Discontinuity induced bifurcations in a model of Saccharomyces cerevisiae.

We perform a bifurcation analysis of the mathematical model of Jones and Kompala [K.D. Jones, D.S. Kompala, Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures, J. Biotechnol. 71 (1999) 105-131]. Stable oscillations arise via Andronov-Hopf bifurcations and exist for intermediate values of the dilution rate as has been noted from experiments previously. A variety of discontinuity induced bifurcations arise from a lack of global differentiability. We identify and classify discontinuous bifurcations including several codimension-two scenarios. Bifurcation diagrams are explained by a general unfolding of these singularities.

Analysis of foreign protein overproduction in recombinant CHO cells. Effect of growth kinetics and cell cycle traverse.

Intracellular foreign protein (beta-galactosidase) expression in recombinant CHO cell lines in continuous culture was analyzed by developing a mathematical model that includes the effects of metabolic burden and cell cycle dependence of intracellular foreign protein expression. This combined growth kinetic and cell cycle model, assuming S- or G1-phase-dependent expression, was stimulated to predict productivity on a single-cell and culture-volume basis in continuous cultures. In the case of S-phase-dependent expression, the intracellular foreign protein level increases monotonically, but in the case of G1-phase-dependent expression it decreases monotonically with increasing dilution rate. Also, the trends of foreign protein concentration in the culture volume differ significantly between S- and G1-dependent expression kinetics. Thus, the cell cycle dependency of foreign protein expression should be included in process optimization concepts and operating strategies of continuous bioreactors.

Cybernetic modeling of spontaneous oscillations in continuous cultures of Saccharomyces cerevisiae.

We have developed a 'cybernetic' model to simulate the dynamic competition between all the available metabolic pathways of yeast Saccharomyces cerevisiae. This computer model predicts all the key experimentally observed aspects of the sustained oscillations in all the measured concentrations in continuous cultures, such as the spontaneous generation of oscillations as well as the variations in period and amplitude of oscillations when the dilution rate or agitation rate are changed.

Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures.

Growth of Saccharomyces cerevisiae on glucose in aerobic batch culture follows the well-documented diauxic pattern of completely fermenting glucose to ethanol during the first exponential growth phase, followed by an intermediate lag phase and a second exponential growth phase consuming ethanol. In continuous cultures over a range of intermediate dilution rates, the yeast bioreactor exhibits sustained oscillations in all the measured concentrations, such as cell mass, glucose, ethanol, and dissolved oxygen, the amounts of intracellular storage carbohydrates, such as glycogen and trehalose, the fraction of budded cells as well as the culture pH. We present here a structured, unsegregated model for the yeast growth dynamics developed from the 'cybernetic' modeling framework, to simulate the dynamic competition between all the available metabolic pathways. This cybernetic model accurately predicts all the key experimentally observed aspects: (i) in batch cultures, duration of the intermediate lag phase, sequential production and consumption of ethanol, and the dynamics of the gaseous exchange rates of oxygen and carbon dioxide; and (ii) in continuous cultures, the spontaneous generation of oscillations as well as the variations in period and amplitude of oscillations when the dilution rate or agitatin rate are changed.

Characterization of gene expression in recombinant Escherichia coli cells infected with phage lambda.

Phage lambda infection was investigated for possible production of toxic foreign proteins in Escherichia coli. The target gene transcription was regulated by a T7 promoter, which was initiated under the action of T7 RNA polymerase delivered by infecting phage. Two types of phage infection were investigated. In both cases, deletion of the int gene prevents lysogenic integration. One phage, lambda CE6, contains the Sam7 lysis mutation, so that infectious phage particles remain intracellular. The other phage, lambda CE6M, undergoes the complete lytic pathway so that the infected cell is eventually lysed. The dynamics of phage adsorption, foreign protein synthesis, and cell growth were analyzed as a function of various parameters, such as MOI (multiplicity of infection), cell concentration at infection, culture temperature, and different carbon sources. A low basal level of the foreign protein, beta-galactosidase, was obtained prior to infection, whereas it reached about 0.1 g/L after phage "induction" under appropriate infection conditions. Due to low basal expression, this expression system is useful for the production of toxic foreign proteins.

Growth and induction kinetics of inducible and autoinducible expression of heterologous protein in suspension cultures of recombinant mouse L cell lines.

Mouse Ltk- cells were transfected with four different plasmids for autoinducible and highly-inducible expression of the bacterial lacZ gene and cultivated in suspension. Two selection genes, thymidine kinase (tk) and neomycin resistance (neor), were used to select the clones in both cell lines. The resulting two cell lines, designated M4 and R2, differ in that the inducible MMTV promoter from mouse mammary tumor virus (MMTV) controls glucocorticoid receptor (gr) gene and lacZ gene expression in the M4 cell line ("autoinducible"), while the constitutive rous sarcoma virus (RSV) promoter controls gr gene expression and the MMTV promoter controls lacZ gene expression in the R2 cell line ("highly-inducible"). Both cell lines were stable with respect to reproducibility of growth rate in spinner flasks and inducibility of beta-galactosidase expression. The exponential growth rate of R2 cells was slower than that of M4 cells before induction because the R2 cell line continuously expressed gr genes under the constitutive RSV promoter, and the percent reduction of exponential growth rate mainly caused by gr gene expression was about 20%. The inducibility of the M4 cell line was greater than that of the R2 cell line because in the M4 cell line MMTV promoter controlled gr and lacZ gene expression autoinducibly. Maximum induction of the M4 cell line occurred after induction with the hormone dexamethasone (Dex) at 10(-7) M, and the final beta-galactosidase content increased 400-fold after induction. The optimum conditions for inducer concentration and induction time were determined, and the highest production of beta-galactosidase occurred when Dex was added after the cell concentration had reached its maximum in batch culture. Dex (10(-9) M) is a critical inducer concentration in view of inducibility between M4 and R2 cell lines. The inducibility of R2 cell line is higher than that of the M4 cell line from 0 to 10(-9) M Dex, but the inducibility of M4 was higher than that of the R2 cell line at Dex concentrations of more than 10(-9) M.

Viable cell recycle with an inclined settler in the perfusion culture of suspended recombinant Chinese hamster ovary cells.

The perfusion culture of suspended mammalian cells requires a cell retention device, the best of which will retain all viable cells and reject all nonviable cells and debris. The inclined settler is a passive, simple, inexpensive, and easy-to-maintain device that has been shown in the past to selectively remove single nonviable cells of hybridoma cultures. In this work, we have demonstrated the preferential return of viable recombinant Chinese hamster ovary (CHO) cells through the use of a three-port settler maintained at lower temperatures and vibrated to reduce cell attachment and enhance cell return to the bioreactor. The residence time of CHO cells in the cooled, vibrated settler was determined by flow-cytometric discrimination of tracer recombinant CHO cells. Cells returning to the bioreactor through the underflow had an average residence time of 1.46 h in the settler. During perfusion cultures with cell densities above 10(6) cells/mL, cells seen to be stalled within the settler were easily dislodged by periodic air bubbling using a simple back-flushing procedure in which headspace gas was brought through the settler underflow port. The resuspended cells were returned to the bioreactor within an average of 32 min after bubbling. This study demonstrates that inclined sedimentation technology can be utilized to selectively recycle viable recombinant CHO cells with only a short retention time in an inclined settler.

Inclined sedimentation for selective retention of viable hybridomas in a continuous suspension bioreactor.

The continuous separation of nonviable hybridoma cells from viable hybridoma cells by using a narrow rectangular channel that is inclined from the vertical has been investigated experimentally. The effectiveness of the settler in selectively retaining viable hybridomas in the bioreactor while permitting the removal of nonviable hybridomas has been shown to depend on the flow rate through the settler. Intermediate flow rates through the settler have been found to provide the highest removal of nonviable hybridomas relative to viable hybridoma retention. At high dilution rates through the chemostat, over 95% of the viable cells could be partitioned to the bottom of the settler while over 50% of the nonviable cells are removed through the top of the settler. This successful separation is due to the significantly larger size of the viable hybridomas than the nonviable ones. A continuous perfusion experiment was performed in which an external inclined settler was used to retain virtually all of the viable hybridomas in the culture, while selectively removing from the culture approximately 20% of the nonviable cells that entered the settler. A stable viable cell concentration of 1.0 x 10(7) cells/mL was achieved, as was an antibody productivity of over 50 micrograms/(mL.day). These represent 3- and 6-fold increases, respectively, over the values obtained from a chemostat culture without cell retention.

A novel structured kinetic modeling approach for the analysis of plasmid instability in recombinant bacterial cultures.

The instantaneous specific growth rate of a recombinant bacterial culture is directly calculated using a simple structured kinetic modeling approach. Foreign plasmid replication and foreign protein expression represent metabolic burdens to the host cell. The individual effects of these plasmid-mediated activities on the growth rate of plasmid-bearing cells are estimated separately. The dynamic and steady state simulations of the model equations show remarkable agreement with widely observed experimental trends in plasmid copy number and foreign protein content. The model provides an important tool for understanding and controlling plasmid instability in recombinant bacterial fermentations. The modeling framework employed here is suitable for studying the metabolism and growth of a variety of microbial cultures.

A structured kinetic modeling framework for the dynamics of hybridoma growth and monoclonal antibody production in continuous suspension cultures.

A structured kinetic model is developed to describe the dynamics of hybridoma growth and the production of monoclonal antibodies and metabolic waste products in suspension culture. The crucial details of known metabolic processes in hybridoma cells are incorporated by dividing the cell mass into four intracellular metabolic pools. The model framework and structure allow the dynamic calculation of the instantaneous specific growth rate of a hybridoma culture. The steady state and dynamic simulations of the model equations exhibit excellent agreement with experimentally observed trends in substrate utilization and product formation. The model represents the first to include any degree of metabolic detail and structure in describing a hybridoma culture. In so doing, it provides the basic modeling framework for incorporating further details of metabolism and can be a useful tool to study various strategies for enhancing hybridoma growth as well as viability and the production of monoclonal antibodies in suspension cultures.

Overexpression of cloned genes using recombinant Escherichia coli regulated by a T7 promoter: I. Batch cultures and kinetic modeling.

A novel Eschericha coli expression system directed by bacteriophage T7 RNA Polymerase utilized for overexpression of the cloned gene. The recombinant cell contains the plasmid with a bacteriophage promoter, the T7 promoter, to regulate the expression of the target gene. This promoter is recognized only by T7 RNA polymerase, whose gene has been fused into the host chromosome and is under control of the lacUV5 promoter. Therefore, the target gene on the plasmid can be expressed only in the presence of T7 RNA polymerase, which is induced by isopropyl-beta-D-thiogalactopyranoside (IPTG). The batch cultures were performed to investigate the effect of induction on kinetics of cell growth and foreign protein formation and to determine the optimal induction strategy. It was observed that the specific growth rates of the recombinant cells dramatically decrease after induction, and that there is an optimal induction time for maximizing the accumulated intracellular foreign protein. This optimal induction time varies significantly with inducer concentration. To better understand the optimal behavior, a lumped mechanistic model was constructed to analyze the induced cell growth and foreign protein formation rates.

Verification of immune response optimality through cybernetic modeling.

An immune response cascade that is T cell independent begins with the stimulation of virgin lymphocytes by antigen to differentiate into large lymphocytes. These immune cells can either replicate themselves or differentiate into plasma cells or memory cells. Plasma cells produce antibody at a specific rate up to two orders of magnitude greater than large lymphocytes. However, plasma cells have short life-spans and cannot replicate. Memory cells produce only surface antibody, but in the event of a subsequent infection by the same antigen, memory cells revert rapidly to large lymphocytes. Immunologic memory is maintained throughout the organism's lifetime. Many immunologists believe that the optimal response strategy calls for large lymphocytes to replicate first, then differentiate into plasma cells and when the antigen has been nearly eliminated, they form memory cells. A mathematical model incorporating the concept of cybernetics has been developed to study the optimality of the immune response. Derived from the matching law of microeconomics, cybernetic variables control the allocation of large lymphocytes to maximize the instantaneous antibody production rate at any time during the response in order to most efficiently inactivate the antigen. A mouse is selected as the model organism and bacteria as the replicating antigen. In addition to verifying the optimal switching strategy, results showing how the immune response is affected by antigen growth rate, initial antigen concentration, and the number of antibodies required to eliminate an antigen are included.

Overexpression of cloned genes using recombinant Escherichia coli regulated by a T7 promoter: II. Two-stage continuous cultures and model simulations.

A two-stage culture strategy was studied for continuous high-level production of a foreign protein in the chemically inducible T7 expression system. The first stage is dedicated to the maintenance of plasmid-bearing cells and the second stage to the target protein synthesis by induction of cells coming from the first stage. On entering the second stage, recombinant cells undergo a gradual induction of the target gene expression. These plasmid-bearing cells experience dynamic changes in intracellular compositions and specific growth rates with their individual residence times. Therefore, the overall cultural characteristics in the production stage are really averages of the contributions from the various cells with different residence times. The behavior of the two-stage culture is described by a model, which accounts for dynamic variations of cell growth and protein synthesis rates with cell residence times. Model simulations were compared with experimental results at a variety of operating conditions such as inducer concentration and dilution rate. This model is useful for understanding the behavior of two-stage continuous cultures.

Cybernetic modeling of microbial growth on multiple substrates.

The internal regulatory processes, which underlie a variety of behavior in microbial growth on multiple substrates, are viewed as a manifestation of an invariant strategy to optimize some goal of the cells. A goal-seeking or cybernetic model is proposed here, with the optimization obased on a short-term perspective of response to the environment. The model parameters are determined from the growth data on single substrates. The model predicts the entire range of microbial growth behavior on multiple substrates from simultaneous utilization of all sugars to sequential utilization with pronounced diauxic lags. It is shown to predict the many variations of the diauxic phenomenon in different growth conditions. The transients in continuous culture growth on mixed substrates caused by varying the feed strategies are easily simulated by this model. The framework of this model can be applied to batch or continuous culture growth of many bacteria on different combinations of substrates.

Foreign protein expression from S phase specific promoters in continuous cultures of recombinant CHO cells.

Foreign protein expression from the commonly used SV40 promoter has been found to be primarily during the S-phase of the cell cycle. Simple mathematical models with this cell cycle phase dependent expression of foreign protein suggest that the specific production rate will be proportional to the cell growth rate, which is particularly disadvantageous in high cell density fed-batch or perfusion bioreactors. In this study we investigate this predicted relationship between the production rate and growth rate by culturing recombinant CHO cells in a continuous suspension bioreactor. One CHO cell line, GS-26, has been stably transfected with the plasmid pSVgal, which contains the E. coli lac Z gene under the control of the SV40 promoter. This GS-26 cell line was grown in suspension cultures over a range of specific growth rates in batch and continuous modes. The intracellular ß-galactosidase activity was assayed using a standard spectrophotometric method after breaking the cells open and releasing the enzyme. A strong growth associated relationship is found between the intracellular ß-galactosidase content and the specific growth rate in batch and continuous cultures, as predicted.

Cell cycle analysis of foreign gene (beta-galactosidase) expression in recombinant mouse cells under control of mouse mammary tumor virus promoter.

The cell cycle dependency of foreign gene expression in recombinant mouse L cells was investigated. Two different recombinant mouse L cell lines having the glucocorticoid receptor-encoding gene and the lacZ reporter gene were used in this study. The lacZ gene expression was controlled by the glucocorticoid-inducible mouse mammary tumor virus (MMTV) promoter in both cell lines. In "M4" cells the gr gene was under the control of another MMTV promoter, but in "R2" cells it was under the control of the constitutive Rous sarcoma virus promoter. These normally attachment-grown cells were adapted to suspension culture, and a dual-laser flow cytometer was used to simultaneously determine the DNA and foreign protein (beta-galactosidase) content of single living cells. Expression of beta-galactosidase as a function of cell cycle phase was evaluated for cells in exponential growth without any addition of the glucocorticoid inducer, dexamethasone. Cell cycle positions in the S phase were estimated on the basis of DNA content per cell, and position in the G1 phase was estimated on the basis of cell size as measured by pulse-width time of flight. The results showed that beta-galactosidase synthesis occurred through all cell cycle phases, but the expression rate in the G1 phase was much lower than that in the S and G2/M phases in both cell lines. On the basis of cell size analysis, beta-galactosidase expression in M4 cells (with autoinducible promoter) was found to be higher than that in R2 cells (with inducible promoter) during the G1 phase.

Large-scale production of murine bone marrow cells in an airlift packed bed bioreactor.

Large-scale cultivation of murine bone marrow cells was accomplished in an airlift packed bed bioreactor system designed to mimic the in vivo bone marrow environment. The attachment-dependent stromal cell population, which provides the necessary microenvironment, including growth factors for subsequent hematopoietic activity, was first established within the bioreactor. This attachment-dependent cell growth occurred on the fiber-glass matrix packed in the annular region of the bioreactor. Once the stromal cell layer was established, fresh bone marrow cells were inoculated to initiate hematopoiesis. However, traditional culture medium was found to be inadequate for the initiation of hematopoiesis, but the use of stromal cell "conditioned" medium (with no exogenously added growth factors) yielded sustained cell production. The extent of stromal cell subculturing prior to inoculation into the bioreactor and the inoculation density were also important factors for the successful initiation of hematopoietic activity. A 500-mL perfusion culture experiment resulted in the production and harvest of 3.6 x 10(8) suspended bone marrow cells over the course of 11 weeks.

Dynamics of induced CAT expression in E. coli.

The dynamics of chemically induced chloramphenicolaceyl-transferase (CAT) expression are determined in batch cultures of Escherichia coli DH5alphaF'IQ [pKK262-1]. This article is directed towards understanding the coupling of induced cloned-protein synthesis and reduced cell growth which are balanced in the optimal system. Experimental results indicate that the best inducer (IPTG) concentration is near 1.0 mM when added during midexponential growth. Lower concentrations cause only weak induction, whereas higher concentrations cause sufficiently strong induction that cell growth is suppressed. Induction at the onset of the stationary phase results in high expression but is accompanied by stimulated protease activity. Also, cell mass yield is adversely affected by enhanced protein synthesis. A structured metabolic model is shown to predict the responses of instantaneous growth rate and productivity which result from protein overexpression. This model can be employed to predict alternative reactor strategies and operating conditions necessary for the design of efficient bioprocess.

Metabolic burden in recombinant CHO cells: effect ofdhfr gene amplification andlacZ expression.

Foreign protein production levels in two recombinant Chinese hamster ovary (CHO) cell lines were compared in cells transfected with different expression vectors. One vector pNL1 contained the gene for neomycin resistance (neo ( r )) and thelacZ gene which codes for intracellular ß-galactosidase, with both genes controlled by the constitutive simian virus (SV40) promoter. The other vector CDßG contained the amplifiabledhfr gene andlacZ gene, controlled by the constitutive SV40 and cytomegalovirus (CMV) promoters, respectively. Cell growth and ß-galactosidase expression were compared quantitatively after cells were selected in different concentrations of the neomycin analog G418 and methotrexate, respectively. A 62% reduction in growth rate occurred in recombinant CHO cells in which thelacZ anddhfr genes were highly amplified and expressed. In contrast, the combined effects of the unamplifiedneo ( r ) gene andlacZ gene expression on the growth kinetics were small. Any metabolic burden caused bylacZ gene expression, which was evaluated separately from the effect ofneo ( r ) gene expression, must be negligible, as higher expression of ß-galactosidase (1.5×10(-6) units/cell) occurred in unamplified cells compared to the cells in whichlacZ was amplified by thedhfr-containing vector (3×10(-7) units/cell). Thus, the main factor causing severe growth reduction ("metabolic burden") in cells containing the amplifieddhfr gene system was not overexpression of ß-galactosidase butdhfr andlacZ gene co-amplification anddhfr gene expression.