/*
 * Mechanism of constant contractile efficiency under cooling inotropy
 * of myocardium: simulationy
 * 
 * Model Status
 * 
 * This model is known to run in both OpenCell and COR. It is an
 * accurate match to the paper equations but it does not recreate
 * all the published results.
 * 
 * Model Structure
 * 
 * Abstract: We have reported that, in canine hearts, cardiac cooling
 * to 29C enhanced left ventricular contractility but changed neither
 * the contractile efficiency of cross-bridge (CB) cycling nor
 * the excitation-contraction coupling energy. The mechanism of
 * this intriguing energetics remained unknown. To get insights
 * into this mechanism, we simulated myocardial cooling mechanoenergetics
 * using basic Ca2+ and CB kinetics. We assumed that both adenosinetriphosphatase
 * (ATPase)-dependent sarcoplasmic reticulum (SR) Ca2+ uptake and
 * CB detachment decelerated with cooling. We also assumed that
 * all the ATPase-independent SR Ca2+ release, Ca2+ binding to
 * and dissociation from troponin, and CB attachment remained unchanged.
 * The simulated cooling shifted the CB force-free Ca2+ concentration
 * curve to a lower Ca2+ concentration, increasing the Ca2+ responsiveness
 * of CB force generation, and increased the maximum Ca2+-activated
 * force. The simulation most importantly showed that these cooling
 * effects combined led to a constant contractile efficiency when
 * Ca2+ uptake and CB detachment rate constants changed appropriately.
 * This result seems to account for our experimentally observed
 * constant contractile efficiency under cooling inotropy.
 * 
 * model diagram Schematic diagram of the Mikane et al model. The
 * effect of calcium and troponin on cross bridge (CB) cycling
 * is also demonstrated.
 * 
 * The complete original paper reference is cited below:
 * 
 * Mechanism of constant contractile efficiency under cooling inotropy
 * of myocardium: simulation, Takeshi Mikane, Junichi Araki, Kunihisa
 * Kohno, Yasunori Nakayama, Shunsuke Suzuki, Juichiro Shimizu,
 * Hiromi Matsubara, Masahisa Hirakawa, Miyako Takaki, and Hiroyuki
 * Suga, 1997, American Journal of Physiology, 273, H2891-H2898.
 * PubMed ID: 9435629
 */

import nsrunit;
unit conversion on;
unit per_second=1 second^(-1);
unit uM_per_kg=1E-6 kilogram^(-1)*mole^1;
unit uM_per_kg_per_second=1E-6 kilogram^(-1)*second^(-1)*mole^1;
unit kg_per_uM_per_second=1E6 kilogram^1*second^(-1)*mole^(-1);

math main {
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real Ca_t(time) uM_per_kg;
	when(time=time.min) Ca_t=0;
	real TnCa_t(time) uM_per_kg;
	when(time=time.min) TnCa_t=0;
	real CB_on_t(time) uM_per_kg;
	when(time=time.min) CB_on_t=0;
	real Ca_released(time) uM_per_kg;
	when(time=time.min) Ca_released=0;
	real Ca_sequestered(time) uM_per_kg;
	when(time=time.min) Ca_sequestered=0;
	real cumCB_on_t(time) uM_per_kg;
	when(time=time.min) cumCB_on_t=0;
	real cumCB_off_t(time) uM_per_kg;
	when(time=time.min) cumCB_off_t=0;
	real Ca_release_rate(time) uM_per_kg_per_second;
	real dTnCa_t_dt(time) uM_per_kg_per_second;
	real Ca_tot_released uM_per_kg;
	Ca_tot_released=35;
	real total_Tn uM_per_kg;
	total_Tn=70;
	real total_CB uM_per_kg;
	total_CB=150;
	real k_1 kg_per_uM_per_second;
	k_1=5e6;
	real k_2 per_second;
	k_2=10;
	real k_3 per_second;
	k_3=1000;
	real f kg_per_uM_per_second;
	f=0.4e6;
	real g per_second;
	g=10;

	// <component name="environment">

	// <component name="equations">
	Ca_release_rate=(if (time>(.1 second)) (0 uM_per_kg_per_second) else (20 per_second)*Ca_tot_released*(1-(10 per_second)*time));
	Ca_t:time=(Ca_release_rate-k_3*Ca_t-dTnCa_t_dt);
	TnCa_t:time=(k_1*Ca_t*(total_Tn-TnCa_t)-k_2*TnCa_t);
	dTnCa_t_dt=(k_1*Ca_t*(total_Tn-TnCa_t)-k_2*TnCa_t);
	CB_on_t:time=(f*TnCa_t*(total_CB-CB_on_t)-g*CB_on_t);
	Ca_released:time=Ca_release_rate;
	Ca_sequestered:time=(k_3*Ca_t);
	cumCB_on_t:time=(f*TnCa_t*(total_CB-CB_on_t));
	cumCB_off_t:time=(g*CB_on_t);
}