Mathematical modelling of reversible transition between quiescence and proliferation

Cells switch between quiescence and proliferation states for maintaining tissue homeostasis and regeneration. At the restriction point (R-point), cells become irreversibly committed to the completion of the cell cycle independent of mitogen. The mechanism involving hyper-phosphorylation of retinoblastoma (Rb) and activation of transcription factor E2F is linked to the R-point passage. However, stress stimuli trigger exit from the cell cycle back to the mitogen-sensitive quiescent state after Rb hyper-phosphorylation but only until APC/C(Cdh1) inactivation. In this study, we developed a mathematical model to investigate the reversible transition between quiescence and proliferation in mammalian cells with respect to mitogen and stress signals. The model integrates the current mechanistic knowledge and accounts for the recent experimental observations with cells exiting quiescence and proliferating cells. We show that Cyclin E:Cdk2 couples Rb-E2F and APC/C(Cdh1) bistable switches and temporally segregates the R-point and the G1/S transition. A redox-dependent mutual antagonism between APC/C(Cdh1) and its inhibitor Emi1 makes the inactivation of APC/C(Cdh1) bistable. We show that the levels of Cdk inhibitor (CKI) and mitogen control the reversible transition between quiescence and proliferation. Further, we propose that shifting of the mitogen-induced transcriptional program to G2-phase in proliferating cells might result in an intermediate Cdk2 activity at the mitotic exit and in the immediate inactivation of APC/C(Cdh1). Our study builds a coherent framework and generates hypotheses that can be further explored by experiments.