ferrel2011 - autonomous biochemical oscillator in cell cycle in Xenopus laevis v2

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Model Identifier
BIOMD0000000936
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 BIOMD0000000936
BioModels Database MODEL1809040002

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

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Model files
Ferrel2011_V2.xml SBML L2V4 representation of ferrel2011 - autonomous biochemical oscillator in cell cycle in Xenopus laevis v2 18.13 KB Preview | Download

Additional files
Ferrel2011_V2.cps COPASI version 4.27 (Build 217) file for reproducing figure 3C I in the reference publication 43.32 KB Preview | Download
Ferrel2011_V2.sedml SEDML file to reproduce Figure 3C in the reference publication 1.79 KB Preview | Download

  • Model originally submitted by : Matthieu MAIRE
  • Submitted: Sep 4, 2018 3:39:11 PM
  • Last Modified: Apr 24, 2020 5:33:58 PM
Revisions
  • Version: 6 public model Download this version
    • Submitted on: Apr 24, 2020 5:33:58 PM
    • Submitted by: Ahmad Zyoud
    • With comment: Automatically added model identifier BIOMD0000000936
  • Version: 4 public model Download this version
    • Submitted on: Sep 4, 2018 3:39:11 PM
    • Submitted by: Matthieu MAIRE
    • With comment: Update annotation of compartments

(*) 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
CDK1 active

Cyclin-dependent kinase 1-A ; active 		0.0 mmol
Reactions
Reactions Rate Parameters
=> CDK1_active compartment*a1 a1 = 0.1
CDK1_active => compartment*b1*CDK1_active^(n1+1)/(k1^n1+CDK1_active^n1) n1 = 8.0; b1 = 1.0; k1 = 0.5
Curator's comment:
(added: 04 Sep 2018, 14:31:00, updated: 04 Sep 2018, 14:31:00)
Figure 3C of the reference publication has been reproduced using Copasi 4.23. Use attached SED-ML to reproduce the simulation.