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BIOMD0000000003 - Goldbeter1991 - Min Mit Oscil

 

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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]
Model
Original Model: BIOMD0000000003.origin
Submitter: Nicolas Le Novère
Submission ID: MODEL6614271263
Submission Date: 13 Sep 2005 12:24:56 UTC
Last Modification Date: 16 May 2013 14:38:01 UTC
Creation Date: 06 Feb 2005 23:39:40 UTC
Encoders:  Bruce Shapiro
   Vijayalakshmi Chelliah
set #1
bqbiol:occursIn Taxonomy Amphibia
bqbiol:isVersionOf KEGG Pathway Cell cycle - Homo sapiens (human)
Gene Ontology mitotic cell cycle
bqbiol:isHomologTo Reactome REACT_152
Notes
Goldbeter1991 - Min Mit Oscil

Minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase.

This model has been generated by MathSBML 2.4.6 (14-January-2005) 14-January-2005 18:33:39.806932.

This model is described in the article:

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

Abstract:

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 of the 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]. This conjecture 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 cyclin proteolysis 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 the origin 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.

Model
Publication ID: 1833774 Submission Date: 13 Sep 2005 12:24:56 UTC Last Modification Date: 16 May 2013 14:38:01 UTC Creation Date: 06 Feb 2005 23:39:40 UTC
Mathematical expressions
Reactions
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  
Rules
Assignment Rule (variable: V1) Assignment Rule (variable: V3)    
Physical entities
Compartments Species
cell Cyclin CDC-2 Kinase Cyclin Protease
Global parameters
V1 V3 VM1 VM3
Kc      
Reactions (7)
 
 creation of cyclin  → [Cyclin];  
 
 default degradation of cyclin [Cyclin] → ;  
 
 cdc2 kinase triggered degration of cyclin [Cyclin] → ;   {Cyclin Protease}
 
 activation of cdc2 kinase  → [CDC-2 Kinase];  
 
 deactivation of cdc2 kinase [CDC-2 Kinase] → ;  
 
 activation of cyclin protease  → [Cyclin Protease];  
 
 deactivation of cyclin protease [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)
 
 Cyclin
Compartment: cell
Initial concentration: 0.01  (Units: substance)
 
 CDC-2 Kinase
Compartment: cell
Initial concentration: 0.01  (Units: substance)
 
 Cyclin Protease
Compartment: cell
Initial concentration: 0.01  (Units: substance)
 
Global Parameters (5)
 
  V1
Value: NaN
 
  V3
Value: NaN
 
 VM1
Value: 3.0
Constant
 
 VM3
Value: 1.0
Constant
 
 Kc
Value: 0.5
Constant
 
creation of cyclin (1)
 
 vi
Value: 0.025
Constant
 
default degradation of cyclin (1)
 
 kd
Value: 0.01
Constant
 
cdc2 kinase triggered degration of cyclin (2)
 
 vd
Value: 0.25
Constant
 
 Kd
Value: 0.02
Constant
 
activation of cdc2 kinase (1)
 
 K1
Value: 0.0050
Constant
 
deactivation of cdc2 kinase (2)
 
 V2
Value: 1.5
Constant
 
 K2
Value: 0.0050
Constant
 
activation of cyclin protease (1)
 
 K3
Value: 0.0050
Constant
 
deactivation of cyclin protease (2)
 
 K4
Value: 0.0050
Constant
 
 V4
Value: 0.5
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000003

Curator's comment: (updated: 10 Aug 2009 14:41:21 BST)

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

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