/*
 * Biophysical Characteristics of the Pig Kidney Na/Glucose Cotransporter
 * SGLT2 Reveal a Common Mechanism for SGLT1 and SGLT2
 * 
 * Model Status
 * 
 * This CellML model has been curated, the units are consistent
 * and the model runs in COR and PCEnv. This model recreates the
 * published results.
 * 
 * Model Structure
 * 
 * Abstract: The Na-dependent, low affinity glucose transporter
 * SGLT2 cloned from pig kidney is 76% identical (at the amino
 * acid level) to its high affinity homologue SGLT1. Using two-microelectrode
 * voltage clamp, we have characterized the presteady-state and
 * steady-state kinetics of SGLT2 expressed in Xenopus oocytes.
 * The kinetic properties of the steady-state sugar-evoked currents
 * as a function of external Na and a-methyl-D-glucopyranoside
 * (aMG) concentrations were consistent with an ordered, simultaneous
 * transport model in which Na binds first. Na binding was voltage-dependent
 * and saturated with hyperpolarizing voltages. Phlorizin was a
 * potent inhibitor of the sugar-evoked currents (Ki ~10 mM) and
 * blocked an inward Na current in the absence of sugar. SGLT2
 * exhibited Na-dependent presteadystate currents with time constants
 * 3-7 ms. Charge movements were described by Boltzmann relations
 * with apparent valence ~1 and maximal charge transfer ~11 nC,
 * and were reduced by the addition of sugar or phlorizin. The
 * differences between SGLT1 and SGLT2 were that (i) the apparent
 * affinity constant (K0.5) for aMG (~3 mM) was an order of magnitude
 * higher for SGLT2; (ii) SGLT2 excluded galactose, suggesting
 * discrete sugar binding; (iii) K0.5 for Na was lower in SGLT2;
 * and (iv) the Hill coefficient for Na was 1 for SGLT2 but 2 for
 * SGLT1. Simulations of the six-state kinetic model previously
 * proposed for SGLT1 indicated that many of the kinetic properties
 * observed in SGLT2 are expected by simply reducing the Na/glucose
 * coupling from 2 to 1.
 * 
 * The original paper reference is cited below:
 * 
 * Biophysical Characteristics of the Pig Kidney Na/Glucose Cotransporter
 * SGLT2 Reveal a Common Mechanism for SGLT1 and SGLT2, M. Mackenzie,
 * D.D.F. Loo, M. Panayotova-Heiermann, and E. M. Wright, 1996,
 * Journal of Biological Chemistry, 271, 32678-32683. PubMed ID:
 * 8955098
 * 
 * model diagram
 * 
 * [[Image file: mackenzie_1996.png]]
 * 
 * Schematic diagram of the Mackenzie et al 1996 SGLT2 model. C'
 * represents the external-facing carrier. C'' represents the internal-facing
 * carrier.
 */

import nsrunit;
unit conversion on;
unit per_second=1 second^(-1);
unit per_second5=1 second^(-5);
unit per_mol=1 mole^(-1);
unit umol=1E-6 mole^1;
unit M=1E3 meter^(-3)*mole^1;
unit um2=1E-12 meter^2;
unit mol_per_um2=1E12 meter^(-2)*mole^1;
unit mM=1 meter^(-3)*mole^1;
unit mV=.001 kilogram^1*meter^2*second^(-3)*ampere^(-1);
unit J_per_K_per_mol=1 kilogram^1*meter^2*second^(-2)*kelvin^(-1)*mole^(-1);
unit pA_per_cm2=1E-8 meter^(-2)*ampere^1;
unit uA=1E-6 ampere^1;
unit uA_per_um2=1E6 meter^(-2)*ampere^1;
unit uA_per_A=1E-6  dimensionless;
unit umol_per_mol=1E-6  dimensionless;
unit umol_per_second=1E-6 second^(-1)*mole^1;
unit C_per_mol=1 second^1*ampere^1*mole^(-1);
unit per_M2_per_second=1E-6 meter^6*second^(-1)*mole^(-2);
unit M2=1E6 meter^(-6)*mole^2;
unit M3=1E9 meter^(-9)*mole^3;
unit M2_per_second=1E6 meter^(-6)*second^(-1)*mole^2;
unit per_M2_per_second5=1E-6 meter^6*second^(-5)*mole^(-2);
unit M_per_second=1E3 meter^(-3)*second^(-1)*mole^1;
unit per_M_per_second=.001 meter^3*second^(-1)*mole^(-1);
unit volt_per_second=1 kilogram^1*meter^2*second^(-4)*ampere^(-1);

math main {
	realDomain time second;
	time.min=0;
	extern time.max;
	extern time.delta;
	real k0_12 per_M_per_second;
	k0_12=20000;
	real k0_21 per_second;
	k0_21=400;
	real k0_23 per_M_per_second;
	k0_23=1e4;
	real k0_32 per_second;
	k0_32=20;
	real k0_34 per_second;
	k0_34=50;
	real k0_43 per_second;
	k0_43=50;
	real k0_45 per_second;
	k0_45=800;
	real k0_54 per_M_per_second;
	k0_54=6.7e6;
	real k0_25 per_second;
	k0_25=0.01;
	real k0_52 per_second;
	k0_52=0.17;
	real k0_56 per_second;
	k0_56=48;
	real k0_65 per_M_per_second;
	k0_65=50;
	real k0_61 per_second;
	k0_61=35;
	real k0_16 per_second;
	k0_16=100;
	real delta dimensionless;
	delta=0.7;
	real alpha_p dimensionless;
	real alpha_pp dimensionless;
	alpha_pp=0;
	real N_C dimensionless;
	N_C=8.4e10;
	real N_Avo per_mol;
	N_Avo=6.022e23;
	real area um2;
	area=1e6;
	real C_T umol;
//	Var below replaced by constant in model eqns to satisfy unit correction
//	real n dimensionless;
//	n=1;
	real z_c dimensionless;
	z_c=-1;
	real z_Na dimensionless;
	z_Na=1;
	real F C_per_mol;
	F=96485.34;
	real R J_per_K_per_mol;
	R=8.314;
	real T kelvin;
	T=310;
	real V(time) volt;
	when(time=time.min) V=-150e-3;
	real mu(time) dimensionless;
	real Na_i M;
	Na_i=10e-3;
	real Na_o M;
	Na_o=100e-3;
	real glucose_i M;
	glucose_i=0e-3;
	real glucose_o M;
	glucose_o=1e-3;
	real k_12(time) per_second;
	real k_21(time) per_second;
	real k_23 per_second;
	real k_32 per_second;
	real k_34(time) per_second;
	real k_43(time) per_second;
	real k_45 per_second;
	real k_54(time) per_second;
	real k_25(time) per_second;
	real k_52(time) per_second;
	real k_56(time) per_second;
	real k_65(time) per_second;
	real k_61(time) per_second;
	real k_16(time) per_second;
	real ks_12(time) per_M_per_second;
	real k0_54_temp(time) per_M_per_second;
	real k_52_temp(time) per_second;
	real C_1(time) umol;
	when(time=time.min) C_1=3.923e-9;
	real C_2(time) umol;
	when(time=time.min) C_2=1.016e-7;
	real C_3(time) umol;
	when(time=time.min) C_3=1.515e-8;
	real C_4(time) umol;
	when(time=time.min) C_4=8.912e-10;
	real C_5(time) umol;
	when(time=time.min) C_5=1.485e-8;
	real C_6(time) umol;
	real C_6_temp(time) umol;
	when(time=time.min) C_6_temp=3.06798e-9;
	real C1_sum(time) per_second5;
	real C2_sum(time) per_second5;
	real C3_sum(time) per_second5;
	real C4_sum(time) per_second5;
	real C5_sum(time) per_second5;
	real C6_sum(time) per_second5;
	real C_sum(time) per_second5;
	real C1(time) umol;
	real C2(time) umol;
	real C3(time) umol;
	real C4(time) umol;
	real C5(time) umol;
	real C6(time) umol;
	real I_NaGl_pSS(time) uA;
	real I_NaGl_SS(time) uA;
	real J_Na(time) umol_per_second;
	real epsilon(time) per_second;
	real lambda(time) per_M2_per_second5;
	real chi(time) M;
	real alpha(time) M2;
	real beta(time) M;
	real gamma(time) M2_per_second;
	real phi(time) M_per_second;
	real Imax_Na(time) uA;
	real Imax_gluc(time) uA;
	real Khalf_Na(time) M;
	real Khalf_gluc(time) M;

	// <component name="environment">

	// <component name="parameters">
	alpha_p=(1-delta-alpha_pp);
	C_T=((1E6 umol_per_mol)*N_C/N_Avo);
	mu=(F*V/(R*T));

	// <component name="ion_concentrations">
	V:time=(9.999999999999999E-5 volt_per_second);

	// <component name="rate_constants">
	ks_12=(k0_12*exp((-1)*1*alpha_p*mu/2));
	k_12=(ks_12*Na_o^1);
	k_21=(k0_21*exp(1*z_Na*alpha_p*mu/2));
	k_23=(k0_23*glucose_o);
	k_32=k0_32;
	k_34=(k0_34*exp((-1)*(z_c+1)*delta*mu/2));
	k_43=(k0_43*exp((z_c+1)*delta*mu/2));
	k_45=k0_45;
	k_54=(k0_54_temp*glucose_i);
	k_25=(k0_25*exp((-1)*(z_c+1)*delta*mu/2));
	k_52_temp=(k0_52*exp((z_c+1)*delta*mu/2));
	k_56=(k0_56*exp((-1)*1*z_Na*alpha_pp*mu/2));
	k_65=(k0_65*Na_i^1*exp(1*z_Na*alpha_pp*mu/2));
	k_61=(k0_61*exp(z_c*delta*mu/2));
	k_16=(k0_16*exp((-1)*z_c*delta*mu/2));
	k_52=(k0_12*k_25*k0_56*k0_61/(k0_21*k0_16*k0_65));
	k0_54_temp=(k0_23*k_34*k_45*k_52/(k_43*k_32*k_25));

	// <component name="kinetic_equations">
	C_1:time=(k_21*C_2+k_61*C_6-(k_12+k_16)*C_1);
	C_2:time=(k_12*C_1+k_32*C_3+k_52*C_5-(k_21+k_23+k_25)*C_2);
	C_3:time=(k_23*C_2+k_43*C_4-(k_32+k_34)*C_3);
	C_4:time=(k_34*C_3+k_54*C_5-(k_45+k_43)*C_4);
	C_5:time=(k_45*C_4+k_65*C_6+k_25*C_2-(k_54+k_52+k_56)*C_5);
	C_6_temp:time=(k_16*C_1+k_56*C_5-(k_61+k_65)*C_6_temp);
	C_6=(C_T-(C_1+C_2+C_3+C_4+C_5));

	// <component name="king_altman_states">
	C1_sum=(k_21*k_32*k_43*k_54*k_65+k_21*k_34*k_45*k_52*k_65+k_21*k_32*k_45*k_52*k_65+k_21*k_32*k_43*k_52*k_65+k_25*k_34*k_45*k_56*k_61+k_23*k_34*k_45*k_56*k_61+k_21*k_34*k_45*k_56*k_61+k_25*k_32*k_45*k_56*k_61+k_21*k_32*k_45*k_56*k_61+k_25*k_32*k_43*k_56*k_61+k_21*k_32*k_43*k_56*k_61+k_21*k_32*k_43*k_54*k_61+k_21*k_34*k_45*k_52*k_61+k_21*k_32*k_45*k_52*k_61+k_21*k_32*k_43*k_52*k_61);
	C2_sum=(k_16*k_32*k_43*k_54*k_65+k_12*k_32*k_43*k_54*k_65+k_16*k_34*k_45*k_52*k_65+k_12*k_34*k_45*k_52*k_65+k_16*k_32*k_45*k_52*k_65+k_12*k_32*k_45*k_52*k_65+k_16*k_32*k_43*k_52*k_65+k_12*k_32*k_43*k_52*k_65+k_12*k_34*k_45*k_56*k_61+k_12*k_32*k_45*k_56*k_61+k_12*k_32*k_43*k_56*k_61+k_12*k_32*k_43*k_54*k_61+k_12*k_34*k_45*k_52*k_61+k_12*k_32*k_45*k_52*k_61+k_12*k_32*k_43*k_52*k_61);
	C3_sum=(k_16*k_25*k_43*k_54*k_65+k_12*k_25*k_43*k_54*k_65+k_16*k_23*k_43*k_54*k_65+k_12*k_23*k_43*k_54*k_65+k_16*k_21*k_43*k_54*k_65+k_16*k_23*k_45*k_52*k_65+k_12*k_23*k_45*k_52*k_65+k_16*k_23*k_43*k_52*k_65+k_12*k_23*k_43*k_52*k_65+k_12*k_23*k_45*k_56*k_61+k_12*k_23*k_43*k_56*k_61+k_12*k_25*k_43*k_54*k_61+k_12*k_23*k_43*k_54*k_61+k_12*k_23*k_45*k_52*k_61+k_12*k_23*k_43*k_52*k_61);
	C4_sum=(k_16*k_25*k_34*k_54*k_65+k_12*k_25*k_34*k_54*k_65+k_16*k_23*k_34*k_54*k_65+k_12*k_23*k_34*k_54*k_65+k_16*k_21*k_34*k_54*k_65+k_16*k_25*k_32*k_54*k_65+k_12*k_25*k_32*k_54*k_65+k_16*k_21*k_32*k_54*k_65+k_16*k_23*k_34*k_52*k_65+k_12*k_23*k_34*k_52*k_65+k_12*k_23*k_34*k_56*k_61+k_12*k_25*k_34*k_54*k_61+k_12*k_23*k_34*k_54*k_61+k_12*k_25*k_32*k_54*k_61+k_12*k_23*k_34*k_52*k_61);
	C5_sum=(k_16*k_25*k_34*k_45*k_65+k_12*k_25*k_34*k_45*k_65+k_16*k_23*k_34*k_45*k_65+k_12*k_23*k_34*k_45*k_65+k_16*k_21*k_34*k_45*k_65+k_16*k_25*k_32*k_45*k_65+k_12*k_25*k_32*k_45*k_65+k_16*k_21*k_32*k_45*k_65+k_16*k_25*k_32*k_43*k_65+k_12*k_25*k_32*k_43*k_65+k_16*k_21*k_32*k_43*k_65+k_12*k_25*k_34*k_45*k_61+k_12*k_23*k_34*k_45*k_61+k_12*k_25*k_32*k_45*k_61+k_12*k_25*k_32*k_43*k_61);
	C6_sum=(k_16*k_25*k_34*k_45*k_56+k_12*k_25*k_34*k_45*k_56+k_16*k_23*k_34*k_45*k_56+k_12*k_23*k_34*k_45*k_56+k_16*k_21*k_34*k_45*k_56+k_16*k_25*k_32*k_45*k_56+k_12*k_25*k_32*k_45*k_56+k_16*k_21*k_32*k_45*k_56+k_16*k_25*k_32*k_43*k_56+k_12*k_25*k_32*k_43*k_56+k_16*k_21*k_32*k_43*k_56+k_16*k_21*k_32*k_43*k_54+k_16*k_21*k_34*k_45*k_52+k_16*k_21*k_32*k_45*k_52+k_16*k_21*k_32*k_43*k_52);
	C_sum=(C1_sum+C2_sum+C3_sum+C4_sum+C5_sum+C6_sum);
	C1=(C_T*C1_sum/C_sum);
	C2=(C_T*C2_sum/C_sum);
	C3=(C_T*C3_sum/C_sum);
	C4=(C_T*C4_sum/C_sum);
	C5=(C_T*C5_sum/C_sum);
	C6=(C_T*C6_sum/C_sum);

	// <component name="NBC_current">
	I_NaGl_pSS=((-1)*F*(1*z_Na*alpha_p*(k_12*C_1-k_21*C_2)+z_c*delta*(k_16*C_1-k_61*C_6)+1*z_Na*alpha_pp*(k_56*C_5-k_65*C_6)));
	I_NaGl_SS=((-1)*F*(z_c*(k_16*C1-k_61*C6)+(z_c+z_Na*1)*(k_25*C2-k_52*C5)+(z_c+z_Na*1)*(k_34*C3-k_43*C4)));
	J_Na=(k_25*C2-k_52*C5+(k_34*C3-k_43*C4));

	// <component name="phenomonological_constants">
	lambda=(ks_12*k0_23*k_43*k_54*k_65+ks_12*k0_23*k_34*k_54*k_65+ks_12*k0_23*k_45*k_52*k_65+ks_12*k0_23*k_43*k_52*k_65+ks_12*k0_23*k_34*k_52*k_65+ks_12*k0_23*k_34*k_45*k_65+ks_12*k0_23*k_45*k_56*k_61+ks_12*k0_23*k_43*k_56*k_61+ks_12*k0_23*k_34*k_56*k_61+ks_12*k0_23*k_43*k_54*k_61+ks_12*k0_23*k_34*k_54*k_61+ks_12*k0_23*k_45*k_52*k_61+ks_12*k0_23*k_43*k_52*k_61+ks_12*k0_23*k_34*k_52*k_61+ks_12*k0_23*k_34*k_45*k_61+ks_12*k0_23*k_34*k_45*k_56);
	chi=(1/lambda*(ks_12*k_32*k_43*k_54*k_65+ks_12*k_25*k_43*k_54*k_65+ks_12*k_25*k_34*k_54*k_65+ks_12*k_25*k_32*k_54*k_65+ks_12*k_34*k_45*k_52*k_65+ks_12*k_32*k_45*k_52*k_65+ks_12*k_32*k_43*k_52*k_65+ks_12*k_25*k_34*k_45*k_65+ks_12*k_25*k_32*k_45*k_65+ks_12*k_25*k_32*k_43*k_65+ks_12*k_34*k_45*k_56*k_61+ks_12*k_32*k_45*k_56*k_61+ks_12*k_32*k_43*k_56*k_61+ks_12*k_32*k_43*k_54*k_61+ks_12*k_25*k_43*k_54*k_61+ks_12*k_25*k_34*k_54*k_61+ks_12*k_25*k_32*k_54*k_61+ks_12*k_34*k_45*k_52*k_61+ks_12*k_32*k_45*k_52*k_61+ks_12*k_32*k_43*k_52*k_61+ks_12*k_25*k_34*k_45*k_61+ks_12*k_25*k_32*k_45*k_61+ks_12*k_25*k_32*k_43*k_61+ks_12*k_25*k_34*k_45*k_56+ks_12*k_25*k_32*k_45*k_56+ks_12*k_25*k_32*k_43*k_56));
	beta=(1/lambda*(k0_23*k_16*k_43*k_54*k_65+k0_23*k_16*k_34*k_54*k_65+k0_23*k_16*k_45*k_52*k_65+k0_23*k_16*k_43*k_52*k_65+k0_23*k_16*k_34*k_52*k_65+k0_23*k_16*k_34*k_45*k_65+k0_23*k_34*k_45*k_56*k_61+k0_23*k_16*k_34*k_45*k_56));
	alpha=(1/lambda*(k_21*k_32*k_43*k_54*k_65+k_16*k_32*k_43*k_54*k_65+k_16*k_25*k_43*k_54*k_65+k_16*k_21*k_43*k_54*k_65+k_16*k_25*k_34*k_54*k_65+k_16*k_21*k_34*k_54*k_65+k_16*k_25*k_32*k_54*k_65+k_16*k_21*k_32*k_54*k_65+k_21*k_34*k_45*k_52*k_65+k_16*k_34*k_45*k_52*k_65+k_21*k_32*k_45*k_52*k_65+k_16*k_32*k_45*k_52*k_65+k_21*k_32*k_43*k_52*k_65+k_16*k_32*k_43*k_52*k_65+k_16*k_25*k_34*k_45*k_65+k_16*k_21*k_34*k_45*k_65+k_16*k_25*k_32*k_45*k_65+k_16*k_21*k_32*k_45*k_65+k_16*k_25*k_32*k_43*k_65+k_16*k_21*k_32*k_43*k_65+k_25*k_34*k_45*k_56*k_61+k_21*k_34*k_45*k_56*k_61+k_25*k_32*k_45*k_56*k_61+k_21*k_32*k_45*k_56*k_61+k_25*k_32*k_43*k_56*k_61+k_21*k_32*k_43*k_56*k_61+k_21*k_32*k_43*k_54*k_61+k_21*k_34*k_45*k_52*k_61+k_21*k_32*k_45*k_52*k_61+k_21*k_32*k_43*k_52*k_61+k_16*k_25*k_34*k_45*k_56+k_16*k_21*k_34*k_45*k_56+k_16*k_25*k_32*k_45*k_56+k_16*k_21*k_32*k_45*k_56+k_16*k_25*k_32*k_43*k_56+k_16*k_21*k_32*k_43*k_56+k_16*k_21*k_32*k_43*k_54+k_16*k_21*k_34*k_45*k_52+k_16*k_21*k_32*k_45*k_52+k_16*k_21*k_32*k_43*k_52));
	gamma=(1/lambda*(k_16*k_21*k_32*k_43*k_54*k_65+k_16*k_21*k_34*k_45*k_52*k_65+k_16*k_21*k_32*k_45*k_52*k_65+k_16*k_21*k_32*k_43*k_52*k_65));
	phi=(1/lambda*((-1)*ks_12*k_25*k_34*k_45*k_56*k_61-ks_12*k_25*k_32*k_45*k_56*k_61-ks_12*k_25*k_32*k_43*k_56*k_61));
	epsilon=(1/lambda*((-1)*ks_12)*k0_23*k_34*k_45*k_56*k_61);
	Imax_gluc=(2*F*C_T*epsilon*Na_o/(beta+Na_o));
	Imax_Na=(2*F*C_T*(phi+epsilon*glucose_o)/(chi+glucose_o));
	Khalf_gluc=((alpha+chi*Na_o)/(beta+Na_o));
	Khalf_Na=((alpha+beta*glucose_o)/(chi+glucose_o));
}