Mathematical descriptions of hybridoma culture kinetics: II. The relationship between thiol chemistry and the degradation of serum activity

The growth rate of the hybridoma cell line ATCC-CRL-1606 in low serum medium declines rapidly with time after inoculation. To characterize this phenomenon, the stability of the growth-promoting activity of serum was investigated. The activity of serum was found to de grade with time, and was stabilized by alterations in the medium formulation that acted to lower the oxidation/reduction potential. This included both the addition of thiols and the elimination of disulfides from the medium. Additionally, cysteine and other thiols were shown to stimulate growth in low serum, low cell density cultures, suggesting that thiols may be rate-limiting in low serum medium. Stimulation of growth by thiol addition was less significant at high cell levels, implying that the cells themselves may be acting to reduce their environment. A hypothesis is presented based on these results which suggests that the actual rate-limiting moieties in low serum cultures may be dithiols.     

Mathematical modelling of dynamics and control in metabolic networks. I. On Michaelis-Menten kinetics

As a starting point for modeling of metabolic networks this paper considers the simple Michaelis-Menten reaction mechanism. After the elimination of diffusional effects a mathematically intractable mass action kinetic model is obtained. The properties of this model are explored via scaling and linearization. The scaling is carried out such that kinetic properties, concentration parameters and external influences are clearly separated. We then try to obtain reasonable estimates for values of the dimensionless groups and examine the dynamic properties of the model over this part of the parameter space. Linear analysis is found to give excellent insight into reaction dynamics and it also gives a forum for understanding and justifying the two commonly used quasi-stationary and quasi-equilibrium analyses. The first finding is that there are two separate time scales inherent in the model existing over most of the parameter space, and in particular over the regions of importance here. Full modal analysis gives a new interpretation of quasi-stationary analysis, and its extension via singular perturbation theory, and a rationalization of the quasi-equilibrium approximation. The new interpretation of the quasi-steady state assumption is that the applicability is intimately related to dynamic interactions between the concentration variables rather than the traditional notion that a quasi-stationary state is reached, after a short transient period, where the rates of formation and decomposition of the enzyme intermediate are approximately equal. The modal analysis reveals that the generally used criterion for the applicability of quasi-stationary analysis that total enzyme concentration must be much less than total substrate concentration, et much less than St, is incomplete and that the criterion et much less than Km much less than St (Km is the well known Michaelis constant) is the appropriate one. The first inequality (et much less than Km) guarantees agreement over the longer time scale leading to quasi-stationary behavior or the applicability of the zeroth order outer singular perturbation solution but the second half of the criterion (Km much less than St) justifies zeroth order inner singular perturbation solution where the substrate concentration is assumed to be invariant. Furthermore linear analysis shows that when a fast mode representing the binding of substrate to the enzyme is fast it can be relaxed leading to the quasi-equilibrium assumption. The influence of the dimensionless groups is ascertained by integrating the equations numerically, and the predictions made by the linear analysis are found to be accurate.(ABSTRACT TRUNCATED AT 400 WORDS)     

Influence of inoculum age on hybridoma culture kinetics

To determine the influence of the inoculum age on the kinetics of hybridoma growth and metabolism, spinner flasks have been inoculated with cells previously propagated in T flasks for 43, 52, 62 and 71 hr respectively. Increasing the age of the inoculum is found to result in a longer lag phase, in a lower maximum specific growth rate and in a reduced maximal cell density. During the growth phase specific rates of glucose and glutamine uptake and of ammonia and lactate production are similar. However, with the older inoculum, much higher metabolic activities are observed during the lag phase. The production of antibodies is delayed with increasing inoculum age, but the final antibody concentrations are similar, which indicates a higher specific antibody production rate when inoculating with older cells.     

Growth, metabolic, and antibody production kinetics of hybridoma cell culture: 1. Analysis of data from controlled batch reactors.

A mouse-mouse hybridoma cell line (167.4G5.3) was cultivated in a 1.5-L stirred-tank bioreactor under constant pH and dissolved oxygen concentration. The transient kinetics of cell growth, metabolism, and antibody production were followed by biochemical and flow cytometric methods. The cell-specific kinetic parameters (growth and metabolic rates) as well as cell size were constant throughout the exponential phase. Intracellular protein and RNA content followed a similar trend. Cell growth stopped when the glutamine in the medium was depleted. Glucose could not substitute for glutamine, as glucose consumption ceased after glutamine depletion. Ammonia and lactate production followed closely glutamine and glucose consumption, respectively. Alanine, glutamate, serine, and glycine were produced but other amino acids were consumed. The cells are estimated to obtain about 45% of the total energy from glycolysis, with the balance of the metabolic energy provided by oxidative phosphorylation. The antibody was produced at a constant rate in both the exponential and decline phases of growth. The intracellular antibody content of the cells remained relatively constant during the exponential phase of growth and decreased slightly afterwards.     

Comparison of growth kinetics of producing and nonproducing hybridoma cells in batch culture.

Several clones of nonproducing cells were isolated from a continuous culture of hybridoma cells, which were originally producing antibody. Their behavior was compared to that of the producing cells in batch culture. The growth kinetics of five out of six clones exhibited higher specific growth rate, higher yield of cell mass on glutamine, and lower yields of lactate and ammonium. The implications of the comparisons for growth of hybridoma cultures are discussed.     

Cell cycle kinetics and monoclonal antibody productivity of hybridoma cells during perfusion culture

The flow-cytometric (FCM) analysis of bivariate DNA/lgG distributions has been conducted to study the cell cycle kinetics and monoclonal antibody (MAb) production during perfusion culture of hybridoma cells. Three different perfusion rates were employed to demonstrate the dependency of MAb synthesis and secretion on cell cycle and growth rate. The results showed that, during the rapid growth period of perfusion culture, the level of intracellular igG contents of hybridoma cells changed significantly at each perfusion rate, while the DNA histograms showing cell cycle phases were almost constant. Meanwhile, during the reduced growth period of perfusion culture, the fraction of cells in the S phase decreased, and the fraction cells in the G1/G0 phase increased with decreasing growth rate. The fraction of cells in the G2/M phase was relatively constant during the whole period of perfusion culture. Positive correlation was found between mean intracellular IgG contents and the specific MAb production rate, suggesting that the deletion of intracellular IgG contents by a flow cytometer could be used as a good indicator for the prediction of changes in specific MAb productivity following manipulation of the culture condition. (c) 1994 John Wiley & Sons, Inc.     

A study of hybridoma cell growth and antibody production kinetics in continuous culture

Summary A detailed study of cell growth and antibody production kinetics in continuous culture found that the specific rate of antibody production reached a maximum saturated profile at a specific growth rate less than the maximum. This observation is novel and of importance in the understanding of the mechanism of antibody production and/or antibody transport.     

Growth, metabolic, and antibody production kinetics of hybridoma cell culture: 2. Effects of serum concentration, dissolved oxygen concentration, and medium pH in a batch reactor.

The effects of serum, dissolved oxygen (DO) concentration, and medium pH on hybridoma cell physiology were examined in a controlled batch bioreactor using a murine hybridoma cell line (167.4G5.3). The effect of serum was also studied for a second murine hybridoma cell line (S3H5/gamma 2bA). Cell growth, viability, cell density, carbohydrate and amino acid metabolism, respiration and energy production rates, and antibody production rates were studied. Cell growth was enhanced and cell death was decreased by increasing the serum level. The growth rates followed a Monod-type model with serum being the limiting component. Specific glucose, glutamine, and oxygen uptake rates and specific lactate and ammonia production rates did not change with serum concentrations. Amino acid metabolism was slightly influenced by the serum level. Cell growth rates were not influenced by DO between 20% and 80% air saturation, while the specific death rates were lowest at 20-50% air saturation. Glucose and glutamine uptake rates increased at DO above 10% and below 5% air saturation. Cell growth rate was optimal at pH 7.2. Glucose and glutamine uptake rates, as well as lactate and ammonia production rates, increased above pH 7.2. Metabolic rates for glutamine and ammonia were also higher below pH 7.2. The consumption or production rates of amino acids followed the glutamine consumption very closely. Cell-specific oxygen uptake rate was insensitive to the levels of serum, DO, and pH. Theoretical calculations based on experimentally determined uptake rates indicated that the ATP production rates did not change significantly with serum and DO while it increased continually with increasing pH. The oxidative phosphorylation accounted for about 60% of total energy production. This contribution, however, increased at low pH values to 76%. The specific antibody production rate was not growth associated and was independent of serum and DO concentrations and medium pH above 7.20. A 2-fold increase in specific antibody production rates was observed at pH values below 7.2. Higher concentrations of antibody were obtained at high serum levels, between 20% and 40% DO, and at pH 7.20 due to higher viable cell numbers obtained.     

Kinetic study of hybridoma cell growth in continuous culture. I. A model for non-producing cells

The kinetic behavior of a nonproducing hybridoma clone AFP-27-NP was investigated in continuous culture under glucose-limited conditions. A total of more than 21, 000 h of cultures were operated at dilution rates ranging from 0.01 to 0.06 h(-1). The viable cell concentrations, dead cell concentrations, and cell volumes all varied with the dilution rate. A steady-state model was developed based on the biomass concentration and the glucose concentration. The specific growth rate as a function of glucose concentration is described by a model similar to the Monod model with a threshold glucose concentration and a minimum specific growth rate incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. A death rate is included in the model which is described by an inverted Monod-type function of glucose concentration. The yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper region of specific growth rates. No maintenance term for glucose consumption was needed; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepted the specific growth rate axis at a value close to the minimum growth rate. The values for the model parameters were determined from regression analysis of the steady-state data. The model predictions and experimental results fit very well.     

Transient responses of hybridoma cells to nutrient additions in continuous culture: I. Glucose pulse and step changes

Glucose and glutamine are the main nutrients used by mammalian cells in culture. Each provides unique biosynthetic precursors but are complementary for production of other metabolites and energy. The transient and steady-state responses of hybridoma growth and metabolism to glucose pulse and step changes have been examined. Metabolic quotients are reported for oxygen, glucose, lactate, ammonia, glutamine, alanine, and other amino acids. The glucose consumption rate increased by 100-200% immediately after glucose was added to the reactor, and the increased glycolytic ATP production appears to be responsible for the concurrent rapid decrease in the oxygen consumption rate. The effects on glutamine consumption were delayed, probably due to buffering by the TCA cycle and interrelated pathways. A period of increased biosynthetic activity, as evidenced by an increase in the estimated specific ATP production rate and lower by-product yields from glutamine, preceded the increase in cell concentration after the glucose step change. The biosynthetic yield of cells from ATP was calculated, and it was estimated that maintenance accounted for about 60% of the energy used by the cells at a specific growth rate of 0.66 day(-1). The estimated 22% ATP production due to glycoysis was twice as great as that before the step change.     

Effects of dissolved oxygen on hybridoma cell growth, metabolism, and antibody production kinetics in continuous culture.

The effects of dissolved oxygen concentration (DO) on hybridoma cell physiology were examined in a continuous stirred tank bioreactor with a murine hybridoma cell line (167.4G5.3). Dissolved oxygen concentration was varied between 0% and 100% air saturation. Cell growth and viability, carbohydrate, amino acid, and energy metabolism, oxygen uptake, and antibody production rates were investigated. Cell growth was inhibited at both high and low DO. Cells could grow at 0% DO and maintain viability under a nitrogen atmosphere. Cell viability was higher at low DO. Glucose, glutamine, and oxygen consumption rates changed little at DO above 1% air saturation. However, the metabolic uptake rates changed below 1% DO, where growth became oxygen limited, and a Km value of 0.6% DO was obtained for the specific oxygen uptake rate. The metabolic rates of glucose, glutamine, lactate, and ammonia increased 2-3-fold as the DO dropped from 1% to 0%. Amino acid metabolism followed the same general pattern as that of glutamine and glucose. Alanine was the only amino acid produced. The consumption rates of amino acids changed little above 1% DO, but under anaerobic conditions the consumption rates of all amino acids increased severalfold. Cells obtained most of their metabolic energy from glutamine oxidation except under oxygen limitation, when glucose provided most of the energy. The calculated ATP production rate was only slightly influenced by DO and rose at 0% DO. Antibody concentration was highest at 35% DO, while the specific antibody production rate was insensitive to DO.     

Studies on the lysyl hydroxylase reaction. I. Initial velocity kinetics and related aspects

The kinetics of the lysyl hydroxylase (peptidyllysine, 2-oxoglutarate:oxygen 5-oxidoreductase, EC 1.14.11.4) reaction were studied using enzyme from chick embryos by varying the concentration of one substrate in the presence of different fixed concentrations of the second substrate, while the concentrations of the other substrates were held constant. Intersecting lines were obtained in double-reciprocal plots for all possible pairs involving Fe2+, alpha-ketoglutarate, O2 and the peptide substrate, whereas parallel lines were obtained for pairs comprising ascorbate and each of the other substrates. The pair composed of Fe2+ and alpha-ketoglutarate gave an asymmetrical initial veolcity pattern, indicating binding of these two reactants in this order, that of Fe2+ being at thermodynamic equilibrium. The initial velocity patterns are identical with those reported for prolyl 4-hydroxylase, and the apparent Km and Kd values calculated from these data are also very similar. The largest difference was fo-nd in Km and Kd for alpha-ketoglutarate, which were about 4 times the corresponding values for prolyl 4-hydroxylase. Ascorbate was found to be a quite specific requirement for lysyl hydroxylase, but the enzyme catalyzed its reaction for a short time at a high rate in the complete absence of this vitamin, suggesting that the reaction with ascorbate does not occur during each catalytic cycle. Lysyl hydroxylase catalyzed an uncoupled decarboxylation of alpha-ketoglutarate in the absence of the peptide substrate, the rate being about 4% of that observed in the presence of a saturating concentration of the peptide substrate. This uncoupled decarboxylation required the same cosubstrates as the complete reaction.     

Initial rates. A new plot.

Excellent estimations of initial rates can be obtained from plots of delta P/t versus product formed (where P is the instantaneous concentration of the product). delta P/t is the chord from P0,t0 to P,t on an ordinary P-versus-t plot. When the chord is plotted as a function of product, the intercept at P0 of the resulting curve is necessarily dP/dt0. This curve approximates to a straight line extremely closely in all cases tested thus far. If delta P/t versus product is calculated from the integrated rate equation for a first-order reaction, and if a straight line is fitted through points representing the first 50% of the reaction, the discrepancy between the true initial rate and dP/dt0 estimated from the plot is 0.68%. For the most common form of the integrated rate equation for catalysed reactions the discrepancy varies between 0 and 0.90%. Because of the complexities of the integrated rate equations, catalysed second-order reactions have not been evaluated directly; uncatalysed reactions have been done instead. For a reaction with one reactant and two products, the discrepancy varies from 0.68 to 2.02%. For two reactants and one product, it varies from 0 to 0.68%; for two and two, 0 to 2.02%. The larger discrepancies occur only when unfavourable equilibrium constants are being overcome by the initial conditions.     

IgG production in hybridoma batch culture: kinetics of IgG mRNA, cytoplasmic-, secreted- and membrane-bound antibody levels

During batch cultivation of the I.13.17. hybridoma cell line, there is a 15 to 20-fold decrease in the levels of cytoplasmic and membrane-bound mAb, and a 7 to 10-fold decrease in the cellular levels of kappa and gamma chain mRNAs, as the cells pass from the exponential into the decline phase of growth. The profile of the specific mAb production rate does not correlate with the kinetics of either the cytoplasmic mAb or the specific mRNAs throughout the culture. Flow cytometry analyses have revealed that dead cells, which account for 40 to 70% of total cells during the decline phase, might significantly interfere with the determination of cytoplasmic mAb levels of cell-lysates ELISA and with the calculation of the specific mAb production rate. Possible influences of these parameters on mAb synthesis and secretion during hybridoma batch culture are discussed.     

A combined cell-cycle and metabolic model for the growth of hybridoma cells in steady-state continuous culture

The Model presented in this work demonstrates the combination of cell-cycle model with a model describing the growth and conversion kinetics of hybridoma cells in a steady-state continuous culture. The cell-cycle model is based upon a population balance model as described by Cazzador et al. and assumes the existence of a cycling-and apoptotic-cell population, which together form the viable-cell population. In this part the fraction of apoptotic cells, the age distribution of the cycling and apoptotic-cell population, the mean volume and biomass content per cell of the cycling, apoptotic, and viable cells, and the specific growth and death rates of the cells are calculated. The metabolic part consists of a Monod-type growth equation, four elemental balances, an equation assuming a constant yield of ammonia on glutamine, an equation for product formation, and the relation of Glacken for energy production. Furthermore, a maintenance-energy model for the consumption of glucose and glutamine is introduced, which combines the approaches of Herbert and Pirt into one model in a way similar to Beeftink et al. For energy consumption a Pirt model is assumed. The model is capable of predicting trends in steady-state vaues of a large number of variables of interest like specific growth rate, specific death rate, viability, cell numbers, mean viable-cell volume, and concentrations and conversion rates of product, glucose, glutamine, lactate, and ammonia. Also the concentrations and conversion rates of oxygen and carbon dioxide are qualitatively predicted. The values of the model predictions are generally close to experimental data obtained from literature. (c) 1995 John Wiley & Sons, Inc.     

Mathematical analysis of a mechanism for autonomous metabolic oscillations in continuous culture of Saccharomyces cerevisiae.

Autonomous metabolic oscillations were observed in aerobic continuous culture of Saccharomyces cerevisiae. Experimental investigation of the underlying mechanism revealed that several pathways and regulatory couplings are involved. Here a hypothetical mechanism including the sulfate assimilation pathway, ethanol degradation and respiration is transformed into a mathematical model. Simulations confirm the ability of the model to produce limit cycle oscillations which reproduce most of the characteristic features of the system.     

The kinetics of granulopoiesis in long-term mouse bone marrow culture. Part I

The spontaneous stratification in long-term bone marrow cultures was illustrated and quantified. The cultures were separated into three hematopoietic layers: nonadherent cells in the supernatant medium, lightly adherent cells on top of the stromal layer, and remaining cells buried within the stromal layer. The cells of each layer were subcultured for 10 days in plastic tubes that inhibit the formation of a stromal layer. Daily samplings with absolute and differential cell counts were obtained. We identified three families of cell disappearance curves and cell types: CFU-s, hemocytoblasts, myeloblasts, and promyelocytes (G1, 2); myelocytes (G3); and postmitotic granulocytes (G4). Also, the numbers of mitotic and necrotic cells were determined. The longest half-time of CFU-s was 2.5 days. Lacking stromal support, CFU-s disappeared faster than other differentiated cells. Generally, these cells maintained their numbers for the first week of subcultures, which was attributable to a temporarily maintained balance of cell death and fresh cell production. After more than 7 days, there was a rapid decline of all differentiated cell types.