In this thesis, we studied a mathematical modelling approach of systems biology in plants. We have concentrated on two different issues related to the cell cycle and cell division (especially in the plant Arabidopsis). The first issue is that of the epidermal cell population in the Arabidopsis leaf and the second issue deals with gene networks which play an important role during the cell cycle. The chapters are grouped into four parts. In Part I, we described the cell cycle as the series of events that takes place in a cell leading to its division and duplication. We also stated the general objective of the study. We addressed the various aspects of the problems and the key factors that are assumed to influence or cause the problems. We provided a comprehensive mathematical framework in Part II to be used in the other chapters for the modelling, simulation and analysing purposes. Here we introduced and studied Michaelis-Menten kinetics (a model of enzyme kinetics) and the quasi-steady state assumption to reduce the complexity of the model. We also introduced two basic mathematical models for the growth of cell size in plants. In Part III, we considered two case studies related to the cell cycle and cell division in Arabidopsis. The first case study is the temporal control of epidermal cell divisions in the Arabidopsis leaf. The growth of plant organs is the result of two processes acting on the cellular level, namely cell division and cell expansion. The precise nature of the interaction between these two processes is still largely unknown as it is experimentally challenging to disentangle them. The lower epidermal tissue layer of the Arabidopsis leaf is composed of two cell types, puzzle shaped pavement cells and guard cells, which build the stomata. We determined the cell number and the individual cell areas separately for both cell types during development. To dissect the rules whereby different cell types divide and expand, the experimental data were fit into a computational model that describes all possible changes a cell can undergo from a given day to the next day. The model allows to calculate the probabilities for a precursor cell to become a guard or pavement cell, the maximum size at which it can divide into two pavement cells or two guard cells, the cell cycle duration and two different growth rates for two kinds of cells (pavement and guard cells) in one population. The second case study deals with the fact that atypical E2F activity restrains APC/CCCS52A2 function obligatory for endocycle onset. We have demonstrated that the atypical E2F transcription factor E2Fe/DEL1 controls the onset of the endocycle through a direct transcriptional control of APC/C activity. Because E2Fe/DEL1 represses the CCS52A2 promoter, we hypothesize that its level must drop below a critical threshold to allow sufficient accumulation of CCS52A2 during late S and G2 phase for cells to proceed from division to endoreduplication. We built a mathematical model to analyse the above hypothesis. The model is based on an ODE model used for the binding of ligands to proteins with the help of Hill functions. This mathematical model helps to understand mechanistically how decreasing E2Fe/DEL1 levels can account for the division-to-endoreduplication transition. Finally, in Part IV, we discussed some future work to extend the above research. We suggested several ideas to design new experiments and increase the value of the models.
The term ”we” is used throughout the text to underline the fact that every single result of the author’s work as represented in the thesis was only possible because of the provision of experiments, equipment, materials and scientific input from others
