/*
 * Intracellular IP3 and Calcium Release in a Smooth Muscle Cell
 * 
 * Model Status
 * 
 * This is the original unchecked version of the model imported
 * from the previous CellML model repository, 24-Jan-2006.
 * 
 * Model Structure
 * 
 * Intracellular calcium dynamics are frequently the subject of
 * theoretical mathematical models (De Young and Keizer, 1992,
 * Li and Rinzel, 1994, Keizer and Levine, 1996, Jafri-Rice-Winslow,
 * 1998, and Snyder et al., 2000 are just a few examples of calcium
 * dynamic models that have been coded up into CellML). The physical
 * and chemical laws of calcium waves and oscillations can be expressed
 * in terms of differential equations describing reaction kinetics,
 * fluxes through membranes, and diffusion.
 * 
 * Inositol-1,4,5-triphosphate (IP3)-mediated calcium release from
 * the endoplasmic reticulum is an important intracellular signalling
 * mechanism in many cell types. In their 1999 study, Fink et al.
 * determine the levels of IP3 required for calcium release in
 * A7r5 cells (a rat smooth muscle cell from the thoracic aorta).
 * Experimental data were used to construct a mathematical model
 * of the IP3-dependent calcium changes (see below). This model
 * considers of several elements, including: the mechanism of the
 * IP3-receptor; IP3 degradation; calcium buffering in the cytosol;
 * and refilling of the endoplasmic reticulum (ER) calcium stores
 * via sarcoplasmic endoplasmic reticulum ATPase (SERCA) pumps.
 * 
 * The calcium response to IP3 release and its subsequent degradation
 * were modelled using Vitual Cell software. By combining experimental
 * and modelling approaches, IP3 and Ca2+ time courses can be directly
 * compared.
 * 
 * Determination of Time-Dependent Inositol-1,4,5-Trisphosphate
 * Concentrations during Calcium Release in a Smooth Muscle Cell,
 * Charles C. Fink, Boris Slepchenko, and Leslie M. Loew, 1999,
 * Biophysical Journal, 77, 617-628. (Full text and PDF versions
 * of the article are available to subscribers on the Biophysical
 * Journal website.) PubMed ID: 10388776
 * 
 * Schematic diagram of model
 * 
 * [[Image file: fink_1999.png]]
 */

import nsrunit;
unit conversion on;
// unit micromolar predefined
// unit micrometre predefined
unit micromolar_micrometre_per_second=1E-9 meter^(-2)*second^(-1)*mole^1;
unit micrometre_per_second=1E-6 meter^1*second^(-1);
unit micrometre_2_per_second=1E-12 meter^2*second^(-1);
unit flux=1E-3 meter^(-3)*second^(-1)*mole^1;
unit second_order_rate_constant=1E3 meter^3*second^(-1)*mole^(-1);

math main {
	//Warning:  the following variables were set 'extern' or given
	//  an initial value of '0' because the model would otherwise be
	//  underdetermined:  Ca_ex
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real Ca(time) micromolar;
	when(time=time.min) Ca=0.05;
	real J_channel(time) flux;
	real J_pump(time) flux;
	real J_leak(time) flux;
	real beta dimensionless;
	real Ca_ER micromolar;
	Ca_ER=400.0;
	real J_max flux;
	J_max=2880.0;
	real h(time) dimensionless;
	when(time=time.min) h=0.667;
	real K_act micromolar;
	K_act=0.17;
	real K_I micromolar;
	K_I=0.03;
	real K_inh micromolar;
	K_inh=0.1;
	real k_on second_order_rate_constant;
	k_on=8.0;
	real I micromolar;
	I=0.01;
	real V_max flux;
	V_max=5.85;
	real K_p micromolar;
	K_p=0.24;
	real B_end micromolar;
	B_end=12.0;
	real B_ex micromolar;
	B_ex=11.35;
	real K_end micromolar;
	K_end=0.3;
	real K_ex micromolar;
	K_ex=0.26;
	extern real Ca_ex micromolar;
	real L flux;
	L=0.0804;

	// <component name="environment">

	// <component name="Calcium_dynamics">
	Ca:time=(beta*(J_channel-J_pump+J_leak));

	// <component name="ER">

	// <component name="Channel_kinetics">
	J_channel=(J_max*(I/(I+K_I)*(Ca/(Ca+K_act))*h)^3*(1-Ca/Ca_ER));
	h:time=(k_on*(K_inh-h*(Ca+K_inh)));

	// <component name="SERCA_pump_kinetics">
	J_pump=(V_max*(Ca^2/(Ca^2+K_p^2)));

	// <component name="Calcium_buffering">
	beta=((1+B_end/K_end+B_ex*K_ex/(Ca_ex+K_ex)^2)^(-1));

	// <component name="Leak">
	J_leak=(L*(1-Ca/Ca_ER));
}