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/(τso) (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).