Goldbeter (1991), Minimal mitotic oscillator
BioModels database contains several models dealing with the cell cycle and related mitotic oscillation. Besides BIOMD0000000005  (see also here) or BIOMD0000000107  (see also here), which are representing M-Phase in fission yeast, one of these models is BIOMD0000000003  which focuses on mitosis in early amphibian embryos.
As shown in figure 1, this simple model of the mitotic oscillator contains only three variables:
Cdc2 kinase is activated by cyclin when it accumulates up to a certain threshold. Both cyclin and cdc2 kinase are forming a complex which is named the M-phase-promoting factor (MPF). The degradation of cyclin, the associated inactivation of cdc2 and, subsequently, mitosis are caused by MPF. The latter leads to a new cell cycle.
In addition to the three variables and to the activation and inactivation rates of cdc2 kinase and cyclin protease, respectively, there are two more rate parameters:
The behaviour of the system can be described with the following three differential equations:
Figure 1: Bicyclic cascade model for oscillating behaviour in Mitosis.
Figure 2: Resulting graph of the minimal mitotic oscillator (parameter values see ).
Figure 2 shows the resulting output graph of the minimal mitotic oscillator. The graph shows two time delays:
Cyclin (C) accumulates up to a certain value before the activation of cdc2 (M) starts, which constitutes the first time delay. The second time delay results from the fact that M also has to increase up to a threshold before it activates the cyclin protease (X).
- J.J. Tyson. Modeling the cell division cycle: cdc2 and cyclin interactions. Proc Natl Acad Sci U S A 88:7328-7332, 1991. [SRS@EBI]
- 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. [SRS@EBI]
- A. Goldbeter. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc Natl Acad Sci U S A 88:9107-9111, 1991. [SRS@EBI]