## From receptor occupation to stimulus and response

From receptor occupation to stimulus

The distinction between agonists and antagonists has been explained by the ability of agonists, but not of antagonists, to initiate (or favour) a conformational modification of the receptor molecule (or molecular complex) and that this modification

intrinsic: efficacy limit! cellular amplification) (with cellular ;i:i.ilili;il > ;

Figure 56 From receptor occupation '[L— R]' to stimulus 'S' to response 'E'.

is the first step in the initiation of the cellular response. This first step represents the stimulus (Figure 56). Major current models assume that receptors can only adopt one active conformation and that the stimulus of a ligand reflects the fraction of occupied receptors residing in this active conformation.

The simplest model to deal with such situation is the 'two-step model'. In this model, the bound agonist induces a conformational change in the receptor by reducing the difference in free energy between both receptor conformations. The ligand (L) binds first to the non-active receptor (Rn) with the 'microscopic' equilibrium dissociation constant (K), and this non-active ligand-receptor complex (L—Rn) is in equilibrium with the active complex (L—Ra). This latter equilibrium represents a first-order reaction with the 'microscopic' equilibrium dissociation constant (K' = [L—Rn]/[L—Ra]).

The second equilibrium forms the key element for discriminating between agonists and antagonists:

• For antagonists, the second equilibrium is completely shifted to the left (i.e. K' » 1): all of the occupied receptors remain in the non-active conformation.

• For agonists, the second equilibrium is shifted more to the right for strong agonists than for weak agonists, so that more of the occupied receptors reside in the active conformation; i.e. K' (full agonist) < K' (partial agonist).

Figure 56 From receptor occupation '[L— R]' to stimulus 'S' to response 'E'.

The fraction of occupied receptors residing in the active conformation is related to K' by the following equation:

Several authors have proposed an alternative 'allosteric model', which is derived from the Monod-Wyman-Changeux 'Plausible Model' (Monod et al., 1965). In this model, both receptor conformations are in equilibrium, even in the absence of ligand. Here, the agonist 'favours' a conformational change of the receptor because of its higher affinity for the active conformation. The equilibrium constant for the transition between the two forms of the receptor (K' = [Rn]/[Ra]) is very high since the great majority of receptors are inactive in the absence of drug. Nevertheless, this model allows unoccupied receptors to produce a small stimulus. Ligands are able to bind both to Rn and Ra with the 'microscopic' equilibrium dissociation constants Kn and Ka, respectively:

In this model, agonists can be discriminated from antagonists based on differences between their binding affinities for the active and non-active receptors. This model also provides an explanation for the existence of so-called 'inverse agonists':

• Antagonists are supposed to bind with equal affinity to both receptor conformations (i.e. Kn = Ka); the [Ra]/[Rn] ratio remains the same as in the basal situation.

• Agonists bind with higher affinity to Ra as compared to Rn (i.e. Kn > Ka) so that the whole equilibrium will be pulled to the right, resulting in an increase in the [Ra]/[Rn] ratio. The Kn/Ka ratio is higher for full agonists than for partial agonists.

• Inverse agonists bind with higher affinity to Rn as compared to Ra (i.e. Ka > Kn) so that the whole equilibrium will be pulled to the left, resulting in a decrease of the [Ra]/[Rn] ratio. Some of the compounds that interact with benzodiazepine receptors are inverse agonists: they decrease the affinity of GABA for the GABAa receptor.

The fraction of occupied receptors residing in the active conformation is related to Ka, Kn and K by the following equation:

Studies during the past few years have led to the introduction of even more complex models to explain the activation of G protein-coupled receptors. They will be developed in Sections 4.10 to 4.14.

The capability of the bound ligand to stimulate the receptor has been termed the 'intrinsic efficacy' (e) of the ligand by Furchgott in 1966 (Furchgott, 1966). £ is proportional to the fraction of occupied receptors residing in the active conformation in the two above models, i.e.:

The stimulus (S) is dependent on the amount of occupied receptors ([L-R]) and on the intrinsic efficacy (e) of the ligand, i.e.:

Substitution of [L-R] by [Rtot]/(1 + KD/[L]) yields:

S depends on properties of the ligand-receptor interaction: e and KD. S also depends on [Rtot], a tissue-dependent property. Figure 57 compares the binding (upper panel) and the stimulus (mid panel) that can be obtained at different concentrations of an agonist with the highest intrinsic efficacy known (emax), one with only half of that intrinsic efficacy (a partial agonist) and an antagonist.

Equation 21 was first presented by Stephenson in a more simplified form (Stephenson, 1956): e X [Rtot] was expressed as a single term, the 'efficacy' (e), which is dependent on the tissue (because of [Rtot]) as well as on the ligand-receptor interaction (because of e).

From Stimulus to response: linear relationship

To deal with the many steps which might succeed this initial stimulus, the 'response' (E) should considered to be an undefined function (F) of S, i.e.:

E = F(S) = F(e X [L-R]) = F(e X [Rtot]/(1 + Kd/[L])) (22)

A special case of Equation 22 occurs when E is proportional to the stimulus. This equation can then be written as:

The maximal response of the most active agonist known (i.e. with emax) is:

-2-10123 Log(agonist concentration) - Loq(Kq)

Figure 57 Linear relationship between receptor occupancy, stimulus and response. Curves are shown for an agonist with the highest intrinsic efficacy known (£max), one with only half of that intrinsic efficacy (a partial agonist) and an antagonist.

When the response (E) of any agonist is expressed relative to this maximum, we have:

E /Emax = (e /Smax)/(1 + Kd/[L]) = a/(1 + KD/[L]) (25)

This equation is similar to the one originally proposed by Ariens (Equation 14, in red). Alpha is an experimental parameter but, under the particular condition of a linear

-2-10123 Log(agonist concentration) - Loq(Kq)

stimulus-response relationship, it corresponds to the ratio between the intrinsic efficacy of the agonist of interest and the intrinsic activity of the most active agonist known to date (a = £ /emax) (Figure 57).

From Stimulus to Response: Non-linear relationship

The equation of Ariens represents only a special case of Equation 22: i.e. when E is proportional to S. Quite often, however, the number of activated receptors will exceed the maximal response capacity of the system. In other words, the maximal response is already attained when only some of the receptors are occupied. In such situations, a is no longer proportional to e /emax.

In Equation 22, the response is an undefined function of the stimulus. F is, in principle, undefined for two potential reasons:

• The undefined nature of the cascade of cellular events following the initial stimulus.

• The undefined relationship between consecutive events.

Although many of these cellular events are already known in great detail, the relationship between consecutive events appears, very often, not to be a linear one. A common reason for such a non-linear relationship is that cellular events are capable of amplifying the signal (stimulus) to an extent that exceeds the response capacity of the subsequent event (Figure 79). In other words, the response capacity of the second event becomes saturated even before the magnitude of the first event has reached its maximum. The stimulus-response relationship may thus be composed of any number of saturable and linear functions arranged in sequence. An overall saturable output will still be expected. The classical (and simplest) way to describe F is to represent it as a rectangular hyperbolic function: i.e. E/Emax = S/(S + 1). However, F should also reflect the efficiency of the cellular events converting receptor stimulus into tissue response, as well as the number of events (i.e. the greater the number of saturable steps, the greater the global amplification). A fitting parameter (P), which deals with the number and efficiency of the intermediate cellular events, is therefore introduced in the stimulus-response relationship:

The relationship between E and £ can now be represented as:

= £ X [Rtot]/(1 + Kd/[L])/(£ X [Rtot]/(1 + Kd/[L]) + ß) = £ X [Rtot]/(£ X [Rtot] + ß + ß X Kd/[L])

Figure 58 Linear and non-linear relationship between E/Emax and S.

Figure 58 Linear and non-linear relationship between E/Emax and S.

Beta is a 'fitting parameter' which is inversely related to the global cellular amplification (Figure 58). It is dependent on the efficiency of intermediary cellular evens to amplify the stimulus. Since each successive event may produce a further amplification of the stimulus, P is also likely to decrease with the 'distance' between the stimulus and the measured response. Graphic representations of Equation 28 allow us to evaluate the consequences of varying P (Figure 59). For different types of agonists, a cellular amplification of the stimulus will produce distinct changes of the dose-response curve:

• Full agonists (e is very high): Dose-response curves will be shifted to the left of the actual binding curves (i.e. EC50 < KD). This effect will be even more pronounced as P decreases (Figure 59, top panel). In the heart, for example, the dose-response curve for the isoproterenol-mediated inotropic effect is shifted to the left by about one order in magnitude when compared to the less distant adenylate cyclase response (Figure 54).

• 'Strong' partial agonists (e intermediate): Their maximal response will increase and dose-response curves will gradually shift to the left (Figure 59, mid panel).

• 'Weak' partial agonists (e very low): The maximal response will increase but the EC50 will remain very similar to KD (Figure 59, lower panel). This implies that compounds, which are almost not distinguishable from antagonists in test systems without amplification system, will show up as partial agonists in test systems with an amplification system.

Figure 59 Theoretical dose-response curves of different types of agonists: effect of introducing cellular amplification of the signal and of decreasing the value of p (red arrow). The blue curve corresponds to actual receptor occupancy.

Log(agonist concentration) - Log(Kp)

Figure 59 Theoretical dose-response curves of different types of agonists: effect of introducing cellular amplification of the signal and of decreasing the value of p (red arrow). The blue curve corresponds to actual receptor occupancy.

EC50 << Kd means (at first glance) that the response may already be maximal when only some of the receptors are occupied by the agonist. The terms 'receptor reserve' or 'spare receptor' were introduced as an attempt to describe this phenomenon. However, one must be aware that this definition is ambiguous since:

• The cellular amplification of the stimulus that is responsible for EC50 << KD is likely to occur at different levels, involving biochemical events well beyond the initial process of receptor stimulation (see Figure 79).

• Strictly speaking, all of the receptors should be required to produce a maximal response. Obviously, this can never be attained experimentally since it should require [L] to be infinitely high.

[Rtot] refers to the total concentration of functionally active receptors (i.e. coupled to a response mechanism). Their densitiy can vary dramatically from one tissue to another, and even within a given tissue. Receptor desensitization (see Section 4.8) constitutes a typical example wherein the cells defend themselves against prolonged stimulation by agonists by decreasing [Rtot], both by decreasing the total receptor number and the fraction of functionally active receptors.

Decreasing [Rtot] may have profound effects on different types of ligands (Figure 60):

• Apparently full agonists may undergo a large increase in EC50 or even become partial agonists.

• Partial agonists (i.e. with a < 1 to start with) may become antagonist-like, with little variation of EC50.

Figure 60 Theoretical dose-response curves of an agonist for different values of e X [Rtot]. Dots correspond to receptor occupancy and p = 1.

Figure 60 Theoretical dose-response curves of an agonist for different values of e X [Rtot]. Dots correspond to receptor occupancy and p = 1.

Log(agonist concentration) -Log(Ko)

Log(agonist concentration) -Log(Ko)

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