Stoichiometric analysis of animal cell growth and its application in medium design

Animal cell cultivation in vitro has been studied for more than 40 years. However, the culture medium composition has not been designed on the basis of the stoichiometric nutritional demands for animal cell growth. In this article, a model was developed to study the stoichiometric demands for nutrients (including glucose, 20 amino acids, and 10 vitamins)for the synthesis of cell mass and product. The coefficients for these nutrients in the stoichiometric equation governing animal cell growth were determined based on cell composition. In addition, a detailed analysis of the nutrients' roles in the synthesis of cell mass and product was also performed. Applications of the stoichiometric analysis in animal cell cultivation, such as culture medium design, supplemental medium formulation, and feeding strategy will also be discussed. The stoichiometric analysis can be potentially employed to analyze results from animal cell cultures, to improve the performance of culture processes, and to design new process rationally. It can also help to provide a better understanding of animal cell metabolism. Simplifications on the cellular energy metabolism were made in order to simplify the model and to provide the preliminary bases to test the process performance. However, this could introduce inaccuracies for the model and results in errors in the calculations of glucose and glutamine concentrations when employed in medium design. (c) 1994 John Wiley & Sons, Inc.     

Multigenerational interstitial growth of biological tissues

This study formulates a theory for multigenerational interstitial growth of biological tissues whereby each generation has a distinct reference configuration determined at the time of its deposition. In this model, the solid matrix of a growing tissue consists of a multiplicity of intermingled porous permeable bodies, each of which represents a generation, all of which are constrained to move together in the current configuration. Each generation’s reference configuration has a one-to-one mapping with the master reference configuration, which is typically that of the first generation. This mapping is postulated based on a constitutive assumption with regard to that generations’ state of stress at the time of its deposition. For example, the newly deposited generation may be assumed to be in a stress-free state, even though the underlying tissue is in a loaded configuration. The mass content of each generation may vary over time as a result of growth or degradation, thereby altering the material properties of the tissue. A finite element implementation of this framework is used to provide several illustrative examples, including interstitial growth by cell division followed by matrix turnover.     

Analysis of the physiological control of replication of ColE1-type plasmids

The physiology of ColE1-type plasmid replication in a growing host has been examined both theoretically, using computer simulation, and experimentally, by observing replication of the plasmid pBR322 after a nutritional shift-up from glycerol minimal medium (doubling time 71 min) to LB medium (doubling time 24 min). The theory was based on a negative control model and uses three rate equations: for the accumulation of cell mass, for the accumulation of the replication inhibitor, and for the rate of plasmid synthesis. The implications of the theory were explored by simulating the effects of changes in the expression of replication control genes. The nutritional shift-up experiment showed that plasmid replication was blocked immediately after the shift for about half a mass doubling time; after that time, replication rapidly increased until plasmid numbers per unit volume of culture parallelled the increase in culture mass. After the establishment of steady-state growth in the post-shift medium, the plasmid concentration (plasmids per cell mass) was reduced in comparison to pre-shift growth in the same proportion as the culture doubling time. The results showed that plasmid replication factors are under metabolic control and that the changes in the control of these factors compensate one another during steady-state growth, but not immediately after the medium shift.     

Monitoring biomass in root culture systems

This paper presents a technique for accurate estimation of growth in root culture systems. Biomass correlations, were used to estimate fresh weight time course data in shake flasks and reactors based on a model of liquid nutrient uptake and osmolality, to account for changing specific water content of roots. This mass balance technique has been developed to permit accurate aseptic on-line estimation of dry weight (DW), fresh weight (FW), and liquid volume (V) in root cultures utilizing either refractive index or electrical conductivity of the liquid medium along with liquid medium osmolality. The ability to predict fresh weight is particularly important since this is proportional to the biomass volume fraction which determines mass transfer and other culture transport characteristics. The proposed model has been validated with time course information (DW, FW, and V) from 125 mL shake flasks and corroborated with data obtained from 2 L reactors. Copyright 1999 John Wiley & Sons, Inc.     

Clone size variation in the human diploid cell strain, WI-38

By mapping the location of isolated single cells; and then counting the number of cells at each location as a function of time. it was possible to accumulate data on the growth history for each of a large group of clones. The clone size distribution, its mean and standard deviation were computed for each day in culture. Variations in schedule of medium change and time of exposure to trypsin, did not measurably affect variation in clone size. Neither could clone size variation be accounted for on the basis of (1) occurrence of nondividing cells nor (2) presence of heritable growth rate variants in the population. It is probable that clone size variation under our conditions is primarily a consequence of a highly variable interdivision time among the constituent cells.     

Quantitative Growth of Naegleria in Axenic Culture

A strain of Naegleria gruberi, isolated from a Vero cell culture and designated TS-1, was axenically cultivated in monolayer and mass aerating suspension culture. Cultural conditions for constant growth parameters and high-exponential cell densities were defined. Serum or other supplemented fractions were found essential in both Trypticase-yeast extract-glucose (TYG) and Casitone (CAS)-based media. Monolayer cultures grown in the CAS medium required lower levels of serum to reach maximum stationary densities of amoebae than cultures grown in the TYG medium. Heat-killed (121 C, 10 min) whole cell and cell lysate bacterial fractions were capable of replacing the serum in both the TYG and CAS media. Heat-killed bacterial fractions provided the same levels of growth as attained with serum in TYG medium, whereas the bacterial lysate supported only minimal growth in the same medium. In the CAS medium, both bacterial fractions resulted in the same level of growth which was equal to that obtained in reduced serum content. Strain TS-1 was established in suspension culture with the CAS medium used in monolayer culture. The addition of sheep red blood cells (RBC) or RBC lysate greatly enhanced growth responses. Further modifications resulted in a final medium for suspension culture consisting of Casitone-yeast extract-glucose-vitamin base, supplemented with serum and RBC lysate. This medium supported growth with a mean generation time of 9 h at 30 C and a stationary phase yield of greater than 5 x 10(6) amoebae per ml.     

Comprehension of attachment and multiplication properties by observing individual cell behaviors in anchorage-dependent culture

The behavioral properties of cell attachment and division were characterized by direct observation of individual cells in the culture of murine fibroblasts. At the cell attachment stage in the culture for early 10 h, the extent of cell spreading, which was defined as a ratio of the projected area of each cell against its saturated value, had a relatively broad distribution at 0.25 h, and it shifted to a higher level with elapsed time up to 10 h with narrowing in the distribution. The critical value of the extent of cell spreading was determined to be 0.54 as a threshold at which a cell is assumed to complete its adhesion to culture surface. The ratio of the number of cells with the extent of cell spreading over 0.54 against the total number of examined cells fairly followed the profile of cell adhesion which was obtained by measuring the number of adherent cells on culture surface.

At the cell growth stage in the culture for 20–64 h, doubling time of cell population increased gradually as the culture progressed toward confluence. Generation times (or cell-dividing spans) of individual cells, however, did not show a discriminating dependency on cell concentration and culture time. To clarify the influence of local congestion on the cell division, the generation time was formulated as a function of the number of contact cells around each target cell. Applying the cell placement growth model to estimating the extent of contact inhibition, the reciprocal value of doubling time could be correlated with the average of reciprocal generation times, implying that the doubling time on a cell-population basis is explained by considering the variation in dividing spans of individual cells affected by local contact environment.     

A semicontinuous culture model that links cell growth to extracellular nutrient concentration

During semicontinuous culture, a sample of fixed volume is removed at regular time intervals to make measurements and/or harvest culture components, and an equal volume of fresh medium is immediately added to the culture, thereby instantaneously enhancing nutrient concentrations and diluting cell concentration. The resulting cell concentration versus time curve (i.e., the actual cell growth curve) has a saw-toothed appearance because of the periodic dilution of cell concentration. The observed cell concentrations correspond to the peaks of the saw-toothed curve. Cell growth rates are estimated from the locus of observed cell concentrations (i.e., from the apparent growth curve obtained by connecting the peaks of the saw-toothed curve). The sole preexisting model (Fencl's mode) for estimating cell growth rate is valid only when the cells are growing exponentially at a constant rate between samplings. This model has limited validity: despite the periodic enhancement of nutrient concentration, cell growth between samplings eventually causes nutrient depletion, and the cells cease to grow exponentially. Failure to recognize the limits of validity for Fencl' model has resulted in many erroneous applications of the model and, consequently, many incorrect estimates of cell growth rates. To provide a means for correctly estimating cell growth rates, Fencl's exponential model was extended, and a new model that describes the effects of nutrient depletion on cell growth in semi-continuous culture was obtained. The new model shows that exhaustion of a single growth-limiting nutrient in semicontinuous culture causes the locus of cell concentrations observed at time intervals of Deltat to follow a logistic growth curve. The actual cell growth rate was shown to equal the apparent logistic growth rate plus the effective dilution rate -Deltat(-1) In (1 - f), where f is the ratio of sample volume to total culture volume. Moreover, the model predicts that both the apparent logistic growth rate and the apparent steady-state cell concentration should rise linearly with the concentration of growth-limiting nutrient in the input medium, but fall linearly with increases in the effective dilution rate. The new logistic model for nutrient-limited cell growth in semicontinuous culture was successfully tested using published data for Asterionella formosa, Cyclotella meneghiniana, Daucus carota, and strain L mouse cells.     

Toward a stochastic formulation of microbial growth in relation to bioreactor performances: case study of an E. coli fed-batch process

A stochastic microbial growth model has been elaborated in the case of the culture of E. coli in fed-batch and scale-down reactors. This model is based on the stochastic determination of the generation time of the microbial cells. The determination of generation time is determined by choosing the appropriate value on a log-normal distribution. The appropriateness of such distribution is discussed and growth curves are obtained that show good agreement compared with the experimental results. The mean and the standard deviation of the log-normal distribution can be considered to be constant during the batch phase of the culture, but they vary when the fed-batch mode is started. It has been shown that the parameters related to the log-normal distribution are submitted to an exponential evolution. The aim of this study is to explore the bioreactor hydrodynamic effect on microbial growth. Thus, in a second time, the stochastic growth model has been reinforced by data coming from a previous stochastic bioreactor mixing model (1). The connection of these hydrodynamic data with the actual stochastic growth model has allowed us to explain the scale-down effect associated with the glucose concentration fluctuations. It is important to point out that the scale-down effect is induced differently according to the feeding strategy involved in the fed-batch experiments.     

A systems approach to plant bioprocess optimization

A dynamic model for plant cell metabolism was used as a basis for a rational analysis of plant production potential in in vitro cultures. The model was calibrated with data from 3-L bioreactor cultures. A dynamic sensitivity analysis framework was developed to analyse the response curves of secondary metabolite production to metabolic and medium perturbations. Simulation results suggest that a straightforward engineering of cell metabolism or medium composition might only have a limited effect on productivity. To circumvent the problem of the dynamic allocation of resources between growth and production pathways, the sensitivity analysis framework was used to assess the effect of stabilizing intracellular nutrient concentrations. Simulations showed that a stabilization of intracellular glucose and nitrogen reserves could lead to a 116% increase in the specific production of secondary metabolites compared with standard culture protocol. This culture strategy was implemented experimentally using a perfusion bioreactor. To stabilize intracellular concentrations, adaptive medium feeding was performed using model mass balances and estimations. This allowed for a completely automated culture, with controlled conditions and pre-defined decision making algorithm. The proposed culture strategy leads to a 73% increase in specific production and a 129% increase in total production, as compared with a standard batch culture protocol. The sensitivity analysis on a mathematical model of plant metabolism thus allowed producing new insights on the links between intracellular nutritional management and cell productivity. The experimental implementation was also a significant improvement on current plant bioprocess strategies.     

Human granulopoiesis in vitro: an advantage in the use of Iscove's modified Dulbecco's medium

With the aim of determining whether Iscove's Dulbecco's medium (IMDM) provides a growth advantage in the support of granulopoiesis from cultures of human bone marrow in agar, samples from 20 normal subjects were examined in triplicate after 7, 10 and 14 days in parallel cultures containing IMDM or Dulbecco's medium. From every sample, more granulocyte-macrophage colonies were obtained at each culture interval with IMDM. In particular, the number of colonies with IMDM at 14 days (96 +/- 13 per 2x10(5) bone marrow cells) was almost double that with Dulbecco's medium (50 +/- 10). This increment consisted almost entirely of pure granulocyte colonies (P less than 0.001). No significant change in the proportion of eosinophil colonies was observed. These data indicate that IMDM does provide a growth advantage over Dulbecco's medium in the generation of granulocyte (neutrophil and eosinophil) colonies from agar cultures of normal human bone marrow.     

Dynamic optimization of hybridoma growth in a fed-batch bioreactor

This study addressed the problem of maximizing cell mass and monoclonal antibody production from a fed-batch hybridoma cell culture. We hypothesized that inaccuracies in the process model limited the mathematical optimization. On the basis of shaker flask data, we established a simple phenomenological model with cell mass and lactate production as the controlled variables. We then formulated an optimal control algorithm, which calculated the process-model mismatch at each sampling time, updated the model parameters, and re-optimized the substrate concentrations dynamically throughout the time course of the batch. Manipulated variables were feed rates of glucose and glutamine. Dynamic parameter adjustment was done using a fuzzy logic technique, while a heuristic random optimizer (HRO) optimized the feed rates. The parameters selected for updating were specific growth rate and the yield coefficient of lactate from glucose. These were chosen by a sensitivity analysis. The cell mass produced using dynamic optimization was compared to the cell mass produced for an unoptimized case, and for a one-time optimization at the beginning of the batch. Substantial improvements in reactor productivity resulted from dynamic re-optimization and parameter adjustment. We demonstrated first that a single offline optimization of substrate concentration at the start of the batch significantly increased the yield of cell mass by 27% over an unoptimized fermentation. Periodic optimization online increased yield of cell mass per batch by 44% over the single offline optimization. Concomitantly, the yield of monoclonal antibody increased by 31% over the off-line optimization case. For batch and fed-batch processes, this appears to be a suitable arrangement to account for inaccuracies in process models. This suggests that implementation of advanced yet inexpensive techniques can improve performance of fed-batch reactors employed in hybridoma cell culture.     

The multilayer growth of epithelium-like ESK cells in perfused cultures]

The multilayer growth of an epithelium-like ESK [correction of SPEV] cell culture was achieved under condition of culture medium perfusion. The growth of the ESK [correction of SPEV] cells is described under conditions excluding medium movement above the cells in the chamber with a semipermeable membrane separating the cells from the perfused medium. Under these conditions the multilayer (30-40 layers) growth of culture was observed. The data observed are in favour of our suggestion that it is the diffusional limitations in mass exchange, rather than intracellular interaction contacts, that may be responsible for cell growth in culture. A dependence of culture growth on the initial inoculation density, under condition of medium perfusion immediately above the cells, was determined. The dependence of the multilayer saturation density on the perfusion rate and on the complete replacement of the perfused medium is discussed. The existence of a limiting saturation density of perfused culture was shown.     

Clonal derivation of a rat muscle cell strain that forms contraction-competent myotubes

Summary A muscle cell strain capable of forming contracting myotubes was isolated from an established rat embryo cell line. The myogenic cells, termed rat myoblast omega or RMo cells, have a diploid complement of chromosomes (n=42). In the presence of mitogen-containing growth medium, RMo cells proliferated with a cell generation time of about 12 hours. In mitogen-depleted medium, RMo cells withdrew from the cell cycle and formed myotubes that spontaneously contracted. Differentiated RMo cells produced creatine kinase isozymes in a ratio characteristic of skeletal muscle cells. RMo cells were easy to cultivate. Cells proliferated and differentiated equally well on gelatin-coated or noncoated culture dishes, at clonal or mass culture densities, and in all basal media tested. In most experiments, growth medium consisted of horse serum-containing medium supplemented with either chicken embryo extract or FGF activity; cells proliferated equally well in medium containing unsupplemented calf serum. RMo cells differentiated if growth medium was not replenished regularly. Alternatively, differentiation was induceable by incubation in mitogen-depleted medium consisting of basal medium supplemented either with 10⁻⁶ M insulin, 0.5% serum, or 50% conditioned growth medium. RMo cells were competently transformed with cloned exogenous genes. Because it forms functional myofibrils, the RMo cell line constitutes a useful model system for studying the cell biology and biochemistry of proteins involved in contractile apparatus assembly and muscle disease. This work was supported by NIH research grant GM34432 and Research Career Development Award AG00334. Editor's Statement This report documents the characterization of a differentiating rat cell line that does not show the karyotypic shift toward polyploidy usually observed in rodent cell lines. Investigators already are finding this line valuable in studies of regulation of growth and differentiation.     

Kinetic analysis of the uptake of glucose and corn oil used as carbon sources in batch cultures of <Emphasis Type="Italic">Gibberella fujikuroi</Emphasis>

This study determined the specific uptake rate of glucose and corn oil substrates used as carbon sources in batch cultures of Gibberella fujikuroi. We tested three biological models of growth rate: Monod, logistic and lag-exponential. With respect to the substrate consumption rate, we tested two models: constant cell yield (CCY) and law of mass action (LMA). The experimental data obtained from the culture with glucose as substrate correlated satisfactorily with the logistic/LMA model, indicating that the cell yield was variable. In the case of corn oil as carbon source, considering total residual lipids as substrate in the culture broth, the model with the best correlation was the lag-exp/CCY model. The quantification by GC of the three main fatty acids (linoleic, oleic and palmitic) in the culture medium showed a cumulative behavior, with a maximum concentration of each acid at 36 h. We established a more explicit mechanism of the consumption of corn oil, consisting of two stages: generation of fatty acids by hydrolysis and consumption by cellular uptake. The kinetic of hydrolysable lipids was of first order. We found that the hydrolysis rate of corn oil is not a limiting factor for the uptake of fatty acids by the microorganism. We also established, based on the analysis of the identical mathematical structure of consumption kinetics, that the uptake of fatty acids is faster than the uptake of glucose.     

The relationship between yeast cell size and cell division in Candida albicans

The mean size and percentage of budded and unbudded cells of Candida albicans grown in batch culture over a wide range of doubling times have been measured. Cell volume decreased with increased doubling time and a nonlinear approach to an asymptotic minimum was observed. When cells were separated by age according to bud scars, each age showed a similar decrease. During each cell division cycle, size increased slowly during both budded and unbudded periods so that each generation was significantly larger than the preceding. There was no difference in size between the parent portion of budded cells and unbudded cells of the same age. Time-lapse photomicroscopy of cells growing on solid medium showed that cells divide asymmetrically with larger parents having a shorter subsequent cycle time than the smaller daughter, although the time utilized for bud formation was similar. When cells were shifted from a medium supporting a low growth rate and small size to a medium supporting a faster growth rate and larger size, both budded and unbudded cells increased significantly in size. As the doubling time increased, both the budded and unbudded portions of parental and daughter cycles increased.     

Potassium Uptake in Synchronous and Synchronized Cultures of Escherichia coli

Criteria are presented for distinguishing between synchronous and synchronized cultures (natural vs. forced synchrony) on the basis of characteristics of growth and division during a single generation. These criteria were applied in an examination of the uptake of potassium during the cell growth and division cycle in synchronous cultures and in a synchronized culture of Escherichia coli. In the synchronous cultures the uptake of ⁴²K doubled synchronously with cell number, corresponding to a constant rate of uptake per cell throughout the cell cycle. In the synchronized culture, uptake rates also remained constant during most of the cycle, but rates doubled abruptly well within the cycle. This constancy of ⁴²K uptake per cell supports an earlier interpretation for steady-state cultures that uptake is limited in each cell by a constant number of functional sites for binding, transport, or accumulation of compounds from the growth medium, and that the average number of such sites doubles late in each cell cycle. The abrupt doubling of the rate of uptake of potassium per cell in the synchronized culture appears because of partial uncoupling of cell division from activation or synthesis of these uptake sites.     

Theory of cell age distribution in suspension culture with feed and/or drain

A mixed problem for the M'Kendrick-von Foerster equation satisfied by the number density function in terms of the age of the viable cells in a suspension culture with feed and/or drain is solved, and a method of calculating the number density function and time-dependent generation time from observed data of cell number and cell mass is presented. This theory is adequate to analyze the growth of cells that undergo binary fission. The equation of mass balance follows as a natural consequence of this treatment. The equation of substrate balance in consideration of the effect of cell volume is derived rigorously.     

THE EXPRESSION OF DIFFERENTIATION BY CHICK EMBRYO THYROID IN CELL CULTURE : II. Modification of Phenotype in Monolayer Culture by Different Media

Previous results with thyroid secretory cells in monolayer culture seem contradictory with respect to phenotypic stability of this cell type. On the one hand, in "minimal" medium the cells lose structural and functional specializations which can be returned only by three-dimensional growth in organ culture upon addition of fibroblasts derived from the thyroid capsule. On the other hand, in "rich" medium used for cloning, cytoarchitecture and function remain unaltered in either mass or clonal cultures. The apparent discrepancy has been resolved by plating cell suspensions in both media and changing to the alternate medium once the cells have become established. It has been shown that a number of characteristics, including hormone levels, are reversed each time such a change in medium is made. These modulations are discussed in terms of the normal variations in structure and function of the gland in vivo.