/* * 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 Na-H 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_diagram1 * * [[Image file: chang_2001a.png]] * * State diagram of the Na-H exchanger. In this model, the Na-H * exchanger has a single binding site (E) to which Na+, H+, and * NH4 + bind competitively. 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 micromolar predefined 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, ENa, ENH4, EH, ENa_, EH_, ENH4_, 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=3.27E6; real k3 second_order_rate_constant; k3=1.0E8; real k4 first_order_rate_constant; k4=3.52E0; real k5 second_order_rate_constant; k5=1.0E8; real k6 first_order_rate_constant; k6=7.13E5; real ENa(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) ENa=0; real ENH4(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) ENH4=0; real EH(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) EH=0; real H millimolar; H=1.0; real Na millimolar; Na=1.0; real NH4 millimolar; NH4=1.0; real k13 first_order_rate_constant; real k14 first_order_rate_constant; real ENa_(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) ENa_=0; real k15 first_order_rate_constant; real k16 first_order_rate_constant; real EH_(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) EH_=0; real k17 first_order_rate_constant; real k18 first_order_rate_constant; real ENH4_(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) ENH4_=0; real E_(time) millimolar; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) E_=0; real k7 second_order_rate_constant; k7=1.0E8; real k8 first_order_rate_constant; k8=3.27E6; real k9 second_order_rate_constant; k9=1.0E8; real k10 first_order_rate_constant; k10=3.52E0; real k11 second_order_rate_constant; k11=1.0E8; real k12 first_order_rate_constant; k12=7.13E5; real H_ millimolar; H_=1.0; real Na_ millimolar; Na_=9.5; real NH4_ millimolar; NH4_=1.3; real W dimensionless; real KH micromolar; KH=1.0; // // E:time=(k2*ENa+k4*EH+k6*ENH4-(k1*Na*E+k3*H*E+k5*NH4*E)); // ENa:time=(k1*E*Na+k14*ENa_-(k2*ENa+k13*ENa)); // EH:time=(k3*H*E+k16*EH_-(k4*EH+k15*EH)); // ENH4:time=(k5*NH4*E+k18*ENH4_-(k6*ENH4+k17*ENH4)); // E_:time=(k8*ENa_+k10*EH_+k12*ENH4_-(k7*Na_*E_+k9*H_*E_+k11*NH4_*E_)); // ENa_:time=(k7*E_*Na_+k13*ENa-(k8*ENa_+k14*ENa_)); // EH_:time=(k9*H_*E_+k15*EH-(k10*EH_+k16*EH_)); // ENH4_:time=(k11*NH4_*E_+k17*ENH4-(k12*ENH4_+k18*ENH4_)); // W=(H_/(H_+KH)); k13=((2.41 first_order_rate_constant)*W); k14=((2.41 first_order_rate_constant)*W); k15=((.48 first_order_rate_constant)*W); k16=((.48 first_order_rate_constant)*W); k17=((2.41 first_order_rate_constant)*W); k18=((2.41 first_order_rate_constant)*W); }