Cell cycle modeling began in the early 90s with minimal models that captured the main experimental observations of Xenopus extracts. Since then, several experimental studies discovered new proteins participating in the cell cycle and revealed the interactions among them. Despite this progress, there is still significant uncertainty in the structure of the underlying reaction network. Several models with increasing degrees of complexity have attempted to quantitatively describe the dynamics of the mitotic oscillator. Although these studies have provided us with valuable new insights, a systematic study of the relationship between the key structural features of the reaction network and the dynamics of the mitotic oscillator is still notably lacking.

We started from a base, simplified model for the mitotic oscillator consisting of three coupled subsystems or modules: a) The subsystem responsible for activating the metaphase promoting factor (MPF) which triggers cellular division when it reaches some critical concentration. b) The subsystem producing phosphorylated Cdc25 species that activate MPF and are activated or stabilized by MPF, thereby forming a positive feedback loop. c) The subsystem leading to the activation of the anaphase promoting complex (APC) which becomes activated by MPF and in turn contributes to the degradation of MPF and Cdc25 species, thus forming a negative feedback loop.

We gradually incorporated different known structural components of the cell cycle in the previous, thereby building models with increasing degrees of complexity. At each level of sophistication, we employed tools from bifurcation theory to study the effect of each structural component on both the transient and asymptotic system behavior. Of particular interest to us was the region of the parameter space where steady-state multiplicity and oscillations were observed as well, as the oscillation characteristics. Utilizing this systematic approach allowed us to gradually reveal the complexity of the mitotic oscillator and quantitatively assess the role of each network component.

Specifically, six different mechanisms for activating the metaphase promoting factor (MPF) were studied. In addition, we analyzed the role of the extra Wee1 positive feedback loop, which is known to act synergistically with Cdc25 in the activation of MPF. Moreover, we formulated and tested different hypotheses in order to quantify the uncertainty characterizing the mechanisms for the formation and activation of APC. Finally, we examined the phosphorylation mechanisms in the positive feedback loops as well as in the MPF and APC subsystems to determine the role of multisite phosphorylation in system behavior. Thus, this work represents an important step towards quantitatively elucidating the biological significance of different reaction network components and their association with the dynamics of the mitotic oscillator.

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