Relation Between Drug Concentration & Response

RELATION BETWEEN DRUG CONCENTRATION & RESPONSE

The relation between dose of a drug and the clinically observed response may be complex. In carefully controlled in vitro systems, however, the relation between concentration of a drug and its effect is often simple and can be described with mathematicalprecision. This idealized relation underlies the more complex rela-tions between dose and effect that occur when drugs are given to patients.

Concentration-Effect Curves & Receptor Binding of Agonists

Even in intact animals or patients, responses to low doses of a drug usually increase in direct proportion to dose. As doses increase, however, the response increment diminishes; finally, doses may be reached at which no further increase in response can be achieved. In idealized or in vitro systems, the relation between drug concen-tration and effect is described by a hyperbolic curve (Figure 2–1A) according to the following equation:

where E is the effect observed at concentration C, E_max is the maximal response that can be produced by the drug, and EC₅₀ is the concentration of drug that produces 50% of maximal effect.

This hyperbolic relation resembles the mass action law, which describes association between two molecules of a given affinity. This resemblance suggests that drug agonists act by binding to (“occupy-ing”) a distinct class of biologic molecules with a characteristic affin-ity for the drug receptor. Radioactive receptor ligands have been used to confirm this occupancy assumption in many drug-receptor sys-tems. In these systems, drug bound to receptors (B) relates to the concentration of free (unbound) drug (C) as depicted in Figure 2–1B and as described by an analogous equation:

in which B_max indicates the total concentration of receptor sites (ie, sites bound to the drug at infinitely high concentrations of free drug) and K_d (the equilibrium dissociation constant) represents the concentration of free drug at which half-maximal binding is observed. This constant characterizes the receptor’s affinity for binding the drug in a reciprocal fashion: If the K_d is low, binding affinity is high, and vice versa. The EC₅₀ and K_d may be identical, but need not be, as discussed below. Dose-response data are often presented as a plot of the drug effect (ordinate) against the loga-rithm of the dose or concentration (abscissa). This mathematicalmaneuver transforms the hyperbolic curve of Figure 2–1 into a sigmoid curve with a linear midportion (eg, Figure 2–2). This expands the scale of the concentration axis at low concentrations (where the effect is changing rapidly) and compresses it at high concentrations (where the effect is changing slowly), but has no special biologic or pharmacologic significance.

Receptor-Effector Coupling & Spare Receptors

When a receptor is occupied by an agonist, the resulting conforma-tional change is only the first of many steps usually required toproduce a pharmacologic response. The transduction process that links drug occupancy of receptors and pharmacologic response is often termed coupling. The relative efficiency of occupancy-response coupling is partially determined by the initial conformational change

in the receptor; thus, the effects of full agonists can be considered more efficiently coupled to receptor occupancy than can the effects of partial agonists (described in text that follows). Coupling effi-ciency is also determined by the biochemical events that transduce receptor occupancy into cellular response. Sometimes the biologic effect of the drug is linearly related to the number of receptors bound. This is often true for drug-regulated ion channels, eg, in which the ion current produced by the drug is directly proportional to the number of receptors (ion channels) bound. In other cases, the biologic response is a more complex function of drug binding to receptors. This is often true for receptors linked to enzymatic signal transduction cascades, eg, in which the biologic response often increases disproportionately to the number of receptors occupied by drug.

Many factors can contribute to nonlinear occupancy-response coupling, and often these factors are only partially understood. The concept of “spare” receptors, regardless of the precise bio-chemical mechanism involved, can help us to think about these effects. Receptors are said to be “spare” for a given pharmacologic response if it is possible to elicit a maximal biologic response at a concentration of agonist that does not result in occupancy of the full complement of available receptors. Experimentally, spare receptors may be demonstrated by using irreversible antagonists to prevent binding of agonist to a proportion of available receptors and showing that high concentrations of agonist can still produce an undiminished maximal response (Figure 2–2). Thus, the same maximal inotropic response of heart muscle to catecholamines can be elicited even under conditions in which 90% of the β adreno-ceptors are occupied by a quasi-irreversible antagonist. Accordingly, myocardial cells are said to contain a large proportion of spare β adrenoceptors.

How can we account for the phenomenon of spare receptors? In the example of the β adrenoceptor, receptor activation pro-motes binding of guanosine triphosphate (GTP) to an interme-diate signaling protein and activation of the signaling intermediate may greatly outlast the agonist-receptor interaction (see the following section on G Proteins & Second Messengers). In such a case, the “spareness” of receptors is temporal. Maximal response can be elicited by activation of relatively few receptors because the response initiated by an individual ligand-receptor binding event persists longer than the binding event itself.

In other cases, in which the biochemical mechanism is not understood, we imagine that the receptors might be spare in num-ber. If the concentration or amount of cellular components otherthan the receptors limits the coupling of receptor occupancy to response, then a maximal response can occur without occupancy of all receptors. Thus, the sensitivity of a cell or tissue to a particu-lar concentration of agonist depends not only on the affinity of the receptor for binding the agonist (characterized by the K_d) but also on the degree of spareness—the total number of receptors present compared with the number actually needed to elicit a maximal biologic response.

The concept of spare receptors is very useful clinically because it allows one to think precisely about the effects of drug dosage without needing to consider biochemical details of the signaling response. The K_d of the agonist-receptor interaction determines what fraction (B/B_max) of total receptors will be occupied at a given free concentration (C) of agonist regardless of the receptor concentration:

Imagine a responding cell with four receptors and four effec-tors. Here the number of effectors does not limit the maximal response, and the receptors are not spare in number. Consequently, an agonist present at a concentration equal to the K_d will occupy 50% of the receptors, and half of the effectors will be activated, producing a half-maximal response (ie, two receptors stimulate two effectors). Now imagine that the number of receptors increases 10-fold to 40 receptors but that the total number of effectors remains constant. Most of the receptors are now spare in number. As a result, a much lower concentration of agonist suf-fices to occupy 2 of the 40 receptors (5% of the receptors), and this same low concentration of agonist is able to elicit a half-maximal response (two of four effectors activated). Thus, it is possible to change the sensitivity of tissues with spare receptors by changing receptor number.

Competitive & Irreversible Antagonists

Receptor antagonists bind to receptors but do not activate them. The primary action of antagonists is to prevent agonists (other drugs or endogenous regulatory molecules) from activating recep-tors. Some antagonists (so-called “inverse agonists,”), also reduce receptor activity below basal levels observed in the absence of bound ligand. Antagonists are divided into two classes depending on whether or not they reversibly compete with agonists for binding to receptors.

In the presence of a fixed concentration of agonist, increasing concentrations of a reversible competitive antagonist progres-sively inhibit the agonist response; high antagonist concentra-tions prevent response completely. Conversely, sufficiently high concentrations of agonist can surmount the effect of a given con-centration of the antagonist; that is, the E _max for the agonist remains the same for any fixed concentration of antagonist (Figure 2–3A). Because the antagonism is competitive, the pres-ence of antagonist increases the agonist concentration required

for a given degree of response, and so the agonist concentration-effect curve is shifted to the right.The concentration (C′) of an agonist required to produce a given effect in the presence of a fixed concentration ([I]) of com-petitive antagonist is greater than the agonist concentration (C) required to produce the same effect in the absence of the antago-nist. The ratio of these two agonist concentrations (dose ratio) is related to the dissociation constant (K_i) of the antagonist by the Schild equation:

Pharmacologists often use this relation to determine the K_i of a competitive antagonist. Even without knowledge of the relation between agonist occupancy of the receptor and response, the K_i can be determined simply and accurately. As shown in Figure 2–3, concentration-response curves are obtained in the presence and in the absence of a fixed concentration of competitive antagonist; comparison of the agonist concentrations required to produce identical degrees of pharmacologic effect in the two situations reveals the antagonist’s K_i . If C′ is twice C, for example, then [I]= K_i.

For the clinician, this mathematical relation has two important therapeutic implications:

1. The degree of inhibition produced by a competitive antagonist depends on the concentration of antagonist. The competitive β-adrenoceptor antagonist propranolol provides a usefulexample. Patients receiving a fixed dose of this drug exhibit a wide range of plasma concentrations, owing to differences among individuals in clearance of propranolol. As a result, inhibitory effects on physiologic responses to norepinephrine and epinephrine (endogenous adrenergic receptor agonists) may vary widely, and the dose of propranolol must be adjusted accordingly.

2. Clinical response to a competitive antagonist also depends on the concentration of agonist that is competing for binding to receptors. Again, propranolol provides a useful example: When this drug is administered at moderate doses sufficient to block the effect of basal levels of the neurotransmitter norepinephrine, resting heart rate is decreased. However, the increase in the release of norepinephrine and epinephrine that occurs with exercise, postural changes, or emotional stress may suffice to overcome this competitive antagonism. Accordingly, the same dose of propranolol may have little effect under these condi-tions, thereby altering therapeutic response.

Some receptor antagonists bind to the receptor in an irrevers-ible or nearly irreversible fashion, either by forming a covalentbond with the receptor or by binding so tightly that, for practical purposes, the receptor is unavailable for binding of agonist. After occupancy of some proportion of receptors by such an antagonist, the number of remaining unoccupied receptors may be too low for the agonist (even at high concentrations) to elicit a response com-parable to the previous maximal response (Figure 2–3B). If spare receptors are present, however, a lower dose of an irreversible antagonist may leave enough receptors unoccupied to allowachievement of maximum response to agonist, although a higher agonist concentration will be required (Figure 2–2B and C; see Receptor-Effector Coupling & Spare Receptors).

Therapeutically, irreversible antagonists present distinct advan-tages and disadvantages. Once the irreversible antagonist has occupied the receptor, it need not be present in unbound form to inhibit agonist responses. Consequently, the duration of action of such an irreversible antagonist is relatively independent of its own rate of elimination and more dependent on the rate of turnover of receptor molecules.

Phenoxybenzamine, an irreversible α-adrenoceptor antagonist, is used to control the hypertension caused by catecholamines released from pheochromocytoma, a tumor of the adrenal medulla. If administration of phenoxybenzamine lowers blood pressure, blockade will be maintained even when the tumor epi-sodically releases very large amounts of catecholamine. In this case, the ability to prevent responses to varying and high concen-trations of agonist is a therapeutic advantage. If overdose occurs, however, a real problem may arise. If the α-adrenoceptor blockade cannot be overcome, excess effects of the drug must be antago-nized “physiologically,” ie, by using a pressor agent that does not act via α receptors.

Antagonists can function noncompetitively in a different way; that is, by binding to a site on the receptor protein separate from the agonist binding site, and thereby modifying receptor activity without blocking agonist binding (see Figure 1–3C and D). Although these drugs act noncompetitively, their actions are reversible if they do not bind covalently. Such drugs are often called allosteric modulators. For example, benzodiazepines bind noncompetitively to ion channels activated by the neurotransmit-ter γ-aminobutyric acid (GABA), enhancing the net activating effect of GABA on channel conductance.

Partial Agonists

Based on the maximal pharmacologic response that occurs when all receptors are occupied, agonists can be divided into two classes: partial agonists produce a lower response, at full receptor occu-pancy, than do full agonists. Partial agonists produce concentra-tion-effect curves that resemble those observed with full agonists in the presence of an antagonist that irreversibly blocks some of the receptor sites (compare Figures 2–2 [curve D] and 2–4B). It is important to emphasize that the failure of partial agonists to pro-duce a maximal response is not due to decreased affinity for binding to receptors. Indeed, a partial agonist’s inability to cause a maximal pharmacologic response, even when present at high concentrations that saturate binding to all receptors, is indicated by the fact that partial agonists competitively inhibit the responses produced by full agonists (Figure 2–4C). Many drugs used clinically as antagonists are actually weak partial agonists. Partial agonism can be useful in some clinical circumstances. For example, buprenorphine, a partial agonist of μ-opioid receptors, is a generally safer analgesic drug than mor-phine because it produces less respiratory depression in overdose. Buprenorphine is effectively antianalgesic when administered to morphine-dependent individuals, however, and may precipitate a drug withdrawal syndrome due to competitive inhibition of mor-phine’s agonist action.

Other Mechanisms of Drug Antagonism

Not all the mechanisms of antagonism involve interactions of drugs or endogenous ligands at a single type of receptor, and some types of antagonism do not involve a receptor at all. For example, protamine, a protein that is positively charged at physiologic pH, can be used clinically to counteract the effects of heparin, an anti-coagulant that is negatively charged. In this case, one drug acts as a chemical antagonist of the other simply by ionic binding that makes the other drug unavailable for interactions with proteins involved in blood clotting.

Another type of antagonism is physiologic antagonism between endogenous regulatory pathways mediated by different receptors. For example, several catabolic actions of the glucocorticoidhormones lead to increased blood sugar, an effect that is physio-logically opposed by insulin. Although glucocorticoids and insulin act on quite distinct receptor-effector systems, the clinician must sometimes administer insulin to oppose the hyperglycemic effects of a glucocorticoid hormone, whether the latter is elevated by endogenous synthesis (eg, a tumor of the adrenal cortex) or as a result of glucocorticoid therapy.

In general, use of a drug as a physiologic antagonist produces effects that are less specific and less easy to control than are the effects of a receptor-specific antagonist. Thus, for example, to treat bradycardia caused by increased release of acetylcholine from vagus nerve endings, the physician could use isoproterenol, a β-adrenoceptor agonist that increases heart rate by mimickingsympathetic stimulation of the heart. However, use of this physi-ologic antagonist would be less rational—and potentially more dangerous—than would use of a receptor-specific antagonist such as atropine (a competitive antagonist at the receptors at which acetylcholine slows heart rate).