Methods
Expression, electrophysiology, analysis. Human embryonic
kidney (HEK) 293 cells were maintained in Dulbecco’s minimal essential
medium supplemented with 10% fetal bovine serum and 1%
penicillin–streptomycin, pH 7.4. AChRs were expressed by transient
transfection of mouse α, β, δ, and ε subunits in the ratio 2:1:1:1
(Trans IT® 293 transfection reagent; Mirus Bio,
Madison, WI). Electrophysiological experiments started
~48 hrs post-transfection. No animals were used in this
study.
Our goal was to calculate agonist efficiencies from equilibrium
dissociation constants extracted from CRCs, by using equations derived
from Scheme 1 (Fig. 1). Whole-cell currents contain events that are not
included in this scheme, for instance from desensitization or from modal
activity. In order to match the ‘response’ (PO) with
Scheme 1 as closely as possible, we constructed pseudo-macroscopic CRCs
from single-channel currents, as follows.
Single-channel currents were recorded in the cell-attached patch
configuration at 23o C. The bath solution was (in mM):
142 KCl, 5.4 NaCl, 1.8 CaCl2, 1.7 MgCl2,
10 HEPES/KOH (pH 7.4). Patch pipettes were fabricated from borosilicate
glass and fire polished to a resistance of ~10 MΩ when
filled with the pipette solution that was Dulbecco’s phosphate-buffered
saline (in mM): 137 NaCl, 0.9 CaCl2, 2.7 KCl, 1.5
KH2PO4, 0.5 MgCl2, and
8.1 Na2HPO4 (pH 7.3/NaOH). Currents were
recorded using a PC505 amplifier (Warner instruments, Hamden, CT),
low-pass filtered at 20 kHz and digitized at a sampling frequency of 50
kHz using a data acquisition board (SCB-68, National instruments,
Austin, TX). Agonists were added to the pipette solution at the desired
concentration.
When the diliganded opening rate constant
(A2C→A2O in Fig. 1) is sufficiently
large, AChR openings occur in clusters (Sakmann, Patlak & Neher, 1980).
Shut intervals within clusters represent mainly agonist-binding and
receptor-gating events (Fig. 1, Scheme 2) whereas shut intervals between
clusters represent mainly long-lived desensitized events. We selected
for analysis clusters that appeared by eye to arise from a homogeneous
PO population, and limited the analysis to intra-cluster
events in order to remove sojourns in long-lived desensitized states
from the responses.
Because of the high extracellular [K+], the cell
membrane potential (Vm) was 0 mV. The AChR agonists we
examined also are channel-blockers. To both generate measurable currents
and reduce the effect of channel block on PO, the
membrane was depolarized to +70 mV by holding the pipette at -70 mV.
This effectively eliminated agonist binding to the blocking site in the
transmembrane domain but did not affect agonist binding to the
neurotransmitter sites in the extracellular domain.
Analyses of the (outward) currents were performed by using QUB software
(Nicolai & Sachs, 2013). A cluster was defined as a group of openings
flanked by shut intervals ≥7 ms. Currents within clusters were idealized
into noise-free intervals by using the segmental k-means algorithm (SKM)
after digitally low-pass filtering the data at 10 kHz (Qin, 2004).
Distributions of idealized interval durations were fitted by multiple
exponential components using a maximum interval likelihood algorithm
(MIL)(Qin, Auerbach & Sachs, 1997). Starting with a kinetic model
having one shut and one open state (C↔O), additional shut states were
connected to O until the log likelihood no longer improved by> 10 units. Usually only 1 extra shut state was
necessary. PO was calculated from the time constant of
the predominant component of the shut time distribution
(τs) and the time constant of the open time distribution
(τo):
τo/(τs+τo) (Purohit &
Grosman, 2006). With this approach, short-duration shut intervals within
clusters arising from sojourns in a short-lived desensitized state were
eliminated from the accounting (Elenes & Auerbach, 2002). The CRCs
reflect absolute PO values and were not normalized to a
maximum value.
Estimating binding constants from CRC parameters . The midpoint,
maximum and slope of the CRC (EC50,
POmax, and n) were estimated by
fitting by an empirical equation,
PO=POmax/(1+(EC50/[agonist])n)
Eq. 1
We used 3 equations to calculate KdC and
KdO from EC50 and
POmax. From microscopic reversibility
and Scheme 1,
\(\frac{E_{2}}{E_{0}}=\left(\frac{K_{\text{dC}}}{K_{\text{dO}}}\right)^{2}\)Eq. 2
E2 is the diliganded gating equilibrium constant and
E0 is the unliganded (intrinsic) gating equilibrium
constant. The exponent reflects that in adult-type AChRs there are 2
approximately equivalent and independent neurotransmitter binding sites
(Nayak & Auerbach, 2017).
Constitutive and mono-liganded activation are infrequent so in wild-type
AChRs the main pathway connecting C to A2O
(unliganded-resting to diliganded-active) is Scheme 2 (Fig. 1). In terms
of equilibrium constants, the CRC parameters for Scheme 2 are:
\(\text{EC}_{50}=\frac{K_{\text{dC}}\sqrt{E_{2}+2}}{E_{2}+1}\) Eq.
3\(P_{O}^{\max}=\frac{1}{1+\frac{1}{E_{2}}}\) Eq. 4
The procedure for calculating KdC and
KdO from the CRC parameters was as follows. We
calculated E2 from
POmax using Eq. 4, then calculated
KdC from E2 and EC50using Eq. 3, then calculated KdO from E2and KdC using Eq. 2 and a known value of
E0 (see below).
A k-means cluster analysis algorithm (Matlab) was used to define groups
regarding agonist efficiency and volume.
Background mutations . Depolarization to Vm=+70 mV
(to reduce channel block by the agonist) has the undesired consequence
of shortening τo to make current detection and
idealization more difficult. To compensate, we added the background
mutation εS450W (in the M4 transmembrane segment of the ε subunit) that
has the equal-but-opposite effect on gating as does depolarization by
+140 mV but does not alter agonist binding (Jadey, Purohit, Bruhova,
Gregg & Auerbach, 2011). With this mutation, τO and the
unliganded gating equilibrium constant E0 at +70 mV were
the same as in wild-, adult-type AChRs at -70 mV. E0 at
-100 mV is 7.4 x 10-7 and is reduced e-fold with a 60
mV depolarization (Nayak, Purohit & Auerbach, 2012), so we estimate
that Eo=4.5 x 10-7 at
Vm=+70 mV with εS450W.
Clusters of open-current intervals were poorly defined with the
low-efficacy agonist varenicline. To increase the diliganded opening
rate constant and generate higher PO clusters we added
two background mutations in the ε subunit, εL269F (in the M2 helix) and
εE181W (in strand β9) without εS450W. Together, these two substitutions
increase the unliganded gating equilibrium constant by 1084-fold
(E0mut=4.9x10-4)
without affecting agonist binding (Jha, Purohit & Auerbach, 2009;
Purohit, Gupta, Jadey & Auerbach, 2013).
Agonists . Agonist structures are shown in Figs. 2 and 3. The
agonist head-group volumes were calculated using Chimera (Pettersen et
al., 2004). Cytisine and varenicline were from Sigma®lifesciences (St. Louis, MO). Epibatidine was obtained from Tocris
Biosciences (Briston, UK). The sources for other agonists is in a
previous publication (Bruhova & Auerbach, 2017).