The cell cycle plays a crucial role in all biological growth, reproduction and development, and the molecular machinery underlying the cell cycle is known to be highly conserved among all eukaryotes 
. Faithful transmission of genetic information depends on accurate chromosome segregation as cells exit from mitosis, and the penalty for errors in chromosome segregation is severe; failures in this process lead to aneuploidy which is responsible for many cases of spontaneous abortions, birth defects and cancer 
. In eukaryotes, an elaborate molecular control system ensures the proper orchestration of events at mitotic exit (ME). Understanding how cell division is controlled by this network of interacting genes and proteins is clearly important to the life sciences, the biotech industry and medical science.
The molecular events during ME are particularly well delineated in budding yeast, Saccharomyces cerevisiae
, for which a large collection of well characterized ME-mutant strains are available. From the phenotypes of these mutants, yeast geneticists are able to propose a hypothetical network of interactions among the proteins encoded by ME genes. However, the resulting network (e.g., ) is so complex that it defies understanding by intuitive reasoning alone. As an aid to intuition, we propose a mathematical model of the ME control system. We show that the model is consistent with the observed phenotypes of most ME-mutants in budding yeast, and we use the model to predict the behavior of the ME network under novel conditions. This methodology has been used to advantage for many years to create mathematical models of cell cycle regulation in fission yeast 
, budding yeast 
, and mammalian cells 
. Embryonic cell cycles have been modeled in frog eggs 
, the fruit fly 
and the sea urchin 
. Not only have these models reproduced large amounts of experimental data, but also they have made successful predictions and guided further experimental studies 
Proposed wiring diagram of mitotic exit control in the budding yeast cell cycle.
Since 2004, when Chen et al.
published their comprehensive model of the budding yeast cell cycle, many more molecular details of ME have come to light, and several updated models of ME have been proposed 
. In this paper, we present a mathematical model of ME control, taking into account the essential role that Polo kinase (Cdc5) plays in the phosphorylation of Net1 and the subsequent release of Cdc14 from the nucleolus 
. We propose a novel mechanism for phosphorylation of Net1 on distinct sites by the ME-relevant kinases: Cdc28, Cdc5 and Dbf2/Mob1 (through activation by Cdc15). The model also integrates proteolytic and nonproteolytic functions of Esp1 into the Cdc14 early anaphase release (FEAR) pathway and the mitotic exit network (MEN). The model accounts for the observed properties of ME in wild-type yeast cells and 110 mutant strains, and it predicts the phenotypes of numerous mutant yeast cells that have not yet been studied to our knowledge.
The precise molecular mechanism by which Cdc5 promotes Net1 phosphorylation, FEAR activation, and ME is not known. Cdc5 promotes FEAR activation in part by inducing degradation of Swe1 (an inhibitor of Cdk/Clb2 activity), which enables Cdk/Clb2 to phosphorylate Net1 
. Cdc5 reduces the affinity between Net1 and Cdc14 
. Cdc5 phosphorylates Net1 extensively in vitro
, and it may influence the phosphorylation state of Net1 in vivo
Our model of ME is based on well-known biochemical interactions in budding yeast and on the assumption that Cdc5 phosphorylates Net1 in vivo on its own. In our model, dissociation of Cdc14 from Net1 relies on Net1 being phosphorylated solely by Cdc5 or being multiply phosphorylated by Cdk/Clb2, by MEN and by Cdc5. In this paper, we gather all the evidence supporting Net1 phosphorylation by Cdc5 in vivo on its own, using observed phenotypes of mutant yeast cells to clarify the mechanism of Cdc14 activation during ME.
The exact role of Polo kinase (Cdc5) in the ME process and the exact mechanism by which Net1 gets phosphorylated and Cdc14 is released are the most controversial aspects of ME. Our view that Net1 can be solely phosphorylated by Cdc5 has been challenged by others 
. Recent models of ME consider Net1 phosphorylation to be dependent on Cdk and MEN-kinases 
. In Queralt's model 
, Cdc5 cannot phosphorylate Net1 on its own, and the essential role of Cdc5 in ME is attributed to its role in MEN. Later on, Vinod et al.
extended Queralt's model with more cell cycle regulators, including Net1 phosphorylation by Cdc5. However, Vinod's model assumes that Net1 phosphorylation by Cdc5 is dependent on a priming phosphorylation by Cdk/Clb2 or MEN kinases. At the heart of our model, unique to this paper, lies the assumption that Cdc5 may phosphorylate Net1 on its own, independent of Cdk and MEN phosphorylation.
For further contextualization, we refer readers to Text S1
, where we summarize some details of ME kinetics in budding yeast and the interactions among major components of the control system. In the next section, we provide details about how these interactions are implemented in our mathematical model.