Binding, gating, affinity and efficacy: The interpretation of structure‐activity relationships for agonists and of the effects of mutating receptors (1998)

British Journal of Pharmacology (1998) 125, 923–947; doi:10.1038/sj.bjp.0702103 The nature of the problem is illustrated by the curves in Figure 1. A mutation in a receptor is seen to produce 100 fold increase in the EC50 for an agonist (Figure 1a). A ligand binding experiment with the same agonist, on the same mutant receptor (Figure 1b) shows that the measured affinity for the binding of the agonist has also been reduced by about 100 fold. Obviously the mutation has affected the agonist-binding site, and the mutated amino acid is likely to be part of that site? No! It is not in the least obvious. The example in Figure 1 was calculated on the basis that the affinity for the binding step of the reaction was totally unaffected by the mutation (the equilibrium constant for this step was 100 μM for both wild type and mutant). The only difference between wild type and mutant receptor in this example is the ability of the receptor, once the agonist has bound, to change conformation to its active state. There is no reason at all why the amino acids that affect the ability to change conformation should be anywhere near the agonist binding site. Concentration-response curves (left) and agonist-binding curves (right). Calculated from the del Castillo-Katz (Scheme 1). The binding reaction has an equilibrium constant of KA= 100 μM for both wild type and mutant receptors, so the mutation does not affect the binding site at all. The equilibrium constant for isomerisation to the open state (the gating reaction) is 200 for the wild type (high efficacy), but only 1 for the mutant. The mutation has affected only the ability of the protein to change its conformation; the binding site is unaffected. Binding experiments do not measure affinity (in any sense that is useful for learning about the binding site), for any ligand that causes a conformation change. The term ‘apparent affinity’ is often used to describe EC50 for the response but it is meaningless (unless you define what you mean by ‘apparent'). Making this distinction between effects on binding and effects on conformation change is arguably the fundamental problem of modern molecular studies of receptors. It is not an easy distinction to make, but unless it can be solved, the interpretation of structure-function studies is quite likely to be nonsense. It is not just a theoretical problem; this is how ion channels actually behave. Nevertheless, the very existence of the problem has not always been recognized. For example, statements like the following are not at all uncommon*. (a)‘Simplistically, the efficacy of a full agonist can be set equal to 1, that of an antagonist to 0, and that of a partial agonist to a value between 0 and 1’ (Ross, 1996, in Goodman & Gilman, 9th Edition). This statement obscures the point that is crucial, both for the interpretation of structure-activity relations and of mutant studies, that efficacy has no upper limit in principle, and that when it is large, changes in it are indistinguishable from changes in affinity. (b)‘This change in the sensitivity of the Y190F mutant could be due either to a change in the binding affinity of the receptor or to a change in the energetics of opening of the channel after binding. To distinguish between these possibilities, we assessed the ACh binding affinity of the mutants by measuring the ability of ACh to compete for [125I]-α-bungarotoxin binding’ (Tomaselli et al., 1991). Figure 1 shows clearly that such measurements do not make the required distinction. (c)‘Of particular interest in this regard is the ability to measure independently both ligand receptor affinity (by ligand binding techniques) and biological activity (ED50 and Emax). These two independent processes provide information about …’ (Hollenberg, 1991). The whole point of the problem is, of course, that these measures are far from being independent. If binding affects activation (transduction, gating), then activation must affect binding. (d)‘Measurement of full-agonist-affinity can be made by a procedure developed by Furchgott’ Kenakin (1997a, p272). This would be true only if activation had no effect on binding, which is not true for any currently proposed mechanism of agonist action (Colquhoun, 1987). The problem of interpreting the effect of mutations has been discussed before (Colquhoun & Farrant, 1993). It now seems timely to consider what can be done about it. Although difficult, it is not impossible, and, at least for ion channels, there are sensible things that can be done. Before going on to the modern problem, it is appropriate to recognise that this is not a new problem at all. Essentially the same difficulty occurs in the interpretation of the structure-activity relationships of a series of different agonists on the same receptor, and in this context it has been around since the 1950s. Stephenson (1956) had pointed out the very important fact that the action of an agonist could not be described by an affinity constant alone. In addition some measure of the ability of the agonist to activate the receptor (e.g. to open an ion channel) was essential too (he termed the latter, the efficacy of the agonist). This postulate was, very rightly, enormously influential. Two quantities (at least!) were needed to describe the action of an agonist, affinity (for the initial binding reaction), and efficacy (to measure the ability to activate once bound). No sense could be made of structure-activity relationships for agonists unless these two quantities could be disentangled, because the effects of a change in agonist structure may be (and often is) quite different for each of them. Unfortunately these separate quantities, affinity and efficacy (for which, in an ion channel context we may read binding and gating), have proved very hard to measure. Various methods have been proposed to measure them, but because of an error in Stephenson's argument these methods are not valid. Stephenson's original error has been propagated to the progeny of his paper. In particular, it is present in Furchgott's (1966) method for measuring the affinity and efficacy of a full agonist (which is unfortunate because it is essentially the only method that has been proposed for use when no mechanism is known). It is also present in the ‘operational model’ of Black & Leff (1983), which is identical with Stephenson's argument except for the addition of the additional assumption of a particular (hyperbolic or Hill) stimulus-response relationship. The same error has propagated to many other papers e.g. the method of Venter (1997), and the discussion of Clarke & Bond (1998). Likewise, attempts to ‘validate’ Furchgott's method by showing that the ‘affinity’ it produces agree with those by direct binding measurements (e.g. Morey et al., 1998) are futile because agreement is expected (Figure 1 and Colquhoun, 1987), but the value produced by both methods is not affinity in the sense intended by Stephenson, or in the sense that is useful for making inferences about the binding site (e.g. see eq. 1, below). These methods cannot, therefore, be expected to work, and it is the purpose of this discussion to consider what can be done about it. The nature of Stephenson's error is enlightening. There are various ways in which it can be stated, but the essential point is that his theory contained a parameter, p, described as the receptor occupancy, which he supposed to be related to concentration in a simple Langmuirean manner, and to depend only on affinity. In fact, in any physically realistic mechanism, the receptor occupancy must depend on all the reaction steps, not on only the affinity for the initial binding reaction. This is a consequence of the basic physical principle of reciprocity (if A affects B then B must affect A; see Edsall & Wyman, 1958; Wyman & Gill, 1990). This reciprocity is built into every current proposal for the mechanisms of both ion channels and G protein-coupled receptors, but it is absent from Stephenson and his progeny. That is why they are wrong. Stephenson's paper is ambiguous about whether the term ‘occupancy’ is intended to represent what you would measure in a ligand binding experiment, though that is actually what he had in mind (R. P. Stephenson, personal communication). The problem lies in the fact that, for any ligand that produces a conformation change, the total amount of binding (as measured in a ligand binding experiment) depends not only on the affinity of the initial binding, but also on the extent to which the conformation change takes place once ligand has become bound. The result of a binding experiment depends on both affinity and efficacy (or, in ion channel language, on both binding and gating). Stephenson's approach was essentially rooted in the classical era. The approach to receptor problems hardly changed between 1909, when A. V. Hill first derived the Langmuir equation, and the early 1950s. An enormous advance was made when it was realized that some proteins could undergo global conformation changes, and that the ligand binding properties of the two conformations might be very different. The first clear statement of that idea was, as far as I am aware, in a seminal paper by Wyman & Allen (1951). Enough was known of the structure of haemoglobin at that time for it to be realised that the molecule existed in two distinct conformations. Wyman and Allen suggested that the properties of haemoglobin (and perhaps of enzymes too) could be explained very economically if the change in affinity during binding of oxygen were actually based on a concerted change in structure from one conformation to the other (i.e. all four subunits flip together). Furthermore it was known that the structure of oxyhaemoglobin was very similar to that of carboxyhaemo-globin, so this hypothesis also provided an elegant explanation for the identity of the Bohr effect for both oxygen and carbon monoxide. The ion-channel equivalent of this prescient statement would be to say that the properties of an open ion channel should be independent of the agonist that caused it to open (the only difference being the length of time the channel is open for), a prediction that has generally been found to be true. Indeed the direct observation of a single channel ‘snapping’ from one conductance state to another has provided the most direct evidence available in any field that a functional receptor protein exists, to a good approximation, in two (or a few) distinct conformations. The idea of a conformation change also appeared, during the same decade, when del Castillo & Katz (1957) wrote the binding step and the conformation change as two separate steps, as an attempt to explain partial agonism. Their paper was a year after Stephenson's, and it took a very different approach. Stephenson had tried to formulate the transduction mechanism as a black box, and to provide a very general treatment. This had worked very well for the analysis of competitive antagonists, in the way suggested by Schild a bit earlier. For antagonists the use of null methods allowed valid estimates of antagonist equilibrium binding constants in a way that was remarkably independent of any knowledge of the transduction mechanism (e.g. Colquhoun, 1973). For a long time it was hoped that a similar trick would work for agonists too (e.g. Furchgott, 1966; Black & Leff, 1983), but sadly it is not so simple. Katz, on the other hand, postulated a simple and explicit transduction mechanism (for the endplate nicotinic receptor-channel). Their mechanism postulated that binding of the agonist (A) to a receptor (R) resulted in a complex (AR) which was still inactive (channel shut), which could then undergo a conformation change to the active (open) state. The del Castillo-Katz mechanism was This depends on both binding (KA) and on conformation change (E), so knowledge of its value does not tell us anything directly about the binding site The problem is to separate these two quantities. The EC50 in (1) is what is often known as Kd when talking about binding or ‘apparent affinity’ when talking about responses For the example in Figure 1 the EC50 is 0.498 μM for wild type and 50 μM for mutant, whether binding or response is measured. The actual equilibrium (or rate) constants for individual reaction steps (like KA and E) are known as microscopic constants, and they are what tell us about what is going on. In contrast, equation (1) defines a macroscopic constant; it describes what we see, but does not tell us what is going on underneath. Illustration of the effect of changing the ability to change conformation (the value of E in the del Castillo-Katz scheme) for a series of agonists (or of the receptors) that all have the same affinity for the binding reaction, (a) shows the fraction of active receptors, (b) shows the corresponding agonist binding curves. The curves in Figure 2a are very similar to the theoretical and experimental curves shown in Stephenson (1956) (though he calculated them in a different way). Now, as then, they show that any attempt to measure the efficacy of an agonist on a scale from 0 to 1 (as maximum response as fraction of that for a ‘full agonist) is unhelpful and misleading, if the aim is to discover something about the structure-activity relationships of agonists, or about the effects of a mutation in a receptor. Of course, if real receptors always had rather low efficacies then this objection would not be serious, but that is not the case. For the muscle nicotinic receptor, E is at least 30-100 for acetylcholine (see Table 1). In the case of a protein that is better characterized than most receptors, E has been estimated as 3000 for haemoglobin (see below). The problem is not pedantic, it is real. Once the idea of a global conformation change had taken root, it was natural, indeed it was a thermodynamic necessity, to consider how much of the receptor was in its active conformation in the absence of agonist. Wyman's postulate converged with Katz's approach when Monod et al. (1965) proposed their well-known mechanism for cooperative enzymes. In the case of a single subunit, this amounts merely to addition of one extra state to the del Castillo-Katz mechanism, the unliganded active state (R*) which will produce ‘constitutive activity', as shown in Scheme 2. Here E0 is the conformational equilibrium constant in the absence of agonist and is therefore a measure of constitutive activity whereas E1 is (like E above) a measure of efficacy. As before, both response and binding are hyperbolic at equilibrium, and again both have the same EC50. And as before this EC50 depends on all of the equilibrium constants. If we want to know about the binding site we have to find a way to estimate KA. This sort of mechanism (extended to four subunits, by analogy with Scheme 5, below) has been applied to haemoglobin (e.g. Edelstein, 1975), though it is only an approximate description. This makes an interesting analogy with a drug receptor. The deoxy (or T) state of haemoglobin corresponds to the resting receptor (denoted R here). Addition of oxygen (the ‘agonist') causes, in a proportion of molecules, a concerted conformation change of the entire molecule to the oxy- conformation (known in the haemoglobin literature as the R state, corresponding to the active state, R*, here). In the absence of ‘agonist', only about 1 in 9,000 molecules are active (E0=1.1 × 10−4, very little constitutive activity, in receptor terms). The ‘agonist’ binds more tightly to the ‘active form’ by a factor of M=KA/KA*=71. Thus (see eq. 3) the conformational equilibrium constant for the mono-liganded molecules is E1=E0M1=7.8 × 1O−3 (still little effect), for bi-liganded molecules it is E2=E0M2=0.55 (about 36% change conformation), for molecules with three ligands bound it is E3=E0M3=39 (about 98% change conformation), and for the fully-liganded molecule it is E4=E0M4=2795, i.e. almost all molecules are in the ‘active state’ (the oxy-conformation) at high ‘agonist’ concentration. In these terms, oxygen is a very high efficacy agonist. The fact that, for such agonists, it is difficult to distinguish a change in efficacy from a change in affinity has caused problems for the interpretation of experiments on haemoglobin, just as it has for receptors. In the context of receptors, the description allosteric is now widely used. It is, perhaps, not helpful for clarity of thought that different authors often use it to mean somewhat different things. At one extreme, the term ‘allosteric antagonist’ can often be translated as ‘we have got an antagonist and we are not sure what it does, but it appears not to be competitive'. This means much the same as ‘non-competitive', a word which pharmacologists had always supposed to mean action at a different site, though with no postulate as to how the effect was mediated. In fact ‘non-competitive’ usually (and still more than and therefore about At the other extreme, Monod et al. (1965) a Their were as for proteins are the of which are in such a way that they all equivalent There is one site on each for each ligand that can with it. The conformation of each is by its with other Two (at are to allosteric As a the affinity of one (or of the the corresponding ligand is when a occurs from one to the other state. the protein from one state to another state, its molecular is The term allosteric was by Monod & in a discussion of the point of of the most of the of the of a by is that the is not a of the therefore to this mechanism as ‘allosteric At this the word allosteric little other than what pharmacologists would have to as Monod et al. such of activity, The effect of these appears to result from a conformational in the protein when it binds the This the the of conformation changes, as postulated by Wyman & and discussed This in the paper by Monod et al. (1965) (see also for an of the the there is to a at the is that allosteric to any mechanism in which a protein can in two (or distinct which in their affinity for a This has been by Wyman & Gill, 1990). And an allosteric is anything that binds better to one conformation than the other (i.e. almost Although the of Monod et al., (1965) the term to molecules that show it is now to use the term for mechanisms like that in Scheme which do not into this It is that the binding equilibrium, in 1 and in the sense that us about the binding site. the equilibrium constant for conformation change in the receptor efficacy (e.g. E in 1, E1 in and in It is that the of and of partial and in the receptor rather than (i.e. in constants like or their for G protein-coupled these receptor properties are the only things that the maximum For example, in the case of an ion the of the response receptor will depend on the single channel conductance too (and on many other things if or some response is being for G protein-coupled receptors, the nature of the to G protein (and the concentration of G also affect the efficacy (see as well as the to the Of these things to the efficacy of two agonists the same only as they are on the nature of the agonist, and often they are the other hand, when wild type and mutant receptors, it is not for things like single channel conductance to change (though that, at is consider the case one agonist is on two receptors, say a wild type and a mutant receptor. A binding would mean that both KA and were changed by the same factor when the mutation was and both E0 and E1 were This would be good evidence for an effect on the binding site. At the other extreme, a gating would mean a change in the constant i.e. a change in the of constitutive activity (though it is quite that the value would too little constitutive activity to be in an For a gating both KA and would be by the so the E1 would be changed in direct proportion to the change in consider the case we two agonists on the same receptor. the difference between their a result of different binding, or different ability to activate once In some ways this is a bit The to activate in the absence of agonist is measured by the equilibrium constant so E0 is the same for both Thus if the E1 changes this means that or must change is this a or is it a For a binding both KA and would have to by the same factor for each agonist, so E1 would be the same for both of them. This would be good evidence for a change in the binding site For a gating effect the initial binding to the state, KA would have to be the same for both agonists, but E1 would be different for each agonist, and binding to the open state, must also be different. The change in binding to the active state means that the active state produced by each agonist to some be different. In that case how can we the mechanism know from ion channel studies (see below) that the active (open) state from one agonist to because different agonists the channel open for different of it is also found that the conductance of the open channel does not depend on which agonist is used. It seems that the global conformation of the active (open) state is much the same for all agonists, but that some agonists can the open state better than This sort of has to much discussion in the context of G protein-coupled receptors, which are with There is, of course, another the reaction could change changing the equilibrium constants. For example, the opening constant for an ion channel as and the constant as so A mutant receptor in which both and were would have the same E1 but would show a change in gating (the mean open time would be but would be An experimental example of this is shown in Table 1. of the discussion that the binding site is a set of amino acids that with the bound agonist. since the agonist binds more tightly to the active conformation of the receptor, the binding site changes when the receptor changes proteins undergo quite conformation changes (e.g. binding so it is quite that in the active conformation some part of the molecule the agonist and causes it to be If this is the it is likely that more amino acids will with the ligand in the active conformation (and it is that that are present in the inactive conformation would be in those in which it is to estimate the value we will tell us only about binding to the inactive and that is something we want to know because that is the first in a the for all that (at least for receptors with low constitutive In the context of the it is clear from the discussion that binding to the active conformation is part of the the point of that is the case in the sense that binding to the active state will depend on the ability to change and is likely to be affected by mutations which affect that the other hand, it is easy to a different that, when the receptor is in its active amino acids were not to the ligand in the inactive now the ligand and part of its binding site. A mutation in one of these amino acids could have no effect at all on the ability of the receptor to change conformation (e.g. E0 in Scheme but might the extent to which the ligand was bound This would the and if that were reduced could result in partial agonism. It is the general of this paper that it is futile to that can be about structure-activity relationships of agonists, or the effect of mutations on receptors, some knowledge of To that aim is to a mechanism that describes physical (to a and to the and equilibrium constants for the between the in which the receptor can for example, changes in KA will tell us something about the structure of the binding site in the inactive and changes in will tell us something about the structure of the binding site in the active The affinity and efficacy are from this point of the other hand, they do well to to a general problem, in the of particular and to that extent I still find them The is that we It seems likely that knowledge of G protein-coupled receptor mechanisms is still (see below). In the case of ion channels the is It seems very for example, that physically can be about channel The is but it seems quite likely that, in a at this may also be in a physically realistic Nevertheless, there for ion channels, many A of these are as all work has or that the effect of changing the receptor structure (e.g. making a or changing the agonist has the effect of changing the between of the receptor. In other like (1) to (and of them that are still good of the physical that is that the structure change the (and constants, changing the between the various There is actually to no hard evidence about whether or not this is true. It is not hard to that this is an but such time as there is evidence to the this approach can be by of is that the agonist binding a conformation change, which and is separate the global conformation change that is such conformation change is but it is usually to be and (see It is also to be so to this change could not produce partial agonism. It is a simple to such a conformation change in any mechanism, but once again there is no hard evidence that there is for such a so It is a of the more that are that the mechanisms on which they are based may be to the point that the aim of measuring physically quantities may be In the of the does not with as I would to you a as to produce a simple and elegant but only a which, In the case of ion channels, us to the active state of the receptor very If we could see with equal clarity when a molecule bound to the receptor, the problems would