Delayed-rectifier (KV2.1) regulation of pancreatic {beta}-cell calcium responses to glucose: inhibitor specificity and modeling

Natalia A. Tamarina, Andrey Kuznetsov, Leonid E. Fridlyand, and Louis H. Philipson

Department of Medicine, University of Chicago, Chicago, Illinois

Submitted 8 February 2005 ; accepted in final form 5 May 2005


    ABSTRACT
 TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
The delayed-rectifier (voltage-activated) K+ conductance (KV) in pancreatic islet {beta}-cells has been proposed to regulate plasma membrane repolarization during responses to glucose, thereby determining bursting and Ca2+ oscillations. Here, we verified the expression of KV2.1 channel protein in mouse and human islets of Langerhans. We then probed the function of KV2.1 channels in islet glucose responses by comparing the effect of hanatoxin (HaTx), a specific blocker of KV2.1 channels, with a nonspecific K+ channel blocker, tetraethylammonium (TEA). Application of HaTx (1 µM) blocked delayed-rectifier currents in mouse {beta}-cells, resulting in a 40-mV rightward shift in threshold of activation of the voltage-dependent outward current. In the presence of HaTx, there was negligible voltage-activated outward current below 0 mV, suggesting that KV2.1 channels form the predominant part of this current in the physiologically relevant range. We then employed HaTx to study the role of KV2.1 in the {beta}-cell Ca2+ responses to elevated glucose in comparison with TEA. Only HaTx was able to induce slow intracellular Ca2+ concentration ([Ca2+]i) oscillations in cells stimulated with 20 mM glucose, whereas TEA induced an immediate rise in [Ca2+]i followed by rapid oscillations. In human islets, HaTx acted in a similar fashion. The data were analyzed using a detailed mathematical model of ionic flux and Ca2+ regulation in {beta}-cells. The results can be explained by a specific HaTx effect on the KV current, whereas TEA affects multiple K+ conductances. The results underscore the importance of KV2.1 channel in repolarization of the pancreatic {beta}-cell plasma membrane and its role in regulating insulin secretion.

delayed-rectified potassium conductance; hanatoxin; tetraethylammonium; intracellular calcium


STIMULUS-SECRETION COUPLING in pancreatic islet {beta}-cells involves multiple ion channels that regulate the plasma membrane potential (Vm), intracellular free Ca2+ concentration ([Ca2+]i), and insulin secretion (13). One aspect of this process involves glucose-induced closure of ATP-sensitive K+ channels (KATP), leading to depolarization of the Vm (1, 7, 8), and opening of voltage-dependent Ca2+ channels followed by an increase in Ca2+ cytoplasmic concentration, which initiates insulin secretion (33).

Pancreatic islets display characteristic fast spikes and bursts in electrical activity and [Ca2+]i oscillations, which are important in generating pulsatile insulin secretion (11). Periodic depolarization and repolarization of the Vm is critical to the regulation of Ca2+ influx through voltage-dependent Ca2+ channels and oscillatory [Ca2+]i responses of the {beta}-cell. Alterations of the balance between depolarizing and repolarizing currents in the {beta}-cell can lead to severe perturbations of insulin secretion (13). Repolarization of the Vm can, in principle, be mediated by several K+-selective ion channel proteins such as KATP, voltage-gated channels (KV), and Ca2+-activated K+ channels (KCa), which include small-conductance and large-conductance channels (12, 23, 28, 31). The identification and characterization of specific K+ channels that regulate this process in normal {beta}-cells remains incomplete.

Voltage-operated K+ channels regulate the Vm of electrically excitable cells (5) and are important components of the {beta}-cell plasma membrane. Patch-clamp studies and whole cell microelectrode studies on {beta}-cell outward K+ currents have demonstrated that they are predominantly (80%) of the delayed-rectifier type and are sensitive to external tetraethylammonium (TEA) with Kd values of 1–5 mM (4, 25, 26, 30). The KV currents in human cells are similar to those in mouse and rat and are all sensitive to the blocker TEA (Kd in the 5–7 mM range; see Refs. 2 and 16). It has been suggested that the fast spike repolarization of rodent {beta}-cell membrane results from the opening of delayed-rectifier K+ channels (26). TEA blockade of K+ channels has been shown to dramatically increase glucose-dependent electrical activity and insulin secretion in mouse islets (16). Several groups have made an effort to define the KV channel gene or genes encoding this current. Some of the genes expressed in insulin-secreting cell types include members of the KV1.x, KV 2.x, and KV 3.x gene families (3, 19, 22, 24, 35). Dominant-negative mouse transgenes for KV1.x channels strongly suggest that this class of K channels does not play a significant role in regulation of Vm repolarization (23). On the other hand, KV2.1 channels contribute significantly to the {beta}-cell delayed-rectifier current (9, 19, 20, 24). It has also been shown that increased action potential burst frequency and increased insulin secretion result from the block of the KV2.1 channels in mouse {beta}-cells and insulinoma cell lines by pharmacological agents or by coexpression of dominant-negative KV2.1 subunits (19, 20).

Here we have examined the role of KV2.1 channels in glucose-dependent [Ca2+]i oscillations. Western blot analysis indicated that KV2.1 protein is expressed in mouse and human islets. In these islets, we found that hanatoxin (HaTx), the most specific KV2.1 channel inhibitor known, profoundly affects oscillatory [Ca2+]i responses. Although HaTx also blocks KV4 channels, these are not present in {beta}-cells (4, 9, 35). HaTx also inhibits the {beta}-cell delayed-rectifier K+ current by inducing a right shift in the current-voltage (I-V) relationship, just as described for its effect on KV2.1 expressed in Xenopus oocytes (30). However, its action on [Ca2+]i is not identical to that of TEA, and here we show using a modeling approach that the different responses are most likely because of the specific nature of the HaTx blockade of KV2.1. These new observations provide evidence that the critical delayed-rectifier channel in mouse and human islet {beta}-cells is comprised of KV2.1 subunits.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Isolation of mouse islets. Islets of Langerhans were isolated from the pancreas of 8- to 10-wk-old C57BL/6J by collagenase digestion and discontinuous Ficoll gradient using methods described previously (24, 27, 34). Islets were cultured in RPMI-1640 medium supplemented with 10% FCS, 11.6 mM glucose, 100 IU/ml penicillin, and 100 µg/ml streptomycin (islet complete medium) for 2–5 days.

Human islets. Human islets were provided by Dr. B. Herring (University of Minnesota). Human islets were cultured in the same conditions as mouse islets.

Immunoblots. Anti-KV2.1 rabbit polyclonal IgG (raised against amino acids 837–853 of rat KV2.1, well conserved among mammalian KV2.1 proteins) was obtained from Upstate Biotechnology (32). For immunoblots, 5–20 mg membrane protein or whole cell lysates were denatured in reducing sample buffer, fractionated on 9% polyacrylamide-SDS gels adjacent to marker proteins, and transferred to nylon membranes. These were blocked, incubated with affinity-purified rabbit IgG followed by goat anti-rabbit horseradish peroxidase, and detected using an enhanced chemiluminescence technique (Amersham).

Electrophysiology. Dissociated {beta}-cells were prepared by mild trypsin digestion of isolated mouse islets. Bath solution contained (in mM) 135 NaCl, 5 KCl, 2 MgCl2, 2 CaCl2, and 10 HEPES, pH 7.3. Pipette solution contained (in mM) 140 KCl, 2 MgCl2, 2 CaCl2, 11 EGTA, 5 MgATP, and 10 HEPES, pH 7.3. In some experiments, the bath solution was supplemented with up to 1 µM HaTx (generously provided by Dr. K. Swartz, National Institutes of Health). For whole cell current recordings, the cells were held at –70 mV, and voltage steps were applied in the interval from –80 to 60 mV in 10 mM increments. Experiments were performed at room temperature using an Axopatch 200B amplifier and DigiData 1500A interface (Axon Instruments). pClamp software (Axon Instruments) was used for both data acquisition and data analysis (modified from Ref. 24).

Measurement of [Ca2+]i. Cells were loaded with fura 2 for 25 min at 37°C in Krebs-Ringer bicarbonate buffer [containing (in mM): 119 NaCl, 4.7 KCl, 1.8 CaCl2, 1.2 MgSO4, 1.2 KH2PO4, and 25 NaHCO3] supplemented with 5 µM fura 2-AM (Molecular Probes, Eugene, OR). [Ca2+]i was estimated as described elsewhere (22). Dual-wavelength digitized video fluorescent microscopy with fura 2 in islets and {beta}-cells was performed using an intensified charge-coupled device (Hammatsu C2400) and Metafluor imaging software (Universal Imaging).

Statistical analysis. Statistical significance was determined by t-test, and the results were reported as averages ± SE.

Mathematical simulation and analysis. To analyze the experimental results, we used our previously described detailed mathematical model of ionic flux in {beta}-cells that includes the critical channels and pumps in the plasma membrane: delayed-rectifying K+ channels, voltage-independent small-conductance KCa channels, KATP channels, and others. This model is coupled to the equations describing cytoplasmic Ca2+, inositol 1,4,5-trisphosphate, ATP, and sodium homeostasis (10). This model is available for direct simulation on the website "Virtual Cell" (http://www.nrcam.uchc.edu) in "MathModel Database" on the "math workspace" in the library "Fridlyand" under the name "Chicago.1."


    RESULTS
 TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
The expression of KV2.1 protein was detected in Western blots of homogenates of mouse and human islets with anti-KV2.1 antiserum (Fig. 1). Both types of extracts contained a single 95–97 Kd polypeptide that reacted with this antiserum. Control lanes containing homogenates of cell lines (HEK 293) not expressing KV2.1 were negative (data not shown). This indicates the presence of KV2.1 protein in islet cells of both species, extending the previous detection of mRNA in {beta}-cells (24, 35).



View larger version (87K):
[in this window]
[in a new window]
 
Fig. 1. Voltage-dependent K+ (KV2.1) protein is present in isolated mouse and human islets of Langerhans. Western blot of mouse islets (1), MIN6 cells (2), HEK cells transfected with human KV2.1 cDNA (3), and human islet (4) homogenates probed with anti-KV2.1 antibody. Lanes 1 and 4 contain the total protein extracted from 20 islets each.

 
HaTx, a peptide toxin from the Chilean Rose tarantula, Phrixotrichus spatulata, is the most specific KV2.1 antagonist known (29). HaTx binds to the surface of the KV2.1 channel at four equivalent sites within voltage-sensor domains and shifts channel opening to more depolarized voltages (18, 30). Although it also affects KV4 channels, these are not present in {beta}-cells.

To evaluate the effect of HaTx on the outward K+ current in mouse {beta}-cells, the I-V relationship was determined in the absence and presence of 1 µM HaTx (Fig. 2), a concentration well above the Kd of 42 nM (29). In the control cells, activation of the voltage-dependent outward current is seen at –20 ± 5 mV (n = 10), whereas in cells exposed to HaTx it was +20 ± 5 mV (n = 10). Because no current is left at –20 mV, these results clearly show that essentially all the KV current in mouse {beta}-cells is sensitive to HaTx.



View larger version (22K):
[in this window]
[in a new window]
 
Fig. 2. Effect of hanatoxin (HaTx) on delayed-rectifier outward currents in a mouse {beta}-cell. A: whole cell currents evoked by a series of voltage-step stimulations of the untreated cell as described in MATERIALS AND METHODS. B: currents acquired from the same cell 1 min after application of 1 µM HaTx. C: current-voltage relations for the peak currents in A and B show the rightward shift of the current activation after the application of HaTx. Graphs represent 1 of 10 similar experiments.

 
To evaluate the effect of HaTx on mouse islet [Ca2+]i, imaging studies with fura 2 were performed (Fig. 3). Representative experiments examining the effects of HaTx (1 µM) on glucose-induced (20 mM glucose) elevation of [Ca2+]i in islets are shown on Fig. 3B. At high glucose concentration, islets did not display oscillations, but rather maintained a sustained high level of [Ca2+]i as in the control (Fig. 3A). Under these conditions, the addition of HaTx (1 µM) induced "slow" [Ca2+]i oscillations with a frequency of 0.37 ± 0.04/min (n = 7 in 4 independent experiments). TEA (20 mM) was added after HaTx to compare the effects of these two compounds. With TEA present simultaneously with HaTx, the amplitude of oscillations was increased by 54.5 ± 8.3% (n = 7, P < 0.01). There was also a trend toward increased oscillation frequency, but this change was not statistically significant (P > 0.05).



View larger version (17K):
[in this window]
[in a new window]
 
Fig. 3. HaTx is able to induce oscillatory intracellular Ca2+ concentration ([Ca2+]i) changes in mouse islets. Mouse islets were incubated at 2 mM glucose, then stimulated with 20 mM glucose (n = 10 islets; A), 20 mM glucose and subsequently 1 µM HaTx and 20 mM tetraethylammonium (TEA, n = 7 islets; B), and 20 mM glucose and subsequently various concentrations of TEA (n = 10 islets; C). Each trace represents 1 islet . In "B," note sudden induction of [Ca2+]i oscillations after the addition of HaTx and a characteristic change in [Ca2+]i waveform (compare Fig. 4)

 
In similar experiments, islets were treated with glucose (20 mM) and TEA (1, 5, and 20 mM), omitting HaTx (Fig. 3C). TEA-induced oscillations had higher frequency than HaTx-induced [Ca2+]i oscillations (4.5 ± 0.3/min, n = 10). The addition of TEA resulted in an immediate sharp increase in [Ca2+]i, whereas the first response to addition of HaTx was a decrease in [Ca2+]i. Neither TEA nor HaTx affected the [Ca2+]i level when added in the presence of lower glucose concentration (2 mM; data not shown), indicating that actions of both compounds are glucose dependent.

Mouse islets cultured at 11–14 mM glucose demonstrate regular [Ca2+]i oscillations of the slow type (31). HaTx (0.2 µM, Fig. 4A and 1 µM, data not shown) had an effect on the waveform of [Ca2+]i oscillations, in that each peak had a shorter duration (decreased by 39.8 ± 4.2%, P < 0.01 in 0.2 µM HaTx), with fast oscillations at the plateau of each peak (2.03 ± 0.2 oscillations/min in 0.2 µM HaTx). This pattern remained similar after the addition of TEA (20 mM) except for an increase in the amplitude of oscillations by 29.4 ± 2.4% (n = 9) and 32.4 ± 4.2% (n = 4) in experiments with 0.2 and 1 µM HaTx correspondingly (the difference between the two concentrations is not significant, P > 0.05).



View larger version (25K):
[in this window]
[in a new window]
 
Fig. 4. Effects of HaTx and TEA on steady-state glucose-stimulated [Ca2+]i oscillations. Mouse islets were stimulated by 14 mM glucose in Krebs-Ringer bicarbonate (KRB). Representative experiments showing change of [Ca2+]i oscillations in a mouse islet by 200 nM HaTx, followed by 20 mM TEA (n = 9 islets; A) and 20 mM TEA without HaTx (n = 7 islets; B). Each trace represents 1 islet.

 
The effect of TEA alone on slow [Ca2+]i oscillations in mouse islets consisted of both an increase in oscillation amplitude by 1.41 ± 0.05 times (n = 7, P < 0.05) and an increase in frequency (highly variable, between 2- and 10-fold; Fig. 4B). TEA also produced a prominent change in the [Ca2+]i waveform with sharper oscillations that was also characteristic of HaTx-treated islets (see Figs. 3B and 4A).

The effects of 1 µM HaTx on glucose-induced elevation of [Ca2+]i in human islets are illustrated on Fig. 5. The addition of HaTx induced an initial decrease in [Ca2+]i similar to one observed in mouse islets (Figs. 3B and 4A). In several independent experiments, among eight islets that responded to 20 mM glucose with an increase of [Ca2+]i, six displayed oscillations after the application of HaTx. The frequency of HaTx-induced oscillations was 0.54 ± 0.11/min. In other experiments using freshly isolated human islets, the response to TEA was similar to that observed with HaTx (data not shown).



View larger version (18K):
[in this window]
[in a new window]
 
Fig. 5. HaTx is able to stimulate [Ca2+]i oscillations in human islets. Human islets were incubated sequentially (in KRB) in 2 mM glucose, 20 mM glucose, 20 mM glucose with 1 µM HaTx, and 20 mM glucose with 1 µM HaTx and 20 mM TEA. Each trace represents 1 human islet.

 
To understand the disparate effects of these KV2.1 inhibitors, the data were analyzed using a detailed mathematical model of ionic flux and Ca2+ regulation in {beta}-cells (10) that simulates slow [Ca2+]i oscillations in {beta}-cells at a medium glucose level. According to our electrophysiological experiments (Fig. 2), HaTx shifts the I-V relationship so that KV channels are essentially closed when the Vm is below 0 mV. There is no evidence for other KV channels that might be exposed by this right shift of KV2.1. Therefore, the action of HaTx is equivalent to closing the KV channels below 0 mV. In our mathematical model, during simulation of Ca2+ oscillations, Vm is indeed <0mV, consistent with experimental observations (2, 13). Because the model employs a single term to create an aggregated KV channel expression, HaTx action can be simulated by simply decreasing the conductance of the KV channel.

To simulate elevated glucose concentration conditions, we adjusted the rate coefficient for ATP production (Fig. 6, left). In "high glucose conditions," a constant [Ca2+]i level and constant spikes in the Vm could be seen in the model trace. In these conditions, complete block of KV channels results in the expected plasma membrane depolarization and a sustained increase in [Ca2+]i (data not shown).



View larger version (18K):
[in this window]
[in a new window]
 
Fig. 6. Simulation of KV channel inhibition at high glucose level. High glucose-induced electrical bursting and [Ca2+]i changes were simulated by a step increase of the rate constant of ATP production from a low to a high value (from KADP = 0.03 s–1 to 3 s–1) at time 0 at initial concentration and parameters as in Tables 1–3 from Ref. 10. Established levels of parameters are shown on left. The transition changes from low to high glucose are not shown. For simulation of HaTx action, the maximal KV conductance (g'mKDr) was decreased from 3,000 to 2,500 pS at the arrow (1) in part 1. 1, [Ca2+]i; 2, membrane potential (Vm); 3, KV gating variable (n); 4, Na+/Ca2+ exchange current (INa/Ca); 5, cytoplasmic Na+ concentration ([Na+]).

 
Surprisingly, decreasing KV conductance by just 5–20% leads to slow [Ca2+]i oscillations (Fig. 6, after KV channel block), which is consistent with the induction of [Ca2+]i oscillations by HaTx in islets (Fig. 3). In our model, the ability to induce oscillations is specific for KV channel blockade, since a similar decrease in the conductance of the other principal K+ channels, KCa and KATP, does not lead to oscillations, but instead acts to increase [Ca2+]i above its sustained elevation level in Fig. 6, left (data not shown).

To differentiate separate processes and parameters more precisely, we also performed an analysis of model simulation at higher time resolution, where single spikes can be represented (Fig. 7). The oscillatory behaviors of Vm, [Ca2+]i, KV channel gating variable (n), and delayed-rectifying K+ current (IKDr) are shown. The detailed solution from Fig. 6, left (before application of KV "blocker"), is shown in Fig. 7A. However, a similar analysis at decreased KV conductance (as in Fig. 6, right, after KV "block") is hindered by the influence of slow [Ca2+]i oscillations, since spikes in the plasma Vm are absent in the "rest" period (low [Ca2+]i ) and spikes change during the "active" period (high [Ca2+]i; Fig. 6). Our general model (10) indicates the importance of ATP, Na+, and inositol 1,4,5-trisphosphate for generation of slow oscillations, but not for spiking. For this reason, for the analysis only, we fixed intracellular ATP, intracellular Na+, and inositol 1,4,5-trisphosphate concentrations at levels equivalent to their values established in Fig. 6, left, at "high glucose" simulation before simulation of KV channel block. No slow [Ca2+]i oscillations occur in this case; therefore, changes in spike activity introduced by KV inhibition became clearly apparent (Fig. 7B). The corresponding spike frequency and amplitude were also increased in the active period of slow Ca+ oscillations in Fig. 6 in the same manner as in Fig. 7B (data not shown).



View larger version (27K):
[in this window]
[in a new window]
 
Fig. 7. Simulation of single spikes. A: detailed model solution was shown at an increased time resolution pattern for Fig. 6, left. [Ca2+]i (1), Vm (2), gating variable (n; 3), and delayed-rectifying K+ current (IKDr; 4) are represented for several characteristic spikes. B: simulation of single spikes at decreased g'mKDr as in Fig. 6, right. Intracellular [Na+] ([Na+]i), ATP, and intracellular inositol 1,4,5-trisphosphate ([IP3]i) concentrations were fixed at levels equivalent to their values established in Fig. 6, left.

 

    DISCUSSION
 TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
In the present report, we have confirmed our previous conclusion that KV2.1 is expressed in mouse pancreatic {beta}-cells (24) by Western blot analysis of mouse islet extracts. We also show for the first time that KV2.1 protein is expressed in human islets.

In addition, we employed an inhibitor of KV2.1, HaTx (29), as a specific pharmacological probe for its role in the glucose-induced Ca2+ responses in {beta}-cells within intact normal islets. We first found that HaTx caused a shift in the I-V relation for the {beta}-cell delayed-rectifier, resulting in a 40-mV rightward shift in threshold of activation (Fig. 2). We compared HaTx effects on [Ca2+]i with those of the less-specific K+ channel blocker TEA. The effect of HaTx on [Ca2+]i oscillations was similar to that of TEA at 14 mM glucose. However, at higher glucose only HaTx, but not TEA, was able to stimulate slow [Ca2+]i oscillations.

To analyze these results, we used a detailed mathematical model of ionic flux in {beta}-cells based on Fridlyand et al. (10). In our model, the following equation (Eq. 16 from Ref. 10) was used for KV channels: IKDr = g'mKDr x n(Vm – VK), where g'mKDr is the maximal whole cell conductance, n is a voltage- and time-depending general gating variable, and VK is K+ equilibrium potential. In this equation, "n" increases with membrane depolarization in a similar fashion to the current in Fig. 2, and the term Vm – VK determines the dependence of outward K+ flux through the open channels on Vm.

According to our mathematical model, slow [Ca2+]i oscillations can be created by stimulation of a {beta}-cell at an intermediate glucose level (5–14 mM) by closing KATP channels followed by depolarization of the plasma membrane. These simulated slow [Ca2+]i oscillations (see Fig. 3 from Ref. 10) closely resemble the experimental [Ca2+]i oscillations in the left part of Fig. 4, A and B.

A computer simulation of the effect of high glucose concentration (20 mM) is shown in Fig. 6. In this case, slow [Ca2+]i oscillations are absent, replaced by a constant elevation of [Ca2+]i (Fig. 6 1, left) which, as evident at higher time resolution, is actually a row of continuous fast small spikes (shown in Fig. 7A). This is in agreement with the [Ca2+]i data shown in Fig. 3A. The electrical activity, illustrated in Fig. 62 (before channel block), also consists of continuous spiking (Fig. 7, A-2). A decrease in IKDr conductance (consistent with a block of delayed-rectifier K+ channels) stimulates slow [Ca2+]i oscillations and a burst behavior in Vm (Fig. 6, right). These simulated [Ca2+]i oscillations closely resemble the HaTx-generated oscillation in Fig. 3B.

Spike activity can be generated by the alternate activation of delayed-rectifying K+ channels and voltage-gated Ca2+ channels (2, 6, 26). However, KV channels have a dual function. These channels serve to create the Vm spikes, since their gating variable ("n") has oscillatory properties, and second, they dampen down depolarization at the spike peaks and help to terminate the depolarization. Our modeling of single spikes (Fig. 7) illustrates this mechanism. As can be seen in Fig. 7A, the acceleration of Vm increases n. This in turn increases IKDr (see equation above), which serves to drive membrane repolarization and limits the increase in Vm.

A partial decrease in KV conductance in the model diminishes the dampening effect on spike amplitude and increases both the amplitude and the frequency of spikes (Fig. 7B). This leads to increased amplitude and frequency of outward KV currents (IKDr) during Vm spikes (Fig. 7.4), as well as, accordingly, total IKDr per unit of time (data not shown). The spike frequency and IKDr were also increased in the active period of slow Ca+ oscillations in Fig. 6 (data not shown). This shows that our analysis is also applicable to the simulation of slow Ca+ oscillations.

Our model reproduces the stimulation of Ca2+ oscillations by HaTx (Figs. 3B and 6). The intracellular [Na+] is a dynamic variable that governs slow [Ca2+]i oscillations in our model (10) and is likely to play a role in the stimulation of Ca2+ oscillations by the block of KV channels. A decrease in KV conductance in Fig. 6 leads to increased [Ca2+] flux through voltage-gated Ca2+ channels because the dwell time in the depolarized state increases with increasing amplitude and frequency of Vm spikes (Fig. 7.2, A and B). The increased [Ca2+]i activates the inward Na+ flux through Na+/Ca2+ exchangers (Fig. 6.4). The resulting increase in intracellular [Na+] leads to a slow rise of outward current through electrogenic Na+-K+ pumps. The resulting plasma membrane repolarization promotes a transition to the silent phase. During the silent phase, the declining intracellular [Na+] leads to the decreased outward current through electrogenic Na+-K+ pumps and then in turn to plasma membrane depolarization (Fig. 6, also see Ref. 10). This explains the experimental stimulation of [Ca2+]i oscillations by HaTx (Fig. 3B). We were able to identify the decrease in [Ca2+]i and the subsequent oscillations after addition of HaTx. The brief increase in [Ca2+]i, predicted by the model (Fig. 6), was not seen in the experiments because of the relatively slow rate of image acquisition.

Quite different conditions are created by application of TEA, which blocks KCa and KATP channels in addition to KV. The block of KCa and KATP channels in the model leads to decreased current through these channels and to membrane depolarization. The inability of TEA to stimulate slow [Ca2+]i oscillations (Fig. 3C) can be explained by the opposite effects of various K+ channel block on channel currents.

We also have modeled the effect of KV channel inhibition at intermediate glucose concentrations. In this case, the decrease in KV channel conductance (similar to that in Fig. 6) only leads to a small additional decrease in K+ outward current per unit time, with a corresponding small increase in membrane depolarization (as opposed to membrane repolarization at high glucose level) and in the amplitude of simulated slow [Ca2+]i oscillations (data not shown), which is in accordance with experimental data in Fig. 4, A and B.

Despite the overall similarity in the effects of TEA and HaTx at intermediate glucose concentrations (Fig. 4, A and B), there are also interesting differences. The ability of TEA to induce oscillations is more robust than that of HaTx, suggesting that TEA is capable of additional depolarization of the Vm by inhibiting additional K+ channels compared with HaTx. This suggestion was confirmed by model simulations, where an additional decrease in the conductance of every K+ channel leads to increased amplitude and frequency of slow [Ca2+]i oscillations at intermediate glucose concentrations (data not shown).

This can also help to explain the similarity in TEA action in Figs. 3B and 4B. HaTx action on the {beta}-cell at high glucose creates the same oscillatory pattern as the one that occurs at intermediate glucose levels without HaTx (Figs 3B and 4B). Therefore, a subsequent addition of TEA in both cases leads to a similar effect, i.e., existing [Ca2+]i oscillations became more robust.

Modeling was able to closely reproduce the effect of HaTx on [Ca2+]i oscillations in islets by using partial block (10–20%) of aggregated KV channels. In electrophysiological experiments performed on single mouse {beta}-cells, the delayed-rectifier current at potentials more negative than 0 mV was totally blocked (Fig. 2). Similar HaTx concentrations were employed when monitoring [Ca2+]i.

One way to resolve this disparity is to assume that HaTx did not block all the KV channels in islets, as it did in single dissociated {beta}-cells. HaTx is a relatively large protein molecule compared with TEA, and its ability to penetrate the islet may be low, since even glucose diffusion is limited within cultured islets (15). In addition, in a recent report studying HaTx-related toxins, it was suggested that there is an important role of membrane binding and partitioning in the successful encounter of the toxin with the channel (17). It is likely that these processes are less efficient in islets as opposed to single cells.

It is also possible that, since our model (10) was developed for a single cell, it does not take into account the multicellularity of a mouse islet, in particular the electrical coupling by gap-junctions (14). Neighboring cells could contribute to repolarization in the intact islet.

Our results extend recent data (19, 20), which emphasized the possible importance of KV2.1 in mouse islet physiology. A dominant-negative KV2.1 mutant construct delivered to islet cells by adenoviral vector was used to inhibit endogenous KV2.1 assembly (18). These islets were shown to secrete more insulin than nontransfected controls, which indicates that KV2.1 represents some of the repolarizing current in pancreatic {beta}-cells. In a more recent study by the same group, a KV 2.1 inhibitor termed C-1 (structure not given) was shown to increase insulin secretion, electrical activity, and [Ca2+]i response in {beta}-cells (20).

Our experimental data and computer simulations confirm these results and show increased electrical activity and [Ca2+]i concentration after KV block at intermediate glucose concentration. In our model, further decrease in KV conductance below the level used for simulation in Fig. 6 leads to termination of the slow [Ca2+]i oscillations and to generation of stable elevated level of [Ca2+]i (several µM, data not shown) due to increased membrane depolarization. Simulation with increased [Ca2+]i is in good agreement with the experimental data from Ref. 20. The results of our simulations show that the effect of KV inhibition depends on the relative activity of channels and the glucose concentration.

Regulation of the electrical response of {beta}-cells to glucose is clearly a complex process. Although KATP channels are critical for maintaining the resting Vm, the mechanisms for establishing bursting and spiking behavior and their modulation are less well understood. We found that there is the glucose dependence to the effect of KV channel blockade by both a general and a more specific KV channel inhibitor. Our model simulations have helped to resolve these differences by showing that, although moderate changes in KV modulate oscillatory behavior, a further decrease in K+ conductance leads to extremely high levels of [Ca2+]i. Our model also demonstrates that the effects of different K+ channel block can be offsetting. These results show explicitly how the effect of KV inhibitors on {beta}-cell depends on both their relative specificity and the glucose concentration.

Multiple drugs and molecular genetic approaches have been shown to modulate KV2.1 conductance and assembly (21). These approaches have been extremely useful to further understand the complex interrelationship of ion channels in the regulation of insulin secretion and may lead to further understanding of {beta}-cell functional defects in type 2 diabetes and approaches to amelioration of these defects.


    GRANTS
 TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
This work has been partially supported by National Institute of Diabetes and Digestive and Kidney Diseases Grants DK-444840, DK-48494, DK-63493, and DK-20595 (Diabetes Research and Training Grant at the University of Chicago) and the Blum-Kovler Foundation.


    ACKNOWLEDGMENTS
 
We are grateful to Drs. Deborah Nelson and Khaled Houamed for constructive comments on the manuscript, Dr. Bernard Herring for the gift of some of the human islets used in this work, and Ying Li Duan for excellent technical assistance.


    FOOTNOTES
 

Address for reprint requests and other correspondence: L. H. Philipson, Dept. of Medicine, The Univ. of Chicago, MC 1027, 5841 S. Maryland Ave., Chicago, IL 60637 (e-mail: l-philipson{at}uchicago.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


    REFERENCES
 TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 

  1. Ashcroft FM, Ashcroft SJ, and Harrison DE. Properties of single potassium channels modulated by glucose in rat pancreatic {beta}-cells. J Physiol 400: 501–527, 1988.[Abstract]
  2. Ashcroft FM and Rorsman P. Electrophysiology of the pancreatic {beta}-cell. Prog Biophys Mol Biol 54: 87–143, 1989.[CrossRef][Medline]
  3. Betsholtz C, Baumann A, Kenna S, Ashcroft FM, Ashcroft SJ, Berggren PO, Grupe A, Pongs O, Rorsman P, and Sandblom J. Expression of voltage-gated K+ channels in insulin-producing cells. Analysis by polymerase chain reaction. FEBS Lett 263: 121–126, 1990.[CrossRef][ISI][Medline]
  4. Bokvist K, Rorsman P, and Smith PA. Effects of external tetraethylammonium ions and quinine on delayed rectifying K+ channels in mouse pancreatic {beta}-cells. J Physiol 423: 311–325, 1990.[Abstract]
  5. Bou-Abboud E, Li H, and Nerbonne JM. Molecular diversity of the repolarizing voltage-gated K+ currents in mouse atrial cells. J Physiol 529: 345–358, 2000.[Abstract/Free Full Text]
  6. Chay TR. Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic {beta}-cells. Biophys J 73: 1673–1688, 1997.[Abstract]
  7. Cook DL and Hales CN. Intracellular ATP directly blocks K+ channels in pancreatic B-cells. Nature 311: 271–273, 1984.[CrossRef][ISI][Medline]
  8. Dean PM and Matthews EK. Electrical activity in pancreatic islet cells. Nature 219: 89–90, 1968.[ISI][Medline]
  9. Dukes ID and Philipson LH. K+ channels: generating excitement in pancreatic beta-cells. Diabetes 45: 845–853, 1996.[Abstract]
  10. Fridlyand LE, Tamarina N, and Philipson LH. Modeling of Ca2+ flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores. Am J Physiol Endocrinol Metab 285: E138–E154, 2003.[Abstract/Free Full Text]
  11. Gilon P, Shepherd RM, and Henquin JC. Oscillations of secretion driven by oscillations of cytoplasmic Ca2+ as evidences in single pancreatic islets. J Biol Chem 268: 22265–22268, 1993.[Abstract/Free Full Text]
  12. Henquin JC. Role of voltage- and Ca2+-dependent K+ channels in the control of glucose-induced electrical activity in pancreatic B-cells. Pflügers Arch 416: 568–572, 1990.[CrossRef][ISI][Medline]
  13. Houamed K, Fu J, Roe MW, and Philipson LH. Electrophysiology of the pancreatic {beta}-cell. In: Diabetes Mellitus: A Fundamental and Clinical Text (3rd ed.), edited by LeRoith D, Taylor SI, and Olefsky JM. Philadelphia, PA: Lippincott Williams & Wilkins, 2004, p. 51–70.
  14. Kanno T, Gopel SO, Rorsman P, and Wakui M. Cellular function in multicellular system for hormone-secretion: electrophysiological aspect of studies on {alpha}-, {beta}- and {delta}-cells of the pancreatic islet. Neurosci Res 42: 79–90, 2002.[CrossRef][ISI][Medline]
  15. Kauri LM, Jung SK, and Kennedy RT. Direct measurement of glucose gradients and mass transport within islets of Langerhans. Biochem Biophys Res Commun 304: 371–377, 2003.[CrossRef][ISI][Medline]
  16. Kelly RP, Sutton R, and Ashcroft FM. Voltage-activated calcium and potassium currents in human pancreatic {beta}-cells. J Physiol 443: 175–192, 1991.[Abstract]
  17. Lee SY and MacKinnon R. A membrane-access mechanism of ion channel inhibition by voltage sensor toxins from spider venom. Nature 430: 232–235, 2004.[CrossRef][ISI][Medline]
  18. Li-Smerin Y and Swartz KJ. Gating modifier toxins reveal a conserved structural motif in voltage-gated Ca2+ and K+ channels. Proc Natl Acad Sci USA 95: 8585–8589, 1998.[Abstract/Free Full Text]
  19. MacDonald PE, Ha XF, Wang J, Smukler SR, Sun AM, Gaisano HY, Salapatek AM, Backx PH, and Wheeler MB. Members of the Kv1 and Kv2 voltage-dependent K+ channel families regulate insulin secretion. Mol Endocrinol 15: 1423–1435, 2001.[Abstract/Free Full Text]
  20. MacDonald PE, Sewing S, Wang J, Joseph JW, Smukler SR, Sakellaropoulos G, Wang J, Saleh MC, Chan CB, Tsushima RG, Salapatek A, and Wheeler MB. Inhibition of Kv2.1 voltage-dependent K+ channels in pancreatic {beta}-cells enhances glucose-dependent insulin secretion. J Biol Chem 277: 44938–44945, 2002.[Abstract/Free Full Text]
  21. Nerbonne JM, Nichols CG, Schwarz TL, and Escande D. Genetic manipulation of cardiac K+ channel function in mice: what have we learned, and where do we go from here? Circ Res 89: 944–956, 2001.[Abstract/Free Full Text]
  22. Philipson LH, Hice RH, Schaefer K, LaMendola J, Bell GI, Nelson DJ, and Steiner DF. Sequence and functional expression in Xenopus oocytes of a human insulinoma and islet potassium channel. Proc Natl Acad Sci USA 88: 53–57, 1991.[Abstract/Free Full Text]
  23. Philipson LH. Beta-cell ion channels: keys to endodermal excitability. Horm Metab Res 31: 455–461, 1999.[ISI][Medline]
  24. Roe MW, Worley JF III, Mittal AA, Kuznetsov A, DasGupta S, Mertz RJ, Witherspoon SM III, Blair N, Lancaster ME, McIntyre MS, Shehee WR, Dukes ID, and Philipson LH. Expression and function of pancreatic {beta}-cell delayed rectifier K+ channels: role in stimulus-secretion coupling. J Biol Chem 271: 32241–32246, 1996.[Abstract/Free Full Text]
  25. Rorsman P and Trube G. Calcium and delayed potassium currents in mouse pancreatic {beta}-cells under voltage-clamp conditions. J Physiol 374: 531–550, 1986.[Abstract]
  26. Smith PA, Bokvist K, Arkhammar P, Berggren PO, and Rorsman P. Delayed rectifying and calcium-activated K+ channels and their significance for action potential repolarization in mouse pancreatic {beta}-cells. J Gen Physiol 95: 1041–1059, 1990.[Abstract]
  27. Sturis J, Pugh WL, Tang J, Ostrega DM, Polonsky JS, and Polonsky KS. Alterations in pulsatile insulin secretion in the Zucker diabetic fatty rat. Am J Physiol Endocrinol Metab 267: E250–E259, 1994.[Abstract/Free Full Text]
  28. Su J, Yu H, Lenka N, Hescheler J, and Ullrich S. The expression and regulation of depolarization-activated K+ channels in the insulin-secreting cell line INS-1. Pflügers Arch 442: 49–56, 2001.[CrossRef][ISI][Medline]
  29. Swartz KJ and MacKinnon R. An inhibitor of the Kv2.1 potassium channel isolated from the venom of a Chilean tarantula. Neuron 15: 941–949, 1995.[CrossRef][ISI][Medline]
  30. Swartz KJ and MacKinnon R. Hanatoxin modifies the gating of a voltage-dependent K+ channel through multiple binding sites. Neuron 18: 665–673, 1997.[CrossRef][ISI][Medline]
  31. Tamarina NA, Wang Y, Mariotto L, Kuznetsov A, Bond C, Adelman J, and Philipson LH. Small-conductance calcium-activated K+ channels are expressed in pancreatic islets and regulate glucose responses. Diabetes 52: 2000–2006, 2003.[Abstract/Free Full Text]
  32. Trimmer JS. Immunological identification and characterization of a delayed rectifier K+ channel polypeptide in rat brain. Proc Natl Acad Sci USA 88: 10764–10768, 1991.[Abstract/Free Full Text]
  33. Wollheim C and Sharp W. Regulation of insulin release by calcium. Physiol Rev 69: 914–973, 1981.
  34. Worley JF III, McIntyre MS, Spencer B, and Dukes ID. Depletion of intracellular Ca2+ stores activates a maitotoxin-sensitive nonselective cationic current in beta-cells. J Biol Chem 269: 32055–32058, 1994.[Abstract/Free Full Text]
  35. Yan L, Figueroa DJ, Austin CP, Liu Y, Bugianesi RM, Slaughter RS, Kaczorowski GJ, and Kohler MG. Expression of voltage-gated potassium channels in human and rhesus pancreatic islets. Diabetes 53: 597–607, 2004.[Abstract/Free Full Text]