Linking cell division to cell growth in a spatiotemporal model of the cell cycle

Abstract

Cell division must be tightly coupled to cell growth in order to maintain cell size, yet the mechanisms linking these two processes are unclear. It is known that almost all proteins involved in cell division shuttle between cytoplasm and nucleus during the cell cycle; however, the implications of this process for cell cycle dynamics and its coupling to cell growth remains to be elucidated. We developed mathematical models of the cell cycle which incorporate protein translocation between cytoplasm and nucleus. We show that protein translocation between cytoplasm and nucleus not only modulates temporal cell cycle dynamics, but also provides a natural mechanism coupling cell division to cell growth. This coupling is mediated by the effect of cytoplasmic-to-nuclear size ratio on the activation threshold of critical cell cycle proteins, leading to the size-sensing checkpoint (sizer) and the size-independent clock (timer) observed in many cell cycle experiments.

Longitudinal zonation pattern inArabidopsisroot tip defined by a multiple structural change algorithm

“…Cells have to reach a certain critical size at which cell-cycle transitions are triggered, such as G1-S or G2-mitosis (Ivanov, 1971;Dobrochaev and Ivanov, 2001;Dolznig et al, 2004;Yang et al, 2006;Turner et al, 2012;Robert et al, 2014). Therefore, along the PD it is expected that cells are equal to or smaller than the critical size of dividing cells (L critD ).…”

Cyclin B1–Cdk1 Activation Continues after Centrosome Separation to Control Mitotic Progression

“…Based on the ability of cyclin B1–Cdk1 to inhibit its inhibitor Wee1 [22–25], to activate its activators of the Cdc25 phosphatase family [26,27], and to stimulate cyclin B1 destruction [28], two major theories of mitotic cyclin–cyclin-dependent kinase (Cdk) activation have been proposed (see Text S1 and Figure S1 for additional information on these models). Some models suggest a limit cycle behavior, in which the levels of Cdk activity will never be stable but oscillate between an inactive and an active state [19,29,30]. Other models describe a bistable system, in which thresholds for activation and inactivation differ and Cdk1 is either inactive, active, or approaching one of these stable states [31–33].…”

A mathematical model for cell size control in fission yeast

“…A previous attempt on fission yeast used the membrane control mechanism (Yang et al, 2006), and the growth rate was assumed to be proportional to the cell surface area. The translational control of the key cell cycle proteins, Cdc13 and Cdc25, is recruited as an agent for size control.…”

“…It was suggested (Qu et al, 2003) instead that a Hopf bifurcation is responsible for checkpoints in the cell cycle as well as additional features such as 'sizers' and 'timers'. The cell size control dynamics has been discussed mathematically by Qu et al (2004) and Yang et al (2006), where it was assumed that the cell growth rate is proportional to cell surface area at birth (Qu et al, 2004). Protein translocation between cytoplasm and nucleus was shown to provide a natural mechanism that couples cell growth and cell cycle dynamics (Yang et al, 2006).…”

“…The cell size control dynamics has been discussed mathematically by Qu et al (2004) and Yang et al (2006), where it was assumed that the cell growth rate is proportional to cell surface area at birth (Qu et al, 2004). Protein translocation between cytoplasm and nucleus was shown to provide a natural mechanism that couples cell growth and cell cycle dynamics (Yang et al, 2006). Although the mathematical models for cell growth control have explained the experimental data on cell cycle time versus cell birth size in fission yeast and in Xenopus laevis, other essential features such as the bilinear growth profile for fission yeast, the RCP point, and the role it plays in the size control have not been elucidated.…”