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

In this paper we propose a role for the [Formula: see text] protein in the entry of cells into mitosis. This has not been considered in the literature so far. Recent experiments suggest that [Formula: see text] , upon entry into mitosis, inhibits the appearance of active [Formula: see text] and cyclin B complexes. This paper proposes a mathematical model which incorporates the dynamics of kinase [Formula: see text] , its regulatory protein cyclin B, the regulatory phosphatase [Formula: see text] and the inhibitor [Formula: see text] known to be involved in the regulation of active [Formula: see text] and cyclin B complexes. The experimental data lead us to formulate a new hypothesis that [Formula: see text] slows down the activation of inactive complexes of [Formula: see text] 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 [Formula: see text] 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.