Yeast

Direct transcription

This model is a direct transcription of the Boolean model published by Davidich & Bornholdt [1]. Dynamical rules are defined on the basis of the network structure, as the sum of the positive and negative influences exerted on each nodes by its regulators. (Fig. 1, bottom left in [2]; see text for more details).

The model yields a main stable state, corresponding to G0/G1, that gathers most trajectories in the state transition graph; and several alternative, artefactual states.

Adaptation

This model is derived from the Boolean model published by Davidich & Bornholdt [1]. The two Boolean components representing the different levels of activity of Cdc2_Cdc13 have been replaced by a ternary component. In addition, the loops originally placed on Start, SK, PP, and Slp1 nodes have been removed, as they do not represent true auto-regulations, and compensated by the introduction of priorities to account for the maintenance of the start signal and its effect on Rum1 and Ste9.

For proper logical rules, the model has a single stable state, corresponding to the G1 state of Davidich & Bornholdt (with only Ste9, Rum1 and Wee1_Mick1 activated). This means that the other 11 spurious stable states obtained by these authors have been eliminated.

Activation of Start leads to SK inactivation and then to inhibition of Ste9 and Rum 1, launching a to a sequence of state transitions matching that defined by Davidich & Bornholdt [1], as well as available kinetic data (see Model Documentation for proper setting of the logical simulation).

References

This model is a direct transcription of the Boolean model published by Orlando et al. [1]. Synchronous simulation of this model yields a cyclic attractor gathering most trajectories in the state transition graph, which is robust to parameter choice, as reported in [1]. However, asynchronous simulations all lead to a stable state with all variables OFF, whatever the parameter set proposed by the authors, indicating that the oscillations observed in the synchronous simulations may not be sustained. See [2] for more details.

References

In budding yeast, the morphogenetic checkpoint (MCP) relies upon inhibitory phosphorylation of Cdc2/Cyclin B by Swe1 to condition entry into mitosis to the formation of a bud. Taking inspiration in the ODE model published by Ciliberto et al. (2003) [1], we have developed a logical model of the MCP, with the aim to plug it to our core engine of the budding yeast cell cycle (cf. [2]).

The activity of Cdc28/Clb2 is controlled by the balance between Swe1 and Mih1. Swe1, the budding yeast homologue of the tyrosine kinase wee1, inhibits Cdc28 by phosphorylation, whereas the phosphatase Mih1 (homologue of Cdc25) removes the inhibitory phosphate. Swe1 itself is inhibited by phosphorylation by Cdc28/Clb2, in a positive feed-back loop. Based on Ciliberto's model, we assume that Swe1 is also somehow modified by Hsl1, a protein kinase activated by bud formation, and that this modification of unknown nature - as Swe1 does not appear to be a substrate of Hsl1- has an inhibitory effect on Swe1. The checkpoint is reinforced by a MAPK pathway that inhibits Mih1 through Mpk1 activity in absence of a bud. An important point of the MCP is the possibility for the cell to undergo adaptation, that is to evade the checkpoint and enter mitosis in absence of a bud after some time. Ciliberto's model supports the hypothesis that failure to make a bud creates a second threshold for mass for the G2-M transition (the first threshold being at Start). Mass impacts cell progression by increasing the synthesis of the cyclins, and in particular CycB that is required for entry into mitosis (see the core model -LINK- for details). Here, we have introduced a second threshold for the MASS variable, to represent the idea that increased CycB synthesis can yield enough CycB activity to overcome inhibition by Swe1. Our model accounts for the wild-type as well as 14 mutants phenotypes described by Ciliberto et al. and in Harrison et al (2001) [3] in terms of entry into mitosis – monitored by Clb2 activation. This model has then been to our model of the core cell cycle engine of the budding yeast (see coupled model).

References

Leaning on former models, we have defined a logical model for three regulatory modules involved in the control of the mitotic cell cycle in budding yeast, namely the core cell cycle module, the morphogenetic checkpoint, and a module controlling the exit from mitosis. Consistency with available data has been assessed through a systematic analysis of model behaviours for various genetic backgrounds and other perturbations. See:

• Logical modelling of the core engine
• Logical modelling of the budding yeast morphogenetic checkpoint
• Logical modelling of the budding yeast exit module

Here, we take advantage of compositional facilities of the logical formalism to combine these three models in order to generate a single comprehensive model involving over thirty regulatory components. The resulting logical model preserves all relevant characteristics of the original modules, while enabling the simulation of more sophisticated experiments (cf. [1]).

Chen et al (2004) [2] discussed the possibility to graft the model of the morphogenesis checkpoint published in a “companion study” by Ciliberto et al (2003) [3] to their model of the cell cycle, and to replace the hypothetical PPX by a more accurate version of the network controlling mitotic exit. We have adapted all three modules in the logical formalism, and coupled them together.

Coupling of the MCP module to the core cycling engine model

We have kept and left unchanged all components that were specific of the MCP module (Mih1, Swe1, Mpk1 and Hsl1), and similarly, all components specific of the core model. Among the components that were shared by both modules, MASS, MBF and the BUD received no input from the variables specific of the MCP, while their regulation amounted to a simplification of what had been proposed in the core cycling engine model. Hence, we kept these variables and their regulation from the core model and left them unchanged in the coupled model. In contrast, in the coupled model, CycB get inputs from components specific of each of the two modules. Moreover, in the MCP module, CycB is Boolean, whereas it is multilevel in the core model. Based on the parameters of CycB in each of the modules, we determined that CycB would have to satisfy the two sets of conditions to be active in the coupled model. Consequently, the logical formula giving the conditions of activation of CycB in the coupled model amounts to a logical AND between its formulas in the core cycling engine and in the MCP module. The main characteristics of the behaviour of the two original modules are conserved in the coupled model, in the case of the wild-type as for the different mutations simulated.

Coupling of the exit module to the core cycling engine model

The next step was to fuse the exit module to the core cycling engine. We followed the same method as with the coupling of the MCP. The first step was to identify which components and interactions were to be kept in the coupled model. Obviously, we chose to discard the hypothetical PPX, along with the parameters of the components of the exit network that were present in the core model (Net1, Cdc14, Tem1, Bub2-Bfa1, Cdc15 and Pds1), to replace them with their equivalents from the new exit module, including the SeparaseEsp1, PP2ACdc55 and Cdc5Polo that were not present in the core model. The logical rules for Clb2, Cdh1 and Cdc20 in the exit module amount to simplifications of their counterparts in the core model, so we kept the core model wiring and regulation in the coupled model for these components. Last but not least, we added regulation from Sic1 and Cdc6 towards Clb2 new targets to represent sequestration of the cyclins by the CKI (see the core cycling engine model for more details). The resulting model fits the more recent data used to built the exit module, and the behaviour of the core model is preserved. Still, one difficulty arose regarding mutant simulations for the exit module: the two mutants involving Cdk inhibition (see Queralt [i]et al.[/i], supplementary figure S6.4 [4]) could not be simulated in the coupled model, as inhibition of Cdk1 / Clb2 is the signal for cytokinesis in this model. This points out towards the “TARGET model” hypothesis discussed in Chen et al, where the trigger for cytokinesis would involve both a decrease of Cdk1 / Clb2 kinase activity and an increase in Cdc14 phosphatase activity.

References