/*
 * Quantitative Analysis Of Mitochondrial Ca2+ Uptake And Release
 * Pathways In Sympathetic Neurons
 * 
 * Model Status
 * 
 * This model can not be solved as it is unsuitably constrained.
 * 
 * ValidateCellML verifies this model as valid CellML with consistent
 * units.
 * 
 * Model Structure
 * 
 * One of the central goals in the study of calcium signalling
 * is to understand the basis of [Ca2+] dynamics. This is complicated
 * by the fact that Ca2+ is present in several membrane-bound intracellular
 * compartments, each of which uses a distinct Ca2+ transport system
 * and the rate of Ca2+ transport between these compartments can
 * exhibit a complex non-linear dependence on free [Ca2+].
 * 
 * In their 2000 model, Stephen L. Colegrove, Meredith A. Albrecht
 * and David D. Friel have studied how mitochondrial Ca2+ transport
 * contributes to the redistribution of intracellular Ca2+ during
 * and after depolarisation-evoked Ca2+ entry in sympathetic neurons.
 * The total Ca2+ flux during the recovery phase following membrane
 * depolarisation was divided into three components (see below):
 * one representing net Ca2+ extrusion across the plasma membrane
 * (Jextru), one representing mitochondrial Ca2+ uptake via the
 * uniporter (Juni) and one representing mitochondrial Ca2+ release
 * via the Na+/Ca2+ exchanger (JNaCa). This mathematical model
 * has been translated into a CellML description which can be downloaded
 * in various formats as described in .
 * 
 * The complete original paper reference is cited below:
 * 
 * Quantitative Analysis of Mitochondrial Ca2+ Uptake and Release
 * Pathways in Sympathetic Neurons Reconstruction of the Recovery
 * after Depolarisation-evoked [Ca2+] Elevations , Stephen L. Colegrove,
 * Meredith A. Albrecht and David D. Friel, 2000, The Journal Of
 * General Physiology , 115, 371-388. PubMed ID: 10694264
 * 
 * cell schematic for the model
 * 
 * [[Image file: colegrove_2000.png]]
 * 
 * Schematic of the model indicating Ca2+ compartmentalization
 * in the extracellular matrix, cytosol and the mitochondrial matrix
 * and pathways for Ca2+ ion movement between the compartments.
 */

import nsrunit;
unit conversion on;
unit per_second=1 second^(-1);
// unit millivolt predefined
// unit micromolar predefined
// unit nanomolar predefined
unit nanomolar_per_second=1E-6 meter^(-3)*second^(-1)*mole^1;
unit micromolar_per_second=1E-3 meter^(-3)*second^(-1)*mole^1;
unit micro_litre=1E-9 meter^3;

math main {
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real J_pm(time) nanomolar_per_second;
	real J_leak(time) nanomolar_per_second;
	real J_extru(time) nanomolar_per_second;
	real k_leak per_second;
	k_leak=0.00000037;
	real Vmax_extru nanomolar_per_second;
	Vmax_extru=28.3;
	real EC50_extru nanomolar;
	EC50_extru=378.8;
	real n_extru dimensionless;
	n_extru=1.8;
	real Ca_o nanomolar;
	Ca_o=0.002;
	real Ca_i(time) nanomolar;
	when(time=time.min) Ca_i=0.002;
	real J_uni(time) nanomolar_per_second;
	real kuni_max per_second;
	kuni_max=75.9;
	real EC50_uni micromolar;
	EC50_uni=10.0;
	real n_uni dimensionless;
	n_uni=2.0;
	real J_NaCa(time) nanomolar_per_second;
	real Ca_inhibited_J_NaCa(time) nanomolar_per_second;
	real J_mito(time) nanomolar_per_second;
	real Vmax_NaCa nanomolar_per_second;
	Vmax_NaCa=-35.0;
	real EC50_NaCa nanomolar;
	EC50_NaCa=307.0;
	real n_inhib dimensionless;
	n_inhib=6.0;
	real k_inhib nanomolar;
	k_inhib=500.0;
	real delta_Ca_i(time) dimensionless;
	real Ca_m(time) nanomolar;
	when(time=time.min) Ca_m=50.0e-9;
	real gamma dimensionless;
	gamma=2.0;

	// <component name="environment">

	// <component name="Ca_extrusion_across_the_plasma_membrane">
	J_pm=(J_leak+J_extru);
	J_leak=(k_leak*(Ca_i-Ca_o));
	J_extru=(Vmax_extru/(1+(EC50_extru/Ca_i)^n_extru));

	// <component name="mitochondrial_Ca_uptake">
	J_uni=(kuni_max*Ca_i/(1+(EC50_uni/Ca_i)^n_uni));

	// <component name="mitochondrial_Ca_release">
	J_NaCa=((-1)*Vmax_NaCa/(1+EC50_NaCa/Ca_m));
	Ca_inhibited_J_NaCa=((-1)*(delta_Ca_i*Vmax_NaCa)/(1+EC50_NaCa/Ca_i));
	delta_Ca_i=(1-1/(1-(k_inhib/Ca_i)^n_inhib));
	J_mito=(J_uni+J_NaCa);

	// <component name="intracellular_calcium">
	Ca_i:time=((-1)*(J_pm+J_mito));

	// <component name="mitochondrial_calcium">
	Ca_m:time=(J_mito/gamma);
}