Gardner, Dolnik, Collins, 1998

Model Status

This model has been curated and produces a similar (although not identical) output to the figures shown in the publication. This file is known to run in PCEnv.

Model Structure

Experimental analysis of the cell division cycle has lead to the elucidation of many of the genes and proteins that control cell division. In turn, this has allowed scientists to manipulate the cycle, usually by mutating the regulatory genes. However, this often results in unpredictable responses, such as uncontrolled cell division, inhibited cell division, or fatal errors during the cell cycle. A more controlled way to manipulate the cell cycle is to add a reversibly binding inhibitor. In this study described here, Timothy Gardner, Milos Dolnik and James Collins develop a mathematical model of cell division cycle dynamics under the influence of an inhibitory protein. This protein reversibly binds to cyclin (one of the key cell cycle proteins), and acts to alter the frequency of the cell cycle oscillations.

In order to characterise the features of their model, Gardner et al. applied it to two previously published models of the cell cycle. The specific model discussed here is the model developed by Goldbeter in 1991 (for more details of this model please see Goldbeter, 1991). Although this model is based on certain assumptions and is a simplification of the biological cell cycle, it has sufficient detail to describe the dynamics of the molecular mechanisms underlying the cell cycle oscillations. The model reduces the cell cycle to cyclin, cdc2 kinase and cyclin protease. Cyclin is continually synthesised, and once it exceeds a threshold concentration, activates cdc2 kinase, which activates cyclin protease, witch in turn degrades cyclin, and creates a negative feedback loop (see the figure below). Cycle oscillations are generated by threshold mechanisms for the activation of cdc2 kinase and cyclin protease, and also the time lags associated with these threshold mechanisms.

Simulations of the combined model show that the frequency of the cell cycle oscillations can be altered by regulating the rate of inhibitor synthesis, the inhibitor-cyclin binding rate, or the equilibrium constant of the of the inhibitor binding protein.

The complete original paper reference is cited below:

A theory for controlling cell cycle dynamics using a reversibly binding inhibitor, Timothy S. Gardner, Milos Dolnik and James J. Collins, 1998, Proceedings of the National Academy of Sciences , 95, 14190-14195. (A PDF version of the article is available to subscribers on the journal website.) PubMed ID: 9826676

Control of the Goldbeter 1991 model with a cyclin inhibitor. M represents cdc2 kinase, X represents the fraction of active (phosphorylated) cyclin protease, and * represents the fraction of inactive enzymes. The Goldbeter model is outlined by the dashed box. Solid arrows indicate protein synthesis, degradation or enzymatic conversion. Dashed arrows represent activation.