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:

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 .

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