Goldbeter, 1991

Model Status

This model has been built by James Lawson (24/05/07) with the differential expressions in Goldbeter's 1991 paper, instead of reaction elements. This file is known to run in PCEnv, and parameters for rate constants can be altered to produce various figures in the paper. With the current parameterization, the primary timecourse figure is reproduceable. A PCEnv session file is also available for this model, including an embedded SVG diagram of the model, which uses the CellML Javascript API. Clicking on a species represented in the diagram will bring up the concentration-time trace for that species.

Model Structure

Better understanding of the molecular mechanisms underlying the cell cycle has given rise to the theory that there may be one universal, homologous mechanism controlling the onset of mitosis. Studies with yeast and embryonic cells suggest that mitosis is triggered by the periodic activation of cdc2 kinase. Using this experimental data, Albert Goldbeter developed a minimal mathematical model which describes the mitotic oscillator involving cyclin and cdc2 kinase (see the figure below). This model is based on the situation in amphibian embryos. As cyclin, a protein signalling molecule, accumulates and exceeds a certain threshold concentration, mitosis is triggered. In the first cycle of the bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation. In the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. Since cyclin activates cdc2 kinase, and in turn, active cdc2 kinase indirectly triggers the degradation of cyclin, cyclin oscillations may originate from a negative feedback loop.

Model simulations support this theory. Oscillations can arise as long as thresholds exist in the activation of cdc2 kinase by cyclin, and in the activation of cyclin protease by cdc2 kinase. Time lags associated with these thresholds, together with the delayed negative feedback from the cdc2-induced cyclin degradation, can readily lead to sustained mitotic oscillations.

Albert Goldbeter acknowledges that the model is a simplification of the biological situation, and it is based on a number of assumptions, but in its simplified form, the model highlights the conditions in which the cyclin-cdc2 kinase system can operate as an autonomous oscillator. The model is also useful in considering the mechanisms underlying the more complex situation in yeast and somatic cells. By highlighting the ways in which oscillations may be stopped, the models suggests how the products of other genes could play a role in the control of mitosis.

The complete 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

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.