Cell Size at S Phase Initiation: An Emergent Property of the G1/S Network

The eukaryotic cell cycle is the repeated sequence of events that enable the division of a cell into two daughter cells. It is divided into four phases: G1, S, G2, and M. Passage through the cell cycle is strictly regulated by a molecular interaction network, which involves the periodic synthesis and destruction of cyclins that bind and activate cyclin-dependent kinases that are present in nonlimiting amounts. Cyclin-dependent kinase inhibitors contribute to cell cycle control. Budding yeast is an established model organism for cell cycle studies, and several mathematical models have been proposed for its cell cycle. An area of major relevance in cell cycle control is the G1 to S transition. In any given growth condition, it is characterized by the requirement of a specific, critical cell size, PS, to enter S phase. The molecular basis of this control is still under discussion. The authors report a mathematical model of the G1 to S network that newly takes into account nucleo/cytoplasmic localization, the role of the cyclin-dependent kinase Sic1 in facilitating nuclear import of its cognate Cdk1-Clb5, Whi5 control, and carbon source regulation of Sic1 and Sic1-containing complexes. The model was implemented by a set of ordinary differential equations that describe the temporal change of the concentration of the involved proteins and protein complexes. The model was tested by simulation in several genetic and nutritional setups and was found to be neatly consistent with experimental data. To estimate PS, the authors developed a hybrid model including a probabilistic component for firing of DNA replication origins. Sensitivity analysis of PS provides a novel relevant conclusion: PS is an emergent property of the G1 to S network that strongly depends on growth rate.: A major property of living cells is their ability to maintain mass homeostasis throughout cell divisions. It has been proposed that in order to achieve such homeostasis, some critical event(s) in the cell cycle will take place only when the cell has grown beyond a critical cell size. In the budding yeast Saccharomyces cerevisiae, a widely used model for the study of the eukaryotic cell cycle, a large body of evidence indicates that cells have to reach a critical size before they start to replicate their DNA and to form bud, which will give rise to the daughter cell. This critical cell size is modulated by growth rate, hence by nutritional conditions and the multiplicity of genetic material (i.e., ploidy). The authors present a mathematical model of the regulatory molecular network acting at the G1 to S transition. The major novel features of this model compared with previous models of this process are (1) the accounting for cell growth (i.e., the increase in cell volume); (2) the explicit consideration of the fact that cells have a nucleus and a cytoplasm, and that key cell cycle regulatory molecules must move between these different compartments and can only react or regulate each other if they are in the same compartment; and (3) the requirement of sequential overcoming of two molecular thresholds given by a cyclin-dependent kinase/cyclin and a cyclin-dependent kinase inhibitor. The model was tested by simulating the processes during G1 to S transition for different growth conditions or for different mutants and by comparing the results with experimental data. A parameter sensitivity analysis (i.e., testing the model predictions when parameters are varied), newly indicates that the critical cell size is an emergent property of the G1 to S network. The model leads to a unified interpretation of seemingly disparate experimental observations and makes predictions to be experimentally verified.