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BIOMD0000000110 - Qu2003_CellCycle

 

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Reference Publication
Publication ID: 14645053
Qu Z, MacLellan WR, Weiss JN.
Dynamics of the cell cycle: checkpoints, sizers, and timers.
Biophys. J. 2003 Dec; 85(6): 3600-3611
Cardiovascular Research Laboratory, Departments of Medicine (Cardiology) and Physiology, David Geffen School of Medicine at University of California, Los Angeles, California 90095, USA. zqu@mednet.ucla.edu  [more]
Model
Original Model: BIOMD0000000110.xml.origin
Submitter: Enuo He
Submission ID: MODEL6931308526
Submission Date: 18 Apr 2007 23:35:28 UTC
Last Modification Date: 16 May 2012 10:13:14 UTC
Creation Date: 29 Sep 2008 13:00:19 UTC
Encoders:  Enuo He
   Lukas Endler
set #1
bqbiol:occursIn Taxonomy Eukaryota
bqbiol:hasVersion KEGG Pathway sce04111
Reactome REACT_152
bqbiol:isVersionOf Gene Ontology regulation of mitotic cell cycle
Gene Ontology mitotic cell cycle
Gene Ontology cell cycle checkpoint
Notes

This model is from the article:
Dynamics of the cell cycle: checkpoints, sizers, and timers.
Qu Z, MacLellan WR, Weiss JN Biophys. J. 2003 Dec; 85(6): 3600-11 14645053 ,
Abstract:
We have developed a generic mathematical model of a cell cycle signaling network in higher eukaryotes that can be used to simulate both the G1/S and G2/M transitions. In our model, the positive feedback facilitated by CDC25 and wee1 causes bistability in cyclin-dependent kinase activity, whereas the negative feedback facilitated by SKP2 or anaphase-promoting-complex turns this bistable behavior into limit cycle behavior. The cell cycle checkpoint is a Hopf bifurcation point. These behaviors are coordinated by growth and division to maintain normal cell cycle and size homeostasis. This model successfully reproduces sizer, timer, and the restriction point features of the eukaryotic cell cycle, in addition to other experimental findings.


Figure6B has been reproduced by both SBMLodeSolver online and MathSBML. We do not include the synthesis of cyclins is proportional to cell size (Equation 2 in Page3604 of the paper) in this model. The author of the paper keep all the variables and parameters dimensionless. But in the model, we choose to use default units of SBML.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2009 The BioModels Team.
For more information see the terms of use .
To cite BioModels Database, please use Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

Model
Publication ID: 14645053 Submission Date: 18 Apr 2007 23:35:28 UTC Last Modification Date: 16 May 2012 10:13:14 UTC Creation Date: 29 Sep 2008 13:00:19 UTC
Mathematical expressions
Reactions
Free cyclin synthesis Cyclin binding with CDK Cyclin degradation z0 phosphorylation
x phosphorylation z1 phosphorylation unphosphorylated wee1 synthesis wee1 phosphorylation
SKP2 synthesis CKI synthesis CKI binding to Active Cyclin:CDK complex ix phosphorylation
SKP2 degradation CKI degradation Cyclin:CDK:CKIp degradation unphosphorylated wee1 degradation
phosphorylated wee1 degradation Unphosphorylated CDC25 degradation One site phosphorylated CDC25 degradaton Two site phosphorylated CDC25 degradation
Unphosphorylation CDC25 synthesis Active cyclin:CDK complex degradation    
Rules
Assignment Rule (variable: Free CDK) Assignment Rule (variable: totalCyclin)    
Physical entities
Compartments Species
cell Inactive Cyclin:CDK complex Active Cyclin:CDK complex Total CDK
Free CDK Unphosphorylated CDC25 One-site phosphorylated CDC25
Two-site phosphorylated CDC25 Unphosphorylated wee1 phosphorylated wee1
Active SKP2 or APC Free CKI Cyclin:CDK:CKI complex with CKI unphosphorylated
Cyclin:CDK:CKI complex with CKI phosphorylated Free cyclin totalCyclin
Global parameters
k1 k2 k3 k4
k5 k6 k7 k8
k9 k10 k11 k12
k13 k14 k15 k16
k2u k7u k16u a
az aw ai bz
bw bi cz cw
ci Tau    
Reactions (22)
 
 Free cyclin synthesis  → [Free cyclin];  
 
 Cyclin binding with CDK [Free cyclin] ↔ [ Inactive Cyclin:CDK complex];   {Free CDK}
 
 Cyclin degradation [Free cyclin] → ;   {Active SKP2 or APC}
 
 z0 phosphorylation [Unphosphorylated CDC25] ↔ [One-site phosphorylated CDC25];   {Active Cyclin:CDK complex}
 
 x phosphorylation [Active Cyclin:CDK complex] ↔ [ Inactive Cyclin:CDK complex];   {Two-site phosphorylated CDC25} , {Unphosphorylated wee1}
 
 z1 phosphorylation [One-site phosphorylated CDC25] ↔ [Two-site phosphorylated CDC25];   {Active Cyclin:CDK complex}
 
 unphosphorylated wee1 synthesis  → [Unphosphorylated wee1];  
 
 wee1 phosphorylation [Unphosphorylated wee1] ↔ [phosphorylated wee1];   {Active Cyclin:CDK complex}
 
 SKP2 synthesis  → [Active SKP2 or APC];   {Active Cyclin:CDK complex}
 
 CKI synthesis  → [Free CKI];  
 
 CKI binding to Active Cyclin:CDK complex [Free CKI] + [Active Cyclin:CDK complex] ↔ [Cyclin:CDK:CKI complex with CKI unphosphorylated];  
 
 ix phosphorylation [Cyclin:CDK:CKI complex with CKI unphosphorylated] ↔ [Cyclin:CDK:CKI complex with CKI phosphorylated];   {Active Cyclin:CDK complex}
 
 SKP2 degradation [Active SKP2 or APC] → ;  
 
 CKI degradation [Free CKI] → ;  
 
 Cyclin:CDK:CKIp degradation [Cyclin:CDK:CKI complex with CKI phosphorylated] → [Active Cyclin:CDK complex];  
 
 unphosphorylated wee1 degradation [Unphosphorylated wee1] → ;  
 
 phosphorylated wee1 degradation [phosphorylated wee1] → ;  
 
 Unphosphorylated CDC25 degradation [Unphosphorylated CDC25] → ;  
 
 One site phosphorylated CDC25 degradaton [One-site phosphorylated CDC25] → ;  
 
 Two site phosphorylated CDC25 degradation [Two-site phosphorylated CDC25] ↔ ;  
 
 Unphosphorylation CDC25 synthesis  → [Unphosphorylated CDC25];  
 
 Active cyclin:CDK complex degradation [Active Cyclin:CDK complex] → ;   {Active SKP2 or APC}
 
Rules (2)
 
 Assignment Rule (name: c) Free CDK = (c0-(x+x1+ix+ixp))/(c0*cell)
 
 Assignment Rule (name: totalCyclin) totalCyclin = x+x1+y
 
 cell Spatial dimensions: 3.0  Compartment size: 1.0
 
  Inactive Cyclin:CDK complex
Compartment: cell
Initial concentration: 0.1
 
 Active Cyclin:CDK complex
Compartment: cell
Initial concentration: 0.1
 
 Total CDK
Compartment: cell
Initial concentration: 200.0
 
  Free CDK
Compartment: cell
Initial concentration: 0.0
 
 Unphosphorylated CDC25
Compartment: cell
Initial concentration: 0.0
 
 One-site phosphorylated CDC25
Compartment: cell
Initial concentration: 0.0
 
 Two-site phosphorylated CDC25
Compartment: cell
Initial concentration: 0.0
 
 Unphosphorylated wee1
Compartment: cell
Initial concentration: 0.0
 
 phosphorylated wee1
Compartment: cell
Initial concentration: 0.0
 
 Active SKP2 or APC
Compartment: cell
Initial concentration: 0.0
 
 Free CKI
Compartment: cell
Initial concentration: 0.0
 
 Cyclin:CDK:CKI complex with CKI unphosphorylated
Compartment: cell
Initial concentration: 0.0
 
 Cyclin:CDK:CKI complex with CKI phosphorylated
Compartment: cell
Initial concentration: 0.0
 
 Free cyclin
Compartment: cell
Initial concentration: 0.0
 
  totalCyclin
Compartment: cell
Initial concentration: 0.0
 
Global Parameters (30)
 
   k1
Value: 300.0
Constant
 
   k2
Value: 5.0
Constant
 
   k3
Value: 30.0
Constant
 
   k4
Value: 30.0
Constant
 
   k5
Value: 0.1
Constant
 
   k6
Value: 1.0
Constant
 
   k7
Value: 10.0
Constant
 
   k8
Value: 100.0
Constant
 
   k9
Value: 1.0
Constant
 
   k10
Value: 10.0
Constant
 
   k11
Value: 1.0
Constant
 
   k12
Constant
 
   k13
Value: 1.0
Constant
 
   k14
Value: 1.0
Constant
 
   k15
Value: 1.0
Constant
 
   k16
Value: 2.0
Constant
 
   k2u
Value: 50.0
Constant
 
   k7u
Constant
 
   k16u
Value: 25.0
Constant
 
   a
Value: 4.0
Constant
 
   az
Value: 10.0
Constant
 
   aw
Value: 10.0
Constant
 
   ai
Value: 10.0
Constant
 
   bz
Value: 0.1
Constant
 
   bw
Value: 0.1
Constant
 
   bi
Value: 0.1
Constant
 
   cz
Value: 1.0
Constant
 
   cw
Value: 1.0
Constant
 
   ci
Value: 1.0
Constant
 
   Tau
Value: 25.0
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000110

Curator's comment: (updated: 18 Jan 2010 16:48:50 GMT)

The model reproduces figure 6B of the reference publication. The model was integrated and simulated using Copasi v4.5 (build 30).

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