Feedback Control of the ATP-Sensitive K⁺ Current by Cytosolic Ca²⁺ Contributes to Oscillations of the Membrane Potential in Pancreatic β-Cells

The medium used for the preparation of islet cells was a bicarbonate-buffered solution that contained (in mmol/l): 120 NaCl, 4.8 KCl, 2.5 CaCl₂, 1.2 MgCl₂, 24 NaHCO₃, 5 HEPES, and 10 mmol/l glucose (pH adjusted to 7.40 with NaOH). The Ca²⁺-free medium used to disrupt the islets into single cells had the following composition (in mmol/l): 138 NaCl, 5.6 KCl, 1.2 MgCl₂, 5 HEPES, and 1 mmol/l EGTA (pH adjusted to 7.40 with NaOH). All solutions used for tissue preparation were gassed with O₂:CO₂ (94:6%) and supplemented with 1 mg/ml BSA (fraction V; Roche Molecular Biochemicals; Mannheim, Germany).

For electrophysiological measurements of I_KATP, the standard extracellular solution contained (in mmol/l): 120 NaCl, 4.8 KCl, 2.5 CaCl₂, 1.2 MgCl₂, 24 NaHCO₃, 5 HEPES (pH adjusted to 7.40 with NaOH), and various concentrations of glucose as indicated. When a Ca²⁺-free solution was needed, CaCl₂ was substituted by MgCl₂, and 2 mmol/l EGTA was added. These solutions were gassed with O₂:CO₂ (94:6%). The pipette solution contained (in mmol/l): 70 K₂SO₄, 10 NaCl, 10 KCl, 3.7 MgCl₂, and 5 HEPES (pH adjusted to 7.1 with KOH). The electrical contact was established by adding a pore-forming antibiotic, amphotericin B or nystatin, to the pipette solution. Amphotericin (stock solution of 60 mg/ml in DMSO) was used at a final concentration of 300 μg/ml. Nystatin (stock solution of 10 mg/ml in DMSO) was used at a final concentration of 200 μg/ml. The tip of the pipette was filled with antibiotic-free solution, and the pipette was then back-filled with the amphotericin- or nystatin-containing solution. The voltage clamp was considered satisfactory when the series conductance was >35–40 nS.

Thapsigargin was obtained from Sigma (St. Louis, MO) or from Alomone Labs (Jerusalem, Israel), diazoxide from Schering-Plough Avondale (Rathdrum, Ireland), and nimodipine from Bayer (Wuppertal, Germany). Unless otherwise stated, all other chemicals were from Sigma.

The pancreases were taken from Naval Medical Research Institute mice killed by cervical dislocation. Pancreatic islets were isolated aseptically by collagenase digestion followed by hand selection. To obtain single cells, the islets were first incubated for 5 min in a Ca²⁺-free medium. After a brief centrifugation, this solution was replaced by culture medium, and the islets were disrupted by gentle pipetting through a siliconized glass pipette. The cells were plated on 22 mm-diameter glass coverslips and maintained for 1–4 days in RPMI 1640 tissue culture medium containing 10 mmol/l glucose, 10% heat-inactivated FCS, 100 IU/ml penicillin, and 100 μg/ml streptomycin.

Two criteria were used to identify β-cells. The capacitance of mouse α-, δ-, and β-cells averages 4.4, 5, and 7.4 pF, respectively (29). Therefore, only large cells with a capacitance >5 pF were chosen for the present study. For 150 randomly chosen cells, the average capacitance was 7.6 ± 0.2 pF. After verification of the capacitance, a depolarizing protocol was applied to identify the properties of the voltage-dependent Na⁺ current, which is known to be inactivated at resting potential in β-cells but not in α- and δ-cells (30). Thus, cells in which a Na⁺ current could be activated by a small depolarizing pulse from a prolonged holding potential of −70 mV were discarded. By contrast, cells that displayed a Na⁺ current only after a hyperpolarizing pulse to −140 mV were considered to be β-cells (30,31) and were used for the experiments.

Patch-clamp measurements were carried out using the perforated whole-cell mode of the patch-clamp technique at 33–35°C, using an EPC-9 patch-clamp amplifier (Heka Electronics, Lambrecht/Pfalz, Germany) and the software Pulsefit, or an Axopatch 200 B patch-clamp amplifier (Axon Instruments, Foster City, CA) and the software pClamp 8. Patch pipettes were pulled from borosilicate glass capillaries (World Precision Instruments, Hertfordshire, U.K.) to give a resistance of 4–5 MΩ.

I_KATP was monitored by 100 ms-duration pulses of ±20 mV from a holding potential of −70 mV (Figs. 1–4) or pulses of −20 mV from a holding potential of −60 mV (Figs. 5 and 6). In the latter protocol, −60 mV was chosen because it corresponds best to the interburst potential in spontaneously oscillating cells within an islet, whereas the depolarizing pulses were omitted to avoid activation of voltage-dependent Ca²⁺ channels. To prevent the capacitive transient due to electrical charge of the pipette, which might complicate I_KATP measurements, each change in voltage was preceded by 100-ms ramps (except for in Fig. 1D). Two protocols of depolarization were used: either a single 30-s pulse to 0 mV (Figs. 2 and 3) or a train of depolarizations mimicking the oscillations of the membrane potential induced by 10 mmol/l glucose in whole islets. These trains consisted in the succession of 18-s hyperpolarizing phases, during which I_KATP was measured (pulses of −20 mV from a holding potential of −60 mV), and 6-s depolarizing phases. During these depolarizing phases, action potentials were mimicked by 50-ms pulses from −40 to 0 mV; their frequency was 10 Hz at the beginning of the pulse and decreased progressively to 5 Hz at the end of the pulse (Figs. 5 and 6).

Islet cells were loaded with 1 μmol/l fura-2/AM (Molecular Probes, Eugene, OR) for 45 min at 37°C in a bicarbonate-buffered solution containing 10 mmol/l glucose. The glass coverslips onto which the loaded cells were attached constituted the bottom of a temperature-controlled perifusion chamber (Intracell, Royston, Herts, U.K.) mounted on the stage of an inverted microscope. The Ca²⁺ probe within the cells was excited at 340 and 380 nm, and the fluorescence emitted at 510 nm was captured at 20 Hz by a photometric-based system (PTI, Lawrenceville, NJ). [Ca²⁺]_c was calculated by comparing the ratio of the 510-nm signals successively acquired at 340 and 380 nm with a calibration curve based on the equation of Grynkiewicz et al. (32) and established by filling the chamber with an intracellular-type solution containing 10 μmol/l fura-2 free acid, and either 10 mmol/l free Ca²⁺ or <1 nmol/l free Ca²⁺. A K_d for the fura-2-Ca²⁺ complex of 224 nmol/l was used.

The experiments are illustrated by traces that are means or representative traces of results obtained with the indicated number of cells from at least three different cultures. The statistical significance of differences between means was assessed by paired or unpaired Student’s t test as appropriate. Differences were considered significant at P < 0.05.

To search for the existence of intrinsic Ca²⁺-independent metabolic oscillations, I_KATP was measured in single metabolically intact β-cells hyperpolarized at −70 mV (Fig. 1). The cells were continuously perifused with a glucose concentration (10 mmol/l) that produces spontaneous [Ca²⁺]_c oscillations in unclamped β-cells (33). In the present experiments, [Ca²⁺]_c was low because of the hyperpolarization and not affected by the 20-mV hyperpolarizing and depolarizing pulses used to monitor I_KATP (see the beginning of the recording in Fig. 2A). I_KATP was small (1.6 ± 0.3 pA/pF, n = 10), corresponding to 3.4 ± 0.6% of the cell total I_KATP estimated by the combined application of diazoxide and azide to open K⁺-ATP channels maximally (34). This result suggests that >95% of K⁺-ATP channels were already closed at 10 mmol/l glucose, as previously reported (35).

During constant stimulation by 10 mmol/l glucose, no oscillations of I_KATP could be detected over a period of ∼8 min (Fig. 1A), which is approximately twice as long as the period of the spontaneous oscillations of [Ca²⁺]_c induced by the sugar in single β-cells (33). In contrast, I_KATP fluctuations were detected when cell metabolism was changed by alternating the glucose concentration of the perifusion medium between 12 and 8 mmol/l (Fig. 1B). Average I_KATP was two times larger in the presence of 8 mmol/l glucose than in the presence of 12 mmol/l glucose (Fig. 1C). Moreover, decreasing the ATP-to-ADP ratio with a low concentration of azide (36), a mitochondrial poison, reversibly increased I_KATP (Fig. 1D). Therefore, the absence of apparent oscillations of I_KATP at stable glucose and [Ca²⁺]_c suggests that no intrinsic metabolic oscillations, independent from changes in [Ca²⁺]_c, exist in β-cells.

The alternative hypothesis, suggesting that metabolic oscillations in β-cells are driven by [Ca²⁺]_c oscillations, was tested by measuring the effect of an imposed increase in [Ca²⁺]_c on I_KATP. In this series, [Ca²⁺]_c and I_KATP were measured simultaneously in the same single β-cells perifused with 10 mmol/l glucose and submitted to a 30-s depolarizing pulse to 0 mV from a holding potential of −70 mV (Fig. 2A and C). In β-cells held hyperpolarized at −70 mV, [Ca²⁺]_c was low and stable, and I_KATP was small. Depolarizing the cells to 0 mV rapidly increased [Ca²⁺]_c, which slowly returned to basal levels upon repolarization to −70 mV. I_KATP was 276 ± 70% larger just after compared with before the depolarizing pulse. This increase was transient, with I_KATP decreasing with time to similar values as those before the depolarizing pulse. To ascertain that the increased current observed after the depolarizing pulse corresponds well to I_KATP, the same experiment was repeated in the presence of 250 μmol/l tolbutamide, a potent blocker of K⁺-ATP channels (Fig. 2B and D). As expected, tolbutamide reduced I_KATP in the presence of 10 mmol/l glucose (compare the beginning of Fig. 2C and D). This inhibition amounted to 63% (0.60 ± 0.01 pA/pF, n = 5, vs. 1.62 ± 0.03 pA/pF, n = 7, in the presence and absence of tolbutamide, respectively; P < 0.001). In contrast, tolbutamide did not affect the rise in [Ca²⁺]_c produced by the depolarizing pulse to 0 mV. However, the increase in current observed after the depolarizing pulse was abolished (compare Fig. 2C and D).

If the current activated by the depolarizing pulse is I_KATP, one could anticipate that it will be decreased by high glucose. This finding was tested by applying a 30-s depolarizing pulse to cells perifused with 3 or 25 mmol/l glucose (Fig. 2E and F). As expected, I_KATP measured before the depolarization to 0 mV was reduced by 45% in the presence of the high concentration of glucose (1.86 ± 0.02 pA/pF in G3, n = 6, vs. 1.03 ± 0.02 pA/pF in G25, n = 7, respectively; P < 0.001). Importantly, the increase in current observed after the 30-s depolarization to 0 mV was threefold smaller in 25 mmol/l glucose than in 3 mmol/l glucose (1.70 ± 0.26 pA/pF in G25, n = 7, vs. 5.10 ± 0.94 pA/pF, n = 6, in G3; P < 0.01), although the rise in [Ca²⁺]_c was similar at both glucose concentrations. The time for I_KATP to return to basal levels was also much reduced in the presence of 25 mmol/l glucose. Altogether, these experiments demonstrate that the increased current observed after the pulse in control cells does correspond to I_KATP and that the negative feedback effect of [Ca²⁺]_c on I_KATP can be modulated by glucose.

To ascertain that the increase in I_KATP is the consequence of the rise in [Ca²⁺]_c produced by the depolarizing pulse, the same protocol was repeated under conditions where Ca²⁺ influx was prevented. In the absence of external Ca²⁺, [Ca²⁺]_c did not increase upon depolarization, and I_KATP was of similar amplitude before and after the pulse (Fig. 3A). In the presence of 2.5 mmol/l Ca²⁺ and 10 μmol/l nimodipine, an L-type Ca²⁺ channel blocker, the depolarizing pulse to 0 mV, increased [Ca²⁺]_c only marginally (Fig. 3B). This small elevation may be attributed to the activity of the Na⁺/Ca²⁺ exchanger working in reverse mode at 0 mV or to an incomplete blockade of L-type Ca²⁺ channels. However, it was too small to affect I_KATP (Fig. 3B).

If a rise in [Ca²⁺]_c is really the cause of the increase in I_KATP, mobilization of intracellular Ca²⁺ should produce a similar effect as that of Ca²⁺ influx. Application of 100 μmol/l acetylcholine (ACh), a potent Ins(1),(4)4,(5)P₃ (IP₃)-producing agent, to hyperpolarized β-cells reversibly augmented I_KATP (Fig. 4A and B). To ascertain whether this effect resulted from a rise in [Ca²⁺]_c, the same protocol was repeated after treatment of the cell with thapsigargin, a potent and specific inhibitor of the sarco-endoplasmic reticulum Ca²⁺-ATPase. Thapsigargin depletes the endoplasmic reticulum of Ca²⁺ in β-cells (37) without impairing the production of IP₃ in response to phospholipase C-linked agonists. Addition of ACh to thapsigargin-pretreated cells did not affect I_KATP (Fig. 4C). Altogether, these experiments demonstrate that the rise in [Ca²⁺]_c is the mechanism that increases I_KATP.

Because 30-s depolarizations to 0 mV might be stronger than spontaneous depolarizations, single cells were depolarized by a voltage clamp protocol mimicking the spontaneous electrical activity in islets. Cycles of 6 s depolarization and 18 s hyperpolarization were chosen to reproduce the durations of the depolarization and repolarization phases elicited by 10 mmol/l glucose (38). During depolarization, the cell was submitted to short depolarizing pulses resembling the burst of action potential of the slow waves (see research design and methods). The left part of Fig. 5 shows spontaneous oscillations of [Ca²⁺]_c induced by 10 mmol/l glucose in a single β-cell. The right part shows [Ca²⁺]_c oscillations imposed by the voltage clamp protocol in the same cell, ∼5 min after establishment of the seal. The imposed [Ca²⁺]_c oscillations were similar to those occurring spontaneously in that cell. The average peak of [Ca²⁺]_c oscillations in several cells was not different during spontaneous oscillations (1,053 ± 91 nmol/l, n = 23) or during oscillations imposed by the pulse protocol (802 ± 132 nmol/l, n = 12) or 30-s depolarizations to 0 mV (823 ± 103 nmol/l, n = 7). Imposed [Ca²⁺]_c oscillations are thus within the physiological range.

The same pulse protocol as that used in Fig. 5 was then applied to measure the influence of [Ca²⁺]_c oscillations on I_KATP (Fig. 6). The cells were initially perifused with 6 mmol/l glucose, a subthreshold concentration at which the islets are electrically silent (1). Increasing glucose from 6 to 10 mmol/l decreased I_KATP from 1.57 to 0.89 pA/pF (n = 8). This difference in current is probably larger than that occurring in a cell that would not be voltage-clamped and in which the decrease in I_KATP produced by the acceleration of ATP production in response to the elevation of the glucose concentration is normally counterbalanced by the increase in I_KATP due to the concomitant rise in [Ca²⁺]_c. In cells voltage-clamped between −60 and −80 mV (Fig. 6), I_KATP is only influenced by the change in glucose metabolism but not by the rise in [Ca²⁺]_c that is prevented by the hyperpolarization. Application of trains of depolarization repetitively increased I_KATP (Fig. 6). The average increase was such that the current after each train was similar (1.68 ± 0.09 pA/pF) to that measured in the presence of 6 mmol/l glucose. This increase in I_KATP might thus be sufficient to repolarize the membrane below the threshold potential for activation of voltage-dependent Ca²⁺ channels. The changes in current induced by the rise of the glucose concentration and by the pulse protocol were all prevented by 250 μmol/l tolbutamide, demonstrating that they really correspond to variations in I_KATP (n = 5, not shown).

We next verified whether the Ca²⁺-induced increase in I_KATP is sufficient to repolarize the plasma membrane to the resting potential. This increase (ΔI_KATP) was calculated by averaging the difference in I_KATP after and before the last four trains of depolarizing pulses (ΔI_KATP1-4 in Fig. 6). It amounted to 0.59 ± 0.06 pA/pF. A current of similar amplitude, adjusted for cell size (0.59 multiplied by the capacitance of the tested cell), was then injected into β-cells studied in the current-clamp mode and stimulated by 10 mmol/l glucose. Figure 7A shows the electrical activity induced by glucose in one of these cells. Injection of a hyperpolarizing current corresponding to the average ΔI_KATP (−5 pA in this cell) suppressed the electrical activity and repolarized the plasma membrane to the resting level. Removal of this current was accompanied by the immediate resumption of action potentials. In other experiments (Fig. 7B), the hyperpolarizing current was increased stepwise by increments corresponding to one-sixth of the average ΔI_KATP. As shown in Fig. 7B, 50% of average ΔI_KATP was sufficient to repolarize the cell below the threshold for activation of voltage-dependent Ca²⁺ channels. This result strongly suggests that the Ca²⁺-induced rise in I_KATP might control the oscillations of the membrane potential.

Oscillations of the membrane potential are one of the major characteristics of the pancreatic β-cell response to glucose. They underlie the periodic influx of Ca²⁺ that triggers oscillations of insulin secretion. Understanding their fine control is thus of utmost importance. The present study demonstrates that [Ca²⁺]_c oscillations in pancreatic β-cells rhythmically increase I_KATP and provide direct support to the proposal (20) that such an effect constitutes a feedback control of the oscillations of membrane potential.

It has been suggested that intrinsic Ca²⁺-independent metabolic oscillations exist in β-cells (24) and that they lead to cycles of K⁺-ATP channel activity (23). To verify this hypothesis, single metabolically intact β-cells were hyperpolarized to keep [Ca²⁺]_c at basal and stable levels, and I_KATP was continuously monitored during perifusion with a stimulatory glucose concentration. In no cell did we find I_KATP oscillations under these conditions. This suggests that either no intrinsic metabolic oscillations exist, or they are unable to modulate K⁺-ATP channel activity and membrane potential because of their nature or small amplitude (smaller than those imposed by 4 mmol/l glucose changes). Experiments monitoring O₂ consumption (39), glucose consumption (27), and the fluorescence of reduced pyridine nucleotides [NAD(P)H) in single islets (6)] have also concluded to the absence of Ca²⁺-independent metabolic oscillations in β-cells.

When [Ca²⁺]_c was increased by stimulating Ca²⁺ influx or mobilizing Ca²⁺ from intracellular Ca²⁺ stores, I_KATP increased. There is no doubt that this increase resulted from the [Ca²⁺]_c rise because I_KATP did not change when Ca²⁺ influx was prevented by omission of external Ca²⁺ and blockade of voltage-dependent Ca²⁺ channels or when Ca²⁺ mobilization was prevented by pretreatment with thapsigargin. It is also clear that the current increased by the rise in [Ca²⁺]_c is I_KATP because it was attenuated by a rise in ambient glucose concentration and completely inhibited by tolbutamide, a blocker of K⁺-ATP channels. K⁺ channels sensitive to sulfonylureas but distinct from K⁺-ATP channels have been described in some systems (40,41), but not in β-cells. It is likely that the current that we studied here is similar to the voltage-independent Ca²⁺-activated K⁺ current previously described in β-cells (14). This current, which was originally thought to not involve K⁺-ATP channels (14), was recently found to be largely sensitive to tolbutamide by the same authors (42).

A rise in [Ca²⁺]_c could increase I_KATP by different mechanisms, including a direct action of Ca²⁺ on K⁺-ATP channels, an indirect action through Ca²⁺-sensitive regulators of the channels, and an indirect action through changes in cell metabolism. A direct effect of Ca²⁺ on K⁺-ATP channels has been reported in inside-out patches of membranes of normal β-cells or tumoral insulin-secreting RINm5F cells in which application of Ca²⁺ inhibited K⁺-ATP channels (millimolar range of Ca²⁺) (43) and attenuated the ADP-induced channel activation (micromolar range of Ca²⁺) (44). Ca²⁺ increased the ability of ATP to block K⁺-ATP channels or inactivated these channels in inside-out patches of skeletal muscle (45) and ventricular (46) membranes. However, all these effects are opposite to the Ca²⁺-induced increase in I_KATP observed in the present study. Others did not find any direct effect of Ca²⁺ on K⁺-ATP channels in β-cells (9). It is worth noting that the K⁺-ATP channels of β-cells and muscle cells have different subunit compositions (SUR1 and Kir6.2 for β-cells and SUR2 and Kir6.2 for muscle cells) (47), which might confer different sensitivities to Ca²⁺.

Several Ca²⁺-dependent processes influencing K⁺-ATP channels have been described in pancreatic β-cells or muscle cells. They involve cytoskeletal proteins (44), the Ca²⁺-dependent protein phosphatase type 2B (48), or other proteins (49). Activation of phospholipase C by Ca²⁺, with subsequent hydrolysis of phosphatidylinositol 4,5-bisphosphate (PIP₂), is unlikely to be involved for two reasons. First, acceleration of PIP₂ breakdown would be expected to decrease I_KATP (44), which is opposite to the effect of a rise in [Ca²⁺]_c observed in the present study. Second, ACh, a potent Ca²⁺-independent activator of phospholipase C, was without effect on β-cell I_KATP when Ca²⁺ mobilization was prevented by thapsigargin pretreatment.

Metabolic oscillations might be driven by [Ca²⁺]_c oscillations. Indeed, each rise in [Ca²⁺]_c could stimulate ATP production (50) and increase the ATP-to-ADP ratio by activating mitochondrial dehydrogenases (51,52). Oscillations of oxygen consumption driven by [Ca²⁺]_c oscillations have recently been reported in islets (27). Our data do not exclude this possibility. Alternatively, each rise in [Ca²⁺]_c could decrease the ATP-to-ADP ratio. This hypothesis is supported by direct measurements of adenine nucleotide levels within mouse islets (25) or of ATP concentration in INS-1 cells expressing luciferase (53). These studies demonstrated that, at a fixed glucose concentration, the ATP-to-ADP ratio and the ATP concentration decreased when [Ca²⁺]_c was raised by high K⁺. By demonstrating that a rise in [Ca²⁺]_c increases I_KATP, the present study supports this proposal. The drop in the ATP-to-ADP ratio could either result from inhibition of ATP production (26,54) or stimulation of ATP consumption (25,53).

In glucose-stimulated β-cells, I_KATP was found to be larger during the interburst intervals than during the depolarizing phases (22). These fluctuations were tentatively ascribed to metabolic oscillations, but no mechanistic explanation was provided. The present study strongly suggests that the rise in [Ca²⁺]_c might be the feedback mechanism controlling I_KATP and hence the oscillations of the membrane potential. Thus, during a voltage clamp protocol mimicking the repetitive changes in electrical activity induced by 10 mmol/l glucose in islets, each imposed [Ca²⁺]_c oscillation evoked a transient increase in I_KATP. This increase had a similar amplitude to that of the difference in I_KATP measured at substimulating (6 mmol/l) and stimulating (10 mmol/l) glucose concentrations. Theoretically, this current should be able to repolarize the membrane to a potential more negative than that of the activation threshold of voltage-dependent Ca²⁺ channels. This finding was amply supported by current-clamp experiments. Injection of current corresponding to 50% of the Ca²⁺-induced I_KATP increase was sufficient to repolarize the β-cell membrane in the presence of 10 mmol/l glucose. Because the voltage-dependent Ca²⁺ current is larger in β-cells within intact islets than in isolated single cells (29), it is possible that the amplitude of the Ca²⁺-induced increase in I_KATP in whole islets exceeds our estimate. We have no explanation why, in a previous report, no oscillations of I_KATP were detected in single β-cells displaying membrane potential oscillations (55). The reported experimental procedures were indeed similar to those used in the present study.

The negative feedback effect of [Ca²⁺]_c on I_KATP might be important for the control of oscillations of the β-cell membrane potential according to the following model. Acceleration of glucose metabolism in β-cells increases the ATP-to-ADP ratio, which closes K⁺-ATP channels. This leads to depolarization of the plasma membrane and opening of voltage-dependent Ca²⁺ channels. Ca²⁺ influx then raises [Ca²⁺]_c, which decreases the ATP-to-ADP ratio (25) and leads to reopening of K⁺-ATP channels, partial repolarization of the plasma membrane, arrest of Ca²⁺ influx, and a drop in [Ca²⁺]_c. The eventual restoration of a high ATP-to-ADP ratio then initiates a new cycle. Our observation that the negative feedback effect of [Ca²⁺]_c on I_KATP is largely attenuated by glucose can explain the lengthening of the depolarized phases and shortening of the repolarized intervals occurring when the glucose concentration is raised within the stimulatory range. Indeed, as the glucose concentration increases, the ATP-to-ADP ratio rises and closes more K⁺-ATP channels. The depolarizing phase progressively becomes longer because a stronger feedback effect of Ca²⁺ on I_KATP is required to counteract the effects of increased metabolism on I_KATP. Continuous electrical activity occurs at glucose concentrations that reduce I_KATP to such an extent that it is no longer counteracted by the [Ca²⁺]_c rise unless the latter is increased by augmenting the extracellular Ca²⁺ concentration (20).

The central role of K⁺-ATP channels in membrane potential oscillations suggested in our model are compatible with those in most studies on K⁺-ATP channel-deficient mice. Thus, pancreatic β-cells from SUR1 or Kir 6.2 knockout mice display a continuous spike activity (56,57) and a sustained and stable elevation of [Ca²⁺]_c (56,58) at both nonstimulating and stimulating glucose concentrations. Only one abstract reported [Ca²⁺]_c oscillations in β-cells from SUR1 knockout mice, but it is not known whether these oscillations resulted from concomitant changes in membrane potential (59). In view of the important role played by K⁺-ATP channels in the control of pancreatic β-cell membrane potential, further studies should now elucidate the interplay between [Ca²⁺]_c and ATP turnover.

This work was supported by Grant 3.4552.98 from the Fonds de la Recherche Scientifique Médicale (Brussels), by Grants 1.5.212.00 and 1.5.121.00 from the Fonds National de la Recherche Scientifique (Brussels), by Grant ARC 00/05-260 from the General Direction of Scientific Research of the French Community of Belgium, and by the Interuniversity Poles of Attraction Program (P4/21), Federal Office for Scientific, Technical and Cultural Affairs of Belgium. P.G. is Maître de Recherches of the Fonds National de la Recherche Scientifique, Brussels.