/*
 * Signal-induced Ca2+ oscillations: Properties of a model based
 * on (Ca2+)-induced Ca2+ release
 * 
 * Model Status
 * 
 * This model has been built with the differential expressions
 * in Dupont's 1991 paper. This CellML model is known to run in
 * PCEnv and COR to replicate the published results for the response
 * to a transient increase in InsP3 using a pulse and decay of
 * beta at tp=4 (figure 4B).
 * 
 * Paper Abstract
 * 
 * We consider a simple, minimal model for signal-induced Ca2+
 * oscillations based on Ca(2+)-induced Ca2+ release. The model
 * takes into account the existence of two pools of intracellular
 * Ca2+, namely, one sensitive to inositol 1,4,5 trisphosphate
 * (InsP3) whose synthesis is elicited by the stimulus, and one
 * insensitive to InsP3. The discharge of the latter pool into
 * the cytosol is activated by cytosolic Ca2+. Oscillations in
 * cytosolic Ca2+ arise in this model either spontaneously or in
 * an appropriate range of external stimulation; these oscillations
 * do not require the concomitant, periodic variation of InsP3.
 * The following properties of the model are reviewed and compared
 * with experimental observations: (a) Control of the frequency
 * of Ca2+ oscillations by the external stimulus or extracellular
 * Ca2+; (b) correlation of latency with period of Ca2+ oscillations
 * obtained at different levels of stimulation; (c) effect of a
 * transient increase in InsP3; (d) phase shift and transient suppression
 * of Ca2+ oscillations by Ca2+ pulses, and (e) propagation of
 * Ca2+ waves. It is shown that on all these counts the model provides
 * a simple, unified explanation for a number of experimental observations
 * in a variety of cell types. The model based on Ca(2+)-induced
 * Ca2+ release can be extended to incorporate variations in the
 * level of InsP3 as well as desensitization of the InsP3 receptor;
 * besides accounting for the phenomena described by the minimal
 * model, the extended model might also account for the occurrence
 * of complex Ca2+ oscillations.
 * 
 * model diagram
 * 
 * [[Image file: dupont_1991.png]]
 * 
 * Schematic diagram of the cell model for signal-induced, intracellular
 * calcium oscillations.
 * 
 * The complete original paper reference is cited below:
 * 
 * Signal-induced Ca2+ oscillations: properties of a model based
 * on Ca(2+)-induced Ca2+ release, Dupont G, Berridge MJ, Goldbeter
 * A, 1991, Cell Calcium 12, 73-85. PubMedID: 1647878
 */

import nsrunit;
unit conversion on;
// unit micromolar predefined
unit per_second=1 second^(-1);
unit micromolar_s=1E-3 meter^(-3)*second^(-1)*mole^1;

math main {
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real v0 micromolar_s;
	v0=1;
	real v1 micromolar_s;
	v1=7.3;
	real v2(time) micromolar_s;
	real v3(time) micromolar_s;
	real beta(time) dimensionless;
	real VM2 micromolar_s;
	VM2=65;
	real VM3 micromolar_s;
	VM3=500;
	real KR micromolar;
	KR=2;
	real KA micromolar;
	KA=0.9;
	real kf per_second;
	kf=1;
	real k per_second;
	k=10;
	real K2 micromolar;
	K2=1;
//	Var below replaced by constant in model eqns to satisfy unit correction
//	real n dimensionless;
//	n=2;
//	Var below replaced by constant in model eqns to satisfy unit correction
//	real m dimensionless;
//	m=2;
//	Var below replaced by constant in model eqns to satisfy unit correction
//	real p dimensionless;
//	p=4;
	real Z(time) micromolar;
	when(time=time.min) Z=0.1;
	real Y(time) micromolar;
	when(time=time.min) Y=0.64;
	real betaf dimensionless;
	betaf=0.96;
	real tp second;
	tp=4;

	// <component name="environment">

	// <component name="parameters">
	v2=(VM2*Z^2/(K2^2+Z^2));
	v3=(VM3*(Y^2/(KR^2+Y^2))*(Z^4/(KA^4+Z^4)));

	// <component name="cytosol">
	Z:time=(v0+v1*beta-v2+v3+kf*Y-k*Z);

	// <component name="insensitive_pool">
	Y:time=(v2-v3-kf*Y);

	// <component name="beta_pulse">
	beta=(if (time<tp) 0 else if (time>=tp) betaf*exp(((-0.2 per_second))*(time-tp)) else 0);
}