The simplest agonist mechanism that can be used to describe activation of the ligand-gated ion-channel receptors is that first suggested by del Castillo and Katz (1957) for activation of nAChRs at the neuromuscular junction:
Receptors Linked to Ion Channels: Mechanisms of Activation and Block 185
(6.1)
This mechanism makes the vital point that receptor activation must represent a distinct step (most likely several steps) subsequent to agonist binding (see also Chapter 1). However, this mechanism does not allow for the fact that considerable functional, biochemical, and structural evidence now suggests that there are two ACh binding sites on nicotinic acetylcholine receptors of muscle and electric organs (Unwin, 1996), and it is probably the case that other four-transmembrane (4TM)-domain subunit receptors (see Chapter 3) such as the glycine and GABA receptors also require binding of two agonist molecules for efficient activation of the receptor. At present, the mechanism most commonly (e.g., Colquhoun and Sakmann, 1981) used to describe AChR activation is as follows:
(6.2)
Here, the microscopic association and dissociation rate constants for each step in the receptor activation mechanism are given, where k+1 and k+2 refer to agonist binding, k–1 and k–2 refer to agonist dissociation, and β and α are the rate constants for channel opening and closing, respectively.
The factor of 2 before k+1 and k–2 occurs because the mechanism assumes that either of the two agonist binding sites can be occupied or vacated first. In addition, note that the two sites are assumed to be equivalent before agonist binding.
6.2.1 EVIDENCEFOR NONIDENTICAL AGONIST BINDING SITES
The agonist binding sites on the receptor are some distance from the ion channel and outside the membrane. They are in pockets formed within each α-subunit (Unwin, 1996). The environment of the two binding sites cannot, in principle, be identical because of the nonidentical adjacent subunits and the fact that the receptor is a pentamer. However, functional evidence demonstrating nonequiv-alance of the two binding sites has not been consistent between species.
The best evidence that the binding sites are different comes from studies of the Torpedo AChR, for which both binding studies of native receptors and patch-clamp studies of cloned receptors expressed in fibroblasts suggest that there is on the order of a 100-fold difference in affinity for ACh between the two sites (Lingle et al., 1992). Similar experiments on the BC3H1 cell line also suggest heterogeneity of the agonist binding sites on this embryonic mouse muscle AChR. In contrast, some experiments have found no evidence for a large difference between ACh binding at the two sites on frog endplate AChRs (Colquhoun and Ogden, 1988).
At present, this issue has not been resolved, and further functional and structural work continues to address this question. However, it should be noted that the presence on a receptor of two agonist/antagonist binding sites, which may be different, adds considerably to the complexity of the results expected from binding studies or dose-ratio experiments such as the Schild method, as described later in this chapter. It can also be noted here that homomeric receptors (such as the neuronal nicotinic α7 receptor or homomeric AMPA receptor; see Chapter 3) will have equivalent agonist binding sites before agonist binding. A further interesting point is that if the glutamate receptor subunit stoichiometry is tetrameric, then heteromeric non-NMDA receptors composed of, for example, two GluR1 and two GluR2 subunits will, in principle, have nonidentical binding sites on the equivalent subunits if the subunits are adjacent to each other in the molecule, but they will have equivalent binding sites when the GluR1 and GluR2 subunits alternate in position around the central ion channel. These are very good examples of how information on receptor structure can be indispensable in interpreting the results of functional studies of drug action.
A+R AR AR
−
+ *
k k 1 1
α β
A R+ AR+A A R A R
− +
−
+ *
k k
k k
1 1
2 2 2
2 2 2
α β
186 Textbook of Receptor Pharmacology, Second Edition
6.2.2 APPLICATION OF THE TWO-BINDING-SITE MECHANISM
Equation (6.2) has proved to be a good description of AChR activity in a wide range of experimental situations (reviewed by Edmonds et al., 1995) and more recently has been used as a starting point in developing mechanisms to describe the activation of other ligand-gated ion channels such as glutamate receptors, 5HT3 receptors, and GABA receptors.
Expressions relating the equilibrium occupancy of any state in this mechanism to agonist concentration can be derived as described in Chapter 1. If we define the equilibrium constants for agonist binding as K1 = k–1/k+1 and K2 = k–2/k+2 and a constant E describing the efficiency of channel opening (equivalent to efficacy) as E = β/α, then the equilibrium occupancy of the open state (A2R*) will be:
(6.3)
It is instructive to write this equation in the form analogous to that for a single agonist binding site mechanism,
(6.4)
as this form illustrates the low-concentration dependence of pA2R* on the square of the agonist concentration, which steepens the dose–response curve.
The equilibrium occupancy of the open state of an ion channel is usually referred to as the popen and is the fraction of time that a single channel is open or, equally, the fraction of a population of channels that are open at equilibrium. For a two-binding site agonist mechanism, the relationship between the popen and the agonist concentration (popen curve) has the familiar sigmoid shape (when the agonist concentration is plotted on a logarithmic scale) of a dose–response curve but is steeper than for a single binding site mechanism.
6.2.3 HILL COEFFICIENTS AND COOPERATIVITY
In Chapter 1 (Section 1.2.4.3), the Hill equation and the Hill coefficient, nH, are described. Hill coefficients greater than or less than unity are often interpreted as indicating positive or negative cooperativity, respectively, in the relationship between receptor occupancy and response. For exam-ple, positive cooperativity could arise due to amplification in a transduction mechanism mediated by G-proteins and changes in cell calcium concentration.
If the receptor has two agonist binding sites, the question arises as to whether binding of agonist at one site can influence the binding of the agonist at the other site, referred to as cooperativity between agonist binding sites. Negative cooperativity occurs when binding at one site reduces the affinity at the second site, while positive cooperativity occurs if binding at one site increases the affinity at the second site. Note that there may be cooperativity between agonist binding sites even though the unoccupied sites have the same affinity for the agonist. However, it is also possible that the two agonist binding sites are different before agonist binding occurs (on average, one site is then more likely to be occupied before the other), and in this case it is still possible for the binding of agonist at one site to influence binding at the other site.
The slope of the popen curve for Eq. (6.2) is more complex than for a single agonist binding site; Eq. (6.4) does not have the same form as the Hill–Langmuir equation, and the Hill plot is not
p
E K K
A R
A
[A A
A
2 1
2 2
1
*
[ ]
] [ ]
[ ]
=
+ + ⎛ +
⎝⎜ ⎞
⎠⎟
⎧⎨
⎩
⎫⎬
⎭
p K K
E E
K E
A R*2
A
A A A
=
+ ⎧ + +
⎨⎩
⎫⎬
⎭ [ ]
[ ] [ ] [ ]
2
1 2 2 2