Agonist efficiency
Vertebrate neuromuscular AChRs have 2 neurotransmitter binding sites located in the extracellular domain at α−δ and α−ε subunit interfaces. Three previous experimental results make it possible to calculate KdC and KdO from the CRC parameters EC50 and POmax. First, in adult-type AChRs the two binding sites have approximately the same affinity for ACh and other agonists, so only single values of the constants needed to be estimated for each ligand. Second, Scheme 1 has been proved experimentally to describe receptor activation, so KdC could be calculated using Eqs. 3 and 4. Third, Eo and its voltage dependence are known, so KdO could be calculated using Eq. 2.
Some authors use ‘efficacy’ and ‘efficiency’ interchangeably, but here we use these words to describe different agonist attributes. In our use, efficacy relates to the high-concentration asymptote of the CRC (the maximum response, set by equilibrium constant E2) relative to the zero-concentration asymptote (the constitutive response, set by equilibrium constant E0). As shown by Eq. 2, efficacy depends on the KdC/KdO ratio. The log of an equilibrium dissociation constant is inversely proportional to binding energy, so agonist efficacy depends on thedifference in binding energies, O minus C.
An energy value pertains to the free energy difference between end states. For instance, in Scheme 1, the diliganded gating energy (that is proportional to log E2) is equal to the free energy difference between states A­2O and A2C. These energy differences are not influenced by short-lived intermediate states, for example flip (Lape, Colquhoun & Sivilotti, 2008), prime (Mukhtasimova, Lee, Wang & Sine, 2009) and phi (Purohit, Gupta, Jadey & Auerbach, 2013) in gating. In our use, ‘efficacy’ is determined by everything that happens in the step A2C⟷A2O, as given by the overall equilibrium constant E2.
In contrast, ‘efficiency’ (η; eta) is the useful output energy of a machine divided by the total input energy (Schroeder, 2000). In a receptor, the useful output energy is related to the maximum response relative to the baseline (that is, efficacy) and the total input energy is that for agonist binding to the active state. Hence (Nayak, Vij, Bruhova, Shandilya & Auerbach, 2020),
η=1-logKdC/logKdO. Eq. 5
Agonist efficiency depends on the ratio of binding energies, C versus O. In AChRs the distance dx is correlated inversely with binding energy, so agonist efficiency can be estimated from structures as the ratio of dx values, O versus C.
To highlight the distinction between efficacy and efficiency, consider the actions of carbamylcholine (CCh) and epiboxidine (Ebx) at the human α−δ site (Nayak & Auerbach, 2017). These two ligands produce nearly the same gating equilibrium constant and, hence, have approximately the same efficacy. However, Ebx has a 84-fold higher resting affinity. Hence, CCh is the more-efficient ligand because a greater fraction of its (weaker) binding energy is used to generate the same gating response. This difference in efficiency is also apparent in structures. At the α−δ binding site, dx is smaller in O versus C by ~1.9-fold with CCh but only by ~1.6 fold with Ebx (Tripathy, Zheng & Auerbach, 2019).
CRCs for 7 agonists of adult-type mouse AChRs have been published (Jadey & Auerbach, 2012; Jadey, Purohit & Auerbach, 2013). We used Eq. 1 to estimate EC50 and POmax from these, and Eqns. 2-5 to calculate agonist efficiencies from the fitted CRC parameters (Fig. 2 and Table 1). Although these 7 agonists span a wide range with regard to both EC50 (43 µM to 6.7 mM) and POmax (0.26 to 0.96), they all have approximately the same efficiency, 53+ 2% (mean+ s.d). This efficiency value is similar to those calculated from equilibrium dissociation constants estimated by kinetic modeling. It is also approximately the same as the average efficiency of ACh, CCh, TMA and choline at individual α−δ and α−ε human neurotransmitter binding sites. Overall, the efficiencies estimated from CRCs are the approximately same i) as estimated from modeling, ii) for all 7 ligands, iii) at the two adult-type sites and iv) in mouse and human AChRs.
Next, we measured efficiencies from CRCs for 6 agonists that were not studied previously by CRC analysis (Fig. 3, Table 1). Choline (Cho) has 2 methylenes between its quaternary nitrogen and hydroxyl (OH) group, whereas 3OH-BTMA and 4OH-PTMA have 3 and 4. Cho is a low-affinity, low-efficacy agonist (Purohit & Grosman, 2006) that has an efficiency at the human α−ε site of 52% (Nayak, Vij, Bruhova, Shandilya & Auerbach, 2020). Simulations of structures suggest that an H-bond between the OH group of Cho and the backbone carbonyl of αW149 serves to position the charged quaternary ammonium (QA) group away from the center of the binding cavity, thereby reducing the binding energy (Bruhova, Gregg & Auerbach, 2013; Tripathy, Zheng & Auerbach, 2019). Nonetheless, the opening transition reduces dxapproximately by half with Cho, as it does with the higher-affinity, similar-efficiency agonists ACh, CCh and TMA.
POmax values for Cho, 3OH-BTMA and 4OH-PTMA are 0.05, 0.17 and 0.34, respectively (Table 1). Nonetheless, the efficiencies of 3OH-BTMA and 4OH-PTMA calculated from the CRC parameters are same at 51%, similar to Cho (50%). These 3 structurally-related agonists have widely different affinities and efficacies but approximately the same efficiency as for the ligands shown in Fig. 2.
We also investigated CRCs for ligands related structurally to Ebx (Fig. 3, Table 1). The efficiency estimates for Epi and Ebx were similar to the values at the human α−δ binding site. Analyses of CRCs for two drugs that are used for smoking cessation, cytisine and varenicline, gave efficiencies of 42% and 35%.
Efficiencies have been measured for 16 agonists. These were either estimated from midpoints and maxima of CRCs (Table 1) or calculated from published equilibrium dissociation constants (Nayak, Vij, Bruhova, Shandilya & Auerbach, 2020). Fig. 4 shows these values are clustered, with one group (n=10) having η=52+ 2% and another (n=6) having η=40+ 5%. Fig. 4 also shows that the volume of the ‘head’ group of the higher-efficiency agonists is smaller (70+ 8 A3) than that of the lower-efficiency agonists (101+ 11.2 A3).
To probe for residues that might influence efficiency, we estimated ηACh from published equilibrium dissociation constants measured by kinetic modeling of single-channel currents in mouse adult-type AChRs having a mutation of a binding site residue (Purohit, Bruhova, Gupta & Auerbach, 2014). Fig. 5 shows that for 21 of 22 mutants, ηACh was 52+ 4% or the same as in the WT. The one exception was αY190A for which ηACh was 35%.
Putting efficiency to use .
In this section we show that knowledge of agonist efficiency can simplify and extend CRC analysis. A group of agonists having the same efficiency means that for all members, the resting and active equilibrium dissociation constants are correlated exponentially. From Eq. 5,
KdO=KdC1/(1−η) Eq. 6
This relationship simplifies CRC analysis because there are fewer efficiency values than there are agonists, and because if η is known one of the equilibrium dissociation constants can be calculated from the other. It may be possible to known an agonist’s efficiency a priori , either by assuming it is the same as for a structurally-related ligand or by calculating it from the dx ratio in binding site structures.
Knowledge of η (and the agonist-independent constant E0) allows the estimation of EC50 from the response at a single [agonist]. Combining Eqs. 2 and 6 and rearranging,
logE2 = [2η/(η−1)]logKdC+logE0 Eq. 7
E2 can be calculated directly from POmax (Eq. 4). Hence, given η and E0 it is possible to solve Eq. 7 for KdC, then solve Eq. 3 for EC50. Fig. 6A shows that EC50 values so-calculated (assuming Eo is 4.5 x10-7 and η is either 52% or 40%) match those obtained by fitting experimental CRCs. Further, CRCs calculated from just the high-concentration asymptote describe approximately responses at all [agonist] (Fig. 6B). If agonist efficiency is known, an entire CRC can be estimated from POmax.
Diliganded gating equilibrium constants have been measured experimentally for several different AChR agonists (Bruhova, Gregg & Auerbach, 2013). Table 2 shows the corresponding, calculated EC50 values.
Knowledge of η also allows the estimation of E0 from a single CRC. E0 is an important, ligand-independent constant that sets the basal level from which agonists increase PO, but it can be difficult to measure. The procedure to estimate E0 from a CRC is first to solve for E2 and KdC from POmax and EC50 as described above, and then solve for E0 using Eq. 7. Fig. 7 shows E0 values calculated from the CRC parameters using an η value of either 52% or 40%. The mean result, 7.8 x 10-7, is within a factor of 2 of the correct value, 4.5 x 10‑7 (see Methods). If agonist efficiency is known, an approximate value of the intrinsic gating constant can be estimated from a single CRC.
If there are E2 and KdC estimates for multiple agonists, efficiency can be estimated by using an efficiency plot (Nayak, Vij, Bruhova, Shandilya & Auerbach, 2020).