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.     

Comparison of specific rates of hybridoma growth and metabolism in batch and continuous cultures

For the mouse hybridoma cell line VO 208, kinetics of growth, consumption of glucose and glutamine, and production of lactate, ammonia and antibodies were compared in batch and continuous cultures. At a given specific growth rate, different metabolic activities were observed: a 40% lower glucose and glutamine consumption rate, but a 70% higher antibody production rate in continuous than in batch culture. Much higher metabolic rates were also measured during the initial lag phase of the batch culture. When representing the variation of the specific antibody production rate as a function of the specific growth rate, there was a positive association between growth and antibody production in the batch culture, but a negative association during the transient phase of the continuous culture. The kinetic differences between cellular metabolism in batch and continuous cultures may be result of modifications in the physiology and metabolism of cells which, in continuous cultures, were extensively exposed to glucose limitations.Institut National Polytechnique de Lorraine, ENSAIA BP 172, 2 avenue de la forêt de Haye, 54505, Vandoeuvre Cedex France     

Application of a simple unstructured kinetic and cost of goods models to support T-cell therapy manufacture

Manufacturing of cell therapy products requires sufficient understanding of the cell culture variables and associated mechanisms for adequate control and risk analysis. The aim of this study was to apply an unstructured ordinary differential equation-based model for prediction of T-cell bioprocess outcomes as a function of process input parameters. A series of models were developed to represent the growth of T-cells as a function of time, culture volumes, cell densities, and glucose concentration using data from the Ambr®15 stirred bioreactor system. The models were sufficiently representative of the process to predict the glucose and volume provision required to maintain cell growth rate and quantitatively defined the relationship between glucose concentration, cell growth rate, and glucose utilization rate. The models demonstrated that although glucose is a limiting factor in batch supplied medium, a delivery rate of glucose at significantly less than the maximal specific consumption rate (0.05 mg 1 × 10⁶ cell h⁻¹) will adequately sustain cell growth due to a lower glucose Monod constant determining glucose consumption rate relative to the glucose Monod constant determining cell growth rate. The resultant volume and exchange requirements were used as inputs to an operational BioSolve cost model to suggest a cost-effective T-cell manufacturing process with minimum cost of goods per million cells produced and optimal volumetric productivity in a manufacturing settings. These findings highlight the potential of a simple unstructured model of T-cell growth in a stirred tank system to provide a framework for control and optimization of bioprocesses for manufacture.     

A kinetic analysis of hybridoma growth and metabolism in batch and continuous suspension culture: effect of nutrient concentration, dilution rate, and pH

Hybridomas are finding increased use for the production of a wide variety of monoclonal antibodies. Understanding the roles of physiological and environmental factors on the growth and metabolism of mammalian cells is a prerequisite for the development of rational scale-up procedures. An SP2/0-derived mouse hybridoma has been employed in the present work as a model system for hybridoma suspension culture. In preliminary shake flask studies to determine the effect of glucose and glutamine, it was found that the specific growth rate, the glucose and glutamine metabolic quotients, and the cumulative specific antibody production rate were independent of glucose concentration over the range commonly employed in cell cultures. Only the specific rate of glutamine uptake was found to depend on glutamine concentration. The cells were grown in continuous culture at constant pH and oxygen concentration at a variety of dilution rates. Specific substrate consumption rates and product formation rates were determined from the steady state concentrations. The specific glucose uptake rate deviated from the maintenance energy model(1) at low specific growth rates, probably due to changes in the metabolic pathways of the cells. Antibody production was not growth-associated; and higher specific antibody production rates were obtained at lower specific growth rates. The effect of pH on the metabolic quotients was also determined. An optimum in viable cell concentration was obtained between pH 7.1 and 7.4. The viable cell number and viability decreased dramatically at pH 6.8. At pH 7.7 the viable cell concentration initially decreased, but then recovered to values typical of pH 7.1-7.4. Higher specific nutrient consumption rates were found at the extreme pH values; however, glucose consumption was inhibited at low pH. The pH history also influenced the behavior at a given pH. Higher antibody metabolic quotients were obtained at the extreme pH values. Together with the effect of specific growth rate, this suggests higher antibody production under environmental or nutritional stress.     

A kinetic analysis of hybridoma growth and metabolism in batch and continuous suspension culture: effect of nutrient concentration, dilution rate, and pH. Reprinted from Biotechnology and Bioengineering, Vol. 32, Pp 947-965 (1988)

Hybridomas are finding increased use for the production of a wide variety of monoclonal antibodies. Understanding the roles of physiological and environmental factors on the growth and metabolism of mammalian cells is a prerequisite for the development of rational scale-up procedures. An SP2/0-derived mouse hybridoma has been employed in the present work as a model system for hybridoma suspension culture. In preliminary shake flask studies to determine the effect of glucose and glutaminE, it was found that the specific growth rate, the glucose and glutamine metabolic quotients, and the cumulative specific antibody production rate were independent of glucose concentration over the range commonly employed in cell cultures. Only the specific rate of glutamine uptake was found to depend on glutamine concentration. The cells were grown in continuous culture at constant pH and oxygen concentration at a variety of dilution rates. Specific substrate consumption rates and product formation rates were determined from the steady state concentrations. The specific glucose uptake rate deviated from the maintenance energy model(1) at low specific growth rates, probably due to changes in the metabolic pathways of the cells. Antibody production was not growth-associated; and higher specific antibody production rates were obtained at lower specific growth rates. The effect of pH on the metabolic quotients was also determined. An optimum in viable cell concentration was obtained between pH 7.1 and 7.4. The viable cell number and viability decreased dramatically at pH 6.8. At pH 7.7 the viable cell concentration initially decreased, but then recovered to values typical of pH 7.1-7.4. Higher specific nutrient consumption rates were found at the extreme pH values; however, glucose consumption was inhibited at low pH. The pH history also influenced the behavior at a given pH. Higher antibody metabolic quotients were obtained at the extreme pH values. Together with the effect of specific growth rate, this suggests higher antibody production under environmental or nutritional stress.     

Metabolic and kinetic studies of hybridomas in exponentially fed-batch cultures using T-flasks

Exponentially fed-batch cultures (EFBC) of a murine hybridoma in T-flasks were explored as a simple alternative experimental tool to chemostats for the study of metabolism, growth and monoclonal antibody (MAb) production kinetics. EFBC were operated in the variable volume mode using an exponentially increasing and predetermined stepwise feeding profile of fresh complete medium. The dynamic and steady-state behaviors of the EFBC coincided with those reported for chemostats at dilution rates below the maximum growth rate. In particular, steady-state for growth rate and concentration of viable cells, glucose, and lactate was attained at different dilution rates between 0.005 and 0.05 h^–1. For such a range, the glucose and lactate metabolic quotients and the steady-state glucose concentration increased, whereas total MAb, volumetric, and specific MAb production rates decreased 65-, 6-, and 3-fold, respectively, with increasing dilution rates. The lactate from glucose yield remained relatively constant for dilution rates up to 0.03 h^–1, where it started to decrease. In contrast, viability remained above 80% at high dilution rates but rapidly decreased at dilution rates below 0.02 h^–1. No true washout occurred during operation above the maximum growth, as concluded from the constant viable cell number. However, growth rate decreased to as low as 0.01 h^–1, suggesting the requirement of a minimum cell density, and concomitant autocrine growth factors, for growth. Chemostat operation drawbacks were avoided by EFBC in T-flasks. Namely, simple and stable operation was obtained at dilution rates ranging from very low to above the maximum growth rate. Furthermore, simultaneous operation of multiple experiments in reduced size was possible, minimizing start-up time, media and equipment costs.Abbreviations EFBC exponentially-fed batch culture - CSC continuous suspended culture - MAb monoclonal antibody - D dilution rate - q _i metabolic quotient or specific rate of consumption or production of i     

Hybridoma growth and antibody production as a function of cell density and specific growth rate in perfusion culture

Steady state metabolic parameters for hybridoma cell line H22 were determined over a wide range of cell densities and specific growth rates in a filtration based homogeneous perfusion reactor. Operating the reactor at perfusion rates of 0.75, 2.0, and 2.9 day(-1)(each at four different specific growth rates), viable cell densities as high as 2 x 10(7) cells/mL were obtained. For the cell line under investigation, the specific monoclonal antibody production rate was found to be a strong function of the viable cell density, increasing with increasing cell density. In contrast, most of the substrate consumption and product formation rates were strong functions of the specific growth rate. Substrate metabolism became more efficient at high cell densities and low specific growth rates. The Specific rates of metabolite formation and the apparent yields of lactate from glucose and ammonia from glutamine decreased at low specific growth rates and high cell densities. While the specific oxygen consumption rate was independent of the specific growth rate and cell density, ATP production was more oxidative at lower specific growth rate and higher cell density. These observed shifts are strong indications of the production potential of high-density perfusion culture. (c) 1995 John Wiley & Sons, Inc.     

On‐Line Control of Glucose Concentration in High‐Yielding Mammalian Cell Cultures Enabled Through Oxygen Transfer Rate Measurements

Glucose control is vital to ensure consistent growth and protein production in mammalian cell cultures. The typical fed‐batch glucose control strategy involving bolus glucose additions based on infrequent off‐line daily samples results in cells experiencing significant glucose concentration fluctuations that can influence product quality and growth. This study proposes an on‐line method to control and manipulate glucose utilizing readily available process measurements. The method generates a correlation between the cumulative oxygen transfer rate and the cumulative glucose consumed. This correlation generates an on‐line prediction of glucose that has been successfully incorporated into a control algorithm manipulating the glucose feed‐rate. This advanced process control (APC) strategy enables the glucose concentration to be maintained at an adjustable set‐point and has been found to significantly reduce the deviation in glucose concentration in comparison to conventional operation. This method has been validated to produce various therapeutic proteins across cell lines with different glucose consumption demands and is successfully demonstrated on micro (15 mL), laboratory (7 L), and pilot (50 L) scale systems. This novel APC strategy is simple to implement and offers the potential to significantly enhance the glucose control strategy for scales spanning micro‐scale systems through to full scale industrial bioreactors.     

On-line characterization of a hybridoma cell culture process

The on-line determination of the physiological state of a cell culture process requires reliable on-line measurements of various parameters and calculations of specific rates from these measurements. The cell concentration of a hybridoma culture was estimated on-line by measuring optical density (OD) with a laser turbidity probe. The oxygen uptake rate (OUR) was determined by monitoring dynamically dissolved oxygen concentration profiles and closing oxygen balances in the culture. The base addition for neutralizing lactate produced by cells was also monitored on-line via a balance. Using OD and OUR measurements, the specific growth and specific oxygen consumption rates were determined on-line. By combining predetermined stoichiometric relationships among oxygen and glucose consumption and lactate production, the specific glucose consumption and lactate production rates were also calculated on-line. Using these on-line measurements and calculations, the hybridoma culture process was characterized on-line by identifying the physiological states. They will also facilitate the implementation of nutrient feeding strategies for fed-batch and perfusion cultures. (c) 1994 John Wiley & Sons, Inc.     

Effect of insulin on a serum-free hybridoma culture

Insulin is often included in serum-free media for animal cell cultivation. However, the necessity of insulin for a specific cell line is rather uncertain. In this article we report the effects of insulin on the cultivation of a hybridoma cell line in a serum-free medium. It was found that insulin affected neither the cell growth nor the antibody production. The specific growth rate and specific antibody production rate were very similar in the cultures with or without insulin. However, the presence of insulin affected the nutrient consumption rate and cell metabolism. Including insulin in the medium resulted in a higher specific glucose consumption rate, a shorter exponential growth stage, and a lower final antibody concentration. The elimination of insulin from the medium allowed antibody to accumulate to a concentration substantially higher than that in the insulin-containing cultuvre. (c) 1995 John Wiley & Sons, Inc.     

Serum-free suspension cultivation of PER.C6(R) cells and recombinant adenovirus production under different pH conditions

PER.C6(R) cell growth, metabolism, and adenovirus production were studied in head-to-head comparisons in stirred bioreactors under different pH conditions. Cell growth rate was found to be similar in the pH range of 7.1-7.6, while a long lag phase and a slower growth rate were observed at pH 6.8. The specific consumption rates of glucose and glutamine decreased rapidly over time during batch cell growth, as did the specific lactate and ammonium production rates. Cell metabolism in both infected and uninfected cultures was very sensitive to culture pH, resulting in dramatic differences in glucose/glutamine consumption and lactate/ammonium production under different pH conditions. It appeared that glucose metabolism was suppressed at low pH but the efficiency of energy production from glucose was enhanced. Adenovirus infection resulted in profound changes in cell growth and metabolism. Cell growth was largely arrested under all pH conditions, while glucose consumption and lactate production were elevated post virus infection. Virus infection induced a reduction in glutamine consumption at low pH but an increase at high pH. The optimal pH for adenovirus production was found to be 7.3 under the experimental conditions used in the study. Deviations from this optimum resulted in significant reductions of virus productivity. The results indicate that culture pH is a very critical process parameter in PER.C6(R) cell culture and adenovirus production.     

Glucose-limited chemostat culture of Chinese hamster ovary cells producing recombinant human interferon-gamma

A Chinese hamster ovary (CHO) cell line expressing recombinant human interferon-gamma (IFN-gamma) was grown under glucose limitation in a chemostate at a constant dilution rate of 0.015 h(-1) with glucose feed concentrations of 2.75 mM and 4.25 mM. The changes in cell concentration that accompanied changes in the glucose feed concentration indicated that the cells were glucose-limited. The cell yield on glucose remained constant, but there was a decline in residual glucose concentration and a reduced lactate yield from glucose in the latter stages of the culture. The consumption rates for many of the essential amino acids were increased later in the culture. The volumetric rate of interferon-gamma production was maintained throughout the course of this culture, indicating that IFN-gamma expression was stable under these conditions. However, the specific rate of IFN-gamma production was significantly lower at the higher glucose feed concentration. Under glucose limitation, the proportion of fully glycosylated IFN-gamma produced by these cells was less than that produced in the early stages of batch cultures. The proportion of fully glycosylated IFN-gamma increased during transient periods of glucose excess, suggesting that the culture environment influences the glycosylation of IFN-gamma.     

Control of L-phenylalanine production by dual feeding of glucose and L-tyrosine

Control of L-phenylalanine production by a recombinant of Escherichia coli AT2471 by means of the dual feeding of glucose and L-tyrosine was investigated. A novel method was developed for on-line monitoring of the maximum glucose uptake rate (MGUR), in which the length of time required for the consumption of added glucose was measured. Accumulation of acetic acid was successfully prevented throughout the whole period of the culture when the glucose concentration was kept below 0.1 g/L by controlling the glucose feeding on the basis of on-line monitoring of the MGUR and the cell concentration with a laser sensor.In a batch culture with glucose feeding, after L-tyrosine was depleted cell growth and the L-phenylalanine production rate decreased along with decreases in the specific enzyme activities of chorismate mutase-p-prephenate dehydratase (CMP) and 3-deoxy-D-arabinoheputulosonate 7-phosphate synthase (DAHP), which are the key enzymes in the L-phenylalanine synthesis pathway. Increasing the L-tyrosine feed rate by an appropriate amount, but not so far as to cause L-tyrosine accumulation in the culture, increased the activities of the enzymes and the specific rates of growth and production while the product yield based on glucose consumption decreased.The average specific rates of growth, production, and MGUR could be expressed as functions of the specific L-tyrosine consumption rate during both the earlier and later periods of L-tyrosine feeding. Estimations of the amount of L-phenylalanine produced, the product yield, and the cost factor by using these functions with several different combinations of two specific L-tyrosine consumption rates for two 10-h periods resulted in a suggested optimum L-tyrosine feeding strategy giving a lower specific L-tyrosine consumption rate in the later period, to suppress cell growth, in comparison to that in the earlier period. During L-tyrosine feeding, the three specific rates (growth, production, and MGUR) could be successfully controlled by adjusting the specific L-tyrosine consumption rate to the predicted value. The cost factor was lowest in this controlled culture, demonstrating experimentally the effectiveness of the strategy. (c) 1996 John Wiley & Sons, Inc.     

A kinetic analysis of hybridoma growth and metabolism in continuous suspension culture on serum-free medium

The steady-state metabolic parameters for a murine hybridoma cell line have been determined in continuous suspension culture over a wide range of dilution rates. Long-term adaption occurred over seven months in culture and resulted in lower glucose consumption rates, reduced lactate production, higher cell viability, and, consequently, growth rates more nearly matching the dilution rate. Antibody production rates decreased over the first two months and then remained stable for at least 75 days. The antibody production rate was not found to be growth associated. Steadystate amino acid uptake rates are presented for a wide range of growth rates.     

Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH.

Tumors and multicellular tumor spheroids can develop gradients in oxygen concentration, glucose concentration, and extracellular pH as they grow. In order to calculate these gradients and assess their impact on tumor growth, it is necessary to quantify the effect of these variables on tumor cell metabolism and growth. In this work, the oxygen consumption rates, glucose consumption rates, and growth rates of EMT6/Ro mouse mammary tumor cells were measured at a variety of oxygen concentrations, glucose concentrations, and extracellular pH levels. At an extracellular pH of 7.25, the oxygen consumption rate of EMT6/Ro cells increased by nearly a factor of 2 as the glucose concentration was decreased from 5.5 mM to 0.4 mM. This effect of glucose concentration on oxygen consumption rate, however, was slight at an extracellular pH of 6.95 and disappeared completely at an extracellular pH of 6.60. The glucose consumption rate of EMT6/Ro cells increased by roughly 40% when the oxygen concentration was reduced from 0.21 mM to 0.023 mM and decreased by roughly 60% when the extracellular pH was decreased from 7.25 to 6.95. The growth rate of EMT6/Ro cells decreased with decreasing oxygen concentration and extracellular pH; however, severe conditions were required to stop cell growth (0.0082 mM oxygen and an extracellular pH of 6.60). Empirical correlations were developed from these data to express EMT6/Ro cell growth rates, oxygen consumption rates, and glucose consumption rates, as functions of oxygen concentration, glucose concentration, and extracellular pH. These empirical correlations make it possible to mathematically model the gradients in oxygen concentration, glucose concentration, and extracellular pH in EMT6/Ro multicellular spheroids by solution of the diffusion/reaction equations. Computations such as these, along with oxygen and pH microelectrode measurements in EMT6/Ro multicellular spheroids, indicated that nutrient concentration and pH levels in the inner regions of spheroids were low enough to cause significant changes in nutrient consumption rates and cell growth rates. However, pH and oxygen concentrations measured or calculated in EMT6/Ro spheroids where quiescent cells have been observed were not low enough to cause the cessation of cell growth, indicating that the observed quiescence must have been due to factors other than acidic pH, oxygen depletion, or glucose depletion.     

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.     

Effects of ammonia and lactate on hybridoma growth, metabolism, and antibody production

The influence of ammonia and lactate on cell growth, metabolic, and antibody production rates was investigated for murine hybridoma cell line 163.4G5.3 during batch culture. The specific growth rate was reduced by one-half in the presence of an initial ammonia concentration of 4 mM. Increasing ammonia levels accelerated glucose and glutamine consumption, decreased ammonia yield from glutamine, and increased alanine yield from glutamine. Although the amount of antibody produced decreased with increasing ammonia concentration, the specific antibody productivity remained relatively constant around a value of 0.22 pg/cell-h. The specific growth rate was reduced by one-half at an initial lactate concentration of 55 mM. Although specific glucose and glutamine uptake rates were increased at high lacatate concentration, they showed a decrease after making corrections for medium osmolarity. The yield coefficient of lactate from glucose decreased at high lactate concentrations. A similar decrease was observed for the ammonia yield coefficient from glutamine. At elevated lactate concentrations, specific antibody productivities increased, possibly due to the increase in medium osmolarity. The specific oxygen uptake rate was insensitive to ammonia and lactate concentrations. Addition of ammonia and lactate increased the calculated metabolic energy production of the cells. At high ammonia and lactate, the contribution of glycolysis to total energy production increased. Decreasing external pH and increasing ammonia concentrations caused cytoplasmic acidification. Effect of lactate on intracellular pH was insignificant, whereas increasing osmolarity caused cytoplasmic alkalinization.     

High viable cell concentration fed-batch cultures of hybridoma cells through on-line nutrient feeding

A hybridoma cell line was cultivated in fed-batch cultures using a low-protein, serum-free medium. On-line oxygen uptake rate (OUR) measurement was used to adjust the nutrient feeding rate based on glucose consumption, which was estimated on-line using the stoichiometric relations between glucose and oxygen consumption. Through on-line control of the nutrient feeding rate, not only sufficients were supplied for cell growth and antibody production, but also the concentrations of glucose and other important nutrients such as amino acids were maintained at low levels during the cell growth phase. During the cultivation, cell metabolism changed from high lactate production and low oxygen consumption to low lactate production and high oxygen consumption. As a result the accumulation of lactate was reduced and the growth phase was extended. In comparison with the batch cultures, in which cells reached a concentration of approximately 2 x 10(6) cells/mL, a very high concentration of 1.36 x 10(7) cells/mL with a high cell viability (>90%) was achieved in the fed-batch culture. By considering the consumption of glucose and amino acids, as well as the production of cell mass, metabolites, and antibodies, a well-closed material balance was established. Our results demonstrate the value of coupling on-line OUR measurement and the stoichiometric realations for dynamic nutrient feeding in high cell concentration fed batch cultures. (c) 1995 John Wiley & Sons, Inc.     

Optimization of the cell seeding density and modeling of cell growth and metabolism using the modified Gompertz model for microencapsulated animal cell culture

Cell microencapsulation is one of the promising strategies for the in vitro production of proteins or in vivo delivery of therapeutic products. In order to design and fabricate the optimized microencapsulated cell system, the Gompertz model was applied and modified to describe the growth and metabolism of microencapsulated cell, including substrate consumption and product formation. The Gompertz model successfully described the cell growth kinetics and the modified Gompertz models fitted the substrate consumption and product formation well. It was demonstrated that the optimal initial cell seeding density was about 4-5 x 10(6) cells/mL of microcapsule, in terms of the maximum specific growth rate, the glucose consumption potential and the product formation potential calculated by the Gompertz and modified Gompertz models. Modeling of cell growth and metabolism in microcapsules provides a guideline for optimizing the culture of microencapsulated cells.