Model Identifier
BIOMD0000001079
Short description

Models the production and degradation of cyclin B that drives the early embryonic cell cycle. Cyclin B is degraded by APC/C. The activity of APC/C is modeled not through biochemical interactions, but through a 'functional response curve'. This can be ultrasensitive (with the parameter alpha=0). in this case the system does not oscillate. Importantly the response can be made bistable and the form of the bistability can be easily prescribed. With a bistable response, the system oscillates. The uploaded file corresponds to the model used for Figs.3H, I in the publication.
Format
SBML (L2V4)
Related Publication
  • A modular approach for modeling the cell cycle based on functional response curves. Click here to expand
  • 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.
Contributors
Submitter of the first revision: Jan Rombouts
Submitter of this revision: Lucian Smith
Curators: Tung Nguyen, Lucian Smith
Modellers: Jan Rombouts, Krishna Kumar Tiwari

Metadata information

is (2 statements)
BioModels Database BIOMD0000001079
BioModels Database MODEL2212060001

hasProperty (4 statements)
Gene Ontology cell cycle
Gene Ontology cell division
Mathematical Modelling Ontology differential equation model
NCIt Cancer Progression

unknownQualifier (1 statement)
Mathematical Modelling Ontology differential equation model

isDescribedBy (2 statements)
occursIn (1 statement)
NCIt Cell

Curation status
Curated
Modelling approach(es)
differential equation model

Connected external resources

Visualisation of this model on Menelmacar platform