/*
 * Multiple Modes of Calcium-induced Calcium Release in Sympathetic
 * Neurons
 * 
 * Model Status
 * 
 * This model is consistently represented within the CellML but
 * contains sets of algebraic equations that prevent the model
 * from being solved in currently available software - 03/08.
 * 
 * Model Structure
 * 
 * Calcium is an important signalling ion, and changes in Ca2+
 * concentration ([Ca2+]) regulate diverse processes in many cellular
 * compartments. In excitable cells, depolarisation-induced Ca2+
 * entry increases [Ca2+]i, leading to secondary changes in [Ca2+]
 * within organelles such as mitochondria and ER that regulate
 * specific Ca2+-sensitive targets within these organelles. Although
 * mitochondria accumulate Ca2+ in response to depolarisation-evoked
 * [Ca2+]i elevations (see The Colegrove et al Model Of Mitochondrial
 * Ca2+ Uptake And Release, 2000), the ER has been described as
 * either a Ca2+ source or sink. Different modes of net ER Ca2+
 * transport are expected to have very different effects on cytoplasmic
 * and intraluminal Ca2+ signals and on the processes they regulate.
 * 
 * In their 2001 model, Meredith A. Albrecht, Stephen L. Colegrove,
 * Jarin Hongpaisan, Natalia B. Pivovarova, S. Brian Andrews and
 * David D. Friel have examined the relationship between changes
 * in [Ca2+]i and [Ca2+]ER during weak depolarisation in sympathetic
 * neurons. The total Ca2+ flux during the recovery phase following
 * membrane depolarisation was divided into four components (see
 * below). One representing net Ca2+ extrusion across the plasma
 * membrane (Jextru), one representing Ca2+ entry through voltage-gated
 * Ca2+ channels (JICa), one representing ER Ca2+ uptake via a
 * Ca2+ ATPase (JSERCA) and one representing passive ER Ca2+ release.
 * 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:
 * 
 * Multiple Modes of Calcium-induced Calcium Release in Sympathetic
 * Neurons I: Attenuation of Endoplasmic Reticulum Ca2+ Accumulation
 * at Low [Ca2+]i during Weak Depolarisation, Meredith A. Albrecht,
 * Stephen L. Colegrove, Jarin Hongpaisan, Natalia B. Pivovarova,
 * S. Brian Andrews and David D. Friel, 2001, The Journal Of General
 * Physiology, 118, 83-100. (Full text and PDF versions of the
 * article are available for Journal Members on the JGP website.)
 * PubMed ID: 11429446
 * 
 * cell schematic for the model
 * 
 * [[Image file: albrecht_2001.png]]
 * 
 * Schematic of the model indicating Ca2+ compartmentation in the
 * extracellular matrix, cytosol and the ER and pathways for Ca2+
 * ion movement between the compartments.
 */

import nsrunit;
unit conversion on;
unit per_second=1 second^(-1);
// unit millivolt predefined
// unit millimolar 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;
unit coulomb_per_millimole=1E3 second^1*ampere^1*mole^(-1);
unit picoA=1E-12 ampere^1;

math main {
	//Warning:  the following variables were set 'extern' or given
	//  an initial value of '0' because the model would otherwise be
	//  underdetermined:  v_i, k_i, I_Ca, Ca_i, Ca_ER, k_ER
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real J_ICa nanomolar_per_second;
	extern real v_i micro_litre;
	extern real k_i dimensionless;
	real F coulomb_per_millimole;
	F=96.5;
	extern real I_Ca picoA;
	real J_pm(time) nanomolar_per_second;
	real J_extru(time) nanomolar_per_second;
	real k_leak per_second;
	k_leak=0.00000015;
	real Vmax_extru nanomolar_per_second;
	Vmax_extru=25.0;
	real EC50_extru nanomolar;
	EC50_extru=386.0;
	real n_extru dimensionless;
	n_extru=2.4;
	real Ca_o millimolar;
	Ca_o=2.0;
	real Ca_i(time) nanomolar;
	//Warning:  Assuming zero initial condition; nothing provided in original CellML model.
	when(time=time.min) Ca_i=0;
	real J_SERCA(time) nanomolar_per_second;
	real Vmax_SERCA nanomolar_per_second;
	Vmax_SERCA=70.0;
	real EC50_SERCA nanomolar;
	EC50_SERCA=700.0;
	real n_SERCA dimensionless;
	n_SERCA=1.0;
	real J_ER(time) nanomolar_per_second;
	real P_ER(time) per_second;
	real P_basal per_second;
	P_basal=0.0000178;
	real Pmax_RyR per_second;
	Pmax_RyR=0.0009;
	real EC50_RyR micromolar;
	EC50_RyR=1.0;
	real n_RyR dimensionless;
	n_RyR=1.0;
	real J_release(time) nanomolar_per_second;
	real Ca_ER(time) nanomolar;
	//Warning:  Assuming zero initial condition; nothing provided in original CellML model.
	when(time=time.min) Ca_ER=0;
	real J_i(time) nanomolar_per_second;
	real v_ER micro_litre;
	extern real k_ER dimensionless;
	real gamma_ER dimensionless;
	gamma_ER=0.01;

	// <component name="environment">

	// <component name="total_cytoplasmic_Ca_flux">
	J_ICa=(I_Ca/(2*F*v_i*k_i));

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

	// <component name="Ca_uptake_by_SR_Ca_ATPase">
	J_SERCA=(Vmax_SERCA/(1+(EC50_SERCA/Ca_i)^n_SERCA));

	// <component name="ER_Ca_release">
	J_release=(P_ER*(Ca_i-Ca_ER));
	J_ER=(J_SERCA+J_release);
	P_ER=(P_basal+Pmax_RyR/(1+(EC50_RyR/Ca_i)^n_RyR));

	// <component name="cytoplasmic_calcium">
	Ca_i:time=((-1)*J_i);
	J_i=(J_pm+J_ER);

	// <component name="intraluminal_calcium">
	Ca_ER:time=(J_ER/gamma_ER);
	gamma_ER=(v_ER*k_ER/(v_i*k_i));
}