February 2010, model of the month by Michele Mattioni and Judith Zaugg Original model: BIOMD0000000107
How does the cell cycle engine work? How does a cell know when to divide and by what mechanism is it able to do it always (under normal conditions) in the same time interval? The basic questions were already answered by Tyson (1991)  in a model describing the cell division in Fission yeast (BIOMD0000000005). This model, with only 6 reactions, explains the basic concept of the cell cycle, however, it lacks some detail.
The model published by Novak and Tyson in 1993 (, BIOMD0000000107) extends the above mentioned first cell cycle model. It includes a total of 23 reactions and 14 reacting species. Figure 1A shows the summary of the most important players of the model. The main players are cyclin and cdc2 which together form a dimer that can be active or inactive as well as the phosphatase wee1 and the kinase cdc25 which regulate the activity of the cyclin-cdc2 dimer. The active form of the dimer--called MPF (mitosis promoting factor)--triggers mitosis of the cell. MPF is regulating its own concentration in three ways, on the one hand it promotes its activity by activating cdc25 and inhibiting wee1 (Fig 1B), on the other hand, it is indirectly involved in degradation of cyclin (Fig 1C) and therefore its own destruction. So in summary there are two positive and one negative feedback loop playing together to regulate the concentration of MPF and thereby the regulation of mitosis onset. In addition to MPF, unreplicated DNA plays a role in the regulation of MPF activity. It has the opposite effect of MPF on wee1 and cdc25, meaning it would stop the cell from dividing.
Figure 1. A: Basic model of the cell cycle. Mitosis is triggered by the active MPF which is a dimer of cyclin and cdc2 phosphorylated at the Thr161 The dimer of cdc2 and cyclin is present in 4 different states, phosphorylated at Tyr15, Thr161, both or none. Two pairs of phosphatase/kinase act on the different phosphates: wee1/cdc25 phosphorylate/dephosphorylate Thr161 while CAK/INH phosphorylate/dephosphorylate Tyr15. Figure taken from 1.
Figure 1. B: Feedback loop controlled by wee1. The active form of MPF is involved in a positive feedback loop so as to increase its own concentration by activating cdc25 and deactivating wee1. Unreplicated DNA has the opposite effect on active MPF. Figure taken from 1.
Figure 1. C: Cyclin degradation by UbE. The breakdown of cyclin is activated by UbE which is activated by IE which in turn is activated by active MPF. In this way, MPF promotes its own breakdown. Together those 3 feedback loops plus the time delay in the cyclin degradation are responsible for the oscillating behaviour of the system. Figure taken from 1.
Due to the time delay of the negative feedback loop, this system leads to an oscillatory behaviour of the concentrations of its components as can be seen in figure 2. The dotted line indicates the threshold of active MPF to trigger mitosis. MPF accumulates as long as there is enough cyclin in the system. At the same time, active MPF is promoting cyclin degradation but with a certain time delay. Once the concentration of active MPF reaches mitosis levels, cyclin degradation overcomes the critical cyclin concentration and MPF starts to break down. The simulation output in figure 3 shows the oscillating behaviour of MPF, the inactive form of the cyclin-cdc2 dimer and cyclin.
In addition to their model, Novak and Tyson compare their simulation results to various experiments and find good agreement of their model with data obtained from Xenopus Laevis embryos.
Figure 2: Limit cycle oscillation: The closed orbit show the different values of active MPF and total cyclin at different time points (minutes after the last mitosis.) The dotted line divide the cell cycle into interphase (left side) and M-Phase (right side). Figure taken from 
Figure 3: Cyclin oscillation: Autonomous oscillations in the model of Xenopus extracts. The concentrations of active MPF, cyclin and the inactive dimer of cyclin-cdc2 are shown.
J. J. Tyson. Modeling the cell division cycle: cdc2 and cyclin interactions. Proc Natl Acad Sci U S A., 88(16):7328-7332, 1991. [CiteXplore]
B. Novak, J. J. Tyson. Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos.J Cell Sci, 106:1153-1168, 1993. [CiteXplore]