Discussion and Conclusions
Agonists are distinguished by 3 attributes that are functions of the
binding energies to low- and high-affinity conformations of their target
site. ‘Affinity’ is proportional to the binding energy itself
(logKdC or logKdO), ‘efficacy’ is
proportional to the binding energy difference
(logKdO-logKdC) and ‘efficiency’ depends
only on the binding energy ratio
(logKdC/logKdO). The two equilibrium
dissociation constants can be estimated in any number of different ways,
for instance by kinetic modeling of single-channel currents or by a
ligand binding assay. Here, we have shown that the unliganded gating
equilibrium constant and the equilibrium dissociation constants (and,
hence, agonist efficiency) can be estimated from a single dose-response
curve.
The agonists related structurally to ACh have an average efficiency of
52% (Fig. 4). This value is approximately the same in human/mouse and
at α−δ/α−ε binding sites. The absence of a correlation between
efficiency values estimated from CRCs versus by kinetic modeling
suggests that the narrow range of efficiencies (50-55%; Table 1) can be
attributed to measurement errors rather than to actual, ligand-specific
differences.
The ACh-occupied neurotransmitter binding cavity in equilibrated
homology models of α−δ and α−ε sites has a volume of
~120 Å3 in the resting state and
~9o Å3 in the active state (Tripathy,
Zheng & Auerbach, 2019). The average volume of the head group for the
~52% efficiency agonists is ~70
Å3. Hence, it is likely that all of these ligands fit
comfortably in both the C and O conformations of the binding pocket.
Another group of agonists related structurally to Epi has a lower
efficiency than for the ACh group. For these, we are less certain if the
more-substantial range in efficiency, from 35% for varenicline to 46%
for Ebx, can be attributed to measurement errors or to real differences
between ligands. Epi has the same efficiency in whole receptors as at
the isolated α−δ site, but the efficiency of Ebx is somewhat higher in
whole receptors. It is possible that the efficiency of Ebx is modestly
greater at α−ε compared to α−δ.
All of the low-efficiency agonists had a bridge moiety and, hence a
larger head-group volume that on average was 101 Å3.
Hence, these ligands likely fit comfortably within the C conformation of
the pocket but not within the O conformation. The inverse relationship
between efficiency and head-group volume leads us to speculate that a
large head group limits pocket contraction upon activation, to limit
energy coupling to the rest of the extracellular domain, to limit
agonist efficiency.
η is a quantitative index of the extent of energy coupling between
binding and gating and may thus shed light on the structural link(s)
between these two fundamental processes. The mutation αY190A is the only
binding site mutation we have discovered so far that alters ACh
efficiency, reducing it from 50% to 35%. Linear free energy analyses
of mutant AChRs suggest that within the opening transition, the binding
pocket and the extracellular domain rearrange sequentially (in that
order) (Gupta & Auerbach, 2011), and structural analyses suggest that
both of these regions contract and rotate anticlockwise in the opening
process (Sauguet et al., 2014) . The reduction in efficiency caused by
αY190A supports the suggestion that energy flows out of the binding
pocket, in part, through this residue (Mukhtasimova, Free & Sine,
2005). F and W substitutions at αY190 do not reduce efficiency so the
energy transfer may involve the aromatic ring rather than the hydroxyl
group. A more-extensive map of the effects of mutations on agonist
efficiency might define a linkage pathway(s).
Agonist families can be distinguished by the fraction of their binding
energy that is applied to receptor activation. Results so far suggest
that there are 2 populations with regard to this fraction, at 52% and
at 40% (Fig. 4). The αY190A mutation shifts ACh efficiency from the
higher to the lower population, raising the possibility that the
distribution of efficiency values could be modal rather than continuous.
If so, this suggests that the AChR binding pocket can adopt only a
limited number of discrete C and O shapes rather than a continuum.
Certainly, the efficiency of more ligands needs to be determined to test
this possibility.
Knowing agonist efficiency is useful because it allows affinity to be
estimated from efficacy (EC50 from
POmax). This ability is of potential
clinical relevance because it can facilitate drug screening, in
particular because efficiencies can estimated from structure alone.
There are stipulations with regard to estimating agonist efficiency from
a CRC. First, the CRC must be comprised of absolute responses rather
than those normalized to the maximum. With cellular responses,
normalized CRCs are far more common because it is difficult to know the
number of receptors contributing to the response. Our approach
(single-channels) circumvents this problem because it ensures that
exactly 1 receptor contributed to PO. One way to make a
CRC from absolute, whole-cell responses is to count the number of
receptors (Chang, Ghansah, Chen, Ye & Weiss, 2002) or to calibrate each
response to that of an agonist having a known, absolute response.
Second, the CRC should be largely uncontaminated by events outside the
core activation scheme (Fig. 1). Whole-cell responses arising from
multiple, functionally-different receptor populations, or generated by
slow agonist application onto cells bearing receptors that desensitize
relatively rapidly may not produce CRCs that match Eqs. 3 and 4. For
many receptors, the equations that relate CRC parameters with binding
and gating constants may be more complicated than those we have used for
AChRs.
Figure Legends
Figure 1. Receptor activation cycles (Scheme 1) .
Receptors adopt alternatively resting (C) or active (O) conformations
under the influence of agonists (A). Horizontal, binding and vertical,
gating. En, gating equilibrium constant with n bounds
agonists; KdC, equilibrium dissociation constant to C
(low affinity); KdO, equilibrium dissociation constant
to O (high affinity). In adult-, wild-type human endplate AChRs with 2
bound neurotransmitter molecules, favorable binding energy generated in
the A2C→A2O transition increases
E2 compared to E0 by more than
30-million fold. Scheme 2 (bold) is the main physiological activation
pathway.
Figure 2. Efficiencies from CRCs .
A. The response (PO) as a function of [agonist].
Symbols, (Jadey & Auerbach, 2012); lines, fits by Eq. 1 (Table 1).
There is an inverse correlation between EC50 and
POmax. B. Agonist efficiencies (the
fraction of binding energy used for gating) calculated from
EC50 and POmax (Eqns.
2-5). Despite the wide ranges in EC50 and
POmax, the agonists all have
approximately the same efficiency of 53±2% (dashed line). C. Agonist
structures. TMA, tetramethylammonium; ACh, acetylcholine; CCh,
carbamylcholine; Ana, anabasine; Nor, nornicotine; DMP
dimethylpyrrolidinium; DMT, dimethylthiazolodinium. Red, key nitrogen
atom in the agonist’s head group.
Figure 3. More efficiencies from CRCs .
A. PO as a function of [agonist] for Epi (, n=4),
Ebx (, n=3), Var( , n=2), Cyt (, n=4), 4OH-B (, n=3) and 3OH-B (, n=5).
EC50 and POmax were
estimated by Eq. 1 (Table 1). B. Agonist efficiencies calculated from
fitted CRC parameters. The efficiencies of 3OH-P and 4OH-B are similar
to those of the agonists shown in Fig. 1 (51%) whereas those for Epi,
Ebx, Var and Cyt smaller (40%; dashed line). Shaded, agonist
efficiencies at the α−δ binding site (Nayak, Vij, Bruhova, Shandilya &
Auerbach, 2020). C. Agonist structures. Epi, epibatidine; Ebx,
epiboxidine; Var, varenicline; Cyt, cytisine; 3OH-P,
3-hydroxy-propyltrimethyammonium; 4OH-B,
4-hydroxy-butyltrimethylammonium, Atx, anatoxin-A; Aza,
azabicycloheptane. Red, key nitrogen atom in the agonist’s head group.