ABSTRACT
To contribute to a deeper understanding of M-phase control in eukaryotic cells, we have contructed a model based on the biochemistry of M-phase promoting factor (MPF) in Xenopus oocyte extracts, where there is evi-dence for two positive feedback loops (MPF stimulates its own production by activating Cdc25 and inhibiting Wee1) and a negative feedback loop (MPF stimulates its own destruction by indirectly activating the ubiquitin pathway that degrades its cyclin subunit). To uncover the full dynamical possibilities of the control system, we translate the regulatory network into a set of differential equations and study these equations by graphical techniques and computer simulation. The positive feed-back loops in the model account for thresholds and time lags in cyclin-induced and MPF-induced activation of MPF, and the model can be fitted quantitatively to these experimental observations. The negative feedback loop is consistent with observed time lags in MPF-induced cyclin degradation. Furthermore, our model indicates that there are two possible mechanisms for autonomous oscillations. One is driven by the positive feedback loops, resulting in phosphorylation and abrupt dephosphorylation of the Cdc2 subunit at an inhibitory tyrosine residue. These oscillations are typical of oocyte extracts. The other type is driven by the negative feedback loop, involving rapid cyclin turnover and negligible phosphorylation of the tyrosine residue of Cdc2. The early mitotic cycles of intact embryos exhibit such character-istics. In addition, by assuming that unreplicated DNA interferes with M-phase initiation by activating the phosphatases that oppose MPF in the positive feedback loops, we can simulate the effect of addition of sperm nuclei to oocyte extracts, and the lengthening of cycle times at the mid-blastula transition of intact embryos.
We use Michaelis-Menten kinetics for the activation and inhibition of the regulatory enzymes because this description introduces important nonlinearities into the mathematical equations. To justify this description we must assume that the substrates (Cdc25, etc.) are in great supply over the enzymes (the phosphatases and kinases) and that the effects of MPF on steps a, e and g in Fig. 1 are indirect (otherwise there would be complicated interference among these steps as the substrates compete with each other for the common kinase). These assumptions simplify the model considerably, but they could be relaxed if compelling experimental results call them into question.
Observe that, in interphase (when MPF activity is low), Cdc25 exists primarily in the inactive form and it can be made only slightly more inactive by adding unreplicated DNA to the extract (Fig. 3). Thus, it would appear that Cdc25 is not regulated by unreplicated DNA (Kumagai and Dunphy, 1992). However, in our model, it is not the activity of Cdc25 that is directly affected by unreplicated DNA but rather the phosphatase that opposes MPF in the phosphorylation and dephosphorylation of Cdc25. As a consequence, the level of MPF activity that is required to switch Cdc25 from its inactive to its active state increases with increasing amounts of unreplicated DNA.
