/*
 * Modelling HERG-KCNE2 Functional Interaction
 * 
 * Model Structure
 * 
 * The protein products of the genes HERG and KCNE2 form the subunits
 * of the rapid delayed rectifier potassium channel (IK,r). Mutations
 * in KCNE2 have been associated with acquired long-QT syndrome
 * and ventricular fibrillation, whilst mutations in the HERG gene
 * have been associated with the inherited form of the disease.
 * The mechansisms underlying the KCNE mutation-induced cardiac
 * arrhythmias are not clear. An improved understanding of the
 * functional interactions between the two gene products could
 * facilitate the development of superior therapeutic approaches
 * for particular lesions in either HERG or KCNE2.
 * 
 * In the study described here, Mazhari et al. characterise the
 * functional effects of KCNE2 coexpression with HERG. They develop
 * a Markov state model of both HERG and HERG-KCNE2 coassembly
 * (see below), and use this model to elucidate mechanisms of interaction.
 * In addition, ion channel gating models provide a quantitative
 * description of gating behaviour and they provide clues to channel
 * strcture. In order to predict the consequences of HERG-KCNE2
 * interactions for action potential repolarisation, the Markov
 * state model was embedded within the Winslow et al. Canine Ventricular
 * Cell Model, 1999.
 * 
 * The model has been described here in CellML (the raw CellML
 * description of the Mazhari et al. 2001 model can be downloaded
 * in various formats as described in ).
 * 
 * The complete original paper reference is cited below:
 * 
 * Molecular Interactions Between Two Long-QT Syndrome Gene Products,
 * HERG and KCNE2, Rationalized by In Vitro and In Silico Analysis,
 * Reza Mazhari, Joseph L. Greenstein, Raimond L. Winslow, Eduardo
 * Marban, and H. Bradley Nuss, 2001, Circulation Research, 89,
 * 33-38. PubMed ID: 11440975
 * 
 * reaction diagram
 * 
 * [[Image file: mazhari_2001.png]]
 * 
 * State diagram of the HERG and HERG+hKCNE2 Marcov model. C1,
 * C2, and C3 are closed states. O is the open state, and I is
 * the inactivated state.
 * 
 * While coexpression of HERG and KCNE2 alters both the kinetics
 * and density of the ionic current, including these effects in
 * the Winslow et al. action potential model predicts that only
 * changes in current density significantly affect repolarisation.
 * Therefore the main functional consequence of KCNE2 on action
 * potential morphology is through modulation of IK,r density.
 * The mutations associated with long-QT syndrome that result in
 * only modest changes of gating kinetics may be an epiphenomena
 * or alternatively, they may modulate action potential repoalrisation
 * via interactions with alternative pore-forming potassium channel
 * alpha subunits.
 */

import nsrunit;
// Warning: unit conversion turned off due to unit errors in 9 equation(s)
unit conversion off;
// unit millivolt predefined
// unit micromolar predefined
unit first_order_rate_constant=1 second^(-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:  C1, C2, C3, I, O
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real Vm millivolt;
	Vm=-80.0;
	real C1(time) dimensionless;
	//Warning:  Assuming zero initial condition; nothing provided in original CellML model.
	when(time=time.min) C1=0;
	real alpha_0 first_order_rate_constant;
	real beta_0 first_order_rate_constant;
	real C2(time) dimensionless;
	//Warning:  Assuming zero initial condition; nothing provided in original CellML model.
	when(time=time.min) C2=0;
	real Kf first_order_rate_constant;
	Kf=0.0266;
	real Kb first_order_rate_constant;
	Kb=0.1348;
	real C3(time) dimensionless;
	//Warning:  Assuming zero initial condition; nothing provided in original CellML model.
	when(time=time.min) C3=0;
	real alpha_1 first_order_rate_constant;
	real beta_1 first_order_rate_constant;
	real alpha_i3 first_order_rate_constant;
	real psi first_order_rate_constant;
	real I(time) dimensionless;
	//Warning:  Assuming zero initial condition; nothing provided in original CellML model.
	when(time=time.min) I=0;
	real O(time) dimensionless;
	//Warning:  Assuming zero initial condition; nothing provided in original CellML model.
	when(time=time.min) O=0;
	real alpha_i first_order_rate_constant;
	real beta_i first_order_rate_constant;

	// <component name="environment">

	// <component name="membrane">

	// <component name="C1">
	C1:time=(beta_0*C2-alpha_0*C1);

	// <component name="C2">
	C2:time=(alpha_0*C1+Kb*C3-(beta_0*C2+Kf*C2));

	// <component name="C3">
	C3:time=(beta_1*O+Kf*C2+psi*I-(alpha_i3*C3+alpha_1*C3+Kb*C3));

	// <component name="O">
	O:time=(alpha_1*C3+beta_i*I-(beta_1*O+alpha_i*O));

	// <component name="I">
	I:time=(alpha_i*O+alpha_i3*C3-(beta_i*I+psi*I));

	// <component name="reaction_constants">
	psi=(beta_1*beta_i*alpha_i3/(alpha_1*alpha_i));
	beta_0=((.0227 first_order_rate_constant)*exp((-0.0431)*Vm));
	alpha_0=((.0069 first_order_rate_constant)*exp(.0272*Vm));
	beta_1=((9E-4 first_order_rate_constant)*exp((-0.0269)*Vm));
	alpha_1=((.0218 first_order_rate_constant)*exp(.0262*Vm));
	beta_i=((.0059 first_order_rate_constant)*exp((-0.0443)*Vm));
	alpha_i=((.0622 first_order_rate_constant)*exp(.012*Vm));
	alpha_i3=((1.2899999999999998E-5 first_order_rate_constant)*exp(2.71E-6*Vm));
}