Abstract
BackgroundThe progress through the eukaryotic cell division cycle is driven by an underlying molecular regulatory network. Cell cycle progression can be considered as a series of irreversible transitions from one steady state to another in the correct order. Although this view has been put forward some time ago, it has not been quantitatively proven yet. Bifurcation analysis of a model for the budding yeast cell cycle has identified only two different steady states (one for G1 and one for mitosis) using cell mass as a bifurcation parameter. By analyzing the same model, using different methods of dynamical systems theory, we provide evidence for transitions among several different steady states during the budding yeast cell cycle.ResultsBy calculating the eigenvalues of the Jacobian of kinetic differential equations we have determined the stability of the cell cycle trajectories of the Chen model. Based on the sign of the real part of the eigenvalues, the cell cycle can be divided into excitation and relaxation periods. During an excitation period, the cell cycle control system leaves a formerly stable steady state and, accordingly, excitation periods can be associated with irreversible cell cycle transitions like START, entry into mitosis and exit from mitosis. During relaxation periods, the control system asymptotically approaches the new steady state. We also show that the dynamical dimension of the Chen's model fluctuates by increasing during excitation periods followed by decrease during relaxation periods. In each relaxation period the dynamical dimension of the model drops to one, indicating a period where kinetic processes are in steady state and all concentration changes are driven by the increase of cytoplasmic growth.ConclusionWe apply two numerical methods, which have not been used to analyze biological control systems. These methods are more sensitive than the bifurcation analysis used before because they identify those transitions between steady states that are not controlled by a bifurcation parameter (e.g. cell mass). Therefore by applying these tools for a cell cycle control model, we provide a deeper understanding of the dynamical transitions in the underlying molecular network.
Highlights
The progress through the eukaryotic cell division cycle is driven by an underlying molecular regulatory network
The eukaryotic cell division cycle is driven by an underlying molecular network which centers around complexes of cyclindependent kinases (Cdk's) and cyclins [2,3]
The kinetic equations describe the dynamics of the core cell cycle regulatory components: different Cyclin dependent kinase (Cdk)/cyclin complexes that drive bud formation, DNA replication and mitosis [2,3]; the regulators of cyclin degradation (Cdc20 and Cdh1/Hct1) and synthesis (SBF and Mcm1) and a Cdk inhibitor (Sic1)
Summary
The progress through the eukaryotic cell division cycle is driven by an underlying molecular regulatory network. The kinetic equations describe the dynamics of the core cell cycle regulatory components: different Cdk/cyclin complexes that drive bud formation, DNA replication and mitosis [2,3]; the regulators of cyclin degradation (Cdc and Cdh1/Hct1) and synthesis (SBF and Mcm1) and a Cdk inhibitor (Sic). There are several positive and negative feedback loops among cell cycle control components in the model (Fig. 1) Both Cln and Clb cyclin synthesis are characterized by transcriptional positive feedback loops because the corresponding Cdk/cyclin complexes (Cln2/Cdc and Clb2/Cdc28) activate their own transcription factor (SBF and Mcm1) [13,14,15]. The double-negative feedback is regulated by a negative feedback, because Clb activates Sic and Cdh via Cdc: Clb2 → Cdc20 → (Sic, Cdh1) -| Clb
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