/* * A kinetic model of the thiazide-sensitive Na-Cl cotransporter * * Model Status * * This CellML model runs in OpenCell and COR. The units have ben * checked and they are consistent. We are unsure whether or not * the model recreates the published results as there are no simple * figures of changing concentration against time. Also sodium * and chloride are set to constant values in this model - we suspect * we need to derive an ODE equation based on the reaction figure * (fig 1) in the paper. * * Model Structure * * ABSTRACT: The aim of this study was to construct a numerical * model of the thiazide-sensitive Na-Cl cotransporter (TSC) that * can predict kinetics of thiazide binding and substrate transport * of TSC. We hypothesized that the mechanisms underlying these * kinetic properties can be approximated by a state diagram in * which the transporter has two binding sites, one for sodium * and another for chloride and thiazide. On the basis of the state * diagram, a system of linear equations that should be satisfied * in the steady state was postulated. Numerical solution of these * equations yielded model prediction of kinetics of thiazide binding * and substrate transport. Rate constants, which determine transitional * rates between states, were systematically adjusted to minimize * a penalty function that was devised to quantitatively estimate * the difference between model predictions and experimental results. * With the resultant rate constants, the model could simulate * the following experimental results: 1) dissociation constant * of thiazide in the absence of sodium and chloride; 2) inhibitory * effect of chloride on thiazide binding; 3) stimulatory effect * of sodium on thiazide binding; 4) combined effects of sodium * and chloride on thiazide binding; 5) dependence of sodium influx * on extracellular sodium and chloride; and 6) inhibition of sodium * influx by extracellular thiazide. We conclude that known kinetic * properties of TSC can be predicted by a model which is based * on a state diagram. * * The original paper reference is cited below: * * A kinetic model of the thiazide-sensitive Na-Cl cotransporter, * Hangil Chang and Toshiro Fujita, 1999, American Journal of Physiology, * 276, F952-F959. PubMed ID: 10362783 * * diagram of the model * * [[Image file: chang_1999.png]] * * State diagram for the thiazide-sensitive Na-Cl cotransporter * (TSC). Transporter (E) has binding sites for sodium (Na ) and * chloride (Cl). Thiazide diuretics (D) compete with chloride * for the same binding site. _i is used to indicate which symbols * belong to the intracellular side. */ import nsrunit; unit conversion on; // unit millimolar predefined unit first_order_rate_constant=1 second^(-1); unit second_order_rate_constant=1 meter^3*second^(-1)*mole^(-1); math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real E(time) millimolar; when(time=time.min) E=0.08333; real k23 second_order_rate_constant; k23=1.0E5; real k24 first_order_rate_constant; k24=3.192E1; real k17 first_order_rate_constant; k17=4.587E5; real k18 first_order_rate_constant; k18=1.0E5; real k1 second_order_rate_constant; k1=1.0E5; real k2 first_order_rate_constant; k2=4.183E5; real k3 second_order_rate_constant; k3=1.0E5; real k4 first_order_rate_constant; k4=4.928E6; real ED(time) millimolar; when(time=time.min) ED=0.08333; real E_(time) millimolar; when(time=time.min) E_=0.08333; real ENa(time) millimolar; when(time=time.min) ENa=0.08333; real ECl(time) millimolar; when(time=time.min) ECl=0.08333; real D millimolar; D=1.0E-6; real Na millimolar; Na=50.0; real Cl millimolar; Cl=96.0; real k29 second_order_rate_constant; k29=1.0E5; real k30 first_order_rate_constant; k30=3.514E-1; real k11 second_order_rate_constant; k11=1.0E5; real k12 first_order_rate_constant; k12=4.982E6; real k9 second_order_rate_constant; k9=1.0E5; real k10 first_order_rate_constant; k10=4.183E5; real ED_(time) millimolar; when(time=time.min) ED_=0.08333; real ENa_(time) millimolar; when(time=time.min) ENa_=0.08333; real ECl_(time) millimolar; when(time=time.min) ECl_=0.08333; real D_ millimolar; D_=1.0E-6; real Na_ millimolar; Na_=10.0; real Cl_ millimolar; Cl_=40.0; real k21 second_order_rate_constant; k21=1.0E5; real k22 first_order_rate_constant; k22=4.183E5; real ENaD(time) millimolar; when(time=time.min) ENaD=0.08333; real k27 second_order_rate_constant; k27=1.0E5; real k28 first_order_rate_constant; k28=1.389E5; real ENaD_(time) millimolar; when(time=time.min) ENaD_=0.08333; real k25 second_order_rate_constant; k25=1.0E5; real k26 first_order_rate_constant; k26=3.192E1; real k31 second_order_rate_constant; k31=1.0E5; real k32 first_order_rate_constant; k32=1.166E-1; real k5 second_order_rate_constant; k5=1.0E5; real k6 first_order_rate_constant; k6=1.065E6; real ENaCl(time) millimolar; when(time=time.min) ENaCl=0.08333; real k13 second_order_rate_constant; k13=1.0E5; real k14 first_order_rate_constant; k14=1.065E6; real ENaCl_(time) millimolar; when(time=time.min) ENaCl_=0.08333; real k7 second_order_rate_constant; k7=1.0E5; real k8 first_order_rate_constant; k8=8.940E4; real k15 second_order_rate_constant; k15=1.0E5; real k16 first_order_rate_constant; k16=8.940E4; real k19 first_order_rate_constant; k19=1.0E3; real k20 first_order_rate_constant; k20=2.180E2; // // E:time=(k24*ED+k18*E_+k2*ENa+k4*ECl-(k23*D*E+k17*E+k1*Na*E+k3*Cl*E)); // E_:time=(k30*ED_+k17*E+k10*ENa_+k12*ECl_-(k29*D_*E_+k18*E_+k9*Na_*E_+k11*Cl_*E_)); // ED:time=(k23*E*D+k22*ENaD-(k24*ED+k21*Na*ED)); // ED_:time=(k29*E_*D_+k28*ENaD_-(k30*ED_+k27*Na_*ED_)); // ENaD:time=(k21*Na*ED+k25*D*ENa-(k22*ENaD+k26*ENaD)); // ENaD_:time=(k27*Na_*ED_+k31*D_*ENa_-(k28*ENaD_+k32*ENaD_)); // ENa:time=(k1*Na*E+k26*ENaD+k6*ENaCl-(k2*ENa+k5*Cl*ENa+k25*D*ENa)); // ENa_:time=(k9*Na_*E_+k32*ENaD_+k14*ENaCl_-(k10*ENa_+k13*Cl_*ENa_+k31*D_*ENa_)); // ECl:time=(k3*Cl*E+k8*ENaCl-(k7*Na*ECl+k4*ECl)); // ECl_:time=(k11*Cl_*E_+k16*ENaCl_-(k15*Na_*ECl_+k12*ECl_)); // ENaCl:time=(k5*Cl*ENa+k7*Na*ECl+k20*ENaCl_-(k6*ENaCl+k8*ENaCl+k19*ENaCl)); // ENaCl_:time=(k13*Cl_*ENa_+k15*Na_*ECl_+k19*ENaCl-(k14*ENaCl_+k16*ENaCl_+k20*ENaCl_)); // }