Advances and challenges in logical modeling of cell cycle regulation: perspective for multi-scale, integrative yeast cell models

Abstract

The eukaryotic cell cycle is robustly designed, with interacting molecules organized within a definite topology that ensures temporal precision of its phase transitions. Its underlying dynamics are regulated by molecular switches, for which remarkable insights have been provided by genetic and molecular biology efforts. In a number of cases, this information has been made predictive, through computational models. These models have allowed for the identification of novel molecular mechanisms, later validated experimentally. Logical modeling represents one of the youngest approaches to address cell cycle regulation. We summarize the advances that this type of modeling has achieved to reproduce and predict cell cycle dynamics. Furthermore, we present the challenge that this type of modeling is now ready to tackle: its integration with intracellular networks, and its formalisms, to understand crosstalks underlying systems level properties, ultimate aim of multi-scale models. Specifically, we discuss and illustrate how such an integration may be realized, by integrating a minimal logical model of the cell cycle with a metabolic network.

Keywords: cell cycle; constraint-based modeling; logical modeling; metabolism; multi-scale modeling; network integration.

Figure 1.

The wiring diagram for the Li threshold model. The network includes cyclins (the G1 cyclins Cln3 and Cln1,2, and the S/M cyclins Clb5,6 and Clb1,2, which all form binary complexes with the kinase Cdk1), the inhibitors of the cyclin/Cdk1 complexes (Sic1, Cdh1, Cdc20, Cdc14), the transcription factors (SBF, MBF, Swi5 and Mcm1,SFF), and the checkpoint Cell Size. Lines with arrowheads represent activators, whereas lines with barbs represent inhibitors. When a yeast cell grows, Cell Size is active (the cell responds to nutrients), leading to the activation of the cyclin Cln3 (G1 phase), which in turn activates by phosphorylation the transcription factors SBF and MBF that activate transcription of the genes of cyclins Cln1,2 and Clb5,6, respectively. Clb5,6 (S phase) activate by phosphorylation the transcription factors Mcm1,SFF that activate transcription of Clb1,2, which continue to promote by phosphorylation the activation of Mcm1,SFF and the inactivation of SBF. Mcm1, SFF also activates transcription of Swi5, which in turns activates transcription of Sic1 that binds to, and inhibits the activity of, the cyclins Clb5,6 and Clb1,2. Cln1,2 and all Clb cyclins phosphorylate and inactivate Sic1, and Clb1,2 (entry into M phase) phosphorylate Swi5 to prevent its entry into the nucleus and inactivate Sic1 transcription. Clb1,2 phosphorylate and activate Cdc20,Cdh1 and Cdh1, which in turn degrades and inactivate Clb1,2 itself (exit from M phase), thus promoting activation of Sic1 (G1 phase). For modeling purposes, the kinase Cdk1, partner of both Cln and Clb cyclins, is not indicated in the network because its activity is driven by the cyclins. Adapted from Li et al. (2004).

Figure 2.

The wiring diagram for the model of Barberis and colleagues. The network includes the S cyclins Clb5,6 and the G2/M cyclins Clb3,4 and Clb1,2, which all form binary complexes with the kinase Cdk1, and the inhibitors of the Clb/Cdk1 complexes Sic1. Lines with arrowheads represent activators, whereas lines with barbs represent inhibitors. In G1 phase, all Clb cyclins are inhibited by Sic1. When Sic1 is degraded and inactivated at the G1/S transition, Clb5,6 (S phase) promote the transcription of CLB3 and CLB2 genes, thus activating both Clb3,4 (G2 phase) and Clb1,2 (M phase) through phosphorylation of the transcription factor Fkh2. Clb3,4 also promotes the transcription of CLB2 gene through Fkh2 phosphorylation. All Clb cyclins phosphorylate and inactivate Sic1. Furthermore, the cyclins that are activated later inhibit the ones activated earlier: (1) Clb1,2 phosphorylate and activate Cdc20 and Cdh1, which in turn degrades and inactivate Clb5,6 and Clb3,4, and (2) Clb3,4 inactivate Clb1,2, thus promoting activation of Sic1 (G1 phase). For modeling purposes, the kinase Cdk1, partner of Clb cyclins, is not indicated in the network because its activity is driven by the cyclins. Adapted from Linke et al. (2017).

Figure 3.

The integrative model linking cell cycle to metabolism highlights a phase-dependent regulation of threalose metabolism. The minimal model of cell cycle regulation described in Fig. 2, including Sic1 (G1 phase), Clb5 (S phase), Clb3 (G2 phase) and Clb2 (M phase), has been connected to the iMM904 metabolic map (Mo, Palsson and Herrgård 2009). The presence of Clb2 stimulates the activity of the threalase Nth1, which converts threalose (TRE) into glucose (Glu_int). A flux of trehalase is observed in M phase when Clb2 is active (indicated in violet), which results in a high flux through the glycolysis (indicated in red). Conversely, no flux of threalase is observed in G1 and S phases (indicated in gray), inhibited by the absence of Clb2, which results in a reduced glycolytic flux (indicated in purple).