1.6 Inhibitory Actions at Receptors: II. Insurmountable Antagonism
1.6.5 Reversible Noncompetitive Antagonism
In this variant of insurmountable antagonism, the antagonist acts by combining with a separate inhibitory site on the receptor macromolecule. Agonist and antagonist molecules can be bound at
* See Eq. (1.36) and also the worked answer in Section 1.10 to Problem 1.3 (Section 1.8).
the same time, though the receptor becomes active only when the agonist site alone is occupied (Figure 1.25). This is sometimes referred to as allosteric or allotopic antagonism (see Appendix 1.6A [Section 1.6.7.1] for further comments on these terms).
In the presence of a large enough concentration of such an antagonist, the inhibition will become insurmountable; too few receptors remain free of antagonist to give a full response, even if all the agonist sites are occupied. The point at which this occurs in a particular tissue will depend on the numbers of spare receptors, just as with an irreversible competitive antagonist (see Section 1.6.3.).
If a full agonist is used and the tissue has a large receptor reserve, the initial effect of a reversible noncompetitive antagonist will be to shift the log concentration–response curve to the right.
Eventually, when no spare receptors remain, the maximum will be reduced. In contrast, without a receptor reserve, the antagonist will depress the maximum from the outset.
If we apply the law of mass action to this form of antagonism, the proportion of inhibitory sites occupied by the antagonist will be given by the Hill–Langmuir equation:
Hence, the proportion free of antagonist will be:
We now make the following additional assumptions: (1) Each receptor macromolecule carries one agonist and one antagonist (inhibitory) site. (2) Occupation of the inhibitory site by the antagonist does not alter either the affinity of the other site for the agonist or the equilibrium between the active and the inactive states of the receptor according to the del Castillo–Katz scheme;
however, if the antagonist is bound, no response ensues even if the receptor has isomerized to the active form. (3) The affinity for the antagonist is not affected by the binding of the agonist.
Based on these rather extensive and not entirely realistic assumptions,* the fraction of the receptors in the AR* state is given by Eq. (1.32); however, only some of these agonist-combined, isomerized, receptor macromolecules are free of antagonist and thus able to initiate a response. To FIGURE 1.25 Noncompetitive antagonism. A stylized receptor carries two sites, one of which can combine with agonist (A) and the other with antagonist (B). Four conditions are possible, only one of which (agonist site occupied, antagonist site empty; see upper right) is active.
* A more plausible model follows (see Section 1.6.6).
pBR KB B
= B + [ ]
[ ]
1 − =
p K+
BR K
B B [B]
obtain the proportion (pactive) in this condition, we simply multiply the fraction in the AR* state by the fraction free of antagonist:
(1.55)
Figure 1.26 shows log concentration–response curves drawn according to this expression. In A, the response has been assumed to be directly proportional to pactive; there are no spare receptors.
In B, spare receptors have been assumed to be present, and accordingly the presence of a relatively low concentration of the antagonist causes an almost parallel shift before the maximum is reduced.
The initial near-parallel displacement of the curves in Figure 1.26B raises the question of whether the Schild equation would be obeyed under these conditions. If we consider the two concentrations of agonist that give equal responses before and during the action of the antagonist ([A] and r[A], respectively, where r is the concentration ratio) and repeat the derivation set out in Section 1.5.2 (but using Eq. (1.55) rather than (1.49)), we find that the expression equivalent to the Schild equation is:
Here, Keff is as defined in Section 1.4.4. If r[A]/Keff << 1 (i.e., if the proportion of receptors occupied by the agonist remains small even when the agonist concentration has been increased to overcome the effect of the reversible noncompetitive antagonist), this expression approximates to:
Hence, the Schild equation would apply, albeit over a limited range of concentrations that is determined by the receptor reserve. Moreover, the value of KB obtained under such conditions will FIGURE 1.26 The effect of a reversible noncompetitive antagonist on the response to an agonist, A. Each set of curves has been constructed using Eq. (1.55) and shows the effect of four concentrations of the antagonist (5, 20, 50, and 300 µM). KA, KB, and E have been taken to be 1, 10, and 50 µM, respectively. For (A), the response has been assumed to be directly proportional to the fraction of receptors in the active state. (B) has been constructed using the same values, but now assuming the presence of a large receptor reserve. This condition has been modeled by supposing that the relationship between the response, y, and the proportion of active receptors is given by y = 1.01 × pactive/(0.01 + pactive), so that a half-maximal response occurs when just under 1% of the receptors are activated.
p E
K E
K
active K
A
B B
A
A B]
= + +
⎛
⎝⎜ ⎞
⎠⎟ +
⎛
⎝⎜ ⎞
⎠⎟ [ ]
(1 )[ ] [
r K
r
− = ⎛ + K
⎝⎜ ⎞
⎠⎟ 1 [ ]B 1 [ ]A
B eff
r− =1 [ ]KB
B
provide an estimate of the dissociation equilibrium constant for the combination of the antagonist with its binding sites.
A corollary is that a demonstration of the Schild equation holding over a small range of concentrations should not be taken as proof that the action of an antagonist is competitive. Clearly, as wide as practicable a range of antagonist concentrations should be tested, especially if there is evidence for the presence of spare receptors.
Open Channel Block
Studies of the action of ligand-gated ion channels have brought to light an interesting and important variant of reversible noncompetitive antagonism. It has been found that some antagonists block only those channels that are open by entering and occluding the channel itself. In effect, the antagonist combines only with activated receptors. Examples include the block of neuronal nicotinic receptors by hexamethonium, and of N-methyl-D-aspartate (NMDA) receptors by dizocilpine (MK801).
Such antagonists cause a characteristic change in the log concentration–response curve for an agonist. In contrast to what is observed with the other kinds of antagonism so far considered, the value of [A]50 will become smaller rather than larger in the presence of the antagonist. This is illustrated in Figure 1.27 and is best understood in terms of the del Castillo–Katz mechanism.
Incorporating the possibility that an antagonist, C, is present which combines specifically with active receptors, we have:
(1.56)
Hence, the receptor has four conditions: R, AR, AR*, and AR*C, of which only one, AR*, is active.
This scheme predicts that at equilibrium the proportion of active receptors is given by:
FIGURE 1.27 Curves drawn using Eq. (1.57) to illustrate the effect of three concentrations of an open channel blocker, C, on the response to an agonist acting on a ligand-gated ion channel. Values of 100 nM and 100 and 10 µM were taken for KA, E, and KC, respectively. The vertical arrows show the concentrations of agonist causing a half-maximal response in the absence and presence of C at 50 µM.
A R AR AR C AR C
inactive inactive active inactive
+ +
( ) ( ) ( *) ( * )
(1.57)
where Kc is the dissociation equilibrium constant for the combination of C with the activated receptor, AR*. This equation has been used to draw the curves shown in Figure 1.27. Note how [A]50 decreases as the antagonist concentration is increased. In effect, the combination of the antagonist with AR* causes a rightward shift in the positions of the other equilibria expressed in Eq. (1.56).
Note, too, the convergence at low agonist concentrations of the curves plotted in Figure 1.27.
The antagonist becomes less active when the response is small, because there are fewer receptors in the AR* form available to combine with C. Again, in contrast to the other kinds of antagonism that have been described, there is no initial parallel displacement of the curves (even if many spare receptors are present), and the Schild equation is never obeyed.
Some antagonists combine the ability to block open ion channels with a competitive action at or near the agonist binding site. A well-characterized example is the nicotinic blocker tubocurarine (see Chapter 6). Agonists may also be open channel blockers, thus limiting the maximal response that they can elicit. Such agents (e.g., decamethonium) may therefore behave as partial agonists when tested on an intact tissue.*
The scheme illustrated in Figure 1.25 assumes that the accessory site is inhibitory. It is now known that some agonists (e.g., glutamate) may only be effective in the presence of another ligand (e.g., glycine in the case of the NMDA receptors for glutamate) which binds to its own site on the receptor macromolecule. Glutamate is then referred to as the primary agonist, and glycine as a co-agonist. In principle, an antagonist could act by competing with either the primary agonist or the co-agonist.