/* * Effects of pH on kinetic parameters of the Na-HCO3 cotransporter * in renal proximal tubule * * Model Status * * This CellML model.......................................... * * Model Structure * * ABSTRACT: The effects of pH on cotransporter kinetics were studied * in renal proximal tubule cells. Cells were grown to confluence * on permeable support, mounted in an Ussing-type chamber, and * permeabilized apically to small monovalent ions with amphotericin * B. The steady-state, dinitrostilbene-disulfonate-sensitive current * (DeltaI) was Na+ and HCO3- dependent and therefore was taken * as flux through the cotransporter. When the pH of the perfusing * solution was changed between 6.0 and 8.0, the conductance attributable * to the cotransporter showed a maximum between pH 7.25 and pH * 7.50. A similar profile was observed in the presence of a pH * gradient when the pH of the apical solutions was varied between * 7.0 and 8.0 (basal pH lower by 1), but not when the pH of the * basal solution was varied between 7.0 and 8.0 (apical pH lower * by 1 unit). To delineate the kinetic basis for these observations, * DeltaI-voltage curves were obtained as a function of Na+ and * HCO3- concentrations and analyzed on the basis of a kinetic * cotransporter model. Increases in pH from 7.0 to 8.0 decreased * the binding constants for the intracellular and extracellular * substrates by a factor of 2. Furthermore, the electrical parameters * that describe the interaction strength between the electric * field and substrate binding or charge on the unloaded transporter * increased by four- to fivefold. These data can be explained * by a channel-like structure of the cotransporter, whose configuration * is modified by intracellular pH such that, with increasing pH, * binding of substrate to the carrier is sterically hindered but * electrically facilitated. * * The original paper reference is cited below: * * Effects of pH on kinetic parameters of the Na-HCO3 cotransporter * in renal proximal tubule, E. Gross and U. Hopfer, 1999, Biophysical * Journal, 76, 3066-3075. PubMed ID: 10354432 * * model diagram * * [[Image file: gross_1999.png]] * * A six-state ordered-binding transport model of the Na-HCO3 cotransporter. * The binding of three HCO3- anions to the carrier is described * as a single, lumped step. */ import nsrunit; unit conversion on; unit per_second=1 second^(-1); unit per_second5=1 second^(-5); 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 pmol_per_cm2=1E-8 meter^(-2)*mole^1; unit pA_per_cm2=1E-8 meter^(-2)*ampere^1; unit uA_per_cm2=.01 meter^(-2)*ampere^1; unit nA_per_cm2=1E-5 meter^(-2)*ampere^1; unit uA_per_nA=1E3 dimensionless; unit C_per_mol=1 second^1*ampere^1*mole^(-1); unit C_per_mmol=1E3 second^1*ampere^1*mole^(-1); unit per_mM_per_second=1 meter^3*second^(-1)*mole^(-1); unit per_mM3_per_second=1 meter^9*second^(-1)*mole^(-3); unit mM_per_second=1 meter^(-3)*second^(-1)*mole^1; math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real f0_1 per_mM_per_second; f0_1=65e-3; real b0_1 per_second; b0_1=1.4; real f0_2 per_mM3_per_second; f0_2=1.9e-2; real b0_2 per_second; b0_2=4.5e4; real f0_3 per_second; f0_3=7e3; real b0_3 per_second; b0_3=2.5e3; real f0_4 per_second; f0_4=1.7e3; real b0_4 per_mM3_per_second; b0_4=1.3e-3; real f0_5 per_second; f0_5=1.3; real b0_5 per_mM_per_second; b0_5=61e-3; real f0_6 per_second; f0_6=0.5; real b0_6 per_second; real delta_z dimensionless; delta_z=1.3; real delta_m dimensionless; real delta_n dimensionless; real alpha_p dimensionless; alpha_p=0.04; real alpha_pp dimensionless; alpha_pp=0.04; real beta_p dimensionless; beta_p=0.1; real beta_pp dimensionless; beta_pp=0.1; real C_T pmol_per_cm2; C_T=0.2; // Var below replaced by constant in model eqns to satisfy unit correction // real n dimensionless; // n=1; // Var below replaced by constant in model eqns to satisfy unit correction // real m dimensionless; // m=3; real F C_per_mmol; F=96485.34e-3; real R J_per_K_per_mol; R=8.314; real T kelvin; T=310; real V mV; V=-60; real u dimensionless; real Na_i mM; Na_i=10; real Na_o mM; Na_o=10; real HCO3_i mM; HCO3_i=18; real HCO3_o mM; HCO3_o=18; real f_1 per_second; real b_1 per_second; real f_2 per_second; real b_2 per_second; real f_3 per_second; real b_3 per_second; real f_4 per_second; real b_4 per_second; real f_5 per_second; real b_5 per_second; real f_6 per_second; real b_6 per_second; real C_1(time) pmol_per_cm2; when(time=time.min) C_1=1.02165; real C_2(time) pmol_per_cm2; when(time=time.min) C_2=0.089633; real C_3(time) pmol_per_cm2; when(time=time.min) C_3=0.0004173; real C_4(time) pmol_per_cm2; when(time=time.min) C_4=0.001504; real C_5(time) pmol_per_cm2; when(time=time.min) C_5=0.5685776; real C_6(time) pmol_per_cm2; real C_6_temp(time) pmol_per_cm2; when(time=time.min) C_6_temp=0.318217; real C1_sum per_second5; real C2_sum per_second5; real C3_sum per_second5; real C4_sum per_second5; real C5_sum per_second5; real C6_sum per_second5; real C_sum per_second5; real C1 pmol_per_cm2; real C2 pmol_per_cm2; real C3 pmol_per_cm2; real C4 pmol_per_cm2; real C5 pmol_per_cm2; real C6 pmol_per_cm2; real I_NBC(time) nA_per_cm2; real I_NBC_SS nA_per_cm2; real I_NBC_micro(time) uA_per_cm2; // // b0_6=(f0_1*f0_2*f0_3*f0_4*f0_5*f0_6/(b0_1*b0_2*b0_3*b0_4*b0_5)); u=(F*V/(R*T)); delta_m=(1-beta_p-beta_pp); delta_n=(1-alpha_p-alpha_pp); // // f_1=(f0_1*Na_i^1*exp(1*alpha_p*u/2)); b_1=(b0_1*exp((-1)*1*alpha_p*u/2)); f_2=(f0_2*HCO3_i^3*exp((-1)*3*beta_p*u/2)); b_2=(b0_2*exp(3*beta_p*u/2)); f_3=(f0_3*exp((delta_z+1*delta_n-3*delta_m)*u/2)); b_3=(b0_3*exp((-1)*(delta_z+1*delta_n-3*delta_m)*u/2)); f_4=(f0_4*exp((-1)*3*beta_pp*u/2)); b_4=(b0_4*HCO3_o^3*exp(3*beta_pp*u/2)); f_5=(f0_5*exp(1*alpha_pp*u/2)); b_5=(b0_5*Na_o^1*exp((-1)*1*alpha_pp*u/2)); f_6=(f0_6*exp((-1)*delta_z*u/2)); b_6=(b0_6*exp(delta_z*u/2)); // C_1:time=(b_1*C_2+f_6*C_6-(f_1+b_6)*C_1); C_2:time=(f_1*C_1+b_2*C_3-(b_1+f_2)*C_2); C_3:time=(f_2*C_2+b_3*C_4-(b_2+f_3)*C_3); C_4:time=(f_3*C_3+b_4*C_5-(b_3+f_4)*C_4); C_5:time=(f_4*C_4+b_5*C_6-(b_4+f_5)*C_5); C_6_temp:time=(f_5*C_5+b_6*C_1-(b_5+f_6)*C_6); C_6=(C_T-(C_1+C_2+C_3+C_4+C_5)); // C1_sum=(f_2*f_3*f_4*f_5*f_6+b_1*f_3*f_4*f_5*f_6+b_1*b_2*f_4*f_5*f_6+b_1*b_2*b_3*f_5*f_6+b_1*b_2*b_3*b_4*f_6+b_1*b_2*b_3*b_4*b_5); C2_sum=(f_1*f_3*f_4*f_5*f_6+b_2*f_1*f_4*f_5*f_6+b_2*b_3*f_1*f_5*f_6+b_2*b_3*b_4*f_1*f_6+b_2*b_3*b_4*b_5*f_1+b_2*b_3*b_4*b_5*b_6); C3_sum=(f_1*f_2*f_4*f_5*f_6+b_3*f_1*f_2*f_5*f_6+b_3*b_4*f_1*f_2*f_6+b_3*b_4*b_5*f_1*f_2+b_3*b_4*b_5*b_6*f_2+b_1*b_3*b_4*b_5*b_6); C4_sum=(f_1*f_2*f_3*f_5*f_6+b_4*f_1*f_2*f_3*f_6+b_4*b_5*f_1*f_2*f_3+b_4*b_5*b_6*f_2*f_3+b_1*b_4*b_5*b_6*f_3+b_1*b_2*b_4*b_5*b_6); C5_sum=(f_1*f_2*f_3*f_4*f_6+b_5*f_1*f_2*f_3*f_4+b_5*b_6*f_2*f_3*f_4+b_1*b_5*b_6*f_3*f_4+b_1*b_2*b_5*b_6*f_4+b_1*b_2*b_3*b_5*b_6); C6_sum=(f_1*f_2*f_3*f_4*f_5+b_6*f_2*f_3*f_4*f_5+b_1*b_6*f_3*f_4*f_5+b_1*b_2*b_6*f_4*f_5+b_1*b_2*b_3*b_6*f_5+b_1*b_2*b_3*b_4*b_6); 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); // I_NBC=((-1)*F*(delta_z*(b_6*C_1-f_6*C_6)+(delta_z+1-3)*(f_3*C_3-b_3*C_4))); I_NBC_micro=((.001 uA_per_nA)*((-1)*F)*(delta_z*(b_6*C_1-f_6*C_6)+(delta_z+1-3)*(f_3*C_3-b_3*C_4))); I_NBC_SS=((-1)*F*(delta_z*(b_6*C1-f_6*C6)+(delta_z+1-3)*(f_3*C3-b_3*C4))); }