Goldbeter1991 - Min Mit Oscil, Expl Inact
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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:
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.
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A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase.
- Goldbeter A
- Proceedings of the National Academy of Sciences of the United States of America , 10/ 1991 , Volume 88 , pages: 9107-9111 , PubMed ID: 1833774
- Faculté des Sciences, Université Libre de Bruxelles, Belgium.
- 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.
Submitter of this revision: Nicolas Le Novère
Modellers: Nicolas Le Novère
Metadata information
isDerivedFrom (1 statement)
isDescribedBy (1 statement)
hasTaxon (1 statement)
isVersionOf (2 statements)
isHomologTo (1 statement)
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| Name | Description | Size | Actions |
|---|---|---|---|
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| BIOMD0000000004_url.xml | SBML L2V4 representation of Goldbeter1991 - Min Mit Oscil, Expl Inact | 19.58 KB | Preview | Download |
Additional files |
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| BIOMD0000000004-biopax2.owl | Auto-generated BioPAX (Level 2) | 13.72 KB | Preview | Download |
| BIOMD0000000004-biopax3.owl | Auto-generated BioPAX (Level 3) | 18.72 KB | Preview | Download |
| BIOMD0000000004.m | Auto-generated Octave file | 5.21 KB | Preview | Download |
| BIOMD0000000004.pdf | Auto-generated PDF file | 161.40 KB | Preview | Download |
| BIOMD0000000004.png | Auto-generated Reaction graph (PNG) | 40.51 KB | Preview | Download |
| BIOMD0000000004.sci | Auto-generated Scilab file | 2.81 KB | Preview | Download |
| BIOMD0000000004.svg | Auto-generated Reaction graph (SVG) | 20.87 KB | Preview | Download |
| BIOMD0000000004.vcml | Auto-generated VCML file | 28.34 KB | Preview | Download |
| BIOMD0000000004.xpp | Auto-generated XPP file | 2.99 KB | Preview | Download |
| BIOMD0000000004_manual.png | Manually generated Reaction graph (PNG) | 40.51 KB | Preview | Download |
| BIOMD0000000004_manual.svg | Manually generated Reaction graph (SVG) | 20.87 KB | Preview | Download |
| BIOMD0000000004_urn.xml | Auto-generated SBML file with URNs | 20.74 KB | Preview | Download |
- Model originally submitted by : Nicolas Le Novère
- Submitted: Sep 13, 2005 1:26:49 PM
- Last Modified: Dec 11, 2012 3:30:15 PM
Revisions
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Version: 2
- Submitted on: Dec 11, 2012 3:30:15 PM
- Submitted by: Nicolas Le Novère
- With comment: Current version of Goldbeter1991 - Min Mit Oscil, Expl Inact
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Version: 1
- Submitted on: Sep 13, 2005 1:26:49 PM
- Submitted by: Nicolas Le Novère
- With comment: Original import of Goldbeter1991_MinMitOscil_ExplInact
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: Variable used inside SBML models
| Species | Initial Concentration/Amount |
|---|---|
| C IPR006670 |
0.01 mol |
| M Cyclin-dependent kinase 1-B ; Cyclin-dependent kinase 1-A |
0.01 mol |
| X | 0.01 mol |
| XI | 0.99 mol |
| MI Cyclin-dependent kinase 1-B ; Cyclin-dependent kinase 1-A |
0.99 mol |
| Reactions | Rate | Parameters |
|---|---|---|
| C => ; X | C*cell*vd*X*(C+Kd)^-1 | vd=0.25; Kd=0.02 |
| MI => M | cell*MI*V1*(K1+MI)^-1 | K1=0.005; V1 = NaN |
| XI => X | cell*V3*XI*(K3+XI)^-1 | K3=0.005; V3 = NaN |
| X => XI | cell*V4*X*(K4+X)^-1 | V4=0.5; K4=0.005 |
| M => MI | cell*M*V2*(K2+M)^-1 | K2=0.005; V2=1.5 |
| => C | cell*vi | vi=0.025 |
| C => | C*cell*kd | kd=0.01 |
(added: 10 Aug 2009, 15:12:59, updated: 10 Aug 2009, 15:12:59)