Non-exponential growth by mammalian cells in culture

The concept of exponential growth by mammalian cells in culture is based upon the apparent linearity of semilogarithmic data plots. This method of graphical analysis is known to be an unreliable test of the exponential hypothesis. We have re-examined the question of growth exponentiality using the more sensitive method of Smith plots, in which specific growth rate is plotted against either time or density on transformed graphical coordinates which linearize the mathematical expression of the growth hypothesis being tested. With exponential growth, data points fall on a horizontal straight line when specific growth rate is plotted against time or density. Using both our own and literature data, we have performed Smith plot analyses on the growth of 125 different mammalian and avian cell lines. Of these, only eleven exhibited an exponential phase. The remaining cell lines all had non-exponential growth patterns. The most common of these consisted of an initial period of growth acceleration followed by a later phase of deceleratory growth. A smaller number of lines exhibited deceleratory kinetics at all times after plating. We conclude that mammalian cell growth in culture is predominantly non-exponential, and that the apparent exponentiality of semilogarithmic data plots is usually a methodological artifact.     

A quantitative method for the analysis of mammalian cell proliferation in culture in terms of dividing and non-dividing cells

The application of the exponential growth equation is the standard method employed in the quantitative analyses of mammalian cell proliferation in culture. This method is based on the implicit assumption that, within a cell population under study, all division events give rise to daughter cells that always divide. When a cell population does not adhere to this assumption, use of the exponential growth equation leads to errors in the determination of both population doubling time and cell generation time. We have derived a more general growth equation that defines cell growth in terms of the dividing fraction of daughter cells. This equation can account for population growth kinetics that derive from the generation of both dividing and non-dividing cells. As such, it provides a sensitive method for detecting non-exponential division dynamics. In addition, this equation can be used to determine when it is appropriate to use the standard exponential growth equation for the estimation of doubling time and generation time.     

Growth kinetics of animal cells immobilized within porous support particles in a perfusion culture

The growth kinetics of anchorage-independent animal cells [mouse myeloma MPC-11 (ATCC CCL 167) immobilized within porous polyvinyl formal resin biomass support particles (BSPs; 3 × 3 × 3 mm cubes; mean pore diameter, 60 µm) was analyzed by measuring intracellular and extracellular lactate dehydrogenase (LDH) activities in a perfusion culture. First, the intracellular LDH content of cells immobilized within the BSPs was assayed in a shake-flask culture and found to remain almost comparable to that of non-immobilized cells in the exponential growth phase under static culture. Then, cells inoculated in the BSPs were grown in a continuous stirred-tank bioreactor. Using the LDH content of non-immobilized cells, the density of immobilized cells and the numbers of leaked and dead cells were evaluated, respectively, by the intracellular LDH activity of immobilized and leaked cells and the LDH activity in cell-free culture supernatant. In the initial period, immobilized cells exhibited exponential growth at a constant apparent specific growth rate; however, the acutal specific growth rate, which takes into consideration cell death and cell leakage, decreased significantly. In the stationary phase, the actual specific growth rate maintained a constant but markedly lower value than during exponential growth.     

Bcl-2 over-expression reduced the serum dependency and improved the nutrient metabolism in a NS0 cells culture

The over-expression of Bcl-2 has greatly improved the culture period, specific growth rate, and maximum viable cell density of NS0 cells culture under low serum condition. Further analysis of these data suggests that a saturation model of the Monod type can be used to represent the relationships of specific growth rate and initial serum concentration. The μ_max andK _s for the Bcl-2 cell line is 0.927 day⁻¹ and 0.947% (v/v) respectively, which are 21% greater and 7% lower respectively than its control counterpart. Study on the amino acid supplementation revealed that Bcl-2 cell lines possess greater improvement in the specific growth rate and maximum viable cell density compared to the control cell lines. A further increase in the amino acid supplementation has resulted a 17% decrease in specific growth rate and no improvement in maximum viable cell density in the control culture. However, the Bcl-2 cell line exhibited a better growth characteristic in this culture condition compared to that of control cell lines. The higher specific growth rate and maximum viable cell density of the Bcl-2 cell line in medium fortified with serum and MEM EAA suggested a more efficient nutrient metabolism compared to that in the control cell line. The low serum and amino acid utilisation rate and the higher cell yield may prove to be important in the development of serum/protein free culture.     

Specific monoclonal antibody productivity and the cell cycle-comparisons of batch,continuous and perfusion cultures

A selection of mouse hybridoma cell lines showed a variation of approximately two orders of magnitude in intracellular monoclonal antibody contents. The different levels directly influenced apparent specific monoclonal antibody productivity during the death phase but not during the growth phase of a batch culture. The pattern of changes in specific productivity during culture remained basically similar even though at different levels for all cell lines tested. Arresting the cells in the G₁ phase using thymidine increased the specific productivity, cell volume and intracellular antibody content but at the same time led to decreased viability. In continuous culture DNA synthesis decreased with decreasing dilution rate though without an accompanying change in cell cycle and cell size distributions. The data shows both the decrease in viability and intracellular antibody content to be important factors which influence the negative association between specific antibody productivity and growth rate. In high cell density perfusion culture, when the cell cycle was prolonged by slow growth, viability was low and dead, but not lysed, cells were retained in the system, the specific antibody productivity was nearly two fold higher than that obtained in either batch or continuous cultures. The results imply that the prolongation of G₁ phase and the increase in death rate of cells storing a large amount of antibody together cause an apparent increase in specific antibody productivity.     

Physiological properties of microbial population as a basis for graphical solution of multi-stage continuous cultivations

A proposal for a graphical solution of the design of a multi-stage continuous culture system is presented. The holding times in individual stages are derived from the reciprocal values of the growth rate and of the product formation rate and plotted against the cell and product concentrations. Characteristic changes of physiologically significant paramaters are then projected on these production curves. Dedicated to Academican Ivan Málek on the occasion of his 60th birthday     

High and low affinity binding of heparin-binding growth factor to a 130-kDa receptor correlates with stimulation and inhibition of growth of a differentiated human hepatoma cell

The differentiated human hepatoblastoma-derived cell line, HepG2, displayed two classes of specific membrane receptors for heparin-binding growth factor type 1 (HBGF-1). Specific membrane receptors were distinguished from nonreceptor heparin-like binding sites. Receptors with an apparent Kd of 9.2 +/- 0.9 pM and present at 15,000 +/- 900/cell correlated with HBGF-1 stimulation of HepG2 growth. Receptors with an apparent Kd of 2 +/- 0.4 nM and present at 180,000 +/- 18,000/cell correlated with inhibition of growth and changes in secretory products. Other hepatoma cell lines exhibited a simple positive mitogenic response to HBGF-1 and a single class of high affinity binding sites. HBGF-1 covalently cross-linked to hepatoma cell surface polypeptides of apparent mean molecular mass of 130 kilodaltons. At 37 degrees C, receptor-bound HBGF-1 was internalized (t 1/2 = 45 min) but not degraded for up to 6 h. The display of receptors decreased with increased cell density and expression of HBGF-1 mRNA and HBGF-1-like activity in the culture medium. Proliferating normal human hepatocytes also exhibited two classes of binding sites with affinities for HBGF-1 and apparent molecular weight similar to HepG2 cells. These results implicate HBGF-1 or homologues in human hepatoma cell growth and normal liver cell regeneration.     

Revisiting Verhulst and Monod models: analysis of batch and fed-batch cultures

The paper re-evaluates Verhulst and Monod models. It has been claimed that standard logistic equation cannot describe the decline phase of mammalian cells in batch and fed-batch cultures and in some cases it fails to fit somatic growth data. In the present work Verhulst, population-based mechanistic growth model was revisited to describe successfully viable cell density (VCD) in exponential and decline phases of batch and fed-batch cultures of three different CHO cell lines. Verhulst model constants, K, carrying capacity (VCD/ml or μg/ml) and r, intrinsic growth factor (h⁻¹) have physical meaning and they are of biological significance. These two parameters together define the course of growth and productivity and therefore, they are valuable in optimisation of culture media, developing feeding strategies and selection of cell lines for productivity. The Verhulst growth model approach was extended to develop productivity models for batch and fed-batch cultures. All Verhulst models were validated against blind data (R² > 0.95). Critical examination of theoretical approaches concluded that Monod parameters have no physical meaning. Monod-hybrid (pseudo-mechanistic) batch models were validated against specific growth rates of respective bolus and continuous fed-batch cultures (R² ≈ 0.90). The reduced form of Monod-hybrid model C_L/(K_L + C_L) describes specific growth rate during metabolic shift (R² ≈ 0.95). Verhulst substrate-based growth models compared favourably with Monod-hybrid models. Thus, experimental evidence implies that the constants in the Monod-hybrid model may not have physical meaning but they behave similarly to the biological constants in Michaelis–Menten enzyme kinetics, the basis of the Monod growth model.     

Potassium transport in normal and transformed mouse 3T3 cells

The components of unidirectional K influx and efflux have been investigated in the 3T3 cell and the SV40 transformed 3T3 cell in exponential and stationary growth phase. Over the cell densities used for transport experiments the 3T3 cell goes from exponential growth to density dependent inhibition of growth (4 × 10⁴ to 4 × 10⁵ cell cm^?2) whereas the SV40 3T3 maintains exponential or near exponential growth (4 × 10⁴ to 1 × 10⁶ cell cm^?2). In agreement with previous observations, volume per cell and mg protein per cell decrease with increasing cell density. Thus, transport measurements have been expressed on a per volume basis. Total unidirectional K influx and efflux in the 3T3 cell is approximately double that of the SV40 3T3 cell at all cell densities investigated. Both cell types have similar volumes initially and show similar decreases with increasing cell density. Thus, in this clone of the 3T3 cell SV40 transformation specifically decreases unidirectional K flux. The magnitude of the total K flux does not change substantially for either cell line during transition from sparse to dense cultures. However, the components of the K transport undergo distinct changes. Both cell lines possess a ouabain sensitive component of K influx, presumably representing the active inward K pump. Both also possess components of K influx and efflux sensitive to furosemide. The data suggest this component represents a one-for-one K exchange mechanism. The fraction of K influx mediated by the ouabain sensitive component is reduced to one half its value when exponential versus density inhibited 3T3 cells are compared (63% versus 31% of total influx). No comparable drop occurs in the SV40 3T3 cell at equivalent cell densities (64% versus 56% of total influx). Thus, the pump mediated component of K influx would appear to be correlated with growth. In contrast, the furosemide sensitive component represents approximately 20% of the total unidirectional K influx and efflux in both cell lines in sparse culture. At high cell densities, where growth inhibition occurs in the 3T3 cell but not the SV40 3T3, the furosemide sensitive component doubles in both cell lines. Thus, the apparent K-K exchange mechanism is density dependent rather than growth dependent.     

A comparison of different methods to determine the end of exponential growth in CHO cell cultures for optimization of scale-up

Maximizing cell growth rate and cell yield are among the most important features of a successful mammalian cell culture production process. To minimize time and resources needed to scale up cell mass it is important to maintain the cultures in exponential growth at every scale. Here we report results comparing viable cell counts, packed cell volume, intracellular nucleotide ratios, cell cycle analysis, and on-line oxygen uptake rates (OUR) and optical density for the determination of the end of exponential growth to optimize transfer times during scale-up of CHO cell cultures. Viable cell concentration, packed cell volume, and relative abundance of cells in S-phase were not very reliable at determining the end of exponential growth during the process. In contrast, on-line determination of OUR and off-line determination of intracellular nucleotide ratios (U-ratio) were very sensitive to changes in growth rate, enabling clear determination of the end of exponential growth within a short time. Although on-line OUR was found to be the most convenient and fastest method, it is restricted to instrumented and continuously monitored cultures. In contrast the nucleotide method can be applied with any culture scale and condition but needs the availability of an operator running an HPLC system and takes about an hour from sampling to result. Optical density showed an inflection along with OUR and U-ratio but was less sensitive in determining the end of exponential growth.     

Step-fortifications of nutrients in mammalian cell culture

A series of high-density media for mammalian cell culture were developed by step-fortifications of most nutrient components in RPMI-1640 medium. Each medium constituting the series was constructed to meet in vitro cell growth limitations. Four different cell lines were cultivated in the media series, and their growth characteristics were observed. Maximum cell densities varied in the range of 0.4 to 1.3 x 10(7) cells/mL, depending on cell lines. Cell growth responses to each of the media series were analyzed in terms of cell density and cell mass. Step increases of cell mass in the range of 1.3 to 3.7 g/L were observed according to the step-fortifications of nutrients. Also, the characteristics of each cell line were compared in terms of metabolic yields and specific productions of lactic acid and ammonium ion. The effect of step-fortifications of nutrients on the production of monoclonal antibody was also examined. Apparent differences in metabolic characteristics among cell lines were observed. Experimental results suggested that the different cell sizes and metabolic characteristics of each cell line resulted in cell-line-specific responses to the step-fortifications. The significant influence of nutritional fortifications on high-density culture of mammalian cells was evaluated. (c) 1993 John Wiley & Sons, Inc.     

Enhanced cell culture performance using inducible anti-apoptotic genes E1B-19K and Aven in the production of a monoclonal antibody with Chinese hamster ovary cells

Mammalian cells are used for the production of numerous biologics including monoclonal antibodies. Unfortunately, mammalian cells can lose viability at later stages in the cell culture process. In this study, the effects of expressing the anti-apoptosis genes, E1B-19K and Aven, separately and in combination on cell growth, survival, and monoclonal antibody (MAb) production were investigated for a commercial Chinese Hamster Ovary (CHO) mammalian cell line. CHO cells were observed to undergo apoptosis following a model insult, glucose deprivation, and at later stages of batch cell culture. The CHO cell line was then genetically modified to express the anti-apoptotic proteins E1B-19K and/or Aven using an ecdysone-inducible expression system. Stable transfected pools induced to express Aven or E1B-19K alone were found to survive 1-2 days longer than the parent cell line following glucose deprivation while the expression of both genes in concert increased cell survival by 3 days. In spinner flask batch studies, a clonal isolate engineered to express both anti-apoptosis genes exhibited a longer operating lifetime and higher final MAb titer as a result of higher viable cell densities and viabilities. Interestingly, survival was increased in the absence of an inducer, most likely as a result of leaky expression of the anti-apoptosis genes confirmed in subsequent PCR studies. In fed-batch bioreactors, the expression of both anti-apoptosis genes resulted in higher growth rates and cell densities in the exponential phase and significantly higher viable cell densities, viabilities, and extended survival during the post-exponential phase. As a result, the integral of viable cells (IVC) was between 40 and 100% higher for cell lines engineered to express both Aven and E1B-19K in concert, and the operational lifetime of the fed-batch bioreactors was increased from 2 to 5 days. The maximum titers of MAb were also increased by 40-55% for bioreactors containing cells expressing Aven and E1B-19K. These increases in volumetric productivity arose primarily from enhancements in viable cell density over the course of the fed-batch culture period since the specific productivities for the cells expressing anti-apoptosis genes were comparable or slightly lower than the parental hosts. These results demonstrate that expression of anti-apoptosis genes can enhance culture performance and increase MAb titers for mammalian CHO cell cultures especially under conditions such as extended fed-batch bioreactor operation.     

Acetate accumulation and regulation by process parameters control in Chinese hamster ovary cell culture

Chinese hamster ovary (CHO) cells represent a group of predominantly used mammalian hosts for producing recombinant therapeutic proteins. Known for their rapid proliferation rates, CHO cells undergo aerobic glycolysis that is characterized by fast glucose consumption, that ultimately gives rise to a group of small-molecule organic acids. However, only the function of lactate has been extensively studied in CHO cell culture. In this study, we observed the accumulation of acetate from the late exponential phase to harvest day, potentially contributing to the pH decline in late culture stage regardless of lactate consumption. In addition, we evaluated the acidification of the fresh media and the cell culture suspension, and the data revealed that acetate presented a lower acidification capacity compared to lactate and exhibited limited inhibitory effect on cells with less than 20 mM supplemented in the media. This study also explored the ways to control acetate accumulation in CHO cell culture by manipulating the process parameters such as temperature, glucose, and pH control. The positive correlation between the specific glucose consumption rate and acetate generation rate provides evidence of the endogenous acetate generation from overflow metabolism. Reducing these parameters (temperature, glucose consumption) and HCl-controlled low pH ultimately suppress acetate build-up. In addition, the specific acetate generation rate and relevant glucose consumption rate are found to be a metabolic trait associated with specific cell lines. Taken together, the results presented in these experiments provide a means to advance industrial CHO cell culture process control and development.     

Macromolecule synthesis of Escherichia coli BB at a lower or transient growth state.

Macromolecule synthesis in Escherichia coli BB at lower growth rates was investigated. The results indicate that a deviation in ribonucleic acid (RNA) content per cell at a lower growth rate from the exponential relationship to a specific growth rate is entirely attributable to the presence of nonviable cells, in which the RNA content is lower than in viable cells. Based on this fact, a mathematical expression of macromolecule contents versus specific growth rate was devised. Moreover, continuous changes in macromolecule content during unbalanced growth from late-logarithmic phase to stationary phase were measured. Although growth rates changed continuously, the data on deoxyribonucleic acid (DNA) or RNA content versus the specific growth rate calculated from the increments in cell number satisfactorily fitted the exponential lines obtained under balanced growth at a higher growth rate. However, no such relationship was observed in the plot of DNA or RNA content versus the specific growth rate calculated from the increments in optical density.     

Macromolecule synthesis of Escherichia coli BB at a lower or transient growth state.

Macromolecule synthesis in Escherichia coli BB at lower growth rates was investigated. The results indicate that a deviation in ribonucleic acid (RNA) content per cell at a lower growth rate from the exponential relationship to a specific growth rate is entirely attributable to the presence of nonviable cells, in which the RNA content is lower than in viable cells. Based on this fact, a mathematical expression of macromolecule contents versus specific growth rate was devised. Moreover, continuous changes in macromolecule content during unbalanced growth from late-logarithmic phase to stationary phase were measured. Although growth rates changed continuously, the data on deoxyribonucleic acid (DNA) or RNA content versus the specific growth rate calculated from the increments in cell number satisfactorily fitted the exponential lines obtained under balanced growth at a higher growth rate. However, no such relationship was observed in the plot of DNA or RNA content versus the specific growth rate calculated from the increments in optical density.     

Use of the weighted jackknife method to calculate the variance in cellular-specific protein secretion rate: application to monoclonal antibody secretion rate kinetics in response to osmotic stress

The specific secretion rate (q, mug protein secreted/viable cell-h) and its variance are very useful to compare the capability of cell lines for protein secretion. An assessment of specific secretion rate variability is also beneficial and important when the specific secretion rate is to be used as an on-line process parameter to monitor culture production behavior or for in-process decisionmaking. Experimental errors in mammalian cell culture (e.g., protein concentration measurement and cell counting) and estimation error in the method of calculating q contribute to the total variance of the specific secretion rate. Although the variance of q is essential for comparing the differences between cell lines and the response of the same cell line to different nutrient or environmental conditions, few methods for calculating the variance of the specific secretion rate have been reported. As a model system, we have used the weighted jackknife method and the delta method to calculate the variance in the specific secretion rate of a murine monoclonal antibody (q(mAb)) determined by a differential method. These methods were applied to calculate q(mAb) and its standard deviation to determine the change in q(mAb) kinetics during batch culture of the 9.2.27 hybridoma in response to growth in hyperosmotic media or osmotic stress. Without osmotic stress, during exponential growth in DMEM + 5% FBS spinner culture, the estimate of q(mAb) decreases at least threefold. Results indicate that the 9.2.27 hybridoma responds to hyperosmotic media (400 mOsm, 470 mOsm) by significantly reducing the degree of q(mAb) decrease in the exponential phase, thus maintaining a higher q(mAb) through the stationary phase. The trend of q(mAb) during the batch cultures studied is further confirmed by t-test. Osmotic stress is statistically shown to be able to alter significantly the hybridoma-specific mAb secretion kinetics during batch culture. Determination of the variance of specific secretion rate using the weighted jackknife method offers a powerful approach for establishing the confidence limits of specific protein secretion rate between cell cultures in different nutritional or osmotic environments. (c) 1996 John Wiley & Sons, Inc.     

Continuous stable production of von Willebrand Factor monoclonal antibody in spin filter bioreactor with bleeding technology

The characteristics of two different modes of perfusion culture, intermittent and continuous bleedings, were investigated by culturing the hybridoma cells producing von Willebrand Factor (vWF) monoclonal antibody (McAb) in a 15 L bioreactor without clogging the filter. Both culture methods exhibited similar profiles of cell density and metabolite concentrations during the culture period at the cell concentration of around 1×10⁷ cells/mL. When the perfusion rate was increased, the intermittent bleeding culture showed problems of ammonia accumulation and decrease of cell viability. The continuous bleeding culture exhibited higher physiological activity than that of the intermittent bleeding culture in terms of nutrient consumption and metabolite production kinetics. But the analysis of specific oxygen consumption rate showed that the specific oxygen consumption rate of intermittent bleeding culture was similar to that of exponential growth phase. The continuous bleeding culture showed higher specific vWF McAb productivity and cumulative production than those of the intermittent bleeding culture. Finally we proved the possibility of long-term operation of continuous bleeding culture and produced approximately 40 g of vWF McAb in a 15 L bioreactor after one-month operation.     

Computer programs for modeling mammalian cell batch and fed-batch cultures using logistic equations

A MATLAB^® toolbox was developed for applying the logistic modeling approach to mammalian cell batch and fed-batch cultures. The programs in the toolbox encompass sensitivity analyses and simulations of the logistic equations in addition to cell specific rate estimation. The toolbox was first used to generate time courses of the sensitivity equations for characterizing the relationship between the logistic variable and the model parameters. Subsequently, the toolbox was used to describe CHO cell data from batch and fed-batch mammalian cell cultures. Cell density, product, glucose, lactate, glutamine, and ammonia data were analyzed for the batch culture while fed-batch analysis included cell density and product concentration. In all instances, experimental data were well described by the logistic equations and the resulting specific rate profiles were representative of the underlying cell physiology. The 6-variable batch culture data set was also used to compare the logistic specific rates with those from polynomial fitting and discrete derivative methods. The polynomial specific rates grossly misrepresented cell behavior in the initial and final stages of culture while those based on discrete derivatives had high variability due to computational artifacts. The utility of logistic specific rates to guide process development activities was demonstrated using specific protein productivity versus growth rate trajectories for the 3 cultures examined in this study. Overall, the computer programs developed in this study enable rapid and robust analysis of data from mammalian cell batch and fed-batch cultures which can help process development and metabolic flux estimation.     

Segregated mathematical model for growth of anchorage-dependent MDCK cells in microcarrier culture

To describe the growth behavior of anchorage-dependent mammalian cells in microcarrier systems, various approaches comprising deterministic and stochastic single cell models as well as automaton-based models have been presented in the past. The growth restriction of these often contact-inhibited cells by spatial effects is described at levels with different complexity but for the most part not taking into account their metabolic background. Compared to suspension cell lines these cells have a comparatively long lag phase required for attachment and start of proliferation on the microcarrier. After an initial phase of exponential growth only a moderate specific growth rate is achieved due to restrictions in space available for cell growth, limiting medium components, and accumulation of growth inhibitors. Here, a basic deterministic unstructured segregated cell model for growth of Madin Darby Canine Kidney (MDCK) cells used in influenza vaccine production is described. Four classes of cells are considered: cells on microcarriers, cells in suspension, dead cells, and lysed cells. Based on experimental data, cell attachment and detachment is taken explicitly into account. The model allows simulation of the overall growth behavior in microcarrier culture, including the lag phase. In addition, it describes the time course of uptake and release of key metabolites and the identification of parameters relevant for the design and optimization of vaccine manufacturing processes.