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:

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.

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BIOMD0000000008.
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*/
// unit definitions
import nsrunit;
unit conversion off;
// SBML property definitions
property sbmlRole=string;
property sbmlName=string;
property sbmlCompartment=string;
// SBML reactions
// reaction1: <=> C
// reaction2: C
// reaction3: C
// reaction4: <=> M
// reaction5: M
// reaction6: <=> X
// reaction7: X
// reaction8: C Y <=> Z
// reaction9: Z <=> C Y
// reaction10: Z <=> C
// reaction11: Z <=> Y
// reaction12: <=> Y
// reaction13: Y
math main {
realDomain time second;
time.min=0;
extern time.max;
extern time.delta;
// variable definitions
real Cell = 1 L;
real V1(time);
real K6 = .3;
real V1p = .75;
real V3(time);
real V3p = .3;
real C(time) M;
real X(time) M;
real M(time) M;
real Y(time) M;
real Z(time) M;
real reaction1(time) katal;
real vi = .1;
real reaction2(time) katal;
real k1 = .5;
real K5 = .02;
real reaction3(time) katal;
real kd = .02;
real reaction4(time) katal;
real K1 = .1;
real reaction5(time) katal;
real V2 = .25;
real K2 = .1;
real reaction6(time) katal;
real K3 = .2;
real reaction7(time) katal;
real K4 = .1;
real V4 = .1;
real reaction8(time) katal;
real a1 = .05;
real reaction9(time) katal;
real a2 = .05;
real reaction10(time) katal;
real alpha = .1;
real d1 = .05;
real reaction11(time) katal;
real reaction11_kd = .02;
real reaction11_alpha = .1;
real reaction12(time) katal;
real vs = .2;
real reaction13(time) katal;
real reaction13_d1 = .05;
// equations
V1 = C*V1p*(C+K6)^(-1);
V3 = M*V3p;
when (time=time.min) C = 0;
(C*Cell):time = reaction1 + -1*reaction2 + -1*reaction3 + -1*reaction8 + reaction9 + reaction10;
when (time=time.min) X = 0;
(X*Cell):time = reaction6 + -1*reaction7;
when (time=time.min) M = 0;
(M*Cell):time = reaction4 + -1*reaction5;
when (time=time.min) Y = 1/Cell;
(Y*Cell):time = -1*reaction8 + reaction9 + reaction11 + reaction12 + -1*reaction13;
when (time=time.min) Z = 1/Cell;
(Z*Cell):time = reaction8 + -1*reaction9 + -1*reaction10 + -1*reaction11;
reaction1 = vi;
reaction2 = C*k1*X*(C+K5)^(-1);
reaction3 = C*kd;
reaction4 = (1+(-1)*M)*V1*(K1+(-1)*M+1)^(-1);
reaction5 = M*V2*(K2+M)^(-1);
reaction6 = V3*(1+(-1)*X)*(K3+(-1)*X+1)^(-1);
reaction7 = V4*X*(K4+X)^(-1);
reaction8 = a1*C*Y;
reaction9 = a2*Z;
reaction10 = alpha*d1*Z;
reaction11 = reaction11_alpha*reaction11_kd*Z;
reaction12 = vs;
reaction13 = reaction13_d1*Y;
// variable properties
Cell.sbmlRole="compartment";
V1.sbmlRole="parameter";
K6.sbmlRole="parameter";
V1p.sbmlRole="parameter";
V3.sbmlRole="parameter";
V3p.sbmlRole="parameter";
C.sbmlRole="species";
C.sbmlCompartment="Cell";
X.sbmlRole="species";
X.sbmlCompartment="Cell";
M.sbmlRole="species";
M.sbmlCompartment="Cell";
Y.sbmlRole="species";
Y.sbmlCompartment="Cell";
Z.sbmlRole="species";
Z.sbmlCompartment="Cell";
reaction1.sbmlRole="rate";
vi.sbmlRole="parameter";
reaction2.sbmlRole="rate";
k1.sbmlRole="parameter";
K5.sbmlRole="parameter";
reaction3.sbmlRole="rate";
kd.sbmlRole="parameter";
reaction4.sbmlRole="rate";
K1.sbmlRole="parameter";
reaction5.sbmlRole="rate";
V2.sbmlRole="parameter";
K2.sbmlRole="parameter";
reaction6.sbmlRole="rate";
K3.sbmlRole="parameter";
reaction7.sbmlRole="rate";
K4.sbmlRole="parameter";
V4.sbmlRole="parameter";
reaction8.sbmlRole="rate";
a1.sbmlRole="parameter";
reaction9.sbmlRole="rate";
a2.sbmlRole="parameter";
reaction10.sbmlRole="rate";
alpha.sbmlRole="parameter";
d1.sbmlRole="parameter";
reaction11.sbmlRole="rate";
reaction11_kd.sbmlRole="parameter";
reaction11_alpha.sbmlRole="parameter";
reaction12.sbmlRole="rate";
vs.sbmlRole="parameter";
reaction13.sbmlRole="rate";
reaction13_d1.sbmlRole="parameter";
}