Color Atlas of Pharmacology (Part 6): Quantification of Drug Action

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Quantification of Drug Action the dose at which one-half of the group has responded. The dose range encompassing the dose-frequency relationship reflects the variation in individual sensitivity to the drug. Although similar in shape, a dose-frequency relationship has, thus, a different meaning than does a dose-effect relationship. The latter can be evaluated in one individual and results from an intraindividual dependency of the effect on drug concentration. The evaluation of a dose-effect relationship within a group of human subjects is compounded by interindividual differences in sensitivity. To account for the biological variation, measurements have to be carried out on a...

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52 Quantification of Drug Action Dose–Response Relationship the dose at which one-half of the group has responded. The dose range encom- The effect of a substance depends on the passing the dose-frequency relationship amount administered, i.e., the dose. If reflects the variation in individual sensi- the dose chosen is below the critical tivity to the drug. Although similar in threshold (subliminal dosing), an effect shape, a dose-frequency relationship will be absent. Depending on the nature has, thus, a different meaning than does of the effect to be measured, ascending a dose-effect relationship. The latter can doses may cause the effect to increase in be evaluated in one individual and re- intensity. Thus, the effect of an antipy- sults from an intraindividual dependen- retic or hypotensive drug can be quanti- cy of the effect on drug concentration. fied in a graded fashion, in that the ex- The evaluation of a dose-effect rela- tent of fall in body temperature or blood tionship within a group of human sub- pressure is being measured. A dose-ef- jects is compounded by interindividual fect relationship is then encountered, as differences in sensitivity. To account for discussed on p. 54. the biological variation, measurements The dose-effect relationship may have to be carried out on a representa- vary depending on the sensitivity of the tive sample and the results averaged. individual person receiving the drug, Thus, recommended therapeutic doses i.e., for the same effect, different doses will be appropriate for the majority of may be required in different individuals. patients, but not necessarily for each in- Interindividual variation in sensitivity is dividual. especially obvious with effects of the The variation in sensitivity may be “all-or-none” kind. based on pharmacokinetic differences To illustrate this point, we consider (same dose different plasma levels) an experiment in which the subjects in- or on differences in target organ sensi- dividually respond in all-or-none fash- tivity (same plasma level different ef- ion, as in the Straub tail phenomenon fects). (A). Mice react to morphine with excita- tion, evident in the form of an abnormal posture of the tail and limbs. The dose dependence of this phenomenon is ob- served in groups of animals (e.g., 10 mice per group) injected with increas- ing doses of morphine. At the low dose, only the most sensitive, at increasing doses a growing proportion, at the high- est dose all of the animals are affected (B). There is a relationship between the frequency of responding animals and the dose given. At 2 mg/kg, one out of 10 animals reacts; at 10 mg/kg, 5 out of 10 respond. The dose-frequency relation- ship results from the different sensitiv- ity of individuals, which as a rule exhib- its a log-normal distribution (C, graph at right, linear scale). If the cumulative fre- quency (total number of animals re- sponding at a given dose) is plotted against the logarithm of the dose (ab- scissa), a sigmoidal curve results (C, graph at left, semilogarithmic scale). The inflection point of the curve lies at Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
Quantification of Drug Action 53 A. Abnormal posture in mouse given morphine Dose = 0 = 2 mg/kg = 10 mg/kg = 20 mg/kg = 100 mg/kg = 140 mg/kg B. Incidence of effect as a function of dose % Cumulative frequency Frequency of dose needed 100 80 4 60 3 40 2 20 1 mg/kg 2 10 20 100 140 2 10 20 100 140 mg/kg C. Dose-frequency relationship Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
54 Quantification of Drug Action Concentration-Effect Relationship (A) it would be impossible in the intact organism to follow negative chrono- The relationship between the concen- tropic effects to the point of cardiac tration of a drug and its effect is deter- arrest. mined in order to define the range of ac- tive drug concentrations (potency) and Disadvantages are: the maximum possible effect (efficacy). 1. Unavoidable tissue injury during dis- On the basis of these parameters, differ- section. ences between drugs can be quantified. 2. Loss of physiological regulation of As a rule, the therapeutic effect or toxic function in the isolated tissue. action depends critically on the re- 3. The artificial milieu imposed on the sponse of a single organ or a limited tissue. number of organs, e.g., blood flow is af- fected by a change in vascular luminal Concentration-Effect Curves (B) width. By isolating critical organs or tis- sues from a larger functional system, As the concentration is raised by a con- these actions can be studied with more stant factor, the increment in effect di- accuracy; for instance, vasoconstrictor minishes steadily and tends asymptoti- agents can be examined in isolated cally towards zero the closer one comes preparations from different regions of to the maximally effective concentra- the vascular tree, e.g., the portal or tion.The concentration at which a maxi- saphenous vein, or the mesenteric, cor- mal effect occurs cannot be measured onary, or basilar artery. In many cases, accurately; however, that eliciting a isolated organs or organ parts can be half-maximal effect (EC50) is readily de- kept viable for hours in an appropriate termined. It typically corresponds to the nutrient medium sufficiently supplied inflection point of the concentra- with oxygen and held at a suitable tem- tion–response curve in a semilogarith- perature. mic plot (log concentration on abscissa). Responses of the preparation to a Full characterization of a concentra- physiological or pharmacological stim- tion–effect relationship requires deter- ulus can be determined by a suitable re- mination of the EC50, the maximally cording apparatus. Thus, narrowing of a possible effect (Emax), and the slope at blood vessel is recorded with the help of the point of inflection. two clamps by which the vessel is sus- pended under tension. Experimentation on isolated organs offers several advantages: 1. The drug concentration in the tissue is usually known. 2. Reduced complexity and ease of re- lating stimulus and effect. 3. It is possible to circumvent compen- satory responses that may partially cancel the primary effect in the intact organism — e.g., the heart rate in- creasing action of norepinephrine cannot be demonstrated in the intact organism, because a simultaneous rise in blood pressure elicits a coun- ter-regulatory reflex that slows car- diac rate. 4. The ability to examine a drug effect over its full rage of intensities — e.g., Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
Quantification of Drug Action 55 Portal vein Coronary Basilar Saphenous Mesenteric artery artery artery vein Vasoconstriction 1 min Active tension 1 2 5 10 20 30 40 50 100 Drug concentration A. Measurement of effect as a function of concentration Effect % Effect 50 (in mm of registration unit, 100 (% of maximum effect) e.g., tension developed) 40 80 30 60 20 40 10 20 10 20 30 40 50 1 10 100 Concentration (linear) Concentration (logarithmic) B. Concentration-effect relationship Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
56 Quantification of Drug Action Concentration-Binding Curves c B = Bmax · ––––––– c + KD In order to elicit their effect, drug mole- cules must be bound to the cells of the KD is the equilibrium dissociation con- effector organ. Binding commonly oc- stant and corresponds to that ligand curs at specific cell structures, namely, concentration at which 50 % of binding the receptors. The analysis of drug bind- sites are occupied. The values given in ing to receptors aims to determine the (A) and used for plotting the concentra- affinity of ligands, the kinetics of inter- tion-binding graph (B) result when KD = action, and the characteristics of the 10. binding site itself. The differing affinity of different li- In studying the affinity and number gands for a binding site can be demon- of such binding sites, use is made of strated elegantly by binding assays. Al- membrane suspensions of different tis- though simple to perform, these bind- sues. This approach is based on the ex- ing assays pose the difficulty of correlat- pectation that binding sites will retain ing unequivocally the binding sites con- their characteristic properties during cerned with the pharmacological effect; cell homogenization. Provided that this is particularly difficult when more binding sites are freely accessible in the than one population of binding sites is medium in which membrane fragments present. Therefore, receptor binding are suspended, drug concentration at must not be implied until it can be the “site of action” would equal that in shown that the medium. The drug under study is ra- • binding is saturable (saturability); diolabeled (enabling low concentra- • the only substances bound are those tions to be measured quantitatively), possessing the same pharmacological added to the membrane suspension, mechanism of action (specificity); and allowed to bind to receptors. Mem- • binding affinity of different substanc- brane fragments and medium are then es is correlated with their pharmaco- separated, e.g., by filtration, and the logical potency. amount of bound drug is measured. Binding assays provide information Binding increases in proportion to con- about the affinity of ligands, but they do centration as long as there is a negligible not give any clue as to whether a ligand reduction in the number of free binding is an agonist or antagonist (p. 60). Use of sites (c = 1 and B ≈ 10% of maximum radiolabeled drugs bound to their re- binding; c = 2 and B ≈ 20 %). As binding ceptors may be of help in purifying and approaches saturation, the number of analyzing further the receptor protein. free sites decreases and the increment in binding is no longer proportional to the increase in concentration (in the ex- ample illustrated, an increase in con- centration by 1 is needed to increase binding from 10 to 20 %; however, an in- crease by 20 is needed to raise it from 70 to 80 %). The law of mass action describes the hyperbolic relationship between binding (B) and ligand concentration (c). This relationship is characterized by the drug’s affinity (1/KD) and the maximum binding (Bmax), i.e., the total number of binding sites per unit of weight of mem- brane homogenate. Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.
Quantification of Drug Action 57 Addition of radiolabeled drug in different Organs concentrations Homogenization Membrane Mixing and incubation suspension Determination of radioactivity Centrifugation c=1 c=2 c=5 B = 10% B = 20% B = 30% c = 10 c = 20 c = 40 B = 50% B = 70% B = 80% A. Measurement of binding (B) as a function of concentration (c) % Binding (B) % Binding (B) 100 100 80 80 60 60 40 40 20 20 10 20 30 40 50 1 10 100 Concentration (linear) Concentration (logarithmic) B. Concentration-binding relationship Lüllmann, Color Atlas of Pharmacology © 2000 Thieme All rights reserved. Usage subject to terms and conditions of license.