Mathematical models are playing an important part in the current developments in engineering, science and biotechnology. Within this field the most fashionable and representative organisms are the ones who are genetically and physiologically tractable. Since the fission yeast Schizosaccharomyces pombe plays a role model among them and its behaviour has medical, genetic and industrial links (related to cancer research, metabolic pathways and beer production), this makes it a particularly interesting organism for study. This dissertation presents the first physiological model ever developed for the yeast S. pombe. The model allows for the simulation and prediction of batch and repeated batch experiments which are an important engineering tool in terms of optimization of industrial processes improving yield in bioreactors by predicting precise values of harvest fraction (HF) and dilution cycle times (DCT). The model has been developed within the generic modelling framework of CelCyMUS (Cell Cycle Model University of Surrey). As part of the research being carried out CelCyMUS has been up-dated by introducing the new Fortran 95 features and utilities in order to exploit its powerful new features and to keep the generic model in pace with technological software advancements. The model is a one-dimensional age-based population balance for the fission yeast S. pombe. It includes the four typical phases (S, G2, M and G1) with the G2 phase divided into two phases (G2A, G2B) and two checkpoints that govern the movement of cells between G1 and S, and G2B and M phases. The transitions (movement of cells between phases) are determined by a probability function related to the consumption of glucose. The G2B-M transition is also dependent on cell size, but since individual growth of cells is related to the consumption of the carbon source (in this case glucose), cell size is dependent upon the amount of glucose consumed per cell. The model also includes a phase for cells facing starvation before going into a meiotic cycle, with some chance of coming back to the mitotic cycle, and a death phase that accounts for cells dying with no chance of recovering at all. Parameters in the S. pombe model have been gathered from experimental data in batch culture reported in literature. Data generated from this specific model have been compared with data from experiments (Fotuhi, 2002) in batch and repeated batch cultures of S. pombe following the behaviour of population balance, consumption of nutrients, and production of metabolites. The new code was tested by successftilly reproducing data from mm-321 hybridoma cell line, the first specific model of a cell line developed in CelCyMUS. As a new feature a model of mass transfer has been incorporated in the generic framework. This mass transfer module accounts for interactions of metabolites (oxygen and carbon dioxide) in the gas and liquid phase of bioreactors. The new S. pombe model was fitted to the experiments of Creanor (1992) on synchronised cultures where the consumption of oxygen was being measured. Such experiments identify two points (G2B and G1) where the rate of oxygen uptake increased in the cycle, doubling the consumption at the end of every cycle. With the model fitted to experimental results in synchronised cultures of S. pombe the model was then used to simulate desynchronised cultures. S. pombe was successfully tested when reproducing experimental data generated by Fotuhi (2002) in S.pombe for batch and repeated batch bioreactors. The S. pombe model was able to simulate cell number, oxygen and glucose consumption. Carbon dioxide and ATP production were predicted by the model however there was no experimental data to compare with. Now that the S. pombe model has been tested against experimental data it will be applied in a model-based observer strategy for the online control of bioreactors.

The operating principles of complex regulatory networks are more easily understood with mathematical modelling than by intuitive reasoning. In this thesis, I study the dynamics of the mitotic exit control system in budding yeast. I present a comprehensive mathematical model, which provides a system’s-level understanding of the mitotic exit process. This model captures the dynamics of classic experimental situations reported in the literature, and overcomes a number of limitations present in previous models. Analysis of the model led to a number of breakthroughs in the understanding of mitotic exit control. Firstly, numerical analysis of the model quantified the dependence of mitotic exit on the proteolytic and non-proteolytic functions of separase. It was shown that the requirement for the non-proteolytic function of separase depends on cyclin-dependent kinase activity. Secondly, APC/Cdc20 is a critical node that controls the phosphatase (Cdc14) branch and both cyclin (Clb2 and Clb5) branches of the cell cycle regulatory network. Thirdly, the model proved to be a useful tool for the systematic analysis of the recently discovered phenomenon of Cdc14 endocycles. Most proteins belonging to the cell cycle control network are regulated at the level of synthesis, degradation and activity. Presumably, these multiple layers of regulation facilitate robust cell cycle behaviour in the face of genetic and environmental perturbations. To falsify this hypothesis, I subjected the model to global parameter perturbations and tested viability against pre-defined criteria. According to these analyses, the regulated transcription and degradation of proteins make different contributions to cell cycle control. Regulated degradation confers cell cycle oscillations with robustness against perturbations, while regulated transcription plays a major role in controlling the period of these oscillations. Both regulated transcription and degradation are part of important feedback loops, that combined promote robust behaviour in the face of parametric variations.