Doseresponse curves and associated problems

Stimulation of a membrane-bound receptor by an agonist will provoke the onset of a whole chain of intracellular events. These events will ultimately lead to a 'physiological' response. This response, as well as intermediate intracellular events, can be measured to obtain (indirect) information about the receptor, for example, to investigate the effect of P-adrenergic drugs on the heart. One of the most proximate 'biochemical' responses is adenylate cyclase stimulation. The activity of this enzyme can be measured either in broken cell preparations or purified membranes (i.e. measurement of the conversion of [32P] -ATP into [32P] -cAMP) as well as in intact cell or whole organ preparations (measurement of the cAMP concentration). The more distant 'physiological' events comprise the positive inotropic (i.e. increased force of contraction) and positive chronotropic (i.e. increased rate of contraction) responses. The relationship between the drug-evoked response and receptor occupancy is often complex, especially when a long chain of intermediary events separates both phenomena from each other. In an attempt to define such relationships, pharmacologists have introduced concepts such as 'intrinsic activity', 'efficacy' and 'receptor reserve'.

Ligands may be roughly divided into agonists and antagonists. Figure 52 compares the ability of the P-adrenergic agonists like isoproterenol and of antagonists like propranolol to stimulate lipolysis in (i.e. glycerol release from) rat adipose cells. As expected, the antagonists produce no response, even at very high concentrations. In contrast, the response increases with the agonist concentration until a plateau value is reached. Such representation, wherein the response (ordinate) is expressed as a function of the ligand concentration (abscissa), is called a 'dose-response curve' or 'concentration-response curve' (the concentration is usually expressed in a logarithmic scale since it spans several orders in magnitude).

In 1926, Clark developed the 'occupation theory', wherein he proposed that the agonist-mediated response should be proportional to the number of occupied receptors (Figure 53). The response (E) at a given concentration of agonist ([L]) is then related to the maximal response (Emax) by:

G Protein- Coupled Receptors: Molecular Pharmacology From Academic Concept to Pharmaceutical Research Georges Vauquelin and Bengt von Mentzer © 2007 John Wiley & Sons, Ltd. ISBN: 978-0-470-51647-8

Drug concentration in Log(M)

Figure 52 Dose-dependent effect of the p-adrenergic agonists isoproterenol and CGP12177 and of the p-adrenergic antagonists metoprolol, propranolol and atenolol on the lipolysis (measured by the amount of released glycerol) in rat fat cells. Reproduced from Van Liefde, I., Van Witzenburg, A. and Vauquelin, G. (1992) Multiple beta adrenergic receptor subclasses mediate the l-isoproterenol-induced lipolytic response in rat adipocytes. Journal of Pharmacology and Experimental Therapeutics, 262, 552-558, with permission from the American Society for Pharmacology and Experimental Theraputics.

Drug concentration in Log(M)

Figure 52 Dose-dependent effect of the p-adrenergic agonists isoproterenol and CGP12177 and of the p-adrenergic antagonists metoprolol, propranolol and atenolol on the lipolysis (measured by the amount of released glycerol) in rat fat cells. Reproduced from Van Liefde, I., Van Witzenburg, A. and Vauquelin, G. (1992) Multiple beta adrenergic receptor subclasses mediate the l-isoproterenol-induced lipolytic response in rat adipocytes. Journal of Pharmacology and Experimental Therapeutics, 262, 552-558, with permission from the American Society for Pharmacology and Experimental Theraputics.

The concentration that causes a half-maximal response (denoted as 'EC50') is therefore equal to the KD of the agonist for the receptor. However, the occupation theory is unable to explain two major sets of findings:

• The first complication arises from the observation that, in some situations, the maximal response is already attained when only some of the receptors are occupied. In such situations, the occupation theory is no longer valid since EC50

Response

Receptor occupancy

Response

100-

Con cent ration (Log M)

Figure 53 Essential characteristics of the occupation theory by Clark.

100-

Con cent ration (Log M)

Figure 53 Essential characteristics of the occupation theory by Clark.

Agonist concentration (bars = Log intervals)

Figure 54 Comparison between receptor occupancy by isoproterenol (binding studies), intermediate biochemical events and the final response.

Agonist concentration (bars = Log intervals)

Figure 54 Comparison between receptor occupancy by isoproterenol (binding studies), intermediate biochemical events and the final response.

< Kd (Figure 54). This means (at first glance) that the response may be maximal when only some of the receptors are occupied by the agonist. In other words, cellular amplification systems allow agonists (the natural messengers as well as synthetic drugs) to produce a maximal response at receptor subsaturating levels. The terms 'receptor reserve' or 'spare receptor' were introduced as an attempt to describe this phenomenon: i.e. the receptor reserve is the fraction of receptors greater than that required to produce the maximal tissue response by an agonist.

• A more subtle distinction between agonists also became necessary after the realization that agonists do not necessarily produce the same maximal response. As a typical example Figure 55, compares dose-response curves of different P-adrenergic agonists to produce adenylate cyclase stimulation in turkey erythro-cyte membranes. The maximal degree of adenylate cyclase stimulation is clearly different from one agonist to another. To deal with this finding, Ariens (Ariens, 1954) introduced, in 1954, the term 'intrinsic activity' (a) as an experimental parameter to indicate the maximal response of an agonist of interest compared to the most potent agonist known (Emax).

Depending on the value of a, ligands can be divided into three categories:

• a = 1. This category of ligands produces the maximal response (Emax) at full receptor occupancy. They are called 'full agonists'. Isoproterenol is a full agonist for P-adrenergic receptors (and so are the natural messengers for this receptor: adrenaline and noradrenaline).

partial agonists fenoterol trimethoquilol terbuialine phenylephrine

Concentration (Log M)

Figure 55 Dose-response (adenylate cyclase stimulation in turkey erythrocytes) curves of the full agonist isoproterenol and of partial agonists. Reproduced from Vauquelin, G., Bottari, S. and Strosberg, A. D. (1980) Inactivation of beta-adrenergic receptors by N-ethylmalmeimide: permissive role of beta-adrenergic agents in relation to adenylate cyclase activation. Molecular Pharmacology, 17, 163-171, with permission from the American Society for Pharmacology and Experimental Theraputics.

-i full agonist I isoproterenol partial agonists fenoterol trimethoquilol terbuialine phenylephrine

Concentration (Log M)

Figure 55 Dose-response (adenylate cyclase stimulation in turkey erythrocytes) curves of the full agonist isoproterenol and of partial agonists. Reproduced from Vauquelin, G., Bottari, S. and Strosberg, A. D. (1980) Inactivation of beta-adrenergic receptors by N-ethylmalmeimide: permissive role of beta-adrenergic agents in relation to adenylate cyclase activation. Molecular Pharmacology, 17, 163-171, with permission from the American Society for Pharmacology and Experimental Theraputics.

• 0 < a < 1. These ligands are denoted as 'partial agonists'. At full receptor occupancy, they will produce a response equal to a X Emax. The rank order of the a values for the partial agonists presented (Figure 55) is: phenylephrine (0.09) < terbutaline (0.20) < trimethoquilol (0.33) < fenoterol (0.64). Figure 55 also clearly shows that there is no correlation between a drug's EC50 and its intrinsic activity.

• a = 0. This situation occurs for antagonists. These ligands bind to the receptor without eliciting a response.

A close examination of the molecular events which link receptor occupation by the ligand and the final ligand-evoked response provides a better insight concerning the actual physical meaning of dose-response curves and concepts such as 'intrinsic activity', 'efficacy' and 'receptor reserve'.

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