Kinetics of lactose hydrolysis by beta-galactosidase of Kluyveromyces lactis immobilized on cotton fabric

A mathematic model for describing the Michaelis-Menten-type reaction kinetics with product competitive inhibition and side-reaction is proposed. A multiresponse nonlinear simulation program was employed to determine the coefficients of a four-parameter rate expression. The rate expression was compared with the conventional Michaelis-Menten reaction rate models with and without product inhibition. Experimental data were obtained using beta-galactosidase of Kluyveromyces lactis immobilized on cotton fabric in a batch system at a temperature of 37 degrees C and at various initial concentrations of dissolved lactose ranging from 3-12.5% (w/v). The reaction is followed by concentration changes with time in the tank. Samples were obtained after the outlet stream of the packed bed reactor is mixed in a well-stirred tank. High-performance liquid chromatography (HPLC) was applied to monitor the concentrations of all the sugars (reactants as well as products). The four-parameter rate model is featured with a term to describe the formation of trisaccharides, a side-reaction of the enzymatic hydrolysis. The proposed model simulates the process of lactose hydrolysis and the formation of glucose and galactose, giving better accuracy compared with the previous models.     

Dynamics and modeling of temperature-regulated gene product expression in recombinant yeast fermentation

The dynamic response of temperature-regulated gene expression in the recombinant yeast Saccharomyces cerevisiae, strain XK1-C2 carrying plasmid pSXR125, to temperature changes during fed-batch and continuous (chemostat) cultures was studied. The production of the gene product, beta-galactosidase, in the yeast cell is sensitive to the growth temperature. Gene expression of this product was fully turned on or off by temperature shifts between 24 and 30 degrees C. However, the response for gene turn-on and turn-off in this recombinant yeast was slow, requiring from several hours to over 10 h to fully appear. The continuous reactor took 30-60 h after the temperature shift to reach a new steady state. A dynamic process model was developed to simulate the reactor and cell responses to temperature shift. A first-order model was used to account for the effect of dilution rate on the change of protein concentration in the chemostat. It was found that cell response in gene expression to temperature shift followed first-order plus dead-time dynamics. Also, the response time for gene expression to temperature shift varied with specific growth rate or dilution rate of the continuous reactor. In general, the response was slower at a higher dilution rate and for gene turn-on than for gene turn-off. (c) 1996 John Wiley & Sons, Inc.     

Study of recombinant micro-organism populations characterized by their plasmid content per cell using a segregated model

Numerous observations from recombinant systems have shown that properties such as the specific cell growth rate and the plasmid-free cell formation rate are related, not only to the average plasmid content per cell, but also to the plasmid distribution within a population. The plasmid distribution in recombinant cultures can have an effect on the culture productivity that cannot be modelled using average values of the overall culture. The prediction of the behaviour of a plasmid content distribution and its causes and effects can only be studied using segregated models. A segregated model that describes populations of recombinant cells characterized by their plasmid content distribution has been developed. This model includes critical causes of recombinant culture instability such as the plasmid partition mechanism at cell division, plasmid replication kinetics and the effect of the plasmid content on the specific growth rate. The segregated model allows investigation of the effect of each of these causes and that of the plasmid content distribution on the observable behaviour of a recombinant culture.The effect of two partitioning mechanisms (Gaussian distribution and binomial distribution) on culture stability was investigated. The Gaussian distribution is slightly more stable. A small plasmid replication rate constant results in a very unstable culture even after short periods of time. This instability is dramatically improved for a larger value of this constant, hence improving protein synthesis. For a very narrow initial plasmid distribution, a given plasmid replication rate and partitioning mechanism can become broad even after a relatively short period of time. In contrast, a very "broad" initial distribution gave rise to a "Gamma-like" distribution profile. If we compare the results obtained in the simulations of the segregated model with those of the non-segregated one (average model), the latter model predicts much more stable behaviour, thus these average models cannot predict culture instability with the same precision.When compared with the experimental results, the segregated model was able to predict the practical behaviour with accuracy even in a system with a high plasmid content per cell and a high rate of plasmid-free cell formation which could not be achieved with a non-segregated model.     

Optimum design of a series of CSTRs performing reversible Michaelis-Menten kinetics: a rigorous mathematical study

The optimum design of a given number of CSTRs in series performing reversible Michaelis-Menten kinetics in the liquid phase assuming constant activity of the enzyme is studied. In this study, the presence of product in the feed stream to the first reactor, as well as the effect of the product intermediate concentrations in the downstream reactors on the reaction rate are investigated. For a given number of N CSTRs required to perform a certain degree of substrate conversion and under steady state operation and constant volumetric flow rate, the reactor optimization problem is posed as a constrained nonlinear programming problem (NLP). The reactor optimization is based on the minimum overall residence time (volume) of N reactors in series. When all the reactors in series operate isothermally, the constrained NLP is solved as an unconstrained NLP. And an analytical expression for the optimum overall residence time is obtained. Also, the necessary and sufficient conditions for the minimum overall residence time of N CSTRs are derived analytically. In the presence of product in the feed stream, the reversible Michaelis-Menten kinetics shows competitive product inhibition. And this is, because of the increase in the apparent rate constant K^' _m that results in a reduction of the overall reaction rate. The optimum total residence time is found to increase as the ratio (‚₀) of product to substrate concentrations in the feed stream increases. The isomerization of glucose to fructose, which follows a reversible Michaelis-Menten kinetics, is chosen as a model for the numerical examples.     

A mathematical method for analysing plasmid stability in micro-organisms

A mathematical model describing the instability of plasmids in micro-organisms has been developed. The model is based on the assumption that the overall causes of plasmid instability are described by the segregational instability of the plasmid, R (i.e. the rate at which plasmid-free cells are generated from plasmid-bearing cells), and the growth rate difference, d mu (i.e. the difference in growth rate between plasmid-free and plasmid-bearing cells). A method for determining the values of R and d mu (accompanied by 95% confidence limits) for any plasmid-bearing micro-organism is described. This method is based on the observation that, depending on the plasmid, various exponential patterns of plasmid instability are observed. The stability of Escherichia coli 1B373(pMG169), where d mu much greater than R, and E. coli RV308(pHSG415), where R much greater than d mu, are analysed in order to demonstrate the method.     

Continuous cultivation of recombinant Escherichia coli: Existence of an optimum dilution rate for maximum plasmid and gene product concentration

Growth yield factors, plasmid stability, cellular plasmid content, and cloned gene product activity for Escherichia coli HB101 containing plasmid pDM246 were measured at several dilution rates in continuous culture. Cell mass yield per mass of glucose consumed declined with increasing dilution rate. There was no evidence of plasmid segregational instability in any experiments, none of which employed selective medium. Plasmid content per cell varied with population-specific growth rate as observed in earlier batch experiments with the same strain. Plasmid content declined with increasing specific growth rate following indication of a maximum number of plasmids per cell at specific growth rates of ca. 0.3 h(-1). Cloned gene product (beta-lactamase) activity exhibited a sharp maximum with respect to dilution rate in continuous culture. Qualitatively different results were observed in previous experiments in batch cultivation in which specific growth rate changes were effected by altering medium composition.     

Kinetic analysis of the effects of plasmid multimerization on segregational instability of CoIE1 type plasmids in Escherichia coli B/r

The effect of plasmid multimerization on segregational instability was investigated using a structured, segregated model of genetically modified Escherichia coli cells. By including the multimerization of plasmids, the model can predict the proportion of each multimer in the total plasmid population. Simulation results suggest that the plasmid copy number is controlled by the total plasmid content (i.e., total number of plasmid origins) in the host cell and that multimerization reduces the total number of independent, monomeric segregation units. However, multimerization is found to have a minor effect on decreasing plasmid segregational stability for multicopy plasmids with average copy number per cell greater than about 25. Also model predictions were used to test whether or not a nonrandom plasmid distribution at cell fission could cause segregational instability. Even in the case of severely biased partitioning, plasmids whose copy number is above 45 per cell do not show significant segregational instability. The results suggest that when the ColE1-type plasmid does not encode and express any large or disruptive foreign proteins, the copy number of 45 per cell may be the threshold at which only growth rate-dependent instability is responsible for overall plasmid instability.     

Propagation of an amplifiable recombinant plasmid in Saccharomyces cerevisiae: flow cytometry studies and segregated modeling

Efficient expression of a foreign protein product by the yeastSaccharomyces cerevisiaerequires a stable recombinant vector present at a high number of copies per cell. A conditional centromere yeast plasmid was constructed which can be amplified to high copy number by a process of unequal partitioning at cell division, followed by selection for increased copy number. However, in the absence of selection pressure for plasmid amplification, copy number rapidly drops from 25 plasmids/cell to 6 plasmids/cell in less than 10 generations of growth. Copy number subsequently decreases from 6 plasmids/cell to 2 plasmids/cell over a span of 50 generations. A combination of flow cytometric measurement of copy number distributions and segregated mathematical modeling were applied to test the predictions of a conceptual model of conditional centromereplasmid propagation. Measured distributions of plasmid content displayed a significant subpopulation of cells with a copy number of 4-6, evenin a population whose mean copy number was 13.5. This type of copy number distribution was reproduced by a mathematical model which assumes that amaximum of 4-6 centromere plasmids per cell can be stably partitionedat cell division. The model also reproduces the observed biphasic kinetics of plasmid number instability. The agreement between simulation and experimental results provides support for the proposed model and demonstrates the utility of the flow cytometry/segregated modeling approach for the study of multicopy recombinant vector propagation.     

Plasmid stability in recombinant Saccharomyces cerevisiae

Because of many advantages, the yeast Saccharomyces cerevisiae is increasingly being employed for expression of recombinant proteins. Usually, hybrid plasmids (shuttle vectors) are employed as carriers to introduce the foreign DNA into the yeast host. Unfortunately, the transformed host often suffers from some kind of instability, tending to lose or alter the foreign plasmid. Construction of stable plasmids, and maintenance of stable expression during extended culture, are some of the major challenges facing commercial production of recombinant proteins. This review examines the factors that affect plasmid stability at the gene, cell, and engineering levels. Strategies for overcoming plasmid loss, and the models for predicting plasmid instability, are discussed. The focus is on S. cerevisiae, but where relevant, examples from the better studied Escherichia coli system are discussed. Compared to free suspension culture, immobilization of cells is particularly effective in improving plasmid retention, hence, immobilized systems are examined in some detail. Immobilized cell systems combine high cell concentrations with enhanced productivity of the recombinant product, thereby offering a potentially attractive production method, particularly when nonselective media are used. Understanding of the stabilizing mechanisms is a prerequisite to any substantial commercial exploitation and improvement of immobilized cell systems.     

Kinetics of the enzymatic hydrolysis of cellulose: 1. A mathematical model for a batch reactor process

A mathematical model for enzymatic cellulose hydrolysis, based on experimental kinetics of the process catalysed by a cellulase [see 1,4-(1,3;1,4)-β-d-glucan 4-glucanohydrolase, EC 3.2.1.4] preparation from Trichoderma longibrachiatum has been developed. The model takes into account the composition of the cellulase complex, the structural complexity of cellulose, the inhibition by reaction products, the inactivation of enzymes in the course of the enzymatic hydrolysis and describes the kinetics of d-glucose and cellobiose formation from cellulose. The rate of d-glucose formation decelerated through the hydrolysis due to a change in cellulose reactivity and inhibition by the reaction product, d-glucose. The rate of cellobiose formation decelerated due to inhibition by the product, cellobiose, and inactivation of enzymes adsorbed on the cellulose surface. Inactivation of the cellobiose-producing enzymes as a result of their adsorption was found to be reversible. The model satisfactorily predicts the kinetics of d-glucose and cellobiose accumulation in a batch reactor up to 70–80% substrate conversion on changing substrate concentration from 5 to 100 g l^?1and the concentration of the enzymic preparation from 5 to 60 g l^?1.     

Optimal design for CSTR's in series performing enzymatic lactose hydrolysis

Analytical expressions are derived for the optimal design (based on minimum overall reactors volume) of a series of N CSTR's performing enzymatic lactose hydrolysis. It is assumed that lactose hydrolysis obeys Michaelis-Menten kinetics with competitive product (galactose) inhibition and no enzyme deactivation occurs. The optimum design of a cascade of ideally mixed reactors are compared with equal size reactors and with plug flow reactor required for a given overall degree of lactose conversion. The effect of operating parameters such as temperature, lactose initial (feed) concentration and conversion, enzyme and product initial concentration on the optimal overall holding time are also investigated. Optimization results for a series of N CSTR's up to five are obtained and compared with plug flow reactor.     

Plasmid stability in recombinant Saccharomyces cerevisiae

Because of many advantages, the yeast Saccharomyces cerevisiae is increasingly being employed for expression of recombinant proteins. Usually, hybrid plasmids (shuttle vectors) are employed as carriers to introduce the foreign DNA into the yeast host. Unfortunately, the transformed host often suffers from some kind of instability, tending to lose or alter the foreign plasmid. Construction of stable plasmids, and maintenance of stable expression during extended culture, are some of the major challenges facing commercial production of recombinant proteins. This review examines the factors that affect plasmid stability at the gene, cell, and engineering levels. Strategies for overcoming plasmid loss, and the models for predicting plasmid instability, are discussed. The focus is on S. cerevisiae, but where relevant, examples from the better studied Escherichia coli system are discussed. Compared to free suspension culture, immobilization of cells is particularly effective in improving plasmid retention, hence, immobilized systems are examined in some detail. Immobilized cell systems combine high cell concentrations with enhanced productivity of the recombinant product, thereby offering a potentially attractive production method, particularly when nonselective media are used. Understanding of the stabilizing mechanisms is a prerequisite to any substantial commercial exploitation and improvement of immobilized cell systems.     

Influence of plasmid origin and promoter strength in fermentations of recombinant yeast

The effects of plasmid promoter strength and origin of replication on cloned gene expression in recombinant Saccharomyces cerevisiae have been studied in batch and continuous culture. The plasmids employed contain the Escherichia coli lacZ gene under the control of yeast promoters regulated by the galactose regulatory circuit. The synthesis of beta-galactosidase was therefore induced by the addition of galactose. The initial induction transients in batch culture were compared for strains containing plasmids with 2mu and ARS1 origins. As expected, cloned gene product synthesis was much lower with the ARS1 plasmid: average beta-galactosidase specific activity was an order of magnitude below that with the 2mu-based plasmid. This was primarily due to the low plasmid stability of 7.5% when the plasmid origin of replication was the ARS1 element. The influence of plasmid promoter strength was studied using the yeast GAL1, GAL10, and hybrid GAL10-CYC1 promoters. The rate of increase in beta-galactosidase specific activity after induction in batch culture was 3-5 times higher with the GAL1 promoter. Growth rate under induced conditions, however, was 15% lower than in the absence of lacZ expression for this promoter system. The influence of plasmid promoter strength on induction behavior and cloned gene expression was also studied in continuous fermentations. Higher beta-galactosidase production and lower biomass concentration and plasmid stability were observed for the strain bearing the plasmid with the stronger GAL1 promoter. Despite the decrease in biomass concentration and plasmid stability, overall productivity in continuous culture using the GAL1 promoter was three times that obtained with the GAL10-CYC1 promoter.     

A simulation model for the continuous production of acetoin and butanediol using Bacillus subtilis with integrated pervaporation separation

The potential for producing acetoin and butanediol with a Bacillus subtilis strain was investigated with continuous culture using molasses as carbon substrate. The steady-state results were influenced by both oxygen and undetermined limiting compounds. Employing the known metabolic pathways, four overall stoichiometry relations were used with an energetic assumption on the energy requirements for biomass formation to establish a linear relations were used with an energetic assumption on the energy requirements for biomass formation to establish a linear relation between the overall rates, whose parameters were determined by linear regression. This provided a relationship for the product formation rate. The chemostat culture data were described with a growth kinetics model, which included limitation by molasses and oxygen as well as diauxic effects and product inhibition. The biokinetics model was combined with an experimentally verified model for the membrane Pervaporation. From this combined model were determined the influence of the membrane characteristics (enrichment factors and membrane area) and the dilution rate on the performance of the integrated process. Simulations revealed that an increase of the enrichment factor, possible by membrane improvement, would have counteracting influences, owing to decreased product inhibition but with lower biomass concentration. (c) 1993 Wiley & Sons, Inc.     

A rational approach to improving productivity in recombinant Pichia pastoris fermentation

A Mut(S) Pichia pastoris strain that had been genetically modified to produce and secrete sea raven antifreeze protein was used as a model system to demonstrate the implementation of a rational, model-based approach to improve process productivity. A set of glycerol/methanol mixed-feed continuous stirred-tank reactor (CSTR) experiments was performed at the 5-L scale to characterize the relationship between the specific growth rate and the cell yield on methanol, the specific methanol consumption rate, the specific recombinant protein formation rate, and the productivity based on secreted protein levels. The range of dilution rates studied was 0. 01 to 0.10 h(-1), and the residual methanol concentration was kept constant at approximately 2 g/L (below the inhibitory level). With the assumption that the cell yield on glycerol was constant, the cell yield on methanol increased from approximately 0.5 to 1.5 over the range studied. A maximum specific methanol consumption rate of 20 mg/g. h was achieved at a dilution rate of 0.06 h(-1). The specific product formation rate and the volumetric productivity based on product continued to increase over the range of dilution rates studied, and the maximum values were 0.06 mg/g. h and 1.7 mg/L. h, respectively. Therefore, no evidence of repression by glycerol was observed over this range, and operating at the highest dilution rate studied maximized productivity. Fed-batch mass balance equations, based on Monod-type kinetics and parameters derived from data collected during the CSTR work, were then used to predict cell growth and recombinant protein production and to develop an exponential feeding strategy using two carbon sources. Two exponential fed-batch fermentations were conducted according to the predicted feeding strategy at specific growth rates of 0.03 h(-1) and 0.07 h(-1) to verify the accuracy of the model. Cell growth was accurately predicted in both fed-batch runs; however, the model underestimated recombinant product concentration. The overall volumetric productivity of both runs was approximately 2.2 mg/L. h, representing a tenfold increase in the productivity compared with a heuristic feeding strategy.     

Analysis of unstable recombinant Saccharomyces cerevisiae population growth in selective medium

Widely applied selection strategies for plasmid-containing cells in unstable recombinant populations are based upon synthesis in those cells of an essential, selection gene product. Regular partitioning of this gene product combined with asymmetric plasmid segregation produces plasmid-free cells which retain for some time the ability to grow in selective medium. This theory is elaborated here in terms of a segregated model for an unstable recombinant population which predicts population growth characteristics and composition based upon experimental data for stable strain growth kinetics, plasmid content, and selection gene product stability. Analytical solutions from this model are compared with an unsegregated phenomenological model to evaluate the effective specific growth rate of plasmid-free cells in selective medium. Model predictions have been validated using experimental growth kinetics and flow cytometry data for Saccharomyces cerevisiae D603 populations containing one of the plasmids YCpG1ARS1, YCpG1DeltaR8, YCpG1DeltaR88, YCpG1DeltaH103, YCpG1DeltaH200, pLGARS1, and pLGSD5. The recombinant strains investigated encompass a broad range of plasmid content (from one to 18 plasmids per cell) and probability alpha of plasmid loss at division (0.05 相似文献