumannii) was prepared by entrapment into phosphorylated polyvinyl alcohol (PVA) gel beads. The unsteady-state diffusion mechanism in a gel bead was applied to estimate the effective diffusion coefficients (D(e)) and the partition coefficients (K(p)) of azo dye. In addition, a simple method was developed to determine the intrinsic kinetic parameters of immobilized cells from observed reaction rates and the intrinsic kinetic parameters were then verified by fitting the experimental data into the reaction-diffusion model in a batch reactor running at a well-stirred state. The calculated effectiveness factor (eta(cal)) approached unity at Thiele modulus (Phi) < 0.3 (i.e., d(p) < 0.475 mm). The experimental effectiveness factor (eta(exp)) was in the range of 0.71-0.45 for a corresponding sphere diameter (d(p)) of 1.91 +/- 0.16 to 4.43 +/- 0.07 mm at an initial dye concentration of 200 mg/L. The results show that intraparticle diffusion resistance has a significant effect on the azo dye biodegradation rate.