Abstract
Nicotinic ACh receptor channels (AChRs) exposed to high concentrations of ACh adopt ‘desensitized’ conformations that have a high affinity for the transmitter and no measurable ion conductance. Single-channel currents elicited by 0.1 or 1 mmACh were recorded from human embryonic kidney (HEK) cells that had been transiently transfected with mouse α, β, δ, and ε subunits. On the time scale of ∼0.1 ms to ∼1 h, apparent open intervals are described by a single exponential component, and shut intervals associated with desensitization are described by the sum of four or five exponential components. The kinetic behaviour appeared to be stationary and homogeneous. Desensitization rate constants were estimated by kinetic modelling of currents from cell-attached and outside-out patches (where the number of channels in the patch was measured). A single AChR recovered from the longest-lived desensitized state only after ∼5 min. The occupancy of an AChR for each of the desensitized states was calculated as a function of time after the continuous application of a pulse of saturating ACh. The longest-lived desensitized state accounted for 90 % of the total only after several seconds. The fractional recovery from desensitization (during a 200 ms wash period) decreased as the duration of the desensitizing pulse increased, suggesting that recovery is slower from the longer-lived desensitized states. The free energy landscape for the AChR desensitization reaction in cell-attached patches exhibited an initial destabilization, followed by a plateau region of gradually increasing stability, followed by a deep well.
At the neuromuscular synapse, following a step increase to a high ACh concentration, the endplate current increases rapidly and then declines gradually to a small, but measurable level (Katz & Thesleff, 1957). The initial rise in current is a manifestation of channel activation; two ACh molecules reversibly bind to each endplate ACh receptor (AChR), which then takes on (with a high probability) an ‘open’ conformation that has a high affinity for ACh and an ion-conductive pore. The subsequent decline in current is a manifestation of channel inactivation; with time, diliganded AChRs increasingly adopt ‘desensitized’ conformations that have a high affinity for ACh but no measurable ion conductance. The small steady-state current that is maintained at high ACh concentrations reflects the dynamic equilibrium between diliganded-desensitized and diliganded-open AChRs. Here we describe, at the single-channel level, the kinetics of this process.
Compared to activation, AChR desensitization is poorly understood. The driving energy for AChR activation is the > 1000-fold higher affinity for ACh in the open vs. the closed conformation (Edelstein et al. 1996; Jackson, 1999). The energetic basis of desensitization is less clear because the affinities of desensitized (Sine et al. 1995) and open (Grosman & Auerbach, 2001) AChRs are similar. The extent to which the stability of the diliganded-desensitized conformation arises from more favourable agonist- protein vs. protein-protein contacts is uncertain (Auerbach & Akk, 1998). At the structural level, correlates of activation have been deduced from a comparison of the closed vs. the open Torpedo AChR (at resolutions of 4.6 Å and 9 Å, respectively; Unwin, 2000). Activation entails substantial structural rearrangements at the transmitter binding sites, the membrane domain and in the intervening regions (Unwin, 1995). In addition, mutations, affinity labelling and the atomic-resolution structure of a homologue of the AChR extracellular domain (Brejc et al. 2001) have led to the identification of specific residues that participate in agonist binding and that move during channel gating. In contrast, desensitized AChRs have been imaged only at a resolution of 18 Å (Toyoshima & Unwin, 1988), and the locations and the extent of the conformational perturbations that result in a desensitized AChR, which has high affinity binding sites (open-like) and undetectable ion conduction (closed-like), remain obscure. With regard to physiology, it is well known that the activation (and deactivation) rate constants influence the time course of the endplate synaptic current decay (Magleby & Stevens 1972; Colquhoun & Hawkes, 1977; Hille, 2001). The physiological role of AChR desensitization at the normal vertebrate endplate is, however, a matter of speculation, because the gradual decline in the current in response to the steady application of agonist occurs on a time scale (seconds) that is much longer than the decay of the synaptic current (milliseconds). The fact that desensitization is a conserved and robust feature of endplate AChRs suggests that this process serves an important function at the neuromuscular synapse and has been tuned during the course of natural adaptation (insofar as low phenotypic variance implies evolutionary honing).
Certain features of AChR desensitization are well established. (1) The desensitization reaction is complex (Sakmann et al. 1980; Sine & Steinbach, 1987; Sine et al. 1990; Naranjo & Brehm, 1993). Diliganded AChRs can occupy multiple desensitized states with lifetimes ranging from milliseconds (Magleby & Palotta, 1981; Salamone et al. 1999) to hours (Heidemann & Changeux, 1979; Feltz & Trautmann, 1982). The exact number and properties of such states has not been completely characterized. (2) Upon washout after the sustained application of a high concentration of ACh, desensitized receptors appear to return to the closed conformation without passing through the diliganded-open conformation (Katz & Thesleff, 1957; Franke et al. 1993), although in wild-type AChRs unliganded openings are brief and difficult to detect. (3) The time constant of recovery upon agonist washout increases with the duration of the desensitizing agonist pulse (Paradiso & Brehm, 1998; Reitstetter et al. 1999). (4) Diliganded AChRs desensitize much faster than unliganded and monoliganded AChRs (Cachelin & Colquhoun, 1989; Dilger & Liu, 1992; Franke et al. 1993). This may reflect the fact that only diliganded AChRs occupy an open conformation with a high probability, and desensitization occurs more rapidly from open, compared to closed, conformations (Auerbach & Akk, 1998).
Here, we extend the studies of AChR desensitization by examining, in detail, the number and kinetics of the multitude of diliganded-desensitized states that are present in recombinant adult-type (α, β, δ and ε subunits) mouse AChRs expressed in human embryonic kidney (HEK) cells.
METHODS
Mouse receptor subunits (α, β, δ and ε) in the vector pRBG4 were expressed transiently in HEK 293 cells by calcium phosphate transfection. The α subunit contained a background mutation (valine-to-alanine) at position 433 in the M4 segment (Salamone et al. 1999). A total of 3.5 μg DNA per 35 mm culture dish was used in the subunit ratio 2:1:1:1 (α:β:δ:ε). The DNA was left on the cells for 10-12 h, after which time the cells were replated in fresh medium on cover slips. Patch-clamp recordings were made 1-2 days thereafter.
Macroscopic and single-channel currents were recorded at room temperature (21-25 °C) for outside-out and cell-attached patches. A fast perfusion system was used to exchange the solution with outside-out patches. A double-barrelled pipette was fixed onto a biomorph actuator (model QP22B; ACX, Cambridge, MA, USA) using epoxy resin. The biomorph was controlled by square-wave voltage pulses (which were low-pass filtered at 150 Hz) using pCLAMP 8.0 software (Axon Instruments, Union City, CA, USA) and a homemade amplifier. The perfusion system exchange time (10-90 %) was ≤ 200 μs.
Patch pipettes were pulled from borosilicate capillary tubes (Sutter Instruments, Novato, CA, USA) and coated with Sylgard 184 (Dow Corning, Midland, MI, USA). The pipette resistance ranged from 2 to 15 MΩ. In the outside-out patch experiments, the extracellular solution comprised (mm): 145 KCl, 5 NaCl, 1.8 CaCl2, 0.5 MgCl2 and 10 Hepes (pH 7.4) and the intracellular (pipette) solution comprised (mm): 130 KF, 20 NaCl, 10 Hepes and 10 EGTA; pH 7.0. In the cell-attached experiments, the extracellular solution comprised (mm): 145 NaCl, 5 KCl, 1.8 CaCl2, 0.5 MgCl2 and 10 Hepes (pH 7.4) and the pipette solution comprised (mm): 145 KCl, 5 NaCl, 1.8 CaCl2, 0.5 MgCl2 and 10 Hepes (pH 7.4). The currents were amplified (Axopatch-200B; Axon Instruments), low-pass filtered at 10 kHz (eight-pole Bessel) and digitized at 20 kHz directly to a computer using a Digidata 1322A digital interface (Axon Instruments).
In the outside-out patch experiments, a 2 s pulse of 1 mm ACh was applied to elicit channel activation and desensitization. The peak current was divided by the single-channel amplitude (typically 4.5 pA at −90 mV) to estimate the number of channels in the patch. After the onset of the pulse, the ACh solution was superfused continuously for 10-15 min to record the steady-state single-channel activity. In the cell-attached patch experiments ACh (1 or 0.1 mm) was included in the patch pipette solution. In these experiments, single-channel currents were recorded for 30-120 min. The interior of the pipette was held at +60 mV, and the estimated membrane potential was −90 mV.
The analysis of the macroscopic currents was carried out using pCLAMP 8.0 software (Axon Instruments). In Fig. 10C (fitted line), the decay time constants were computed from the rate constants obtained by single-channel kinetic modelling. Macroscopic currents were also simulated using the mathematic programs Maple 6.0 (Waterloo Maple, Waterloo, Ontario, Canada) and Scientist (MicroMath; no longer available).
Figure 10. Desensitization kinetics of AChRs in outside-out patches exposed to 1 mm ACh.
A, clean single-channel currents. Example currents (boxes) are shown at increased resolution at the bottom left of this figure. In outside-out patches, there appears to be a dearth of long-duration apparent openings compared to cell-attached patches (see Fig. 2.) B, interval duration histograms. The idealized currents were fitted by a model (above) having one open and five desensitized states. The closed interval components were (τ in ms (fractional amplitude)): 1.43 (0.28), 7.26 (0.21), 41.7 (0.24), 541.6 (0.19) and 2247 (0.08). The rate constants for four patches under these conditions is shown in Table 4. The only significant difference between cell-attached and outside-out patches is that the entry (recovery) rate constants regarding the first (shortest-lived) desensitized state are ∼twofold faster (slower) in the outside-out configuration. C, the microscopic rate constants provide a good description of the macroscopic decay. The whole-patch current during a 2 s pulse of 1 mm ACh (average of five pulses) and the current response computed directly from the rate constants and model shown in B (dotted line) are superimposed. The model predicts the current should decay as the sum of five exponentials (τ in ms): 0.75 (29 %), 4.2 (26 %), 16.1 (50 %), 90.3 (18 %) and 1192 (1.4 %). These values compared well with those obtained by fitting directly the current decay by the sum of four exponentials: 1.6 (9 %), 15.1 (66 %), 69.6 (22 %) and 1143 (3 %). The two fast components predicted from the single-channel analysis are merged into a single (truncated) component in the macroscopic current. The number of channels in the patch was estimated by dividing the peak amplitude immediately following the agonist step by the single channel current. The initial recovery rate constant (D5-D4) for the patch was normalized by the number of channels (in this patch, 275) to estimate the rate constant for an individual channel. Overall, this value was 0.00374 s−1, which indicates that a single AChR recovers from the deepest desensitized state in ∼267 s or 4.5 min.
Single-channel currents were analysed with the QUB suite programs from SUNY Buffalo (http://www.qub.buffalo.edu). Idealization was performed using the segmentation k-means hidden Markov algorithm at full bandwidth (10 kHz), and the kinetic modelling of the idealized intervals was performed using the maximum interval likelihood method (Qin et al. 1996). The dead time was 0.25 ms for the experiments performed using 1 mm ACh, and 0.1 ms (to allow the detection and modelling of gaps arising from channel activation) for the experiments performed using 100 μM ACh. The time constants and amplitudes of the open and shut interval distributions were computed from the optimal parameters of the model, with a correction for the imposed dead time.
An important objective was to quantify and model the durations of the open and shut intervals arising from the main population of AChRs. The raw single-channel current signal was, however, contaminated by a number of noise sources. Wild-type AChRs exhibit heterogeneous kinetic properties both in native (Auerbach & Lingle, 1986) and heterologous (Naranjo & Brehm, 1993) expression systems. In some patches, non-AChR channels were active. In addition, seal breakdown and other spurious sources of interference often contributed current to the raw record. In order to focus the analyses on a single kinetic class of AChR, these noise events were eliminated from the analysis. Lacking a clear algorithm to achieve this goal, we employed one of two ‘eyeball’ selection procedures. In some patches, prior to idealization, noisy sections were selected and replaced by a sample of the adjoining baseline (see Fig. 1), while in others only selected sections of the record were idealized and the intervals between such selections were defined as the baseline.
Figure 1. Cleanup procedure.
Raw single-channel currents (cell-attached patch, 100 μM ACh, −80 mV; left) typically include ‘noise’ arising from kinetic heterogeneity of ACh receptors (AChRs; a), endogenous currents from non-AChR channels (b), and vagaries associated with the seal (c). Prior to idealization, noisy sections were selected by eye and replaced with the baseline current (right).
To test for homogeneity, the kinetics of clusters of openings, which presumably arose from individual AChR molecules, were analysed. Clusters were defined as a collection of > 50 open intervals (with no overlapping currents) separated by shut intervals of < 3 s (τcrit). To test for stationarity, the record was divided into 2 min segments and the intervals within each segment were fitted separately.
RESULTS
Time constant analysis
We began our analysis of desensitization by examining the number and characteristics of the open and shut interval time constants produced by diliganded-desensitized AChRs. AChRs can adopt three basic conformations: closed, open, and desensitized. For closed AChRs, the equilibrium dissociation constant of the two transmitter binding sites in physiological solutions is ∼120 μM (Akk & Auerbach, 1996). The affinity of open and desensitized AChRs is > 3000-fold higher (Sine et al. 1995; Grosman & Auerbach, 2001). Therefore, at an ACh concentration of 1 mm, virtually all of the current reflects the activity pattern of diliganded AChRs. The lifetimes of diliganded-closed (∼10 μs; Maconochie & Steinbach, 1998) and diliganded-blocked (∼5 μs; Maconochie & Steinbach, 1995) AChRs are, however, too brief to be detected. Hence, all of the shut intervals, by definition, reflect sojourns in diliganded ‘desensitized’ states.
At 1 mm ACh, the apparent openings occurred in clusters and the pattern of closed intervals in the record was complex (Fig. 2). Apparent ‘open’ intervals, which reflect the aggregate lifetime of diliganded closed/open/blocked AChRs, were described by a single exponential component, whereas closed intervals were composed of multiple exponential components (Fig. 2B). In the patch shown in Fig. 2, shut intervals were described by the sum of five exponential components.
Figure 2. Interval duration distributions in a cell-attached patch exposed to 1 mm ACh.
A, single-channel currents after the cleanup procedure. The traces at the bottom of the figure show the boxed currents on an expanded time scale. B, interval duration histograms. The idealized currents were fitted by a model (top graph) having one open and five shut components (continuous line). The shut interval components were (τ in ms (fractional amplitude)): 1.02 (0.44), 9.26 (0.21), 45.6 (0.22), 733 (0.06) and 8739 (0.06). The time constants and fractional amplitudes for 10 patches under these conditions are given in Table 1 and Fig. 6. The slowest time constant is predicted to scale with the number of channels in the patch and therefore does not pertain to a single AChR.
If all of the AChRs in a patch are homogeneous and stable with regard to their desensitization kinetics, then each component in the shut interval duration distribution reflects a distinct desensitized state of the protein. In order to probe the number of such states, intervals from 10 different patches exposed to 1 mm ACh were fitted by kinetic models having one open component and from three to six shut components (Fig. 3A). In five of the patches, adding a fifth shut component improved the log likelihood (LL) of the fit by at least 10 units, but adding a sixth component afforded no further improvement in the fit. This suggests that on the time scale of our experiments (∼1 h), AChRs can adopt four or five diliganded-desensitized states.
Figure 3. Log likelihood analysis of the number of desensitized components.
The idealized currents were fitted by models having three to six desensitized components. In each panel, each symbol represents a different patch. In half of the cell-attached (1 mm ACh) patches, the log likelihood improved by at least 10 units when the number of shut components was increased from four to five. Overall, we estimate that five states are required to describe the closed intervals arising from desensitization.
If the patch AChR population is not homogeneous and/or if the desensitization rate constants change with time, the number of components observed for the whole patch could reflect the aggregate activity of heterogeneous subpopulations, each having a simpler kinetic behaviour (i.e. < 5 shut components). Figure 4 shows an analysis of the kinetic heterogeneity for a patch with five shut components. Shut intervals within individual clusters (defined as a group of 50 or more openings separated by shut intervals of < 3 s) were described by the sum of three components. If, for example, the middle component (labelled S2 in Fig. 4A) varied between clusters, we would expect to see two distinct populations for this time constant. Although there was some scatter in the time constants and fractional amplitudes, there was no clear indication of kinetically heterogeneous subpopulations of clusters.
Figure 4. Heterogeneity of desensitization kinetics.
A, time constants and fractional amplitudes of intervals within clusters (defined as sequences of > 50 openings containing shut intervals < 3 s), fitted by a three shut/one open component model. There is no evidence of heterogeneity in the fast, intermediate or slow shut components (S1-S3). B, shut and open interval duration histograms for all intra-cluster events combined. The continuous line is a fitted by a four-shut component model, and the dashed line is a fitted by a three-shut component model. This patch contained five shut components in all; the slowest component was eliminated from clusters.
Figure 5 shows an analysis of the stability of the kinetics over time for this same patch. The record was divided into 2 min segments and the intervals within each segment were fitted separately by four shut components. Aside from a small but steady increase in the apparent open lifetime (see Fig. 7, later), there was no clear evidence of a time-dependent variation in the component amplitudes or time constants. These analyses suggest that a single AChR can adopt five desensitized states.
Figure 5. Stability of desensitization kinetics.
A, time constants and fractional amplitudes of intervals within segments (defined as a continuous 2 min period), fitted by a four shut/one open component model and plotted as a function of the mean time of the segment. Aside from a steady increase in the open time constant (see Fig. 8), there is no clear evidence of non-stationary behaviour in the time constants (S1-S4). B, open and shut interval duration histograms for each of the 13 segments. The vertical dashed line shows the open time constant of the first segment, and serves to highlight the drift towards longer open times. The continuous lines in the shut histograms show the fit by four shut components.
Figure 7. Stability of desensitization rate constants.
A, clean single-channel currents (cell-attached patch, 1 mm ACh). B, rate constants and interval duration histograms. The idealized currents were fitted by a model (top) having one open and five desensitized states (continuous heavy line in shut interval duration histogram). A fit with a model having only three desensitized states is shown as a light line. C, in order to test the stability of the rate constants, the record was divided into 13, 2 min segments and the intervals within each segment were fitted by a 3-shut component scheme (to allow for the reduced number of intervals in each segment). The rate constants have been normalized by their mean values, as shown. There was no trend in the rate constant estimates, with the exception of the first desensitization step, which slowed by about 1.5-fold over the course of the recording (∼30 min).
Table 1 and Fig. 6 show the time constants and fractional amplitudes for all 10 cell-attached patches at 1 mm ACh. All of the patches had a short-lived shut component (τ1 ∼1 ms; fractional amplitude ∼0.36) and a very long-lived component (τ5 ∼9 s; fractional amplitude ∼0.09) whose time constant is predicted to scale with the number of channels in the patch. The intermediate time constants of both the four- and five-component patches were scattered and did not fall into distinct groups. We were therefore unable to reach a firm conclusion as to the number of desensitized components. Assuming that there is a total of five components, we used the range of time constant values shown by the dashed boxes in Fig. 6 to estimate the time constants of the intermediate desensitized components from all of the patches. The estimated intermediate time constants in milliseconds (fractional amplitudes) were τ ∼10 (0.26), τ ∼74 (0.19), and τ ∼800 (0.09).
Table 1.
Time constants and amplitudes of open and shut components in the cell-attached patches (1 mM ACh)
| Five-component patches | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Open | Shut | |||||||||||
| Patch | τ0 | τ1 | a1 | τ2 | a2 | τ3 | a3 | τ4 | a4 | τ5 | a5 | nev |
| 01711001 | 22.9 | 0.87 | 0.67 | 9.97 | 0.17 | 202.6 | 0.12 | 1791 | 0.035 | 13570 | 0.012 | 2745 |
| 01815002 | 24.7 | 0.63 | 0.29 | 9.44 | 0.30 | 82.6 | 0.19 | 1867 | 0.105 | 8980 | 0.121 | 2153 |
| 01813008 | 17.8 | 0.36 | 0.15 | 3.69 | 0.29 | 32.4 | 0.28 | 713 | 0.095 | 8982 | 0.194 | 2431 |
| 01726000 | 25.8 | 1.02 | 0.44 | 9.26 | 0.21 | 45.6 | 0.22 | 733 | 0.060 | 8739 | 0.063 | 4923 |
| 01720001 | 8.7 | 0.74 | 0.25 | 4.99 | 0.28 | 33.2 | 0.30 | 659 | 0.005 | 2538 | 0.057 | 16041 |
| Mean | 20.0 | 0.72 | 0.36 | 7.47 | 0.25 | 79.3 | 0.22 | 1152 | 0.06 | 8562 | 0.09 | 5659 |
| s.e.m. | 3.1 | 0.11 | 0.09 | 1.30 | 0.03 | 32.2 | 0.03 | 276 | 0.02 | 1757 | 0.03 | 2641 |
| Four-component patches | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Open | Shut | |||||||||
| Patch | τ0 | τ1 | a1 | τ2 | a2 | τ3 | a3 | τ4 | a4 | nev |
| 01725002 | 27.8 | 0.96 | 0.23 | 14.30 | 0.22 | 650.3 | 0.14 | 3172 | 0.417 | 985 |
| 01725000 | 16.2 | 1.10 | 0.38 | 5.42 | 0.21 | 62.4 | 0.14 | 5121 | 0.272 | 1851 |
| 01815000 | 17.8 | 1.07 | 0.28 | 13.62 | 0.22 | 61.4 | 0.12 | 4056 | 0.378 | 665 |
| 01724000 | 59.1 | 1.27 | 0.43 | 21.78 | 0.34 | 344.0 | 0.10 | 30940 | 0.129 | 647 |
| 01726001 | 33.6 | 0.72 | 0.31 | 7.41 | 0.37 | 71.3 | 0.19 | 6228 | 0.136 | 579 |
| Mean | 30.9 | 1.02 | 0.33 | 12.51 | 0.27 | 237 | 0.13 | 9903 | 0.26 | 945 |
| s.e.m. | 7.7 | 0.09 | 0.04 | 2.89 | 0.035 | 116 | 0.01 | 5284 | 0.06 | 237 |
The time constants (τ) are expressed in milliseconds and the amplitudes (a) are given as a fraction of the total. The number of components refers to the shut interval duration distribution; all patches required a single open component. The dead time was 0.25 ms; nev is the sum of open and shut intervals.
Figure 6. Time constants and amplitudes of shut components from all cell-attached patches (1 mm ACh).
For each of four components, the fractional amplitude (a) is plotted as a function of its time constant (τ). Filled symbols are the five-component patches and open symbols are the four-component patches. The τ and a values were calculated for the regions within the dashed boxes (drawn by eye). The third component in the four-component patches is spread between the third and fourth components of the five-component patches. The slowest shut component of each patch was omitted because its parameters are predicted to scale with the number of channels in the patch, which was different for each patch. See Table 1.
It is possible that the different number of components between patches may reflect a real variability in AChR desensitization, but it may more simply arise from the fact that the patches requiring four components had fewer intervals (mean = 945) than those requiring five (mean = 5659; Table 1, see also Table 4.) Overall, it is likely that on the time scale of these experiments (approximately 10−4-104 s), the AChRs adopted five desensitized states.
Table 4.
Desensitization kinetics of outside-out patches (1 mM ACh)
| A. Time constants (τ, in ms) and fractional amplitudes (a) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Open | Shut | |||||||||||
| τo | τ1 | a1 | τ2 | a2 | τ3 | a3 | τ4 | a4 | τ5 | a4 | nev | |
| 8.19 | 0.77 | 0.19 | 5.30 | 0.29 | 40.3 | 0.24 | 534 | 0.20 | 2082 | 0.08 | 2577 | |
| 12.8 | 0.69 | 0.17 | 5.55 | 0.18 | 22.4 | 0.26 | 131 | 0.20 | 669 | 0.19 | 5349 | |
| 6.70 | 0.70 | 0.25 | 8.11 | 0.43 | 56.5 | 0.14 | 439 | 0.11 | 4643 | 0.07 | 2185 | |
| 12.6 | 1.39 | 0.12 | 6.47 | 0.28 | 35.1 | 0.22 | 201 | 0.20 | 938 | 0.18 | 3185 | |
| Mean | 10.1 | 0.89 | 0.18 | 6.35 | 0.30 | 38.6 | 0.22 | 326 | 0.18 | 2083 | 0.13 | 3324 |
| s.e.m. | 1.5 | 0.17 | 0.03 | 0.64 | 0.03 | 7.1 | 0.03 | 96 | 0.02 | 907 | 0.03 | 705 |
| B. Modelling results Linear model | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| k01 | k10 | k12 | k21 | k23 | k32 | k34 | k43 | k45 | k54* | N | k54 | |
| 133.0 | 386 | 742 | 225 | 117 | 30.6 | 13.7 | 3.3 | 0.3 | 0.6 | 275 | 0.0023 | |
| 90.0 | 580 | 1426 | 326 | 256 | 128.0 | 40.9 | 12.2 | 3.2 | 2.8 | 625 | 0.0045 | |
| 172.0 | 568 | 821 | 193 | 51 | 12.9 | 8.5 | 3.1 | 0.9 | 0.4 | 165 | 0.0023 | |
| 87.4 | 259 | 746 | 278 | 115 | 32.3 | 16.3 | 8.0 | 1.8 | 2.0 | 333 | 0.0059 | |
| Mean | 120 | 448 | 934 | 256 | 135 | 51 | 20 | 6.7 | 1.5 | — | — | 0.0037 |
| s.e.m. | 20 | 77 | 165 | 29 | 43 | 26 | 7 | 2.1 | 0.6 | — | — | 0.0001 |
| Star model | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| k01 | k10 | k02 | k20 | k03 | k30 | k04 | k40 | k05 | k50* | k01 | |
| 33.3 | 1312 | 37.8 | 190.6 | 29.6 | 25.0 | 23.4 | 1.89 | 9.2 | 0.48 | 0.0018 | |
| 19.6 | 1453 | 15.2 | 181.0 | 20.7 | 44.8 | 15.3 | 7.64 | 14.3 | 1.50 | 0.0024 | |
| 54.9 | 1450 | 66.4 | 125.4 | 21.0 | 17.8 | 15.7 | 2.29 | 10.0 | 0.22 | 0.0013 | |
| 12.1 | 722.9 | 23.5 | 155.6 | 17.2 | 28.6 | 15.8 | 4.99 | 13.9 | 1.07 | 0.0032 | |
| Mean | 30.0 | 1234 | 35.7 | 163.1 | 22.1 | 29.1 | 17.6 | 4.20 | 11.8 | — | 0.0028 |
| s.e.m. | 9.4 | 174 | 11.2 | 14.6 | 2.6 | 5.7 | 1.9 | 1.34 | 1.3 | — | 0.0004 |
A, all patches required one open and five shut components; nev is the number of open + closed intervals in the record. B, the linear and star models are shown in Fig. 12; rate constants are given in s−1.
The slowest recovery rate constant is predicted to scale linearly with the number of channels in the patch. The estimated number of channels (N) was determined from the ratio of the peak and single-channel currents for the patch (see Fig. 10C). The recovery rate constant (k54) pertains to a single AChR.
After the cleanup procedure, the open-channel interval durations were always described by a single exponential. However, the time constant of this exponential was quite variable (8.7-59.1 ms; Table 1). This variation reflects the scatter in desensitization rate constants (e.g. k01, using the linear model; Table 2) rather than in channel opening/closing or agonist dissociation rate constants.
Table 2.
Desensitization kinetics of cell-attached patches (1 mM ACh)
| Five-component patches, Linear model | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| k01 | k10 | k12 | k21 | k23 | k32 | k34 | k43 | k45 | k54* | est. N | |
| 46.7 | 644.8 | 844.2 | 113.1 | 56.2 | 11.3 | 7.32 | 0.75 | 0.15 | 0.20 | 53 | |
| 65.7 | 778.9 | 1727.0 | 335.0 | 166.0 | 38.9 | 18.70 | 1.17 | 0.71 | 0.31 | 83 | |
| 67.6 | 969.3 | 303.9 | 61.7 | 48.9 | 6.9 | 1.55 | 0.50 | 0.12 | 0.08 | 21 | |
| 133.0 | 451.2 | 671.6 | 178.0 | 91.7 | 32.5 | 8.30 | 2.39 | 0.33 | 0.42 | 112 | |
| 43.8 | 522.8 | 421.5 | 86.5 | 46.7 | 27.6 | 11.60 | 1.28 | 0.59 | 0.23 | 61 | |
| Mean | 71.4 | 673.4 | 793.6 | 154.9 | 81.9 | 23.4 | 9.49 | 1.22 | 0.38 | 0.25 | 66 |
| s.e.m. | 16.1 | 92.6 | 251.7 | 49.0 | 22.5 | 6.2 | 2.81 | 0.33 | 0.18 | 0.13 | 15 |
| Five-component patches, Star model | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| k01 | k10 | k02 | k20 | k03 | k30 | k04 | k40 | k05 | k50* | |
| 18.0 | 1601 | 12.4 | 106.6 | 7.3 | 12.2 | 4.09 | 0.55 | 4.99 | 0.11 | |
| 16.6 | 2768 | 17.4 | 272.8 | 15.7 | 31.0 | 5.32 | 1.40 | 10.73 | 0.11 | |
| 48.1 | 1389 | 6.4 | 277.0 | 5.7 | 51.6 | 5.98 | 3.16 | 1.99 | 0.20 | |
| 43.0 | 1246 | 35.8 | 167.9 | 35.3 | 20.7 | 15.10 | 1.84 | 4.57 | 0.32 | |
| 22.1 | 988 | 8.3 | 108.5 | 8.7 | 22.0 | 2.30 | 1.37 | 2.45 | 0.11 | |
| Mean | 30 | 1598 | 16 | 187 | 15 | 28 | 6.5 | 1.7 | 4.9 | 0.15* |
| s.e.m. | 7 | 308 | 5 | 38 | 6 | 7 | 2.2 | 0.4 | 1.6 | 0.04 |
| Four component patches, Linear model | ||||||||
|---|---|---|---|---|---|---|---|---|
| k01 | k10 | k12 | k21 | k23 | k32 | k34 | k43* | |
| 38.6 | 302 | 692 | 65.0 | 52.0 | 2.3 | 0.5 | 0.80 | |
| 68.6 | 433 | 418 | 107.0 | 130.0 | 18.1 | 11.5 | 0.64 | |
| 60.9 | 334 | 565 | 65.6 | 45.2 | 8.8 | 13.8 | 1.46 | |
| 18.6 | 394 | 367 | 54.5 | 18.6 | 1.9 | 1.7 | 0.08 | |
| 34.0 | 587 | 708 | 169.0 | 61.9 | 14.0 | 6.9 | 0.31 | |
| Mean | 44 | 410 | 549 | 92 | 62 | 9.0 | 6.8 | 0.66 |
| s.e.m. | 9 | 49 | 69 | 21 | 19 | 3.2 | 2.6 | 0.23 |
| Four component patches, Star model | ||||||||
|---|---|---|---|---|---|---|---|---|
| k01 | k10 | k02 | k20 | k03 | k30 | k04 | k03* | |
| 13.2 | 1398.3 | 11.4 | 134.3 | 5.5 | 13.7 | 4.0 | 0.2 | |
| 29.4 | 919.5 | 13.6 | 186.3 | 8.9 | 16.1 | 16.6 | 0.2 | |
| 20.5 | 946.0 | 12.4 | 74.3 | 7.0 | 16.4 | 21.1 | 0.3 | |
| 8.9 | 789.5 | 5.9 | 46.1 | 1.6 | 2.9 | 2.2 | 0.0 | |
| 13.2 | 1398.3 | 11.4 | 134.3 | 5.5 | 13.7 | 4.0 | 0.2 | |
| Mean | 17 | 1090 | 11 | 115 | 5.7 | 13 | 9.5 | 0.16 |
| s.e.m. | 4 | 128 | 1 | 25 | 1.2 | 2 | 3.9 | 0.03 |
The kinetic models are shown in Fig. 12 (rate constants, s−1).
The slowest recovery rate constant is predicted to scale linearly with the number of channels in the patch. The number of components refers to the shut interval duration distribution. The estimated number of channels (est. N) in the five-component patches is the ratio of k54 * and the single-channel value of for this rate constant (see Table 4). The number of intervals in each patch is shown in Table 1.
Modelling the kinetics of cell-attached patches
The next phase of the analysis was to estimate the diliganded AChR desensitization/recovery rate constants in cell-attached patches. These rates serve as a basis for understanding the energetics of the desensitization reaction, and hence the molecular mechanisms that underlie this process.
Interval durations were fitted by kinetic models having one conducting (O) and five non-conducting (D) states. There are 407 ways to connect this state matrix, and 20 ways to connect these states using only 10 rate constants (i.e. after eliminating models with cycles; see Fig. 8). Since our recordings were obtained under essentially steady-state conditions, all of these possibilities provide statistically equivalent descriptions of the kinetics (Kienker, 1989).
Figure 8. Model-independent aspects of AChR desensitization.
We are unable to distinguish between the 401 different kinetics schemes (20 without cycles) that contain 1 O and 5 D states. A, all 20 non-cyclic models. B, results of fitting intervals in one patch to the 20 models shown in A. Model 20 is completely uncoupled (star) and model 1 is completely coupled (linear). In each case, there was at least one equilibrium constant (entry/recovery) < 0.1 and at least one > 10. For unknown reasons, the recovery rates (towards open) were less model dependent than the entry rates (away from open).
To start, we selected two extreme cases for kinetic modelling. The completely uncoupled (‘star’) model had each D state connected only to the single O state, and the completely coupled (‘linear’) model had D states that were connected in series (see Fig. 12). Table 2 shows the desensitization rate constants estimated from these two models, for all 10 patches at 1 mm ACh. The slowest recovery rate constant, D5→O in the star model and D5→D4 in the linear model, is marked with an asterisk because this rate constant is predicted to scale with the number of channels in the patch, and therefore does not reflect the properties of a single AChR.
Figure 12. The occupancy of diliganded states following a pulse of saturating ACh.
A, the star and the linear models were used to calculate the fractional occupancies as a function of pulse duration (all values are given in s−1). All of the states are diliganded; in addition, a diliganded-closed state connected only to the single open state (not shown) was added to each model (kC→O = 50 000 s−1, kO→C = 2000 s−1). B, the time evolution of diliganded states. At time zero, the fractional occupancy was 0.96 the open state and 0.04 in the closed state. The time (and fractional occupancy) of the peak for each desensitized state after the onset of the agonist is given in the text. The final desensitized state, D5, becomes dominant after ∼0.3 s (star model) and ∼2 s (linear model). The different recovery time courses that have been observed with different durations of agonist pulse (see Fig. 11) are likely to reflect the different agonist dissociation and/or recovery rate constants for desensitized states D1-D5.
In three patches we tested further the stability of the kinetics by estimating rate constants separately for 2 min segments (Fig. 7). The estimates were scattered about the global values to an extent that is expected given the small number of intervals in each segment. In two out of the three patches there was a small (∼twofold) downward drift in the first desensitization rate constant with time (Fig. 7C, upper left). Aside from this, there was no clear indication that the desensitization and recovery parameters were changing significantly during the course of our experiments.
The LL ratio cannot be used to distinguish between kinetic schemes that predict equivalent behaviour under steady-state conditions, thus the rate constants according to the star and linear models are only two of many possible solutions. In order to probe which characteristics of the desensitization landscape are independent of the model, we fitted the interval durations in 1 patch to all 20 non-cyclic models (Fig. 8). In all 20 schemes, least 1 of the equilibrium constants was ≤ 0.1 and 1 was > 10. Thus, in all of the reaction landscapes there was at least one significant (> 2 kBT; kB is Boltzmann's constant and T is absolute temperature) uphill reaction, and 1 significant downhill reaction. This analysis also revealed that, for unknown reasons, the recovery rate constants (i.e. leading towards O) were less model-dependent than the desensitization entry rate constant (i.e. leading away from O).
In our experiments, the ‘desensitized’ states were diliganded, non-conducting, and relatively long-lived (τ > 0.25 ms). Although the ACh channel-blocked state is too brief (∼5 μs) to meet this specification, it is possible that longer-lived channel-blocked species could exist. To test for this possibility, we quantified the desensitization rate constants in cell-attached patches exposed to 100 μM ACh (Fig. 9 and Table 3). At this concentration of ACh, it was expected that the fraction of time spent in the blocked state (Kd,ACh block = 1.9 mm; Akk & Auerbach, 1998) would be significantly less than at 1 mm ACh. In these experiments, a brief gap associated with channel activation was apparent, thus a closed state (connected only to the open state) was added to the linear model (Fig. 9B, top). With this addition, the number of desensitized components (five in all four patches; Fig. 3B) and the desensitization rate and equilibrium constants (Table 3) were similar to those in the 1 mm ACh experiments. This result suggests that the desensitization processes are not highly sensitive to channel blockade by ACh, implying that the desensitized states that we have identified probably reflect distinct conformational states of the AChR.
Figure 9. Desensitization kinetics of AChRs in a cell-attached patch exposed to 100 mm ACh.
A, clean single-channel currents. Example currents (boxed areas) are shown at higher resolution at the bottom. B, kinetic model and interval duration histograms. The idealized currents were fitted by a model (above) having one closed, one open and five desensitized states (continuous line). The inset shows the longer-lived interval distribution on an expanded scale. The closed interval components were (τ in ms (fractional amplitude)): 0.15 (0.91), 1.32 (0.03), 15.6 (0.02), 172.6 (0.016), 2946 (0.0079) and 44361 (0.0142). The briefest component is associated with channel activation. The rate constants for five patches under these conditions are shown in Table 3.
Table 3.
Desensitization kinetics of cell-attached patches (0.1 mM ACh)
| Five-component patches, Linear model | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| kCO | kOC | k01 | k10 | k12 | k21 | k23 | k32 | k34 | k43 | k45 | k54* | nev | est. N | |
| 5692 | 431 | 19 | 124 | 265 | 54 | 37 | 7.6 | 3.6 | 0.32 | 0.175 | 0.06 | 14409 | 16 | |
| 5737 | 887 | 157 | 395 | 362 | 73 | 22 | 5.9 | 1.7 | 0.36 | 0.160 | 0.10 | 14159 | 26 | |
| 3976 | 268 | 57 | 578 | 171 | 35 | 39 | 5.5 | 2.7 | 0.30 | 0.023 | 0.02 | 37786 | 5 | |
| 7070 | 588 | 23 | 277 | 444 | 55 | 41 | 7.3 | 3.6 | 0.32 | 0.18 | 0.06 | 7883 | 16 | |
| Mean | 5619 | 543 | 64 | 344 | 310 | 54 | 35 | 6.5 | 2.9 | 0.33 | 0.13 | 0.058 | 18559 | 16 |
| s.e.m. | 634 | 132 | 32 | 99 | 59 | 8 | 4 | 0.5 | 0.5 | 0.01 | 0.04 | 0.016 | 6584 | 4 |
Rate constants are given in s−1. The slowest recovery rate constant
is predicted to scale linearly with the number of channels in the patch. The estimated number of channels in the patch is the ratio of k54 * and the single-channel value of for this rate constant (see Table 4).
Outside-out patches
In cell-attached patches, the slowest recovery rate constant, which is much smaller than the other recovery rate constants, should scale linearly with the number of channels in the patch. In order to gain an accurate estimate of this rate constant for a single AChR, we examined the kinetics of desensitization in outside-out patches. The number of channels in each patch was estimated as the ratio of the peak amplitude of the whole-patch current following a rapid step application of 1 mm ACh and the single-channel current amplitude.
In outside-attached patches (Fig. 10), the apparent openings appeared to be shorter-lived than in cell-attached patches (Fig. 2). The results from four outside-out patches exposed to 1 mm ACh are shown in Table 4. Compared to cell-attached patches, in outside-out patches the apparent open time constant was twofold shorter (10 vs. 20 ms) and the fraction of brief shut intervals was ∼twofold less (0.18 vs. 0.36). Using the criterion of an LL ratio of 10, all of the outside-out patches required 5 shut components (Fig. 3C).
The only significant difference in the rate constants between cell-attached and outside-out patches was that the initial desensitization rate constant (O→D1, using the linear model) was ∼twofold faster in outside-out compared to cell-attached patches. This rather modest alteration of a single rate constant is sufficient to alter the appearance of the clusters of apparent openings. The main effect of patch excision is to increase the rate of exit from the open state.
The number of channels in the outside-out patches ranged from 165 to 625. We used the estimated number of channels in each patch to normalize the rate constant for the slowest recovery step (D5→D4; using the linear model). The mean was 0.0037 s−1 (linear scheme) or 0.0028 s−1 (star scheme). This indicates that in outside-out patches, it takes ∼5 min for a single AChR to recover from the deepest desensitized state. If we assume that this recovery rate constant is unaltered by patch excision, then we can use this normalized rate constant to estimate the number of channels that were active in the cell-attached patches (Table 2). We estimate that the number of channels in the cell-attached patches ranged from 21 to 112.
There have been several reports that the recovery from desensitization upon washout varies with the duration of the desensitizing pulse of ACh (Naranjo & Brehm, 1993; Paradiso & Brehm, 1998; Reitstetter et al. 1999). An example of this phenomenon is shown in Fig. 11. Initial pulses of ACh (1 mm) of various durations were applied to an outside-out patch, followed by a wash period of 200 ms and then a test pulse of 1 mm ACh. The fraction of AChR that had not recovered at the end of the wash period increased with the duration of the initial pulse. This behaviour will be analysed in light of the kinetic parameters for diliganded AChR desensitization.
Figure 11. The time course of recovery from a desensitizing pulse depends on the duration of the pulse.
A, currents from an outside-out patch. The time scale is logarithmic. A pulse of 1 mm ACh was applied for the indicated durations (bars), followed by a 0.2 s wash in ACh-free solution, followed by a second, test pulse of ACh (arrow). The amplitude of the test pulse indicates the number of AChRs that recovered from desensitization during the wash period. The fraction that does not recover increased as the duration of the initial pulse increased. B, the fraction that does not recover as a function of the initial pulse duration. About half of the AChRs failed to recover during the 0.2 s wash when the initial pulse duration was 0.2 ms. The lines are calculated from the estimated occupancy probabilities in the desensitized state at the start of the wash period (Fig. 12). The data are accounted for if 5 % (D5) and 69 % (D4) of AChRs recover (star scheme), and if 0 % (D5), 25 % (D4) and 64 % (D3) of AChRs recover (linear scheme), during the 0.2 s wash.
DISCUSSION
Limitations of the analysis
It has been known for some time that AChR desensitization is a complex process. We have attempted to provide a quantitative framework for understanding these reactions, as part of developing insight into their molecular foundations and physiological implications. Kinetic modelling is, however, an imperfect tool for achieving such organization. First, we cannot be certain of the number of desensitized states. Based on an LL ratio criterion of 10 units, most of the patches (13 out of 18) required 5 desensitized states. However, many features of the currents (e.g. noise, heterogeneity) are expected to increase the apparent number of components in the shut interval distribution. Second, some of the rate constants are estimated imprecisely. This may reflect the fact that slow rates mean long (and therefore infrequent) sojourns, or may reflect imperfections in the models as well as the currents. Finally, we cannot distinguish between the multitude of models that have one open and five shut states. Although these models all predict identical interval distributions, they differ in their predictions regarding the time evolution of desensitization following a pulse of ACh (Fig. 12) and the energy landscape for the desensitization reactions (Fig. 13). We addressed the issue of ‘model independence’ by reporting the distribution time constants and fractional amplitudes (Table 1 and Fig. 6), by examining in detail two reaction schemes that represent the boundary behaviour of the system (linear and star models; Table 2), and in one patch by estimating rate constants using 20 different schemes (Fig. 8).
Figure 13. The energy landscape of AChR desensitization.
The relative free energy along the desensitization reaction coordinate was calculated from the cell-attached patch (1 mm ACh) rate constants using a five-state linear kinetic model (Table 2). The height of the barriers (dotted lines) is arbitrary. The first step is uphill (∼2 kBT), followed by plateau consisting of three small downhill steps (∼1.5 kBT each) and, finally, a steep downhill step (∼5 kBT). As desensitization proceeded, the barrier heights increased.
Predictions from the rate constants
We used the rate constants to calculate a time course for the macroscopic current decline that occurred following a step application of 1 mm ACh. In Fig. 10C, the time course calculated from the optimal rate constants (obtained from either the linear or the star kinetic model, with rate constants estimated from the interval durations in the same patch) is superimposed on a macroscopic current from an outside-out patch containing 275 channels. The computed and experimental curves are in reasonably good agreement. This result suggests that the desensitization rate constants under continuous- and step-application of ACh are similar.
Other descriptions of AChR desensitization at the macroscopic level (e.g. Dilger & Liu, 1992; Naranjo & Brehm, 1993; Paradiso & Brehm, 1998; Jahn et al. 2001) report one or two components, while we typically required three to four components to fit the whole-patch current decay (Fig. 10C). This difference may arise, in part, from the fact that we used higher sampling and filtering frequencies (20 and 10 kHz vs., typically, 10 and 2 kHz, respectively), and fit the decays over a longer interval (2 vs. 0.4 s). This allowed us to resolve very fast (∼1 ms) and very slow (∼1 s) components. However, it is likely that even under identical recording conditions the single-molecule experiments would resolve more components than the ensemble averages.
The occupancy probabilities in the various diliganded states following a step application of 1 mm ACh were calculated from the average rate constants for the five-component, cell-attached patches (Fig. 12). The decay in the current with time (trace labelled ‘O’; see Fig. 10C) is the same for the star and the linear models. In both schemes, the maximum open probability (0.96) falls by half in ∼33 ms. The two models, however, make different predictions regarding the time evolution of an AChR in desensitized states. Using the linear scheme, the peak times (fractional occupancies) for the first four desensitized states are, respectively, 10 ms (0.05), 22 ms (0.17), 79 ms (0.34) and 600 ms (0.67). Using the star scheme, these values are, respectively, 3 ms (0.02), 14 ms (0.06), 53 ms (0.21) and 355 ms (0.39). In the linear model, the time to reach half of the maximum occupancy of the longest-lived desensitized state (D5) is 2.3 s, and this state accounts for 90 % of the total only after an 8.1 s exposure to ACh. In the star model, the time to reach half-maximum occupancy of D5 is 0.52 s, and this state accounts for 90 % of the total after a 3.1 s exposure to ACh.
The variation in the published estimates of the apparent rate constant for entry into desensitization obtained from single-channel kinetic analysis is likely to be a reflection of which D state was used to define the termination of clusters of openings. Thus, in previous work from this group, a desensitization entry rate constant of 4.6 s−1 (Auerbach & Akk, 1998) corresponds to entry into the longest-lived (D5) state, and a desensitization entry rate constant of 15 s−1 (Grosman & Auerbach, 2001) corresponds to entry into an intermediate desensitized state.
In paired-pulse experiments, the fraction of AChRs that fail to recover during a 0.2 s wash period increased with the duration of the initial desensitizing pulse (Fig. 11). It is likely that this pattern reflects the occupancy distribution of AChRs among the various D states at the start of the wash, which depends upon the duration of the pulse (Fig. 12). For example, after an initial pulse of 0.1 s, most of the desensitized AChRs are in states 2-4, while after a pulse of 4 s most are in states 4-5. If, upon the removal of the agonist, AChRs in different D states recover from desensitization (by a combination of agonist dissociation and conformational change) with different effective rates, then the fraction that recover during the fixed washout period will depend upon the duration of the pulse.
The relationship between the occupancy profile at the end of the pulse (Fig. 12) and the net recovery during the 0.2 s wash (Fig. 11) was quantified by fitting, for each D state, the percentage that failed to recover during the 0.2 s wash. For the star model, the recovery profile was accounted for if 95 ± 2 % of AChRs in D5 and 31 ± 4 % of in D4 failed to recover during the wash, while all of those in D1-D3 recovered. For the linear model, the recovery profile was fitted if 102 ± 2 % of AChRs in D5, 75 ± 3 % in D5 and 36 ± 4 % in D3 failed to recover during the wash, while all of those in D1 and D2 recovered. Thus, the data in Fig. 11 suggest that upon washout of the agonist, AChRs in D1 and D2 recover quickly (τ < 0.2 s) upon washout of the agonist, those in D3 and D4 recovered more slowly (τ ∼0.2 s), and those in D5 recovered even more slowly (τ << 0.2 s). Indeed, each of the five D states may have its own characteristic rate of recovery upon washout. A more complete analysis of the recovery time course as a function of initial pulse duration and agonist washout period is necessary before more quantitative conclusions can be drawn.
Figure 13 shows the free energy profile for the desensitization reaction based on the linear model for the five-component, cell-attached patches at 1 mm ACh. Note that in this plot, the barrier heights are arbitrary and are only significant in relation to each other (i.e. the pre-exponential factor was arbitrary but the same for all steps). The first D state, which is connected to the open state (D1), is ∼1.9 kBT (1.1 kcal mol−1) less stable than the open state. The relative stability of the next three states in the reaction (D2-D4) increases stepwise, but only by an average of 1.3 kBT (0.8 kcal mol−1) for each transition. Finally, there is a large increase in stability of ∼5 kBT (3 kcal mol−1) upon entry into the D5 state. That is, the energy landscape for desensitization for AChR in cell-attached patches shows an initial destabilization, followed by a plateau region of gradually increasing stability, followed by a deep well. Assuming that the pre-exponential factor is similar for all of the desensitization steps, we observe a gradual increase in the barrier heights as the reaction progressed. The extent to which these energies reflect ligand-protein vs. protein-protein interactions remains to be determined.
Stationarity and complexity
We examined, cursorily, the heterogeneity and stability of the rate constants for diliganded AChR desensitization and recovery. With one exception, there was no clear evidence for significant time-dependent or cluster-dependent variations in the kinetic parameters. The exception was the rate constant for entry into the shortest-lived desensitized state, which, in some patches, gradually decreased with time (about fourfold h−1). Interestingly, only this rate constant (linear scheme) was significantly different (∼twofold faster) in outside-out vs. cell-attached patches. The molecular bases for these effects are not known, but they suggest that alterations in the cytoplasmic domain of the AChR can modify the desensitization reaction.
Although we cannot be sure of the number of diliganded desensitized states, and we cannot distinguish between the various connection schemes that might link these states, there is no doubt that AChR desensitization is a complex process. Why? One trivial possibility is that the overall reaction is slow and the intermediates along a sequential reaction pathway were resolvable in our experiments. In this context, it is perhaps noteworthy that there seem to be five steps in the overall reaction and five subunits in the AChR. Another possibility is that each desensitized state allows synaptic activity to be in some way integrated over a number of different time scales. We observed five desensitization time constants that span 1 ms to 5 min, and that are separated from each other by a factor of about 10. These two possibilities are, of course, not exclusive.
Future directions
Our results provide a quantitative description of diliganded AChR desensitization. By perturbing the system, for example with mutations or voltage or different agonists, it may be possible to pinpoint and probe the dynamics of the conformational changes that constitute the desensitization reaction pathways, as has been done with the activation reaction pathway (Grosman et al. 2001). It will also be important to measure the agonist dissociation rate constants from each of the diliganded-desensitized states, as well as the recovery rate constants for mono- and unliganded AChRs. Such analyses of transient kinetics may help distinguish between the different models of desensitization. When combined with structural analyses, such functional studies will eventually allow us to understand the molecular underpinnings of the energy landscape for desensitization, as well as the physiological roles this process may play at the neuromuscular synapse.
Acknowledgments
We thank Claudio Grosman for discussions and advice, Tim Bailey and Mary Teeling for expert technical assistance, and Lorin Milescu and Chris Nicolai for software support. This work was supported by NIH (NS-23513 and RR-11111) and the Keck Foundation.
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