A Minimal Cascade Model for the Mitotic Oscillator Involving Cyclin and cdc2 Kinase
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
The CellML model runs in OpenCell to reproduce figure 3 of the published paper. The model also runs in COR but doe to the long duration of the simulation (100 minutes) COR is not reall suitable for such a simulation. The units have been checked and they are consistent.
Model Structure
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 [Felix, M. A., Labbe, J. C., Doree, M., Hunt, T. and Karsenti, E. (1990) Nature (London) 346, 379-382]. 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.
The original paper reference is cited below:
A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase, Albert Goldbeter, 1991, Proceedings of the National Academy of Sciences, 88, 9107-9111. PubMed ID: 1833774
cell diagram
Minimal cascade model for the mitotic oscillations between cyclin and cdc2 kinase (M) during the cell cycle. X represents the fraction of active (phosphorylated) cyclin protease. * represents the fraction of inactive enzymes.
$\frac{d C}{d \mathrm{time}}=\mathrm{vi}-\frac{\mathrm{vd}XC}{\mathrm{Kd}+C}-\mathrm{kd}C$
$\frac{d M}{d \mathrm{time}}=\frac{\mathrm{V1}\mathrm{M\_star}}{\mathrm{K1}+\mathrm{M\_star}}-\frac{\mathrm{V2}M}{\mathrm{K2}+M}$
$\mathrm{M\_star}=1-M$
$\frac{d X}{d \mathrm{time}}=\frac{\mathrm{V3}\mathrm{X\_star}}{\mathrm{K3}+\mathrm{X\_star}}-\frac{\mathrm{V4}X}{\mathrm{K4}+X}$
$\mathrm{X\_star}=1-X$
$\mathrm{V1}=\frac{\mathrm{VM1}C}{\mathrm{Kc}+C}\mathrm{V3}=M\mathrm{VM3}$
100A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase (Model without MIRIAM annotations)Xfraction of active protease which degrades cyclinLloydCatherineMayProceedings of the National Academy of Sciences USAX_starfraction of inactive protease which degrades cyclinThe University of AucklandAuckland Bioengineering Institutekeywordc.lloyd@auckland.ac.nz1991-10-15Ccyclin concentrationGoldbeterAMfraction of active cdc2 kinaseoscillatorcell cyclecyclinkinase1833774M_starfraction of inactive cdc2 kinase8891079111
A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase
c.lloyd@auckland.ac.nzLloydCatherineMayThe University of AucklandAuckland Bioengineering Institute