Stochastic modelling of the cell cycle
Keywords: mitotic exit
irreversible transitions
spindle assembly checkpoint
stochastic
cell cycle

Precise regulation of cell cycle events by the Cdk-control network is essential for cell proliferation and the perpetuation of life. The unidirectionality of cell cycle progression is governed by several critical irreversible transitions: the G1-to-S transition, the G2-to-M transition, and the M-to-G1 transition. Recent experimental and theoretical evidence has pulled into question the consensus view that irreversible protein degradation causes the irreversibility of those transitions. A new view has started to emerge, which explains the irreversibility of cell cycle transitions as a consequence of systems-level feedback rather than of proteolysis.
This thesis applies mathematical modelling approaches to test this proposal for the Mto- G1 transition, which consists of two consecutive irreversible substeps: the metaphase-to-anaphase transition, and mitotic exit. The main objectives of the present work were: (i) to develop deterministic models to identify the essential molecular feedback loops and to examine their roles in the irreversibility of the M-to-G1 transition; (ii) to present a straightforward and reliable workflow to translate deterministic models of reaction networks into stochastic models; (iii) to explore the effects of noise on the cell cycle transitions using stochastic models, and to compare the deterministic and the stochastic approaches.
In the first part of this thesis, I constructed a simplified deterministic model of the metaphase-to-anaphase transition, which is mainly regulated by the spindle assembly checkpoint (the SAC). Based on the essential feedback loops causing the bistability of the transition, this deterministic model provides explanations for three open questions regarding the SAC: Why is the SAC not reactivated when the kinetochore tension decreases to zero at anaphase onset? How can a single unattached kinetochore keep the SAC active? How is the synchronized and abrupt destruction of cohesin triggered?
This deterministic model was then translated into a stochastic model of the SAC by treating the kinetochore microtubule attachment at prometaphase as a noisy process. The stochastic model was analyzed and simulation results were compared to the experimental data, with the aim of explaining the mitotic timing regulation by the SAC. Our model works remarkably well in qualitatively explaining experimental key findings and also makes testable predictions for different cell lines with very different number of chromosomes. The noise generated from the chemical interactions was found to only perturb the transit timing of the mitotic events, but not their ultimate outcomes: all cells eventually undergo anaphase, however, the time required to satisfy the SAC differs between cells due to stochastic effects.
In the second part of the thesis, stochastic models of mitotic exit were created for two model organisms, budding yeast and mammalian cells. I analyzed the role of noise in mitotic exit at both the single-cell and the population level. Stochastic time series simulations of the models are able to explain the phenomenon of reversible mitotic exit, which is observed under specific experimental conditions in both model organisms. In spite of the fact that the detailed molecular networks of mitotic exit are very different in budding yeast and mammalian cells, their dynamic properties are similar. Importantly, bistability of the transitions is successfully captured also in the stochastic models.
This work strongly supports the hypothesis that uni-directional cell cycle progression is a consequence of systems-level feedback in the cell cycle control system. Systems-level feedback creates alternative steady states, which allows cells to accomplish irreversible transitions, such as the M-to-G1 transition studied here. We demonstrate that stochastic models can serve as powerful tools to capture and study the heterogeneity of dynamical features among individual cells. In this way, stochastic simulations not only complement the deterministic approach, but also help to obtain a better understanding of mechanistic aspects. We argue that the effects of noise and the potential needs for stochastic simulations should not be overlooked in studying dynamic features of biological systems.