INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION NOTES REFERENCES

ATP-sensitive potassium (K_ATP) channels are inhibited by intracellular ATP and thus couple cellular metabolism to membrane potential (Ashcroft, 1988; Nichols and Lederer, 1991). Structurally unique among potassium channels, they are normally formed from an ATP-binding-cassette protein (sulfonylurea receptor, SURx) and an inward rectifier (Kir6.x) subunit (Aguilar-Bryan et al., 1995; Inagaki et al., 1995, 1996) with a 4:4 stoichiometry (Shyng and Nichols, 1997; Clement et al., 1997; Inagaki et al., 1997). The SURx subunit confers sensitivity of the channel to sulfonylureas, MgADP, and potassium channel openers (Nichols et al., 1996; Gribble et al., 1997; Shyng et al., 1997b). Multiple structure-function analyses demonstrate that the Kir6.x subunit forms the pore and controls the hallmark inhibition by ATP (Shyng et al., 1997a; Tucker et al., 1997, 1998; Drain et al., 1998). However, the mechanism of this inhibition remains unclear.

Recent reports indicate that membrane-bound phospholipids bind to various inward rectifier K⁺ channels, stabilizing them in an active conformation (Hilgemann and Ball, 1996; Fan and Makielski, 1997; Huang et al., 1998) and K_ATP channels are no exception in being activated by PIP₂ (Fan and Makielski, 1997; Hilgemann and Ball, 1996). In controlling K⁺ channel activation, the more negatively charged the phospholipid, the more potent is the activating effect (Hilgemann and Ball, 1996; Fan and Makielski, 1997). The inhibitory effect of intracellular nucleotides on K_ATP channels also depends on the number of phosphate groups in the molecule (Ashcroft, 1988; Lederer and Nichols, 1989), which might suggest that PIP₂ activation and ATP inhibition are related phenomena. Consistent with this hypothesis, PIP₂ has a profound effect on the sensitivity of SUR1+Kir6.2 channels to ATP inhibition (Shyng and Nichols, 1998; Baukrowitz et al., 1998). In the present study we have further examined the interaction of PIP₂ and Kir6.2 subunits. The results demonstrate that PIP₂-induced channel activation and desensitization to ATP is also observed for channels formed from Kir6.2 subunits alone (Tucker et al., 1997; Baukrowitz et al., 1998), but with altered quantitative responses. Both PIP₂ and multiple mutations of the Kir6.2 channel pore region affect the intrinsic stability of the channel open state and the apparent affinity for ATP (Shyng et al., 1997a; Tucker et al., 1998; Trapp et al., 1998; Drain et al., 1998). These findings indicate that, rather than causing closure of the K_ATP channel, the inhibitory action of ATP is to stabilize a closed state. Consideration of these constraints suggests kinetic models that can account both for the behavior of K_ATP channels formed from Kir6.2 subunits with or without SUR1, and the action of PIP₂ on the channels.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION NOTES REFERENCES

Molecular biology

Point mutations were prepared by overlap extension at the junctions of the relevant residues by sequential polymerase chain reaction (PCR). Resulting PCR products were subcloned into pECE or pCMV6b vectors and sequenced to verify the correct mutant construct, before transfection.

Expression of K_ATP channels in COSm6 cells

COSm6 cells were plated at a density of ~2.5 × 10⁵ cells per well (30 mm six-well dishes) and cultured in Dulbecco's Modified Eagle Medium plus 10 mM glucose (DMEM-HG), supplemented with fetal calf serum (FCS, 10%). The next day, cells were transfected by incubation for 4 h at 37°C in DMEM containing 10% Nuserum, 0.4 mg/ml diethylaminoethyl-dextran, 100 µM chloroquine, and 5 µg each of pCMV6b-Kir6.2, pECE-SUR1, and pECE-GFP (green fluorescent protein) cDNA. Cells were subsequently incubated for 2 min in phosphate-buffered salt solution containing DMSO (10%), and returned to DMEM-HG plus 10% FCS.

Patch-clamp measurements

K_ATP currents were assayed using patch-clamp measurements 2-4 days after transfection. Experiments were made at room temperature, in an oil-gate chamber which allowed the solution bathing the exposed surface of the isolated patch to be changed in 50 ms. Micropipettes were pulled from thin-walled glass (WPI Inc., New Haven, CT) on a horizontal puller (Sutter Instrument, Co., Novato, CA). Electrode resistance was typically 0.5-1 M (5-10 M for single channel currents) when filled with K-INT solution (see below). Microelectrodes were "sealed" onto cells that fluoresced green under UV illumination, by applying light suction to the rear of the pipette. Inside-out patches were obtained by lifting the electrode and then passing the electrode tip through the oil-gate. Membrane patches were voltage-clamped with an Axopatch 1D or 200A patch-clamp (Axon Inc., Foster City, CA). The standard bath (intracellular) and pipette (extracellular) solution used in these experiments (K-INT) had the following composition: 140 mM KCl, 10 mM K-HEPES, 1 mM K-EGTA, pH 7.3. PIP2 was bath sonicated in ice for 30 min before use. All currents were measured at a membrane potential of 50 mV (pipette voltage = +50 mV). Data were normally filtered at 0.5-20 kHz, signals were digitized at 22 or 88 kHz (Neurocorder, Neurodata, NY) and stored on video tape. Experiments were replayed onto a chart recorder, or digitized into a microcomputer using Axotape or Fetchex software (Axon Inc.). Off-line analysis was performed using Fetchan, pSTAT, and Microsoft Excel programs. The threshold for judging the open state was set at half the single channel amplitude. Wherever possible, data are presented as mean ± SE. (standard error of the mean). Microsoft Solver was used to fit data by a least-square algorithm.

Model simulations

Probability density functions of kinetic models were calculated with Mathcad software (MathSoft, Inc., Cambridge, MA) using matrix mathematics as described by Colquhoun and Hawkes (1977, 1981, 1995). The probability density function of a set of states A with k states is given by:

(1)

where Q_AA is a submatrix of Q and is based on rate constants, , a 1 x k row vector containing the probabilities of starting in each of the states A at time 0, and u_A is a k × 1 column vector whose elements are all 1. The expression "exp(t*Q_AA)" was calculated using the spectral expansion of Q_AA.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION NOTES REFERENCES

Multiple M2 mutations desensitize the channel to ATP and stabilize the channel open state

Recent evidence suggests that ATP may act by stabilizing a closed state of the channel because changes in open probability in zero ATP correlate with changes in apparent ATP sensitivity (Shyng et al., 1997a, Trapp et al., 1998; Koster et al., 1999; Shyng and Nichols, 1998). In particular, systematic mutations of residues in the M2 region of Kir6.2 cause wide variation of ATP sensitivity (Loussouarn et al., 2000). Three such mutations shown in Fig. 1 generate channels that are very insensitive to ATP, and have a very high open probability in the absence of ATP (typically 0.8-0.9), with the channels being in a nearly continuously "bursting" state. We estimated ATP sensitivity and Po_zero (channel open probability in the absence of ATP) from experiments like those in Fig. 1 from amplitude histograms, or by noise analysis of patches containing a large number of channels. Table 1 and Fig. 2 A summarize the Po_zero and K_1/2,ATP estimates for each of the M2 mutant channels coexpressed with SUR1. Although comparison of Po_zero-K_1/2,ATP relationships between isolated mutations is not particularly informative, it is quite clear from the whole data set (Fig. 2 A), that Po_zero and K_1/2,ATP are correlated, i.e., ATP sensitivity depends on the open-state stability.

View larger version (36K): [in this window] [in a new window]   FIGURE 1   M2 cysteine mutations can generate very ATP-insensitive channels with very high open probability. Representative currents recorded from inside-out membrane patches containing only a few (A) I154C[C] + SUR1, (B) L157C[C] + SUR1, or (C) L164C[C] + SUR1 mutant KATP channels at 50 mV in K-INT solution (see Methods). Patches were exposed to differing [ATP] as indicated

View this table: [in this window] [in a new window]   TABLE 1   K1/2,ATP and Pozero values (estimated from noise analysis or single channels) for mutant Kir6.2 + SUR1 channels examined in this study (L164, R176 mutants), in Shyng et al. (1997a, N160 mutants) and in Loussouarn et al. (2000, Cysteine substitutions)

View larger version (13K): [in this window] [in a new window]   FIGURE 2   K1/2,ATP versus Pozero for coexpressed Kir6.2 + SUR1 channels (data summarized with errors in Table 1). (A) Large symbols represent mean values for different Kir6.2 mutant constructs (open squares: cysteine substitutes on C36,C166S background, Loussouarn et al., 2000, and R176A, Shyng and Nichols, 1998; closed squares: N160x mutations, Shyng et al., 1997a; open circles: L164x mutants; double circle: wild-type Kir6.2; double square: I154C[C]). Superimposed smooth lines correspond to predictions of Models III, V, and VI as indicated, with continuousvariation of KCO (see text). (B) Small symbols represent individual patches from Kir6.2 (WT) + SUR1 (closed symbols, from Shyng and Nichols, 1998) or Kir6.2[C25] (WT[C]) + SUR1 (open symbols), before, and with time after, exposure to PIP2. Individual patches are connected by thin lines. The heavy line represents predicted Pozero versus K1/2,ATP relationship calculated from Model V (see text).

The effect of PIP₂ on ATP sensitivity and open probability of K_ATP channels formed of Kir6.2 subunits with or without SUR1

We have concentrated further analysis on wild-type Kir6.2 (full length: WT, or C-terminally truncated: WT[C]) subunits, and on the high open-state stability mutant Kir6.2[I154C,C] subunits (I154C[C]). We previously demonstrated that PIP₂ increases Po_zero and K_1/2,ATP of wild-type K_ATP channels coexpressed with SUR1 (Shyng and Nichols, 1998). Fig. 3 shows representative recordings of currents generated by expression of WT[C] and I154C[C] subunits with (A), or without SUR1 (B, C). In each case, application of PIP₂ leads to an increase of open probability and to a decrease of ATP sensitivity (Shyng and Nichols, 1998; Baukrowitz et al., 1998). For WT, or WT[C] channels co-expressed with SUR1, the time course of channel activation by PIP₂ is variable from patch to patch, and individual patches have quite variable open probability upon first isolation. Nevertheless, when the Po_zero-K_1/2,ATP relationship is plotted, the trajectory, after application of PIP₂, is consistent from patch to patch and, moreover, follows the same trajectory as the relationship that is observed for multiple M2 mutations under ambient conditions after patch excision (Fig. 2 B).

View larger version (21K): [in this window] [in a new window]   FIGURE 3   PIP2 stimulates, and relieves ATP inhibition of, WT[C] and I154C[C] currents, with and without SUR1 coexpression. (A-C) Representative currents recorded from inside-out membrane patches containing WT[C] subunits with (A), or without (B) SUR1, or I154C[C] subunits without SUR1 (C). Currents were recorded at 50 mV in K-INT solution (see Methods). Patches were exposed to differing [ATP] or 5 µg/ml PIP2 as indicated. (D) Mean K1/2,ATP for Kir6.2[C25] channels expressed with or without SUR1, and Kir6.2[C25, I154C] without SUR1, before and after 5-12 min treatment with 5 µg/ml PIP2 (mean ± SE, n = 5-7 in each case).

WT[C] channels have a higher K_1/2,ATP, but lower Po_zero, in the absence of SUR1 than in its presence (Fig. 4 A, Table 2; Tucker et al., 1997; Koster et al., 1999; Trapp et al., 1998), such that the absence of SUR1 does not simply shift the channels to a different position along the same K_1/2,ATP-Po_zero relationship. Table 2 and Fig. 4 A combine multiple data from the present study, as well as from Trapp et al. (1998) and Tucker et al. (1998) to show that M2 mutations expressed without SUR1 do nevertheless lie on a single K_1/2,ATP-Po_zero relationship (Fig. 4 A), but one that is shifted from that observed for SUR-coexpressed constructs (Fig. 2). Also, as shown in Fig. 3, 5 µg/ml PIP₂ does not affect the ATP sensitivity of WT[C] without SUR1 channels to nearly the same degree as WT[C]+SUR1 channels; the Po_zero does not rise to saturating levels, and there is only ~3-fold increase in K_1/2,ATP. However, for I154C[C] channels, which have a higher intrinsic open-state stability (i.e., they are operating on the steeper part of the K_1/2,ATP-Po_zero relationship), stimulation by PIP₂ does lead to a rapid saturation of open probability (~0.9), and then a significant loss of ATP sensitivity (Fig. 3 D), K_1/2,ATP increasing from 2.8 ± 0.6 mM to 18.3 ± 6.0 mM after 11 ± 3 min treatment with PIP₂ (n = 3, Figs. 3 and 4 B, open small circles).

View larger version (12K): [in this window] [in a new window]   FIGURE 4   K1/2,ATP versus Pozero for Kir6.2 subunits expressed without SUR1 subunits (data summarized with errors in Table 2). (A) Large symbols represent different [C] mutant constructs that demonstrate altered ATP-independent open probabilities (squares: data from Tucker et al., 1998, and Trapp et al., 1998; diamond: Kir6.2[C36,C166S, M158C]). (B) Small symbols represent individual patches from WT[C] (closed symbols) or I154C[C] (open symbols), before and after exposure to PIP2 (only peak responses are shown for clarity). Individual patches are connected by thin lines. Continuous lines in A and B represent predicted Pozero versus K1/2,ATP relationships calculated from Models III, V (heavy), and VI in the absence of SUR1 (as indicated), together with the Model III relationship in the presence of SUR1 (dashed, taken from Fig. 2).

Single channel analyses of WT and I154C channels expressed with and without SUR1 subunit

We have measured single channel currents from cells expressing WT subunits in the absence (Fig. 5 A) and presence (Figs. 5 B, 6) of SUR1. Figs. 5-7 also show Sigworth-Sine (Sigworth and Sine, 1987) representations of closed- and open-time histograms obtained from these recordings, after Gaussian filtering at 3-4 kHz (see Note 1 at end of text). As shown in numerous previous studies, wild-type (WT+SUR1) channel activity occurs in bursts. Single exponential functions would adequately describe the open- and closed-time distributions within the burst. However, it is clear that inter-burst closed-time distributions are more complex, consisting of a "mixture of exponentials" (Colquhoun and Hawkes, 1995), and are not adequately described by the sum of a small number of exponentials (not shown). Therefore, we have not attempted to fit probability density functions (pdfs) with the sums of exponential components. The smooth lines superimposed on the experimental data in Figs. 5-7 are the predicted lifetime distributions of the models described below.

View larger version (47K): [in this window] [in a new window]   FIGURE 5   Representative single channel currents of WT[C] alone (A) and WT + SUR1 (B) channels at 50 mV at different time scales, as indicated (left), together with Sigworth-Sine plots of closed- and open-lifetime distributions (right). Channels are shown in the absence and presence of [ATP]. The superimposed simulated probability density functions (pdfs) are predictions of kinetic Models III (thin curve), V (heavy curve), and VI (medium curve) described in the text.

View larger version (33K): [in this window] [in a new window]   FIGURE 6   Representative single channel currents of a WT + SUR1 channel before and after application of PIP2, at 50 mV at different time scales, as indicated (left), together with Sigworth-Sine plots of closed- and open-lifetime distributions (right).The superimposed simulated probability density functions (pdfs) are predictions of kinetic Models III (thin curve), V (heavy curve), and VI (medium curve) described in the text.

View larger version (49K): [in this window] [in a new window]   FIGURE 7   Representative single channel currents of I154C[C] alone (A) and I154C[C] + SUR1 (B) channels at 50 mV at different time scales, as indicated (left), together with Sigworth-Sine plots of closed- and open-lifetime distributions (right). Channels are shown in the absence and presence of [ATP]. The superimposed simulated probability density functions (pdfs) are predictions of kinetic Models III (thin curve), V (heavy curve), and VI (medium curve) described in the text.

Open times show a single exponential distribution with mean ~1 ms both for WT and I154C single channel currents in the presence, or absence, of SUR1. Furthermore, this open time is not altered in the presence of ATP (Figs. 5, 7). After application of PIP₂, the open probability of WT+SUR1 channels increases considerably, but again, the open time is unaffected (Fig. 6). WT and WT[C] channel closed-time distributions consist of at least two temporally distinct components in the absence or presence of SUR1 (Figs. 5, 6). The shortest component (i.e., the intra-burst closures) would be reasonably well-fit with a single exponential with time constant ~0.5 ms, again with or without SUR1. Again, this intra-burst closed time is essentially independent of [ATP] (Fig. 5 B) and is unaffected by PIP₂ (Fig. 6). Consistently, the longer closed times appear as "mixtures of exponentials," i.e., single peaks in "Sigworth-Sine" plots, but spread over much wider time distributions than single exponentials, suggesting multiple overlapping exponential components (Colquhoun and Hawkes, 1995). These longer time components show a general trend of lengthening in the presence of ATP (Fig. 5), and shortening after PIP₂ application (Fig. 6).

We have also obtained single channel patches of high open-state stability I154C[C] channels in the absence and presence of SUR1. Inspection of the single channel records indicates that in each case, channels are almost continuously bursting in the absence of ATP (Fig. 7). As with WT channels, open times are still monoexponential, and with the same time constant, ~1 ms. In the absence of ATP, closed-time distributions are dominated by a single short exponential of ~0.5 ms (Fig. 7). However, there is still a small "second" component in the closed-time distributions, in the presence and absence of SUR1. In both cases the amplitude of this component is increased, and the distribution shifted to longer times, in the presence of high [ATP].

In search of a unifying kinetic model of channel activity

Many models have been put forward to explain various aspects of the gating of K_ATP channels (e.g., Qin et al., 1989; Nichols et al., 1991; Fan et al., 1990; Forestier et al., 1996; Alekseev et al., 1998; Trapp et al., 1998). None has thus far dealt with the interaction of PIP₂ with the channel, and many have not explicitly considered ATP binding, empirically describing only the apparent dependence of rate constants on [ATP]. The following features require explanation in any kinetic model of channel behavior: 1) endogenous K_ATP channels are typically inhibited with a K_1/2,ATP of ~10-40 µM, and with best-fit Hill coefficients of between 1 and 2; 2) channel activity occurs in bursts, with closed times having multi-exponential distributions; 3) the brief closures are independent of ATP or PIP₂, but longer closures become longer still with increasing [ATP]; 4) channel open times are typically ATP-independent and have a single exponential distribution. Recent structure-function analyses raise another important consideration: channel activity is conferred by the Kir6.2 subunit (Shyng et al., 1997a; Tucker et al., 1997), but channel activity is significantly modified by the presence of SUR1 subunits (e.g., Tucker et al., 1997; Baukrowitz et al., 1998; John et al., 1998). Thus, reasonable adjustments should additionally allow any unified model to explain the kinetic behavior of channels in the presence and absence of SUR1. The additional information obtained from PIP₂ experiments further dictates that an appropriate model should also have specific steps that are dependent on, or modulated by, the binding of PIP₂.

The simplest model that could account for the four critical observations requires an ATP-independent closed state (C_f) in rapid equilibrium with the open state, and a longer closed state (C₀) to provide inter-burst closed states (e.g., Model I).
Model I

An indirect action of ATP could then be to shift the equilibrium between the C₀ and O-C_f states so as to prolong C₀. An additional C₁ state, accessed sequentially from C₀ (e.g., Model II, cf. Alekseev et al., 1998) would then allow two long closed states, as seems to be at least required by detailed analyses of wild-type (Kir6.2+SURx) channels (e.g., Nichols et al., 1991; Alekseev et al., 1998; Drain et al., 1998), and again, an undefined modulation of the equilibrium between C₁ and C₀ could prolong closed times in the presence of ATP.
Model II

The lack of any evidence for more than one open state within the burst (see, e.g., Figs. 5-7; Drain et al., 1998; Alekseev et al., 1998) obviates the need to invoke more than one open state and argues that simple linear schemes (like Models I and II) might be appropriate models to explore.

Indirectly coupled models predict steady-state and kinetic data

The present data, which include modulation of channels by PIP₂ and the effect of multiple mutations, indicate a strict relationship between channel open probability and apparent ATP sensitivity. Without constraining ATP binding to a particular kinetic step, Models I and II do not predict any specific relationship between ATP sensitivity and Po_zero. The most reasonable explanation for the strong correlation of ATP sensitivity and open probability is that ATP must bind to, or its "action" be only felt by, a closed state, i.e., ATP acts to stabilize a closed state. This conclusion puts a critical constraint on understanding ATP inhibition, because it obviates a scenario in which ATP binds to the channel, then causes the channel to close. This constraint suggests exploring models that include a critical transition between the open state and a non-ATP-bound closed state (C₀), like the defined model (III) below:
Model III

PIP₂, and numerous mutations (e.g., M2 mutations), "activate" channels by increasing Po_zero (Shyng et al., 1997a; Fan and Makielski, 1997; Shyng and Nichols, 1998; Tucker et al., 1998; Drain et al., 1998; Koster et al., 1999; Loussouarn et al., 2000). Po_zero is correlated in every case with change in ATP sensitivity (Figs. 2 and 4; see Note 2) implicating a mechanistic link between the two phenomena. Such a link is provided in Model III, because ATP binds to state C₀. Hence, if PIP₂, or a mutation in M2, shifts the equilibrium of the C₀-O transition (equilibrium constant K_CO = k_CO/k_OC) toward the open state (i.e., away from ATP-accessible states), then it both increases Po_zero and reduces apparent ATP sensitivity. In Figs. 2 and 4, the Po_zero-K_1/2,ATP relationships predicted by this defined model are superimposed on experimental data (the rate constants are given in Table 3). We previously suggested that SUR1 acts to sensitize the Kir6.2 channels to ATP (Shyng et al., 1997b). Adjustments to Model III suggest that the steady-state behavior of channels expressed without SUR1 (Fig. 4) can be accounted for by assuming that the closed-state C₀ is energetically stabilized 20-fold, relative to the O and C₁ states, in the absence of SUR1. (i.e., SUR1 acts to destabilize this state). By stabilizing state C₀ in the absence of SUR1 (see Table 3), Model III predicts that the Po_zero and K_1/2,ATP of WT[C] channels shift from 0.69 and 15 µM, to 0.13, and 79 µM, in the presence and absence of SUR1, respectively, in good agreement with experimental data (Fig. 4). Moreover, as shown in Fig. 4, this single parameter adjustment shifts the whole Po_zero-K_1/2,ATP curve to that observed for mutant channels expressed without SUR1 (Fig. 4).

Single channel lifetimes for Model III (and others below) were generated by matrix solution of the full kinetic schemes (see Methods), and are superimposed on measured lifetime distributions in Figs. 5-7. Appropriate rate constants were chosen within the constraints of steady-state equilibrium constants to simulate lifetime distributions seen in experiments (Figs. 5-7). Model III predicts a single, fast, open time and fast closed time, with a single, long, closed time in the absence of ATP. Only the long closed time is affected by ATP, becoming a longer "mixture of exponentials" with a single peak (e.g., Fig. 5 B). Model III predicts reasonable lifetime distributions for WT+SUR1 channels (Fig. 5 B) and the appropriate 20-fold increase of k_OC and k_1O (see Table 3) in the absence of SUR1 gives rise to considerably more long closed times in the absence of SUR1 (Fig. 5 A). By increasing k_CO 2-fold, PIP₂ is predicted to shorten the long closed-time distribution, in general agreement with observed lifetimes (Fig. 6).

For simulating lifetime distributions of I154C mutants with Model III (Fig. 7), k_OC was adjusted as shown in Table 4. Although Model III successfully predicts fast intra-burst closed- and open-time distributions, longer closed durations of both WT and I154C[C] channels are not well accounted for, with or without SUR1, and this discrepancy is particularly severe in the absence of SUR1 (Fig. 7 A). Model III predicts single-exponential long closed distributions, at least in the absence of ATP (e.g., Figs. 5 A, 7 A), and not the "mixture of exponentials" that is observed.

Kinetic and steady-state constraints indicate a tetrameric model

In addition to problems with reproducing single channel lifetimes, Model III predicts a sigmoidal steady-state [ATP]-inhibition relationship, with Hill coefficient of 1, but the relationship is not well described by a Hill equation, even raised to a power. Steady-state ATP sensitivity is shallow at low [ATP] (H ~1) and considerably steeper (approaching H = 4) at high [ATP] (Nichols et al., 1991, reviewed in Ashcroft and Gribble, 1998). Fig. 8 shows [ATP]-response relationships for WT+SUR1 channels, obtained by rapid application of multiple [ATP]. The non-sigmoidicity is clearly apparent, both for a single patch and when multiple patches are averaged (inset; see Note 3). This phenomenon, together with the complex kinetics of channel inhibition and activation after [ATP] "jumps," can be explained by models that assume multiple ATP molecules bind sequentially to stabilize closed states. Parameter fitting of such models (Nichols et al., 1991) indicated that a four-site model may be appropriate. Two or three sequential ATP binding steps do not provide adequate steepness at high [ATP], and given the 4-fold stoichiometry of the channel (Shyng and Nichols, 1997; Clement et al., 1997), two or three binding sites are unlikely. An appropriate model (e.g., Model IV) can be generated as a linear extension of Model III:

View larger version (4K): [in this window] [in a new window]   Model IV

View larger version (16K): [in this window] [in a new window]   FIGURE 8   Relative current (Irel)-[ATP] relationship from an inside-out patch from cells expressing WT+SUR1 channels, and averaged data from multiple patches (inset). For the averaged data, individual relationships were "normalized" to the K1/2,ATP in order to avoid the shallowing effect of K1/2,ATP variability from patch to patch. The error bars indicate 95% confidence limits for the mean, (Student's t-distribution, assuming data are normally distributed). Note that the relationship is well described by Models III, IV, and V at low [ATP]. At higher [ATP], inhibition becomes a considerably "steeper" function of [ATP], and is not well described by the single ATP binding site model (III) but requires multiple ATP binding site models (IV and V). Model V lies within the 95% confidence limit for all data points, whereas Model III lies outside this limit for high [ATP]. Solid lines in both graphs are the predictions for Models III, IV, and V as indicated. Model IV assumes the same ATP-independent transitions as Model II, and independent binding of ATP at each subunit, with binding constant = 20 µM.

This model reproduces appropriate steady-state [ATP]-inhibition relationships (Fig. 8), but does not give any better correlation of Po_zero and K_1/2,ATP than Model III (not shown). Moreover, it does not give any better prediction of the single channel kinetics of WT subunits with and without SUR1, because it reduces to Model III in the absence of ATP. Model IV still predicts a bi-exponential closed-time distribution, which is clearly inadequate to explain the observed distributions (e.g., Figs. 5-7). Multi-exponential long closed states with a linear model would require additional ATP-independent closed states between C₀ and O. We suggest instead a coupled model (V) involving four independent subunits, each of which can occupy only three distinct states. Model V assumes that each individual subunit can be in either the open (O) or closed state (C₀), and that a single ATP can bind to state C₀ to generate state C₁ for each subunit. The channel itself is open and conducting only when all four subunits are in the O state. Again, a separate fast closed state (C_f) is accessed from the open channel, giving rise to the "intra-burst" kinetics:

View larger version (19K): [in this window] [in a new window]   Model V

The model, drawn above in full on the left (to show the conformational changes of the whole channel), and on the right (to show the two transitions undergone by each independent subunit), is still governed only by the intra-burst rate constants (opening: k_CfO and closing: k_OCf) rate constants and by four other rate constants ( = k_OC,  = k_CO,  = k₀₁*[ATP],  = k₁₀), but there are now a total of four overlapping inter-burst closed states in the absence of ATP (C₀-C₃), and 14 in the presence of ATP (C₀-C₁₃). This independent subunit model is analogous to the model proposed by Zagotta et al. (1994) to explain voltage-dependent gating of delayed rectifier K⁺ channels. With a single set of parameters (Table 3), Model V not only reproduces steady-state [ATP]-response curves (Fig. 8) and K_1/2,ATP-Po_zero relationships (Figs. 2, 4), in the presence and absence of SUR1, but also predicts multi-exponential closed-time distributions that are generally closer to the experimentally observed distributions, particularly channels without SUR1 (Figs. 5 A, 7 A).

However, this model still fails to account for the very long closed states that are observed with low frequency in all channels and conditions (Figs. 5-7). Further complexity could be achieved by additional closed states. We suggest one final iteration (Model VI), which includes a longer "inactivated" closed state (C_I), accessible from C₀. Such a model still accounts for all of the major considerations, but provides additional long closed channel components in all pdfs, such as is apparent for wild-type channels (Fig. 5). Although this model is still controlled by only four equilibrium constants, the total number of transitions (61, with 36 total states) makes simulation cumbersome, and reaches the limit of what is justified by the data.

View larger version (11K): [in this window] [in a new window]   Model VI

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION NOTES REFERENCES

The mechanism of ATP inhibition and PIP₂ activation

The K_ATP channel is unique among potassium channels in that activity depends strongly on cytoplasmic [ATP]. Understanding this inhibition is a central question, and recent studies have implicated the Kir6.2 subunit in controlling ATP-sensitivity (Shyng et al., 1997a; Tucker et al., 1997, 1998; Drain et al., 1998; John et al., 1998). These studies have not revealed the mechanism of ATP inhibition, although they have highlighted regions and residues (e.g., R50, K185, 334-337) that are involved. A majority of mutations cause changes of ATP sensitivity (K_1/2,ATP) that are correlated with changes of channel open probability (Po_zero) (Tables 1 and 2; Figs. 2 and 4). The same relationship between K_1/2,ATP and Po_zero is traversed, whether open probability is manipulated by PIP₂ treatment or by mutagenesis (Fig. 2, 4). This relationship can be explained by alterations in the equilibrium of a critical transition (K_CO) between the open (O) state and an ATP-accessible closed (C₀) state (Shyng et al., 1997a). Hence we conclude that ATP does not directly cause channel closure, rather ATP stabilizes a closed state. This conclusion was also reached by Shyng et al. (1997a) and Trapp et al. (1998), based on mutagenesis experiments, and can be inferred from the study of Alekseev et al. (1998) based on their analysis of single channel events. These effects of PIP₂ and M2 mutations (together with N-terminal truncations, Koster et al., 1999), are analogous to those of mutations in cyclic nucleotide-activated ion channels that alter the activating efficacy, but not the affinity, of cyclic nucleotides for these channels. For example, Gordon and Zagotta (1995) demonstrated that in chimeras between olfactory and rod cyclic nucleotide gated channels, cyclic nucleotide activating potency could vary over 3 orders of magnitude. This variable potency is a consequence of shifts in the equilibrium of the allosteric conformational change between closed and open states.

The role of SUR subunits in controlling channel kinetics

There exists a strong correlation between the K_1/2,ATP and Po_zero, for channels expressed both with and without, SUR1 (Figs. 2, 4) but the relationship is different in the two cases. The anomaly of a higher K_1/2,ATP and lower Po_zero for Kir6.2 expressed in the absence of SUR1 than in its presence has been noted previously (Tucker et al., 1997; Drain et al., 1998; John et al., 1998), but the mechanistic basis remains undetermined. The modeling in the present paper provides a potential explanation. The two Po_zero-K_1/2,ATP relationships for the coexpressed (Fig. 2) and homomeric channels (Fig. 4) can be predicted by assuming that the presence of the SUR1 subunit destabilizes the ATP-unbound closed state (C₀ in each of the models). In the presence of SUR1, channels entering this state are more likely to transit to the ATP bound state (hence lower K_1/2,ATP in control), and to the open state (hence higher Po_zero). In Model V, for instance, destabilization of state C₀ (w.r.t. states O and C₁) is the only adjustment necessary to reproduce the essential effects of SUR1 on both the K_1/2,ATP-Po_zero relationship and on single channel kinetics. Although there is presently no physical evidence to support or refute such a hypothetical effect of SUR1, it is conceptually simple to visualize the large SUR1 subunit somehow physically destabilizing the closed (C₀) state of Kir6.2.

It is quite clear from the present studies that the effects of PIP₂ on Kir6.2 channels coexpressed with SUR1 and on truncated Kir6.2 channels expressed alone are qualitatively similar, but quantitatively very different, as noted by Baukrowitz et al. (1998). In both cases the open-state stability increases, leading to increased open probability and reduced ATP sensitivity, but the I154C mutant experiments are necessary to conclusively demonstrate an increase in K_1/2,ATP in channels expressed without SUR1. We have no ready explanation for the reduced effect of PIP₂ on channels expressed without SUR1. One obvious possibility is that PIP₂ binding to SUR1 occurs and that this interaction enhances the direct action of PIP₂ on Kir6.2. Clearly, the interaction between SUR1 and Kir6.2 is complex, and more intense biochemical analyses will be required to fully explain the kinetic effects of PIP₂.

Comparison with other mutagenic studies of Kir6.2

During the course of this study several groups examined the effects of Kir6.2 mutations on control of ATP sensitivity. Tucker et al. (1998) introduced random mutations throughout the N- and C-terminal regions of Kir6.2[C26]. They demonstrated that mutations clustered between residues 39-51 in the N-terminus region, and between 166-185 at the end of the M2 segment and beginning of the C-terminal region could significantly decrease ATP sensitivity of channels expressed without SUR1. Of these mutations, R50G and K185Q reduced ATP sensitivity without changing the open probability in the absence of ATP (Po_zero), suggesting that these residues might actually reside within an ATP binding site. We have not examined such mutations in the present study, but their effects could be accounted for in the models by assuming changes of the ATP binding (k₀₁) or unbinding (k₁₀) rate constants. Tucker et al. (1998) isolated mutations C166S, I167M, and T171A, wherein decreased ATP sensitivity was associated with an increase in Po_zero. Trapp et al. (1998) examined ATP sensitivity and gating behavior of multiple mutations at position 166, also showing that altered ATP sensitivity of M2 mutants is in every case associated with a change in Po_zero (see Table 2, Fig. 4). Based on such results, Tucker et al. (1998) suggest that the intracellular end of M2 may contribute to an intracellular gate governing access to the pore. However, mutations that alter Po_zero and K_1/2,ATP are clearly found throughout the M2 segment (Table 1). Rather than suggesting that a specific residue forms a "gate," it may be more reasonable to consider the whole of the M2 helix being the "gate," and the "gating process" (i.e., the C₀-O transition) involving either rotation or tilting of the helices, or both, as proposed for the gating of the bacterial KcsA channel (Perozo et al., 1998, see below).

Drain et al. (1998) also used a scanning mutagenesis strategy to examine the role of Kir6.2 in controlling ATP sensitivity. They identified two regions in the C-terminus that help determine ATP sensitivity. The first included residues 171-182 at the end of M2, mutations in this region being associated with increased Po_zero and further demonstrating that mutations of this region alter the stability of the open channel. The second region included residues 334-337 in the distal C-terminus. As with R50G and K185Q (Tucker et al., 1998; Koster et al., 1999), mutations in this region were not associated with altered Po_zero, consistent with an involvement in ATP binding, rather than control of a "gate." From these intense mutagenesis studies a picture emerges whereby ATP is likely to bind to residues in the cytoplasmic N- and C-termini. Very recently, Tanabe et al. (1999) have provided direct evidence for binding of 8-azido ATP to Kir6.2.

Comparison with other modeling studies

Several papers have attempted to model the complexities of the response of K_ATP channels to activating nucleotides and potassium channel openers (e.g., Fan et al., 1990; Forestier et al., 1996). However, only recently have attempts been made to model even ATP inhibition itself based on analysis of single channel events (Alekseev et al., 1997, 1998; Trapp et al., 1998; Drain et al., 1998). Qin and Noma (1988) developed the oil-gate chamber to examine the response to step changes of [ATP], in analogy to stepped voltage-clamp analysis of voltage-gated channels. In these experiments there is a pronounced lag in the response to step decrease of ATP (Qin et al., 1989), and this is probably explained by diffusion limitations resulting from recession of the membrane in the electrode tip. Taking such limitations into account requires complex analysis (Cannell and Nichols, 1991; Nichols et al., 1991). Baukrowitz et al. (1998) estimated apparent ATP on- and off-rates for inhibition using concentration jumps on inside-out macro-patches. They did not consider potential diffusion limitations, and interpreted their data with a very simplified two-state (active-inhibited) model. They concluded that PIP₂ acts to reduce the apparent on-rate of ATP but does not affect the off-rate. This is generally consistent with the predictions of the present models, in which a shift of the C₀-O equilibrium toward the O state would reduce accessibility of C₀ and reduce the macroscopic ATP inhibition rate. The activation rate would be unaffected because it is dependent on the intrinsic ATP off-rate. Unfortunately, attempts to use photolysis of caged ATP to circumvent the problem of diffusion limitations have thus far been fruitless (Nichols et al., 1990), but further efforts are warranted.

In the first paper to examine K_ATP channel activity, Noma (1983) estimated the [ATP]-inhibition response relationship of cardiac channels. He concluded, based on the steepness of this relationship, that more than one ATP molecule should be involved in channel inhibition. Since that time, other studies have consistently shown that ATP sensitivity is best fit by a Hill coefficient of between 1 and 2 (see e.g., Ashcroft, 1988; Nichols and Lederer, 1991; Ashcroft and Gribble, 1998). Nichols et al. (1991) considered the steepness of the relationship explicitly, and as shown here for recombinant WT+SUR1 channels (Fig. 8), the relationship is not adequately explained by a simple Hill equation, even with a coefficient greater than 1. The linear model of Nichols et al. (1991) predicts a steady-state [ATP]-response relationship in which the limiting slope (Hill coefficient) approaches 1 at low [ATP], but approaches 4 at high [ATP]. A similar prediction arises from the present linear four-site model (IV) and the concerted models (V, VI). As shown in Fig. 8, these models predict the measured ATP sensitivity of Kir6.2+SUR1 channels better than single-site models (e.g., Model III).

Detailed analysis of Shaker Kv channel gating by Zagotta et al. (1994) suggests that independent gating motions of each of the four channel subunits may be required for the channel to conduct. The parallel between these models and the present models (V, VI) is intriguing in raising the possibility of common gating mechanisms. The cyclic nucleotide-gated (CNG) channels are also structurally within the potassium channel superfamily (Zagotta and Siegelbaum, 1996), although they are non-selective and show only very weak voltage-dependence. Nevertheless, detailed kinetic analyses suggest gating schemes that are conceptually similar to the one we propose here (e.g., Karpen et al., 1988). Again, rapid transitions within a burst are cyclic nucleotide-independent and closed times between bursts are [ligand]-dependent (Matthews and Watanabe, 1987; Haynes and Yau, 1990; Taylor and Baylor, 1995; Karpen et al., 1988). Recent data suggest that ligand-independent opening of these channels can occur (Picones and Korenbrot, 1995; Tibbs et al., 1997) necessitating a model in which the channel can open from any liganded or unliganded state (Monod et al., 1965; Stryer, 1987). In the present study we have not considered such models (e.g., VII), because there is as yet no evidence for K_ATP channel opening at saturating [ATP]; analyses of single channels (e.g., Figs. 5-7) do not indicate any dependence of open duration on [ATP].

View larger version (8K): [in this window] [in a new window]   Model VII

At least for WT and other relatively low open-state stability mutants, the effects of manipulating the open-state stability on apparent ATP sensitivity requires that channels must enter a closed state before ATP can act. Very high open-state stability mutants, e.g., L164C, are so ATP-insensitive that we cannot practically measure ATP sensitivity over a full range, and so we cannot exclude the possibility that such channels may actually show ATP-insensitive openings.

The physical basis of the critical transition

It is clear that multiple mutations throughout the Kir6.2 subunit, including N-terminal truncations (Koster et al., 1999), regions in the C-terminal (Trapp et al., 1998; Tucker et al., 1998; Shyng and Nichols, 1998; Drain et al., 1998), and throughout the M2 segment (Fig. 3; Shyng et al., 1997a; Loussouarn et al., 2000), as well as PIP₂ (Shyng and Nichols, 1998; Baukrowitz et al., 1998), all control what may correspond kinetically to the same critical transition between the open state and the ATP-accessible closed state. The physical reality of such a transition is unknown, but disparate lines of evidence lead us to hypothesize the molecular basis. First, the crystal structure of the bacterial KcsA channel indicates that the four -helical M2 domains line the inner vestibule of the channel, forming an inverted teepee, the four helices coming together at the point of the teepee to generate the internal entrance to the pore (Doyle et al., 1998). In lieu of a crystal structure of mammalian inward rectifiers, systematic cysteine scanning of the M2 domain in Kir6.2 reveals that this domain is also an -helix with similar structure to the corresponding KcsA domain (Loussouarn et al., 2000). Moreover, EPR analysis of the M2 domain of KcsA reveals that the teepee-like structure "opens" during channel opening, moving the helices apart (Perozo et al., 1998). Motions of M2, making substituted cysteines less accessible, also occur during gating of Kir6.2 channels (Loussouarn et al., 2000). We hypothesize (Fig. 9), that the "critical-transition" corresponds to M2 helix motions, such that the open channel, stabilized by PIP₂, corresponds to the "opened" arrangement, and the closed channel, stabilized by ATP, corresponds to the "closed," teepee-like, arrangement. This scenario provides a ready explanation for the steric requirement of PIP₂ being in the membrane. It also provides an explanation why M2 mutations should have such profound effects on the equilibrium of the gating transition, because M2 itself is conceptually the "gate," and such mutations will control the stability of the critical open- and closed-conformations of the M2 helices.

View larger version (35K): [in this window] [in a new window]   FIGURE 9   Cartoon to illustrate the hypothesized physical basis of the "critical transition." In the open state of the channel the transmembrane M2 helices that line the pore are opened relative to one another, and are stabilized in this position by association of the positively charged C-terminal domain to the membrane. The "critical transition" involves M2 helix-"collapse," closing off the pore at the cytoplasmic end. The C-terminal domain dissociates from the membrane lipid, and this closed state can then be stabilized by association with ATP.

	NOTES

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION NOTES REFERENCES

1. As in all kinetic analyses, the ability to identify discrete states is limited by the recording bandwidth. Missed events can cause added exponential components, or the elimination of exponential components (Blatz and Magleby, 1986), in lifetime distributions. Cursory analysis of corrections for missed events using the methods of Colquhoun and Hawkes (1995) for the two-state problem indicates that brief closed- and single open-times (Models III or V) would change by at most 2-fold (i.e., 0.3 log units), with longer closed-time components less affected. With an estimated dead-time of <80 µs, any additional components should appear with time constant <160 µs (Blatz and Magleby, 1986), well outside the long closed distributions we observe. As the overall multi-exponential nature of closed-time distributions will remain the same, we made no explicit corrections for missed events. Filtering at >5 kHz introduced rapid events resulting from open- or closed-channel noise and filtering at 1 kHz or less caused progressive prolongation of the apparent mean duration of the shortest open- and closed-times. Lifetime distributions were stable for filtering at 5 kHz and 3 kHz. Accordingly, detailed channel lifetime analyses were made after filtering at 3 or 4 kHz.

2. Some mutations affect ATP sensitivity without altering Po_zero (e.g., R50G, K185Q, Tucker et al., 1998; replacement of residues 334-337, Drain et al., 1998). These may actually affect ATP binding, and so we have not discussed them here. However, the effects of such mutations could be accounted for in Models III-VI by assuming changes of the ATP binding (k₀₁) or unbinding (k₁₀) rate constants (Koster et al., 1999).

3. For multi-patch averaging, intrinsic variation of ATP sensitivity after patch isolation (Findlay and Faivre, 1991), which may well reflect differences in membrane PIP₂ levels, requires normalizing concentrations to the half-maximal effective concentration to avoid causing artefactual shallowing of the relationship.