Thermodynamics of CFTR Channel Gating: A Spreading Conformational Change Initiates an Irreversible Gating Cycle

Cystic fibrosis is caused by mutations in the gene that encodes CFTR (Riordan et al., 1989), the only known ion channel in the ATP-binding cassette (ABC) superfamily of transport proteins. CFTR's two homologous halves are linked via a cytoplasmic regulatory (R) domain not found in other ABC proteins; each half comprises a transmembrane domain, which contributes to the ion pore, attached to a cytoplasmic nucleotide-binding domain (NBD1 or NBD2) (Riordan et al., 1989). CFTR channel gating is driven by ATP binding and hydrolysis at the NBDs (Anderson et al., 1991), but requires prior phosphorylation of the R domain by cyclic AMP–dependent protein kinase (PKA; Tabcharani et al., 1991). Two gating modes have been reported: CFTR channel open bursts are long in the presence of PKA but shorten upon PKA removal, presumably reflecting rapid partial dephosphorylation (Hwang et al., 1994; Zeltwanger et al., 1999; Csanády et al., 2000). The mechanisms by which ATP and PKA together regulate CFTR channel gating are complex (e.g., Gadsby and Nairn, 1999; Gadsby et al., 2006) and controversial (e.g., Aleksandrov et al., 2000; Vergani et al., 2003; Bompadre et al., 2005).

Early observations that phosphorylated wild-type (WT) CFTR channels were opened readily by hydrolyzable, but not by nonhydrolyzable, ATP analogues (Anderson et al., 1991; Nagel et al., 1992; Hwang et al., 1994), and that channel closure was markedly delayed when orthovanadate (Baukrowitz et al., 1994; Gunderson and Kopito, 1994) or the nonhydrolyzable ATP analogue AMPPNP (Hwang et al., 1994; Gunderson and Kopito, 1994; Carson et al., 1995) was included with ATP, led to the interpretation that both opening and closing might require ATP hydrolysis (for review see Gadsby and Nairn, 1999); extreme slowing of both opening and closing of CFTR channels upon removal of free Mg²⁺ supported that proposal (Dousmanis et al., 2002). However, mutations in conserved sequences (Walker A or B; Walker et al., 1982) expected to impair ATP hydrolysis little influenced CFTR gating (at saturating [ATP]) when introduced into NBD1, but greatly prolonged open bursts when made in NBD2 (Carson et al., 1995; Gunderson and Kopito, 1995; Zeltwanger et al., 1999; Powe et al., 2002; Vergani et al., 2003). Also, millimolar concentrations of nonhydrolyzable ATP analogues were found to support CFTR channel opening (Aleksandrov et al., 2000), albeit far less effectively than ATP (Vergani et al., 2003). In addition, although ATPase measurements confirmed that CFTR hydrolyzes ATP (Li et al., 1996), photolabeling studies found ATP hydrolysis only at the catalytic site incorporating NBD2 Walker sequences (Aleksandrov et al., 2002), not that with NBD1 Walker residues (Basso et al., 2003).

Mechanistic interpretation of these results was aided by the finding that prokaryotic NBDs form head-to-tail dimers, X-ray crystal structures of which revealed two interfacial composite catalytic sites each with a bound ATP; each site comprised the Walker A and B residues of one NBD and the conserved ABC signature (LSGGQ-like) sequence of the other (e.g., Hopfner et al., 2000; Smith et al., 2002). Because a Walker-B Glu mutation in CFTR's NBD2, corresponding to a hydrolysis-impairing mutation that promoted stable dimerization of prokaryotic NBDs by ATP (Smith et al., 2002), yielded channels with greatly stabilized open bursts, lasting minutes (Vergani et al., 2003, 2005), the open-channel state was proposed to be a CFTR conformation with an intramolecular NBD1–NBD2 dimer. As mutations impairing ATP binding at either NBD reduced the apparent affinity with which ATP elicits channel opening, it was suggested (Vergani et al., 2003) that formation of the NBD1–NBD2 dimer, and hence of the open channel state, is preceded by ATP binding to both NBDs. On the other hand, disruption of that dimer, and hence channel closure, was suggested to be normally preceded by hydrolysis only of the ATP bound at the composite “NBD2” catalytic site (comprising NBD2 Walker motifs and NBD1 signature sequence).

Analysis of temperature dependence of reaction rates can illuminate molecular mechanisms by dissecting enthalpic and entropic contributions to overall activation free energies of molecules during transitions from one stable conformation to another. Ion channel gating is well suited to such analyses because in patch-clamp recordings the timing of individual conformational transitions of single molecules can be conveniently observed (Hamill et al., 1981) and quantified (e.g., Colquhoun and Sigworth, 1995; Qin et al., 1996). So far, however, the limited analyses of temperature dependence of CFTR channel gating have yielded differing conclusions (Aleksandrov and Riordan, 1998; Mathews et al., 1998b), in part perhaps because gating of CFTR is not a thermodynamic equilibrium process, a fact that rules out the conventional analytical approach used in one of the studies (Aleksandrov and Riordan, 1998).

Here we examine the temperature dependence of opening and closing of WT CFTR channels in both the long-burst (in the presence of PKA), and the shorter-burst (after PKA removal), gating mode. By also studying the temperature dependence of the extremely slow closure of the channel under conditions in which normal rapid closure by a mechanism proposed to involve ATP hydrolysis was prevented, we were able to outline a partial energetic profile of CFTR's irreversible gating cycle. Our results reveal the activation enthalpy for channel closure to be large, and that for opening to be even larger. Phosphorylation extent does not affect the activation enthalpy for closure, suggesting that it modulates the rate, but not the molecular mechanism, of channel closing. Our analysis identifies a conformation of CFTR during channel opening in which its gating machinery (i.e., the NBDs) has already adopted its open-state configuration, believed to require formation of an NBD1–NBD2 dimer (Vergani et al., 2005), while the pore itself is still closed. These results indicate that a spreading conformational change beginning at the cytoplasmic NBDs and propagating to the transmembrane domains precedes CFTR channel opening. Our analysis further suggests that closure of the channel pore is rate limited by a step that does not involve large-scale protein motion, consistent with hydrolysis of a single chemical bond, such as that between the β and γ phosphates of ATP bound at the composite NBD2 catalytic site. These data offer new insight into the mechanism by which the NBD ATPase cycle is coupled to conformational changes of the transmembrane domains in this representative ABC protein.

pGEMHE-WT was constructed as previously described (Chan et al., 2000), and the K1250R and K1250A mutations introduced using QuikChange (Stratagene) as previously described (Vergani et al., 2003, 2005).

Xenopus laevis oocytes were treated with collagenase, isolated, and injected as previously described (Chan et al., 2000). Oocytes were injected with 0.1–10 ng CFTR cRNA to obtain expression levels suitable for single-channel or macroscopic current recordings, respectively, and stored at 18°C in a Ringer's solution supplemented with 1.8 mM CaCl₂ for 2–3 d before recording.

Patch pipettes were pulled from borosilicate glass and fire polished to tip resistances of ∼2 MΩ for recording macroscopic currents or ∼6 MΩ for single-channel recordings. Pipette solution contained (in mM) 136 NMDG-Cl, 2 MgCl₂, 5 HEPES, pH 7.4 with NMDG. Bath solution contained (in mM) 134 NMDG-Cl, 2 MgCl₂, 5 HEPES, 0.5 EGTA, pH 7.1 with NMDG. Seal resistances were typically >100 GΩ, and patches were excised into an inside-out configuration. 2 mM MgATP (Sigma-Aldrich) was added from a 400 mM aqueous stock solution (pH 7.1 with NMDG). 1 mM Li₄-AMPPNP (Sigma-Aldrich) was added from a 400 mM aqueous stock solution, supplemented with equimolar MgCl₂. 300 nM catalytic subunit of PKA was added to activate CFTR channels. This high specific activity PKA (>95% pure) was extracted from bovine heart (Kaczmarek et al., 1980) and stored in a 150 mM potassium-phosphate buffer (pH 7.0) containing 1 mM EDTA and 15 mM β-mercaptoethanol. At the dilution used for our recordings, the final concentration of phosphate was 1.8 mM, a concentration that little affects CFTR channel gating (Carson et al., 1994). Inward unitary and macroscopic currents were recorded at a membrane potential of −80 mV (pipette holding potential = +80 mV), digitized at 1 kHz, and recorded to disk using on-line Gaussian filtering at 50 Hz (pCLAMP 8; Axon Instruments, Inc.). Large macroscopic currents from thousands of channels were occasionally recorded at −40 or −20 mV, which did not influence the results of our analysis, as CFTR gating is largely voltage independent (see Fig. S2, available at http://www.jgp.org/cgi/content/full/jgp.200609558/DC1; also compare Cai et al., 2003).

A custom-made flow chamber accommodated seven flow lines arranged concentrically around a small (∼0.5-mm diameter) thermistor (TH-30; Dagan Corporation). After excision, patches were transferred into this flow chamber in immediate vicinity (∼2 mm) of the thermistor, which therefore faithfully measured the temperature of the solution bathing the patch (see temperature traces in Fig. 1 B, Fig. 3 A, Fig. 4 A, and Fig. 5 A). The temperature of four of the flow lines was held at the desired test temperature (e.g., 15°C, 20°C, 31°C, or 35°C) using a TC-10 temperature contoller (Dagan), while the remaining lines contained solutions at 25°C. Only one flow line was active at any time, and changes in temperature and composition of the solution superfusing the patch were effected by switching the active flow line using electronic valves. Although the composition of the bath could be exchanged with a time constant of ∼100 ms (judged from the rate of decay of endogenous Ca²⁺-activated Cl⁻ current; Csanády et al., 2000, 2005), temperature could be changed only much more slowly due to the heat capacity of the flow chamber; a 10°C temperature jump typically required 20–30 s. Nevertheless, this arrangement allowed recording of channel activity from the same patch exposed to different temperatures in a bracketed fashion, together with faithful recording of the temperature time course.

Current records from patches with few channels, in which individual channel transitions could be clearly resolved, were baseline subtracted to remove slow drifts, e.g., due to temperature-dependent changes in seal current. Baseline-subtracted currents were idealized using half-amplitude threshold crossing, with imposition of a fixed dead time of 6.5 ms (Csanády, 2000a), and the resulting events lists subjected to kinetic analysis as previously described (Csanády et al., 2000). In brief, ATP-dependent slow gating was pooled into a simple closed–open scheme and rapid flickery closures modeled as pore-blockage events. Rate constants (r_CO, r_OC, r_OB, r_BO) of the resulting Closed–Open–Blocked scheme were extracted by a simultaneous maximum likelihood fit to the dwell-time histograms of all conductance levels, using an algorithm that includes a correction for the filter dead time (Csanády, 2000a). Mean closed interburst (τ_ib) and open burst (τ_b) durations were then calculated as τ_ib = 1/r_CO, and τ_b = (1/r_OC)(1 + r_OB/r_BO). Rates of opening to a burst, and closing from a burst, are defined as 1/τ_ib and 1/τ_b, respectively.

The number of active channels in the patch (N) was assumed to equal the maximum number of simultaneously open channels (N′) seen in any record. Correct estimation of opening rates, unlike that of closing rates, depends heavily on correct estimation of N. To eliminate ambiguities arising from uncertainties in channel number, we studied only relative changes in kinetic rates brought about by sudden changes in temperature. Thus, we normalized the opening and closing rate extracted from segments of record at any test temperature to the average of the corresponding rates in bracketing segments of record, from the same channels in the same patch, at our control temperature of 25°C (see Fig. 1). This procedure also corrected both for gradual, temperature-independent, changes in gating parameters occurring in a given patch during an experiment (channel rundown), as well as for heterogeneity in channel kinetics between different patches.

Macroscopic current decay time courses were fit by single or double exponential functions using pCLAMP 8 software (Axon Instruments, Inc.).

Upper limits for activation free energies (ΔG^‡) for single-channel opening and closing transitions were obtained using transition state theory (e.g., Fersht, 1999). According to this formalism, a chemical reaction (in the present case a transition, in either direction, between the relatively stable closed and open-burst conformations of the channel protein, both kinetically zero-order reactions at saturating, 2 mM, [ATP]) proceeds through an unstable high free energy transition state; the activation free energy, ΔG^‡, is the free energy of that transition state relative to the ground state. A transition rate k can be calculated as

where κ (0 ≤ κ ≤ 1; the “transmission coefficient”) is the fraction of formed transition state complexes that proceeds toward the product. One estimate of the prefactor A* was given by Eyring in the form of k_BT/h, where k_B is Boltzmann's constant, T is temperature in °K, h is Planck's constant (k_BT/h ≈ 6 × 10¹² s⁻¹ at 25°C). Although originally developed for reactions in the gas phase, transition state theory has been successfully applied to rates of reactions in solution, such as GTP hydrolysis by the small GTPase p21-ras (Schweins and Warshel, 1996) or protein–protein dimer formation (Frisch et al., 2001), by using Eyring's prefactor and assuming κ = 1. On the other hand, experiments under conditions in which it was assumed that ΔG^‡ ≈ 0 yielded maximal reaction rates on the order of 10⁶ s⁻¹ for protein folding (Hagen et al., 1996) and, perhaps more relevant, also for the pore-opening transition of the liganded nicotinic acetylcholine receptor (Chakrapani and Auerbach, 2005), suggesting that for these reactions the prefactor A* might be much smaller than k_BT/h (because, at least for the latter reaction, κ is not vanishingly small; Zhou et al., 2005). This uncertainty in A* and κ necessarily clouds absolute ΔG^‡ values obtained by this method for reactions that involve large protein conformational changes. Nevertheless, using Eyring's prefactor and setting κ = 1 allows determination of a safe maximum estimate for ΔG^‡. Thus, ΔG^‡ ≤ RTln(k_BT/(kh)) or

Activation enthalpy (ΔH^‡) is obtained by substituting ΔG^‡ = ΔH^‡ − TΔS^‡, so that,

and ΔH^‡ is the slope of a plot of ln(k/T) vs. 1/T (Eyring plot) multiplied by (−R). As that slope does not depend on κ, the ΔH^‡ estimate is not subject to the uncertainty discussed for ΔG^‡. From ΔH^‡ and

Symbols and error bars in figures report mean ± SEM.

This paper contains Fig. S1 shows simultaneous unitary current and temperature records illustrating temperature dependence of gating of highly phosphorylated WT CFTR channels at −80 mV. Figs. S2–S4 show parallel macroscopic current and temperature records illustrating temperature dependence of closure of partially phosphorylated K1250R and K1250A, and of AMPPNP-locked WT, CFTR, respectively, recorded at −80 to −20 mV between 25°C and 31°C. Fig. S5 demonstrates that exposure to millimolar levels of the hydrolysis products ADP+P_i does not cause opening of prephosphorylated WT CFTR channels. Fig. S6 shows the predicted energetic profile of CFTR gating obtained using K1250A, not K1250R (as in Fig. 6), as a model for nonhydrolytic channel closure.

Open probability (P_o) of CFTR channels increases with extent of PKA-mediated phosphorylation (Chang et al., 1993; Mathews et al., 1998a; Csanády et al., 2005). P_o immediately declines by ∼50% on removal of 300 nM PKA catalytic subunit from MgATP-bathed patches excised from Xenopus oocytes expressing WT human CFTR (e.g., Fig. 1 A); this correlates with a greater than twofold reduction in open-burst duration, from ∼700 to <300 ms (Csanády et al., 2000; Fig. 1 A, insets), presumably due to rapid dephosphorylation of some R-domain serine(s) by membrane-bound phosphatases. This rapid partial dephosphorylation is not prevented by inhibition of phosphatases 1 and 2A with microcystin, and of phosphatase 2B by the absence of Ca²⁺ (Csanády, 2000b). It is followed by a much slower decline of average current over a time course of many minutes (e.g., Csanády et al., 2000; compare Fig. 1 and Fig. S4), during which the pattern of CFTR channel gating remains relatively well defined (e.g., Chan et al., 2000; Csanády et al., 2000, 2005; Vergani et al., 2003, 2005). An experimental design incorporating strict bracketing (see Materials and methods) can therefore largely compensate for this slow unidirectional change in gating parameters in the partially dephosphorylated state, reached within a few seconds of PKA removal. On the other hand, in the continued presence of 300 nM PKA, a near-saturating concentration (Csanády et al., 2005), a large fraction of the ∼10 phosphorylatable serines in a CFTR channel's R-domain will remain phosphorylated at any moment. Although dephosphorylation/rephosphorylation events no doubt occur under those conditions, they are expected to have little effect on gating, as the functional impact of a single phosphoserine is small (Cheng et al., 1991; Chang et al., 1993). We could therefore examine the gating behavior of CFTR channels under two distinct, well-characterized conditions, highly phosphorylated in the presence of PKA and partially dephosphorylated shortly after PKA withdrawal.

We first tested the temperature dependence of gating of partially dephosphorylated CFTR channels (Fig. 1) at saturating, 2 mM, [MgATP] (e.g., Csanády et al., 2000; Vergani et al., 2003) after PKA withdrawal, by recording at 25°C (Fig. 1 A, blue), and at some test value (e.g., 31°C in Fig. 1 A, red), in a bracketed fashion. Both opening and closing rates were increased by warming (Fig. 1 A, insets), but the speeding of opening was greater, as overall P_o was larger at more elevated temperatures (Fig. 1 A). Linear fits to Eyring plots (Fig. 1 C) of normalized opening rates (red symbols) and closing rates (black symbols) at 15, 25, 31, and 35°C yielded estimates of ΔH^‡ for the opening and closing transitions that were both large, but ΔH^‡ for opening (117 ± 6 kJ/mol) was much larger than for closing (69 ± 4 kJ/mol).

The longer open burst durations, and enhanced susceptibility to becoming locked open by mixtures of ATP and AMPPNP, of highly phosphorylated CFTR channels (Hwang et al., 1994; Mathews et al., 1998a,b) led to the proposal that their gating cycles might differ qualitatively from those of partially phosphorylated channels, with ATP hydrolysis limiting closure of only highly phosphorylated CFTR (for review see Gadsby and Nairn, 1999). Because different temperature dependence might betray different molecular mechanisms, we repeated experiments like those of Fig. 1 but in the continued presence of 300 nM PKA to sustain high levels of phosphorylation (Fig. S1, available at http://www.jgp.org/cgi/content/full/jgp.200609558/DC1). Once again, despite longer mean burst durations at lower temperatures, average P_o was smaller, indicating that a temperature drop compromised opening even more than closing. Accordingly, as found for partially phosphorylated channels (Fig. 1 C), Eyring plots for highly phosphorylated channels (Fig. 2) revealed steep temperature dependence for both opening rates (red symbols) and closing rates (black symbols), and ΔH^‡ was again larger for the opening transition (96 ± 6 kJ/mol) than for closure (73 ± 5 kJ/mol).

To estimate ΔH^‡ for channel closing when the normal route for channel closure via ATP hydrolysis was unavailable, we studied the temperature dependence of the closing rate of two channel constructs in which the composite NBD2 site was made catalytically inactive by mutation of the conserved NBD2 Walker A lysine, K1250. The mutation K1250A has been shown to abolish ATPase activity of purified CFTR (Ramjeesingh et al., 1999). In another ABC ATPase, P-glycoprotein, the Lys-to-Arg mutation of either Walker A lysine abolishes ATP hydrolysis (Lerner-Marmarosh et al., 1999), and in CFTR, the K1250R mutation prolongs open burst durations by >20-fold (compare Vergani et al., 2005), consistent with abolished, or greatly diminished, ATP hydrolysis. Closure of K1250R or of K1250A mutant CFTR channels is too slow to allow kinetic analysis of individual gating events and so it was assayed as current decay after sudden removal of ATP. Because opening is negligible at 0 [ATP], the time course of current loss gives the time constant of channel closing.

Prephosphorylated K1250R CFTR channels in macropatches were repeatedly opened by brief exposures to 2 mM MgATP at temperatures alternating between 25°C and ∼15°C (Fig. 3 A), or 25°C and ∼31°C (Fig. S2). Current decay after each ATP removal was fitted with a single exponential (Fig. 3 A, smooth lines) and channel closing rate was obtained as the reciprocal of that time constant. The Eyring plot of the normalized closing rates (Fig. 3 B) yielded a ΔH^‡ for nonhydrolytic closure of 43 ± 2 kJ/mol, which is substantially smaller than the value we found for normal closure of WT channels (Fig. 1 C).

Because the K1250A mutation greatly diminishes the affinity for ATP binding (Vergani et al., 2003), 10 mM MgATP was used to repeatedly activate macroscopic K1250A currents at temperatures alternating between 25°C and either ∼15°C (Fig. 4 A) or ∼31°C (Fig. S3). The Eyring plot (Fig. 4 B) of the normalized closing rates obtained from single exponential fits (Fig. 4 A, smooth lines) to the decaying currents after ATP removal yielded a ΔH^‡ for nonhydrolytic closure of 39 ± 4 kJ/mol, similar to that obtained for K1250R channels (Fig. 3 B).

Interestingly, whereas open burst duration of WT channels was greater than twofold longer in the presence of PKA than shortly after its withdrawal, the average closing time constant of K1250R at 25°C, equivalent to its mean open burst duration, was only slightly longer (Fig. 3 A; Fig. S2) upon removal of PKA+ATP (7.3 ± 0.8 s, n = 12) than upon removal of just ATP (5.7 ± 0.4 s, n = 30). But, because the fall in P_o that signals partial dephosphorylation of WT channels upon PKA removal occurs so rapidly (i.e., in 2–3 s; Csanády et al., 2000), the phosphorylation status of K1250R channels after removal of ATP+PKA, during their gradual closure, which takes tens of seconds (compare Fig. 3 A, current segments fitted by magenta lines), is uncertain. For K1250A channels, the closing time constant after simultaneous removal of ATP and PKA was rarely assessed (τ = 38 ± 4 s, n = 3), and is not easily compared with that after removal of just ATP (τ = 25 ± 2 s, n = 29), as the latter usually progressively shortened during an experiment (τ = 29 ± 3 s, n = 18, for the first decay from each experiment). These technical difficulties prevent us from addressing the influence of phosphorylation on ΔH^‡ for nonhydrolytic closure.

As a third, independent, way to estimate ΔH^‡ for nonhydrolytic closure, we measured the temperature dependence of the closing rate of prephosphorylated WT CFTR channels that had been locked in the open-burst state by simultaneous exposure to ATP (1 mM) plus AMPPNP (0.1 mM; Fig. 5 A).

On removal of ATP+AMPPNP, a large fraction of the current decayed rapidly, with a time constant of <1 s, just as after removal of 2 mM ATP alone, but a smaller-amplitude slower component was invariably present, reflecting a small fraction of locked-open channels (first vs. second current decay: Fig. 5 A and Fig. S4 B). This finding with partially phosphorylated CFTR channels contrasts with the ∼90% of current that decays slowly, with ∼30-s time constant, when locking is elicited by ATP+AMPPNP in the presence of PKA to maintain a high stoichiometry of phosphorylation (Csanády et al., 2000). We summed individual decay time courses after repeated exposures to ATP+AMPPNP to construct ensemble current decays, at 25°C and either 15°C (Fig. 5 A, insets) or 31°C (Fig. S4 B). From double-exponential fits to these decays (Fig. 5 A and Fig. S4 B, insets, smooth lines), the average fractional amplitude of the slow component at 25°C was 0.24 ± 0.02 (n = 17), and its average time constant was 10 ± 2 s (n = 17). From an Eyring plot of normalized unlocking rates (Fig. 5 B), the rough estimate of ΔH^‡ for unlocking from AMPPNP of partially phosphorylated WT CFTR was 37 ± 6 kJ/mol, similar to the value obtained above for closure of partially phosphorylated K1250R and K1250A channels opened by just ATP (Fig. 3 B and Fig. 4 B).

Both in the presence of PKA to sustain phosphorylation and shortly after its removal, allowing partial dephosphorylation, opening and closing rates of WT CFTR channels are strongly temperature dependent, though the temperature dependence of opening is steeper. Our results concur with those of one (Mathews et al., 1998b) of two earlier studies, but not with the other, which found practically no temperature dependence for channel closing rate (E_a = 10 kJ/mol; Aleksandrov and Riordan, 1998). The most likely reason for the discrepancy is that the latter study (Aleksandrov and Riordan, 1998) reported the temperature dependence of open times (which reflect the rate of entering the brief intraburst closed state—flickery closures; e.g., Haws et al., 1992), rather than that of open-burst durations (which reflect the rate of closing from bursts), as determined here (also in Mathews et al., 1998b). Because ATP and phosphorylation modulate the slow components of CFTR channel gating, i.e., the durations of interburst closures and of open bursts (e.g., Winter et al., 1994; Csanády et al., 2000; Vergani et al., 2003), but not the kinetics of the brief intraburst flickery closures (Vergani et al., 2003; Winter et al., 1994), analysis of the slow components, with time constants comparable to those of ATP hydrolysis by CFTR (Li et al., 1996), would seem more relevant for probing the mechanism of the ATP-driven CFTR gating cycle.

The fact that we obtained almost identical ΔH^‡ for closure of partially and of highly phosphorylated CFTR channels (69 ± 4 and 73 ± 5 kJ/mol; Fig. 1 C and Fig. 2) does not support the initial proposal that these reflect two qualitatively different closing mechanisms, with ATP hydrolysis at NBD2 limiting closure of only highly phosphorylated channels (Hwang et al., 1994; Gadsby and Nairn, 1999; Zeltwanger et al., 1999; Csanády et al., 2000). The fact that NBD2 catalytic site mutations dramatically prolong burst durations even after removal of PKA (Figs. 3 and 4), implies that ATP hydrolysis also limits the rate of closure of partially phosphorylated channels. The same conclusion may be drawn from the observation that CFTR channels can be locked open by AMPPNP in the absence of PKA (Fig. 5 A; Fig. S4; compare Mathews et al., 1998a; Vergani et al., 2003), albeit with lower efficiency than when PKA is present (Hwang et al., 1994; Mathews et al., 1998a,b). So PKA seems to alter the rate, but not the chemical mechanism (hydrolysis of ATP), of the step that times channel closure. And, in energetic terms, the effect is not large. Thus, the shorter open burst durations that indicate a two- to threefold acceleration of channel closing after removal of PKA correspond to a change in ΔG^‡ for closure of only ∼1kT (i.e., ∼2 kJ/mol).

Because of its lower ΔG^‡ than for reversal of the opening reaction, this irreversible ATP hydrolysis step allows a WT channel to escape the open state by a pathway different from that by which it arrived (Gunderson and Kopito, 1994, 1995; Hwang et al., 1994; Carson et al., 1995; Zeltwanger et al., 1999; Dousmanis et al., 2002; Powe et al., 2002; Vergani et al., 2003, 2005). For this reason, the barrier heights for the opening and closing reactions cannot be compared to obtain thermodynamic state functions of the open state, relative to the closed state before opening. Instead, to estimate ΔH between those two states, ΔH^‡ for opening must be compared with ΔH^‡ for the closing reaction that represents reversal of opening, i.e., in the absence of ATP hydrolysis. We chose NBD2 catalytic site mutant K1250R as one model for nonhydrolytic closure because the mutation conserves charge in the anticipated catalytic interface, and, in P-glycoprotein, the corresponding K-to-R mutation essentially abolishes ATP hydrolysis (Lerner-Marmarosh et al., 1999). We selected the mutant K1250A as a second model for nonhydrolytic closure because it displays much slower closure than K1250R (e.g., Vergani et al., 2003, 2005) and because the K1250A mutation abolishes ATP hydrolysis by CFTR (Ramjeesingh et al., 1999). Finally, the closing rate of WT channels locked open by ATP+AMPPNP allowed an additional, independent, assessment. Although the rates of channel closure for these three nonhydrolytic models spanned a fivefold range (Fig. 3 A, Fig. 4 A, and Fig. 5 A), their temperature dependences, and thus ΔH^‡ values, were virtually identical (Fig. 3 B, Fig. 4 B, and Fig. 5 B).

Our ΔH^‡ estimates for opening, nonhydrolytic closure and normal (hydrolytic) closure allow us to construct a ΔH profile for the part of the CFTR channel (partially phosphorylated) gating cycle that includes a closed (interburst) state and subsequent open-burst state (Fig. 6 A, red line). The open and closed states in general cannot be compared because the system is not at thermodynamic equilibrium; after closure (to state C_ω; Fig. 6 A) the channel protein itself presumably returns to the closed conformation it assumed before opening (state C_α, Fig. 6 A), but the whole system has been changed by hydrolysis of ATP to ADP and inorganic phosphate (P_i). Nor can we compare thermodynamic state functions for the open state and the subsequent closed state, C_ω (Fig. 6 A, dotted lines), because that closing transition cannot be reversed (CFTR channels are not opened by ADP+P_i; Fig. S5) and so we cannot measure its ΔH^‡.

Uncertainty in the product of the prefactor A* and transmission coefficient κ (see Materials and methods) means that we can derive only upper estimates for ΔG^‡ from the measured transition rates at 25°C (Fig. 6 A, blue line; the downward “smear” represents the direction of uncertainty). Moreover, κ might be different for a forward reaction and its reversal; e.g., κ ≈ 0.1 and ≈0.3, respectively, for opening and closure of the diliganded acetylcholine receptor (Zhou et al., 2005). For this reason the errors in our estimates of ΔG^‡ for opening and for nonhydrolytic closure might also differ, so that the exact value of

Despite these limitations, we can safely draw several conclusions about the energetics of the CFTR gating cycle. First, from ΔH^‡ = 117 kJ/mol versus

The paucity of ATPase measurements for CFTR mutants means that we cannot be certain that the charge-sparing mutation K1250R abolishes ATP hydrolysis in CFTR, even though the equivalent mutation in P-glycoprotein abolishes ATP hydrolysis (Lerner-Marmarosh et al., 1999). The charge-neutralizing mutation K1250A, on the other hand, does abrogate ATP hydrolysis in CFTR (Ramjeesingh et al., 1999) and yields an open burst state more stable than that of K1250R (Vergani et al., 2003, 2005). But using the closing rate of K1250A (instead of K1250R) channels as a model for nonhydrolytic closure, and hence for reversal of channel opening, yields barrier values for this step (ΔH^‡ = 39 kJ/mol and

Our thermodynamic measurements indicate that the transition state for opening of CFTR channels is characterized by an extremely large enthalpy, indicating molecular strain, together with a large increase in entropy. The latter supports the recent finding that conserved residues on opposing sides of the anticipated intramolecular NBD1–NBD2 dimer interface became energetically coupled in the transition state for CFTR channel opening, demonstrating that a tight NBD dimer had already then formed (Vergani et al., 2005). The entropy increase would reflect dehydration of the two interacting NBD surfaces and concomitant dispersal of the layer of bound (ordered) water molecules into the (disordered) bulk solution. The large enthalpy suggests that the transition state for opening is a strained CFTR protein conformation, with the tight NBD dimer already formed but the transmembrane pore still closed (Fig. 6 B); this is consistent with nucleotide-dependent channel opening being initiated at the NBDs. Pore opening should then partly relieve this strain, decreasing the enthalpy, as we found (Fig. 6 A). In simple terms, the energy of the power-stroke, provided by the extreme stability of the ATP-bound tight NBD1–NBD2 dimer, is used to load the gating spring (represented by curved connecting rods in Fig. 6 B), which then forces the gate to snap into its open conformation. This spreading conformational change, initiated by the gating machinery in the cytoplasm and propagated toward the transmembrane pore, echoes the mechanism recently proposed for opening of the nicotinic acetylcholine receptor, a true ligand-gated channel, after binding of its ligand acetylcholine some distance from the ion pore (Chakrapani et al., 2004).

But CFTR is not a true ligand-gated channel, because its open bursts appear to be normally terminated by ATP hydrolysis. This reaction invokes an enthalpy increase, unaccompanied by a change in entropy, caused by chemical bond strain without large conformational rearrangements, consistent with our observations on the transition state for closure. Because we can rule out an entropy decrease in this transition state (Fig. 6 A), we can conclude that the interacting NBD surfaces are still dehydrated and, hence, that the NBD1–NBD2 dimer is still intact; insofar as gating signals originate at the NBDs, we may further conclude that the pore is still open (Fig. 6 B). A simple interpretation is that the transition state for the step that rate limits CFTR channel closure represents the transition state for ATP hydrolysis (at the composite NBD2 catalytic site), and that the measured positive ΔH^‡ reflects strain in the ATP β-γ bond. This concurs both with the conclusion that ATP hydrolysis rate limits closure of WT CFTR channels (for example see Hwang et al., 1994; Gunderson and Kopito, 1994, 1995; Carson et al., 1995; Zeltwanger et al., 1999; Dousmanis et al., 2002; Powe et al., 2002; Vergani et al., 2003, 2005), and with ΔH^‡ values measured for turnover of other ATP- and GTPases (Tu et al., 1988; Mejillano et al., 1996). Upon cleavage of the γ-phosphate from the nucleotide, the enthalpy of the strained β-γ bond is used to diminish the entropy of the open state, as the channel pore adopts its closed conformation and an ordered layer of water molecules covers the NBD surfaces exposed by disruption of the tight dimer interface.

We thank Dr. Paola Vergani for helpful discussion and Dóra Takács for oocyte isolation and injection.

This work was supported by NIH DK51767 and NIH Fogarty International Center grant R03-TW05761.

Christopher Miller served as editor.