/* * 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 an anion exchanger 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_diagram2 * * [[Image file: chang_2001b.png]] * * State diagram of the anion exchanger. In this model, the anion * transporter (E) has a single binding site to which Cl- and HCO3 * - competitively bind. Only the bound forms of the transporter * are able to cross the membrane. (Symbols with the asterisk (*) * represent conformations facing the cytosol, symbols without * indicate conformations facing the extracellular environment.) */ import nsrunit; unit conversion on; // unit millimolar predefined unit flux=1 meter^(-3)*second^(-1)*mole^1; unit first_order_rate_constant=1 second^(-1); unit second_order_rate_constant=1 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: E, ECl, EHCO3, ECl_, EHCO3_, E_ realDomain time second; time.min=0; extern time.max; extern time.delta; real E(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) E=0; real k1 second_order_rate_constant; k1=1.0E8; real k2 first_order_rate_constant; k2=7.87E6; real k3 second_order_rate_constant; k3=1.0E8; real k4 first_order_rate_constant; k4=8.28E6; real ECl(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) ECl=0; real EHCO3(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) EHCO3=0; real HCO3 millimolar; HCO3=1.0; real Cl millimolar; Cl=1.0; real k9 first_order_rate_constant; k9=5.14E5; real k10 first_order_rate_constant; k10=9.26E4; real ECl_(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) ECl_=0; real k11 first_order_rate_constant; k11=3.24E5; real k12 first_order_rate_constant; k12=5.83E4; real EHCO3_(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) EHCO3_=0; real E_(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) E_=0; real k5 second_order_rate_constant; k5=1.0E8; real k6 first_order_rate_constant; k6=7.87E6; real k7 second_order_rate_constant; k7=1.0E8; real k8 first_order_rate_constant; k8=8.28E6; real HCO3_ millimolar; HCO3_=1.0; real Cl_ millimolar; Cl_=1.0; real J_Cl_influx(time) flux; real Ki_Cl millimolar; Ki_Cl=0.528; real Ki_HCO3 millimolar; Ki_HCO3=0.423; // // E:time=(k2*ECl+k4*EHCO3-(k1*Cl*E+k3*HCO3*E)); // ECl:time=(k1*Cl*E+k10*ECl_-(k2*ECl+k9*ECl)); // EHCO3:time=(k3*HCO3*E+k12*EHCO3_-(k4*EHCO3+k11*EHCO3)); // E_:time=(k6*ECl_+k8*EHCO3_-(k5*Cl_*E_+k7*HCO3_*E_)); // ECl_:time=(k5*Cl_*E_+k9*ECl-(k6*ECl_+k10*ECl_)); // EHCO3_:time=(k7*HCO3_*E_+k11*EHCO3-(k8*EHCO3_+k12*EHCO3_)); // J_Cl_influx=((k9*ECl-k10*ECl_)*(1+Cl_/Ki_Cl+HCO3_/Ki_HCO3)^(-1)); // }