Tyson1991 - Cell Cycle 2 var

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Short description
Tyson1991 - Cell Cycle 2 var

Mathematical model of the interactions of cdc2 and cyclin.

Description taken from the original Cellerator version of the model ( Tyson (1991, 2 variables) at http://www.cellerator.org ).

This model is described in the article:

Tyson JJ.
Proc. Natl. Acad. Sci. U.S.A. 1991; 88(16); 7328-32

Abstract:

The proteins cdc2 and cyclin form a heterodimer (maturation promoting factor) that controls the major events of the cell cycle. A mathematical model for the interactions of cdc2 and cyclin is constructed. Simulation and analysis of the model show that the control system can operate in three modes: as a steady state with high maturation promoting factor activity, as a spontaneous oscillator, or as an excitable switch. We associate the steady state with metaphase arrest in unfertilized eggs, the spontaneous oscillations with rapid division cycles in early embryos, and the excitable switch with growth-controlled division cycles typical of nonembryonic cells.

This is a two variable reduction of the larger 6-variable model published in the same paper. The equations are:

u'= k4(v-u)(alpha+u^2)-k6*u
v'=kappa-k6*u
z= v-u
with kappa = k1[aa]/[CT]

In the present implementation, an additional variable z is introduced with z = v-u is made, so that the different variables be interpreted as follows:

u=[activeMPF]/[CT]
v=([cyclin]+[preMPF]+[activeMPF])/[CT]
z=([ cyclin]+[preMPF])/[CT]
with [CT]=[CDC2]+{CDC2P]+[preMPF]+[aMPF].

The reactions included are only to show the flows between z and u, and do not influence the species, as they all are set to boundaryCondition=True , meaning, that they are only determined by the rate rules (explicit differential equations) and assignment rules.

If you set boundaryCondition=False and remove the rate rules for v, u and the the assignment rule for z, you get the more symmetrical, but equivalent, version from the Cellerator repository:

u'= k4*z*(alpha+u^2)-k6*u
z'=kappa-z*(alpha+u^2)

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Format
SBML (L2V4)
Related Publication
  • Modeling the cell division cycle: cdc2 and cyclin interactions.
  • Tyson JJ
  • Proceedings of the National Academy of Sciences of the United States of America , 8/ 1991 , Volume 88 , pages: 7328-7332
  • Department of Biology, Virginia Polytechnic Institute and State University, Blacksburg 24061.
  • The proteins cdc2 and cyclin form a heterodimer (maturation promoting factor) that controls the major events of the cell cycle. A mathematical model for the interactions of cdc2 and cyclin is constructed. Simulation and analysis of the model show that the control system can operate in three modes: as a steady state with high maturation promoting factor activity, as a spontaneous oscillator, or as an excitable switch. We associate the steady state with metaphase arrest in unfertilized eggs, the spontaneous oscillations with rapid division cycles in early embryos, and the excitable switch with growth-controlled division cycles typical of nonembryonic cells.
Contributors
Nicolas Le Novère

Metadata information

isDescribedBy
PubMed 1831270
hasTaxon
Taxonomy Homo sapiens
isVersionOf
Gene Ontology GO:0000278
hasVersion
Curation status
Curated
  • Model originally submitted by : Nicolas Le Novère
  • Submitted: 13-Sep-2005 13:32:12
  • Last Modified: 16-May-2013 15:38:56
Revisions
  • Version: 2 public model Download this version
    • Submitted on: 16-May-2013 15:38:56
    • Submitted by: Nicolas Le Novère
    • With comment: Current version of Tyson1991 - Cell Cycle 2 var
  • Version: 1 public model Download this version
    • Submitted on: 13-Sep-2005 13:32:12
    • Submitted by: Nicolas Le Novère
    • With comment: Original import of Tyson1991_CellCycle_2var
Curator's comment:
(added: 08 Apr 2011, 02:56:21, updated: 08 Apr 2011, 02:56:21)
Nullclines (left) and time course trajectories (right) of the 2 variable system for various values of kappa in the u-v plane. The values of kappa were chosen to give similar results to figure 4 in the original publication, but as the exact values used are not known, they only show approximately the same results. The right graph shows time courses trajectories (200 time units) for the various values of kappa, and the u-nullcline (orange). the high and low values of kappa (kappa = 0.13, blue and kappa = 0.0075, green)lead to stable steady states, the intermediate one (kappa=0.018, yellow) approaches a limit cycle. The results were calculated and plotted using XPPaut and the Biomodels.net sbml2xpp converter.