Ferrel2011 - Autonomous biochemical oscillator in regulation of CDK1, Plk1, and APC in Xenopus Laevis cell cycle

  public model
Model Identifier
BIOMD0000000937
Short description 
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.
Format
SBML (L2V4)
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.
Contributors
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 BIOMD0000000937
BioModels Database MODEL1809040004

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
Curated
Modelling approach(es)
ordinary differential equation model
Tags

Connected external resources

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Model files
Ferrel2011_V3.xml SBML L2V4 representation of Ferrel2011 - Autonomous biochemical oscillator in regulation of CDK1, Plk1, and APC in Xenopus Laevis cell cycle 35.38 KB Preview | Download

Additional files
Ferrel2011_V3.cps COPASI version 4.27 (Build 217) for reproducing figure 5C in the reference publication. 71.37 KB Preview | Download
Ferrel2011_V3.sedml sed-ml L1V2 to reproduce Figure 5C in the reference publication 2.89 KB Preview | Download

  • Model originally submitted by : Matthieu MAIRE
  • Submitted: Sep 5, 2018 10:17:40 AM
  • Last Modified: Apr 27, 2020 4:41:05 PM
Revisions
  • Version: 5 public model Download this version
    • Submitted on: Apr 27, 2020 4:41:05 PM
    • Submitted by: Ahmad Zyoud
    • With comment: Automatically added model identifier BIOMD0000000937
  • Version: 3 public model Download this version
    • Submitted on: Sep 5, 2018 10:17:40 AM
    • Submitted by: Matthieu MAIRE
    • With comment: PubMed Id updated

(*) 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.

Legends
: Variable used inside SBML models


Species
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
Plk1 active

Serine/threonine-protein kinase PLK1 ; active 		0.0 mmol
Reactions
Reactions Rate Parameters
=> APC_active; Plk1_active compartment*a3*(1-APC_active)*Plk1_active^n3/(k3^n3+Plk1_active^n3) a3 = 3.0; n3 = 8.0; k3 = 0.5
APC_active => compartment*b3*APC_active b3 = 1.0
=> CDK1_active compartment*a1 a1 = 0.1
CDK1_active => ; APC_active compartment*b1*CDK1_active*APC_active^n1/(k1^n1+APC_active^n1) n1 = 8.0; b1 = 3.0; k1 = 0.5
=> Plk1_active; CDK1_active compartment*a2*(1-Plk1_active)*CDK1_active^n2/(k2^n2+CDK1_active^n2) k2 = 0.5; n2 = 8.0; a2 = 3.0
Plk1_active => compartment*b2*Plk1_active b2 = 1.0
Curator's comment:
(added: 04 Sep 2018, 16:05:05, updated: 04 Sep 2018, 16:09:08)
Figure 5C of the referenced publication has been reproduced using Copasi 4.23 Build 184.