Arresting the mitotic oscillator

Any model for the biochemical oscillator controlling the onset of mitosis should account for the fact that, in some cells or at certain stages of development, mitosis can be prevented and cells cease to divide. In dynamic terms, such a transient or permanent suppression of mitotic activity can be viewed as a switch of the mitotic control system from an oscillatory into a nonoscillatory regime corresponding to a stable steady state. Models for the mitotic oscillator allow the discussion of possible mechanisms whereby the mitotic clock might be arrested. 

Parameters of the first kind are the rate of cyclin synthesis (Vj), the maximum rate of cyclin degradation by the specific protease X (vj), the Michaelis constant of the latter enzyme (K ), and the apparent first-order rate constant for nonspecific cyclin degradation (k ). Clearly the nonspecific degradation of cyclin should remain negligible, since (at least in the absence of positive feedback) no oscillations would occur if such a process predominated over the specific action of protease X. This is confirmed by the construction of stability diagrams showing that the domain of oscillations in parameter space shrinks as the value of fcj increases, until a value of that rate constant is reached beyond which oscillations disappear (Romond et al, 1994). 

An alternative way to halt the mitotic oscillator relies on changes in the parameters that govern the kinetics of the phosphorylation-dephosphorylation cycles in the cascade. Of particular importance for oscillations are the thresholds in the dependence of M on C (curve a, fig. 10.5a) and of A on M (curve a, fig. 10.5b). An effective way to stop the oscillations is to suppress the two thresholds altogether by increasing Ki, K2, X3, X4 above unity. As is clear from fig. 10.8, switching the values of X (i = 1. 4) from 5 x 10 - as in the case considered in fig. 10.6 - to 10 will indeed suppress the oscillations. 

Another way to stop the oscillations is to prevent the system from 

To illustrate the important notion that there exists a window of the ratio (Vi/1 2) producing oscillations, let us divide by 2 in the case of fig. 10.6. We see from eqns (10.5)-(10.6) that when the maximum rate of enzyme Ej in the minimal cascade model of fig. 10.4 is so halved, the threshold in the first cycle cannot be reached at any finite value 

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Arresting the mitotic oscillator and the control of cell proliferation... 

Goldbeter, A. J.M. Guilmot. 1995. Arresting the mitotic oscillator and the control of cell proliferation Insights from a cascade model for cdc2 kinase activation. Experientia, in press. 

Phosphorylation-dephosphorylation see also Period-doubling bifurcations Cascade model for mitotic oscillator, 418-44 arresting the mitotic oscillator, 438-45 double oscillator model, 448-51 extended model with autocatalysis,... 

These results have opened the way to the construction of more realistic models for the mitotic oscillator. The purpose of this chapter is briefly to present these models and to classify them according to the type of regulation responsible for oscillatory behaviour. The way sustained oscillations are generated is examined in detail in a minimal model based on the cascade of phosphorylation-dephosphorylation cycles that controls the onset of mitosis in embryonic cells. Extensions of the cascade model taking into account additional, recently uncovered phosphorylation-dephosphorylation cycles are considered. Ways of arresting the cell division cycle in that model and the control of the mitotic oscillator by growth factors are also discussed. 

Fig. 10.15. Arrest of the mitotic oscillator through inhibiting the cdc25 phosphatase that activates cdc2 kinase. The evolution of the fraction of active cdc2 kinase (M) in the minimal cascade model of fig. 10.4 is shown, together with the cyclin concentration (C) under the conditions of fig. 10.6, with K = K2 = K =...

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