The Dose-Response Curve

The distribution of mortality vs. concentration or dose is drawn so that the cumulative mortality is plotted at each concentration. At each concentration the total numbers of organisms that have died by that concentration are 

Note All of the toxicity data are given as a percentage of the total organisms at a particular treatment group. For example, if 7 out of 100 organisms died or expressed other endpoints at a concentration of 2 mg/kg, then the percentage responding would be 7%. 

Plot of cumulative mortality vs. environmental concentration or dose. The data are plotted as cumulative number of dead by each dose using the data presented in Table 3.1. The X-axis is in units of weight to volume (concentration) or weight of toxicant per unit weight of animal (dose). 

LD50 — The dose that causes mortality in 50% of the organisms tested, estimated by graphical or computational means. 

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Fig. 8. Agonist, dose—response curves, (a) For an agonist where a value of 10 M is indicated at the concentration giving 50% response, (b) For an agonist alone, Aq, and in the presence of increasing amounts of irreversible receptor antagonists, B—F. There is a progressive rightward shift of the dose—response curve prior to reduction of maximum response. This pattern is consistent with the presence of a receptor reserve.

R. J. Taharida and L. S. Jacob, The Dose—Response Curve in Pharmacology, Springer Vedag, New York, 1979. 

However, there are multiple routes of entry to the body for some materials. When a toxic chemical acts on the body or system, the nature and extent of the injurious response depends upon the dose received, that is, the amount of the chemical actually entering the body or system. This relationship of dose and response is shown in Figure 3. The dose-response curve varies with the type of material and the response. 

Hazard characterization, or dose-response characterization, by using experimental animals to reveal target organs and toxic doses, and the shape of the dose-response curve... 

To.xicity values for carcinogenic effects can be e.xprcsscd in several ways. The slope factor is usually, but not always, the upper 95th percent confidence limit of the slope of the dose-response curve and is e.xprcsscd as (mg/kg-day). If the extrapolation model selected is the linearized multistage model, this value is also known as the ql. That is ... 

If the exposure level (E) exceeds tliis tlireshold (i.e., E/RfD exceeds unity), tliere may be concern for potential noncancer effects. As a rule, tlie greater tlie value of E/RfD above unity, tlie greater tlie level of concern. However, one should not interpret ratios of E/RfD as statistical probabilities a ratio of 0.001 does not mean tliat tliere is a one in one tliousand cliance of the effect occurring. Furtlier, it is important to empliasize tliat tlie level of concern does not increase linearly as tlie RfD is approached or exceeded because RfDs do not have equal accuracy or precision and are not based on tlie same severity of toxic effects. Thus, tlie slopes of the dose-response curv e in excess of the RfD can range widely depending on tlie substance. 

The LCjj concept is visualized in the dose-response curve presented in Figure 4-114 [32A]. The dose or concentration is plotted on the abscissa, and... 

Figure 4-114. Determination of lethal toxicity from the dose-response curve [32A]. (Courtesy SPE.)...

The Furchgott method can be effectively utilized by fitting the dose-response curves themselves to the operational model with fitted values of x (before and after alkylation) and a constant KA value. When fitting experimental data, the slopes of the dose-response curves may not be unity. This is a relevant factor in the operational model since the stimulus-transduction function of cells is an integral part of the modeling of responses. Under these circumstances, the data is fit to (see Section 3.13.3 and Equation 3.49)... 

When an antagonist produces parallel shifts to the right of the dose-response curve with no diminution of the maximal response, the first approach used to quantify potency is Schild analysis (see Section 6.3.1). In cases where the value of a is low (i.e., a = 0.01), a tenfold concentration range of the antagonist would cause shifts commensurate with those produced by a simple competitive antagonist. 

A dose-response curve to a full agonist is obtained. Shown are data for the dose response to the full agonist oxotremorine (responses as a percentage of the maximal response to oxotremorine) in Table 12.5a. The dose-response curve is shown in Figure 12.6a. 

The dose-response curve after receptor alkylation is shown in Figure 12.6a (open circles). The same function is used to fit the data as employed for the control curve (for this example, Equation 12.5). The parameters of the fit dose-response curves are shown in Table 12.5b. Equiactive concentrations of oxotremorine are calculated according to the procedure given in Section 12.2.1. 

Fig. 1). If an agonist produces a submaximal system response it is called a partial agonist (Fig. 1). While the potency of an agonist is quantified by the location parameter of the dose-response curve (EC50), a reflection of (but not a direct measure of) the intrinsic efficacy of an agonist is given by its maximal response. 

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