Ferrel2011 - Cdk1 and APC regulation in cell cycle in Xenopus laevis

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Short description
Mathematical model of the regulation of Cdk1 and APC in cell cycle in Xenopus Laevis
Related Publication
  • Modeling the cell cycle: why do certain circuits oscillate?
  • Ferrell JE Jr, Tsai TY, Yang Q
  • Cell , 3/ 2011 , Volume 144 , Issue 6 , pages: 874-885 , PubMed ID: 21414480
  • Department of Chemical and Systems Biology, Stanford University School of Medicine, Stanford, CA 94305-5174, USA. james.ferrell@stanford.edu
  • Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theory of oscillatory biochemical circuits in the context of the Xenopus embryonic cell cycle. We examine Boolean models, delay differential equation models, and especially ordinary differential equation (ODE) models. For ODE models, we explore what it takes to get oscillations out of two simple types of circuits (negative feedback loops and coupled positive and negative feedback loops). Finally, we review the procedures of linear stability analysis, which allow one to determine whether a given ODE model and a particular set of kinetic parameters will produce oscillations.
Submitter of the first revision: Matthieu MAIRE
Submitter of this revision: Ahmad Zyoud
Modellers: Matthieu MAIRE, Ahmad Zyoud

Metadata information

is (2 statements)
BioModels Database MODEL1809040003
BioModels Database BIOMD0000000935

isDescribedBy (1 statement)
PubMed 21414480

hasTaxon (1 statement)
Taxonomy Xenopus laevis

hasPart (1 statement)
Gene Ontology regulation of cell cycle

hasProperty (1 statement)
Mathematical Modelling Ontology Ordinary differential equation model

Curation status


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Model files

Ferrel2011.xml SBML L2V4 representation of Ferrel2011 - Cdk1 and APC regulation in cell cycle in Xenopus Laevis 27.23 KB Preview | Download

Additional files

Ferrel2011.cps COPASI version 4.27 (Build 217) for reproducing figure 5C in the reference publication. 56.09 KB Preview | Download
Ferrel2011.sedml SEDML file to generate Figure 4C 2.32 KB Preview | Download

  • Model originally submitted by : Matthieu MAIRE
  • Submitted: Sep 4, 2018 3:50:20 PM
  • Last Modified: Apr 24, 2020 4:49:45 PM
  • Version: 4 public model Download this version
    • Submitted on: Apr 24, 2020 4:49:45 PM
    • Submitted by: Ahmad Zyoud
    • With comment: Automatically added model identifier BIOMD0000000935
  • Version: 2 public model Download this version
    • Submitted on: Sep 4, 2018 3:50:20 PM
    • Submitted by: Matthieu MAIRE
    • With comment: Edited model metadata online.

(*) You might be seeing discontinuous revisions as only public revisions are displayed here. Any private revisions unpublished model revision of this model will only be shown to the submitter and their collaborators.

: Variable used inside SBML models

Species Initial Concentration/Amount
APC active

Adenomatous polyposis coli homolog ; active
0.0 mmol
CDK1 active

Cyclin-dependent kinase 1-A ; active
0.0 mmol
Reactions Rate Parameters
=> APC_active; CDK1_active nuclear*a2*(1-APC_active)*CDK1_active^n2/(k2^n2+CDK1_active^n2) k2 = 0.5; n2 = 8.0; a2 = 3.0
APC_active => nuclear*b2*APC_active b2 = 1.0
=> CDK1_active nuclear*a1 a1 = 0.1
CDK1_active => ; APC_active nuclear*b1*CDK1_active*APC_active^n1/(k1^n1+APC_active^n1) n1 = 8.0; b1 = 3.0; k1 = 0.5
Curator's comment:
(added: 04 Sep 2018, 15:51:14, updated: 04 Sep 2018, 15:51:14)
Figure 4C of the referenced publication has been reproduced using Copasi 4.23 Build 184. Use attached SED-ML file to reproduce the figure