/* * A mechanistic model of ACTH-stimulated cortisol secretion * * Model Status * * This CellML model runs in both COR and OpenCell to recreate * figure 4 from the original paper. All parameter values are set * to the same as those in table 1, with the exception of P=0.052 * and Q=0.042. There is a small step increase in ACTH concentration * from 12pM to 16pM for a duration of 10 minutes with 15 minutes * between the two pulses. The units have been checked and they * are consistent. * * Model Structure * * ABSTRACT: Adrenal secretory rates of cortisol and arterial concentrations * of adrenocorticotropin (ACTH) were measured in conscious trained * dogs subjected to intravenous infusion of ACTH. To investigate * the causal relation of ACTH to the secretion of cortisol, a * mechanistic mathematical model based on current hypotheses of * adrenocortical function was constructed and tested. It is widely * believed that ACTH stimulates cortisol secretion through adenosine * 3',5'-cyclic monophosphate (cAMP), which provides substrate * cholesterol by activating cholesterol ester hydrolase and facilitating * transport of cholesterol to the side-chain cleavage enzyme. * In addition, cholesterol modulates its own synthesis by inhibiting * beta-hydroxy-beta-methylglutaryl (HMG)-CoA reductase in the * adrenocortical cell. These and other steps in the biosynthetic * reaction sequence were described using differential equations * subject to the additional constraints imposed by available measurements * of intracellular quantities. The resulting model is consistent * with many of the known characteristics of the canine adrenal * response to ACTH. In this model, steady-state nonlinearities * arise from cooperative binding of cAMP to its receptor protein * and saturation of mitochondrial pregnenolone transport. The * transient response is dominated by a depletable pool of intracellular * free cholesterol. Other inferences based on the model are presented, * and a quantifiable cellular basis for increased adrenal sensitivity * to ACTH is proposed. * * A mechanistic model of ACTH-stimulated cortisol secretion, D.P. * Dempsher, D.S. Gann, and R.D. Phair, 1984, American Journal * of Physiology, 246, R587-R596. PubMed ID: 6326602 * * model diagram * * [[Image file: dempsher_gann_phair_1984.png]] * * Schematic diagram of the model describing the effects of ACTH * on cortisol secretion. (note that ECF represents the extracellular * fluid). */ import nsrunit; unit conversion on; unit per_micromolar=1E3 meter^3*mole^(-1); // unit micromolar predefined unit minute=60 second^1; unit flux=1.6666667E-5 meter^(-3)*second^(-1)*mole^1; unit per_minute2=2.7777778E-4 second^(-2); unit micromolar_per_minute2=2.7777778E-7 meter^(-3)*second^(-2)*mole^1; unit micromolar2_per_minute2=2.7777778E-10 meter^(-6)*second^(-2)*mole^2; unit first_order_rate_constant=.01666667 second^(-1); math main { realDomain time minute; time.min=0; extern time.max; extern time.delta; real cAMP(time) micromolar; when(time=time.min) cAMP=0.95; real Ko dimensionless; Ko=0.013; real Ka per_micromolar; Ka=10; real Kb per_micromolar; Kb=1000000.0; real Kdsm micromolar; Kdsm=10.0; real Vmsm flux; Vmsm=6.0; real Vdsm flux; Vdsm=10.0; real ACTH(time) micromolar; real IS(time) dimensionless; real Crpt dimensionless; Crpt=3.0; real K dimensionless; K=80.0; real Kd micromolar; Kd=2.11; // Var below replaced by constant in model eqns to satisfy unit correction // real n dimensionless; // n=4.0; real V(time) flux; when(time=time.min) V=11.3; real P micromolar_per_minute2; P=0.052; real Q first_order_rate_constant; Q=0.042; real W(time) flux; when(time=time.min) W=10.0; real T micromolar2_per_minute2; T=8.0; real U first_order_rate_constant; U=0.0015; real CHOC(time) micromolar; when(time=time.min) CHOC=532.0; real Lmtr first_order_rate_constant; Lmtr=1.65; real Kmtr(time) first_order_rate_constant; when(time=time.min) Kmtr=0.446; real CHOM(time) micromolar; when(time=time.min) CHOM=139.0; real Kbac first_order_rate_constant; Kbac=10.0; real Kfor(time) first_order_rate_constant; when(time=time.min) Kfor=0.370; real Kcb first_order_rate_constant; Kcb=0.01; real Kcf first_order_rate_constant; Kcf=0.00033; real CHON(time) micromolar; when(time=time.min) CHON=3.03; real CHOL(time) micromolar; when(time=time.min) CHOL=3000.0; real C per_minute2; C=6.25; real D first_order_rate_constant; D=125.0; real R per_minute2; R=3.0; real S first_order_rate_constant; S=76.0; real Vm flux; Vm=1890.0; real Km micromolar; Km=270.0; real PREG(time) micromolar; when(time=time.min) PREG=6.56; real Vmptr flux; Vmptr=500.0; real Kmptr micromolar; Kmptr=150.0; real PRO(time) micromolar; when(time=time.min) PRO=0.64; real HA dimensionless; HA=0.5; real AH first_order_rate_constant; AH=16.4; real HYPR(time) micromolar; when(time=time.min) HYPR=0.64; real HY first_order_rate_constant; HY=16.4; real CORT(time) micromolar; when(time=time.min) CORT=5.2; real LH first_order_rate_constant; LH=0.724; // // cAMP:time=(Vmsm*Ko*(1+Kb*ACTH)/(1+Ka*ACTH+Ko*(1+Kb*ACTH))-Vdsm*cAMP/(Kdsm+cAMP)); ACTH=(if ((time>=(0 minute)) and (time<(10 minute))) (1.2E-5 micromolar) else if ((time>=(10 minute)) and (time<(20 minute))) (1.6E-5 micromolar) else if ((time>=(20 minute)) and (time<(35 minute))) (1.2E-5 micromolar) else if ((time>=(35 minute)) and (time<(45 minute))) (1.6E-5 micromolar) else (1.2E-5 micromolar)); // IS=(K*Crpt*cAMP^4/(Kd^4+cAMP^4)); // V:time=(P*IS-Q*V); // W:time=(T*CHOC^(-1)-U*W); // CHOC:time=(V+W+Lmtr*CHOM-Kmtr*CHOC); // CHOM:time=(Kmtr*CHOC+Kbac*CHON+Kcf*CHOL-(Lmtr*CHOM+Kcb*CHOM+Kfor*CHOM)); // CHOL:time=(Kcb*CHOM-Kcf*CHOL); // Kmtr:time=(C*IS-D*Kmtr); // Kfor:time=(R*IS-S*Kfor); // CHON:time=(Kfor*CHOM-(Kbac*CHON+Vm*CHON/(Km+CHON))); // PREG:time=(Vm*CHON/(Km+CHON)-Vmptr*PREG/(Kmptr+PREG)); // PRO:time=(HA*(Vmptr*PREG/(Kmptr+PREG))-AH*PRO); // HYPR:time=(AH*PRO-HY*HYPR); // CORT:time=(HY*HYPR-LH*CORT); // }