The perforated whole-cell configuration of the patch-clamp technique was applied to functionally identified β-cells in intact mouse pancreatic islets to study the extent of cell coupling between adjacent β-cells. Using a combination of current- and voltage-clamp recordings, the total gap junctional conductance between β-cells in an islet was estimated to be 1.22 nS. The analysis of the current waveforms in a voltage-clamped cell (due to the firing of an action potential in a neighbouring cell) suggested that the gap junctional conductance between a pair of β-cells was 0.17 nS. Subthreshold voltage-clamp depolarization (to −55 mV) gave rise to a slow capacitive current indicative of coupling between β-cells, but not in non-β-cells, with a time constant of 13.5 ms and a total charge movement of 0.2 pC. Our data suggest that a superficial β-cell in an islet is in electrical contact with six to seven other β-cells. No evidence for dye coupling was obtained when cells were dialysed with Lucifer yellow even when electrical coupling was apparent. The correction of the measured resting conductance for the contribution of the gap junctional conductance indicated that the whole-cell KATP channel conductance (GK,ATP) falls from approximately 2.5 nS in the absence of glucose to 0.1 nS at 15 mM glucose with an estimated IC50 of approximately 4 mM. Theoretical considerations indicate that the coupling between β-cells within the islet is sufficient to allow propagation of [Ca2+]i waves to spread with a speed of approximately 80 μm s−1, similar to that observed experimentally in confocal [Ca2+]i imaging.
The pancreatic islet is a complex organ consisting of approximately 1000 cells of which the insulin-producing β-cells comprise 70–80 per cent in mice (Pipeleers 1987). Islet cells are electrically excitable and use electrical signals to couple changes in blood glucose concentration to stimulation or inhibition of hormone release (Henquin & Meissner 1984; Ashcroft & Rorsman 1989). The application of the patch-clamp technique to pancreatic islet cells has revolutionized our concepts about the stimulus–secretion coupling of the insulin-producing β-cells (Ashcroft & Rorsman 1989). These studies have revealed that ATP-regulated K+ channels (KATP channels) play a central role in linking changes in plasma glucose concentration to stimulation or inhibition of insulin secretion. The KATP channels are active in the absence of glucose (when the cytoplasmic ATP/ADP ratio is low). An increase in glucose leads, via a metabolically induced increase in the ATP/ADP ratio, to the closure of the KATP channels, which results in membrane depolarization, action potential firing, opening of voltage-gated Ca2+ channels, an increase in cytoplasmic [Ca2+]i and the initiation of exocytosis of insulin-containing secretory granules (Rorsman & Renström 2003). To date, almost all patch-clamp studies on β-cells have been carried out on isolated islet cells maintained in short-term tissue culture. Accumulating evidence indicates that the cellular properties may change during culture in an artificial medium containing foetal calf serum and when the cells are deprived of their normal environment (Göpel et al. 1999b). We have developed methods that allow patch-clamp measurements to be applied to islet cells within the intact islet (Göpel et al. 1999a,b, 2000a,b; Kanno et al. 2002). These studies have revealed that the electrophysiological properties of β-cells within the intact islet differ from those of isolated cells in several respects such as channel density and voltage dependence of their activation and inactivation, etc.
In the intact pancreatic islets, intercellular signalling can occur via both chemical (paracrine; Rorsman et al. 1989; Salehi et al. 2005) and electrical (via gap junctions; Charollais et al. 2000) signals. Both pathways of communication are disrupted when the islet is dissociated into single cells as is traditionally done prior to patch-clamp characterization. The functional significance of intercellular signalling is suggested by the fact that isolated β-cells exhibit a much poorer secretory capacity than β-cells in the intact islet (Pipeleers et al. 1982; Luther et al. 2006).
Evidence for electrical coupling via gap junctions between islet cells has previously been provided by electron microscopy (Orci et al. 1975), recordings of membrane potential and currents using sharp intracellular electrodes (Meissner 1976; Eddlestone et al. 1984; Mears et al. 1995), patch-clamp experiments on isolated islet cell pairs (Perez-Armendariz et al. 1991) and dye coupling (Michaels & Sheridan 1981; Charollais et al. 2000). It has in fact been proposed that the β-cells function as a ‘secretory syncytium’ (Santos et al. 1991). Gap junctions are formed by a family of proteins called connexins (Willecke et al. 2002). The most recent evidence has suggested that islet cells express connexin-36 (Calabrese et al. 2003). The gap junctions probably serve to synchronize electrical activity and secretion in β-cells in different parts of pancreatic islets (Eddlestone et al. 1984; Santos et al. 1991). However, it is less clear whether β-cells are also in electrical contact with neighbouring non-β-cells. Evidence for heterologous coupling was originally provided by dye-injection experiments (Michaels & Sheridan 1981; Meda et al. 1986), but functional studies (Göpel et al. 1999a; Nadal et al. 1999) suggest that coupling between β-cells and non-β-cells is weak.
Here, we have analysed the coupling between β-cells in intact islets using the whole-islet patch-clamp approach (Göpel et al. 1999a). We found that the gap junctional conductance between pairs of β-cells is approximately 0.17 nS and that each β-cell on average makes contact with another seven β-cells.
2. Materials and methods
(a) Islet preparation
Pancreatic islets were isolated from Naval Medical Research Institute mice. The mice were killed by cervical dislocation. Islets were obtained by collagenase digestion and maintained in short-term (6–24 hours) tissue culture as described elsewhere (Göpel et al. 1999a,b).
The standard extracellular solution was used for the recordings from intact islets, which consisted of (in mM) 140 NaCl, 3.6 KCl, 2 NaHCO3, 0.5 NaH2PO4, 0.5 MgSO4, 2.5 CaCl2, 5 HEPES (pH 7.4, adjusted with NaOH) and (unless otherwise indicated) 5 glucose. To block voltage-activated outward delayed rectifying K+ currents, 20 mM tetraethylammonium chloride (TEACl) was included in the extracellular medium in all experiments unless otherwise indicated. When TEA was present in the solution, the concentration of NaCl was correspondingly reduced to maintain iso-osmolarity. The pipette solution used consisted of (in mM) 76 K2SO4, 10 NaCl, 10 KCl, 1 MgCl2 and 5 HEPES (pH 7.35 with KOH).The perfusion solution used in Ca2+ imaging in intact islets contained (in mM) 140 NaCl, 3.6 KCl, 2 NaHCO3, 0.5 NaH2PO4, 0.5 MgSO4, 2.5 CaCl2, 5 HEPES (pH was adjusted to 7.4 with NaOH) and 1 or 20 glucose.
All electrophysiological measurements except those in figure 4 were performed using the perforated patch whole-cell technique using an EPC-9 patch amplifier controlled by the software package Pulse (Heka Electronics, Lambrecht, Germany; see details in Göpel et al. 1999a). Pancreatic β-cells were identified by the absence of voltage-gated Na+ currents when holding at −70 mV and the generation of oscillatory electrical activity when exposed to 10–15 mM glucose as described elsewhere (Göpel et al. 1999a). Non-β-cells were identified by the presence of a prominent voltage-gated Na+ current that remained observable when holding at −70 mV (Göpel et al. 1999a). All electrophysiological experiments were carried out at 32°C. The use of a subphysiological temperature improves membrane stability and thereby facilitates the electrophysiological measurements while maintaining secretory function (Renström et al. 1996).
(d) Ca2+ imaging
Intact islets were loaded in standard RPMI1640 tissue culture medium with the membrane-permeable Ca2+ dye fluo-4AM (1 μM; from Invitrogen) in the presence of 0.01 per cent pluronic acid for 30 min at 37°C. For these experiments, the islets were fixed with a wide-bore holding pipette within a continuously superfused and temperature-controlled (37°C) bath on an Axioskop 2 FS-mot microscope (Carl Zeiss, Jena, Germany; http://www.zeiss.com). Laser scanning confocal microscopy was performed using an LSM 510 META laser scanning module (Carl Zeiss, Jena, Germany). The Ca2+ indicator was excited with a 488 nm argon laser, and emitted fluorescent light was collected through a 500–550 nm band-pass filter. Increases in intracellular Ca2+ are displayed as upward deflections. Images were acquired at 393 ms intervals. The recordings were replayed off-line and regions of interest were selected and analysed using the Zeiss LSM 510 software.
(e) Dye coupling
The intracellular medium was supplemented with 2 μM of Lucifer yellow (Li+ salt; Invitrogen). Lucifer yellow was loaded into the cell via a patch-clamp electrode (during standard whole-cell recordings), filled with an intracellular medium containing (in mM) 125 CsCl, 10 NaCl, 1 MgCl2, 0.05 EGTA, 3 Mg-ATP, 0.1 cAMP and 5 HEPES (pH 7.1 using CsOH). The spread of Lucifer yellow fluorescence was monitored using a Bio-Rad Radiance 2100 confocal system (Carl Zeiss CellScience Ltd, Jena, Germany) using the 457 nm line of an argon laser. The emission of the dye was detected above 500 nm.
(f) Data analysis
All data are presented as mean values±s.e.m. of indicated number of cells. Statistical significances were evaluated with Student's t-test.
(a) Evidence for electrical coupling between β-cells in intact islets
Figure 1a(i) shows a membrane potential recorded from a β-cell within an intact islet exposed to 10 mM glucose using the perforated patch whole-cell technique. Membrane potential oscillated between a depolarized plateau with action potentials superimposed on it, and repolarized electrically silent periods. This type of electrical activity is regarded as a hallmark of the β-cell (Henquin & Meissner 1984) and is traditionally used for the functional identification of the β-cells. In a series of 20 experiments, the most negative voltage between the burst of action potentials and the plateau potential averaged Vi=−55±2 mV and Vp=−40±1 mV, respectively.
The amplifier was then switched into the voltage-clamp mode and the membrane potential was held at −70 mV. Under these conditions, the holding current recorded in the same cell as that used for the membrane potential recordings oscillated spontaneously and waveforms reminiscent of upside down bursts of action potentials were seen (figure 1a(ii)). These current oscillations are attributable to bursts of action potentials in the neighbouring unclamped cell(s) (Mears et al. 1995; Göpel et al. 1999a). In a series of 20 experiments, the holding current oscillated between a level of Ii=−18±3 pA during the silent period and Ip=−35±4 pA during the plateau phase. The measurements reported here were made using voltage and current records containing several bursts and thus represent the average of these parameters in the individual cell. We used the plateau and interburst voltages and currents rather than the action potentials for these calculations as the latter are highly variable and would result in large errors. We and others have previously reported that the gap junctional conductance only changes marginally (approx. 10%, if at all) during the active and silent phases (Mears et al. 1995; Göpel et al. 1999b; but see Andreu et al. 1997). Assuming that the membrane potential in the neighbouring cells oscillates in the same way as it does in the cell in direct contact with the patch electrode, the gap junctional conductance (Gj,tot) can be calculated using the relationship (Mears et al. 1995)(3.1)We thus derived an average value of Gj,tot of 1.22±0.16 nS (n=20) for the total conductance due to cell coupling. The observed current deflections represent the sum of currents injected from all neighbouring cells.
(b) Electrical coupling between individual pairs of β-cells
As previously reported, voltage-clamp currents can be recorded from β-cells in intact islets (Göpel et al. 1999a, 2000a). An example of a perforated patch whole-cell Ca2+ current recording from a β-cell in an intact islet is shown figure 1b. Under these experimental conditions (TEA present in the extracellular medium), the depolarization of the cell membrane to potentials below +10 mV elicited pure voltage-clamp currents (after the removal of linear capacitive and resistive components), i.e. currents flowing through the ion channels localized in the plasma membrane of the cell connected to the recording electrode (figure 1b, black curve in (ii)). However, depolarization of the cell to more positive voltages occasionally caused secondary current waveforms that were superimposed on the voltage-clamp Ca2+ currents recorded (figure 1b, red curve in (ii)). By analogy to what has been described in chromaffin cells (Moser 1998), we attribute these secondary waveforms to the firing of an action potential in neighbouring cells. During the depolarization of the voltage-clamped cell, current spread into the electrically coupled neighbours results in the concurrent depolarization of these cells. As the stimulus is increased, the threshold for firing of an action potential is approached and eventually exceeded. Assuming that the neighbours are not perfectly synchronized or equally connected, the current waveform can be used to estimate the conductance between the voltage-clamped cell and its best coupled neighbour. In a series of seven experiments, secondary action potential waveforms were first observed when the patch-clamped cell was depolarized from −70 mV to an average of 16±4 mV. Thus, the voltage-clamped cell must be depolarized by 86 mV with respect to the holding potential (−70 mV) to elicit an action potential in at least one of its neighbours.
How much of this voltage change is actually sensed by the neighbour? To answer this question, we recorded action potentials from a β-cell in an islet exposed to 10 mM glucose before and after the addition of 20 mM of TEACl (figure 2a), the broad-spectrum blocker of (voltage-gated) K+ channels (Hille 2001). Consistent with earlier reports (Atwater et al. 1979), addition of TEA+ converts the normal oscillatory glucose-induced electrical activity to continuous firing of large overshooting action potentials starting from a fairly repolarized membrane potential. We determined the threshold for action potential firing in the presence of TEA. The threshold was defined as the voltage at which the rapid upstroke of the action potential commenced. In a series of nine experiments, the threshold potential averaged −48±1 mV.
We also determined the threshold when the recordings were made in the presence of 5 mM glucose and 20 mM TEA when the cell was stimulated by depolarizing current pulses, i.e. the conditions used for the voltage-clamp measurements presented in figure 1b. A recording from a cell in which injection of 10 pA was required to evoke an action potential (grey curve) is shown in figure 2b. The corresponding threshold potential was approximately −40 mV (figure 2b). In a series of six experiments, the first action potential was observed 164±49 ms after the onset of the pulse, which required 18±11 pA of injected current and originated from a threshold potential of −43±2 mV. The latter value should be compared with the membrane potential of the β-cell in the presence of 5 mM glucose and 20 mM TEA, which amounted to −70±2 mV (n=16). Thus, the membrane of the neighbouring cell in figure 1b must depolarize by 27 mV, from −70 mV to −43 mV to attain the threshold for action potential firing.
(c) Equivalent circuit of two electrically coupled β-cells
An equivalent electric circuit of the voltage-clamped cell (cell 1) and one of its closest electrically coupled neighbours (cell 2) is shown in figure 2c. Here, the membrane conductance of the first cell (Gm1) and the coupling conductance (Gj) between the two cells are connected in parallel as will be the coupling conductance of any other cell joined directly to cell 1. Accordingly, the coupling of cells in an islet does not interfere with the clamping of the membrane potential in cell 1. The circuit may seem overly simplistic in considering two coupled cells only, but the inclusion of additional cells joined directly to cell 1 (while increasing the total conductance of gap junctions) neither affects the potential difference across the gap junctions nor the current flowing between any pair of cells. The influence on cell 1 of cells coupled with it via other cells is assumed to be negligible (Goforth et al. 2002).
To estimate the potential difference Uj across the gap junction (figure 2c) under conditions that lead to the occurrence of a secondary spike, we made the following considerations. First, as shown above, the spikes occur upon depolarization of cell 1 up to +16 mV. Second, current injection experiments revealed that the threshold for firing an action potential in a β-cell within an intact islet was −43 mV. In terms of the equivalent circuit in figure 2c, a secondary current spike in cell 1 will result if the following two conditions are satisfied:
U(1)−U(2)=16 mV and
Here U(1), U(2) and U(3) are the potentials at the corresponding points of the equivalent circuit (figure 2c). Combining these two conditions yields the potential difference across the gap junction,The conductance of a single gap junction connecting two β-cells can then be estimated by noticing that the voltage drop across the gap junction (Uj) relates to the voltage drop across the membrane of cell 2 (Um2) as the resistance of the gap junction (Rj) relates to the resistance of the membrane of cell 2 (Rm2); thus,(3.2)where Rm2 is the pure input resistance of the membrane with no connections to other cells. We estimated Rm2 by measuring the input resistance of isolated β-cells exposed to 5 mM glucose and 20 mM TEA, i.e. the same conditions as were used for the measurements of the other parameters of the equivalent circuit (figure 2c). In a series of six experiments, Rm2 was determined to be 2.70±1.7 GΩ. Inserting this value into the above equation and taking into account that the average Um2=27 mV (calculated on the basis of the equivalent circuit of coupled cells shown in figure 2c) yields a conductance for the gap junction between two adjacent β-cells of 0.17 nS. Comparing this value with the total gap junctional conductance estimated earlier (1.22 nS) suggests that each β-cell is connected to seven other cells (1.22 nS/0.17 nS). It should be noted that this estimate is based on the firing of an action potential in the best coupled neighbour. Thus, the estimate of the number of electrically coupled cells should be regarded as a lower estimate. The estimate also assumes that TEA does not affect the gap junctional conductance. We acknowledge that TEA has been reported to increase the number of gap junctions in rat β-cells by approximately 15 per cent over 90 min (Sheppard & Meda 1981). It is unlikely that this will occur during the short duration of our experiments (a few minutes) and even if it does such an effect will only have a marginal effect on the above estimate of the number of coupled cells.
(d) Analysis of capacitive currents in islets
An alternative way to detect and evaluate the coupling of cells in islets is the analysis of the transient capacitive currents that are elicited by applying a square voltage stimulus to a patch-clamped cell. As discussed elsewhere (Moser 1998), the transient capacitive current of an isolated cell should consist only of a single rapid component (reflecting the redistribution of charge during the depolarization) that relaxes within less than 1 ms. Usually, this current is cancelled out by the capacitance compensation network of the patch-clamp amplifier (EPC-9, Heka Electronics, Germany). In the presence of electrical coupling, however, the transient capacitive current should consist of at least two components with widely different kinetics: a fast component caused by the recharging of the membrane of the patched cell and a slow component resulting from the charging of the membranes of cells coupled to it. Records of membrane currents obtained using the perforated patch whole-cell technique and evoked by 15 mV depolarizing pulses applied from a holding potential of −70 mV are displayed in figure 3a. Although the fast current component in these recordings was almost completely neutralized by the capacitance compensation network of the patch amplifier, an additional slow component of capacitive current remained in β-cells in situ (figure 3a). This slow current component decayed with a mean time constant of 13.5±1.6 ms (n=5). When the same protocol was applied to a single isolated β-cell, the current response quickly settled at a new steady-state level with no sign of a slow uncompensated component (not shown). Moreover, no evidence for the slow component of capacitive current was observed in non-β-cells. The remaining rapid transients remaining in the non-β-cells we attribute to imperfect compensation of the pipette capacitance.
The capacitance Cm that represents all cells coupled to the patch-clamped cell is charged via the gap junctions with conductance Gj,tot. The time constant of this process is dependent on Gj,tot (or Rj,tot) and the total capacitance Cm and conductance Gm (or resistance, Rm) of the membranes of coupled cells. The set of resistances and capacitances of n identical coupled cells is represented by an equivalent circuit shown in figure 3b. This circuit consists of n branches connected in parallel and made of the resistance of the gap junction from the patched cell Rj (Gj) to the coupled neighbour as well as the neighbour's membrane resistance Rm1 (Gm1) and membrane capacitance Cm1. If we assume that all β-cells within an islet are electrically identical, we can substitute this circuit with the simpler circuit shown in figure 3c.
The simplified circuit is made up of a resistance Rj,tot (Gj,tot), corresponding to the total resistance of all gap junctions, and a resistance Rm (Gm) and a capacitance Cm that represent the total resistance and capacitance, respectively, of all the membranes of the coupled cells. These aggregate values are related to respective values for single cells in the following manner:(3.3)Hence,(3.4)The time constant τ for charging the capacitance Cm in this circuit is equal to(3.5)The derivation of this relationship takes into account that the resistances Rm and Rj,tot are not coupled in series since a response of the circuit to alternating currents is being considered. Note that this is in contrast to our earlier analysis (equation (3.2)) where we consider direct currents. Details of the derivation are given in appendix A. From the observed value of τ, the value of Gj can be determined using these relationships. The value of Gj is dependent on the electrical characteristics of the individual coupled cell. This is because all coupled cells are connected in parallel. Again, we assume that the effects of cells attached to closest neighbours are small and can be neglected in this context (Goforth et al. 2002). Simple rearrangement of the equation (3.5) yields(3.6)Inserting numerical values (Cm1=7.4 pF, Gm1=2.7 GΩ and τ=13.5 ms) into this equation gives an estimate of Gj of 0.18 nS. The latter value is in good agreement with the 0.17 nS derived for Gj based on the analysis of the action currents (figure 2c).
We also estimated the electrical charge Q (integrated current) that is needed to charge the membranes of all cells directly coupled to the patched cell. This charge was found by integrating the slow capacitive current (, where I(t) is the time-dependent capacitive current) from figure 3a. In a series of five experiments carried out on functionally identified β-cells, the charge thus estimated averaged to 217±46 fC. The relationship between charge Q, membrane capacitance Cm1 and voltage change across it ΔV is given by the expression Q=Cm1.ΔV. Given that a neighbouring coupled cell experiences approximately 30 per cent of the voltage applied to the voltage-clamped cells (i.e. 27 mV out of the 86 mV applied to patched cell; see above), then the membrane potential of the electrically coupled cell will change by approximately 5 mV during the 15 mV voltage pulse. This assumption is valid because the electric elements involved are linear and do not depend on voltage. In a cell with a membrane capacitance of 7.4 pF, this voltage change requires a charge transfer of 34 fC. Comparing this value with the 217 fC obtained by the integration of the current response indicates that every β-cell is electrically connected with another six to seven β-cells.
(e) Absence of dye coupling between β-cells
Lucifer yellow has previously been used to visualize coupling between islet cells (Meda et al. 1986; Charollais et al. 2000). Patch electrodes were filled with Lucifer yellow (2 μM) and the cell was imaged on a confocal microscope. A set of images from a representative experiment is shown in figure 4a. Lucifer yellow accumulates within the nucleus (see arrows), providing a means of establishing the number of cells labelled. In a series of 10 experiments, no sign of dye coupling was observed and only the cells connected to the patch electrodes were stained. Despite the lack of dye coupling, the cells were clearly electrically coupled as evidenced by the occurrence of inverted action potentials during whole-cell voltage-clamp recordings (figure 4b). The absence of detectable dye coupling in electrically coupled β-cells is in agreement with recent reports from another laboratory (Quesada et al. 2003).
In many cells (including the one shown in figure 4b), the oscillations in holding current reflecting action potential firing in neighbours fluctuated between different levels. An unusually clear example of three discrete current levels present is seen in figure 4c. The amplitude of these steps was approximately 5 pA in this cell. We attribute these steps to the unsynchronized initiation of action potentials in increasing the number of neighbouring cells. Thus, it appears that the cell in figure 3c was electrically connected to at least three neighbours.
(f) Effects of cell coupling on measurements of KATP conductance
The gap junctional coupling of β-cells in intact mouse pancreatic islets is too weak to affect measurements of the voltage-gated currents over the physiological voltage range (cf. figure 1b). By contrast, cell coupling will affect recordings of currents that are not voltage gated. These include the KATP conductance, which represents the glucose-regulated membrane conductance in the β-cell (Ashcroft & Rorsman 1989). The resting conductance of the cell membrane is traditionally monitored by applying 10–20 mV pulses from a holding potential at −70 mV. In β-cells within intact islets, the resting conductance in the patch-clamped cell is the sum of the gap junctional conductance (Gj), unknown leak conductance (Gleak) and the whole-cell KATP conductance (GK,ATP). For mouse islets, the total resting conductance varies between 3.6 nS in the absence of glucose and 1.1 nS in the presence of glucose concentrations of 20 mM glucose and above or following the addition of the KATP channel blocker tolbutamide (Göpel et al. 1999a). Given that the method used to obtain the data presented in figure 1 measures the gap junctional conductance only and does not detect any leak conductance, it may seem surprising that the resting conductance measured at 20 mM glucose (that will be contaminated by leak currents) is lower (1.1 nS) than the coupling conductance obtained by the evaluation of the coupling currents in figure 1 (1.22 nS). However, there is a simple and functionally significant explanation of this finding.
Consider the equivalent circuit shown in figure 5a. This circuit represents the network of three main conductances GK,ATP, Gleak and Gj for two coupled cells. It can be seen that the gap junctional conductance is in series with all other membrane conductances in the cell coupled to the patch-clamped cell (forthwith referred to as the ‘background conductance’ Gb). The whole-cell resting conductance (GR) is then given by the expression(3.7)In the absence of glucose (i.e when GK,ATP is high), most of the voltage drop will occur across the gap junctions since this resistance is higher than that of the cell membrane coupled in series to the gap junction (5.9 versus 2.7 GΩ). Glucose-induced closure of the KATP channels reduces the resting conductance not only by the closure of the channels located in the patch-clamped cell but also in the neighbouring cells, thus leading to a reduction of Gb. Consequently, measurements of GK,ATP are influenced by cell coupling. When GK,ATP is high, coupling contributes only marginally to the measured GR. This is because Gj is low compared with GK,ATP and most of the current passing through the recording electrode will leave via the KATP channels. As glucose is elevated and GK,ATP falls, an increasing proportion of the current will pass via Gj and eventually (when GK,ATP=0) Gj will become dominant because it consists of several membrane and leak conductances connected in parallel. Accordingly, the contribution of cell coupling to the measured GR will vary at different glucose concentrations.
Figure 5b shows the glucose dependence of the β-cell resting KATP conductance after correction for the variable Gb. The correction was calculated for six coupled identical cells as follows. First, we rewrite, for n coupled cells, the equation for the resting conductance GR taking into account additionally that the background conductance Gb=GK,ATP+Gleak. This gives the following equation:(3.8)Solving this for Gb (dashed curve in figure 5b) results in the expression(3.9)At high glucose concentrations, when GK,ATP approaches zero, Gb becomes equal to Gleak. The corrected curve for GK,ATP (red dashed curve in figure 5b) can then be obtained by subtracting Gb at 25 mM glucose (forthwith referred to as G25G) from Gb, i.e.(3.10)The net GK,ATP (red dashed curve) falls from 2.3 nS at 0 mM glucose to zero at glucose concentrations above 20 mM glucose with an IC50 of 3.7 mM.
(g) Propagation of [Ca2+]i waves in an islet
[Ca2+]i imaging experiments have revealed that the [Ca2+]i oscillations in different parts of an islet are well synchronized (Valdeolmillos et al. 1989; Santos et al. 1991). Can the widespread Ca2+ oscillations be accounted for by the electrical coupling we measure here? To address this question, we performed [Ca2+]i imaging in intact mouse islets in the absence and presence of 20 mM glucose. As shown in figure 6a, addition of 20 mM glucose (after an initial lowering of [Ca2+]i) triggers oscillations in [Ca2+]i in individual β-cells (three examples shown) that were not active in the absence of sugar. These oscillations are sufficiently well coupled to result in synchronized [Ca2+]i oscillations that can be resolved at the whole-islet level.
In addition to the [Ca2+]i oscillations evoked by high glucose, a subset of cells were active in the absence of glucose. These cells are likely to be glucagon-producing α-cells (figure 6b). The [Ca2+]i oscillations in these cells were not synchronized and therefore could not be resolved at the whole-islet level (figure 6a,b; grey shaded areas).
We analysed the spread of the [Ca2+]i wave in intact mouse islets. Figure 6c shows an example where the propagation of a [Ca2+]i wave was monitored along the periphery of the islet in eight different cells. The penetration of the Ca2+ indicator into deeper cell layers was insufficient to allow accurate [Ca2+]i imaging in the islet centre. The wave started in cell 1 and then travelled with a speed ranging between 8 μm s−1 (between cells 3 and 4) and above 149 μm s−1 (between cells 2 and 3 and cells 6 and 7) with an average of 57 μm s−1. In a series of four experiments/islets conducted in the presence of 20 mM glucose and analysed similarly, the [Ca2+]i wave propagated at an average velocity of 81±11 μm s−1.
(h) Is electrical coupling sufficient to account for islet [Ca2+]i synchronization?
We examined whether electrical coupling between β-cells is sufficient to synchronize β-cells across the islets. Consider the time required to charge the membrane capacitance of a β-cell by current injection. For these calculations, the β-cell is represented by an equivalent circuit composed of a resistance R connected in parallel with a capacitance C. If current iinj is applied to the input of this circuit, then, according to Kirchhoff's laws, the time dependence of the amount of charge q on C is described by a differential equation,(3.11)A partial solution of this differential equation with an initial condition q=0 when t=0 is(3.12)Here ΔV is the change of voltage across the cell membrane at time t. Solving equation (3.12) for t yields an expression that allows us to calculate the charging time of the cell,(3.13)In five cells with clear bursting pattern of electrical activity, the amplitude of the burst (from the most hyperpolarized voltage to the peak of the action potential) averaged −42±2 mV. In the same experiments, the ‘pacemaker’ depolarization (ΔV; see figure 2a for definition) between two successive bursts averaged 5±2 mV. With these values of ΔV and taking R, C and the gap junctional conductance to be 2.7 GΩ, 7.4 pF and 0.17 nS, respectively, equation (3.13) can be simplified to(3.14)The expression reveals that the minimum value of iinj that will be capable of charging the cell is 2 pA. With a burst amplitude of 42 mV, iinj can be estimated to be 7.1 pA. Inserting this value into equation (3.14), the time needed to charge a neighbour is approximately 7 ms.
It is well established that electrical activity within a mouse pancreatic islet is synchronized (Meissner 1976; Eddlestone et al. 1984; Mears et al. 1995) and results in coordinated oscillations in [Ca2+]i across the islet (Valdeolmillos et al. 1989; Santos et al. 1991). Cell coupling has been proposed to explain the synchronization of β-cell electrical activity (Meda et al. 1986; Charollais et al. 2000), but it is also possible that signalling by autocrine and paracrine factors is involved (Salehi et al. 2005).
A detailed characterization of the membrane currents in islet cells requires the means of voltage clamping these cells. We have developed techniques that allow patch-clamp recordings from cells in intact islets (Göpel et al. 1999a). It is possible that cell coupling can interfere with these measurements and that regenerative processes in neighbouring cells (that are not voltage clamped) might contaminate the signals measured in the cell in direct contact with the recording electrode. Here, we have analysed the extent of cell coupling in intact mouse pancreatic islets combining voltage-clamp and current-clamp measurements with confocal [Ca2+]i imaging. The fact that some measurements were conducted under voltage-clamp conditions (when the membrane potential is controlled) enables us to distinguish between whole-cell conductances that are attributable to cell coupling and those that arise from the activity of ion channels. We show that whereas cell coupling does not interfere with the measurements of voltage-gated currents, it contributes to the measured resting conductance. Theoretical considerations further suggest that although cell coupling in the islet is fairly weak, it is of sufficient strength to explain the synchronization of electrical activity and [Ca2+]i in the islet that underlie pulsatile insulin secretion (Gilon et al. 1993).
(a) Pancreatic β-cells are weakly coupled to each other
The total gap junctional conductance between a β-cell and its neighbours amounts to approximately 1.22 nS (0.8 GΩ). By analogy to a similar patch-clamp study on the cell coupling between chromaffin cells within adrenal slices (Moser 1998), we conclude that the gap junctional conductance between β-cells in situ is too low to allow voltage clamping of the neighbouring cells. We estimate that only approximately 30 per cent of the voltage change imposed on the voltage-clamped cell spreads into the neighbours (see figure 2). This means that during depolarizations from −70 mV to voltages below 0 mV, the membrane potential in the electrically coupled neighbours will not exceed the threshold for firing an action potential and the observed current responses will principally (if not exclusively) reflect the ionic currents flowing through the membrane of the voltage-clamped cell. During larger voltage steps, however, the threshold will eventually be exceeded and the resultant action potential(s) in the unclamped neighbours will give rise to large transients superimposed on the current responses. However, it takes a fairly long time for these current transients to appear even during strong depolarizations and the current amplitude can be determined accurately during the first approximately 10 ms after the application of the depolarizing pulse. Reassuringly, the voltage dependence of the voltage-gated membrane currents measured in β-cells in intact islets is the same as in isolated cells (Rorsman & Trube 1986; Göpel et al. 1999a).
Based on the analysis of the firing of action potentials and the slow capacitive currents elicited by subthreshold stimuli, we estimate that every β-cell is coupled to approximately seven other β-cells. Interestingly, dye-coupling experiments have indicated a similar value for the number of coupled cells (Charollais et al. 2000). Our value for the gap junctional conductance between two β-cells within the islet is 0.17–0.18 nS. This is in reasonable agreement with previous estimates obtained in isolated pairs of β-cells: 0.15 nS (Andreu et al. 1997) and 0.22 nS (Perez-Armendariz et al. 1991).
(b) Effects of coupling on measurements of the KATP conductance
Because the gap junctions of the cells in direct contact with the patch-clamped cell in electrical terms are connected in parallel, cell coupling will not affect the voltage clamp of the cell connected to the pipette and properties of the voltage-gated currents can thus be expected to be reported accurately. However, cell coupling will affect measurements of the resting conductance. Thus, the relationships between KATP whole-cell conductance (GK,ATP) and the glucose concentration that have been reported previously (figure 5 and Göpel et al. 1999a) must be corrected for the contribution of cell coupling. The original data indicated a drop in conductance from approximately 4 nS to approximately 1 nS when the glucose concentration is increased from 0 to 20 mM (figure 5b). After correction for coupling, GK,ATP instead falls from a maximum value of 2.3 nS in the absence of glucose to values close to or less than 0.1 nS at glucose concentrations exceeding 15 mM (figure 5). Importantly, an increase in glucose from 7 to 17 mM is associated with a reduction of the corrected GK,ATP from 0.61 nS to 0.07 nS (figure 5b, grey shaded area). Thus, glucose influences GK,ATP over a wide range of glucose concentrations in a way that may contribute to the concentration-dependent increase in β-cell electrical activity observed at intermediate glucose concentrations (Henquin & Meissner 1984; Kanno et al. 2002). It also accounts for the ability of the sulphonylureas to convert oscillatory electrical activity into continuous action potential firing.
(c) Non-β-cells are not electrically coupled
In addition to confirming the existence of coupling between β-cells, this study extends previous observations indicating lack of coupling between non-β-cells (Göpel et al. 1999a). Thus, no slow capacitive current was observed in response to subthreshold depolarizations in non-β-cells (identified by the presence of a Na+ current that can be activated from a holding potential of 70 mV). We acknowledge that our failure to detect any evidence for electrical coupling between non-β-cells is at variance with earlier electrophysiological (Meda et al. 1986), dye-coupling (Michaels & Sheridan 1981) and ultrastructural studies (Orci et al. 1975). However, recent experiments employing confocal imaging of the cytoplasmic Ca2+ concentration have revealed that Ca2+ in both glucagon-secreting α-cells and somatostatin-producing δ-cells, unlike the β-cells, oscillates asynchronously (Nadal et al. 1999; Quesada et al. 1999) and our data support these observations (figure 6b). Given that both α- and δ-cells have a high input resistance (Bokvist et al. 1999; Barg et al. 2000; Göpel et al. 2000a,b), it appears that coupling between β- and non-β-cells must be weak as even the small currents entering via the gap junctions would otherwise have dramatic effects on the membrane potential of these cells. Thus, we propose that weak coupling is a prerequisite to allow electrical activity and secretion to be differentially (β- and δ-cells; Zhang et al. 2007) and reciprocally (β- and δ-cells versus α-cells; Macdonald et al. 2007) regulated by glucose.
(d) Cell coupling is sufficient to account for propagation of [Ca2+]i waves
Mouse β-cells exposed to insulin-releasing glucose concentration exhibit [Ca2+]i oscillations that can be resolved at both the single-cell and the whole-islet level. It is possible that these oscillations are due to electrical coupling, but it has also been proposed that diffusible factors co-released with insulin (such as ATP) underlie synchronization (Salehi et al. 2005).
The time to charge a neighbour via the gap junctions is as short as 7 ms. Yet, we observe a delay of several seconds between the onset of a [Ca2+]i wave in different parts of the islet (figure 6). However, the passive electrical spread of impulses across the islet only accounts for a small part of the delay, which is mainly (95%) attributable to the time it takes to initiate an action potential after the depolarization of the cell membrane. In our experiments, this parameter averaged approximately 165 ms, and we thus arrive at a total value of 172 ms for the propagation of an action potential from one cell to another. With a cell diameter of approximately 15 μm, we estimate that the [Ca2+]i wave will travel with a speed of 88 μm s−1 (15 μm/0.17 s). This is in surprisingly good agreement with the 81 μm s−1 observed in the confocal [Ca2+]i imaging experiments (figure 6c,d).
Can cell coupling be of pathophysiological significance? It was recently reported that in mice expressing non-functional KATP channels in 70 per cent of the β-cells, normal KATP channel activity in the remaining cells, the communication between normal and impaired cells, via cell coupling, is sufficient to restore nearly normal glucose regulation of [Ca2+]i and insulin secretion (Rocheleau et al. 2006). Conversely, an increase in KATP channel, due to an impairment of metabolism in a minority of β-cells, will via the reduction in input resistance impede the passive spread of depolarization across the islet (see equation (3.12)). Thus, small changes in either the gap junctional conductance and/or the amplitude of the bursts may have dramatic effects on cell coupling, the synchronization of the [Ca2+]i waves and thus the pulsatility of insulin secretion. Given that type-2 diabetes is associated with the loss of pulsatile insulin secretion in both rodents (Lin et al. 2001) and humans (Lang et al. 1981), it should therefore be considered whether this defect is attributable to impaired electrical coupling between the β-cells.
This work was supported by the Wellcome Trust, the Swedish Research Council (L.E.) and the European Union through BioSim (contract no. LSHB-CT-2004-005137) and Eurodia (contract no. LSHM-CT-2006-518153). F.A. is on leave from the University of São Paulo, Brazil, on a CNPq fellowship—Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazil. L.E. is employed by the Lund University Diabetes Centre and P.R. is a Wolfson-Royal Society Merit Award Fellow.
One contribution of 12 to a Theme Issue ‘Biomedical applications of systems biology and biological physics’.
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