Synchronization and entrainment of cytoplasmic Ca2+ oscillations in cell clusters prepared from single or multiple mouse pancreatic islets

Milos Zarkovic and Jean-Claude Henquin

Unité d'Endocrinologie et Métabolisme, University of Louvain Faculty of Medicine, B-1200 Brussels, Belgium

Submitted 12 February 2004 ; accepted in final form 20 April 2004


    ABSTRACT
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 DISCLOSURES
 REFERENCES
 
In contrast to pancreatic islets, isolated {beta}-cells stimulated by glucose display irregular and asynchronous increases in cytoplasmic Ca2+ concentration ([Ca2+]i). Here, clusters of 5–30 cells were prepared from a single mouse islet or from pools of islets, loaded with fura-2, and studied with a camera-based system. [Ca2+]i oscillations were compared in pairs of clusters by computing the difference in period and a synchronization index {lambda}. During perifusion with 12 mM glucose, the clusters exhibited regular [Ca2+]i oscillations that were quasi-perfectly synchronized ({Delta} period of 1.4% and index {lambda} close to 1.0) between cells of each cluster. In contrast, separate clusters were not synchronized, even when prepared from one single islet. Pairs of clusters neighboring on the same coverslip were not better synchronized than pairs of clusters examined separately (distinct coverslips). We next attempted to synchronize clusters perifused with 12 mM glucose by applying external signals. A single pulse of 20 mM glucose, 10 mM amino acids, or 10 µM tolbutamide transiently altered [Ca2+]i oscillations but did not reset the clusters to oscillate synchronously. On a background of 12 mM glucose, repetitive applications (1 min/5 min) of 10 µM tolbutamide, but not of 20 mM glucose, synchronized separate clusters. Our results identify a level of {beta}-cell heterogeneity intermediate between single {beta}-cells and the whole islet. They do not support the idea that substances released by islet cells serve as paracrine synchronizers. However, synchronization can be achieved by an external signal, if this signal has a sufficient strength to overwhelm the intrinsic rhythm of glucose-induced oscillations and is repetitively applied.

{beta}-cells; intracellular calcium; insulin secretion


ISOLATED PANCREATIC {beta}-CELLS characteristically display heterogeneous metabolic, signaling, biosynthetic, and secretory responses upon stimulation with glucose (4, 17, 18, 24, 37, 39, 42). This heterogeneity is both quantitative (dose-response curves are variable) and qualitative (changes in the cytoplasmic Ca2+ concentration are irregular). Physiologically, however, {beta}-cells are not isolated but associated within the islets of Langerhans, where their behavior is much more homogeneous (2, 10, 23, 27, 30, 38). One important feature of this homogeneity in mouse and human islets is the generation by glucose of well-synchronized oscillations of cytoplasmic Ca2+ concentration ([Ca2+]i) in all {beta}-cells of the organ (10, 25, 38). Combined measurements of [Ca2+]i and insulin secretion have also shown that these [Ca2+]i oscillations trigger pulses of insulin secretion (see review in Ref. 11).

Altered pulsatility of insulin secretion has often been described in diabetic patients (see reviews in Refs. 11 and 31). Although it is still unclear how the pulsatility of individual islets is coordinated to induce pulsatility of insulin secretion in vivo, perturbations of the synchrony between {beta}-cells within the islets is a plausible cause of alterations of islet function in type 2 diabetes. Glucose-induced [Ca2+]i oscillations are perturbed in islets of db/db mice, a model of human type 2 diabetes (35). Poor synchronization of [Ca2+]i changes in the large islets of hyperinsulinemic and hyperglycemic ob/ob mice is also accompanied by an alteration of insulin pulsatility (34). Understanding how the intrinsically heterogeneous behavior of individual {beta}-cells becomes coordinated when the cells associate is thus important from both biological and pathophysiological standpoints.

We have previously reported that mouse {beta}-cells associated in small clusters (2–50 cells) show homogeneous [Ca2+]i changes during stimulation with glucose, but that this association does not suppress the heterogeneity of the responses between clusters (21, 22). However, one possible cause of heterogeneity has not been considered so far. The differences in [Ca2+]i responses of neighboring clusters could be due to the fact that these clusters originate from distinct islets, possibly from different mice. We therefore quantitatively evaluated the synchrony of glucose-induced [Ca2+]i oscillations in pairs of clusters of {beta}-cells prepared from one single mouse islet. We also evaluated whether single or repetitive external signals can reset or entrain the [Ca2+]i pulsatility in pairs of clusters and thereby improve the synchrony.


    METHODS
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 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 DISCLOSURES
 REFERENCES
 
Solutions. The control medium was a bicarbonate-buffered solution that contained (in mM) 120 NaCl, 4.8 KCl, 2.5 CaCl2, 1.2 MgCl2, and 24 NaHCO3. It was gassed with O2-CO2 (94:6) to maintain pH 7.4 and was supplemented with 1 mg/ml bovine serum albumin (fraction V). The Ca2+-free solution used to disperse islets in clusters contained (in mM) 138 NaCl, 5.6 KCl, 1.2 MgCl2, 5 HEPES, 1 EGTA, 100 IU/ml penicillin, and 100 µg/ml streptomycin, and its pH was adjusted to 7.35 with NaOH. The medium used for cultures was RPMI 1640 medium, containing 10 mM glucose, 10% heat-inactivated fetal calf serum, 100 IU/ml penicillin, and 100 µg/ml streptomycin.

Preparation. The research project was approved by, and the experiments were conducted in accordance with, the guidelines of the "Commission d'Ethique d'Expérimentation Animale" of the University of Louvain Faculty of Medicine. Fed male NMRI mice from a local colony were killed by decapitation. Islets were then isolated by collagenase digestion of the pancreas followed by hand-picking (20). To obtain clusters from multiple islets, about 15 islets, usually from several mice, were incubated for 5 min in a Ca2+-free solution. After brief centrifugation, this solution was replaced by 125 µl of culture medium, and the islets were disrupted by gentle pipetting through a siliconized glass pipette. The drop of medium was then deposited on a 22-mm glass coverslip placed in a petri dish and kept overnight at 37°C in a 5% CO2 atmosphere. The next morning, when cells and clusters had attached to the coverslip, 2 ml of culture medium were added in the petri dish, and the preparation was cultured for another 24–30 h before use. To obtain clusters from one single islet, the procedure was slightly modified. A ring of plastic, cut from an Eppendorf tip, was attached to the coverslip with a small amount of sterile silicone grease. The 125 µl of culture medium containing the clusters were deposited within the ring. The next morning, the ring was gently removed, and 2 ml of culture medium were added in the petri dish. This procedure was necessary to ensure attachment of the few clusters in close position and so permit simultaneous examination of at least two clusters with a 40x objective.

Measurements of [Ca2+]i. Clusters attached to the coverslips were loaded with fura-2 during 60 min of incubation in control medium containing 10 mM glucose and 1 µM fura-2 AM. After the preparation had been loaded with fura-2, the coverslip was transferred into a temperature-controlled perifusion chamber (Intracell, Royston, Herts, UK) of which it formed the bottom. The chamber was placed on the stage of an inverted microscope (40x objective), perfused with medium of the indicated composition, and maintained at 37°C. The tissue was successively excited at 340 and 380 nm, and the fluorescence emitted at 510 nm was captured by a charge-coupled device camera (Photonic Science, Turnbridge Wells, UK). The images obtained at 4.7-s intervals were analyzed by the MagiCal system (Applied Imaging, Sunderland, UK). From the ratio of the fluorescence at 340 and 380 nm, the concentration of [Ca2+]i at each pixel was calculated by comparison with an in vitro calibration curve (22).

Clusters of islet cells were selected visually by size only. The number of cells in the studied clusters was determined at the end of the experiment by adding 1 µM bisbenzimide to the chamber and counting the fluorescent nuclei (22). Only those clusters comprising between 5 and 30 cells were used for data analysis.

Analysis of results. To make all series equal in length and correct for small differences in sampling intervals, the data were resampled to 3-s intervals before the analysis. This was done using cubic spline interpolation (32). The period of [Ca2+]i oscillations was then determined by spectral analysis of the [Ca2+]i profiles, according to the Welch method (16). Two methods were used to estimate synchronization of [Ca2+]i oscillations in pairs of clusters. The period of [Ca2+]i oscillations was computed for the two clusters, and the difference in period was expressed as a percentage of the average period for the pair ({Delta} period in %). Only pairs with no {Delta} period or only a small {Delta} period are synchronized, but this does not necessarily mean that they oscillate in phase. Phase synchronization was determined by a recently developed method (36) that evaluates the probability that two periodic series have the same phase. One of the measures of this probability is the synchronization index {lambda} (see Eq. 19 in Ref. 36). This index is based on a stroboscopic approach: whenever the phase of the first oscillator reaches a predetermined fixed value ({theta}), the phase of the second one is determined. This comparison is done for all available oscillations. If the oscillators are synchronized, when the phase of the first oscillator reaches {theta}, the phase of the second oscillator will be similar to {theta}, and its distribution will thus display a peak near {theta}. If the oscillators are not synchronized, the phase of the second oscillator will be scattered over 0–2{pi}, and the phase distribution will be uniformly distributed between 0 and 2{pi}. Repeating this procedure for all values of {theta} in the interval [0,2{pi}], and averaging them, provide the synchronization index {lambda}. In the case of perfect synchronization, the index {lambda} is 1; in the absence of synchronization the index {lambda} approaches 0. Note that this measure is independent of differences in amplitude of the events. The practical procedure of calculation is described in an appendix.

Presentation of results. The experiments are illustrated by representative recordings, and quantified data are presented as means ± SE. The statistical significance of differences between means was assessed by analysis of variance followed by a Games-Howell test for multiple comparisons (19). In some cases, a paired Student's t-test was used.


    RESULTS
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 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 DISCLOSURES
 REFERENCES
 
Synchronization of [Ca2+]i oscillations induced by glucose in pairs of islet cell clusters. During continuous stimulation with 12 mM glucose, clusters of mouse islet cells exhibited repetitive transient elevations of [Ca2+]i (14, 22, 29). Figure 1 illustrates these [Ca2+]i oscillations in two pairs of clusters, each prepared from a single islet. In one pair of clusters (Fig. 1A) the period of the oscillations was similar (3.23 min), although the duration of [Ca2+]i elevations was slightly shorter in cluster 2 than in cluster 1. In the other pair (Fig. 1B), [Ca2+]i oscillations occurred at very different frequencies (periods of 4.22 and 2.74 min). In the 89 clusters studied, the period of [Ca2+]i oscillations ranged from 1.59 to 6.56 min, with a mean of 3.62 ± 0.10 min (Fig. 2A).



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Fig. 1. Cytoplasmic Ca2+ concentration ([Ca2+]i) oscillations in 2 pairs of islet cell clusters prepared from single islets. The preparations were perifused with a medium containing 12 mM glucose for 65 min, of which only the last 35 min are shown. Thick lines show [Ca2+]i changes in the whole clusters, and thin lines show [Ca2+]i changes in two distinct noncontiguous regions of each cluster. A: [Ca2+]i oscillations were virtually synchronous between cluster 1 (10 cells) and cluster 2 (6 cells). B: [Ca2+]i oscillations were clearly asynchronous between cluster 1 (9 cells) and cluster 2 (16 cells). A and B: [Ca2+]i oscillations were consistently synchronous within each individual cluster.

 


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Fig. 2. Period of [Ca2+]i oscillations and evaluation of the synchronization of these oscillations between pairs of islet cell clusters prepared from single islets. Preparations were perifused for 65 min with a medium containing 12 mM glucose, as illustrated in Fig. 1. A: period of [Ca2+]i oscillations in 89 clusters prepared from 26 islets, obtained from 13 mice. B: {Delta} period of [Ca2+]i oscillations between pairs of clusters originating from a single islet. The {Delta} period, expressed as a percentage of the mean period for the 2 clusters, is shown for all pairs of clusters (n = 129) and for pairs differing by 0–2 (n = 63) or >2 cells (n = 66) in number. The {Delta} period is also shown for pairs of regions within clusters. C: index {lambda}, expressing the phase synchronization of [Ca2+]i changes between pairs of clusters or between pairs of regions within clusters. An index {lambda} of 1.0 would correspond to perfect synchrony (see METHODS).

 
The synchrony of [Ca2+]i changes between pairs of clusters was estimated in two ways. First, the difference in the period ({Delta} period) was measured and expressed as a percentage of the mean period for the pair. It ranged from 0% (pairs with identical periods) to 71%, with a mean of 17.9 ± 1.3% (Fig. 2B). Second, the synchronization index {lambda} was computed to assess whether the two clusters oscillate in phase, a value of 1 corresponding to oscillators perfectly in phase. It ranged from 0.15 to 0.85, with a mean of 0.32 ± 0.01 (Fig. 2C). For the pair of well-synchronized clusters shown in Fig. 1A, {Delta} period was 0% and index {lambda} was 0.85, smaller than 1.0 because the increases in [Ca2+]i are slightly different in duration. For the pair of poorly synchronized clusters shown in Fig. 1B, {Delta} period amounted to 43% and index {lambda} 0.26, greater than zero because 4 of the 9 oscillations in cluster 1 start at about the same time as 1 of the 13 oscillations in cluster 2.

The degree of synchrony of [Ca2+]i oscillations in pairs of clusters was independent of differences in cluster size. The {Delta} period was not smaller, and the synchronization index {lambda} was not higher when the two clusters of the pair differed by only 0–2 cells or by more than 2 cells (on average by 4.3 ± 0.4 cells; Fig. 2, B and C).

This poor synchronization of separate clusters contrasts with the excellent synchrony of [Ca2+]i oscillations between regions within each cluster. This is illustrated for two regions of each of the four clusters shown in Fig. 1 and is quantified in Fig. 2. The {Delta} period between regions within clusters was only 1.4 ± 0.3% of the mean period (Fig. 2B), i.e., less than the average sampling interval (4.7 s). The synchronization index {lambda} was close to 1.0 (Fig. 2C).

We next compared the synchronization of [Ca2+]i oscillations between pairs of clusters prepared from one single islet or from multiple islets obtained from several mice. This comparison was done in another series of experiments in which the clusters were initially perifused with 12 mM glucose for 20 min. As expected, the average period of [Ca2+]i oscillations was similar in the two groups of clusters (Fig. 3A). The {Delta} period and the synchronization index {lambda} were not different whether pairs of clusters originated from a single islet or multiple islets (Fig. 3, B and C). Thus pairs of clusters prepared from a single islet are not better synchronized than pairs prepared from multiple islets.



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Fig. 3. Comparison of the synchronization of [Ca2+]i oscillations in pairs of clusters prepared from single or multiple islets. These results were computed over a 20-min period of stimulation with 12 mM glucose (start of experiments illustrated by Fig. 4) for 61 clusters prepared from single islets and 46 clusters prepared from multiple islets.

 
If an extracellular signal originating from islet cells themselves influenced synchronization of neighboring clusters, the degree of synchrony should be higher between pairs of clusters on the same coverslip than between clusters on distinct coverslips. This was not the case. For all pairs of clusters studied on the same coverslip, {Delta} period and index {lambda} averaged 19.2 ± 1.7% and 0.47 ± 0.02, respectively (n = 103). These values are not different from those obtained from the comparison of clusters on different coverslips: {Delta} period of 21.6 ± 1.2% and index {lambda} of 0.43 ± 0.02 (n = 236). There is thus no evidence for a better synchronization of adjacent than of completely separated clusters.

Attempts to synchronize [Ca2+]i oscillations in pairs of clusters by a single pulse or repetitive stimulatory pulses. In a first series of experiments, we determined whether a single, 5-min pulse of 20 mM glucose, 5 mM leucine + 5 mM glutamine, or 10 µM tolbutamide could reset [Ca2+]i oscillations induced by 12 mM glucose and improve the synchrony of these oscillations between pairs of clusters. Each type of pulse induced a more sustained [Ca2+]i rise than during stimulation with 12 mM glucose alone, 20 mM glucose being less efficient than the amino acids or tolbutamide (Fig. 4). After the pulse, the oscillations induced by 12 mM glucose resumed, without obvious difference in the degree of synchronization of the two clusters. These changes were quantified over two periods, early and late after the pulse (Table 1). The pulse of 20 mM glucose did not affect the period of [Ca2+]i oscillations subsequently induced by 12 mM glucose. It also had no impact on the synchronization of pairs of clusters ({Delta} period and index {lambda}). The pulse of leucine + glutamine produced a small, early increase in index {lambda} and a minor, delayed increase in {Delta} period. The pulse of tolbutamide caused a transient increase in the {Delta} period. Overall, none of these three pulses was able to reset pairs of clusters to oscillate synchronously (Table 1).



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Fig. 4. Attempt to synchronize [Ca2+]i oscillations in pairs of clusters by a single stimulatory pulse. Pairs of clusters were prepared from single or multiple islets. They were perifused with a medium containing 12 mM glucose, and a pulse of 20 mM glucose (A), 5 mM leucine + 5 mM glutamine (B), or 10 µM tolbutamide (C) was applied between 20 and 25 min. Traces are representative of results obtained in 38 (A), 33 (B), and 36 (C) clusters from 39 islet preparations.

 

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Table 1. Impact of a single stimulatory pulse on the period of [Ca2+]i oscillations induced by 12 mM glucose and their synchrony in pairs of islet cell clusters

 
In a second series of experiments, pairs of clusters were repetitively stimulated by pulses (1 min every 5 min) of 20 mM glucose on a background of 3 mM glucose, 20 mM glucose on a background of 12 mM glucose, or 10 µM tolbutamide on a background of 12 mM glucose. In the presence of 3 mM glucose, [Ca2+]i was low and stable. Pulses of 20 mM glucose on this low-glucose background triggered repetitive elevations of [Ca2+]i that occurred almost at the pacing rhythm (period of 4.68 ± 0.21 min; Fig. 5A). The difference with the theoretical period of 5 min is due to the rare occurrence of a [Ca2+]i rise during the intervening 4-min period at 3 mM glucose (not illustrated). These imposed [Ca2+]i changes were well synchronized in pairs of clusters, with a {Delta} period of only 3.3 ± 0.9% and an index {lambda} of 0.86 ± 0.04. These values reflect a much better synchrony than during continuous stimulation with 12 mM glucose (Fig. 2, Table 1).



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Fig. 5. Attempt to synchronize [Ca2+]i oscillations in pairs of clusters by repetitive stimulatory pulses. Pairs of clusters were prepared from single or multiple islets. They were perifused simultaneously with a medium containing 3 mM glucose (A) or 12 mM glucose (B and C), and pulses of 20 mM glucose (A and B) or 10 µM tolbutamide (C) were applied for 1 min every 5 min. Traces are representative of results obtained in 15, 25, and 20 clusters from 35 islet preparations.

 
The reference values given in Table 1 should also be used to evaluate the impact of the pulses with 20 mM glucose or 10 µM tolbutamide on a background of 12 mM glucose, because the initial 10-min period of perifusion with 12 mM glucose alone in these experiments (Fig. 5, B and C) is too short to compute period, {Delta} period, and index {lambda} reliably. When the preparations were stimulated by 1-min pulses of 20 mM glucose every 5 min, the period of [Ca2+]i oscillations remained well below 5 min (3.27 ± 0.20 min), because additional [Ca2+]i oscillations occasionally occurred during the intervening periods in 12 mM glucose (Fig. 5B). In addition, the synchrony of [Ca2+]i elevations between clusters was not improved, as shown by a {Delta} period of 30.0 ± 5.0% and an index {lambda} of 0.37 ± 0.02.

The pulses of tolbutamide were more efficient in pacing the system to a period of 4.82 ± 0.15 min. The synchronization of pairs of clusters was also improved with a {Delta} period of 8.5 ± 3.8% and an index {lambda} of 0.81 ± 0.03. However, the degree of synchronization of distinct clusters remained well below that of regions within individual clusters, with an index {lambda} of 0.97 in the three groups.


    DISCUSSION
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 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 DISCLOSURES
 REFERENCES
 
The glucose-induced slow oscillations of [Ca2+]i that we studied in mouse islet-cell clusters are abolished by omission of extracellular Ca2+, by blockers of the L-type Ca2+ channels, or by membrane repolarization with diazoxide (22, 29). They correspond to depolarization-mediated periodic influx of Ca2+ into {beta}-cells.

To be synchronous, [Ca2+]i oscillations in distinct {beta}-cells, clusters, or islets must have a similar period. This was assessed here by computing the {Delta} period. However, two oscillations with similar periods can occur out of phase or display different shapes (e.g., Fig. 1A). We therefore determined the probability of phase synchronization by the index {lambda} (36). The results show that the {Delta} period is virtually zero (smaller than the recording interval) and the index {lambda} close to one for [Ca2+]i oscillations occurring in different {beta}-cells within single clusters. These quantifications therefore validate previous, more subjective, conclusions that glucose-induced [Ca2+]i oscillations are quasi-perfectly synchronized within islet cell clusters (22).

We also show that the synchronization is far less between physically separated clusters. Overall, the average {Delta} period of 20% corresponds to ~45 s. This poor (or lack of) synchronization cannot be explained by differences in the size of the compared clusters. Previous experiments have also shown that, above 5 cells, the size of the cluster does not influence the period of glucose-induced [Ca2+]i oscillations (22). An important novel finding is that the synchronization is not better between clusters prepared from one single islet than between clusters prepared from several islets taken from pools of islets from several animals. This unanticipated observation refutes the hypothesis that distinct origins of the clusters significantly contribute to the lack of synchronization.

In addition, these findings point to a level of heterogeneity that is intermediate between the individual {beta}-cell and the whole islet. Association of functionally heterogeneous {beta}-cells in clusters ensures regularity and synchrony of the [Ca2+]i response in the group, but juxtaposition of such groups in the islet is not enough. All cluster subunits must associate for the homogeneous response of the islet to emerge.

The coupling of {beta}-cells via gap junctions has generally been proposed as mediator of the synchronization (5, 22, 26, 27, 30), but doubts have sometimes been expressed. These are based on observations that dye and metabolic coupling are restricted to small territories of the islet (4, 28) and on the inability of putative blockers of gap junctions to disrupt the synchrony of [Ca2+]i oscillations in primary or reconstituted islets (3, 40). These arguments are probably not valid for several reasons: first, the tested drugs were not shown to effectively block gap junctions in the above experiments; second, electrical coupling is much more widespread than dye coupling and resistant to these drugs in the islets (26, 30, 33); third, disruption of gap junctions between insulin-secreting MIN6 cells by transfection of a connexin-36 antisense (to downregulate the protein composing these gap junctions) altered the synchrony of [Ca2+]i transients evoked by a mixture of glucose and tetraethylammonium (5).

An alternative and nonexclusive explanation is that synchronization is achieved by extracellular signals. ATP, acting on purinergic receptors (6), and nitric oxide (13) have been suggested to serve that function, but these proposals have been disputed (3, 15). As-yet-unidentified signals could be released either by nerve endings to coordinate different islets in situ, or by islet cells themselves, to aid in the intraislet coordination. The latter proposal is often made by exclusion, because the alleged blockers of gap junctions are ineffective (3, 40). It can also be made for positive reasons, because [Ca2+]i transients are sometimes synchronous (that is, they occur within 10–20 s) in nontouching {beta}-cells (12, 13). Again, the arguments should be qualified for the following reasons. These experiments were done with {beta}-cells from leptin-deficient ob/ob mice, which are known to produce [Ca2+]i responses that partly differ from those in normal {beta}-cells (1, 9, 34). Some of these transients, observed during perifusion with a medium containing a blocker of voltage-dependent Ca2+ channels and glucagon (13), reflect brief mobilizations of [Ca2+] that are extremely rare in normal {beta}-cells (1). Other transients are similar to those we studied here, but their synchrony in pairs of cells was only 7%, and improved to no more than 20% in the presence of glucagon (12). The present results and their analysis by a more stringent definition of synchronization do not support the proposal that an extracellular signal synchronizes the system. Thus the synchrony was not better between clusters on the same coverslip than between clusters on different coverslips. Although one could argue that we failed to detect such a paracrine action because extracellular fluid circulation in our in vitro system differs too much from that in the interstitial space of an islet, the inescapable conclusion is that no such signal is necessary to ensure quasi-perfect synchrony within clusters.

Signals (metabolic, neural) extrinsic to the islet might influence the synchronization. Injection of an electrical current within an islet or a single pulse of high KCl (8) has been shown to reset the rhythm without changing the characteristics of the membrane potential oscillations induced by glucose in {beta}-cells. Here, a single pulse of high glucose, amino acids, or tolbutamide was applied on pairs of clusters. The pulse transiently affected the [Ca2+]i signals but did not reset the two clusters to oscillate in synchrony. In each cluster the endogenous, initial rhythm resumed.

When short (1-min) glucose pulses were repetitively superimposed on a nonstimulatory background, pairs of clusters were well entrained to produce synchronous [Ca2+]i increases. The synchronization was much less efficient when similar pulses were applied on a background of 12 mM glucose, which already induced [Ca2+]i oscillations. However, pulses of tolbutamide almost succeeded in pacing pairs of clusters in the presence of 12 mM glucose. Overall, our data show that the intrinsic rhythm of [Ca2+]i oscillations observed in the presence of glucose alone is solid enough to overwhelm a single resetting attempt or too-weak repetitive external signals. This does not imply that synchronization by extrinsic signals is impossible, but the signals probably must be of another chemical or temporal nature. Previous experiments have indeed succeeded in entraining insulin secretion in vitro from groups of perifused rat islets by imposing glucose excursions of 5% above and below the ambient concentration of 5.5 or 7 mM (7, 41). The efficacy of these pulses is remarkable and may be linked to a slower (10–40 min) pacing around the threshold for glucose-induced insulin secretion.


    APPENDIX
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 DISCLOSURES
 REFERENCES
 
The synchronization index {lambda} can be calculated using Octave or Matlab packages, which both contain all necessary routines. In the following procedure, Octave/Matlab reserved words and functions are typed in bold, whereas variables are typed in italics.

1) Import the data: read tab delimited file using appropriate functions (fopen and fscanf for example), and name the imported data as data1 and data2.

2) Calculate the instantaneous phase: a) Detrend the data using the detrend function:


b) Perform a Hilbert transform of the detrended data using Hilbert function:


c) Calculate the instantaneous phase:


d) The function (hilb_phase), summarizing a-c, can be used to compute phase (data xx):




3)Calculate the synchronization index {lambda}:
a) Calculate mod 2{pi} of the previously calculated phases:



b) Bin the phase of the first oscillator (data1), i.e., divide the interval [0,2{pi}] into N equal bins. The number of bins must be the same in all experiments to be compared, with no empty bin.

The hist function gives the number of points in each bin.
The sort function gives the position (index) of the point in the data vector.


c) Calculate {lambda} values for each bin, and average {lambda} of all bins using the function (strobo):

% determination of synchronization using stroboscopic function as described by Rosenblum et al. (Ref 36)

Summary: With use of the previously described Octave/Matlab functions, (10 bins) can be calculated by the following procedure:




    GRANTS
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 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 DISCLOSURES
 REFERENCES
 
This work was supported by the "Interuniversity Attraction Poles Programme (PAI 5/17) Belgian Science Policy", by Grant 00/05–260 from the General Direction of Scientific Research of the French Community of Belgium, and by grants from the Fonds National de la Recherche Scientifique (Brussels).


    DISCLOSURES
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 DISCLOSURES
 REFERENCES
 
M. Zarkovic was holder of a research fellowship from the Belgian Science Policy. His present address: Institute of Endocrinology, Diabetes and Metabolism, University of Belgrade, 11000 Belgrade, Serbia.


    ACKNOWLEDGMENTS
 
We are grateful to J. C. Jonas for helpful comments on the appendix.


    FOOTNOTES
 

Address for reprint requests and other correspondence: J. C. Henquin, Unité d'Endocrinologie et Métabolisme, UCL 55.30, Ave. Hippocrate 55, B-1200 Brussels, Belgium (E-mail: henquin{at}endo.ucl.ac.be).

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
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 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 DISCLOSURES
 REFERENCES
 

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