Gardner et al., (1998). A theory for controlling cell cycle dynamics using a reversibly binding inhibitor.
March 2013, model of the month by Maciej Swat
Original model: BIOMD0000000008
Gardner and colleagues [1,BIOMD0000000008] present an interesting analysis on how to gain more precise control on the cell division cycle (CDC) dynamics. They analyse two previously published models [2,3] of varying complexity. First, a model of a checkpoint free cell cycle as encountered in early amphibian embryos is analysed, whereas in the second model of Schizosaccharomyces pombe, also called "fission yeast", size-control checkpoints are included. The control schema developed is general and simple in that it requires the expression of only one protein, the target of an inhibitor. Nevertheless, it allows for describing the mechanisms of how to
- start or stop the cell division
- modulate the frequency of the division
- control the size of dividing cells
Goldbeter [2,BIOMD0000000003,BIOMD0000000004] presents most intuitive and simple description of the CDC. Several abstraction steps leads to a three variable/proteins (cyclin, Cdc2 kinase and cyclin protease) CDC model capable to characterize the G2/M phase transition. The cyclin, which is synthesized continuously activates the Cdc2 kinase. This activates the cyclin protease which in turn degrades the cyclin. As a result a limit cycle is observed.
Novak and Tyson [3,BIOMD0000000007] introduced a more realistic model equipped with several threshold activation/degradation mechanisms for both G1/S and G2/M phase transitions. An autocatalytic activation of the M-phase promoting factor phase is incorporated and also size-controlled DNS replication start at the beginning of M-phase.
Both models show that in the absence of checkpoints, the frequency of the CDC oscillator is modulated by the expression of a cyclin or cyclin-Cdc2 inhibitor. Interestingly, it is illustrated that the qualitative features of this control mechanism are almost identical in both cases even though the two models are very different in their mechanistic structure.
Figure 2 Model Equation - Model for the Control of Cell Division. Figure implemented from .
Results and conclusion
- Reducing the frequency of oscillation – for the Goldbeter model it has been found that if the binding of the inhibitor to the cyclin is rapid compared to the CDC oscillation frequency, the frequency of the cell divisions is decreased, see Figure 3A, lower curve (a).
- Effect of inhibitor strength – the maximum reduction in frequency occurs at intermediate values of Kd. It is caused by the variation of inhibitor strength with the dissociation constant. For large concentration of the inhibitor the oscillations are completely supressed forcing the system into a stable equilibrium, see Figure 3B.
- Increasing the frequency of the cell division – for slow binding of the inhibitor to the cyclin-Cdc2 the increase on oscillation frequency of CDC can be observed, see Figure 3A, upper curve (b).
- Effect of cell cycle checkpoints – in general the checkpoint can impact the effects of the control schema assuming they are active. The Tyson-Novak model has been used for it contains both G1/S and G2/M phase transition checkpoints. The general observation is that whether or not the frequency of oscillations is increased or decreased is mainly determined by the rate of inhibitor binding. However, the rate of synthesis of the inhibitor primarily determines the magnitude of the effect up to the point where the oscillations are completely blocked.
Figure 1 Control of the Goldbeter model with cyclin inhibition. Figure taken from .
Model for the control of cell division
The general scheme for the expression of an inhibitor of one of the CDC proteins is shown in Figure 2.
Ui – CDC oscillators
U1 – concentration of the target protein of the inhibitor
U2,…,Un – other proteins in network
Y – inhibitor concentration
Z – concentration of the inhibitor-target complex
a1, a2 – rates of binding and release
Kd = a2/a1 – dissociation constant
vs – rate of inhibitor synthesis
d1 - basal rate of inhibitor degradation
Figure 3 Goldbeter model – frequency modulation. (A) Effect of the rate of inhibitor synthesis on CDC frequency. (B) Effect of inhibitor synthesis rate and inhibitor binding rate on CDC frequency. Figure taken from .
- Gardner et al. A theory for controlling cell cycle dynamics using a reversibly binding inhibitor. Proc Natl Acad Sci U S A. 1998 Nov 24;95(24):14190-5.
- Goldbeter A. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc Natl Acad Sci U S A. 1991 Oct 15;88(20):9107-11.
- Novak and Tyson Modeling the control of DNA replication in fission yeast. Proc Natl Acad Sci U S A. 1997 Aug 19;94(17):9147-52.