Abstract
This research develops a detailed mathematical model of the fission yeast Schizzosaccharomyces pombe. The objectives were to produce a mathematical model of a periodically fed system and to fit this model to experimental data, in order to investigate the cells' response to different periodic feeding strategies. Models that can accurately reproduce the dynamics of cell populations are potentially important in the design and control of bioreactors and can possibly be used to identify the dynamics of cell cycle checkpoints. A simple mathematical model based on Monod kinetics was found to be inadequate for this research as it was unable to replicate the results seen experimentally in periodically fed cultures. Hence a detailed mathematical model is required in order to consider the behaviour of the individual cells as a part of the overall population. CelCyMUS is a structured, segregated model based on the cell cycle that has been developed in previous research, and used as a basis for this study. In this work, the original CelCyMUS framework has been modified to include periodic feeding and the specific cell line used in this research. Three different versions of CelCyMUS have been investigated in order to determine which provides the closest match to the experimental data available. Modifications made to the model include an alternative glucose uptake rate expression and alternative transition rules for cells at the M/Gla phase boundary and within the G1b phase of the cell cycle. The modifications also remove any discontinuities from the mathematical models of the cell cycle. The key conclusions that can be drawn from this research are: The new model provides a much closer fit to the experimental data than all previous models. The new model is capable of producing chaotic behaviour. Simple mathematical models, including Monod, are not able to generate a chaotic response. The chaotic behaviour shown by the new version of CelCyMUS is not solely due to discontinuities that were present within the model. When CelCyMUS produces periodic behaviour under periodic feeding conditions, it can be seen that the cell population is highly synchronised. When a chaotic response is produced, the cell population shows partial or no synchronisation. It is suggested that the failure of the cell population to synchronise is the cause of the chaotic behaviour. When attempting to fit the model to experimental data, there is no single set of parameter values that will fit the model to the experimental data over the range of feed periods investigated. This suggests that the system dynamics are changing as the feed period is changed. Two major areas for further research work have been identified. The first is to modify CelCyMUS further to account for the changing behaviour of the cells at longer feed periods, possibly by introducing a quiescent phase that runs in parallel with the cell cycle. The second is to obtain more experimental data for both cells and glucose across a range of feed periods. This will give a better understanding of the cell dynamics within the system and allow further development of the mathematical model.