A Simple Mitotic Oscillator

This example is a Modelica version of the model presented in A. Goldbeter, "A Minimal Cascade Model for the Mitotic Oscillator Involving Cyclin and cdc2 Kinase," Proceedings of the National Academy of Sciences of United States of America, 88(20), 1991 pp. 9107–9111. https://www.pnas.org/doi/pdf/10.1073/pnas.88.20.9107.

Abstract

A minimal model for the mitotic oscillator is presented. The model, built on recent experimental advances, is based on the cascade of post-translational modification that modulates the activity of cdc2 kinase during the cell cycle. The model pertains to the situation encountered in early amphibian embryos, where the accumulation of cyclin suffices to trigger the onset of mitosis. In the first cycle of the bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation, and in the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. That cyclin activates cdc2 kinase while the kinase triggers the degradation of cyclin has suggested that oscillations may originate from such a negative feedback loop [M. A. Félix, J. C. Labbé, M. Dorée, T. Hunt, and E. Karsenti, "Triggering of Cyclin Degradation in Interphase Extracts of Amphibian Eggs by cdc2 Kinase," Nature, 346, 1990 pp. 379–382. doi:10.1038/346379a0.] This conjecture is corroborated by the model, which indicates that sustained oscillations of the limit cycle type can arise in the cascade, provided that a threshold exists in the activation of cdc2 kinase by cyclin and in the activation of cyclin proteolysis by cdc2 kinase. The analysis shows how miototic oscillations may readily arise from time lags associated with these thresholds and from the delayed negative feedback provided by cdc2-induced cyclin degradation. A mechanism for the origin of the thresholds is proposed in terms of the phenomenon of zero-order ultrasensitivity previously described for biochemical systems regulated by covalent modification.

Simulations

The simulation results are shown in the figure below. This plot corresponds to Figure 3 of the paper (Goldbeter 1991).