Model to simulate

This is a modification of the widely cited Goldbeter (1991) minimal (3-variable) model for a mitotic oscillator. The three variables represent Cyclin ( C), inactive cdc-2 Kinase (M), and an active cdc-2 Kinase (X). Two additional variables Y, Z control the dynamics of the inhibitor.

Reference:

Gardner TS, Dolnik M, Collins JJ. A theory for controlling cell cycle dynamics using a reversibly binding inhibitor. PNAS 95: 14190-14195 (1998).

Model file (CellDesigner 2.0) to download

Simulation Step by Step

1. Set the value and formulas

1. "Species" list: Set the initial value
   

   type

   positionTo Compartment

   id

   name

   compartment

   quantity type

   initial Quantity

   substance Units

   spatial SizeUnits

   hasOnly SubstanceUnits

   b.c.

   charge

   constants

   UNKNOWN

   inside

   EmptySet

   EmptySet

   cytoplasm

   Amount

   0

   FALSE

   TRUE

   0

   FALSE

   UNKNOWN

   inside

   C

   C

   cytoplasm

   Amount

   0

   FALSE

   FALSE

   0

   FALSE

   UNKNOWN

   inside

   M

   M

   cytoplasm

   Amount

   0

   FALSE

   FALSE

   0

   FALSE

   UNKNOWN

   inside

   X

   X

   cytoplasm

   Amount

   0

   FALSE

   FALSE

   0

   FALSE

   UNKNOWN

   inside

   Y

   Y

   cytoplasm

   Amount

   1

   FALSE

   FALSE

   0

   FALSE

   UNKNOWN

   inside

   Z

   Z

   cytoplasm

   Amount

   1

   FALSE

   FALSE

   0

   FALSE

2. Set the Kinetic Law at "math" column in "Raction" list.
   

   type	id	name	reversible	fast	reactants	products	modifiers	math
   STATE_TRANSITION	Reaction1	Reaction1	FALSE	FALSE	EmptySet	C		vi
   STATE_TRANSITION	Reaction2	Reaction2	FALSE	FALSE	C	EmptySet		C*kd
   STATE_TRANSITION	Reaction3	Reaction3	FALSE	FALSE	C	EmptySet		C*vd*X/(C+kd)
   STATE_TRANSITION	Reaction4	Reaction4	FALSE	FALSE	EmptySet	Y		VS
   STATE_TRANSITION	Reaction5	Reaction5	FALSE	FALSE	Y	EmptySet		d1*Y
   STATE_TRANSITION	Reaction6	Reaction6	FALSE	FALSE	C,Y	Z		a1*C*Y
   STATE_TRANSITION	Reaction7	Reaction7	FALSE	FALSE	Z	C,Y		a2*Z
   STATE_TRANSITION	Reaction8	Reaction8	FALSE	FALSE	Z	Y		Z*alpha
   STATE_TRANSITION	Reaction9	Reaction9	FALSE	FALSE	Z	C		Z*alpha
   STATE_TRANSITION	Reaction10	Reaction10	FALSE	FALSE	EmptySet	M		(1-M)*VM1*C/(1+K1-M)*(Kc+C)
   STATE_TRANSITION	Reaction11	Reaction11	FALSE	FALSE	EmptySet	X		VM3*(1-X)*M/(1+K3-X)
   STATE_TRANSITION	Reaction12	Reaction12	FALSE	FALSE	M	EmptySet		M*V2/(K2+M)
   STATE_TRANSITION	Reaction13	Reaction13	FALSE	FALSE	X	EmptySet		V4*X/(K4+X)

3. Set the Parameters
   

   scope	id	name	value	units	constant
   local:Reaction(Reaction1)	vi		0.025		TRUE
   local:Reaction(Reaction2)	kd		0.01		TRUE
   local:Reaction(Reaction3)	kd		0.01		TRUE
   local:Reaction(Reaction3)	vd		0.25		TRUE
   local:Reaction(Reaction4)	VS		0		TRUE
   local:Reaction(Reaction5)	d1		0.05		TRUE
   local:Reaction(Reaction6)	a1		0.5		TRUE
   local:Reaction(Reaction7)	a2		0.5		TRUE
   local:Reaction(Reaction8)	alpha		0.1		TRUE
   local:Reaction(Reaction9)	alpha		0.1		TRUE
   local:Reaction(Reaction10)	K1		0.005		TRUE
   local:Reaction(Reaction10)	Kc		0.3		TRUE
   local:Reaction(Reaction10)	VM1		3		TRUE
   local:Reaction(Reaction11)	K3		0.005		TRUE
   local:Reaction(Reaction11)	VM3		1		TRUE
   local:Reaction(Reaction12)	K2		0.005		TRUE
   local:Reaction(Reaction12)	V2		1.5		TRUE
   local:Reaction(Reaction13)	K4		0.005		TRUE
   local:Reaction(Reaction13)	V4		0.5		TRUE

2. Run Simulator

1. Select "SBW" menu of CellDesigner.
2. Select "Simulation Service" menu.
   The following screen appears.
3. Set [Start Time], [End Time], [Number of Points]
4. Select [Output Variables] from [Hidden Variables] list.
5. Click [Start] button.
   The [State] changes to "Running" in red.
   When the [State] changes to "Not Running" in green, it indicates the calculation is completed.
6. Now Plot.
   Select the item to plot on [X-Axis], then [Y-Axis].
7. Select [Plot].
   The plot screen will pop-up to display the simulation result.