/*
 * Modelling Sarcoplasmic Reticulum Calcium APTase and its Regulation
 * in Cardiac Myocytes
 * 
 * Model Status
 * 
 * This CellML model runs in PCenv, COR and OpenCell to recreate
 * the published results. This model only describes the standalone
 * SERCA pump, and is based on the original matlab code dy_buffering_serca.
 * Other versions of this model couple the SERCA pump to a reduced
 * cardiac myocyte model.
 * 
 * Model Structure
 * 
 * ABSTRACT: When developing large-scale mathematical models of
 * physiology, some reduction in complexity is necessarily required
 * to maintain computational efficiency. A prime example of such
 * an intricate cell is the cardiac myocyte. For the predictive
 * power of the cardiomyocyte models, it is vital to accurately
 * describe the calcium transport mechanisms, since they essentially
 * link the electrical activation to contractility. The removal
 * of calcium from the cytoplasm takes place mainly by the Na(+)/Ca(2+)
 * exchanger, and the sarcoplasmic reticulum Ca(2+) ATPase (SERCA).
 * In the present study, we review the properties of SERCA, its
 * frequency-dependent and beta-adrenergic regulation, and the
 * approaches of mathematical modelling that have been used to
 * investigate its function. Furthermore, we present novel theoretical
 * considerations that might prove useful for the elucidation of
 * the role of SERCA in cardiac function, achieving a reduction
 * in model complexity, but at the same time retaining the central
 * aspects of its function. Our results indicate that to faithfully
 * predict the physiological properties of SERCA, we should take
 * into account the calcium-buffering effect and reversible function
 * of the pump. This 'uncomplicated' modelling approach could be
 * useful to other similar transport mechanisms as well.
 * 
 * model diagram
 * 
 * [[Image file: koivumaki_2009a.png]]
 * 
 * Schematic diagram of SERCA pump.
 * 
 * The original paper reference is cited below:
 * 
 * Modelling Sarcoplasmic Reticulum Calcium APTase and its Regulation
 * in Cardiac Myocytes, Jussi T. Koivumaki, Jouni Takalo, Topi
 * Korhonen, Pasi Tavi, Matti Weckstrom, 2009, Phil. Trans. R.
 * Soc. A, volume 367, 2181-2202. PubMed ID: 19414452
 */

import nsrunit;
unit conversion on;
unit uM=1E-3 meter^(-3)*mole^1;
unit per_uM2=1E6 meter^6*mole^(-2);
unit msec=.001 second^1;
unit per_msec=1E3 second^(-1);
unit uM_per_msec=1 meter^(-3)*second^(-1)*mole^1;
unit per_msec_per_uM2=1E9 meter^6*second^(-1)*mole^(-2);

math main {
	realDomain time msec;
	time.min=0;
	extern time.max;
	extern time.delta;
	real Ca_cyt uM;
	Ca_cyt=0.25;
	real Ca_NSR uM;
	Ca_NSR=760;
	real CaMKII_reg dimensionless;
	CaMKII_reg=0;
	real SERCA_TOT uM;
	SERCA_TOT=47;
	real PSR dimensionless;
	PSR=1;
	real Kmf_PLBKO uM;
	Kmf_PLBKO=0.15;
	real Kmf_PLB uM;
	Kmf_PLB=0.15;
	real Kmr_PLBKO uM;
	Kmr_PLBKO=2500;
	real Kmr_PLB uM;
	Kmr_PLB=1110;
	real EC_50_fwd uM;
	real EC_50_rev uM;
	real k_cyt_serca per_msec_per_uM2;
	real k_serca_cyt per_msec;
	real k_serca_sr per_msec;
	real k_sr_serca per_msec_per_uM2;
	real br_cyt_serca per_msec_per_uM2;
	real br_serca_sr per_msec;
	br_serca_sr=0.00625;
	real J_cyt_serca(time) uM_per_msec;
	real J_serca_sr(time) uM_per_msec;
	real Ca_serca(time) uM;
	when(time=time.min) Ca_serca=12;

	// <component name="environment">

	// <component name="general_parameters">

	// <component name="serca_parameters">
	EC_50_fwd=((Kmf_PLBKO+Kmf_PLB*PSR)*(1+.27*CaMKII_reg));
	EC_50_rev=(Kmr_PLBKO-Kmr_PLB*PSR);

	// <component name="transition_parameters">
	br_cyt_serca=((1E3 per_uM2)*br_serca_sr);
	k_cyt_serca=(br_cyt_serca*(1+.7*CaMKII_reg));
	k_serca_cyt=(EC_50_fwd^2*br_cyt_serca);
	k_serca_sr=(br_serca_sr*(1+.7*CaMKII_reg));
	k_sr_serca=(br_serca_sr/EC_50_rev^2);

	// <component name="calcium_fluxes">
	J_cyt_serca=(k_cyt_serca*Ca_cyt^2*(SERCA_TOT-Ca_serca)-k_serca_cyt*Ca_serca);
	J_serca_sr=(k_serca_sr*Ca_serca-k_sr_serca*Ca_NSR^2*(SERCA_TOT-Ca_serca));

	// <component name="calcium_bound_serca">
	Ca_serca:time=(J_cyt_serca-J_serca_sr);
}