/*
* Mathematical Models of Ionic Transport in the Distal Tubule
* of the Rat
*
* Model Status
*
* This CellML model is a description of Chang and Fujita's 2001
* mathematical model of a H-ATPase in the distal tubule of the
* rat: it is one component of an overall model of acid/base transport
* in a distal tubule.
*
* Model Structure
*
* ABSTRACT: The purpose of this study is to develop a numerical
* model that simulates acid-base transport in rat distal tubule.
* We have previously reported a model that deals with transport
* of Na(+), K(+), Cl(-), and water in this nephron segment (Chang
* H and Fujita T. Am J Physiol Renal Physiol 276: F931-F951, 1999).
* In this study, we extend our previous model by incorporating
* buffer systems, new cell types, and new transport mechanisms.
* Specifically, the model incorporates bicarbonate, ammonium,
* and phosphate buffer systems; has cell types corresponding to
* intercalated cells; and includes the Na/H exchanger, H-ATPase,
* and anion exchanger. Incorporation of buffer systems has required
* the following modifications of model equations: new model equations
* are introduced to represent chemical equilibria of buffer partners
* [e.g., pH = pK(a) + log(10) (NH(3)/NH(4))], and the formulation
* of mass conservation is extended to take into account interconversion
* of buffer partners. Furthermore, finite rates of H(2)CO(3)-CO(2)
* interconversion are taken into account in modeling the bicarbonate
* buffer system. Owing to this treatment, the model can simulate
* the development of disequilibrium pH in the distal tubular fluid.
* For each new transporter, a state diagram has been constructed
* to simulate its transport kinetics. With appropriate assignment
* of maximal transport rates for individual transporters, the
* model predictions are in agreement with free-flow micropuncture
* experiments in terms of HCO reabsorption rate in the normal
* state as well as under the high bicarbonate load. Although the
* model cannot simulate all of the microperfusion experiments,
* especially those that showed a flow-dependent increase in HCO
* reabsorption, the model is consistent with those microperfusion
* experiments that showed HCO reabsorption rates similar to those
* in the free-flow micropuncture experiments. We conclude that
* it is possible to develop a numerical model of the rat distal
* tubule that simulates acid-base transport, as well as basic
* solute and water transport, on the basis of tubular geometry,
* physical principles, and transporter kinetics. Such a model
* would provide a useful means of integrating detailed kinetic
* properties of transporters and predicting macroscopic transport
* characteristics of this nephron segment under physiological
* and pathophysiological settings.
*
* The original paper reference is cited below:
*
* A numerical model of acid-base transport in rat distal tubule,
* Hangil Chang and Toshiro Fujita, 2001, American Journal of Physiology,
* 281, F222-F243. PubMed ID: 11457714.
*
* reaction_diagram3
*
* [[Image file: chang_2001c.png]]
*
* Conceptual diagram of the H-ATPase. The transporter consists
* of two components: a transmembrane channel and an intracellular
* catalytic unit. Between these two components there is a buffer
* space known as the antechamber, in which hydrogen ions (Ha)
* are in equilibrium with extracellular hydrogen ions (H) due
* to a large conductance of the transmembrane channel. Hydrogen
* ions are also moved between the antechamber and the cytosol
* via the catalytic unit. This ion transport is coupled to ATP
* hydrolysis/synthesis.
*
* reaction_diagram4
*
* [[Image file: chang_2001d.png]]
*
* State diagram of the catalytic unit of the H-ATPase. The catalytic
* unit (E) has two binding sites for H. Symbols with the asterisk
* (*) indicate conformations of the catalytic unit in which the
* binding sites face the cytosol, and symbols without the asterisk
* represent conformations in which the binding sites face the
* antechamber. Transition between the unloaded conformations is
* coupled with ATP synthesis/hydrolysis.
*/
import nsrunit;
unit conversion on;
// unit millimolar predefined
// unit micromolar predefined
unit first_order_rate_constant=1 second^(-1);
unit second_order_rate_constant=1 meter^3*second^(-1)*mole^(-1);
unit third_order_rate_constant=1 meter^6*second^(-1)*mole^(-2);
// unit millivolt predefined
unit joule_per_mole_kelvin=1 kilogram^1*meter^2*second^(-2)*kelvin^(-1)*mole^(-1);
unit coulomb_per_mole=1 second^1*ampere^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: EH, E, EH2, E_, EH2_, EH_
realDomain time second;
time.min=0;
extern time.max;
extern time.delta;
real EH(time) millimolar;
//Warning: Assuming zero initial condition; nothing provided in original CellML model.
when(time=time.min) EH=0;
real k1 second_order_rate_constant;
k1=8.33E9;
real k2 first_order_rate_constant;
k2=1.00E3;
real k3 second_order_rate_constant;
k3=8.33E9;
real k4 first_order_rate_constant;
k4=1.00E4;
real E(time) millimolar;
//Warning: Assuming zero initial condition; nothing provided in original CellML model.
when(time=time.min) E=0;
real EH2(time) millimolar;
//Warning: Assuming zero initial condition; nothing provided in original CellML model.
when(time=time.min) EH2=0;
real Ha millimolar;
real k9 second_order_rate_constant;
k9=1.00E9;
real k10 third_order_rate_constant;
k10=1.80E5;
real E_(time) millimolar;
//Warning: Assuming zero initial condition; nothing provided in original CellML model.
when(time=time.min) E_=0;
real ATP_ millimolar;
ATP_=1.0;
real ADP_ millimolar;
ADP_=1.0;
real Pi_ millimolar;
Pi_=1.0;
real k11 first_order_rate_constant;
k11=5.00E2;
real k12 first_order_rate_constant;
k12=1.00E2;
real EH2_(time) millimolar;
//Warning: Assuming zero initial condition; nothing provided in original CellML model.
when(time=time.min) EH2_=0;
real EH_(time) millimolar;
//Warning: Assuming zero initial condition; nothing provided in original CellML model.
when(time=time.min) EH_=0;
real k5 second_order_rate_constant;
k5=2.5E10;
real k6 first_order_rate_constant;
k6=1.0E3;
real k7 second_order_rate_constant;
k7=2.5E10;
real k8 first_order_rate_constant;
k8=2.5E2;
real H_ millimolar;
H_=1.0;
real psi millivolt;
psi=1.0;
real psi_ millivolt;
psi_=-89.6;
real H millimolar;
H=1.0;
real R joule_per_mole_kelvin;
R=8.314;
real T kelvin;
T=310.0;
real F coulomb_per_mole;
F=96500.0;
//
//
EH:time=(k1*Ha*E+k4*EH2-(k2*EH+k3*Ha*EH));
//
E:time=(k10*ADP_*Pi_*E_+k2*EH-(k1*Ha*E+k9*ATP_*E));
//
EH2:time=(k3*Ha*EH+k12*EH2_-(k4*EH2+k11*EH2));
//
EH_:time=(k5*H_*E_+k8*EH2_-(k6*EH_+k7*H_*EH_));
//
E_:time=(k9*ATP_*E+k6*EH_-(k5*H_*E_+k10*ADP_*Pi_*E_));
//
EH2_:time=(k7*H_*EH_+k11*EH2-(k8*EH2_+k12*EH2_));
//
Ha=(H*exp(F*(psi+psi_)/(R*T)));
}