Perspective on the Relationship between GABAA Receptor Activity and the Apparent Potency of an Inhibitor.

BACKGROUND: In electrophysiological experiments, inhibition of a receptor-channel, such as the GABAA receptor, is measured by co-applying an agonist producing a predefined control response with an inhibitor to calculate the fraction of the control response remaining in the presence of the inhibitor. The properties of the inhibitor are determined by fitting the inhibition concentration- response relationship to the Hill equation to estimate the midpoint (IC50) of the inhibition curve Objective: We sought to estimate sensitivity of the fitted IC50 to the level of activity of the control response
Methods: The inhibition concentration-response relationships were calculated for models with distinct mechanisms of inhibition. In Model I, the inhibitor acts allosterically to stabilize the resting state of the receptor. In Model II, the inhibitor competes with the agonist for a shared binding site. In Model III, the inhibitor stabilizes the desensitized state.
RESULTS: The simulations indicate that the fitted IC50 of the inhibition curve is sensitive to the degree of activity of the control response. In Models I and II, the IC50 of inhibition was increased as the probability of being in the active state (PA) of the control response increased. In Model III, the IC50 of inhibition was reduced at higher PA.
CONCLUSION: We infer that the apparent potency of an inhibitor depends on the PA of the control response. While the calculations were carried out using the activation and inhibition properties that are representative of the GABAA receptor, the principles and conclusions apply to a wide variety of receptor- channels. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.net.

INTRODUCTION

Binding of the transmitter γ-aminobutyric acid (GABA) to the γ-aminobutyric acid type A receptor (GABAAR) enhances activation of the receptor. As the concentration of GABA in the surrounding environment is increased, the probability of being in the active state (PA) rises. In electrophysiological recordings, the increase in PA manifests as higher whole-cell peak current. At saturating GABA concentrations, the peak PA of the GABAA receptor varies between ~0.4 (α4β2δ; [1]) and ~0.9 (α1β2γ2; [2, 3]). The maximal PA can vary considerably when the receptor is activated by other agonists. For example, the peak PA of the α1β2γ2 GABAA receptor in the presence of a saturating concentration of piperidine-4-sulfonic acid is <0.2 [4]. The agonist concentration-response relationships are typically fitted to the Hill equation and characterized by estimating the midpoint (EC50) and slope (nHill) of the curve.

In electrophysiological experiments, inhibition is described as fraction of the control response to agonist in the absence of an inhibitor. The concentration of agonist producing the control response is usually defined in terms of an “effective concentration” (EC) as the fraction of the maximal response elicited by a saturating concentration of the agonist. The properties of the inhibitor are presented in terms of a fitted Hill equation, described by IC50 (midpoint of the inhibition curve) and nHill of the inhibition curve. Comparison of the effects of different inhibitors, or the effects of mutations to the receptor on inhibition are then expressed through changes in the IC50 value [5-9]. Statistical approaches can be employed to determine if a change is statistically significant.

Here, we show that the fitted IC50 of an inhibitor is sensitive to the level of the control response. As a result, IC50s measured at different activity levels cannot be meaningfully compared and statistical analysis is not appropriate. While EC and PA values can be easily interconverted, we emphasize that any comparison of inhibition among subtypes of a receptor, including receptors with introduced mutations, needs to be conducted at a constant PA rather than a constant EC value, because the latter may not equivalently correlate with PA in different receptors.

We simulated the effects of an inhibitor employing three models with distinct mechanisms of inhibition. The models are based on the Monod-Wyman-Changeux allosteric model adapted to describe ion channel currents [10-13]. In the first model (Model I), the inhibitor binds to an allosteric site, i.e., a site not involved in the action of the agonist. By having a higher affinity to the resting (R) than the active (A) state, the inhibitor stabilizes the R-state and reduces PA. Model II represents competitive inhibition, where the inert inhibitor competes with the agonist for a shared binding site. Models I and II contain two states, R and A. Model III is a three-state model containing, besides the R- and A-states, a state corresponding to the desensitized (D) receptor. In this model, the inhibitor stabilizes the D-state. The models are illustrated in Fig. ().

In all cases, the PA of steady-state responses was calculated. For Model I, the PA in the absence and presence of the inhibitor was calculated as follows [14]:

In this equation, X and Y stand for the agonist and inhibitor, respectively. KR,i is the equilibrium dissociation constant of drug i (X or Y) in the resting receptor, ci is the ratio of the equilibrium dissociation constants in the active and resting states, and Ni is the number of binding sites. L (=R/A) expresses the level of activity in the absence of agonist or inhibitor.

For Model II, receptor activation was calculated as follows [15]:

where N is the number of shared binding sites for X and Y (constrained to 2). Other terms are as described above. Models I and II behave identically in the absence of inhibitor.

For Model III, the PA was calculated as follows [16]:

where Q (=A/D) is a measure of desensitization in the absence of active drugs. Q was constrained to 100 to minimize desensitization in the absence of an inhibitor. dY is the ratio of equilibrium dissociation constants of the inhibitor in the desensitized and active states. Other terms have been defined above. It is assumed in Model III that the agonist (X) does not desensitize and the inhibitor (Y) does not activate.

For all simulations, L = 8000, KR,X = 10 μM, cX = 0.004 and NX = 2. Initial calculations of inhibition were conducted at a control PA of 0.5 (Fig. ). The concentration of agonists producing a response with PA of 0.5 was 5.5 µM in Models I and II. The presence of the term Q in eq. 3 (Model III) slightly affects the activation in the absence of Y (the concentration of X producing the steady-state PA of 0.5 is 5.55 μM). The specific properties, i.e., KR,Y, cY, and dY of the inhibitor within a model were adjusted to generate curves with similar IC50s (~5 µM). In Model I, the KR,Y was 5.8 µM, cY was 10, i.e., the inhibitor had a ten-fold higher affinity to the resting than the active state, and NY was 2. In Model II, the KR,Y was 4.3 µM, and cY was 1. Model II simulates Y-mediated competitive inhibition of receptor activation by X. In Model III, KR,Y was 250 µM, dY was 1×10-4, and NY was set to 1.

Next, we altered the concentration of the agonist to generate control responses with PA ranging from 0.05 to 0.85, and calculated the effect of the inhibitor in the framework of each model. In Models I and II, the concentration of the agonist X was varied between 0.85 µM (PA = 0.05) and 57 µM (PA = 0.85). In Model III, [X] varied between 0.85 μM and 71 μM. The inhibition concentration-response curves were fitted with the Hill equation, and the relationships between PA of the control response and the IC50 of the inhibitor are given in Fig. (-).

Fig. (2)

The effect of the P (A) The inhibition concentration-response relationships were calculated using eq. 1 (Model I), eq. 2 (Model II), or eq. 3 (Model III). The control response (i.e., no inhibitor present) had a PA of 0.5 In Model I, the inhibitor had a KR (equilibrium dissociation constant in the resting receptor) of 5.8 µM, a c (ratio of equilibrium dissociation constants in the active and resting receptors) of 10, and an N (number of binding sites) of 2. In Model II, the inhibitor had a KR of 4.3, a c of 1, and an N of 2. In Model III, the inhibitor had a KR of 250 µM, a d (ratio of equilibrium dissociation constants in the desensitized and active receptors) of 0.0001, and an N of 1. The curves were fitted to the Hill equation, yielding IC50s of 5.0 µM (Model I), 5.0 µM (Model II), and 4.9 µM (Model III). With these parameters inhibition is essentially complete at high inhibitor concentrations. (B) The relationships between the PA of the control response and the associated IC50 for the inhibitor. Inhibition concentration-response relationships were calculated using eqs. 1-3, and fitted to the Hill equation. The data indicate that in Models I and II, the inhibitor becomes less potent (higher IC50) when the PA of the control response is increased. In Model III, higher PA of the control response is associated with higher potency of the inhibitor. (C) The panel illustrates the relationship between PA and IC50 at a higher resolution of the ordinate.

The data indicate that in Models I and II, an increase in agonist concentration, leading to an increase in PA, is associated with an increase in the IC50 of the inhibitor. For example, in Model I, the IC50 of the inhibition curve is 2.9 µM when measured at PA of 0.05, and 12.7 µM when measured at PA of 0.85. In Model II, that simulates competitive inhibition between the agonist and the inhibitor, the IC50 of the inhibition curve is 2.2 µM when measured at PA of 0.05, and 52 µM when measured at PA of 0.85. In contrast, Model III predicts lower IC50 of inhibition at a higher PA of the control response. When inhibition is measured at PA of 0.05, the IC50 is 42 µM. At PA of 0.85, the IC50 is 2.9 µM.

Previous studies of competitive antagonists (our Model II) and partial agonists at the muscle nicotinic receptor have demonstrated that IC50 values increase when determined at higher levels of activation [17, 18]. The analysis of inhibition using the Schild equation [19, 20] also relies on the underlying concept that the IC50 for a competitive antagonist will be larger when tested against a higher concentration of agonist. Open-channel blocking drugs are well-known to inhibit responses with high PA more efficaciously than those of low PA [21], consistent with a reduction in IC50 in Model III. Similarly, for the inhibitory steroid pregnenolone sulfate that acts by stabilizing a desensitized state (our Model III), the IC50 is reduced at higher agonist concentrations [16].

CONCLUSION

In sum, we have shown here that the IC50 of an inhibitor is sensitive to the PA of the control response to the agonist in the absence of inhibitor. As the PA of the control response increases, the IC50 can decrease or increase, depending on the mechanism of action of the inhibitor. In models where the inhibitor acts allosterically to stabilize the resting state, or competes with the agonist for a shared binding site (competitive inhibition), the IC50 is increased at higher PA of the control response. In a model where the inhibitor stabilizes the desensitized state or another non-conducting, post-active state, the IC50 is decreased at higher control PA. For example, a change in control PA from 0.2 to 0.3 increases the calculated IC50 for our hypothetical inhibitor by 10% (Model I) to 20% (Model II), or decreases the IC50 by 30% (Model III). Our simulations also indicate that the IC50 is most sensitive to changes in control PA over different ranges, depending on the model (high PA for models I and II, low PA for model III).

A corollary of the data presented in Fig. () is that comparison of inhibition among mutated or different subtypes of a receptor requires the determination of PA of the control response; measurement of inhibition at a constant EC value is inadequate because a change in receptor structure may modify the relationship between PA and EC values. An approach to estimate PA of the macroscopic current response has been described previously [22, 23].

Our simulations were conducted using control PA values and the activation and inhibition properties that are representative of the mammalian GABAA receptor. The underlying principles, however, likely apply to a wide variety of receptor-channels.