Temperature Dependence of Acetylcholine Receptor Channels Activated by Different Agonists

Abstract

The temperature dependence of agonist binding and channel gating were measured for wild-type adult neuromuscular acetylcholine receptors activated by acetylcholine, carbamylcholine, or choline. With acetylcholine, temperature changed the gating rate constants (Q₁₀ ≈ 3.2) but had almost no effect on the equilibrium constant. The enthalpy change associated with gating was agonist-dependent, but for all three ligands it was approximately equal to the corresponding free-energy change. The equilibrium dissociation constant of the resting conformation (K_d), the slope of the rate-equilibrium free-energy relationship (Φ), and the acetylcholine association and dissociation rate constants were approximately temperature-independent. In the mutant αG153S, the choline association and dissociation rate constants were temperature-dependent (Q₁₀ ≈ 7.4) but K_d was not. By combining two independent mutations, we were able to compensate for the catalytic effect of temperature on the decay time constant of a synaptic current. At mouse body temperature, the channel-opening and -closing rate constants are ∼400 and 16 ms⁻¹. We hypothesize that the agonist dependence of the gating enthalpy change is associated with differences in ligand binding, specifically to the open-channel conformation of the protein.

Introduction

Nicotinic acetylcholine receptors (AChRs) are ligand-gated ion channels at vertebrate nerve-muscle synapses. These five subunit allosteric proteins regulate the flow of cations across muscle cell membranes by alternatively adopting conformations that have either a low affinity for agonists and a closed channel (resting, R) or a high affinity for agonists and an open channel (active, R^∗) (1–4). Each AChR has two ligand-binding sites in the extracellular domain. The neurotransmitter acetylcholine (ACh) is a potent activator of AChRs because when the protein changes shape from resting to active, the affinity for this ligand increases by ∼6300-fold at each binding site (5,6). Other partial agonists are weaker activators because they experience a smaller increase in affinity.

The logarithm of an equilibrium constant is proportional to the free-energy difference between the ground states (here, R and R^∗), and the logarithm of a rate constant is proportional to the free-energy difference between the ground and transition states (7). Free energy is comprised of enthalpy and entropy components. At constant pressure, the enthalpy change between R and R^∗ informs us about the heat absorbed (or emitted) within the isomerization, and is revealed experimentally as the degree to which the equilibrium constant changes with temperature. Knowing the amount of heat exchange that takes place within AChR gating may help illuminate its mechanism, i.e., the ensemble of energy and structural changes that occur when the protein changes shape between R and R^∗.

The temperature dependence of neuromuscular AChR gating has been investigated previously, but not at the level of rate and equilibrium constants. Earlier studies measured the temperature dependence of single-channel bursts or end-plate-current (epc) decay time constants, which reflect a combination of binding and gating processes. In those studies, the temperature coefficient (Q₁₀) of this time constant was in the range of 2–4, which translates to an activation enthalpy of 13–24 kcal/mol (8–12). Based on the correlation between the polarization of the lipid probe laurdan and the single-channel burst time constant, Zanello et al. (11) proposed that the temperature dependence of gating (as well as conductance) is primarily influenced by the physical state of the membrane, which in turn is influenced by temperature.

In this work, we separately quantified the effects of temperature on agonist binding and channel gating in adult mouse AChRs activated by ACh, carbamylcholine (CCh), or choline (Cho). The results indicate that the different abilities of these agonists to activate the receptor can be attributed to different enthalpies associated with binding to the high-affinity R^∗ conformation.

Materials and Methods

HEK 293 cells plated on 22 mm polylysine-coated glass coverslips were transiently transfected with a mixture of cDNAs encoding wt or mutant mouse AChR subunits via calcium phosphate precipitation (α, β, δ, and ɛ; 1.8 μg total DNA in a 2:1:1:1 ratio). The culture medium was changed after 16 h and electrophysiological recordings commenced 18–24 h later. Mutations were made using the QuikChange Mutagenesis Kit (Stratagene, La Jolla, CA) and confirmed by dideoxy sequencing.

Single-channel recordings were from cell-attached patches. Rate constants at a given temperature were estimated for each construct from several patches obtained on different days and from different culture dishes. The pipette potential was +80 mV (except where noted), which corresponds to a membrane potential of ∼−100 mV. Pipettes were pulled from borosilicate capillaries and coated with Sylgard (Dow Corning, Midland, MI). The bath and pipette solutions were Dulbecco's phosphate-buffered saline containing (mM) 137 NaCl, 0.9 CaCl₂, 2.7 KCl, 1.5 KH₂PO₄, 0.5 MgCl₂, and 8.1 Na₂HPO₄ (pH 7.4), except for the current-voltage relationship experiments, in which both the bath and pipette solutions contained (mM) 142 KCl, 5.4 NaCl, 1.8 CaCl₂, 1.7 MgCl₂, and 10 HEPES/KOH (pH 7.4).

The temperature of the bath was maintained at ±0.2°C of the desired value and was allowed to stabilize before each recording. This took ∼3 min for every 5°C change in temperature. The temperature was controlled by a Peltier device mounted on a copper plate under the perfusion chamber (Brook Industries, Lake Villa, IL). The temperature of the patch during the experiment was monitored with a miniature thermocouple placed ∼1 mm from the pipette tip. Single-channel currents were first recorded at 20°C and then the temperature was either increased or decreased in 5°C increments. Recordings were made for ∼3 min at each temperature. Each point in the Arrhenius and van 't Hoff plots is the average obtained from at least three different patches.

Single-channel currents were low-pass filtered at 20 kHz and digitized at a sampling frequency of 50 kHz. Agonists were added only to the pipette solution. Kinetic analyses were carried out with the use of QUB software (http://www.qub.buffalo.edu). At high agonist concentrations, channel openings occurred in clusters that represent binding and gating activity of individual AChRs. Usually, we selected the clusters by eye and idealized the currents into noise-free intervals after digitally low-pass filtering the currents at 12 kHz and using the segmental k-means algorithm (13), or after low-pass filtering the currents at 5 kHz and using half-amplitude detection. We estimated the rate constants from the idealized interval durations by using a maximum log-likelihood algorithm (14) and a two-state, C(losed)↔O(pen) model after imposing a dead-time correction (applied to both open and shut intervals) of 25 or 35 μs (15).

A major problem in the analysis of AChRs is that binding and gating reactions together often determine the apparent kinetic parameters. Our primary objective was to measure the temperature dependencies for each of these processes separately. The single-site equilibrium dissociation constant for binding to the R conformation (K_d) is the ratio of the agonist dissociation (k₋) and association (k₊) rate constant (K_d = k₋/k₊). The diliganded gating equilibrium constant (E₂) is the ratio of the forward (channel-opening, f₂) and backward (channel-closing, b₂) rate constant (E₂ = f₂/b₂). We usually were unable to obtain estimates of these rate and equilibrium constants directly by using wt AChRs, so instead we obtained estimates of effective opening/closing rates that depended on both binding and gating.

We define the inverse, principle shut interval lifetime within clusters to be the effective opening rate (f^∗) and the inverse, principle open interval lifetime to be the effective closing rate (b^∗). The effective activation equilibrium constant is f^∗/b^∗, and the open probability of clusters (P_o) is f^∗/(f^∗ + b^∗). The relationship between f^∗ and f₂ depends on the agonist concentration ([A]) and K_d, and f^∗ < f₂ except when both binding sites are fully occupied by the agonist ([A] >> K_d). The relationship between b^∗ and b₂ depends on the ratio f₂/k₋₂, where k₋₂ is the rate constant for agonist dissociation from either of the two binding sites. Ignoring desensitization and dissociation of the agonist from R^∗:

$${\text{b}}^{\ast }\approx {\text{b}}_2/\left(1+{\text{f}}_2{/\text{k}}_{\mathrm{-2}}\right),$$ (1)

when f₂ << k_-2, b^∗ ≈ b₂. The values reported in the tables are f^∗ and b^∗ (except where noted).

Another problem with rate constant estimation is open-channel block by the agonist. We estimated the block equilibrium dissociation constant (K_B) from the reduction in the single-channel current amplitude with increasing agonist concentration:

$${\text{K}}_{\text{B}}=\left[\mathrm{A}\right]{\text{i}}_{\text{B}}/\left({\text{i}}_{\text{0}}-{\mathrm{i}}_{\mathrm{B}}\right),$$ (2)

where i₀ is the single-channel current amplitude in the absence of block (measured at a low agonist concentration), and i_B is the observed single-channel current amplitude measured at a high agonist concentration where block is apparent. Equation 2 is an approximation that assumes that the dissociation rate constant of the blocker from the R^∗ conformation is relatively small compared with that from R (16,17).

The apparent open lifetime is also influenced by block:

$${\text{b}}^{\ast }\approx {\text{b}}_2\left(1+\left[\mathrm{A}\right]{/\text{K}}_{\mathrm{B}}\right)\text{.}$$

If K_B is not temperature-dependent, the temperature dependence of b^∗ is not affected by channel block.

K_d was estimated for two mutant AChRs: αY127E and αG153S. αY127E was activated by ACh and αG153S was activated by Cho. We fit the interval durations within clusters at different agonist concentrations together by using a linear kinetic scheme (R↔RA↔RA₂↔R^∗A₂), where A is the agonist. We assumed that the two binding steps were equal and independent (5,18), and that the association rate constant scaled linearly with the agonist concentration.

The temperature coefficient Q₁₀ is defined as Q₁₀ = (P₂/P₁)^10/[T2-T1], where P₁ and P₂ are the parameter values obtained at temperatures T₁ and T₂. The activation enthalpy was estimated by using the Arrhenius equation:

$$\text{ln}\left({\text{k}}_{\text{rate}}\right)=\ln \left({\mathrm{A}}^{\ast }\right)-{\mathrm{E}}_{\mathrm{a}}/\mathrm{RT,}$$ (3)

where k_rate is an experimentally determined rate constant, A^∗ is the prefactor, E_a is the activation enthalpy (kcal/mol), and R is the gas constant (1.987 cal/K/mol) at temperature T (K). E_a is an approximation of the activation enthalpy of the transition state relative to a ground state, according to transition-state theory. E_a^f pertains to the forward, opening rate constant (from the R ground state) and E_a^b pertains to the backward, closing rate constant (from the R^∗ ground state). Because the Arrhenius plots for all the constructs were approximately linear in this study, we assumed that the heat capacity was constant with temperature. In our temperature range (5–35°C), E_a ≈ 17ln(Q₁₀), in kcal/mol.

We quantified the equilibrium enthalpy (ΔH) and entropy (ΔS) changes associated with the transition between R and R^∗ by using the van 't Hoff equation:

$$\text{ln}\left({\text{K}}_{\text{eq}}\right)=-\Delta \mathrm{H}/\mathrm{RT}+\Delta \mathrm{S/R,}$$ (4)

where K_eq is an equilibrium constant. Each point in the Arrhenius and van 't Hoff plots is the average obtained from at least three different patches. The Gibbs free-energy change (ΔG) at a given temperature was calculated from the van 't Hoff plots as:

$$\Delta \text{G}=\Delta \mathrm{H}-\mathrm{T}\Delta \mathrm{S}$$

Ф was estimated as the linear slope of a rate equilibrium relationship that is a log-log plot of the f₂ versus E₂ for a family of perturbations of a single position in the protein (19). Points in the plot represent the mean of at least three patches for each construct.

Results

Acetylcholine

Fig. 1 shows the temperature dependence of gating in adult wt mouse AChRs activated by the neurotransmitter ACh. At 100 μM ACh, single-channel openings occurred in clusters that reflect diliganded R↔R^∗ gating of individual AChRs. The silent periods between clusters are epochs when all AChRs in the patch are desensitized. Cluster duration increased with decreasing temperature, indicating that entry into states associated with desensitization became slower at lower temperatures (Fig. 1 A).

Figure 1.

Temperature dependence of wt AChRs activated by ACh. (A) Low time-resolution traces showing clusters of openings at different temperatures (open is down; low-pass filtered at 2 kHz). At 100 μM ACh, activity within a cluster reflects a combination of binding and gating processes. (B) Example single-channel clusters. (C) The cluster open probability (P_o) is approximately constant with temperature at both 30 and 100 μM ACh. (D) The effective closing rate at 2 μM ACh increases with increasing temperature (activation enthalpy, E_a=+19 kcal/mol; Q₁₀ ≈ 3.1). (E) Left and center: Arrhenius plots for the effective opening (f^∗) and closing rate constants (average E_a=+20 kcal/mol; Table S1). Right: van 't Hoff plots for the effective-gating equilibrium constant with corresponding ΔH values.

At 23°C, K_d^ACh ≈ 140 μM (5); therefore, at 100 μM ACh ([A] < K_d), the durations of intervals within clusters reflect both binding and gating processes. Fig. 1 B shows example clusters at 100 and 30 μM ACh at different temperatures. Fig. 1 C shows that cluster P_o increased with the ACh concentration, but at both concentrations it was approximately constant with temperature. The Arrhenius (see Table S1 in the Supporting Material) and van 't Hoff (Table 1) analyses of the apparent activation rate and equilibrium constants are shown in Fig. 1 E. At both concentrations, ΔH for the effective activation equilibrium constant with ACh as the agonist was ∼+0.7 kcal/mol.

Table 1.

van 't Hoff analysis of wt AChRs

Agonist	ΔH (kcal/mol)	TΔS (cal/mol)	ΔG (25°C) (kcal/mol)
30 μM ACh	0.8 (0.5)	0.95(0.3)	−0.15
100 μM ACh	0.6 (0.3)	1.8 (0.3)	−1.2
500 μM CCh	1.5 (0.3)	1.9 (0.4)	−0.4
5000 μM CCh	1.8 (0.6)	2.9 (0.6)	−1.1
1000 μM Cho	4.2 (0.3)	3.6 (0.3)	0.6

ΔH, enthalpy change (R↔R^∗); TΔS, entropy change at 25°C; ΔG, free-energy change (= ΔH-TΔS) at 25°C. Standard errors (in parentheses) are from the least-square linear fit obtained by using Eq. 4. Agonists: ACh, acetylcholine; CCh, carbamylcholine; Cho, choline.

At 2 μM, ACh channel openings occur as bursts with an effective closing rate (b^∗) that is a function of both the diliganded channel-closing rate constant (b₂) and the agonist dissociation rate constant (Eq. 1). The Arrhenius plot of ln (b^∗) versus 1/T was well described by a straight line, with an activation enthalpy of +19.0 kcal/mol (Fig. 1 D).

The above experiments show that P_o is not highly temperature-dependent in wt AChRs activated by ACh. Because both binding and gating contribute to P_o, it was possible that the opposite temperature sensitivities of these two distinct processes could cancel each other. Our first goal was to measure separately the temperature dependencies of ACh binding and gating. We could not achieve this objective using wt AChRs activated by ACh because the channel-opening rate constant was too fast. We could, however, separate binding and gating parameters in the mutant αY127E activated by ACh (Fig. 2). Mutations of this residue do not influence K_d^ACh (20), so at 500 μM ACh the transmitter binding sites are almost fully saturated (Eq. 1). Because this mutation also substantially slows the channel-opening rate constant, the apparent activation parameters of intervals within clusters at this concentration reflect mainly gating. By examining currents activated by several different ACh concentrations, we could also estimate the temperature dependence of K_d^ACh in this mutant.

Figure 2.

Temperature dependence of αY127E AChRs activated by ACh. (A) Clusters of openings at different temperatures and ACh concentrations, with the corresponding shut interval-duration histograms. Solid lines in histograms were calculated from the global fit using a model with two equal and independent binding steps followed by a gating step. (B) Equilibrium dissociation constant for ACh from the low-affinity conformation (K_d^Ach) is approximately constant with temperature (Table S3). (C) Left: Single-channel current amplitude, Q₁₀ ≈1.3. Right: Equilibrium dissociation constant for channel block by the agonist (K_B) is not temperature-dependent.

Fig. 2 A shows clusters of currents from αY127E AChRs activated by different ACh concentrations and at different temperatures, along with the corresponding shut interval duration histograms. At the highest ACh concentration, the open and shut intervals associated with gating are clearly resolved. Fig. 2 B (Table S3) shows that in αY127E, K_d^ACh was approximately the same as in wt AChRs and was constant with temperature. Further, the ACh association and dissociation rate constants (which were also about the same as in the wt) did not change significantly with temperature. These results demonstrate that ACh binding to the R conformation is not temperature-dependent in αY127E. Fig. 2 C shows the temperature dependencies of the single-channel current amplitude (i₀) and the equilibrium dissociation constant for channel block by ACh (K_B). Between 20°C and 30°C, the Q₁₀ of i₀ was ∼1.3 and K_B was essentially constant.

If we assume that in wt AChRs K_d is independent of temperature (as it is in αY127E), then the temperature dependence of the effective gating rate constants at 30 and 100 μM ACh (Fig. 1 E, right) can be used to approximate the temperature dependence of E₂^ACh. Hence, we estimate ΔH for gating in wt AChRs activated by ACh is +0.7 kcal/mol (Q₁₀ ≈ 1.04). This indicates that when ACh is the agonist, there is almost no heat absorbed by wt AChRs during the R-to-R^∗ conformational change. However, temperature has a large catalytic effect on gating and substantially influences both the forward and backward isomerization rate constants. This indicates that there is a large enthalpic component in the free energy of the gating transition state.

Choline

Fig. 3, A–C, show the results for wt AChRs activated by the partial agonist Cho. Cho is a breakdown product of ACh that is present physiologically at cholinergic synapses and has a low affinity for the AChR (K_d^Cho ≈ 4 mM). Cho is a low-efficacy agonist because this ligand experiences only a small increase in affinity when the protein changes shape from R to R^∗. The gating free-energy difference between these two agonists (calculated from the natural logarithm of the gating equilibrium constant ratio, E₂^ACh/E₂^Cho) is ΔΔG^o = +3.9 kcal/mol. Because measurements with these agonists were made using the same background AChR (wt), this free-energy difference can be attributed exclusively to the R/R^∗ equilibrium dissociation constant ratio, which is 6300 for ACh but only 270 for Cho (5,6).

Figure 3.

Temperature dependence of AChRs activated by Cho. (A–C) wt. (D–F) αG153S. (A) Example wt clusters activated by 10 mM Cho at different temperatures. (B) Top left and center: Arrhenius plots for opening (f^∗) and closing rate (b^∗) constants at 10 mM Cho (Table S1). Bottom left: van 't Hoff plot for the effective equilibrium constant (f^∗/b^∗) (ΔH = +4.2 kcal/mol). Bottom right: Arrhenius plot for the closing rate constant at 200 μM Cho. (C) Top: Single-channel current-voltage (I/V) relationships at different temperatures (200 μM Cho). The zero-current potential changes little with temperature (range: −6.9 to +3.4 mV). Bottom: The single-channel conductance has a Q₁₀ of 1.3 (20–30°C). (D) Clusters and corresponding shut interval-duration histograms for αG153S AChRs at different Cho concentrations and temperatures. Solid lines in histograms were calculated from the global fit using a model with two equal and independent binding steps followed by a gating step (Table S3). (E) Arrhenius plots for the dissociation (k₋) and association (k₊) rate constants (average. Q₁₀ ∼ 7.4). (F) The equilibrium dissociation K_d^Cho shows little temperature dependence.

For Cho, the channel-opening rate constant is small and at 200 μM (where there is little channel block), b₂ ≈ b^∗. In wt AChRs activated by Cho, this closing rate constant became smaller at lower temperatures with an apparent activation enthalpy (E_a^b) of +20.7 kcal/mol (Fig. 3 B, lower right), which is slightly larger than the temperature dependence of b^∗ for ACh-activated wt AChRs. Example clusters of wt AChRs activated by 10 mM Cho at different temperatures are shown in Fig. 3 A. At this concentration, both binding and gating contribute to the activation kinetics (Table S2), but we were unable to use higher Cho concentrations because of channel-block by agonist molecules. The temperature dependence of the effective rate and equilibrium constants at 10 mM Cho are shown in Fig. 3 B (Table 1 and Table S1). ΔH for this equilibrium constant was +4.2 kcal/mol.

To separately estimate the effects of temperature on Cho binding and gating, we studied the mutant αG153S. This residue is in the vicinity of the transmitter-binding site and causes a human slow-channel myasthenic syndrome (21). The Ser mutation increases E₂ by an approximately parallel change in the unliganded gating equilibrium constant but has only a small effect on the R/R^∗ equilibrium dissociation constant ratio (22). The main advantage of using this mutation is that it increases the affinity of the R conformation for Cho.

Fig. 3 D shows example αG153S clusters and shut interval duration histograms at different Cho concentrations and temperatures. Table S3 shows the binding rate and equilibrium constant estimates. At 25°C, K_d^Cho in αG153S was ∼265 μM, which is ∼15 times lower than the wt. Fig. 3 B shows the corresponding Arrhenius plots for binding. In sharp contrast to αY127E^ACh, the αG153S^Cho association and dissociation rate constants both decreased markedly with a decrease in temperature (activation enthalpies of 32 ± 3 and 34 ± 4 kcal/mol; Q₁₀ ≈ 7.4). Fig. 3 C (Table S3) shows that both of these rate constants changed to about the same extent with temperature, so that in αG153S K_d^Cho was approximately constant between 25°C and 5°C. Thus, temperature has a mainly catalytic effect on Cho binding to αG153S AChRs.

If we assume that K_d^Cho is also approximately temperature-independent in wt AChRs, we can use the van 't Hoff slope obtained at 10 mM Cho as an estimate of the enthalpy change of gating in wt AChRs (Table 1). This value was larger than that for ACh-activated wt AChRs. Relative to ACh, Cho-activated wt AChRs exchange more heat with the bath in the gating conformational change (ΔΔH^Cho = +3.5 kcal/mol).

Fig. 3 C shows the temperature dependence of the single-channel current/voltage relationship for wt AChRs activated by Cho. The conductance had a Q₁₀ of 1.3 (between 20°C and 30°C) and the zero-current potential did not change significantly with temperature.

Carbamylcholine

We also studied the partial agonist, CCh. At 25°C, E₂ for CCh is 5.3 (ΔΔG^o = +0.9 kcal/mol, compared with ACh) (6). The R/R^∗ equilibrium dissociation constant ratio for CCh is ∼2870, which is larger than that for Cho but less than that for ACh (6).

Fig. 4 A shows example clusters of wt AChRs activated by 5 mM CCh at different temperatures. In wt AChRs, K_d^CCh ≈ 1 mM, so the intracluster intervals at 5 mM reflect mainly the gating conformational change. Fig. 4 B shows the temperature dependence of the rate and equilibrium constants at 5 mM and 500 μM CCh (where both binding and gating contribute to the estimates). The activation and equilibrium enthalpy estimates were approximately the same at both concentrations (Table 1 and Table S1). This result suggests that in wt AChRs, K_d^CCh is not temperature-dependent. We estimate that compared with ACh-activated wt AChRs, ΔΔH^CCh = +1.0 kcal/mol for gating.

Figure 4.

Temperature dependence of wt AChRs activated by CCh. (A) Example clusters activated by 5 mM CCh at different temperatures. (B) Left and center: Arrhenius plots for the effective gating rate constants. (Table S1) Right: van 't Hoff plot for the effective gating equilibrium constant (average ΔH = +1.7 kcal/mol).

Φ-Value analysis

Agonists and mutations change E₂ by changing f₂, b₂, or both. The slope of the rate equilibrium plot (Φ) is a measure of the extent to which a perturbation changes f₂ versus b₂. Φ-Values are fractions between 0 and 1, with higher numbers indicating a greater effect on f₂ compared with b₂. Fig. 5 A shows the rate equilibrium plot for ACh, CCh, and Cho (wt AChRs) at two different temperatures. Fig. 5 B shows that at all tested temperatures, Φ ∼ 1.

Figure 5.

Rate-equilibrium analyses. (A) Log-log plots of the forward, opening rate constant versus the gating equilibrium constant for different agonists at two different temperatures. The slope (±SE) of the least-squares linear fit (Φ) is shown in each panel. (B) Φ (ACh, CCh, and Cho) is approximately independent of temperature.

Temperature dependence of the epc

The approximate time constant of the epc decay is the same as the mean lifetime of bursts:

$${\tau }_{\text{epc}}\approx \left({1+\text{f}}_2{/\text{k}}_{-2}\right){/\text{b}}_2,$$ (5)

where k₋₂ is the sum of the rate constants for agonist dissociation from the two resting AChR transmitter-binding sites. τ_epc approaches 1/b₂ only when the ratio f₂/k_-2 is small. This is not the case at the neuromuscular synapse because the number of openings per burst (=1+f₂/b₂) is >1. The temperature dependence of τ_epc is therefore a function of the temperature dependencies of all three rate constants in Eq. 5.

We were able to estimate the temperature dependence of τ_epc in two ways. One estimate is simply the temperature dependence of b^∗ in wt AChRs activated by 2 μM ACh (19.0 ± 0.9 kcal/mol; Table S1). We made a second estimate assuming that in wt AChRs, the temperature dependencies of f₂ and b₂ are the same (E_a^f,b ≈ 20 kcal/mol) and that k₋₂ is temperature-independent. Accordingly, we calculated τ_epc at different temperatures and fitted the values by the Arrhenius equation. The estimated activation enthalpy was 18.3 ± 1.2 kcal/mol. The agreement between these two values supports the assumptions.

We then used this activation enthalpy to compute the epc decay at mouse body temperature (39°C). At 23°C (∼−100 mV), the adult mouse ACh gating rate constants are f₂ = 66,000 s⁻¹ and b₂ = 2600 s⁻¹ (6), and τ_epc ≈ 1.0 ms. Using an activation enthalpy of 19 kcal/mol for both the forward and backward rate constants (and the relationship Q_ΔT = Q₁₀^ΔT/10), we estimate that at 39°C the rate constants are ∼6 times faster than at 23°C. We calculate that in the mouse, f₂ ≈ 396,000 s⁻¹, b₂ ≈ 15,600 s⁻¹, and τ_epc ≈ 0.7 ms, and that the average number of openings per burst is ∼11. Despite the high Q₁₀ for the gating rate constants, τ_epc decreases only modestly at high temperatures. This is because the number of openings per burst increases with temperature (f₂ >> k_-2), so that τ_epc ≈ E₂/k₋₂. With the natural transmitter and under this condition, E₂, k₋₂, and τ_epc change little with temperature.

Finally, we carried out an exercise in protein engineering. We sought to mutate the wt AChR to compensate for the effect of temperature on the gating rate constants, and hence, τ_epc. Specifically, our goal was to design and express AChRs that would give rise to a τ_epc at 10°C that would be the same as for wt AChRs at 23°C, but without altering the equilibrium dose-response properties, which depend on both K_d and E₂ (we did not try to compensate for channel conductance or the amplitude of the epc). In wt AChRs activated by ACh, a 13°C reduction in temperature would be expected to slow the gating rate constants by ∼4.3-fold and τ_epc by ∼2.3-fold (Eq. 5).

Almost all point mutations in the AChR that have been studied so far alter both the gating rate and equilibrium constants; therefore, to achieve our goal, we had to combine two separate mutations. One mutation was αD97Q (in loop A of the extracellular domain), which was previously shown to increase E₂ mainly by increasing f₂ (a gain-of-function, high-Φ mutation) (23). The other mutation was ɛI257A (in the pore-lining M2 helix), which was shown to decrease E₂ approximately to the same extent, but by increasing b₂ (a loss-of-function, low-Φ mutation) (24). If these two mutations are energetically independent, we might expect the E₂ of the double-mutant construct to be the same as for the wt, but with faster opening and closing rate constants. In this case, the two mutations in combination would compensate for the catalytic effect of temperature but have little effect on K_d or E₂.

Table S4 shows the experimental results. αD97Q alone increased E₂, mostly by virtue of an ∼50-fold increase in f₂. ɛI257A alone decreased E₂ by about the same extent, partly because it increased b₂ by ∼5-fold. Fig. 6 shows example single-channel currents from AChRs having either or both of these mutations. The single-channel analysis shows that the αD97Q+ɛI257A double mutant approximately changed the gating parameters by the expected amounts, assuming energy independence. Further, at 10°C the double-mutant construct exhibited gating rate constants that were similar to those for wt AChRs at 23°C (Table S4). We used these rate constants to simulate synaptic currents at each temperature, keeping k₋₂ constant at 40 ms⁻¹. Fig. 6 B shows that this mutant pair can approximately compensate for the catalytic effect of temperature on the synaptic current decay time constant.

Figure 6.

Engineering the synaptic response. The AChR was mutated to compensate for the catalytic effect of temperature on gating and the time course of the synaptic current decay. (A) Example clusters from wt, αD97Q, ɛI257A, and the double mutant αD97Q+ɛI257A. αD97Q, and ɛI257A had approximately equal and opposite effects on the gating equilibrium constant (see Fig. 4A for an example cluster, 5 mM CCh and 20°C). αD97Q increases the opening rate constant and ɛI257A increases the closing rate constant (Table S4). The cluster P_o (the gating equilibrium constant ≈ 0.05) was approximately the same in the wt at 23°C and double mutant at 10°C. (B) Simulated synaptic current decay for the wt and double mutant AChRs at different temperatures. The decay time constant for the wt at 23°C (τ_epc ≈ 1.0 ms) is similar to that for the double mutant at 10°C (∼1.1 ms) but faster than that for the wt at 10°C (∼2.3 ms). When combined, these two mutations compensate for the catalytic effect of temperature.

Discussion

With the natural transmitter, the wt AChR gating equilibrium constant is almost constant with temperature (5–35°C). We estimate that in the R-to-R^∗ isomerization, only ∼+0.7 kcal/mol (2.9 kJ/mol) of heat is absorbed from the bath. The relative temperature insensitivity of the gating equilibrium constant is remarkable because many residues in this >2000 residue (∼300 kD), five-subunit membrane protein change free energy in the gating isomerization. A priori, we expected a larger net heat exchange in such a large, widespread, and complex reaction. In wt AChRs, the equilibrium dissociation constants for agonist binding to the transmitter-binding site or to the channel-blocking site in the pore hardly changed with temperature; however, these results are easier to rationalize because the conformational changes associated with these processes are likely to be less extensive. We cannot think of a natural selection pressure that would tend to eliminate temperature dependence from the gating of mouse muscle AChRs.

In wt AChRs, the activation enthalpy for gating is large (∼20 kcal/mol; Q₁₀ ∼ 3.2) for both the opening and closing rate constants. Activation enthalpies of similar magnitudes have been reported for gating of other ion channels (25–28) and for protein folding (29–32). The AChR channel-opening rate constant is fast (at 23°C, ∼66 ms⁻¹) and mutations can make it even faster (33). Although the free energy of the transition state is not known with certainty, two separate lines of evidence suggest that it may be ∼4 kcal/mol (33,34). Apparently, the large barrier enthalpy is offset by a correspondingly large entropy, which allows the reaction to proceed apace at body temperature.

We examined the temperature dependencies of binding and gating in wt AChRs for three agonists: ACh, CCh, and Cho. For all three, the equilibrium dissociation constant of the resting conformation was approximately independent of temperature. The association and dissociation rate constants were also temperature-independent for ACh and αY127E AChRs, but those for Cho and αG153S varied sharply with temperature (Q₁₀ ≈ 7.4). We speculate that this difference can be attributed to the αG153S mutation rather than to the agonist. Perhaps a loss of backbone flexibility here causes the extra enthalpy at the transition state of the binding process (22).

At 25°C, the gating ΔG^o (calculated from the natural logarithm of the gating equilibrium constant, E₂) is different for AChRs activated by ACh, CCh, or Cho (−1.9, −1.0, and +1.8 kcal/mol, respectively). Compared with ACh, the relative gating free-energy change with two CCh or Cho molecules bound is ΔΔG^o= +0.9 or +3.7 kcal/mol. From our measurements, we conclude that the enthalpy components of these free-energy differences are also agonist-dependent. In comparison with ACh, we estimate that the relative gating enthalpy change with two CCh or Cho molecules bound is ΔΔH = +1.0 or +3.5 kcal/mol. The net free energy and enthalpy values are approximately equal. The differences in the free energy between the three agonists can be attributed entirely to differences in enthalpy, and hence the entropy change associated with gating is approximately the same for these ligands.

To a first approximation, enthalpy changes can be associated with bonds, and entropy changes can be associated with water and structural dynamics. These results suggest that the change in bonding, R-to-R^∗, is different for different agonists. The physical event that determines agonist differences in E₂ is the R/R^∗ equilibrium dissociation constant ratio (K_d/J_d). We observed that K_d is temperature-independent for all three agonists, so we can specifically associate the gating enthalpy differences between agonists with differences in ligand-protein bonds in the high-affinity, open-channel complex (J_d).

Without high-resolution structures of AChRs in R and R^∗ occupied by ACh, CCh, and Cho, it is difficult to pinpoint the exact nature of the bond differences between these agonist molecules. K_d is influenced in part by cation-π interactions between the quaternary amine group of ACh and αW149 (35), and it is possible that this interaction increases to different extents with ACh, CCh, and Cho when the protein adopts R^∗. It is also possible that the differences in chemical bonding in R^∗ between the three agonists arise from interactions of the ligand with other atoms in the protein or with water, or even from bond strain within the ligand itself. Probing the relative free energy and enthalpy changes for more agonists and AChRs with mutations of binding-site residues may shed light on this matter.

We sometimes made multiple perturbations and found that their effects were in all cases energetically independent. αY127E did not change K_d (or the binding rate constants) for ACh, which indicates that this side-chain substitution does not interact with the agonist molecule or with residues that determine resting affinity. The channel conductance was the same with all agonists and mutations, indicating that regions of the pore that influence ion permeation rates were also not perturbed. The effects of αD97A and ɛI257A on the gating equilibrium constant were independent. It is this independence of free-energy consequences on both the transition and ground states that allowed us to engineer AChRs so that the catalytic effect of temperature could be eliminated.

Our results indicate that at adult mouse neuromuscular synapses, each AChR opens an average of ∼11 times in rapid succession before a transmitter molecule dissociates to terminate the burst. At 39°C, the gaps arising from sojourns in the diliganded-R state are extremely brief (∼2 μs) and would not be apparent in electrophysiological recordings. Indeed, gaps arising from channel block by the agonist would probably be longer in duration. The opening rate constant at mouse body temperature approaches the estimated maximum for the forward isomerization rate constant (33). It appears that the process of natural selection has generated an allosteric protein that operates near its physical-chemical speed limit.

Elsewhere, we consider the effects of mutations (including αY127E and αG153S) on the enthalpy and entropy changes in the AChR gating conformational change (36).