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BIOMD0000000004 - Goldbeter1991 - Min Mit Oscil, Expl Inact


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Reference Publication
Publication ID: 1833774
Goldbeter A.
A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase.
Proc. Natl. Acad. Sci. U.S.A. 1991 Oct; 88(20): 9107-9111
Faculté des Sciences, Université Libre de Bruxelles, Belgium.  [more]
Original Model: BIOMD0000000004.origin
Submitter: Nicolas Le Novère
Submission ID: MODEL6614389071
Submission Date: 13 Sep 2005 12:26:49 UTC
Last Modification Date: 11 Dec 2012 15:30:15 UTC
Creation Date: 08 Feb 2005 17:34:02 UTC
Encoders:  Bruce Shapiro
set #1
bqmodel:isDerivedFrom BioModels Database Goldbeter1991_MinMitOscil
bqbiol:hasTaxon Taxonomy Amphibia
bqbiol:isVersionOf KEGG Pathway Cell cycle - Homo sapiens (human)
Gene Ontology mitotic cell cycle
bqbiol:isHomologTo Reactome REACT_152
Goldbeter1991 - Min Mit Oscil, Expl Inact

This model represents the inactive forms of CDC-2 Kinase and Cyclin Protease as separate species, unlike the ODEs in the published paper, in which the equations for the inactive forms are substituted into the equations for the active forms using a mass conservation rule M+MI=1,X+XI=1. Mass is still conserved in this model through the explicit reactions M<->MI and X<->XI. The terms in the kinetic laws are identical to the corresponding terms in the kinetic laws in the published paper.

This model has been generated by MathSBML 2.4.6 (14-January-2005) 14-January-2005 18:37:35.503857.

This model is described in the article:

Goldbeter A.
Proc. Natl. Acad. Sci. USA 1991 Oct; 88(20):9107-11


A minimal model for the mitotic oscillator is presented. The model, built on recent experimental advances, is based on the cascade of post-translational modification that modulates the activity of cdc2 kinase during the cell cycle. The model pertains to the situation encountered in early amphibian embryos, where the accumulation of cyclin suffices to trigger the onset of mitosis. In the first cycle ofthe bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation, and in the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. That cyclin activates cdc2 kinase while the kinase triggers the degradation of cyclin has suggested that oscillations may originate from such a negative feedback loop [Félix, M. A., Labbé, J. C., Dorée, M., Hunt, T. & Karsenti, E. (1990) Nature (London) 346, 379-382]. Thisconjecture is corroborated by the model, which indicates that sustained oscillations of the limit cycle type can arise in the cascade, provided that a threshold exists in the activation of cdc2 kinase by cyclin and in the activation of cyclinproteolysis by cdc2 kinase. The analysis shows how miototic oscillations may readily arise from time lags associated with these thresholds and from the delayed negative feedback provided by cdc2-induced cyclin degradation. A mechanism for theorigin of the thresholds is proposed in terms of the phenomenon of zero-order ultrasensitivity previously described for biochemical systems regulated by covalent modification.

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.

Publication ID: 1833774 Submission Date: 13 Sep 2005 12:26:49 UTC Last Modification Date: 11 Dec 2012 15:30:15 UTC Creation Date: 08 Feb 2005 17:34:02 UTC
Mathematical expressions
creation of cyclin default degradation of cyclin cdc2 kinase triggered degration of cyclin activation of cdc2 kinase
deactivation of cdc2 kinase activation of cyclin protease deactivation of cyclin protease  
Assignment Rule (variable: V1) Assignment Rule (variable: V3)    
Physical entities
Compartments Species
cell Cyclin Active CDC-2 Kinase Active Cyclin Protease
Inactive CDC-2 Kinase Inactive Cyclin Protease  
Global parameters
V1 V3 VM1 VM3
Reactions (7)
 creation of cyclin  → [Cyclin];  
 default degradation of cyclin [Cyclin] → ;  
 cdc2 kinase triggered degration of cyclin [Cyclin] → ;   {Active Cyclin Protease}
 activation of cdc2 kinase [Inactive CDC-2 Kinase] → [Active CDC-2 Kinase];  
 deactivation of cdc2 kinase [Active CDC-2 Kinase] → [Inactive CDC-2 Kinase];  
 activation of cyclin protease [Inactive Cyclin Protease] → [Active Cyclin Protease];  
 deactivation of cyclin protease [Active Cyclin Protease] → [Inactive Cyclin Protease];  
Rules (2)
 Assignment Rule (name: V1) V1 = C*VM1*(C+Kc)^-1
 Assignment Rule (name: V3) V3 = M*VM3
 cell Spatial dimensions: 3.0  Compartment size: 1.0  (Units: Predefined unit volume)
Compartment: cell
Initial concentration: 0.01  (Units: substance)
 Active CDC-2 Kinase
Compartment: cell
Initial concentration: 0.01  (Units: substance)
   Active Cyclin Protease
Compartment: cell
Initial concentration: 0.01  (Units: substance)
 Inactive CDC-2 Kinase
Compartment: cell
Initial concentration: 0.99  (Units: substance)
   Inactive Cyclin Protease
Compartment: cell
Initial concentration: 0.99  (Units: substance)
Global Parameters (5)
Value: NaN
Value: NaN
Value: 3.0
Value: 1.0
Value: 0.5
creation of cyclin (1)
Value: 0.025
default degradation of cyclin (1)
Value: 0.01
cdc2 kinase triggered degration of cyclin (2)
Value: 0.25
Value: 0.02
activation of cdc2 kinase (1)
Value: 0.005
deactivation of cdc2 kinase (2)
Value: 1.5
Value: 0.005
activation of cyclin protease (1)
Value: 0.005
deactivation of cyclin protease (2)
Value: 0.005
Value: 0.5
Representative curation result(s)
Representative curation result(s) of BIOMD0000000004

Curator's comment: (updated: 10 Aug 2009 15:12:59 BST)

Figure 3 of the reference publication is reproduced. The model was integrated and simulated using Copasi v4.5 (Build 20).