The number of receptors occupied is dependent on the concentration of the drug in a unit area or volume5 and on the total number of receptors, Rt, in it. As more receptors are
Figure 1-6. Relationship of drug action to drug concentration.
occupied, the pharmacological effect becomes more intense until, when all are filled, a maximal effect, Em, is achieved.
Finally, the intensity of the effect will be dependent on the drug-receptor complex concentration, [/?D],
and on total receptor concentration
Maximal effect is proportional to total receptor concentration.
By dividing Equation 1.12 by Equation 1.14
it can be shown that
Equation 1.16 can be graphically represented in Figure 1-6.
The occupancy theory is most applicable when the drug-receptor interaction is the same for all drugs being considered in a series (i.e., when all drugs produce the same maximal response irrespective of dose).
Soon after this theory was proposed, it was discovered that it had loopholes. With certain series of drugs a maximal response was never achieved even at extremely high doses. The biological effect does not always appear to follow the law of mass action, nor does it seem to be dependent on the affinity of a drug for the receptors.
Ariens (1954) and Stephenson (1956) proposed modifications to the theory in an attempt to explain such anomalous factors. They visualized the drug-receptor interactions as being a two-step phenomenon:
1. Complexation of the drug with its receptor;
2. Production of the effect.
5 Such a unit volume may be considered a hypothetical compartment.
Log Drug Concentration
Figure 1-7. Dose-response curves of drugs with equal intrinsic activity.
Affinity of the drug for the receptor alone is not sufficient. The compound must also have what Ariens called intrinsic activity.6 The Ariens-Stephenson idea describes the ability of the drug-receptor complex to produce a biological effect. Their modification brings in the concept of agonists and antagonists, both of which are thought to have a strong affinity for the receptor and a tendency to form a complex. However, only the agonist gives rise to the stimulus and has intrinsic activity. In the original theory, however, intrinsic activity was assumed to be constant.
Equation 1.17 takes this modification into account by introducing a proportionality constant, a, thus changing Equation 1.12 as follows:
When a = 1, the compound is a full agonist. If the intensity of action of such drugs is plotted against increasing concentrations, there are obtained similarly shaped dose-response curves (Fig. 1-7) having the same maximum values (Em), but, of course, at different drug concentrations. Thus full agonists, although having different affinities for a given receptor, have the same intrinsic activity.
Partial agonists have a values of less than 1; they do not produce a full maximal effect, although affinities for the receptor remain the same (Fig. 1-8). Antagonists have zero a values and show an absence of intrinsic activity. They do have affinity for the receptor sites and will therefore block effects of agonists added subsequently.
In spite of the obvious appeal of the occupancy theory, it fails to explain several important facts of drug action: primarily that drugs vary in their action. It does not solve the puzzle regarding why agonists are active and antagonists only weakly or not at all, even though they occupy the same receptor. Therefore, its main drawback is that it does not suggest a mechanism of action at the molecular level. In the final analysis drug action cannot be totally explained by simple receptor occupation models.
6 Stephenson preferred the term efficacy.
Log Drug Concentration
Figure 1-8. Dose-response curves of drugs with different intrinsic activity.
The rate theory proposed by Paton (1961) as an alternate to the occupancy theory is based on the idea that a drug is effective only at the moment of encounter with its receptor. Thus receptor activation is proportional to the total number of encounters that the drug has with the receptors per unit of time. Pharmacological activity is a function only of the rate of association and disassociation of the drug and receptor. No stable drug-receptor complex is necessary. Agonists are thought to have high rates of association and dissociation; antagonists dissociate slowly, but they may associate quickly.7
The rate theory also has serious flaws. Experimentally, we find that agonists often do form relatively stable complexes. The drug phenomena on a molecular level cannot be explained. The question regarding why two similar compounds are antagonistic to each other is also left unanswered.
Considerable knowledge exists about the nature of the active site of enzymes, their secondary, tertiary, and quaternary structures. In the case of those enzymes that have been obtained in crystalline form and subjected to X-ray analysis, conformational appearance has been deduced. However, the geometry of such an active site, as elucidated on an isolated crystalline enzyme, need not necessarily be complementary to the natural substrate, or drug molecule, to complex and interact with it. Since we visualize such a site as being flexible rather than rigid, the substrate or drug can induce such a complementary fit.
Figure 1-9 illustrates in an oversimplified manner how a substrate-induced conformational change in an enzyme might occur. H, +, and - represent the hydrophobic and electrostatic attractions between the substrate or drug molecule and an area on the protein. The resulting complex can dissociate again, and both components can return to their original shapes. The initial geometry of the protein molecule is also critical. The combination with the enzyme seems to induce a change in its conformation, which in turn can result in an
7 Antagonists frequently cause a brief period of stimulation prior to blockade.
active orientation of catalytic groups. The biological effect obtained is not only caused by the relatively strong binding between substrate and enzyme; the effect may actually be caused by the induction of a proper conformational change.
A change in the size, shape, and, therefore, volume of the normal substrate that interacts with the enzyme could likely bring about a change in the proper alignment. This results in molecules that are either more efficient, or even antagonistic. It should also be kept in mind that the induced conformational changes being considered need not be limited to the protein; they may also be brought about in the substrate (drug) molecule resulting in an even more effective interaction. It is essential that an additional point be considered, namely that the interaction of a drug with a receptor protein need not necessarily be produced as a result of complexation with catalytic groups at so-called active sites. Rather, the interaction can also occur at a modifier or allosteric site, which is a regulatory site on enzymes that controls feedback mechanisms.
The induced-fit theory was originally proposed to help explain enzyme-substrate interactions. The subsequent extension of this theory (Koshland, 1961) to explain the mode of drug action seems logical. However, with drugs, biopolymers other than enzymes must also be considered: noncatalytic proteins, for example. Several variations have been added to help explain cooperative effects in which the binding of one type of substrate, not necessarily a drug, may accelerate or otherwise enhance the binding of subsequent types of substrates. The conformationally induced changes in the receptors during the reversible association with a drug can be invoked to help explain, in part at least, the initiation of the pharmacological responses observed.
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