Investigation of robustness and dynamic behaviour of G1/S checkpoint/DNA-damage signal transduction pathway based on mathematical modelling and a novel neural network approach

The control of cell cycle checkpoints in cell cycle regulation is an extremely important function in living organisms. Mutation of the checkpoint regulators can cause gene or chromosome instability, which eventually results in different types of human cancers or cell apoptosis (death). A critical task in biological and medical research is to gain a thorough understanding of the mechanisms and dynamics of checkpoints in cell cycle regulation. In this thesis, a combined approach of mathematical modelling, computational simulations, analytical techniques and an artificial neural network (ANN) has been used to obtain deeper insights into the robustness and dynamic behaviour of the G1/S transition, as well as the DNA-damage signal transduction pathway and the p53-Mdm2 oscillation systems. The first part of this thesis focuses on mathematically representing the cellular processes involved in detecting DNA-damage in cells, and their repair mechanisms, during cell division. This study uses a novel mathematical model of the G1/S transition that involves the DNA-damage signal transduction pathway, as published in 2008 by Iwamoto et al. [2008]. We develop a new analytical approach which includes: a choice of biomarkers (peak time of E2F and CycE), local and global sensitivity analysis, Type II error and mathematical definitions of biological robustness, to investigate the dynamic behaviour and robustness of biomarkers in the G1/S checkpoint in response to various levels of parameter perturbations and different DNA-damage intensities. More specifically, we concentrate on investigating the probability of accurately distinguishing healthy cells from defective cells in the G1/S transition. The results revealed from the model simulation, in terms of percentages of damaged cells passing as healthy cells, were in good agreement with very recent experimental findings and observations. The mathematical simulation outcomes from the first part, with corroboration from the phenomenon that the damaged cells are caught not in the pre-tumor stage but in the pre-malignant tissue where a non-invasive tumour is formed through activation of cellular senescence (another form of cell death), gives us the inspiration to develop new research questions. In the second part of this thesis, we are interested in whether the proposed G1/S model can highlight cellular senescence and so formulated scenarios, based on currently established biology, for lowering the threshold for senescence to enable cells to catch damaged cells before they reach the pre-malignant stage and evaluate the model’s efficacy and outcome in this respect. Our analysis showed that cellular senescence can be highlighted through investigating the probability of DNA-damaged cells passing the G1/S checkpoint while lowering the critical trigger – CDK2 (Cyclin dependent kinase 2). We then analysed the relationship between CDK2 and its corresponding CKIs (CDK inhibitory proteins) in order to find other effective ways to bring forward cellular senescence. Finally, we validated the robustness of CDK2 for lowering the bar for cellular senescence. The final part of the thesis introduces a novel ANN approach for modelling regulatory pathways. The developed ANN model is a new recurrent neural network which exactly represented the interactions among molecules in a pathway and its internal parameters are the corresponding kinetic parameters. Importantly, the proposed method solves the perennial problem of parameter estimation in differential equation based models by simply evolving the parameter values iteratively based on data. We applied the ANN model to simulate the p53-Mdm2 oscillation system with negative feedback and investigate the robustness of this system. Results from the ANN and corresponding ordinary differential equation based models published in 2006 by Geva-Zatorsky [2006] were then compared. By means of simulations, we showed that the proposed network can successfully represent the behaviour of the p53-Mdm2 oscillation system and solve the parameter estimation problem with 100% accuracy. Furthermore, we also investigated the robustness of the p53-Mdm2 system using the trained network, in the presence of various levels of parameter perturbation, to gain a greater understanding of the inner workings of the p53-Mdm2 system and the results revealed robustness and stability of the system and sensitivity to parameters. In summary, the success of this research demonstrated the value of mathematical models and artificial neural networks for interpreting experimental observations, gaining novel insights into the dynamic behaviour of the G1/S checkpoint integrating the DNA-damage signal transduction pathway and the p53-Mdm2 oscillation system. In particular, the demonstration of the value of neural networks for estimating unknown kinetic parameters from data is a significant contribution of the thesis along with the analysis of the developed neural networks to investigate the robustness of the studied system. Furthermore, the thesis extended the mathematical model to elucidate a possible way, through understanding cellular senescence, for developing an effective cancer treatment.