Dataset Information

Tyson1991 - Cell Cycle 2 var

ABSTRACT: Tyson1991 - Cell Cycle 2 var Mathematical model of the interactions of cdc2 and cyclin. Description taken from the original Cellerator version of the model ( Tyson (1991, 2 variables) at http://www.cellerator.org ). This model is described in the article: Modeling the cell division cycle: cdc2 and cyclin interactions. Tyson JJ. Proc. Natl. Acad. Sci. U.S.A. 1991; 88(16); 7328-32 Abstract: The proteins cdc2 and cyclin form a heterodimer (maturation promoting factor) that controls the major events of the cell cycle. A mathematical model for the interactions of cdc2 and cyclin is constructed. Simulation and analysis of the model show that the control system can operate in three modes: as a steady state with high maturation promoting factor activity, as a spontaneous oscillator, or as an excitable switch. We associate the steady state with metaphase arrest in unfertilized eggs, the spontaneous oscillations with rapid division cycles in early embryos, and the excitable switch with growth-controlled division cycles typical of nonembryonic cells. This is a two variable reduction of the larger 6-variable model published in the same paper. The equations are: u'= k4(v-u)(alpha+u^2)-k6*u v'=kappa-k6*u z= v-u with kappa = k1[aa]/[CT] In the present implementation, an additional variable z is introduced with z = v-u is made, so that the different variables be interpreted as follows: u=[activeMPF]/[CT] v=([cyclin]+[preMPF]+[activeMPF])/[CT] z=([ cyclin]+[preMPF])/[CT] with [CT]=[CDC2]+{CDC2P]+[preMPF]+[aMPF]. The reactions included are only to show the flows between z and u, and do not influence the species, as they all are set to boundaryCondition=True , meaning, that they are only determined by the rate rules (explicit differential equations) and assignment rules. If you set boundaryCondition=False and remove the rate rules for v, u and the the assignment rule for z, you get the more symmetrical, but equivalent, version from the Cellerator repository: u'= k4*z*(alpha+u^2)-k6*u z'=kappa-z*(alpha+u^2) This model is hosted on BioModels Database and identified by: BIOMD0000000006 . To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models . 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.

OTHER RELATED OMICS DATASETS IN: 196

SUBMITTER: Nicolas Le Novère

PROVIDER: BIOMD0000000006 | BioModels | 2024-09-02

REPOSITORIES: BioModels

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			Action	DRS
	BIOMD0000000006?filename=BIOMD0000000006-biopax2.owl	Owl
	BIOMD0000000006?filename=BIOMD0000000006-biopax3.owl	Owl
	BIOMD0000000006?filename=BIOMD0000000006-matlab.m	Other
	BIOMD0000000006?filename=BIOMD0000000006-octave.m	Other
	BIOMD0000000006?filename=BIOMD0000000006.m	Other

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Publications

Modeling the cell division cycle: cdc2 and cyclin interactions.

Tyson J J JJ

Proceedings of the National Academy of Sciences of the United States of America 19910801 16

The proteins cdc2 and cyclin form a heterodimer (maturation promoting factor) that controls the major events of the cell cycle. A mathematical model for the interactions of cdc2 and cyclin is constructed. Simulation and analysis of the model show that the control system can operate in three modes: as a steady state with high maturation promoting factor activity, as a spontaneous oscillator, or as an excitable switch. We associate the steady state with metaphase arrest in unfertilized eggs, the s ...[more]

PMID: 1831270

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Project description: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: A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. 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. This model is hosted on BioModels Database and identified by: BIOMD0000000003 . To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models . 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.

Project description: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 MMI and XXI. 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: A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. 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. This model is hosted on BioModels Database and identified by: BIOMD0000000004 . To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models . 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.