Lambert, Anna; (2019) Mathematical Analysis for Two Cell Culture Problems: Population Balance Frameworks & Glycoprotein Production. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Genetically engineered cells are grown in bioreactors, and produce a wide range of important products, including many new medicines. Mathematical modelling of cell populations can increase our understanding of their behaviour, potentially leading to increased manufacturing efficiency. This thesis considers two problems in cell culture modelling; population balance frameworks and glycoprotein production, both of which use analytical techniques to provide insight. Population balance equations provide a mathematical framework for the modelling of heterogeneous cells. They have few analytical solutions and multi-dimensional models are poorly understood. A novel analytical method for the solution of one dimensional models is developed in this thesis by converting the governing equation to an ordinary differential equation with delay. This provides insight into how the growth and division rate functions affect the shape of the cell distribution. In the two-dimensional case, a thorough investigation is presented on the shape of the cell distribution, given different growth rate functions and equal/unequal cell division. These interactions are complex, with several cases counterintuitively leading to biologically implausible solutions. A wide family of cases show limited heterogeneity across multiple dimensions, in line with results reported in the literature. The study highlights that careful consideration should be given to the use of multi-dimensional cell population balance models. Many new medicines produced in cell culture are glycoproteins: a protein with a large complex glycan molecule attached. These glycans are critical to medicine quality, but there is significant heterogeneity between the molecules. A novel ordinary differential equation model of glycoprotein production within cell culture is presented, which consists of two coupled submodels. The bioreactor submodel describes behaviour at the population and cell level, and the glycosylation submodel describes the molecular basis for glycosylation. Analytical solutions are found for both. Combining the two models shows that the quality of glycoproteins can vary through time depending on the substrate configuration.

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