BioModels Database logo

BioModels Database

spacer

BIOMD0000000004 - Goldbeter1991 - Min Mit Oscil, Expl Inact

 

 |   |   |  Send feedback
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: BIOMD0000000004.xml.origin
Submitter: Nicolas Le Novère
Submission ID: MODEL6614389071
Submission Date: 13 Sep 2005 20:26:49 UTC
Last Modification Date: 11 Dec 2012 23:30:15 UTC
Creation Date: 09 Feb 2005 01:34:02 UTC
Encoders:  Bruce Shapiro
set #1
bqbiol:isVersionOf KEGG Pathway hsa04110
Gene Ontology mitotic cell cycle
bqbiol:isHomologTo Reactome REACT_152
bqbiol:occursIn Taxonomy Amphibia
bqmodel:isDerivedFrom BioModels Database Goldbeter1991_MinMitOscil
Notes
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

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 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.

Model
Publication ID: 1833774 Submission Date: 13 Sep 2005 20:26:49 UTC Last Modification Date: 11 Dec 2012 23:30:15 UTC Creation Date: 09 Feb 2005 01:34:02 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 Active CDC-2 Kinase Active Cyclin Protease
Inactive CDC-2 Kinase Inactive 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] → ;   {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)
 
 Cyclin
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)
 
   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 BIOMD0000000004

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

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

spacer
spacer