The relationship between apparent potentiation and the magnitude of the control response

Drug-induced potentiation of receptor-channel function can manifest in numerous behavioral endpoints, including sedation and anesthesia (GABA_A receptor), cognitive enhancement (NMDA receptor), or heightened pain sensation (TRPV channel) (Numazaki and Tominaga, 2004; Garcia et al., 2010; Collingridge et al., 2013). In electrophysiological recordings, potentiation is measured by calculating the response ratio (RR) from the ratio of amplitudes of current responses to an agonist in the presence and absence of a modulator. A difference in RR at a given modulator concentration is typically taken as evidence of distinct potentiation properties when comparing modulation by different compounds.

One issue with this approach is that it does not take into consideration the relative magnitude of the control response, i.e., the response to agonist in the absence of the modulator, which can vary considerably in different studies. As a result, the RR measured at, for example, the EC₂ concentration of an agonist in one study may be, inappropriately as we show below, compared with the RR measured at, for example, the EC₂₅ concentration of agonist in a different study (Belelli et al., 2002; Bracamontes et al., 2011; Germann et al., 2021). While it is intuitively clear that due to saturation the RR is reduced at larger fractional values of the control response, the precise relationship between the two is not obvious. Here, we have investigated how the magnitude of the response to agonist modifies the apparent potentiating effect. Essentially, we asked whether, for example, a modulator-induced tripling of an EC₂ control response is energetically equivalent to tripling of an EC₂₅ response. An alternative way to put this is whether a fixed free energy change associated with the binding of a modulator is expected to generate the same RR at different EC values.

We can now address the question about the energies required to, for example, triple an EC₂ response as compared with an EC₂₅ response. It takes −1.30 kcal/mol to triple the EC₂₅ response and only −0.67 kcal/mol for the EC₂ response. Fig. 1 A illustrates the relationship between the energy required to triple the response and EC_agonist. The main inference is that the energetics of receptor function do not scale linearly with changes in current responses.

Inspection of Fig. 1 indicates that the value of ΔG_M required to triple the response approaches an infinitely large negative number when the control EC value approaches 1/3.

In the majority of receptor–agonist combinations, the EC and P_A values are not equivalent; that is even at saturating concentrations, the agonist cannot activate all receptors, and P_A is less than EC/100. In addition or alternatively, a receptor may be constitutively active, in which case, and particularly at low agonist concentrations, P_A exceeds EC/100. This necessitates the conversion of EC_agonist to P_A,agonist. In macroscopic recordings, this can be done by normalizing the amplitude of the response to a given agonist to those of a known inhibitor expected to block all receptors (P_A = 0) and a high-efficacy agonist or a combination of agonists that through independent means or experiments has been shown to generate a response with a P_A of 1. For example, in the case of the GABA_A receptor, picrotoxin is used to reach a current response with P_A of 0, and the combination of the transmitter GABA with allosteric agonists propofol or pentobarbital is employed to generate a response with P_A of 1 (Chang and Weiss, 1999; Ziemba and Forman, 2016; Shin et al., 2017; Shin et al., 2019). In single-channel recordings, the P_A of the response can be calculated directly from the mean open and closed time durations (Steinbach and Akk, 2001; Mortensen et al., 2004; Lema and Auerbach, 2006).

Fig. 2 A shows the energy required to triple the control response for two partial agonists. Fig. 2 B shows the relationship between the RR and P_A of the control response in the presence of a modulator contributing −1 kcal/mol of free energy change. The calculations were done for cases where EC₁₀₀ corresponds to P_A of 0.5 (a medium-efficacy agonist) and where EC₁₀₀ corresponds to P_A of 0.25 (a low-efficacy agonist). As in Fig. 1, the energy required increases with increasing EC (Fig. 2 A) and the RR is reduced at higher levels of control activity (Fig. 2 B). Unlike in Fig. 1 B, potentiation is observed even at EC₁₀₀ because the P_A at saturating concentrations of agonist remains sub-maximal.

It is also the case that the effect of a negative allosteric modulator that stabilizes the resting state shows a similar relationship to the control activity. In this case, the RR is between 0 and 1 and ΔG_M >0. As shown in Fig. 3 A, as the level of control activity increases, the energy required to produce a given RR increases and approaches infinity as the control P_A approaches 1. Analogously, the efficacy of the inhibitor decreases at a fixed (1 kcal/mol) ΔG_M (Fig. 3 B). It is important to note that the effects of negative modulators may not conform to the two-state approach we are using (Germann et al., 2022).

Experiments have demonstrated reduction in potentiation as a function of increasing agonist concentration for a number of receptors, including potentiation of GABA_A receptors by diazepam (Gielen et al., 2012) or neurosteroids (Bracamontes and Steinbach, 2009) and potentiation of neuronal nicotinic receptors by β-estradiol (Paradiso et al., 2001), CMPI (Deba et al., 2022), or calcium ions (Natarajan et al., 2020), of serotonin type 3 receptors by alcohols and anesthetics (Machu and Harris, 1994), or NMDA receptors by the synthetic compound GNE-9278 (Wang et al., 2017). Our demonstration does not require any particular hypothesized mechanism for potentiation. However, it is based on the idea that receptor function is adequately described by a simple, two-state system. This can be appropriate as long as slowly equilibrating states (desensitized, for example) can be reduced by an appropriate protocol that entails fast and standardized drug perfusion so that the measured peak response corresponds to the equilibrium response in the two-state model.

In sum, we have investigated here the relationship between the ability of a compound to potentiate the response to agonist and the relative magnitude of the control response. As EC_agonist increases, the RR decreases. Accordingly, comparison of potentiation efficacy among different compounds measured at different EC_agonist is inappropriate. Eq. 7 (or 5 in the case of an efficacious control agonist with high maximal P_A,agonist and receptor with low constitutive P_A) enables calculation of ΔG for a modulator based on the amplitudes of current responses in the presence and absence of the modulator. Eq. 8 (or 6 with high-efficacy control agonist) enables calculation of the predicted RR if the level of the control response and the ΔG for the modulator are known. Alternatively, Eqs. 6 and 8 can be used to predict potentiation RRs at fixed ΔG_M at different levels of control response.