Encyclopedia of Biophysics
Introduction CFTR (cystic fibrosis transmembrane conductance regulator) is an integral membrane protein that functions as an epithelial Clchannel, which is rendered defective by inherited gene mutations in patients with cystic fibrosis (Riordan et al. 1989 ). Its function underlies fluid secretion in the airways, sweat ducts, pancreatic duct, and vas deferens, and it mediates the excessive intestinal water loss in secretory diarrhoeas 2 (Verkman and Galietta 2009). CFTR belongs to the large ABC
... gs to the large ABC (ATP-binding cassette) transporter superfamily, of which most members are ATP-hydrolyzing pumps. CFTR is the sole ABC protein known to function as an ion channel. Despite this difference in function, the gates of CFTR channels are opened and closed by interactions with ATP similar to those that in other ABC proteins result in energetically uphill substrate transport. CFTR is an ion channel A CFTR channel in its open conformation provides a pathway for Clions (or other small anions, such as bicarbonate) to cross the cell membrane, down the gradient of their electrochemical potential. Because the ions moving through the channel carry an electrical current across the membrane, the patch-clamp recording technique (Gibb 1995) can be employed to study CFTR function. Once a saline-filled glass pipette connected to an electrode is sealed tightly against a small patch of membrane, the gating of any CFTR channels present in the patch can be accurately monitored by observing how the current flowing through the membrane patch changes with time. If the patch contains few channels, individual events reflecting opening and closing of single-channel gates can be detected as abrupt changes in the current level (Fig. 1A , black trace, recorded in a patch with one active CFTR channel). For quantitative analysis of such current records, gating is treated as a stochastic process described by a kinetic scheme (which includes the states the channel can visit, how those states are connected, and rates of transitions between the states; e.g. Fig. 1B inset, Hidden Markov modeling). The first task for the analysis is collection of all dwell 3 times in the closed state (represented by green bars in Fig 1A) , and of all dwell times in the open state (red bars). In general, dwell times in a particular state provide information about the rates of leaving that state. Simple calculation of average dwell times can yield useful information, but a more powerful approach is analysis of distributions of dwell times (e.g., simulated open dwell-time distribution shown in Fig. 1B , Data analysis, Single Molecule Kinetic methods; Colquhoun and Hawkes 1995; Colquhoun and Sigworth 1995) . In this analysis, the time axis is subdivided into bins and the ordinate reports the number of dwell times observed to have a duration that falls within the period encompassed by each bin. Dwell times in a single conformational state are exponentially distributed, which means that the bins containing brief durations have the highest event count, and the distribution decays monotonically. This is because the probability of leaving a state is the same for each time interval spent in that state, so that the chance for a channel to survive in a given state declines with time. Fitting of dwell-time distributions using a statistical procedure called maximum likelihood (ML) can give rate estimates for the underlying kinetic scheme. For example, in Fig. 1B the red curve superimposed on the depicted simulated open dwell-time distribution data is the theoretical open dwelltime distribution predicted for a C↔O model that has a closing rate, k OC , of ~ 4 s -1 (Fig. 1B, inset; this was the model used to simulate the data). According to the ML criterion, this curve is the "best fit" to the observed distribution. Thus, given a kinetic scheme, ML fitting finds values for the rates (e.g. rate k OC for the open dwell-time distribution in Fig.1B) such that the likelihood of obtaining the observed distribution is maximized. CFTR_Fig1.tif 4 Figure 1A. Single CFTR channel current trace (black), in which upward deflections correspond to channel-opening events that allow Clions to flow across the patch. [Note 1: in this case, anions flow from cytoplasmic to extracellular side of the membrane, constituting an inward current; but, for consistency between figures, in this review channel openings are plotted as upward deflections in all figures, regardless of the actual direction of ion flow determined in each case by the Clelectrochemical gradient.] The current flowing through open channels corresponds to ~3 million Clions per second. [Note 2: although not evident in the traces shown in this review, at a higher time resolution CFTR can be seen to open into "bursts" of openings: clusters of openings separated by short-lived, "flickery" closures. Duration and frequency of flickery closures are not nucleotide-dependent. Rather, NBD dimer formation and dissociation drive initiation and termination of bursts; here, for simplicity, we use the terms opening and closing to indicate entry and exit from bursts.] Red and green bars illustrate length of individual dwell-times in open and closed states, respectively. Figure 1B. Example of an open dwell-time distribution (yellow histogram), and ML fit (red line), for a current trace simulated using the simple kinetic scheme in the inset, with k OC =4 s -1 . Two main factors influence the gate in a CFTR channel: they are phosphorylation, principally by (cAMP-dependent) protein kinase A (PKA), and interaction with ATP ( Fig. 2 ; Gadsby et al. 2006) . Phosphorylation is a prerequisite for CFTR channel gating in 5 response to binding and hydrolysis of ATP. By adding PKA and ATP to the cytosolic side of the patch, channels become phosphorylated; after that the current starts fluctuating in a stepwise fashion. This pattern reflects fluctuations in the number of channels that are open at any point in time. Once the channels have been phosphorylated, ATP is sufficient and necessary for channel gating: adding ATP can activate them, but after washing the ATP away no further openings occur (Fig. 2) . CFTR_Fig2.tif Figure 2. Current trace from patch containing at least 3 CFTR channels; the number simultaneously open is indicated at the right. Solid lines below the trace signify the presence at the cytosolic face of the patch of the specified reagent: red line, 5 mM ATP; blue line, catalytic subunit of PKA. At the molecular level, ATP interacts with CFTR's two cytosolic nucleotide binding domains (NBDs), NBD1 in the N-terminal half of CFTR, and NBD2 near the C terminus, whereas phosphorylation occurs at several serines within the cytosolic "regulatory" (R) domain, a region unique to CFTR and absent from other ABC proteins. On the other hand, the permeation pathway through which Clions cross the membrane is constructed by the two transmembrane domains (TMDs, Fig. 3A ). CFTR's NBDs and their role in channel gating High resolution crystal structures have been determined for many NBDs, including CFTR's NBD1 and a modified NBD2. In all ABC proteins, nucleotide interacts 6 directly with conserved sequences of residues (Walker motifs) in the "head" of an NBD ( Fig. 3B ). But the conserved ABC signature (LSGGQ-like) sequence occurs in the helical "tail" of the NBD, quite distant from where the nucleotide is found bound in monomeric crystals. However, NBDs can interact to form head-to-tail dimers, with an ATP molecule buried within each of the two composite nucleotide-binding sites created at the dimer interface (Fig. 3B ). The ATP acts as "molecular glue", with the two ATP molecules, and in particular their γ-phosphates, providing molecular contacts to both sides of the composite binding sites and thereby making important contributions to dimer stability. CFTR_Fig3.tif Figure 3. A: CFTR topology including TMDs (grey), NBD1 (green), NBD2 (blue) and R domain (white). Intracellular linking loops are shown in magenta. B: crystal structure of an NBD homodimer, from a bacterial ABC transporter. C: schematic representation of a head-to-tail NBD dimer. NBD1 and NBD2 form an intramolecular heterodimer with two distinctly different composite binding sites at the interface, referred to as composite site 1 and composite site 2, comprising Walker motifs in the head of NBD1 and head of NBD2, respectively (Heteromeric versus homomeric association). Quantitative analysis of how ATP affects CFTR channel gating has been carried out by exposing patches to different test [ATP] and monitoring how gating parameters are altered (Fig. 4). Closing rate (reciprocal of the mean open dwell time) shows no clear dependence on [ATP] over a three orders of magnitude concentration range (Fig. 4C). In 7 contrast, over the same [ATP] range, the opening rate (reciprocal of the mean closed dwell time) first increases and then saturates (Fig.4B). The data are described by Michaelis-Menten kinetics, with apparent ATP affinity ~50 µM (or the Hill equation, with Hill coefficient of 1). Therefore, at low [ATP] CFTR channel opening is rate-limited by an ATP binding step, which means that ATP binding must occur on closed channels, and precedes channel opening; the Hill coefficient of 1 is consistent with a single binding step controlling opening. CFTR_Fig4.tif Figure 4. [ATP]-dependence of CFTR gating. A: current trace from patch containing multiple CFTR channels, exposed to a test concentration of 50 µM ATP, in between control exposures to 5 mM ATP. Red and green bars highlight duration of dwell times at conductance levels 1 (one open channel) and zero (no open channel). B, C: [ATP]-dependence of opening rate and closing rate, respectively. ABC proteins do not merely bind ATP, they also catalyse ATP hydrolysis (ATPase: Overview). Native, wild-type (WT) CFTR, too, is an active ATPase, with a measured turnover rate on the order of 1 ATP s -1 (Li et al. 1996) . How this hydrolysis affects gating is most readily observed by studying channel closing rates in patches containing large numbers (hundreds, or even thousands) of CFTR channels (e.g. records in Fig. 5 -compare current scale to those in Figs. 1, 2; Analysis of macroscopic currents). In such recordings, individual opening and closing events are lost in noise. Upon removal 8 of ATP, the opening rate falls to almost 0 (see Figs. 2, 4B), so the time course of current decline reflects only the channel closing rate. WT channels close with a time constant below 1s (Fig. 5A ). Mutation of a crucial catalytic lysine, K1250, in the Walker A motif of composite site 2, abolishes ATPase activity of purified, reconstituted CFTR (Li et al. 1996), and K1250A CFTR channels close extremely slowly (time constant tens of seconds, Fig. 5B ). Mutation of other catalytic residues in composite site 2 (e.g. E1371, the "catalytic glutamate", and D1370, see below) also slows channel closure. These observations suggest that hydrolysis at site 2 is required for normal, fast channel closure. CFTR_Fig5.tif Figure 5. Current recordings from patches containing hundreds of WT (A) or mutant K1250A (B) CFTR channels. Macroscopic current decay upon abrupt removal of ATP monitors channel closing rate (superimposed blue lines are single exponential fits). In contrast, CFTR channels carrying a mutation at the equivalent conserved lysine, K464, in the Walker A motif of composite site 1, appear to close normally and display average open dwell times not different from those of WT channels. In fact, biochemical experiments suggest that, even in WT CFTR, ATP binds tightly in composite site 1 but remains there for minutes without being hydrolyzed. This lack of activity is accounted for by several non-canonical substitutions of otherwise conserved key residues on both sides of the NBD1-NBD2 heterodimer interface in composite site 1. Although gating kinetics of K464A mutant channels look very similar to those of WT, 9 biochemical measurements show that the ATPase rate of K464A is only one tenth that of WT (Ramjeesingh et al. 1999). This will be considered again later (see Evidence for a non-equilibrium gating scheme for CFTR). Other ABC proteins (e.g., multidrugresistance related proteins, sulfonylurea receptors, transporter associated with antigen processing) share with CFTR the presence of a non-canonical interfacial ATP binding site, so that only one of their two composite sites catalyzes ATP hydrolysis at a measurable rate. The inference from findings like these is that a scheme that relates ATP interactions with the NBDs to channel gating must include the following features. ATP binds tightly to the Walker motifs at the NBD1 head (in composite site 1) where it remains, unhydrolyzed, for several gating cycles. Then, after ATP binds to the Walker motifs at the NBD2 head of composite site 2, i.e., once ATP is bound at both sites, the channel can open. The open state of the channel, with 2 ATP molecules bound, is very stable, and rapid closure can occur only after the ATP at composite site 2 is hydrolyzed. Fig. 6A shows a working hypothesis for such a CFTR gating scheme, in terms of channel closed (C 1 , C 2 ) and channel open (O 1 , O 2 ) conformations (only the nucleotide boundand hydrolyzed -at site 2 is indicated; ATP bound at site 1, assumed present in all 4 states, is omitted for simplicity). A structural interpretation of this scheme can be made in the light of structural knowledge recently obtained for other ABC proteins (Locher 2009): conformational changes in the TMDs that open and close the Clion pathway could be coupled to the ATPase cycle via formation and dissociation of the NBD1-NBD2 dimer (Fig. 6B). Formation of an NBD1-NBD2 dimer after binding of both ATPs could be coupled to opening of the channel pore. Then hydrolysis of the ATP at site 2 would 10 destabilize the NBD dimer, triggering fast channel closure. So, while ATP at site 1 remains bound, without being hydrolyzed, for many gating cycles, the ATPase cycle at site 2 is coupled to opening and closing of the Clpermeation pathway. This interpretation is supported by experimental evidence, obtained using double mutant cycle analysis, that opening of the CFTR pore corresponds to closure of the NBD1-NBD2 dimer interface gap at composite site 2 (Gadsby et al. 2006). CFTR_Fig6.tif Figure 6. Working hypothesis linking ATPase and gating cycles of CFTR. A: Proposed gating scheme relating nucleotide present at site 2 to channel state (closed states, C 1 and C 2 ; open states, O 1 and O 2 ). B: Structural interpretation of gating scheme in A, colour coding as in Figure 3. The small orange balls represent Clions flowing through CFTR's transmembrane pore. Phosphorylation of the R domain relieves gating inhibition R-domain phosphorylation is required for CFTR channel activation, and can be considered the major regulatory mechanism in vivo because the millimolar range of [ATP] in cells is enough to fully activate channel gating (Fig. 4) . Studies on full-length CFTR in intact cells, and on isolated R-domain peptides in vitro, have identified at least ten R-domain serines that become phosphorylated by PKA, most of them occurring within dibasic PKA recognition consensus sequences (R/K,R/K,X,S). This large number of target serines allows for a graded functional response, and CFTR channel activity 11 increases in rough proportion to phosphorylation stoichiometry(reviewed in Gadsby et al. 2006). Either of two kinds of regulatory mechanisms could account for the findings. The unphosphorylated R domain could inhibit channels that would be active in its absence, or the phosphorylated R domain could stimulate channels that would be otherwise inactive. Experiments show that excision of the R domain results in constitutive, phosphorylationindependent, channel activity; indeed, cutting CFTR in half and coexpressing the two segments TMD1-NBD1 and TMD2-NBD2 yields "cut ∆R" CFTR channels whose ATPdependent gating in the absence of PKA phosphorylation is comparable to that of phosphorylated WT CFTR. Because the stimulation of WT channels by PKA corresponds to a >100-fold increase in open probability (P o ), while the constitutive P o of cut ∆R is about half that of fully phosphorylated WT, the dominant role of the R domain appears to be inhibition of channel activity when the R domain is dephosphorylated. A small, <2fold, stimulation by the phosphorylated R domain has also been proposed(reviewed in Gadsby et al. 2006) . How phosphorylation influences R-domain structure and its interactions with the rest of CFTR remains unclear. The R domain lacks sequence homology to any known protein, and CD spectral analysis and NMR studies of isolated R-domain peptide indicate the absence of stable 3-dimensional structure (Structurally disordered Proteins). Nevertheless, phosphorylation of R-domain peptide by PKA diminished the -helical contribution to its CD spectrum. Correspondingly, NMR measurements revealed stretches of dephosphorylated R-domain peptide, near target serines, with distinct helical propensity and a tendency to interact with isolated NBD1 protein; and both 12 characteristics were weakened by phosphorylation. But whether such interactions between the R domain and NBD1 occur in intact CFTR and, if so, whether they are modulated by phosphorylation is not known (Gadsby et al. 2006; Baker et al. 2007 ). Phosphorylation is unlikely to exert its effect through mere accumulation of negative charge. Although mutation of 8 consensus serines to negatively charged aspartates or glutamates results in some constitutive, PKA-independent, channel activity, this constitutive P o is very low compared to that of fully phosphorylated WT, suggesting that negative charge per se is a poor mimic of phosphorylation. Also, phosphorylation of serines 737 and 768 decreases P o , which again argues against a simple effect of charge accumulation. Similarly, the graded increase of channel P o with phosphorylation stoichiometry is hard to reconcile with initial suggestions that the unphosphorylated R domain might physically obstruct the pore; and phosphorylation has no major effect on ATP binding affinity of the NBDs. Because phosphatase-mediated dephosphorylation essentially abolishes ATP hydrolysis of purified CFTR protein (Li et al. 1996) , the catalytic cycle appears to be stalled in unphosphorylated CFTR, rather than uncoupled from gating. However, because catalytic and pore-gating cycles appear to be strictly coupled (Csanády et al., 2010) , the "brake" could arrest either the NBDs (e.g., by preventing NBD dimer formation, see below) or the TMDs (e.g., by preventing conformational changes associated with pore opening) -just as a see-saw can be stopped by immobilizing either end. Interestingly, two non-conserved segments in NBD1, both containing phosphorylatable serines, had been suggested to prevent NBD dimerization in their nonphosphorylated states, but deletion of neither segment affected strict phosphorylation 13 dependence of gating. Instead, mounting evidence suggests that the "brake" acts on the TMDs rather than on the NBDs. First, simple severing of covalent linkage between the R domain and TMD2 (between residues 835 and 837) disrupts strict phosphorylationdependence of gating, yielding channels with ~20% of maximal activity in the absence of phosphorylation. More importantly, the completely ATP-independent gating of truncated CFTR channels, lacking the entire NBD2 domain, remains strictly dependent on phosphorylation. This suggests that the R domain directly interacts with the intracellular linking loops of the TMDs, consistent with conclusions from low-resolution cryo-EM imaging. By altering the specific pattern of interactions between the R domain and the intracellular linking loops and/or CFTR's N terminal tail, phosphorylation likely lowers the energetic cost of the TMD conformational change associated with pore opening. Once the "weight" on the TMD-end of the see-saw has been thus diminished, the energy released during ATP-dependent NBD dimer formation, in WT CFTR, becomes sufficiently "heavy" to flip the see-saw from an open-dimer/closed-pore conformation into a tight-dimer/open-pore state (Gadsby et al. 2006; Zhang et al. 2009; . Besides PKA, other kinases can phosphorylate the R domain, some targeting the same serines as PKA, others distinct sets of residues. Phosphorylation of serine 686 by protein kinase C (PKC) seems to play a permissive role: PKA-dependent CFTR activation requires prior phosphorylation of serine 686 by PKC. Recently, the "inhibitory" serine 768 (see above) was shown to be a substrate of AMP-kinase (AMPK), which explains the suppressive effect of AMPK activity on whole-cell CFTR currents (Hallows et al. 2000) . Still unclear are functional and physiological consequences of 14 CFTR phosphorylation by cyclic GMP-dependent protein kinase (PKG), and calcium/calmodulin-dependent protein kinase I (CaM kinase I) (Gadsby et al. 2006; King et al. 2009; Kongsuphol et al. 2009 ). Evidence for a non-equilibrium gating scheme for CFTR The cyclic kinetic scheme underlying CFTR gating (Fig. 6) is not yet universally accepted. Some researchers believe a simple equilibrium kinetic scheme best describes CFTR gating (Aleksandrov et al. 2009 ). In an equilibrium scheme (within blue dotted line, Fig. 7 top), closing and opening occur along the same pathway (i.e. closing is simply reversal of the opening transition). Such a scheme predicts a monotonically decaying open dwell-time distribution (as in Fig. 1B ). In the non-equilibrium, cyclic, gating scheme in Fig 6A, for most opening events, closing occurs through a different pathway than opening. After opening (to state O 1 ·ATP), because the non-hydrolytic closing pathway (O 1 ·ATP to C 1 ·ATP) is slow, the channel usually proceeds to a second open state. It transits through these two sequential open states, and only then it closes. This causes a rarity of brief open events. Therefore the non-equilibrium scheme predicts a peaked open dwell-time distribution with a rising phase, reflecting low event counts in the bins corresponding to shortest open dwell times. For a given observed dwell-time distribution, two alternative ML fits can be obtained: one assuming the equilibrium scheme, and another assuming the nonequilibrium scheme. The log-likelihood score (LL) quantitatively describes the "goodness" of a fit. A LL EQUILIBRIUM , assuming the equilibrium scheme, can be calculated as well as a LL NON-EQUILIBRIUM , assuming the non-equilibrium scheme. If the number of 15 free parameters is the same in the two schemes being compared, the model that yields a higher LL value is the one that best describes the data. But if the number of free parameters is different, the choice is not as simple. More free parameters often allow a better fit, even if the extra parameters are not really required. In cases in which models have different numbers of free parameters, can the significance of a better fit be quantified? The answer is yes, if the model with fewer parameters is a submodel of the more complex one. Since the equilibrium scheme is a submodel of the cyclic scheme (Fig. 7 top) the significance of a better fit can be quantified. This is done using the log-likelihood ratio (∆LL), which quantifies the improvement in fit: ∆LL = LL NON-EQUILIBRIUM -LL EQUILIBRIUM . The distribution of expected ∆LL can be calculated assuming the simple model is true, and the observed value of ∆LL (∆LL obs ) can be used to calculate a P value: the probability of observing the ∆LL obs assuming the simple scheme is true (Csanády 2006). Fig. 7A shows the WT open dwell-time distribution (yellow histogram bars). The ML fit assuming the equilibrium model is the blue dotted line, and the ML fit assuming the non-equilibrium model is the red line. Using ∆LL obs the alternative gating schemes can be ranked. The cyclic scheme provides a far better fit to the observed data: the P value (the probability of obtaining the observed distribution, with several of the leftmost bins having relatively low counts, assuming that the underlying scheme is the equilibrium one) is very low, 2·10 -9 . Thus the data are consistent with a kinetic scheme in which rate k -1 (non-hydrolytic closing) is negligibly small (i.e. the ATP-bound open state is very stable) so that for most openings the channel must hydrolyze ATP before it can close. It 16 must go through two sequential steps before closing, resulting in a rarity of very brief open events. So, for WT CFTR, gating and ATP hydrolysis are strictly coupled. CFTR_Fig7.tif Figure 7. Open dwell-time distributions (yellow histograms) for WT (A), D1370N mutant (B) and K464A mutant (C) CFTR channels, and ML fits assuming either the equilibrium scheme (top left scheme, dotted blue lines) or the non-equilibrium scheme (top right scheme, solid red lines). For each distribution P values are shown, which describe significance of improvement of fit by using the nonequilibrium scheme. If a mutation is introduced into CFTR's catalytic composite site 2, at the conserved Walker B motif aspartate (D1370N, a mutation that in other ABC proteins abolishes hydrolysis), the open dwell-time distribution becomes monotonically decaying (Fig. 7B ). There is no significant improvement using the more complex model, and the observed data are consistent with the hydrolytic rate k 1 falling to zero. Thus, for this mutant, the cyclic scheme is reduced to the equilibrium scheme.