Verhulst and stochastic models for comparing mechanisms of MAb productivity in six CHO cell lines.

The present study validates previously published methodologies-stochastic and Verhulst-for modelling the growth and MAb productivity of six CHO cell lines grown in batch cultures. Cytometric and biochemical data were used to model growth and productivity. The stochastic explanatory models were developed to improve our understanding of the underlying mechanisms of growth and productivity, whereas the Verhulst mechanistic models were developed for their predictability. The parameters of the two sets of models were compared for their biological significance. The stochastic models, based on the cytometric data, indicated that the productivity mechanism is cell specific. However, as shown before, the modelling results indicated that G2 + ER indicate high productivity, while G1 + ER indicate low productivity, where G1 and G2 are the cell cycle phases and ER is Endoplasmic Reticulum. In all cell lines, growth proved to be inversely proportional to the cumulative G1 time (CG1T) for the G1 phase, whereas productivity was directly proportional to ER. Verhulst's rule, "the lower the intrinsic growth factor (r), the higher the growth (K)," did not hold for growth across all cell lines but held good for the cell lines with the same growth mechanism-i.e., r is cell specific. However, the Verhulst productivity rule, that productivity is inversely proportional to the intrinsic productivity factor (r x ), held well across all cell lines in spite of differences in their mechanisms for productivity-that is, r x is not cell specific. The productivity profile, as described by Verhulst's logistic model, is very similar to the Michaelis-Menten enzyme kinetic equation, suggesting that productivity is more likely enzymatic in nature. Comparison of the stochastic and Verhulst models indicated that CG1T in the cytometric data has the same significance as r, the intrinsic growth factor in the Verhulst models. The stochastic explanatory and the Verhulst logistic models can explain the differences in the productivity of the six clones.

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 (R(2) > 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 (R(2) ≈ 0.90). The reduced form of Monod-hybrid model CL/(KL + CL) describes specific growth rate during metabolic shift (R(2) ≈ 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.

Application of statistical techniques for elucidating flow cytometric data of batch and fed-batch cultures.

The objective of this work is to develop structured, segregated stochastic models for bioprocesses using time-series flow cytometric (FC) data. To this end, mammalian CHO cells were grown in both batch and fed-batch cultures, and their viable cell numbers (VCDs), monoclonal antibody (MAb), cell cycle phases, mitochondria membrane potential/mitochondria mass, Golgi apparatus, and endoplasmic reticulum (ER) were analyzed. For the fed-batch mode, soy hydrolysate was introduced at 24-H intervals. The cytometric data were analyzed for early indicators of growth and productivity by multiple linear regression analysis, which involved taking into account multicollinearity diagnostics, Durbin-Watson statistics, and Houston tests to determine and refine statistically significant correlations between categorical variables (FC parameters) and response variables (yield parameters). The results indicate that the percentage of G1 cells and ER was significantly correlated with VCD and MAb in the case of batch culture, whereas for fed-batch culture, the percentage of G2 cells and ER was correlated significantly. There was a significant difference between cells in the batch and fed-batch cultures in their ER content, suggesting that the increase in protein synthesis as reflected by the ER content and consequent increase in growth rate and MAb productivity both can be monitored at the cellular level by FC analysis of ER content.

Process model comparison and transferability across bioreactor scales and modes of operation for a mammalian cell bioprocess.

A Monod kinetic model, logistic equation model, and statistical regression model were developed for a Chinese hamster ovary cell bioprocess operated under three different modes of operation (batch, bolus fed-batch, and continuous fed-batch) and grown on two different bioreactor scales (3 L bench-top and 15 L pilot-scale). The Monod kinetic model was developed for all modes of operation under study and predicted cell density, glucose glutamine, lactate, and ammonia concentrations well for the bioprocess. However, it was computationally demanding due to the large number of parameters necessary to produce a good model fit. The transferability of the Monod kinetic model structure and parameter set across bioreactor scales and modes of operation was investigated and a parameter sensitivity analysis performed. The experimentally determined parameters had the greatest influence on model performance. They changed with scale and mode of operation, but were easily calculated. The remaining parameters, which were fitted using a differential evolutionary algorithm, were not as crucial. Logistic equation and statistical regression models were investigated as alternatives to the Monod kinetic model. They were less computationally intensive to develop due to the absence of a large parameter set. However, modeling of the nutrient and metabolite concentrations proved to be troublesome due to the logistic equation model structure and the inability of both models to incorporate a feed. The complexity, computational load, and effort required for model development has to be balanced with the necessary level of model sophistication when choosing which model type to develop for a particular application.