Dose–Response Relationships

An agonist is defined as an agent that can bind to a receptor and elicit a biologic response. The magnitude of the drug

 Graded dose–response relations

As the concentration of a drug increases, the magnitude of its pharmacologic effect also increases. The relationship between dose and response is a continuous one, and it can be mathematically described for many systems by application of the law
of mass action, assuming the simplest model of drug binding: The response is a graded effect, meaning that the response is continuous and gradual. This contrasts with a quantal response, which describes an all-or-nothing response. A graph of this relationship is known as a graded dose–response curve. Plotting the magnitude of the response against increasing doses of a drug produces a graph that has the general shape depicted in 

Figure A. The curve can be described as a rec-tangular hyperbola—a very familiar curve in biology, because it can be applied to diverse biological events, such as ligand binding, enzymatic activity, and responses to pharmacologic agents. 

1. Potency:  Two important properties of drugs can be determined by graded dose–response curves. The first is potency, a measure of the amount of drug necessary to produce an effect of a given magnitude. For a number of reasons, the concentration producing an effect that is fifty percent of the maximum is used to determine potency; it commonly designated as the EC50. 

Figure above  The effect of dose on the magnitude of pharmacologic response. Panel A is a linear graph. Panel B is asemilogarithmic plot of the same data. EC50 = drug dose that shows fifty percent of maximal response.

In Figure above , the EC50 for Drugs A and B are indicated. Drug A is more potent than Drug B because less Drug A is needed to obtain 50 percent effect. Thus, therapeutic preparations of drugs will reflect the potency. For example, candesartan and irbesartan are angiotensin–receptor blockers that are used alone or in combination to treat hypertension. Candesartan is more potent than irbesartan because the dose range for candesartan is 4 to 32 mg, as compared to a dose range of 75 to 300 mg for irbesartan. Candesartan would be Drug A and irbesartan would be Drug B in Figure 2.6. An important contributing factor to the dimension of the EC50 is the affinity of the drug for the receptor. Semilogarithmic plots are often employed, because the range of doses (or concentrations) may span several orders of magnitude. By plotting the log of the concentration, the complete range of doses can be graphed.  As shown in Figure  above B, the curves become sigmoidal in shape. It is also easier to visually estimate the EC50.

2. Efficacy [intrinsic activity]: The second drug property that can be determined from graded dose–response plots is the efficacy of the drug. This is the ability of a drug to illicit a physiologic response when it interacts with a receptor. Efficacy is dependent on the number of drug–receptor complexes formed and the efficiency of the coupling of receptor activation to cellular responses. Analogous to the maximal velocity for enzyme-catalyzed reactions, the maximal response (Emax) or efficacy is more important than drug potency. A drug with greater efficacy is more therapeutically beneficial than one that is more potent. Figure 2.7 shows the response to drugs of differing potency and efficacy. 

3. Drug–receptor binding: The quantitative relationship between drug concentration and receptor occupancy applies the law of mass action to the kinetics of the binding of drug and receptor molecules. By making the assumption that the binding of one drug molecule does not alter the binding of subsequent molecules, we can mathematically express the relationship between the percentage (or fraction) of bound receptors and the drug concentration: 

where [D] = the concentration of free drug; [DR] = the concentration of bound drug; [Rt] = the total concentration of receptors, and is equal to the sum of the concentrations of unbound (free) receptors and bound receptors and; Kd = [D][R]/[DR], and is the dissociation constant for the drug from the receptor. The value of Kd can be used to determine the affinity of a drug for its receptor. Affinity describes the strength of the interaction (binding) between a ligand and its receptor. The higher the Kd value, the weaker the interaction and the lower the affinity. The converse occurs when a drug has a low Kd. The binding of the ligand to the receptor is strong, and the affinity is high. Equation (1) defines a curve that has the shape of a rectangular hyperbola

Figure  The effect of dose on the magnitude of drug binding.

As the concentration of free drug increases, the ratio of the concentrations of bound receptors to total receptors approaches unity. Doses are often plotted on a logarithmic scale, because the range from lowest to highest concentrations of doses often spans several orders of magnitude. It is important to note the similarity between these curves and those representing the relationship between dose and effect

4. Relationship of binding to effect: The binding of the drug to its receptor initiates events that ultimately lead to a measurable biologic response. The mathematical model that describes drug concentration and receptor binding can be applied to dose (drug concentration) and response (or effect), providing the following assumptions are met: 

1) The magnitude of the response is proportional to the amount of receptors bound or occupied,
 2) the Emax occurs when all receptors are bound, 
and 3) binding of the drug to the receptor exhibits no cooperativity. 
In this case,

where [E] = the effect of the drug at concentration [D] and [Emax] = the maximal effect of the drug

5. Agonists: If a drug binds to a receptor and produces a biologic response that mimics the response to the endogenous ligand, it is known as an agonist. For example, phenylephrine is an agonist at α1-adrenoceptors, because it produces effects that resemble the action of the endogenous ligand, norepinephrine. Upon binding to α1-adrenoceptors on the membranes of vascular smooth muscle, phenylephrine mobilizes intracellular Ca2+, causing contraction of the actin and myosin filaments. The shortening of the muscle cells decreases the diameter of the arteriole, causing an increase in resistance to the flow of blood through the vessel. Blood pressure therefore rises to maintain the blood flow. As this brief description illustrates, an agonist may have many effects that can be measured, including actions on intracellular molecules, cells, tissues, and intact organisms. All of these actions are attributable to interaction of the drug molecule with the receptor molecule. In general, a full agonist has a strong affinity for its receptor and good efficacy

6. Antagonists: Antagonists are drugs that decrease the actions of another drug or endogenous ligand. Antagonism may occur in several ways. Many antagonists act on the identical receptor macromolecule as the agonist. Antagonists, however, have no intrinsic activity and, therefore, produce no effect by themselves. Although antagonists have no intrinsic activity, they are able to bind avidly to target receptors because they possess strong affinity. If both the antagonist and the agonist bind to the same site on the receptor, they are said to be “competitive.” For example, the antihypertensive drug prazosin competes with the endogenous ligand, norepinephrine, at α1-adrenoceptors, decreasing vascular smooth muscle tone and reducing blood pressure. Plotting the effect of the competitive antagonist characteristically causes a shift of the agonist dose–response curve to the right. Competitive antagonists have no intrinsic activity. If the antagonist binds to a site other than where the agonist binds, the interaction is “noncompetitive” or “allosteric” 

Figure 2.9 Effects of drug antagonists. EC 50 = drug dose that shows fifty percent of maximal response.

[Note: A drug may also act as a chemical antagonist by combining with another drug and rendering it inactive. For example, protamine ionically binds to heparin, rendering it inactive and antagonizing heparin's anticoagulant effect.] 

7. Functional antagonism: An antagonist may act at a completely separate receptor, initiating effects that are functionally opposite those of the agonist. A classic example is the antagonism by epinephrine to histamine-induced bronchoconstriction. Histamine binds to H1 histamine receptors on bronchial smooth muscle, causing contraction and narrowing of the bronchial tree. Epinephrine is an agonist at β2-adrenoceptors on bronchial smooth muscle, which causes the muscles to actively relax. This functional antagonism is also known as “physiologic antagonism

8. Partial agonists: Partial agonists have efficacies (intrinsic activities) greater than zero, but less than that of a full agonist. Even if all the receptors are occupied, partial agonists cannot produce an Emax of as great a magnitude as that of a full agonist. However, a partial agonist may have an affinity that is greater than, less than, or equivalent to that of a full agonist. A unique feature of these drugs is that, under appropriate conditions, a partial agonist may act as an antagonist of a full agonist. Consider what would happen to the Emax of an agonist in the presence of increasing concentrations of a partial agonist

Figure : Effects of partial agonists.

As the number of receptors occupied by the partial agonist increases, the Emax would decrease until it reached the Emax of the partial agonist. This potential of partial agonists to act both agonistically and antagonistically may be therapeutically exploited. For example, aripiprazole, an atypical neuroleptic agent, is a partial agonist at selected dopamine receptors. Dopaminergic pathways that were overactive would tend to be inhibited by the partial agonist, whereas pathways that were underactive may be stimulated. This might explain the ability of aripiprazole to improve many of the symptoms of schizophrenia, with a small risk of causing extrapyramidal adverse effects .

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