/*
 * Model Status
 * 
 * This CellML model runs in both OpenCell and COR, however it
 * does not recreate the published results - the CellML model does
 * not oscillate. The units have been checked and they are consistent.
 * This particular version of the model describes the third control
 * system of a circuit with limit cycles. We suspect the CellML
 * model does not oscillate because it does not include time delays.
 * These are mentioned in the main body of text in the published
 * paper, but they are not descibed mathematically in the model
 * equations.
 * 
 * Model Structure
 * 
 * ABSTRACT: THE demonstration of negative feedback control processes
 * operating at the molecular level in cells is one of the most
 * significant developments in modern biology. The phenomena of
 * feedback inhibition and feedback repression, whereby enzymatic
 * activities are controlled at the level of the enzyme and the
 * gene, respectively, provide a firm experimental basis for the
 * construction of dynamic models which represent the fundamental
 * regulatory activity of cells. The behavior of these and other
 * molecular control circuits thus constitutes the basis of cell
 * physiology, and in effect provides the physiologist with his
 * elementary units of function. The purpose of this paper is to
 * illustrate the type of periodic behavior which can arise in
 * model systems incorporating the essential control features of
 * enzymatic regulatory processes, and to discuss the significance
 * of oscillatory motion in relation to the organization of cellular
 * processes in time.
 * 
 * The complete original paper reference is cited below:
 * 
 * Oscillatory behavior in enzymatic control processes, Brian C.
 * Goodwin, 1965, Advances in Enzyme Regulation, 3, 425-438. (An
 * abstract and a PDF version of the article are available to subscribers
 * on the journal website.) PubMed ID: 5861813
 * 
 * cell diagram
 * 
 * [[Image file: goodwin_1965b.png]]
 * 
 * Schematic diagram of the third control system modelled in this
 * study: a control circuit with limit-cycle characteristics.
 */

import nsrunit;
unit conversion on;
unit first_order_rate_constant=1 second^(-1);
unit flux=1E-6 meter^(-3)*second^(-1)*mole^1;
// unit nanomolar predefined
unit per_nanomolar=1E6 meter^3*mole^(-1);

math main {
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real X1(time) nanomolar;
	when(time=time.min) X1=7;
	real a1 flux;
	a1=360;
	real b1 first_order_rate_constant;
	b1=1;
	real A1 dimensionless;
	A1=43;
	real k1 per_nanomolar;
	k1=1;
	real Z1(time) nanomolar;
	when(time=time.min) Z1=0;
	real Y1(time) nanomolar;
	when(time=time.min) Y1=0;
	real beta_1 first_order_rate_constant;
	beta_1=0.6;
	real alpha_1 first_order_rate_constant;
	alpha_1=1;
	real gamma_1 first_order_rate_constant;
	gamma_1=1;
	real delta_1 first_order_rate_constant;
	delta_1=0.8;

	// <component name="environment">

	// <component name="X1">
	X1:time=(a1/(A1+k1*Z1)-b1*X1);

	// <component name="Y1">
	Y1:time=(alpha_1*X1-beta_1*Y1);

	// <component name="Z1">
	Z1:time=(gamma_1*Y1-delta_1*Z1);
}