/* * Theoretical analysis of biochemical pathways of nitric oxide * release from vascular endothelial cells * * Model Status * * This CellML model runs in OpenCell and COR and is known to be * mathematically consistent with the publication it was based * on. The units are consistent. An additional variable and equation * has been added to allow the CellML model to reproduce Figure * 2 of the publication. The three different graphs of this figure * can be produced by altering the variable 'Fe3' in the 'Fe3' * component (this variable represents the concentration of eNOS * in its Fe3+ bound state) to 0.045, 0.030 or 0.015 micromolar. * In this particular version of the model it has been set to 0.045. * * Model Structure * * ABSTRACT: Vascular endothelium expressing endothelial nitric * oxide synthase (eNOS) produces nitric oxide (NO), which has * a number of important physiological functions in the microvasculature. * The rate of NO production by the endothelium is a critical determinant * of NO distribution in the vascular wall. We have analyzed the * biochemical pathways of NO synthesis and formulated a model * to estimate NO production by the microvascular endothelium under * physiological conditions. The model quantifies the NO produced * by eNOS based on the kinetics of NO synthesis and the availability * of eNOS and its intracellular substrates. The predicted NO production * from microvessels was in the range of 0.005-0.1 microM/s. This * range of predicted values is in agreement with some experimental * values but is much lower than other rates previously measured * or estimated from experimental data with the help of mathematical * modeling. Paradoxical discrepancies between the model predictions * and previously reported results based on experimental measurements * of NO concentration in the vicinity of the arteriolar wall suggest * that NO can also be released through eNOS-independent mechanisms, * such as catalysis by neuronal NOS (nNOS). We also used our model * to test the sensitivity of NO production to substrate availability, * eNOS concentration, and potential rate-limiting factors. The * results indicated that the predicted low level of NO production * can be attributed primarily to a low expression of eNOS in the * microvascular endothelial cells. * * model diagram * * [[Image file: chen_2006.png]] * * Schematic diagram of the mathematical model. Pathway of nitric * oxide (NO) synthesis catalysed by endothelial nitric oxide synthase * (eNOS, or eNOS3). The heme iron (Fe) is the main catalysis site * and is used to represent the enzyme in this figure and also * in the model. The heme ion of eNOS binds L-arginine (Arg), hydroxyl-L-arginine * (NOHA), and oxygen (O2), and undergoes a series of oxygenation * and reduction reactions. * * The original paper reference is cited below: * * Theoretical analysis of biochemical pathways of nitric oxide * release from vascular endothelial cells, Kejing Chen and Aleksander * S. Popel, 2006, Free Radical Biology and Medicine , 41, 668-680. * PubMed ID: 16864000 */ import nsrunit; unit conversion on; // unit micromolar predefined unit first_order_rate_constant=1 second^(-1); unit second_order_rate_constant=1E3 meter^3*second^(-1)*mole^(-1); unit flux=1E-3 meter^(-3)*second^(-1)*mole^1; math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real Arg(time) micromolar; when(time=time.min) Arg=100.0; real S(time) flux; real Fe3(time) micromolar; when(time=time.min) Fe3=0.045; real Fe3_Arg(time) micromolar; when(time=time.min) Fe3_Arg=0.0; real Fe2_Arg(time) micromolar; when(time=time.min) Fe2_Arg=0.0; real Fe2(time) micromolar; when(time=time.min) Fe2=0.0; real k1 second_order_rate_constant; k1=0.1; real k_1 first_order_rate_constant; k_1=0.1; real k4 second_order_rate_constant; k4=1.89; real k_4 first_order_rate_constant; k_4=11.4; real Fe3_NO(time) micromolar; when(time=time.min) Fe3_NO=0.0; real Fe2_NO(time) micromolar; when(time=time.min) Fe2_NO=0.0; real O2 micromolar; O2=172.0; real Fe3_NOHA(time) micromolar; when(time=time.min) Fe3_NOHA=0.0; real NOHA(time) micromolar; when(time=time.min) NOHA=0.0; real k2 first_order_rate_constant; k2=0.91; real k13 second_order_rate_constant; k13=0.033; real k14 first_order_rate_constant; k14=53.9; real k8 first_order_rate_constant; k8=0.1; real k_8 second_order_rate_constant; k_8=0.1; real k3 first_order_rate_constant; k3=0.91; real Fe2_NOHA(time) micromolar; when(time=time.min) Fe2_NOHA=0.0; real k9 first_order_rate_constant; k9=11.4; real k_9 second_order_rate_constant; k_9=1.89; real Fe3_O2_Arg(time) micromolar; when(time=time.min) Fe3_O2_Arg=0.0; real k5 second_order_rate_constant; k5=2.58; real k_5 first_order_rate_constant; k_5=98.0; real k6 first_order_rate_constant; k6=12.6; real k7 first_order_rate_constant; k7=0.91; real Fe3_O2_NOHA(time) micromolar; when(time=time.min) Fe3_O2_NOHA=0.0; real k_10 first_order_rate_constant; k_10=89.9; real k10 second_order_rate_constant; k10=3.33; real k11 first_order_rate_constant; k11=29.4; real k12 first_order_rate_constant; k12=0.91; real NO(time) micromolar; when(time=time.min) NO=0.0; real dNOdt(time) flux; real citrulline(time) micromolar; when(time=time.min) citrulline=0.0; real NO3(time) micromolar; when(time=time.min) NO3=0.0; // // Arg:time=(k_1*Fe3_Arg+k_4*Fe2_Arg+S-(k1*Arg*Fe3+k4*Arg*Fe2)); S=(k1*Arg*Fe3+k4*Arg*Fe2-(k_1*Fe3_Arg+k_4*Fe2_Arg)); // Fe3:time=(k_1*Fe3_Arg+k14*Fe3_NO+k13*Fe2_NO*O2+k8*Fe3_NOHA-(k1*Arg*Fe3+k2*Fe3+k_8*NOHA*Fe3)); // Fe3_Arg:time=(k1*Fe3*Arg-(k_1*Fe3_Arg+k3*Fe3_Arg)); // Fe2:time=(k2*Fe3+k_4*Fe2_Arg+k9*Fe2_NOHA-(k4*Fe2*Arg+k_9*Fe2*NOHA)); // Fe2_Arg:time=(k3*Fe3_Arg+k_5*Fe3_O2_Arg+k4*Fe2*Arg-(k5*Fe2_Arg*O2+k_4*Fe2_Arg)); // Fe3_O2_Arg:time=(k5*Fe2_Arg*O2-(k6*Fe3_O2_Arg+k_5*Fe3_O2_Arg)); // Fe3_NOHA:time=(k6*Fe3_O2_Arg+k_8*Fe3*NOHA-(k7*Fe3_NOHA+k8*Fe3_NOHA)); // Fe2_NOHA:time=(k7*Fe3_NOHA+k_10*Fe3_O2_NOHA+k_9*Fe2*NOHA-(k9*Fe2_NOHA+k10*Fe2_NOHA*O2)); // Fe3_O2_NOHA:time=(k10*Fe2_NOHA*O2-(k11*Fe3_O2_NOHA+k_10*Fe3_O2_NOHA)); // Fe3_NO:time=(k11*Fe3_O2_NOHA-(k14*Fe3_NO+k12*Fe3_NO)); // Fe2_NO:time=(k12*Fe3_NO-k13*Fe2_NO*O2); // NO:time=(k14*Fe3_NO); dNOdt=(k14*Fe3_NO); // citrulline:time=(k11*Fe3_O2_NOHA); // NO3:time=(k13*Fe2_NO*O2); // NOHA:time=(k8*Fe3_NOHA+k9*Fe2_NOHA-(k_8*Fe3*NOHA+k_9*Fe2*NOHA)); // }