Dębowski M et al. (2019), Mathematical Model Explaining the Role of CDC6 ...

XB-ART-56518

Cells 2019 Nov 28;812:. doi: 10.3390/cells8121537.

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Mathematical Model Explaining the Role of CDC6 in the Diauxic Growth of CDK1 Activity during the M-Phase of the Cell Cycle.

Dębowski M, Szymańska Z, Kubiak JZ, Lachowicz M.

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In this paper we propose a role for the CDC 6 protein in the entry of cells into mitosis. This has not been considered in the literature so far. Recent experiments suggest that CDC 6 , upon entry into mitosis, inhibits the appearance of active CDK 1 and cyclin B complexes. This paper proposes a mathematical model which incorporates the dynamics of kinase CDK 1 , its regulatory protein cyclin B, the regulatory phosphatase CDC 25 and the inhibitor CDC 6 known to be involved in the regulation of active CDK 1 and cyclin B complexes. The experimental data lead us to formulate a new hypothesis that CDC 6 slows down the activation of inactive complexes of CDK 1 and cyclin B upon mitotic entry. Our mathematical model, based on mass action kinetics, provides a possible explanation for the experimental data. We claim that the dynamics of active complexes CDK 1 and cyclin B have a similar nature to diauxic dynamics introduced by Monod in 1949. In mathematical terms we state it as the existence of more than one inflection point of the curve defining the dynamics of the complexes.

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Species referenced: Xenopus laevis
Genes referenced: cdc6 cdk1

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	Figure 1. CDK1/CYCBA activity in the control extract containing physiological amounts of CDC6 (a) and in the extract immunodepleted of CDC6 (b). Note a slow and diauxic growth of CDK1/CYCBA activity in the control extract (a) and the very rapid activation in the absence of CDC6 (b). Curves reprinted from El Dika et al. [1].
	Figure 2. Differences in dynamics of CDK1/CYCBA activation curves in control extracts containing physiological amounts of CDC6. Two extreme examples are shown: Rapid activation taking 16 min (a) and slow activation taking 28 min (b). Note that the inflection points of the curves appear at different moments in relation to the maximum activity.
	Figure 3. The smoothed curve obtained on the basis of experimental data presented in Figure 1a. Red circles indicate approximate location of inflection points for the setting with CDC6 upon M-phase entry.
	Figure 4. The schematic diagram of the considered system. Colours of arrows and dots correspond to colours of Equations (1)â€“(5). For simplicity we do not consider the potential marginal separation of the complex CDK1/CYCBN into CDK1 and CYCB. On the diagram we indicate this by â€œ*â€.
	Figure 5. Concentration of CDK1, CDK1/CYCBA, CDC6 in the presence of CDC6.
	Figure 6. Concentration of CDK1, CDK1/CYCBA, CDC6 in the absence of CDC6.
	Figure 7. Comparison between concentration of CDK1/CYCBA in the absence and presence of CDC6. Solid lineâ€”system with CDC6; dotted lineâ€”system without CDC6.
	Figure 8. Graphs presenting second derivatives of xa showing the number of zeros, which indicates the number of inflection points. (a) corresponds to the case with the second derivative starting from a positive value and having three zeros. (b) corresponds to the case with the second derivative starting from a negative value and having four zeros.

References [+] :

Aguda, The kinetic origins of the restriction point in the mammalian cell cycle. 1999, Pubmed