Derivation, response curve

Dose-response curves to a full agonist [A] and a partial agonist [P] are obtained in the same receptor preparation. From these curves, reciprocals of equiactive concentrations of the full and partial agonist are used in the following linear equation (derived for the operational model see Section 5.9.2)... 

It can be seen that when there is no effect on the affinity of the receptor for the agonist (a=l) Equation 7.6 is identical to the describing orthosteric noncompetitive antagonism derived by Gaddum and colleagues [31] (see Equation 6.10). However, while the equation is identical and the pattern of concentration-response curves is the same as that for an orthos teric antagonist it should be... 

FIGURE 11.17 Symmetrical and asymmetrical dose-response curves, (a) Symmetrical Hill equation with n = 1 and EC5o = 1.0. Filled circle indicates the EC50 (where the abscissa yields a half maximal value for the ordinate). Below this curve is the second derivative of the function (slope). The zero ordinate of this curve indicates the point at which the slope is zero (inflection point of the curve). It can be seen that the true EC50 and the inflection match for a symmetrical curve, (b) Asymmetrical curve (Gompertz function with m = 0.55 and EC50= 1.9). The true EC50 is 1.9, while the point of inflection is 0.36. 

Estimated Upper-Bound Human Cancer Risk Levels This is the range associated with the upper-bound for lifetime cancer risk of 1 in 10,000 to 1 in 10,000,000. These risk levels are derived from the EPA s Human Health Assessment Group s upper-bound estimates of the slope of the cancer dose response curve at low dose levels (qi ). 

Figure 4. dj-vinyl acetate (MW=89) response curves derived from a long term multipulse sequence with a premixed dj-acetic acid + ethylene + oxygen feed. 

Bythismethod.theinfluenceoftheBodensteinnumberandresidencetimeon the response curves was derived [12], For short mean residence times, the inlet squarewavefunctionisonlyslightlymodified sinefunctionsareformedonapply-inglongerresidencetimes.Thelargerthedispersion,themoresignificantisthis dependence. 

Allowing a step input disturbance of magnitude Co, as shown in Fig. 2.23, the constants x and to are derived by drawing a tangent to the step response curve at the point of inflexion. 

Zero-Threshold Linear Hypothesis—The assumption that a dose-response curve derived from data in the high dose and high dose-rate ranges may be extrapolated through the low dose and low dose range to zero, implying that, theoretically, any amount of radiation will cause some damage. 

Although several data sets could be used to derive AEGL-3 values, the 1-h exposure data from the mouse study by Peterson and Bhattacharyya (1985) provided the most sound basis and were selected to derive AEGL-3 values. Due to the steep concentration-response curve for arsine, the 15-ppm exposure (where there was no lethality) was considered an estimate of the lethality threshold. An uncertainty factor of 30-fold was applied to account for interspecies extrapolation (10-fold) and intraspecies variability (3-fold) (see Section 6.3). 

The severe headache accompanied by slight loss of equilibrium in one of several sensitive equilibrium tests after a 6.25-h (rounded down to 6 h) exposure at 0.5 ppm was considered the threshold for inability to escape and was used to derive the AEGL-2 values. A UF of 3 was used to adjust the value as no susceptible populations were identified and the threshold for narcosis for most anesthetics does not differ among individuals by more than a factor of 2 (Kennedy and Longnecker 1996 Marshall and Longnecker 1996). The intraspecies UF of 3 is supported by the steep dose-response curve for the induction of headaches namely, a 2-fold difference in the threshold concentration of PGDN and the concentration that induces headache in the majority of healthy individuals (Stewart et al. 1974). The 6-h 0.5-ppm concentration was... 

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