/*
 * Complex intracellular calcium oscillations. A theoretical exploration
 * of possible mechanisms
 * 
 * Model Status
 * 
 * This CellML model runs in both OpenCell and COR to reproduce
 * the published output (figure 12). The units have been checked
 * and they are consistent.
 * 
 * Model Structure
 * 
 * ABSTRACT: Intracellular Ca2+ oscillations are commonly observed
 * in a large number of cell types in response to stimulation by
 * an extracellular agonist. In most cell types the mechanism of
 * regular spiking is well understood and models based on Ca2+-induced
 * Ca2+ release (CICR) can account for many experimental observations.
 * However, cells do not always exhibit simple Ca2+ oscillations.
 * In response to given agonists, some cells show more complex
 * behaviour in the form of bursting, i.e. trains of Ca2+ spikes
 * separated by silent phases. Here we develop several theoretical
 * models, based on physiologically plausible assumptions, that
 * could account for complex intracellular Ca2+ oscillations. The
 * models are all based on one- or two-pool models based on CICR.
 * We extend these models by (i) considering the inhibition of
 * the Ca2+-release channel on a unique intracellular store at
 * high cytosolic Ca2+ concentrations, (ii) taking into account
 * the Ca2+-activated degradation of inositol 1,4,5-trisphosphate
 * (IP3), or (iii) considering explicitly the evolution of the
 * Ca2+ concentration in two different pools, one sensitive and
 * the other one insensitive to IP3. Besides simple periodic oscillations,
 * these three models can all account for more complex oscillatory
 * behaviour in the form of bursting. Moreover, the model that
 * takes the kinetics of IP3 into account shows chaotic behaviour.
 * 
 * Complex intracellular calcium oscillations. A theoretical exploration
 * of possible mechanisms, Jose A.M. Borghans, Genevieve Dupont,
 * Albert Goldbeter, 1997, Biophysical Chemistry, 66, 25-41. PubMed
 * ID: 17029867
 * 
 * cell diagram
 * 
 * [[Image file: borghans_1997c.png]]
 * 
 * Schematic representation of the two-pool model for complex Ca2+
 * oscillations.
 */

import nsrunit;
unit conversion on;
unit min=60 second^1;
unit per_min=.01666667 second^(-1);
unit uM=1E-3 meter^(-3)*mole^1;
unit per_uM4=1E12 meter^12*mole^(-4);
unit uM_per_min=1.6666667E-5 meter^(-3)*second^(-1)*mole^1;

math main {
	realDomain time min;
	time.min=0;
	extern time.max;
	extern time.delta;
	real Z(time) uM;
	when(time=time.min) Z=0.0;
	real Y(time) uM;
	when(time=time.min) Y=0.0;
	real X(time) uM;
	when(time=time.min) X=0.5;
	real V_in uM_per_min;
	real V_2i(time) uM_per_min;
	real V_3i(time) uM_per_min;
	real V_2s(time) uM_per_min;
	real V_3s(time) uM_per_min;
	real K_f per_min;
	K_f=0.5;
	real K per_min;
	K=1;
	real beta dimensionless;
	beta=1;
	real v_0 uM_per_min;
	v_0=0.015;
	real v_1 uM_per_min;
	v_1=0.012;
	real V_M2i uM_per_min;
	V_M2i=3.1;
	real K_2i uM;
	K_2i=0.005;
	real V_M3i uM_per_min;
	V_M3i=25;
	real K_3z uM;
	K_3z=0.022;
	real K_3y uM;
	K_3y=0.065;
	real V_M2s uM_per_min;
	V_M2s=1.5;
	real K_2s uM;
	K_2s=0.0265;
	real V_M3s uM_per_min;
	V_M3s=0.169;
	real K_3s uM;
	K_3s=0.1;

	// <component name="environment">

	// <component name="Ca">
	Z:time=(V_in+(-1)*V_2i+V_3i+K_f*Y+(-1)*V_2s+V_3s+K_f*X+(-1)*(K*Z));
	Y:time=(V_2i+(-1)*V_3i+(-1)*(K_f*Y));
	X:time=(V_2s+(-1)*V_3s+(-1)*(K_f*X));

	// <component name="Ca_flux">

	// <component name="V_in">
	V_in=(v_0+v_1*beta);

	// <component name="V_2i">
	V_2i=(V_M2i*(Z^2/(K_2i^2+Z^2)));

	// <component name="V_3i">
	V_3i=(V_M3i*(Y^2/(K_3y^2+Y^2))*(Z^2/(K_3z^2+Z^2)));

	// <component name="V_2s">
	V_2s=(V_M2s*(Z^2/(K_2s^2+Z^2)));

	// <component name="V_3s">
	V_3s=(beta*V_M3s*(X^2/(K_3s^2+X^2)));
}