Enzyme hydrolysis of plasma proteins in a CSTR ultrafiltration reactor: Performances and modeling

By investigating the effects of four operating variables-volume (V), Ultrafiltration flux (J), enzyme concentration (E), and substrate concentration (S)-on capacity (K) and conversion rate (epsilon) of a hollow fiber CSTR, the performances of the CSTR and the kinetic constants of the reaction were determined. A model which takes into account the course of fractional conversion (X) according to the modified space-time parameter, tau (integrated form of V, J, S, and E), was devised by employing the relationship to integrate the equation for the reaction rate of the CSTR and the expression of the modified space time. Correlation of this model and the experimentally obtained results demonstrates that the characteristics for an ultrafiltration membrane reactor for enzymatic hydrolysis by alcalase of plasma proteins are close to those of an ideal CSTR. Optimal scaling up, however, remains dependent on the compromise which may be obtained between capacity and the conversion rate.     

Kinetic analysis of bacterial bioluminescence

Bioluminescence from the lux-based bacterial reporter Pseudomonas fluorescens HK44 was experimentally investigated under growth substrate-rich and limiting conditions in batch, continuous stirred tank (CSTR), and turbidostat reactors. A mechanistically based, mathematical model was developed to describe bioluminescence based on 1) production and decay of catalytic enzymes, and 2) reactant cofactor availability. In the model, bioluminescence was a function of inducer, growth substrate, and biomass concentration. A saturational dependence on growth substrate concentration accommodated dependence on cofactor availability and inducer concentration to accommodate enzyme production was incorporated in the model. Under growth substrate and inducer limiting conditions in the batch reactor and CSTR, bioluminescence was found to decrease in response to cellular energy limitations. The effective lux system enzyme decay rate was determined in independent measurements to be 0.35 hr(-1) and the model captured most of the bioluminescent behavior, except at long growth times and high cell density.     

Operational stability of immobilized d-glucose isomerase in a continuous feed stirred tank reactor

d-Glucose isomerization has been studied using immobilized cells of Streptomyces phaeochromogenes in a continuous feed stirred tank reactor (CSTR) where the external film diffusion resistance was negligible. Experiments conducted with various sizes of enzyme particles indicated that a strong internal diffusion resistance improved the apparent stability of these particles. The performance equations of the CSTR were constructed by associating the material balances for the inside porous support matrix with the bulk liquid phase, and enzyme deactivation was also taken into consideration. An iterative method together with the orthogonal collocation method is proposed for the evaluation of effectiveness factor and the substrate concentration profile within the enzyme particles. The numerical results offer an alternative analytical proof for the observation that under strong internal diffusion control the apparent operational stability of immobilized enzyme is improved.     

Enzymatic resolution of (S)-(+)-naproxen in a trapped aqueous-organic solvent biphase continuous reactor

A trapped aqueous-organic biphase system for the continuous production of (S)-(+)-2-(6-methoxy-2-naphthyl) propionic acid (Naproxen) has been developed. The process consists of a stereoselective hydrolysis of the racemic Naproxen methyl ester by Candida rugosa lipase in a trapped aqueous-organic biphase system. The reaction has been carried out in a laboratory-scale continuous-flow stirred tank reactor (CSTR). The staring material has been supplied in and remaining substrate recovered by organic phase. YWG-C(6)H(5), a poorly polar synthetic support, has been employed to immobilize the lipase and to restrict the aqueous phase. Lipase immobilized on YWG-C(6)H(5) containing aqueous phase has been added into the CSTR to catalyze the hydrolysis. A dialysis membrane tube containing a continuous flow closed-loop buffer has been applied in the CSTR for the extraction of product and recruiting of the aqueous part consumed. Various reaction conditions have been studied. The activity of immobilized enzyme was effected by the polarity of support, the substrate concentration, logP value of organic phase and the product inhibition. At steady-state operating conditions, an initial conversion of 35% has been obtained. The CSTR was allowed to operate continuously for 60 days at 30 degrees C with a 30% loss of activity. The hydrolysis reaction yielded (S)-(+)-Naproxen with >90% enantiomeric excess and overall conversion of 30%.     

Analysis of the transient response of a CSTR containing immobilized enzyme particles: Part II. Minimum existence criterion and determination of substrate effective diffusivity and main reaction rate constant

A minimum existence criterion in the transient response of the bulk substrate concentration in a CSTR containing immobilized enzyme (IMEs) in porous solid supports has been obtained from simulation results using several kinetic expressions for the main reaction and the enzyme deactivation reaction. A simple method for the determination of the substrate effective diffusivity and the reaction rate constant is also presented, and applied to the decomposition of hydrogen peroxide, that reacts in a CSTR that contains silica–alumina porous catalyst particles, in which horseradish peroxidase enzyme had been previously immobilized.     

A CSTR-hollow fiber system for continuous hydrolysis of proteins. Performance and kinetics

The effect of four operating variables (enzyme concentration, substrate concentration, flow rate, and reaction volume) on the performance of CSTR-hollow fiber membrane reactor was studied for the continuous hydrolysis of a soy protein isolate using Pronase. Based on a residence time distribution study, the reactor system was modeled as an ideal CSTR in combination with the Michaelis-Menten equation of enzyme kinetics. This kinetic model correlated conversion with a space-time parameter modified to include all four independent variables. An empirical model based on curvilinear regression analysis was also developed. Both models predicted conversion fairly well, although the kinetic model slightly underpredicts at high conversion.     

Development of an ultrahigh-temperature process for the enzymatic hydrolysis of lactose. III. Utilization of two thermostable beta-glycosidases in a continuous ultrafiltration membrane reactor and galacto-oligosaccharide formation under steady-state conditions.

Hydrolysis of lactose by hyperthermophilic beta-glycosidases from the archaea Sulfolobus solfataricus (SsbetaGly) and Pyrococcus furiosus (CelB) was carried out at 70 degrees C in a continuous stirred-tank reactor (CSTR) coupled to a 10-kDa cross-flow ultrafiltration module to recycle the enzyme. Recirculation rates of > or =1 min(-1), reaction of proteins with reducing sugars, and enzyme adsorption onto the membrane are major "operational" factors of enzyme inactivation in the CSTR. They cause the half-life times of SsbetaGly and CelB to be reduced two- and eight-fold, respectively, the average value for both enzymes now being approximately 5 to 7 days. Using lactose at initial concentrations of 45 and 170 g/L, the CSTR was operated at a constant conversion level of approximately 80% for more than 2 weeks without the occurrence of microbial contamination. The productivities for the SsbetaGly-catalyzed conversion of lactose were determined at different dilution rates and initial substrate concentrations, and exceed by a factor of < or =2 those observed with CelB under otherwise identical conditions. This difference reflects the approximately eight-fold stronger product inhibition of CelB by D-glucose. While the maximum total galacto-oligosaccharide production (90-100 mM) at 170 g/L lactose in the CSTR was not different from that in the batch reactor (CelB) or was greater by approximately 25% (SsbetaGly), continuous and batchwise reactions with both enzymes differed markedly with regard to relative proportions of the individual saccharide components present at 80% substrate conversion. The CSTR yielded an up to four-fold greater ratio of disaccharides to trisaccharides concomitant with a 5- to 30-fold larger relative proportion of beta-D-Galp-(1-->3)-D-Glc in the product mixture. The results show that apart from continuous hydrolysis of lactose at 70 degrees C, a CSTR charged with SsbetaGly or CelB and operated at steady-state conditions could be a useful reaction system for the production of galacto-oligosaccharides in which composition is narrower and more easily programmable, in terms of the individual components contained, as compared to the batchwise reaction.     

Modelling amperometric enzyme electrode with substrate cyclic conversion

A mathematical model of amperometric enzyme electrodes in which chemical amplification by cyclic substrate conversion takes place in a single enzyme membrane has been developed. The model is based on non-stationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetic of the enzymatic reaction. The digital simulation was carried out using the finite difference technique. The influence of the substrate concentration, the maximal enzymatic rate as well as the membrane thickness on the biosensor response was investigated. The numerical experiments demonstrate significant (up to dozens of times) gain in biosensor sensitivity at low concentrations of substrate when the biosensor response is under diffusion control.     

Modeling and simulation of enzymatic gluconic acid production using immobilized enzyme and CSTR–PFTR circulation reaction system

Objectives

Production of gluconic acid by using immobilized enzyme and continuous stirred tank reactor-plug flow tubular reactor (CSTR–PFTR) circulation reaction system.

Results

A production system is constructed for gluconic acid production, which consists of a continuous stirred tank reactor (CSTR) for pH control and liquid storage and a plug flow tubular reactor (PFTR) filled with immobilized glucose oxidase (GOD) for gluconic acid production. Mathematical model is developed for this production system and simulation is made for the enzymatic reaction process. The pH inhibition effect on GOD is modeled by using a bell-type curve.

Conclusions

Gluconic acid can be efficiently produced by using the reaction system and the mathematical model developed for this system can simulate and predict the process well.

     

Performance of batch membrane reactor: Glycerol-3-phosphate synthesis coupled with adenosine triphosphate regeneration.

Glycerol-3-phosphate (G3P) was synthesized from glycerol using glycerol kinase (GK). This reaction requires adenosine triphosphate (ATP) and was coupled with the ATP regeneration reaction using acetate kinase (AK) in a batch-operated ultrafiltration hollow-fiber reactor. By taking into consideration the dynamic nature of the bioreactor performance under non-steady-state conditions, a model for the performance of a batch membrane reactor for G3P synthesis coupled with ATP regeneration was developed and studied. The simulation results showed good agreement with the experimental results. The simulation studies have provided some insight into the process dynamics of the coupled reactions in the reactor system studied. For the reactor operational model used, in which the enzymes are retained in the shell side and the substrates are also initially placed in the shell side, it was found that the substrate concentration in the lumen side increased to a level higher than that in the shell side, and a backdiffusion occurred from the lumen side to the shell side during reactor operation. The ratio of the reaction rate to diffusion rate goes through a sharp peak during the time that the direction of diffusion is reversed. For another reactor operational model, in which the substrates were initially placed in the lumen side and enzymes were retained in the shell side, it was found that the rate-controlling step between the reaction and diffusion was switched during the reactor operation. Initially, the reaction rate increased while the diffusion rate was high and the substrate concentrations increased in the shell side. The ratio of reaction rate to diffusion rate increased to a maximum and remained at a constant level as the diffusion rate decreased to a low level due to the nonlinear characteristics of mass transfer process. This study provides information that is useful for optimization of batch membrane enzyme reactor operation and for a fed-batch-type process with an intermittent feeding strategy for efficient use of substrates.     

Prediction of substrate consumption rate, average biofilm density and active thickness for a thin spherical biofilm at pseudo-steady state

In this work, a new approach is proposed to evaluate substrate consumption rate, average biofilm density and active thickness of a spherical bioparticle in a completely mixed fluidized bed system. The substrate consumption rate and average biofilm density are predicted for a given biofilm surface substrate concentration and operational biofilm thickness. A diffusion and reaction model is developed with an effective diffusion coefficient that depends on the average biofilm density. This approach, a first in the literature, predicts the optimum average density of a biofilm to yield the maximum substrate consumption rate within the biofilm. A reasonable correlation was observed between the model prediction and experimental results for substrate consumption rate and average biofilm density for thin and fully active biofilms.     

Prediction of continuous reactors performance based on batch reactor deactivation kinetics data of immobilized lipase

Experiments on deactivation kinetics of immobilized lipase enzyme fromCandida cylindracea were performed in stirred batch reactor using rice bran oil as the substrate and temperature as the deactivation parameter. The data were fitted in first order deactivation model. The effect of temperature on deactivation rate was represented by Arrhenius equation. Theoretical equations were developed based on pseudo-steady state approximation and Michaelis-Menten rate expression to predict the time course of conversion due to enzyme deactivation and apparent half-life of the immobilized enzyme activity in PFR and CSTR under constant feed rate policy for no diffusion limitation and diffusion limitation of first order. Stability of enzyme in these continuous reactors was predicted and factors affecting the stability were analyzed.     

The exponential model for a regulatory enzyme: its extension to describe catastrophic changes in function.

The exponential model for a regulatory enzyme (Ainsworth, 1977) is extended to describe catastrophic changes in function (as measured by the apparent association constant for the substrate under investigation) that are brought about by the binding of the substrate itself. The characteristics of the binding function are examined and an example of a protein reaction that might be described by the model is considered.     

An Efficient, Nonlinear Stability Analysis for Detecting Pattern Formation in Reaction Diffusion Systems

Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological applications. I present a relatively simple and efficient, nonlinear stability technique that greatly aids such analysis when rates of diffusion are substantially different. This technique reduces a system of reaction diffusion equations to a system of ordinary differential equations tracking the evolution of a large amplitude, spatially localized perturbation of a homogeneous steady state. Stability properties of this system, determined using standard bifurcation techniques and software, describe both linear and nonlinear patterning regimes of the reaction diffusion system. I describe the class of systems this method can be applied to and demonstrate its application. Analysis of Schnakenberg and substrate inhibition models is performed to demonstrate the methods capabilities in simplified settings and show that even these simple models have nonlinear patterning regimes not previously detected. The real power of this technique, however, is its simplicity and applicability to larger complex systems where other nonlinear methods become intractable. This is demonstrated through analysis of a chemotaxis regulatory network comprised of interacting proteins and phospholipids. In each case, predictions of this method are verified against results of numerical simulation, linear stability, asymptotic, and/or full PDE bifurcation analyses.     

Evaluation of half-life of immobilized enzyme during continuous reaction in bioreactors: A theoretical study

A theoretical study has been carried out on the evaluation of the apparent half-life of immobilized enzyme activity during continuous reaction both in a plug-flow reactor (PFR) and in a continuous-flow stirred-tank reactor (CSTR). Two apparent half-lives have been defined: the elapsed time at which the feedrate becomes half of the initial one when the feedrate of the substrate solution is lowered to keep the conversion fixed (constant-conversion policy), and the elapsed time at which the conversion becomes half of the initial one when the feedrate (or space velocity) is kept constant (constant-feedrate policy or constant-space-velocity policy). Under no intraparticle diffusional limitation, the constant-conversion policy of operation in the PFR and CSTR gives the same half-life as that of the enzyme inactivation regardless of the formula of the reaction rate, and the constant-feedrate policy of operation in the PFR and CSTR offers the same half-life as that of the enzyme inactivation only when the reaction is zero-order. Under intra-particle diffusional limitation, apparent half-lives are always greater than that of enzyme denaturation, depending on many factors such as order of reaction, feeding policy (constant-conversion and constant-feedrate policies), initial conversion, and bioreactor configuration. It is suggested to perform the continuous operation with changing feedrate to keep the conversion (or outlet substrate concentration) fixed under the domain of zero-order kinetics so as to obtain an apparent half-life as close to the real one in industrial operation.     

Immobilized α-chymotrypsin: Pore diffusion control owing to pH gradients in the catalyst particles

The fast enzymatic hydrolysis of D ,L -phenylalanine methylester (DLE) to L -phenylalanine (LA) and D -phenylalanine methylester (DE) with immobilized α-chymotrypsin was chosen as a model reaction. Under the experimental conditions applied in the present investigations the pore diffusion is the rate-limiting step of this reaction owing to the pH gradient in the particles. The effectiveness of the catalyst is experimentally determined as a function of the substrate concentration based on measurements of the enzyme protein content of native and immobilized enzyme. The proteolytic reaction is theoretically treated by also using a pore diffusion model which takes into account the concentration gradients of substrate and product, pH- and enzyme activity profiles, as well as the change of buffer capacity of the solute in the catalyst particles. The model parameters were experimentally determined for the investigated system. It can be shown that conditions are possible for which the effectiveness of the catalyst exceeds unity.     

Prediction of average biofilm density and performance of a spherical bioparticle under substrate inhibition

In this article, a model was proposed to predict the average performance and biofilm density of a spherical bioparticle under substrate inhibition in a fluidized bed system. The average biofilm density and substrate consumption rates were predicted for a definite biofilm thickness and limiting substrate concentrations. A diffusion and reaction model was developed over the bioparticle with biofilm-density dependent effective diffusion coefficients for maximum substrate consumption theory. This theory predicts the optimum density of a biofilm to yield a maximum substrate consumption rate within the biofilm, developed for the first time with this study and experimentally verified. A good correlation was observed between the model prediction and experimental results for biofilm density and substrate consumption rates. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 319-329, 1997.     

Modeling of continuous Ph-stat stirred tank reactor with Lactococcus lactis ssp. lactis bv. diacetylactis immobilized in calcium alginate gel beads

A dynamic diffusion-reaction-growth model is proposed for the study of lactic fermentation, the bioconversion of citric acid, and cell release in an immobilized cell reactor [pH-stat continuous stirred tank-reactor (CSTR)]. The model correctly simulates the onset of fermentation and colonization of the gel, followed by the steady state. External diffusion is nonlimiting and internal diffusion is limited by high cell densities at the periphery of the gel beads. Lactose-citrate cometabolism in the gel is related to the distribution of active included biomass within the gel and to gradients of substrates (lactose, citrate) and products (lactate, pH) in the beads. The utilization of lactose is limited by reaction, whereas that of citrate is limited by diffusion. Cell release from gel to the liquid medium occurs in the external spherical cap of the beads. In this peripheral zone viability is maintained at around 90%. (c) 1995 John Wiley & Sons Inc.     

Studies on the modeling and simulation of a sequential bienzymatic reaction system immobilized in emulsion liquid membrane

Experiments have been carried out to study the reaction engineering behavior of the liquid membrane-encapsulated, sequential bienzymatic reaction system, n 2n glucose. A dynamic mathematical model, free from adjustable parameters, has been developed taking into account peri-emulsion mass transfer, intra-emulsion diffusion, membrane-related mass transfer limitations and substrate and product inhibitions. A finite difference-based, user-friendly software has been developed to solve the model equations. Experimental data satisfactorily correlate with the model. While it is understood that study of sequential bienzymatic reaction system immobilized in emulsion liquid is essential for their industrial exploitation, reaction engineering behavior of such a system in presence of both substrate and product inhibitions has not yet been reported in the literature. Therefore, the model predictions of the present investigations are expected to pave the way for scale-up and design of industrial bioreactors in this field.