Entrainability of cell cycle oscillator models with exponential growth of cell mass

Among various aspects of cell cycle, understanding synchronization mechanism of cell cycle is important because of the following reasons. (1)Cycles of cell assembly should synchronize to form an organ. (2) Synchronizing cell cycles are required to experimental analysis of regulatory mechanisms of cell cycles. (3) Cell cycle has a distinct phase relationship with the other biological rhythms such as circadian rhythm. However, forced as well as mutual entrainment mechanisms are not clearly known. In this study, we investigated entrainability of cell cycle models of yeast cell under the periodic forcing to both of the cell mass and molecular dynamics. Dynamics of models under study involve the cell mass growing exponentially. In our result, they are shown to allow only a limited frequency range for being entrained by the periodic forcing. In contrast, models with linear growth are shown to be entrained in a wider frequency range. It is concluded that if the cell mass is included in the cell cycle regulation, its entrainability is sensitive to a shape of growth curve assumed in the model.