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The Hill equation can be used to describe dose–response relationships, for example ion channel-open-probability vs. ligand concentration. [ 9 ] Dose is usually in milligrams, micrograms , or grams per kilogram of body-weight for oral exposures or milligrams per cubic meter of ambient air for inhalation exposures.
The Hill equation is useful for determining the degree of cooperativity of the ligand(s) binding to the enzyme or receptor. The Hill coefficient provides a way to quantify the degree of interaction between ligand binding sites. [5] The Hill equation (for response) is important in the construction of dose-response curves.
The EC 50 of a quantal dose response curve represents the concentration of a compound where 50% of the population exhibit a response, [5] after a specified exposure duration. For clarification, a graded dose response curve shows the graded effect of the drug (y axis) over the dose of the drug (x axis) in one or an average of subjects.
This equation represents a simplified model of reaction dynamics that can be studied mathematically through tools such as free energy maps. IUPAC definition Pharmacodynamics : Study of pharmacological actions on living systems, including the reactions with and binding to cell constituents, and the biochemical and physiological consequences of ...
The IC 50 of a drug can be determined by constructing a dose-response curve and examining the effect of different concentrations of antagonist on reversing agonist activity. IC 50 values can be calculated for a given antagonist by determining the concentration needed to inhibit half of the maximum biological response of the agonist. [4]
A reversible competitive antagonist should cause a rightward shift in the dose response curve, such that the new curve is parallel to the old one and the maximum is unchanged. This is because reversible competitive antagonists are surmountable antagonists. The magnitude of the rightward shift can be quantified with the dose ratio, r.
Intrinsic activity (IA) and efficacy (E max) refer to the relative ability of a drug-receptor complex to produce a maximum functional response. This must be distinguished from the affinity, which is a measure of the ability of the drug to bind to its molecular target, and the EC 50, which is a measure of the potency of the drug and which is proportional to both efficacy and affinity.
The Hill equation is important in the construction of dose-response curves. The Hill equation is the following formula, where is the magnitude of the response, [] is the drug concentration (or equivalently, stimulus intensity), is the drug concentration that produces a half-maximal response and is the Hill coefficient.