/* * 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))); }