A novel calcium-dependent potassium current (Kslow) that slowly activates in response to a simulated islet burst was identified recently in mouse pancreatic β-cells (Göpel, S.O., T. Kanno, S. Barg, L. Eliasson, J. Galvanovskis, E. Renström, and P. Rorsman. 1999. J. Gen. Physiol. 114:759–769). Kslow activation may help terminate the cyclic bursts of Ca2+-dependent action potentials that drive Ca2+ influx and insulin secretion in β-cells. Here, we report that when [Ca2+]i handling was disrupted by blocking Ca2+ uptake into the ER with two separate agents reported to block the sarco/endoplasmic calcium ATPase (SERCA), thapsigargin (1–5 μM) or insulin (200 nM), Kslow was transiently potentiated and then inhibited. Kslow amplitude could also be inhibited by increasing extracellular glucose concentration from 5 to 10 mM. The biphasic modulation of Kslow by SERCA blockers could not be explained by a minimal mathematical model in which [Ca2+]i is divided between two compartments, the cytosol and the ER, and Kslow activation mirrors changes in cytosolic calcium induced by the burst protocol. However, the experimental findings were reproduced by a model in which Kslow activation is mediated by a localized pool of [Ca2+] in a subspace located between the ER and the plasma membrane. In this model, the subspace [Ca2+] follows changes in cytosolic [Ca2+] but with a gradient that reflects Ca2+ efflux from the ER. Slow modulation of this gradient as the ER empties and fills may enhance the role of Kslow and [Ca2+] handling in influencing β-cell electrical activity and insulin secretion.

β-Cells of the islets of Langerhans control blood glucose levels by secreting insulin in response to an increase in extracellular glucose. At glucose concentrations ≥7 mM, glucose metabolism triggers rhythmical electrical activity in mouse islets. This activity consists of periodic depolarizing plateaus with superimposed rapid spikes, separated by silent phases of −65 mV (Dean and Matthews, 1968, 1970; Meissner and Schmelz, 1974; Rosario et al., 1993; Satin and Smolen, 1994). Glucose-induced closure of ATP-dependent potassium (KATP) channels depolarizes islets to about −50 mV, where bursting commences. The spikes and plateaus are mediated by voltage-activated Ca2+ channels (Meissner and Schmeer, 1981; Ribalet and Beigelman, 1981) and increasing glucose increases calcium influx, [Ca2+]i, and insulin secretion by prolonging the spiking plateau phase and concomitantly shortening the silent phase (Cook, 1984). β-Cell electrical activity is tightly coupled to insulin secretion, since the spiking phase duration and the rate of insulin secretion have the same dependence on glucose concentration (Meissner and Schmelz, 1974; Wollheim and Sharp, 1981; Ashcroft and Rorsman, 1989).

Despite extensive investigation, the ionic basis of islet pacemaking is still incompletely understood. The cyclic activation of Ca2+-activated K+ (KCa) current has long been considered a candidate ionic pacemaker mechanism (Atwater et al., 1979; for reviews see Satin and Smolen, 1994; Sherman, 1996), since islet bursting is readily simulated by theoretical models that incorporate the activation and deactivation of KCa channels by bursting-induced [Ca2+]i oscillations (i.e., Chay and Keizer, 1985). However, direct characterization of the rapidly activating, large conductance KCa channels of β-cells that were the first KCa channels identified in these cells (Cook et al., 1984) raised doubts that they constituted the primary pacemaker mechanism. In particular, charybdotoxin, a selective inhibitor of large conductance KCa channels, was reported to have no effect on islet electrical activity (Kukuljan et al., 1991), and the voltage dependence of these channels is incompatible with their mediating a sustained repolarization to −65 mV after each burst. In addition, studies using [Ca2+]-sensing fluorescent dyes to monitor temporal changes in [Ca2+]i during islet bursting suggest that islet [Ca2+]i rises rapidly to a steady-state plateau at the beginning of each burst (Santos et al., 1991). This observation would seem to be incompatible with models requiring that [Ca2+]i accumulate slowly during each burst and gradually activate Ca2+-dependent K+ current to terminate the burst (for review see Satin and Smolen, 1994).

The recent report of a slowly activating KCa current (Kslow) observed in in situ β-cells has led to renewed interest in a KCa-dependent model of islet bursting (Göpel et al., 1999). Göpel et al. (1999) presented evidence that Kslow tracks [Ca2+]i as it slowly rises in response to a voltage clamp command designed to mimic an islet burst. In contrast to the fast β-cell KCa channel (Kukuljan et al., 1991), Kslow was insensitive to charybdotoxin or low concentrations of TEA, and its conductance was voltage-independent between −80 and −40 mV (Göpel et al., 1999). Together, these properties make Kslow a more attractive candidate than the large conductance KCa channel for mediating islet pacemaking.

In this study, we examined whether agents known to alter the [Ca2+]i dynamics of β-cells affect Kslow. Of special interest to us was the possibility that altering the Ca2+ filling state of the β-cell endoplasmic reticulum would alter Kslow. Recent reports suggested that thapsigargin (Tg),* a well-known blocker of the sarco/endoplasmic calcium ATPase (SERCA), partially suppresses Kslow in in situ β-cells (Göpel et al., 1999) and inhibits K+ efflux through tolbutamide- and charybdotoxin-insensitive K+ channels in islets (Hennige et al., 2000). Here we show that Tg has a biphasic effect on Kslow, consisting of transient potentiation followed by sustained inhibition of the channel. Further, we show that insulin, which has also been reported to block SERCA through insulin receptor phosphorylation of IRS-1 in β-cells (Xu et al., 1999), has the same biphasic effect on Kslow as Tg. These results can be accounted for by a novel model in which Kslow activation depends on the buildup of [Ca2+] in a restricted submembrane space between the ER and the plasma membrane of the β-cell. In contrast, a more simplified model of β-cell Ca2+ handling including an ER component but lacking the subspace is unable to duplicate our experimental findings. The subspace model is a variant of our recent Phantom Burster Model of islet bursting (Bertram et al., 2000), in which two slow negative feedback processes combine to produce a range of intermediate electrical oscillations. In addition to reproducing Kslow currents measured in voltage-clamp, the model also reproduces the electrical bursting we see in elevated glucose. Finally, the model accounts for the previously reported depolarizing effects of Tg on islet electrical activity (Worley et al., 1994a, Bertram et al., 1995) without recourse to store-operated (SOC or CRAC) currents.

Cell Culture

Pancreatic islets were isolated from male Swiss-Webster mice that were killed by cervical dislocation. The bile duct of the pancreas was cannulated and injected with collagenase (2 mg/ml) dissolved in Kreb's solution consisting of (in mM): 135 NaCl, 5 KCl, 1 CaCl2, 1.2 MgCl2, 10 HEPES, 5 NaHCO3, 5 glucose, 1 mg/ml bovine serum albumin, and 1% penicillin-streptomycin, pH. 7.35. Alternatively, collagenase was dissolved in Kreb's and then injected directly into the pancreas. The pancreas was then removed, placed in a culture dish, and incubated at 37°C for 5–10 min until the exocrine tissue was digested. Collagenase digestion was stopped by the addition of cold Kreb's solution. Tissue was then washed, triturated using a Pasteur pipette, and centrifuged. Islets were picked and placed into fresh Kreb's solution cooled to 4°C. Islets were then picked a second time, transferred to culture dishes containing enriched RPMI-1640 culture medium, and incubated at 37°C for 2–4 d.

To produce dispersed β-cells, islets were placed in a Ca2+-free solution containing 9.5 mg/ml Spinners salts, 3 mM EGTA, 16 mM glucose, 1 mg/ml bovine serum albumin, pH 7.35, incubated at 37°C for 3 min and triturated lightly until the islets were fully dispersed into single cells. The resulting cell suspension was then centrifuged for 5 min. Following removal of the supernatant, cells were washed with Kreb's solution, and centrifuged again for 5 min. The supernatant was removed and the dispersed cells were resuspended in enriched RPMI-1640 medium (as above) and then plated onto glass coverslips. Cells were kept at 37°C in an air/CO2 incubator and fed every 2–3 d.

Electrophysiology

Glass coverslips containing dispersed β-cells were transferred to a recording chamber held at 35°C mounted on an Olympus IX70 inverted microscope. Intact islets were immobilized using a large diameter suction pipette (Göpel et al., 1999). Electrical activity and whole-cell currents were recorded using an Axopatch 200 B amplifier (Axon Instruments, Inc.) and the perforated patch technique (Falke et al., 1989,). Patch electrodes were pulled from borosilicate glass capillaries (WPI) and their tips were filled with a solution containing (in mM) 76 K2SO4, 10 NaCl, 10 KCl, 1 MgCl2, and 5 mM HEPES, pH 7.35. The pipettes were then back-filled with the same internal solution containing 0.3 mg/ml amphotericin B. Increased pipette-cell capacitance and decreased series resistance signaled successful perforation. Experiments commenced when a steady zero current potential was obtained, usually within 2–15 min of obtaining a gigaseal. The external recording solution contained (in mM): 140 NaCl, 3.6 KCl, 2 NaHCO3, 0.5 NaH2PO4, 0.5 MgSO4, 5 HEPES, pH 7.4. External solution was prewarmed to 35°C and the recording chamber was perfused at a rate of 2.5 ml/min. Data were filtered at 1 kHz and digitized at 2–5 kHz using a Macintosh G4 computer (Apple Computer) equipped with an Instrutech ITC-16 interface (Instrutech) and Pulse Control (Herrington and Bookman, 1994) and Igor Pro software (Wavemetrics). To identify β-cells in situ, only cells that displayed rhythmic bursting activity in the presence of 10 mM glucose were selected for study. Single cell capacitance was calculated by integrating the transient current response to a small hyperpolarizing voltage step. In the voltage clamp mode, cells were clamped to a standard holding potential of −65 mV. Kslow current was assayed using a simulated pulse burst protocol similar to that used by Göpel et al. (1999). This protocol consisted of a 5-s depolarizing step from −65 to −40 mV followed by either a train of 26 voltage ramps, each lasting 200 ms, from −40 to 0 mV and back to −40 mV or by a train of 26 voltage steps from −40 to 0 mV, each lasting 150 ms with a 50-ms interval in between each step (Fig. 2 A). The train of depolarizations was followed by a step back to −40 mV for 10 s before the membrane potential was returned to −65 mV. In experiments where voltage-gated Ca2+ current was studied, current was measured in whole-cell mode in response to a series of 200-ms voltage steps from −65 to 10 mV applied at 0.2 Hz. To isolate Ca2+ current, Na+ and K+ currents were blocked by the addition of TTX (0.5 μM) and TEA (20 mM), respectively, to the extracellular solution, and CsCl substituted for K2SO4 in the patch pipette solution. Tg and cyclopiazonic acid were prepared as stock solutions in DMSO and insulin and apamin were prepared as stock solutions in water. All stocks were diluted 1:1,000 to 1: 5,000 for experiments. Cytochrome C was added to control and drug solutions when insulin or apamin were used.

Data Analysis

Statistical analysis was performed using Microsoft Excel for Macintosh or GraphPad Prism 2.0. Data are expressed as mean ± SEM. Significance was determined using Student's t tests or ANOVA.

Modeling

To test the hypothesis that Kslow is activated by Ca2+ that is released from the ER and accumulates in a small submembrane compartment, we constructed a mathematical model. Our main goal was to determine if such a model could account for the biphasic response of Kslow to SERCA inhibition. Additionally, we used the model to explore what role such a Ca2+-activated K+ current could play in mediating the oscillatory electrical activity that is characteristic of islets.

As in other β-cell models, we started with a current balance equation that determines the membrane potential, V,

\[\mathrm{C}_{\mathrm{m}}\mathrm{d}{V}/{\mathrm{dt}}={-}I_{\mathrm{Ca}}{-}I_{\mathrm{Kv}}{-}I_{\mathrm{KCa}}{-}I_{\mathrm{KATP}}{-}I_{\mathrm{Leak}}\mathrm{.}\]
(1)

The relatively fast voltage-dependent Ca2+ current ICa and delayed rectifying K+ current IKv mediate the fast spiking of the active phase; IKCa is the Ca2+-activated K+ current corresponding to Kslow; and IKATP is the ATP-dependent K+ current. To isolate the rhythmogenic potential of Kslow, IKATP was modeled as a current having a constant conductance. We describe the dependence of IKCa on Ca2+ by a steep Hill function,

\[I_{\mathrm{KCa}}={g_{\mathrm{KCa}}\left[\mathrm{Ca}^{\mathrm{2+}}\right]^{\mathrm{q}}}/{\left(\left[\mathrm{Ca}^{\mathrm{2+}}\right]^{\mathrm{q}}+K_{\mathrm{d}}^{\mathrm{q}}\right)}\left(V{-}V_{\mathrm{K}}\right)\mathrm{.}\]
(2)

A complete list of parameter values and details of the remaining ionic currents, which are similar to those in previous models, are available. The main emphasis here is on the compartmentalization of Ca2+ into intracellular pools. We first considered the simplest model (Model I) that could conceivably simulate the effects of SERCA inhibition. This model consisted of two compartments, the cytosol and the ER, with their Ca2+ concentrations denoted c and cER, respectively,

\[{\mathrm{d}c}/{\mathrm{dt}}=f_{\mathrm{CYT}}\left(\mathrm{J}_{\mathrm{IN}}{-}\mathrm{J}_{\mathrm{PMCA}}{-}\mathrm{J}_{\mathrm{SERCA}}+\mathrm{J}_{\mathrm{RELEASE}}\right)\]
(3)
\[\mathrm{d}{c_{\mathrm{ER}}}/{\mathrm{dt}}=f_{\mathrm{ER}}\left({\mathrm{V}_{\mathrm{CYT}}}/{\mathrm{V}_{\mathrm{ER}}}\right)\left(\mathrm{J}_{\mathrm{SERCA}}{-}\mathrm{J}_{\mathrm{RELEASE}}\right)\mathrm{.}\]
(4)

The Js are fluxes into the cell through plasma membrane Ca2+ channels (JIN), out of the cell through the plasma-membrane Ca2+-ATPase (JPMCA), from the cytosol to the ER through the SERCA pump (JSERCA), and from the ER to the cytosol through ER Ca2+ channels (JRELEASE). Ca2+ efflux mediated by the plasma membrane Ca2+-ATPase (PMCA) takes the form JPMCA = kPMCA c, whereas the SERCA pump flux is JSERCA = kSERCA c. The plasma membrane influx is related to the Ca2+ current by JIN = −α ICa, where α is a proportionality constant that converts Ca2+ current to Ca2+ flux. Ca2+ efflux corresponding to Ca2+ release from the ER was taken to be proportional to the Ca2+ concentration gradient between the ER and the cytosol,

\[\mathrm{J}_{\mathrm{RELEASE}}=\mathrm{p}_{\mathrm{ER}}\left(\mathrm{c}_{\mathrm{ER}}{-}\mathrm{c}\right)\mathrm{.}\]
(5)

JRELEASE could represent flux mediated by either inositol 1,4,5 trisphospate (IP3) or ryanodine (RyR) receptors (Ämmala et al., 1991; Barker et al., 1994; Gromada et al., 1996; Liu et al., 1996; Islam et al., 1998); our model does not require that the detailed properties of these specific channel mechanisms be taken into account. The ratio of cytosolic to ER volume, VCYT/VER, incorporates the differential effects of Ca2+ uptake and release on the ER and cytosol due to differences in their respective volumes.

As will be shown in the results section, this simple model could not account for the inhibition of Kslow after SERCA inhibition. One way to resolve this discrepancy is to add regenerative Ca2+-induced Ca2+ release (CICR) to the model. Such a model can indeed account for the biphasic response of Kslow to thapsigargin, because the loss of CICR when stores are depleted results in lower levels of [Ca2+]i. However, previously published experimental data show that depolarization-induced [Ca2+]i elevations are increased and not decreased by thapsigargin (Liu et al., 1995; Miura et al., 1997; Gilon et al., 1999; Arredouani et al., 2002).

Thus, we rejected the CICR model and considered an alternative. We added a third pool to the model, a submembrane compartment (referred to as the subspace for brevity) having concentration denoted cSS. We refer to this version as Model II. In this case, c represents [Ca2+] in a bulk cytoplasmic compartment, which is distinct from a more restricted subspace and is referred to as just the cytosol for brevity. In this model, Ca2+ that passively enters the cell through plasmalemmal Ca2+ channels is actively sequestered into the ER via SERCA and then leaks out of the ER to increase cSS. The subspace in turn passively exchanges Ca2+ with the cytosol, whence it is pumped out of the cell. See the diagram in Fig. 1. Although flux from the cytosol to the subspace can occur, release of Ca2+ from the ER maintains a standing gradient between the ER and the cytosol, which tends to drive Ca2+ from the subspace to the cytosol. As long as the ER is replete, subspace [Ca2+] will be greater than bulk cytosolic [Ca2+]. We further postulate that this elevated fraction of Ca2+ is essential for Kslow activation. The corresponding equations for Model II are:

\[{\mathrm{d}c}/{\mathrm{dt}}=f_{\mathrm{CYT}}\left(\mathrm{J}_{\mathrm{IN}}{-}\mathrm{J}_{\mathrm{PMCA}}{-}\mathrm{J}_{\mathrm{SERCA}}+\mathrm{J}_{\mathrm{X}}\right)\]
(6)
\[\mathrm{d}{c_{\mathrm{ER}}}/{\mathrm{dt}}=f_{\mathrm{ER}}\left(\left[{\mathrm{V}_{\mathrm{CYT}}}/{\mathrm{V}_{\mathrm{ER}}}\right]\mathrm{J}_{\mathrm{SERCA}}{-}\mathrm{J}_{\mathrm{RELEASE}}\right)\]
(7)
\[\mathrm{d}{c_{\mathrm{SS}}}/{\mathrm{dt}}=f_{\mathrm{SS}}\left(\left[{\mathrm{V}_{\mathrm{ER}}}/{\mathrm{V}_{\mathrm{SS}}}\right]\mathrm{J}_{\mathrm{RELEASE}}{-}{\mathrm{V}_{\mathrm{CYT}}}/{\mathrm{V}_{\mathrm{SS}}\mathrm{J}_{\mathrm{X}}}\right)\mathrm{.}\]
(8)

JIN, JPMCA, and JSERCA are the same as in Model I, but Ca2+efflux from the ER is now proportional to the Ca2+ concentration gradient between the ER and the subspace rather than the bulk cytosol,

\[\mathrm{J}_{\mathrm{RELEASE}}=\mathrm{p}_{\mathrm{ER}}\left(\mathrm{c}_{\mathrm{ER}}{-}\mathrm{c}_{\mathrm{SS}}\right)\mathrm{,}\]
(9)

and the exchange flux between subspace and cytosol is proportional to the concentration gradient between those two compartments,

\[\mathrm{J}_{\mathrm{X}}=\mathrm{p}_{\mathrm{X}}\left(\mathrm{c}_{\mathrm{SS}}{-}\mathrm{c}\right)\mathrm{.}\]
(10)

The volume ratios again take into account the differential effect of each of the fluxes due to differences in the volumes of the communicating compartments, and now include the volume of the subspace, VSS. The numerical values we used were VCYT/VER = 25.0 and VCYT/VSS = 2.5. Note that in the model, the subspace is not microscopically small—it merely needs to be small enough to generate about a twofold Ca2+ concentration gradient between the subspace and the cytosol.

In the absence of quantitative details of these compartments, we made the model as simple as possible, while still consistent with the observed integrated behavior of the β-cells under varying conditions. These include both voltage clamp and free running conditions, and the presence and absence of SERCA inhibitors. For example, we have not included SERCA and PMCA pumps in the subspace compartment since they are not needed, but these could be included, provided they are not so strong as to destroy the concentration gradient between the subspace and the cytosol. Similarly, some degree of Ca2+ release from the ER directly to the cytosol can be accommodated, but in excess would flatten the subspace-cytosol gradient. Finally, pER could have been formulated as a Ca2+-dependent parameter to incorporate some degree of CICR in the model. However, we omitted it to make clear that this added complexity is not needed to explain the data.

Model equations were integrated using standard numerical methods as implemented in the public domain program XPP (http://www.math.pitt.edu/~bard/xpp/xpp.html) running under Linux (XPP is also available for Windows). Visualization and graphical analysis were performed using XPP or XMGR for Linux (http://plasma-gate.weizmann.ac.il/Xmgr).

Online Supplemental Material

List of parameter values and details of ionic currents are available.

Kslow Is Modulated by SERCA Inhibitors

Because it has been reported that Kslow is Ca2+ dependent (Göpel et al., 1999), we investigated the effect of agents that are known to alter [Ca2+]i on Kslow current. We first examined the effect of Tg, a SERCA pump inhibitor, which reduces Ca2+ influx into the ER, ultimately resulting in depletion of the ER Ca2+ store (Thastrup et al., 1990; Islam et al., 1992). Using the perforated patch technique (Falke et al., 1989), isolated β-cells were voltage clamped to a holding potential of −65 mV and ionic current was measured in response to a voltage command that simulated an islet burst (see materials and methods). Application of this voltage protocol elicited a slowly activating outward current that closely resembled Kslow, as described previously (Göpel et al., 1999). Fig. 2 A shows the total current (top trace) elicited by the simulated burst protocol (bottom trace) in a single dispersed mouse β-cell. Stepping membrane potential from −65 to −40 mV produced a small net increase in outward current in most cells (arrow 1). The subsequent 5-Hz train of membrane depolarizations from −40 to 0 mV activated transient outward currents during each pulse of the train (arrow 2). Kslow activation was manifested as a slow increase in outward holding current at −40 mV, which typically continued for the duration of the burst (arrow 3). Upon cessation of the pulse train, the slowly activating outward current gradually decreased as Kslow deactivated (arrow 4). Kslow amplitude was measured as the difference between the maximal “tail” current at the end of the train of fast depolarizations and the steady-state current at −40 mV after the burst (arrow 5).

Dispersed β-cells possessed robust Kslow current having a mean amplitude of 10.8 ± 1.4 pA (n = 51) that exhibited the same pharmacological properties and current-voltage (I-V) relationship reported previously by Göpel et al. (1999). Thus, the tail of Kslow current measured at the end of the pulse train reversed at −69 mV (inset, Fig. 2 A) and was completely blocked by the Ca2+ channel blockers nimodipine (10 μM) or CdCl2 (200 μM); or intracellular Cs+, which blocks K+ channels. The current was partially blocked (48%) by 20 mM TEA, and was insensitive to 100 nM charybdotoxin or 1 μM apamin (unpublished data). Although similar to Göpel et al. (1999), the pharmacological properties of the Kslow current in the present study differ slightly from an apamin-insensitive KCa channel found in murine βTC-3 cells, which is inhibited by 100 nM charybdotoxin (Kozak et al., 1998). In contrast to Göpel et al. (1999), who reported that dispersed β-cells possessed much smaller Kslow current than in situ β-cells, we found that the amplitudes of Kslow currents measured from dispersed and in situ β-cells exhibited significant overlap (Fig. 2 B).

The application of 5 μM Tg to dispersed β-cells resulted in the biphasic modulation of Kslow current (Fig. 3). Thus, in 10 of 13 cells tested, the addition of Tg transiently increased Kslow amplitude within 3 min, and continued Tg exposure nearly completely suppressed Kslow within 5–15 min (Fig. 3, A and B). In 3 of 13 cells, we found that Tg suppressed Kslow current without exhibiting the initial potentiation phase. After Tg treatment, the mean Kslow current density for all cells rose significantly from 1.9 ± 0.3 pA/pF to 2.6 ± 0.3 pA/pF, and then decreased to 0.2 ± 0.1pA/pF (n = 13, P < 0.05) (Fig. 3 C). This is in contrast to a preliminary report that Tg only partly reduces Kslow in in situ β-cells (Göpel et al., 1999, 2001). The changes in Kslow amplitude we observed were not accompanied by changes in the activation or decay rate of Kslow (Fig. 3 D). The mean time for 10–90% activation of Kslow current was 1.8 ± 0.3 versus 1.9 ± 0.3 s (n = 13; P > 0.05) before and after Tg treatment, respectively, whereas the mean 50% decay time was 0.8 ± 0.2 versus 0.7 ± 0.1 s (n = 13; P > 0.05), for control and Tg treatment, respectively. Changes in Kslow amplitude produced by Tg were not due to current rundown or drift since control experiments showed that the current amplitude was stable over the length of the experiments (unpublished data). We also considered whether Kslow potentiation might be secondary to an increase in [Ca2+]i due to the activation of CRAC channels (Worley et al., 1994a,b; Liu and Gylfe, 1997; Roe et al., 1998). Although Tg application did result in an increase in the inward holding current at −65 mV or the step in current resulting from changing V from −65 to −40 mV in some cells (unpublished data), these changes were not statistically significant. Thus, it is unlikely that CRAC activation accounts for the large changes we observed in Kslow after Tg treatment.

Similar results were obtained with the application of 1 μM Tg or 50 μM cyclopiazonic acid (CPA). The lower dose of Tg transiently increased then inhibited Kslow in one of six cells and inhibited Kslow without potentiation in five of six cells. This effect was irreversible. Likewise, CPA, a reversible SERCA inhibitor, transiently increased then inhibited Kslow in two of four cells and only inhibited Kslow in the remaining two cells. The effects of CPA were reversible.

The application of 1 μM Tg to unclamped dispersed β-cells resulted in an initial hyperpolarization then depolarization of membrane potential and could increase fast spiking (n = 4), consistent with previous reports (Worley et al., 1994a; Bertram et al., 1995; Gilon et al., 1999).

It has been shown recently that insulin activation of β-cell insulin receptors increases [Ca2+]i by inhibiting SERCA via an IRS-1–dependent pathway (Xu et al., 1999). Therefore, we tested the hypothesis that insulin inhibition of β-cell SERCA would modulate Kslow similarly to Tg. We found that the application of 200 nM insulin to dispersed β-cells produced effects that indeed closely resembled those observed with Tg (Fig. 4). Thus, in 10 of 12 cells tested, exogenous insulin increased Kslow current amplitude within 2 min, and continued insulin exposure suppressed Kslow within 5 min (Fig. 4 B). Insulin increased the mean Kslow current density of all cells from 1.0 ± 0.1 pA/pF to 1.6 ± 0.3 pA/pF, followed by a reduction to 0.5 ± 0.2 pA/pF (n = 12; P < 0.05) (Fig. 4 C). As we found with Tg, insulin did not change the 10–90% activation rate of Kslow, which was 1.2 ± 0.3 versus 1.1 ± 0.3 s (n = 12; P > 0.05) for control and insulin treatment, respectively. However, Kslow decayed more slowly in the presence of insulin (Fig. 4 D), such that the mean time for 50% decay of Kslow increased from 0.3 ± 0.1 to 0.6 ± 0.2 s (n = 12; P < 0.05). Insulin exposure did not significantly change the amplitude of inward holding current at −65 mV. However, insulin did increase the size of the step current evoked by changing membrane potential from −65 to −40 mV. This current increased from 5.6 ± 1.6 to 9.5 ± 3.1 pA (n = 12, P < 0.05), consistent with our recently reported finding that insulin activates KATP channels in mouse β-cells (Khan et al., 2001) (Fig. 4 E).

Because it had been reported that insulin can augment L-type Ca2+ channel current in isolated rat ventricular myocytes (Aulbach et al., 1999), we considered whether the transient increase in Kslow current amplitude we observed might be secondary to an insulin-induced increase in Ca2+ influx through voltage-sensitive Ca2+ channels. Therefore, we examined the effect of insulin on the voltage-sensitive Ca2+ currents of β-cells in a parallel study. As shown in Fig. 4 F, insulin did not significantly alter β-cell Ca2+ current, suggesting that Kslow potentiation does not appear to be due to the potentiation of β-cell Ca2+ channels.

Our finding that the depletion of ER Ca2+ stores by SERCA inhibitors modulates Kslow, ultimately leading to its suppression, is consistent with the hypothesis that ER Ca2+ stores are involved in the activation and regulation of Kslow current in β-cells. Since the long-term consequence of Tg exposure is to deplete the ER of Ca2+, this suggests that filling of the β-cell Ca2+ stores is required for Kslow activation. This hypothesis was developed further by constructing a mathematical model of β-cell Ca2+ handling (see below).

Modulation of Kslow by Glucose

We next examined the sensitivity of Kslow to changes in extracellular glucose, which may alter intracellular Ca2+ handling by changing the energetics of the β-cell, since plasmalemmal Ca-ATPases and SERCA consume ATP. In dispersed β-cells, raising extracellular glucose from 5 to 10 mM shifted the holding current at −65 mV in the inward direction, from −5.2 ± 1.9 pA to −10.9 ± 2.6 pA (n = 8, P < 0.05), which would be expected for glucose-induced closure of KATP channels after a rise in ATP/ADP (Cook and Hales, 1984; Rorsman and Trube, 1985). In contrast to Göpel et al. (1999)(2001), we found that raising extracellular glucose reduced Kslow current density more than twofold, from 4.7 ± 1.3 to 2.2 ± 0.8 pA/pF (n = 8, P < 0.01) (Fig. 5).

One possible explanation for the inhibitory effect of glucose on Kslow is that the net current measured at the end of the pulse train is actually an aggregate of Kslow and KATP channel currents, as has been suggested recently (Göpel et al., 2001). To determine whether this is the case, we tested the sensitivity of Kslow to tolbutamide, a specific blocker of KATP channels. The application of 100 μM tolbutamide to dispersed β-cells shifted the holding current measured at −65 mV from −10.8 ± 2.2 pA to −16.2 ± 3.6 pA (n = 4, P > 0.05), and reduced the current step elicited by the step from −65 to −40 mV, from 10.5 ± 5.8 pA to 5.8 ± 2.4 pA (n = 4, P > 0.05). More importantly, tolbutamide was without significant effect on Kslow amplitude, which was 11.2 ± 1.7 pA and 9.0 ± 0.6 pA (n = 4, P > 0.05), before and after the application of tolbutamide, respectively. This result stands in contrast with the 75% suppression reported in in situ mouse β-cells by Göpel et al. (2001). Thus, it appears that, in our hands, KATP channels do not significantly contribute to the total Kslow current in dispersed mouse β-cells. In addition, the enhanced current amplitude observed for Kslow in 5 mM glucose (relative to that in 10 mM glucose) persisted despite the presence of 100 μM tolbutamide (two of two cells), confirming that the glucose sensitivity of Kslow is unlikely to be due to the contamination of Kslow by KATP channels (unpublished data).

Modulation of Kslow by SERCA Inhibitors Can be Modeled by the ER-dependent Buildup of Ca2+ in a Submembrane Space

The earliest β-cell models considered only a single Ca2+ compartment, the cytosol. Obviously, such models cannot account for the effects of Tg and insulin that we observed—at minimum it is necessary to include the ER. Simulations demonstrate, however, that simply adding a conventional ER component is not sufficient to explain the biphasic effects of SERCA inhibitors in β-cells. Thus, Fig. 6 shows the result of applying the same protocol used in the experiments (Fig. 2) to a model cell incorporating an ER and a cytosolic compartment. As in the experiments, Kslow mainly activates during the imposed spike train, which in the model produces a sharp rise in c (Fig. 6, A and B). During each simulated burst command, cER rises slightly during the pulse train and then recovers during the holding period as Ca2+ drains from the ER (Fig. 6 F). When the SERCA pump is blocked, the rise in c during the pulse train is exaggerated because all of the Ca2+ that enters the cell remains in the cytosol without being diverted to the ER. Consequently, the amount of Kslow activated by a simulated burst command increases and remains elevated as the ER store is depleted (Fig. 6, C and D). However, this prediction does not agree with the experimental data (Figs. 3 and 4), which show only a transient increase in Kslow after SERCA inhibition followed by current suppression. In summary, a model consisting of only the ER and cytosolic compartments, and with Kslow depending exclusively on c, failed to account for the transient rise and fall in Kslow observed experimentally.

This compelled us to include additional features in this minimal model. Following suggestions raised in other cell types (Jafri et al., 1998; Liu et al., 1998; Frieden and Graier, 2000), we hypothesized that Kslow could be dependent on Ca2+ released from the ER, as has been suggested previously for an apamin-insensitive KCa current in β-cells (Ämmala et al., 1991). Specifically, we postulate that Kslow channels are located in intimate proximity to ER Ca2+ efflux channels (Model II). Although there is no direct evidence that β-cells have the morphologic specializations of cells such as cardiac myocytes, where L-type Ca2+ channels are colocalized with RyR channels (Carl et al., 1995; Bers and Perez-Reyes, 1999) our modeling suggests that it is merely necessary for a portion of the ER to lie close to plasma membrane regions containing Kslow channels to account for our data. The presence of a subspace created by this juxtaposition would generate a local Ca2+ concentration gradient as long as there is a maintained Ca2+ flux from the ER into the subspace. Given such an arrangement, it follows that depletion of the ER would necessarily reduce Kslow current by eliminating the gradient; in this case, cSS would fall to the level of c. If we further assume that the activation curve of Kslow is steeply dependent on [Ca2+] and that the binding constant (Kd) of Kslow for Ca2+ is significantly higher than basal levels of c, then Kslow current would be significantly depressed after ER store depletion. This would be expected to occur on the time scale of ER depletion after SERCA inhibition. Data from permeabilized cells indicate that the ER in β-cells empties over several minutes, comparable to the times we observed for the decay of Kslow after either thapsigargin or insulin application (Tengholm et al., 1998, 2000, 2001). Whether Kslow is nearly abolished or merely reduced depends on the affinity of Kslow for Ca2+, and on the chosen flux parameters, which determine the magnitude of the Ca2+ concentration gradient between the subspace and the cytosol. Although we do not know the molecular identity of Kslow, nor its affinity for Ca2+, our assumed Kd of 0.7 μM is comparable to that reported for small conductance (SK) KCa channels, which have been theorized to mediate the Kslow current (Hirschberg et al., 1998).

Not only is it clear that Model II can account for the loss of Kslow over a period of minutes following SERCA block, but this model can also reproduce the transient increase in Kslow observed in the first few minutes following SERCA blockade (Fig. 7 G). As shown in Fig. 7, A and B, before the block of SERCA (Episode # 0), Kslow develops in seconds during the pulse train and decays in seconds afterwards, as in the simpler model lacking a subspace (Model I; Fig. 6, A and B). In the subspace model, however, Kslow is activated by cSS, not c. The subspace Ca2+ concentration, cSS, has two components, a fast component that tracks the rapid changes in c and a nearly constant component that reflects the contribution of cER. Therefore, the rapid rise in Kslow observed during the spike train mainly reflects the rapid rise in c due to Ca2+ entry.

It may seem paradoxical that cSS, which is fed by Ca2+ released from the ER, can rise when cER is essentially constant. However, examination of Eqs. 8 and 10 (materials and methods) reveals that a rise in c will diminish the gradient for Ca2+ efflux from the subspace into the bulk cytosol. Like a bathtub with a constant inflow, partially blocking the drain will cause the subspace to fill.

The dependence of cSS on c and cER can be made more precise. Because the fluxes in and out of the subspace are large, the subspace is always nearly in equilibrium with the ER and the cytosol. Setting Eq. 8 to equilibrium and substituting the formulas for the fluxes (Eqs. 9 and 10), we obtain the following useful relation:

\[c_{\mathrm{SS}}={\left(\mathrm{V}_{\mathrm{ER}}\mathrm{p}_{\mathrm{ER}}\mathit{c}_{\mathrm{ER}}+\mathrm{V}_{\mathrm{CYT}}\mathrm{p}_{\mathrm{X}}\mathit{c}\right)}/{\left(\mathrm{V}_{\mathrm{ER}}\mathrm{p}_{\mathrm{ER}}+\mathrm{V}_{\mathrm{CYT}}\mathrm{p}_{\mathrm{X}}\right)}\mathrm{.}\]
(11)

That is, one can approximate cSS by a weighted average of cER and c, with the weights determined by the volumes of the ER and cytosol and the exchange rates between those compartments and the subspace.

After SERCA blockade, the amount of Kslow elicited by a simulated burst command initially rises (Episode # 4) because the fast component of cSS increases due to the increase in c. The increase in c results from the loss of the SERCA pump, exactly as in Model I. The reason Kslow rises before it falls is that cER declines very slowly after SERCA is blocked. This creates a window of time in which the rise in c due to Tg has not yet been compensated for by the fall in cER that ultimately results. Thus, only after several minutes does the gradient between the subspace and the cytosol collapse, decreasing cSS to the level of c. By Episode # 10 (Fig. 7, E and F), the gradient between cSS and c and hence Kslow, are nearly abolished. Even though the change in c during the simulated burst command is larger after store depletion than before, cSS remains below threshold for activation of Kslow. Our assumption that Kslow has a steep dependence on Ca2+ is critical for this to occur. Recall that some of our cells exhibited only inhibition, with no prior potentiation of Kslow after SERCA blockade. This can be accounted for in the model by quantitative variation of parameters, for example, reducing the pump rate kPMCA by 1/4.

The Role of Kslow in Islet Bursting

Thus far, the modeling results allow us to say that a minimal implementation of the subspace idea qualitatively accounts for the experimental data we observed, whereas a simpler model consisting of only the ER and the cytosol is insufficient. The model also suggests a possible role of Kslow in β-cell electrical activity. Göpel et al. (1999) proposed a model based on the properties of Kslow deactivation after the pulse train of the simulated burst protocol. However, the subspace model suggests that the kinetics of Kslow activation and deactivation mainly reflect only the fast dynamics of c. We will show below (Fig. 9) that this fast component of Kslow is not sufficient to make Kslow a pacemaker for bursts lasting longer than a few seconds, whereas we and others observe burst periods ranging up to tens of seconds or minutes in situ.

However, if Kslow responds to cSS, which is essentially a weighted average of c and cER (compare Eq. 11), then the ER will impart a very slow component to Kslow. This is illustrated in Fig. 8, where we simulate bursting with the same model used for the voltage-clamp simulation shown in Fig. 7 (see the legend of Fig. 8 for minor parameter changes). The fast and slow components of Kslow reflect the fast and slow components in cSS (Fig. 8 C). Thus, at the beginning of each active phase, cSS jumps up rapidly, but the corresponding rise in Kslow that follows is not sufficient to terminate the burst. The maintained depolarization produces a slow rise in cER (Fig. 8 E), which is reflected in a progressive slow increase in cSS. In the model, it is this slow rise in cSS, and hence Kslow, that ultimately repolarizes the burst. A mirror image sequence occurs in the silent phase, where an initial rapid drop in cSS is followed by a slow decaying phase that over many seconds removes enough Kslow to permit a new phase of depolarization. In addition to the concentrations of Ca2+ in all three compartments, Fig. 8 D shows cAVG, the average of c and cSS weighted by the cytosol and subspace volumes, since this would be expected to more closely correspond to the Ca2+ level that would actually be measured experimentally using Ca2+-sensitive dyes. Note that cAVG exhibits a fast rise and fall at the beginning of each active and silent phases, followed by a slow rise in the active phase and a slow fall in the silent phase. These features resemble data contained in several reports in the literature (Santos et al., 1991; Gilon and Henquin, 1992; Hellman et al., 1992), as well as our own unpublished observations (unpublished data). It is of interest that cAVG actually starts to decline somewhat even before the end of the active phase. This highlights the need for caution in interpreting the role of [Ca2+]i: it may be that a component of Ca2+ that is not directly measured is actually driving the system. Thus, in the present model, it is subspace [Ca2+] that rises monotonically to terminate the bursts, not [Ca2+] in the cytosol.

The simulated bursts shown, which have a period of 1.5 min, are at the upper end of our data set. However, this period can be varied over two orders of magnitude, covering the full range of periods we and others have reported in the literature, by varying either the ER leak rate pER or other parameters (unpublished data). This may be one factor to account, at least in part, for the heterogeneous electrical activity of dispersed cells and islets reported in the literature.

Further, cSS, as modeled here, transmits the slow drive originating in the ER to the plasma membrane. An immediate consequence of this is that membrane potential oscillations disappear if the ER is depleted by thapsigargin, resulting in continuous spike activity (Fig. 9). Due to the loss of Kslow, there is no longer any negative feedback in this case to turn off the spikes. (We restrict the SERCA blocker in this simulation to be thapsigargin, and not insulin, to avoid the complication that insulin also opens K[ATP] channels [Khan et al., 2001]). Thus, the subspace model offers an alternative theory to the activation of CRAC or CRAN channels after store depletion of Ca2+(Worley et al., 1994a,b; Roe et al., 1998; Satin and Kinard, 1998), which has been proposed to account for Tg-induced β-cell depolarization and continuous spiking (Worley et al., 1994a; Bertram et al., 1995; Gilon et al., 1999). That is, it may be the loss of outward Kslow current associated with Tg, rather than the activation of an inward CRAC current, that is responsible for β-cell depolarization.

It is no surprise that without negative feedback there is no bursting. However, even if the Kd of Kslow for Ca2+ is reduced in the model, so that the channel now opens at the lower cSS levels that prevail after store depletion, only fast bursting is supported (Fig. 9 B). This underscores the point that in the subspace model, the slow drive in β-cell electrical oscillations stems from the ER; the faster kinetics of cytosolic Ca2+, reflected in the Kslow tail, can produce bursts on a time scale of at most a few seconds. This suggests that the slow dynamics of ER Ca2+ coupled to Kslow through a restricted subspace may be essential for the production of 10–60 s long oscillations seen in classic in vitro islet bursts.

Two KCa channels are known to be present in β-cells: a “fast,” large conductance KCa, which is strongly voltage dependent and selectively blocked by charybdotoxin (Kukuljan et al., 1991), and a slowly activating and deactivating KCa current, Kslow, which is relatively voltage independent and as yet has no selective blocker (Göpel et al., 1999). It has been proposed that Kslow is responsible for islet pacemaking and that its activation and deactivation kinetics strongly correlate with islet electrical activity (Göpel et al., 1999). It has further been hypothesized that the slower electrical behavior sometimes observed in dispersed β-cells (Larsson et al., 1996) compared with in situ β-cells results from their having less Kslow current (Göpel et al., 1999). In our hands, Kslow current amplitude in dispersed β-cells was not vastly different from that of in situ β-cells on a cell to cell basis, despite their heterogeneous electrical activity (Kinard et al., 1999). In fact, we observed more variability in Kslow amplitude from cell to cell than between the two groups of cells. Thus, we conclude that differences in Kslow current amplitude are not sufficient to explain the differences observed in the electrical behavior of dispersed versus in situ β-cells, which remains an open question.

In the present study, we demonstrated that Kslow was modulated by either thapsigargin or insulin. Exposing cells to either agent resulted in an initial potentiation of Kslow amplitude, followed by a nearly complete and sustained suppression. The observation that insulin and thapsigargin had nearly identical effects on Kslow means that it is likely that both agents act on the channel secondary to SERCA inhibition and ER Ca2+ depletion (Thastrup et al., 1990; Islam et al., 1992; Xu et al., 1999). These data are consistent with the hypothesis that an essential component of the Ca2+ that activates Kslow channels during a burst of action potentials is provided by Ca2+ from ER stores and maintained SERCA activity.

We developed a mathematical model to quantitatively test this hypothesis. In this model, Ca2+ entering the cytosol during a burst of action potentials is pumped into the ER by SERCA. Ca2+ then tunnels through the organelle (Petersen et al., 2001) and exits via ER Ca2+ channels in a region of the cytosol that is in close proximity to plasmalemmal Kslow channels. The focal source of Ca2+ leaving the ER would provide a local gradient of [Ca2+]i between the subspace and the rest of the cytosol. We further postulated that the elevated Ca2+ in this subspace is adequate to activate Kslow channels, whereas bulk cytosolic Ca2+ is not. For simplicity, we have modeled this condition with two discrete compartments, but we conjecture that a sufficient gradient and comparable results could be obtained using a model of continuous, buffered diffusion between the Ca2+ release zone and the bulk cytosol, without the need for specialized structures to hinder diffusion.

According to this model, the initial potentiation of Kslow after inhibition of SERCA results from a rise in c that in turn reduces Ca2+ efflux from the subspace and increases cSS. c rises because all the Ca2+ ions that enter the cell through voltage-gated Ca2+ channels are now free to contribute to c rather than splitting their effects between the ER and the cytosolic compartments. However, because the ER contribution is critical for the activation of Kslow in this model, as the ER empties, the response of Kslow to an imposed pulse train progressively declines. This scenario requires a steeply nonlinear dependence of Kslow on Ca2+, such that an increment of [Ca2+]i on top of a super-threshold level of [Ca2+]SS can increase the current, whereas the same increment is ineffective once the ER component is abolished.

Although this model involves a number of assumptions, we find the hypothesis appealing because we could not account for the biphasic effects of SERCA blockade with any simpler model. In Fig. 6, we show explicitly that a model incorporating only two Ca2+ compartments, the cytosol and the ER, could account for the rise in Kslow but not the fall. An alternative explanation would be to assume that both Tg and insulin have direct bi-directional effects on the channel, but this seems highly unlikely for two agents that are so structurally dissimilar.

We also considered an alternative hypothesis. In this hypothesis, store depletion activates a calcium release–activated current (CRAC/CRAN) (Worley et al., 1994a,b) that raises c sufficiently to maximally activate Kslow even under basal conditions. No additional Kslow conductance could then be elicited by the burst protocol. We rejected this model, however, because it predicts a significant increase in the size of the holding current at −65 mV, which was not observed. The hypothesis also predicts an increase in the total current elicited by stepping the command potential from −65 to −40 mV following store depletion. We did not see such an increase in cells that exhibited a loss of Kslow with Tg. Nor did we observe an increase in total current upon stepping from −40 to 0 mV under steady-state conditions in Tg, as would be expected if Kslow were maximally activated by Ca2+ entry through CRAC channels (Figs. 3 and 4).

Several previous studies support the hypothesis that K+ channels can be activated by localized Ca2+ in a submembrane space controlled by ER calcium efflux (Berridge, 1998; Bootman et al., 2001). First, it has been shown that during the active phase of glucose-stimulated oscillations, rises in [Ca]i are buffered by Ca2+ uptake into the ER (Gilon et al., 1999). The passive leak of Ca2+ from the ER during the subsequent silent phase contributes to the slow decay in cytosolic [Ca2+] that is observed. Second, it has been directly demonstrated that glucose stimulation induces microgradients of Ca2+ localized just beneath the plasma membrane of the β-cell (Martín et al., 1997; Quesada et al., 2000). Lastly, similar mechanisms of ER-dependent activation of KCa channels have been reported in other systems. Thus, histamine-induced activation of BK KCa channels in a human umbilical vein endothelial cell line was shown to depend upon ryanodine-sensitive calcium release from intracellular Ca2+ stores (Frieden and Graier, 2000), and Ca2+-induced Ca2+ release has been reported to trigger the activation of the KCa channels that mediate the after hyperpolarizations of nodose neurons (Cordoba-Rodriguez et al., 1999).

In addition to being regulated by insulin and Tg, Kslow was sensitive to changes in extracellular glucose concentration. This contrasts with the reports by Göpel et al. (1999)(2001) that changes in [glucose] altered the kinetics but not the amplitude of Kslow. In our hands, increasing glucose from 5 to 10 mM decreased Kslow current density in dispersed β-cells by ∼50%. Thus, in addition to KATP channels, Kslow may be metabolically regulated in β-cells (Cook and Hales, 1984; Rorsman and Trube, 1985).

We also used our mathematical model to explore the consequences of the subspace hypothesis for the production of islet electrical activity. We found that the slow kinetic component imparted by ER Ca2+ allows Kslow to drive oscillations with periods up to minutes in duration (Fig. 8). The period of this bursting can be reduced to tens of seconds or seconds by increasing the ER leak rate, decreasing K-ATP conductance, or varying other parameters (unpublished data). Thus, the model can reproduce the full range of bursting time scales observed experimentally. This dynamic flexibility stems from the interaction of two slow negative feedback processes, c and cER, with time scales of a few seconds and a few minutes, respectively, which can mix to produce a range of intermediate time scales. Thus, the subspace model is an exemplar of the general class of models we call “phantom bursters” (Bertram et al., 2000).

In contrast, with the ER inhibited, burst period is limited to at most a few seconds (Fig. 9, bottom), unless the PMCA pump rate is reduced to make the kinetics of cytosolic Ca2+ much slower than what we observe (unpublished data). Note that some previous models (Chay, 1996, 1997) also exhibit a wide range of burst periods based on the interaction of cytosol and ER compartments. However, since these models lack a Ca2+ subspace, they fail to account for the effects of SERCA blockade on Kslow.

The behavior of the subspace model is also compatible with experiments in which modulation of β-cell ER Ca2+ stores influences islet electrical activity and insulin secretion. Thus, the exposure of mouse islets to 1–5 μM Tg has been shown to disrupt regular bursting, leading to sustained depolarization, continuous spiking and increased glucose-induced insulin secretion (Worley et al., 1994a,b; Bertram et al., 1995; Gilon et al., 1999). These findings have been interpreted previously to reflect the activation of a store-dependent depolarizing current, CRAC. However, as shown in the present study, depleting ER Ca2+ stores by SERCA pump blockade could alternatively result in islet depolarization via Kslow inhibition. On the other hand, an additional inward current such as CRAC/CRAN may still be required to explain depolarization following activation of ER efflux, which does not inhibit Kslow in the subspace model (unpublished data).

In summary, the model proposed here sheds new light on the potential role of KCa channels in islet pacemaking, a role that we suggest can only be fully realized in partnership with ER Ca2+ stores and a submembrane compartment. Because Kslow activation is dependent on the ER and regulated by agents that alter ER Ca2+, these agents may provide novel tools to further investigate the role of KCa channels and intracellular Ca2+ stores in the electrical activity of β-cells. While we have focused on Kslow in this paper, we believe that there may well be other important slow negative feedback mechanisms involved in β-cell pacemaking. These include inactivation of Ca2+ channels or activation of KATP channels due to depolarization, Ca2+ entry, and/or insulin secretion (Cook et al., 1991). Further work will be needed to dissect the rhythmogenic roles played by these complementary mechanisms.

We thank Heather Strange for preparing the cell cultures. Modeling was done by A. Sherman and R. Bertram and experiments were done by P. Goforth, M. Zhang, F. Khan, and L.S. Satin.

This work was partially supported by National Science Foundation grants DMS-9981822 and DBI-9602233 to R. Bertram and National Institutes of Health grant RO1 DK-46409 to L. Satin.

The online version of this article contains supplemental material.

*

Abbreviations used in this paper: CICR, Ca2+-induced Ca2+ release; CPA, cyclopiazonic acid; PMCA, plasma membrane Ca2+-ATPase; SERCA, sarco/endoplasmic reticulum calcium ATPase; TG, thapsigargin.

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