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BIOMD0000000008 - Gardner1998 - Cell Cycle Goldbeter

 

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Reference Publication
Publication ID: 9826676
Gardner TS, Dolnik M, Collins JJ.
A theory for controlling cell cycle dynamics using a reversibly binding inhibitor.
Proc. Natl. Acad. Sci. U.S.A. 1998 Nov; 95(24): 14190-14195
Center for BioDynamics and Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215, USA.  [more]
Model
Original Model: BIOMD0000000008.xml.origin
Submitter: Nicolas Le Novère
Submission ID: MODEL6614879888
Submission Date: 13 Sep 2005 20:36:20 UTC
Last Modification Date: 24 Jul 2014 18:59:34 UTC
Creation Date: 30 Jan 2005 21:02:57 UTC
Encoders:  Bruce Shapiro
set #1
bqbiol:isHomologTo Reactome REACT_152
bqmodel:isDerivedFrom BioModels Database Goldbeter1991_MinMitOscil
BioModels Database Goldbeter1991 - Min Mit Oscil, Expl Inact
bqbiol:hasTaxon Taxonomy Amphibia
bqbiol:isVersionOf Gene Ontology mitotic cell cycle
Notes
Gardner1998 - Cell Cycle Goldbeter

Mathematical modeling of cell division cycle (CDC) dynamics.

The SBML file has been generated by MathSBML 2.6.0.p960929 (Prerelease Version of 29-Sept-2006) 1-October-2006 15:36:36.076517.

This model is described in the article:

Gardner TS, Dolnik M, Collins JJ.
Proc. Natl. Acad. Sci. U.S.A. 1998 Nov; 95(24): 14190-14195

Abstract:

We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, we show that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo.

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: 9826676 Submission Date: 13 Sep 2005 20:36:20 UTC Last Modification Date: 24 Jul 2014 18:59:34 UTC Creation Date: 30 Jan 2005 21:02:57 UTC
Mathematical expressions
Reactions
creation of cyclin cdc2 kinase triggered degration of cyclin default degradation of cyclin activation of cdc2 kinase
deactivation of cdc2 kinase activation of cyclin protease deactivation of cyclin protease reaction8
reaction9 desinhibition of cyclin degradation of inhibited cyclin creation of cyclin inhibitor
degradation of cyclin inhibitor      
Rules
Assignment Rule (variable: V1) Assignment Rule (variable: V3)    
Physical entities
Compartments Species
Cell cyclin protease cdc2k
cyclin inhibitor complex inhibitor-cyclin  
Global parameters
V1 K6 V1p V3
V3p      
Reactions (13)
 
 creation of cyclin  → [cyclin];  
 
 cdc2 kinase triggered degration of cyclin [cyclin] → ;   {protease}
 
 default degradation of cyclin [cyclin] → ;  
 
 activation of cdc2 kinase  → [cdc2k];  
 
 deactivation of cdc2 kinase [cdc2k] → ;  
 
 activation of cyclin protease  → [protease];  
 
 deactivation of cyclin protease [protease] → ;  
 
 reaction8 [cyclin] + [cyclin inhibitor] → [complex inhibitor-cyclin];  
 
 reaction9 [complex inhibitor-cyclin] → [cyclin] + [cyclin inhibitor];  
 
 desinhibition of cyclin [complex inhibitor-cyclin] → [cyclin];  
 
 degradation of inhibited cyclin [complex inhibitor-cyclin] → [cyclin inhibitor];  
 
 creation of cyclin inhibitor  → [cyclin inhibitor];  
 
 degradation of cyclin inhibitor [cyclin inhibitor] → ;  
 
Rules (2)
 
 Assignment Rule (name: V1) V1 = C*V1p*(C+K6)^(-1)
 
 Assignment Rule (name: V3) V3 = M*V3p
 
 Cell Spatial dimensions: 3.0  Compartment size: 1.0  (Units: Predefined unit volume)
 
 cyclin
Compartment: Cell
Initial amount: 0.0  (Units: substance)
 
 protease
Compartment: Cell
Initial amount: 0.0  (Units: substance)
 
 cdc2k
Compartment: Cell
Initial amount: 0.0  (Units: substance)
 
   cyclin inhibitor
Compartment: Cell
Initial amount: 1.0  (Units: substance)
 
 complex inhibitor-cyclin
Compartment: Cell
Initial amount: 1.0  (Units: substance)
 
Global Parameters (5)
 
   V1
Value: NaN
 
   K6
Value: 0.3
Constant
 
   V1p
Value: 0.75
Constant
 
   V3
Value: NaN
 
   V3p
Value: 0.3
Constant
 
creation of cyclin (1)
 
   vi
Value: 0.1
Constant
 
cdc2 kinase triggered degration of cyclin (2)
 
   k1
Value: 0.5
Constant
 
   K5
Value: 0.02
Constant
 
default degradation of cyclin (1)
 
   kd
Value: 0.02
Constant
 
activation of cdc2 kinase (1)
 
   K1
Value: 0.1
Constant
 
deactivation of cdc2 kinase (2)
 
   V2
Value: 0.25
Constant
 
   K2
Value: 0.1
Constant
 
activation of cyclin protease (1)
 
   K3
Value: 0.2
Constant
 
deactivation of cyclin protease (2)
 
   K4
Value: 0.1
Constant
 
   V4
Value: 0.1
Constant
 
reaction8 (1)
 
   a1
Value: 0.05
Constant
 
reaction9 (1)
 
   a2
Value: 0.05
Constant
 
desinhibition of cyclin (2)
 
   alpha
Value: 0.1
Constant
 
   d1
Value: 0.05
Constant
 
degradation of inhibited cyclin (2)
 
   kd
Value: 0.02
Constant
 
   alpha
Value: 0.1
Constant
 
creation of cyclin inhibitor (1)
 
   vs
Value: 0.2
Constant
 
degradation of cyclin inhibitor (1)
 
   d1
Value: 0.05
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000008

Curator's comment: (updated: 10 Aug 2009 15:53:31 PDT)

Figure 4B of the reference publication is reproduced here. The model was simulated using Copasi v4.5 (Build 30)

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