Model of the mammalian cell cycle as a chain of bistable switches. There are three bistable responses: response of E2F to Cyclin D, of Cdk1 to Cyclin B and of APC/C to Cdk1 activity. The model for the given parameters admits a complex limit cycle characterized by transitions through the bistable switches. The bistable responses are modeled directly using a functional motif, not through biochemical interactions. This modular approach allows to easily modify the properties of the bistable response curves. This version of the model correspond to Fig. 7 in the publication. We illustrated how, using this model, the system can be coupled to the circadian clock, by periodically modifying thresholds of one of the switches. We also illustrated how to implement the restriction point checkpoint using this model (those applications are not coded in the associated sbml file and can be seen in Fig. 8 of the publication). A related, simpler model that illustrates the bistable motif is MODEL2212060001
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A modular approach for modeling the cell cycle based on functional response curves.
- De Boeck J, Jan Rombouts, Gelens L
- PLoS computational biology , 8/ 2021 , Volume 17 , Issue 8 , pages: e1009008 , DOI: 10.1371/journal.pcbi.1009008
- Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, University of Leuven, Leuven, Belgium.
- Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that qualitatively describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill function. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, S-shaped response curves, which by definition have multiple output values for certain input values and are often encountered in bistable systems, are not easily modeled in such an explicit way. Here, we extend the classical Hill function into a mathematical expression that can be used to describe both ultrasensitive and S-shaped responses. We show how three ubiquitous modules (ultrasensitive responses, S-shaped responses and time delays) can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can incorporate events such as DNA damage and coupling to the circadian clock in a phenomenological way.
Submitter of this revision: Lucian Smith
Curators: Tung Nguyen, Lucian Smith
Modellers: Jan Rombouts, Krishna Kumar Tiwari
Metadata information
hasProperty (4 statements)
Gene Ontology cell division
Mathematical Modelling Ontology differential equation model
NCIt Cancer Progression
unknownQualifier (1 statement)
isDescribedBy (2 statements)
occursIn (1 statement)
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