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).