Leader β-cells coordinate Ca2+ dynamics across pancreatic islets in vivo

Pancreatic β-cells form highly connected networks within isolated islets. Whether this behaviour pertains to the situation in vivo, after innervation and during continuous perfusion with blood, is unclear. In the present study, we used the recombinant Ca2+ sensor GCaMP6 to assess glucose-regulated connectivity in living zebrafish Danio rerio, and in murine or human islets transplanted into the anterior eye chamber. In each setting, Ca2+ waves emanated from temporally defined leader β-cells, and three-dimensional connectivity across the islet increased with glucose stimulation. Photoablation of zebrafish leader cells disrupted pan-islet signalling, identifying these as likely pacemakers. Correspondingly, in engrafted mouse islets, connectivity was sustained during prolonged glucose exposure, and super-connected ‘hub’ cells were identified. Granger causality analysis revealed a controlling role for temporally defined leaders, and transcriptomic analyses revealed a discrete hub cell fingerprint. We thus define a population of regulatory β-cells within coordinated islet networks in vivo. This population may drive Ca2+ dynamics and pulsatile insulin secretion. Pancreatic β-cells are highly connected, and this network is crucial for the pulsatile release of insulin. Here Salem and colleagues demonstrated the existence of leader β-cells that respond first to glucose and are more closely linked to the other β-cells. They also showed that glucose increases β-cell calcium dynamics and connectivity between the leader and non-leader β-cells.

D efective insulin secretion underlies diabetes mellitus, a disease affecting almost one in eight of the adult population worldwide, consuming 10% of healthcare budgets of westernized societies (https://www.idf.org). Impaired secretion is absolute in type 1 diabetes and relative in type 2 diabetes 1 .
Individual β-cells within the pancreatic islets possess all of the enzymatic machinery required for glucose sensing and insulin secretion 2,3 , although marked heterogeneity exists at the transcriptomic 4-7 , metabolic 8 , electrophysiological 9,10 and secretory [11][12][13] levels. Questions remain over whether this heterogeneity has any functional significance, and whether it could, for example, contribute to the pulsatile release of insulin 14 .
Connections between individual β-cells 15,16 are essential for the normal control of hormone secretion 10,14,17 . Using Ca 2+ imaging of isolated islets in vitro, two distinct, but complementary, ways of analysing β-cell connectivity have emerged. Earlier studies described an increase in the number of correlated cell pairs using Pearson-based analysis, which assesses similarities between the Ca 2+ traces for individual cells over time 18,19 . This strategy revealed that stimulation with glucose or glucagon-like peptide-1 causes pan-islet increases in β-cell connectivity, which are disrupted under conditions mimicking type 2 diabetes (for example, 'gluco(lipo)toxicity'). More recently, we have applied an approach based on signal binarization 20 and reported that a subset of 5-8% β-cells form super-connected 'hubs' within the interconnected network 18 . We also demonstrated that these cells are likely to serve as pacemakers 21 . Both of these approaches utilize the term 'connectivity' to describe the functional co-activity of β-cells within an islet.
The behaviour of the isolated islet in culture 18,21 is likely to differ notably from that in vivo, where islets are continuously perfused with blood and receive complex neural inputs. Imaging of the islet within the intact pancreas in vivo is, however, challenging and requires exteriorization of the whole organ. A powerful alternative approach is the engraftment of islets into the anterior eye chamber (ACE) 22 . Combined with the use of stably expressed, recombinant fluorescent probes 23,24 , this creates an optically accessible platform allowing repeated measurements over time if required 25 . In the present study, we use this strategy, alongside an analogous genetic modification of the zebrafish 26 , to record multilayer β-cell Ca 2+ dynamics in the intact living animal 27 . Pancreatic islets display a largely conserved size, but partly species-specific 28 arrangement, of neuroendocrine cell types 29 , important for the proper control of insulin secretion 17 . In the zebrafish, most of the pancreatic endocrine cells are located in a single primary islet 27 . By 5 days post-fertilization (dpf) (as used in these experiments) zebrafish larvae have developed a primary islet that contains an average of 30 β-cells that express mature markers such as Ucn3l 26 . Later, in the juvenile stage, the zebrafish still possesses the large, embryonically derived, primary islet and has also developed many smaller secondary islets 30 . We have previously shown that the primary zebrafish islet responds in vitro to glucose 26 and ablation of β-cells at this developmental stage leads to glucose intolerance in the larva 31 . Thus, by 5 dpf the primary islet is glucose responsive and systemically connected, serving as an excellent model to study islet β-cell coordination.
It was demonstrated that glucose induces strongly coordinated pan-islet Ca 2+ responses in each setting, with a definable point of origin and propagation characteristics in three dimensions. In zebrafish, the ablation of 'leader' cells, that is, those that respond first to glucose challenge, results in a dampening of the response of the islet to subsequent stimulation with glucose, redolent of the effects of optogenetic inactivation of 'hub' cells in the isolated mouse islet 21 . In mice, analyses based on signal binarization and Monte Carlo-like shuffling/randomization 21 demonstrate the existence of a population of super-connected cells under stimulatory conditions in vivo. Moreover, causality analysis 32,33 unites these observations in fish and mouse by demonstrating that temporally defined 'leader cells' are also those that were causally the most closely linked to other β-cells, whereas analyses of single-cell RNA-sequencing (RNA-seq) data suggest they may possess a unique transcriptional profile. Hence, we demonstrate that a functional β-cell hierarchy exists in vivo, and may control pulsatile insulin secretion.

Results
Glucose controls β-cell connectivity in living zebrafish. To explore Ca 2+ dynamics in vivo with single-cell resolution the study first imaged, at low acquisition speeds (0.1 Hz; see Supplementary  Fig. 1a), zebrafish larvae (4-5 dpf) expressing GCaMP6 under the insulin promoter (Fig. 1a) and the nuclear β-cell marker Tg(ins:cdt1-mCherry), which marks 86 ± 6.6% (n = 5 islets) of all β-cells by 5 dpf. The present study focused on the primary zebrafish islet, which is the only islet present at this stage. First, ex vivo imaging was used for a direct comparison of the glucose responsiveness of the primary and secondary islets dissected from adult fish 34 . As expected, β-cells from the primary and secondary islets showed apparent Ca 2+ influx on stimulation with 10 and 20 mM glucose or depolarization with potassium chloride (n = 3 primary and n = 3 secondary islets) (see Supplementary Video 1). Thus, the primary islet is an adequate system for studying the glucose-stimulated Ca 2+ dynamics in zebrafish β-cells, as well as representing the major site of insulin storage.
In vivo imaging of GCaMP6-expressing β-cells in larvae revealed the existence of endogenous oscillations in cytosolic free Ca 2+ (12 out of 12 animals studied; see Supplementary Fig. 1a-c and Supplementary Video 2). This activity was inhibited by pericardial injection of insulin, which lowered whole-animal glucose (see Supplementary Fig. 1c-f and Supplementary Video 3), indicating that the oscillatory Ca 2+ signal was due to elevated circulating levels of glucose that are measurable by 4-5 dpf (ref. 35 ). Ca 2+ dynamics were also decreased after a transient suppression of blood flow by a temporally controlled heart block (see Supplementary Video 4). Time-lapse imaging of red blood cells and β-cells confirmed that the zebrafish islet is perfused in larvae (see Supplementary Video 5). Taken together, these results reveal that endogenous β-cell Ca 2+ oscillations are likely to be involved in the systemic sensing of glucose in vivo in zebrafish.
Next the impact of increasing the levels of glucose in the zebrafish circulation was explored. Pericardial injection of glucose was performed, allowing for rapid entry of the sugar into the circulation (Fig. 1b-d). After a short lag (20-50 s), this manoeuvre led to a rapid increase in cytosolic Ca 2+ concentrations (assessed as the time taken to achieve a GCaMP6 signal >20% above baseline) in β-cells across the islet (Fig. 2b-d and Supplementary Video 6), and corresponded to the time-dependent increases in whole-animal glucose concentrations assessed separately (Fig. 1e).
Next attempts were made to determine the degree to which the β-cell population in these experiments was connected before and after stimulation with glucose, first at low imaging speeds of 0.1 Hz ( Fig. 2 and Supplementary Figure 2), and then at high imaging speeds of 3 Hz (Fig. 3a-d). Pearson-based functional connectivity maps (see Methods) were derived of pairwise comparisons between the Ca 2+ traces of individual cells 21,36 . At low imaging speeds, 10-15% of cells hosted a connection to another cell before glucose injection, and this rose significantly to ~50% after glucose injection (P <0.001; Fig. 2c-f). A similar, dramatic increase (P <0.01) was seen for connection strength (that is, Pearson's correlation, R; Fig. 2e). Of note, the temporally defined 'leader' cells (first responders to glucose stimulation) were among the most highly connected. For example, in the animal shown in Fig. 2, Ca 2+ increases were first observed in two out of nine cells (cell 2 and cell 6; Fig. 2b), and these cells were the most connected on Pearson's analysis at high glucose (connected to seven or eight other cells out of a total of nine analysed; see Supplementary Table 1).
Recorded at a higher acquisition rate (3 Hz) across a single plane, β-cells again displayed modest connectivity at low glucose (preinjection ~ 20%; Fig. 3d). The increases in intracellular Ca 2+ that followed glucose injection (Fig. 3a,b) were associated with a significant rise in the correlation coefficient (Fig. 3c), as well as a marked increase in the number of functionally connected cell pairs (postinjection ~88%, P <0.0001, Fig. 3d). Approached using Pearson's analysis at high glucose, essentially every cell became strongly connected to every other cell. Finally, whole-islet live imaging at an acquisition rate of 0.8 Hz, covering ~700 µm 3 , was achieved. In this way, it was possible to resolve most (20) of the cells within the primary islet of the zebrafish (Fig. 3e) and extract their signal spatially in three dimensions ( Fig. 3f and Supplementary Video 7). We then undertook three-dimensional (3D) connectivity analysis on three separate zebrafish islets before and after glucose stimulation (as before). Fig. 3g shows the 3D connectivity analysis for one fish islet, with the mean coefficient of correlation rising from 40.1 to 89.1, and the fraction of connected cells rising from 11.2% to 92.3% with a glucose bolus. Results for the other two islets showed the same rise in Pearson's coefficient (83.2 to 91.7 and 44.9 to 85.1) and rise in connected cells (33.3% to 55.5% and 16.7% to 38.1%). We therefore concluded that functional connectivity occurs across the entire fish islet and that two-dimensional (2D; single plane) connectivity analysis in the fish accurately reflects what occurs across the entire islet.
Ablation of leader cells prevents subsequent Ca 2+ waves in the zebrafish embryo. To determine whether 'leader' (first responder) cells may serve a regulatory role, as demonstrated previously for mouse islets in vitro 21 , cell ablation through two-photon laser irradiation was used ( Fig. 4 and Supplementary Videos 8 and 9). Animals were challenged with three separate pulses of pericardial glucose introduced before and after irradiation of either leader or follower cells (n = 20 leader and n = 20 follower cell ablation experiments). Whereas ablation of follower cells had no discernible effect on the subsequent Ca 2+ spikes, ablation of leader cells led to a significant reduction in the total islet GCaMP response (Fig. 4). Only targeted cells revealed evidence of nuclear destruction, whereas the neighbouring cells showed no obvious damage (see Supplementary  Fig. 4). Moreover, it was shown that islet blood flow remains unaltered after the ablation of the cells using bright-field imaging both before and after the ablation (see Supplementary Videos 8 and 9). Thus, the targeted ablation of a single β-cell in vivo does not appear to perturb either local endothelial cells or the rest of the β-cells in the islet.
Leader cells do not preferentially derive from the dorsal or ventral buds in the zebrafish embryo. The primary zebrafish Articles Nature MetabolisM islet contains both dorsal bud-derived β-cells (DBCs) and ventral bud-derived β-cells (VBCs). To interrogate whether embryonic derivation affected the identity of leader cells, we performed injection of messenger RNA (mRNA) encoding the histone H2B-RFP to distinguish between DBCs and VBCs based on label dilution 37 Fig. 1 | Glucose-stimulated Ca 2+ influx imaged in vivo in living zebrafish. a, Cartoon representing a transgenic zebrafish larva expressing the genetically encoded Ca 2+ indicator GCaMP6 (green) and the nuclear marker cdt1-mCherry (red) under the insulin promoter. GCaMP6 allows the examination of glucose-induced Ca 2+ influx in the β-cell reported by changes of the green fluorescence in a Ca 2+ concentration-dependent fashion. b, Maximum intensity projections of an islet imaged before, during and after the pericardial injection of 5 nl of 25 mM glucose solution. Imaging and glucose stimulation were performed simultaneously. Note the near-synchronous increase in GCaMP6 fluorescence intensity across all the β-cells in the islet on glucose injection. c, A trace showing cumulative normalized fluorescence intensity over time for the cells shown in a. The black arrow marks the instance of the glucose injection. cʹ, Normalized fluorescence intensity over time for each individual cell, with each cell represented by a square. The normalized GCaMP6 fluorescence is displayed as a heat-map, showing the degree of cell activity (n = 10 animals, not graphically represented here). d, Quantification of the islet response to glucose stimulation. The graph depicts the GCaMP6 AUC covering 100 s before and 100 s after glucose stimulation (n = 3, paired, two-tail, Student's t-test, P = 0.0108, data are mean ± s.d.). The injection of glucose led to a dramatic increase in GCaMP6 fluorescence intensity. e, Changes in measured free glucose concentration in larvae after glucose injection as in a. Each dot represents a pool of 10 injected larvae (n = 3 for each time point; one-tailed ANOVA, with Tukey's multiple comparisons test, P = 0.0488 for 0 versus 5 min and P = 0.0152 for 5 versus 15 min). Data are mean ± s.d. Scale bars, 10 μm. The cartoons shown in a belong to the authors of this study. The experiments in b,c were performed independently three times with several samples showing similar results. d, A quantification from thee biological replicates from one of the repeats. The experiment in e was performed once with multiple samples. of one representative experiment in which the leader cell was H2B-RFP positive. This implies that both the DBCs and the VBCs can become leader cells. It is important to note that, in these experiments, we did not observe impaired responsiveness of DBCs to glucose stimulation as such, indicating that DBCs indeed exhibit characteristics of functional β-cells.
Glucose enhances Ca 2+ dynamics and elicits increases in β-cellβ-cell connectivity in islets in living mice. We next extended our analysis to islets from adult mice, with superficial β-cell layers infected with adenoviral GCaMP6m (AV-GCaMP6m), before engraftment into the AEC of recipient mice 22 . Non-β-cells are not infected by this protocol due to the absence of the cognate receptor (Coxsackie virus receptor 38 ). Using animals maintained under general anaesthetic, we collected data at acquisition speeds of 1 Hz, before and after intraperitoneal glucose injection (see Methods).
Ca 2+ dynamics were increased in response to a rise in circulating glucose. The proportion of significantly Pearson-connected cells increased on average from 38 ± 11% to 65 ± 9% (n = 5 islets in 5 animals, P = 0.028) with a non-significant (P = 0.11) rise in the mean coefficient of connectivity from 0.54 ± 0.03% to 0.63 ± 0.04%.
Subsequently, islets were generated from transgenic mice that highly selectively expressed GCaMP6f in the β-cell, under the control of Cre recombinase expressed from the Ins1 locus 39,40 , and transplanted into the mouse ACE as above. Almost every β-cell (~95%) 21 within the transgenic islet expressed the Ca 2+ probe, allowing interrogation of the activity of many more cells per islet, including those localized more deeply in the islet core (typically 50-100). Data were captured at higher rates (up to 3 Hz) under low and high circulating glucose conditions (see Methods).
Strikingly, and in contrast to islets infected with adenoviral GCaMP6f, it was observed that the wave-like behaviour of the β-cell Ca 2+ increases in all islets (examined separately and in ten different animals) at high circulating glucose levels (see Supplementary Videos 11, 12 and 13; Figs. 5b and 6c). Ca 2+ waves were initiated at discrete sites (see Supplementary Video 12), with propagation velocities of 12.0 ± 3.4 μm s -1 (n = 5 wave bursts). As shown in the example in Fig. 5b and Supplementary Video 13, although most cells were quiescent under low glucose conditions, high circulating glucose levels were associated with runs of highly coordinated oscillations, even after prolonged glucose exposure (10 min, Figs. 5b and Fig. 6a).
It was possible to quantify connectivity using both Pearson's and binarized data approaches (Figs. 5 and 6). As observed in the fish, high circulating glucose was associated with a notably higher mean coefficient of connectivity and proportion of connected cells, versus the low glucose condition, as revealed by Pearson's analysis (Fig. 5c-e and Supplementary Fig. 5a). A piezo device was also used to allow for fast acquisition of β-cell readouts in three separate cell layers under low and high circulating glucose conditions, to investigate whether β-cell connectivity existed in three dimensions (see Methods). Of note, the notable rise in pan-islet β-cell connectivity at high circulating glucose levels also occurred between cells that were more than a layer apart on 3D imaging (Fig. 5c-e and Supplementary  Fig. 5a). Pearson's analysis was, however, unable to detect important differences in co-activities required for identification of super-connected cells/hubs. In contrast, application of a binarized approach (see Methods) 21 revealed a scale-free network topography in which 8.7 ± 3.7% of cells hosted the majority (60-100%) of connections (Fig. 6a,b and Supplementary Fig. 6). Pooled over all five islets examined, the R 2 value for this power-law distribution was 0.62.
Finally, we examined islet Ca 2+ dynamics over 10 min at steadystate high glucose levels (and also acquired medium and low glucose acquisitions from the same cells in the same 1-h-long imaging study), to exclude the possibility that pan-islet connectivity is related to spatially aggregated β-cells simply responding acutely and synchronously to a rise in circulating glucose concentration. Blood sugar readings recorded over these imaging sessions did not reveal oscillating glucose levels, excluding the trivial possibility that glucose oscillations themselves are driving Ca 2+ oscillations (Fig. 5b). A concerted, elevated Pearson's correlation and percentage β-cell connectivity were achieved over these longer acquisitions with higher (and sustained) circulating glucose levels (Fig. 6a).

Prospective analysis (Granger causality).
Given the challenges of a direct interventional strategy such as photoablation in the mouse eye, an alternative, mathematical approach was deployed to examine the potential role of leader cells as pacemakers. Granger analysis 32 provides a means of assessing whether a given time series may be useful in forecasting another, that is predictive of a causal relationship. This supported our visual identification of first responding (leader) cells. As shown in Fig. 6c-e, it was observed that those four cells ('leaders' , Fig. 6c; this islet is shown in Supplementary Video 11), which fired first during a prolonged run of Ca 2+ pulses, were always represented as leaders in the second and third bursts, but not always in the fourth and fifth bursts (if present). However, leader cells identified temporally as among the first five responding cells under high glucose conditions were invariably the most highly connected on independent Granger analysis (see Supplementary  Table 2). Granger analysis of the top ten most highly connected cells during the prolonged imaging sessions (10 min acquisitions at high, medium and low glucose, of the same cross-section of islet/same β-cell regions of interest (ROIs)) revealed one cell to be a Granger leader in all three states and, interestingly, to be in the same region (neighbouring) as two to five other Granger leaders in the medium and high state-which was also the segment of islet from which waves emanated (data not shown).
It is of interest that this analysis provided no evidence that pericapillary cells were more likely to be 'Granger leaders' (average  (1)). e, During time window iii (that is, at time of glucose injection); the mean positive Pearson's coefficient for connected cell pairs is 0.75 ± 4.08 (s.e.m.), much higher than before or after glucose injection (window i, R = 43. 8 1.46; ii, R = 0.48 ± 2.59; iv, R 46.4 ± 5.3; and v, R = 0.35 ± 3.45) (P <0.001 on one-way ANOVA with Tukey's multiple comparison). f, The overall percentage of connected cell pairs is elevated (46% ± 6.18 (s.e.m.)) during the glucose injection compared with the rest of the time points (window i, 15.3 ± 2.4%; ii, 10 ± 1.86%; iv, 18.6 ± 4.6%; and v, 11.1 ±1 2.7%) (n = 6; P <0.001, one-way ANOVA with Tukey's multiple comparison). distance from leader cells to the nearest capillary: 2.2 ± 1.9 µm versus 2.3 ± 1.8 µm for follower cells; n = 25, P >0.05). Hence, differences between cells in the arrival time for glucose from the bloodstream are unlikely to be the determining factor for initiating Ca 2+ waves.
Engrafted human islets are highly connected. To corroborate our findings in a further species, the behaviour of 11 human islets transduced with adenovirus-expressing GCaMP6m (AV-GCaMP6m) and transplanted into the ACE of (immunocompromised) BALB/c nu/ As described in Fig. 2, the time to 20% rise in Ca 2+ signal after the glucose injection was measured, and tabulated to identify the first responders or 'temporal leaders'. c, Pooled data for the five animals imaged. The mean Pearson coefficient of correlation rose significantly from the low glucose state to the high glucose state (n = 5, data are mean ± s.e.m., P <0.001 on a paired, two-tailed, Student's t-test). d, The percentage of significantly connected cell pairs also increased significantly after glucose administration. Data are mean ± s.e.m. and **P <0.01 after a paired, two-tailed, Student's t-test. e, 3D islet projections acquired at 0.8 Hz before and during glucose injection. f, Associated 3D map showing the time of response in a colour-key fashion (red colour represents the fastest response). g, Cartesian connectivity map and Pearson's heat-maps for the islet shown in e (n = 3 animals, not graphically represented here). The experiment in e-g was performed once with three samples showing similar results.

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nu mice was studied (see Methods). A non-significant rise in human islet coefficient of correlation was observed, from 0.39 to 0.59, and a corresponding rise in β-cell connectivity from 56% to 76%, between low and high circulating glucose conditions (see Supplementary Fig.  5b). Intriguingly, in the two islets that came from a donor with longstanding type 2 diabetes (see Methods), the switch from low to high circulating blood sugar was associated with an unexpected drop in Pearson's R (53 to 24 and 44 to 32), and an equivalent fall in the proportion of connected β-cells (from 30% to 20% and 29% to 27%; see Supplementary Fig. 5c). This observation opens up the possibility that the loss of insulin secretory function occurring in type 2 diabetes is linked to abnormal connectivity patterns.

Transcriptomic analysis.
To determine whether hub/leader cells may possess a discrete molecular signature versus followers, RNA-Seq data from fish and mouse β-cells were analysed. We have previously reported 21 that hub cells in the mouse islet are characterized by relatively high levels of glucokinase (Gck) immunoreactivity, and lower levels of Insulin, Pdx1 and Nkx6.1 staining. First, a zebrafish transcriptomic data-set (10x Genomics) was generated and analysed, and a cluster of mainly endocrine cells expressing sst1.1, gcga or ins was identified. Further clustering of these 'endocrine' cells produced clusters of probable δ-cells (sst1.1), α-cells (gcga) and β-cells (ins) (see Supplementary Fig. 6a,b). Putative hub cells were identified based on the higher Gck and lower insulin expression previously observed in mouse islets. The intersection of the upper quartile of gck expression and the lower quartile of ins expression identified 9% of β-cells as putative hub cells (see Supplementary Fig. 6c). Enrichment and gene ontology analysis revealed elevated expression of genes in hub/leaders associated with mitochondrial metabolism (oxidative phosphorylation and respiratory electron transport chain) and generation of precursor metabolites and energy, among other terms (see Supplementary Fig. 6d,e). Interestingly, the re-clustering of the 'endocrine' cluster resulted in two distinct and approximately equally sized β-cell populations. The putative hub cells identified here came almost entirely from a single cluster, suggesting that these may represent one end of a continuous distribution within this cluster rather than a distinct subset.
Similar analysis of mouse islet data revealed that the intersection of the upper quartile of Gck and the lower two quartiles of Ins1 expression contained 11% β-cells (see Supplementary Fig. 6f-h). Genes upregulated in this cluster were overrepresented in the Gene Ontology terms 'Glycolysis' and 'Generation of precursor metabolites and energy' (see Supplementary Fig. 6i,j), potentially indicating that these are more metabolically active cells, as observed above in the zebrafish case.

Discussion
The principal aim of the present study was to explore β-cell coordination in the islet in vivo in living animals. In the present study, the zebrafish islet was studied in its natural state and the mouse islet was studied under conditions of vascularization and innervation that closely copy those of the islet within the pancreas [41][42][43] . It was shown that, despite the quite profound differences between the isolated and in vivo islets, coordinated β-cell responses to glucose stimulation display many of the features previously described in vitro, including the emergence of cells that may govern islet-wide Ca 2+ dynamics and hence pulsatile insulin secretion.
It was demonstrated first that, in zebrafish, increases in blood glucose lead to a coordinated increase in β-cell cytosolic Ca 2+ across the islet. Using Pearson's R analysis, a well-connected network of β-cells in the zebrafish islet was described that responded in a coordinated fashion to glucose stimulation. These findings align well with those of Markovic et al. 36 in murine pancreatic slices, and our own findings in isolated mouse islets 18 . Given the small size of the zebrafish islet at this developmental stage, it was not possible to apply scale-free network theory to these datasets. However, it was possible, using a direct interventional approach akin to the use of optogenetics in isolated murine islets 21,44 , to demonstrate that those cells that were the first to exhibit a Ca 2+ increase ('leaders') may perform a role as regulators of the activity of other β-cells. Photoablation of leader, but not follower, cells resulted in a significant abrogation of Ca 2+ dynamics in the remaining β-cells, in terms of their time to response as well as their overall calcium response to a glucose challenge. Evidence was also provided to establish that this methodology produced no collateral damage; that is, it did not affect cells other than the single β-cell that was targeted. It should be emphasized that this approach offers significant advantages over the use of optogenetics for β-cell targeting, notably the fact that further genetic modification required to express an optogene (for example, a photoswitchable channel or pump shown to influence β-cell activity) 21,44,45 is avoided, and axial resolution is high. Photoablation of leader, but not follower, cells resulted in the abrogation of Ca 2+ dynamics (see Fig. 4c), pointing to a role for the former as regulators of β-cell activity across the islet.
It was particularly interesting to note the findings of the ex vivo imaging studies that directly compared in vitro glucose responsiveness of the primary and secondary zebrafish islets. The only discernible difference observed between the primary and the much later-forming secondary islets ex vivo pertained to a faster Ca 2+ response of the latter, which was evident at 10 mM glucose. This faster response is likely to reflect the much smaller size of the secondary islets and, hence, the easier penetration to the islet core of glucose when added ex vivo. It is important to note also that impaired responsiveness to glucose stimulation of β-cells originating from the dorsal pancreatic buds in vivo has not been observed, consistent with our recent findings that DBCs are functional 26 . Finally, when imaged in culture, the zebrafish islets exhibit seemingly uncoupled behaviours, revealing the glucose sensitivity of individual β-cells 26,46 . In contrast, β-cells show synchronized responses to glucose in vivo (this study and Ammala et al. 46 ). Thus, the unperturbed conditions of the in vivo environment might be critical for the coupling of β-cells.
In mammalian islets, routine observation was made of clear, trans-islet, glucose-induced Ca 2+ waves (10/10 Ins1Cre-GCaMP6expressing islets examined in independent experiments), whereas these are not always observed in Fluo8-loaded isolated islets in vitro 21 . This may reflect the presence of nerves and blood vessels in our in vivo model as well as, conceivably, the better preservation of β-cell identity, gap junctions, and so on. 2 . Moreover, the use of transgenic islets, in which the genetically encoded Ca 2+ sensor is present in almost the entire (~95%) β-cell population after recombination using the Ins1Cre transgene 21,39,40 , is likely to facilitate the detection of waves. Thus, we were able to image cells located some distance away from the islet periphery, with adequate resolution to four-to five-cell depths in the Z-plane (see Supplementary Video 14). Furthermore, with a rapid piezo device it was possible to demonstrate that Ca 2+ dynamics were strongly coordinated across β-cells that were separated by another layer of cells. However, the present studies do not address the question of how connections across the islet are established (for example, roles for islet interneurons, paracrine factors). Other interventional approaches (for example, using multiphoton, light sheet or other imaging techniques) will be necessary to explore these phenomena in the future.
By imaging large numbers of cells simultaneously, and subjecting the resulting datasets to binarization analysis, the existence of scalefree networks was revealed, as previously described in vitro 21 . This set of experiments examined the nature of islet behaviour in vivo through two different but complementary lenses. Pearson's R analysis highlights the pan-islet β-cell connectivity (in terms of both the number of connected cells and their strength of correlation) in response to elevated circulating glucose levels. Separately, it was demonstrated, using data binarization and shuffling 21 , that these Articles Nature MetabolisM cells are connected in a way that fits with the presence of superconnected hubs. Recently, Rupnik and colleagues 47 have reported, using mouse islets located within pancreatic slices, that, at adequate acquisition speeds (10 Hz), Pearson's analysis can reveal a connectivity probability distribution function that obeys a power law, at least initially after glucose stimulation.

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To corroborate our zebrafish findings, where disruption of the temporally defined 'leader' cells abrogated subsequent islet-wide Ca 2+ responses to glucose, independent, mathematical causal-ity analysis of all the β-cells that were recorded in the mouse islet was performed. Selecting a causality time lag consistent with that observed between the first responders and the rest of the β-cells

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(that is, 1 s) 32 , it was revealed that these were indeed the most highly causally linked to the activity of all other cells in the islet. Both the experimentally established zebrafish 'leaders' and the mathematically causally identified mouse 'leaders' are reminiscent of previously identified in vitro hub cells 21 , insofar as both regulate the Ca 2+ dynamics observed in the rest of the islet being imaged. The present findings also indicate that temporal and spatial dynamics need to be considered in identifying probable regulatory populations. For example, essentially normal blood flow is maintained in the engrafted islet. One may have predicted, therefore, that 'leader' β-cells would be those located immediately adjacent to blood vessels. In contrast, no greater likelihood of cells in this domain of the islet initiating waves was observed than for cells more remotely located. It was also observed that islets retained a baseline Ca 2+ activity (and indeed a degree of connectedness between β-cells) even in the low glucose state. Thus, at low circulating glucose levels, Ca 2+ waves were occasionally observed above noise levels, with the same amplitude and frequency of bursts as at high glucose, but less commonly. Within a single train of waves, the starting point was often, but not always, conserved, and was frequently seen at the islet rim. Such waves often propagated circumferentially, although there were some that appeared to move towards the islet core. Taken together, this hints that functional networks already exist at low glucose concentrations, under conditions in which most cells are not yet firing. These pre-activated networks may then expand and work as a coordinating unit to drive the recruitment of followers.
It was also important to demonstrate a retention of the high connectivity readouts in islets that had been exposed to prolonged elevated glucose levels. Many previous studies on isolated islets and β-cells reveal heterogeneous Ca 2+ responses to glucose stimulation 48 . Indeed, we are not aware of existing literature supporting the notion that β-cells have an identifiable (and identical) resting Ca 2+ oscillation signature. Nevertheless, it was important here to exclude the possibility that the high connectivity observed at high glucose levels is a phenomenon related to spatially aggregated (that is, intra-islet) β-cells simply responding acutely and synchronously to a rise in circulating glucose concentration. The high connectivity findings in islets that had been imaged for an hour at elevated circulating glucose levels serve to argue against the possibility that connectivity is an acute phenomenon of this type because, in an uncoordinated system, over a 60-min imaging protocol, with glucose levels that are not rapidly varying, one would expect desynchrony to emerge. Finally, the first responders (and Granger leaders) are defined during Ca 2+ pulses at essentially constant glucose (although glucose may drift gradually over multiple Ca 2+ waves during these recordings).
Several questions remain with respect to the Ca 2+ waves identified here: to what extent are their starting points spatially defined relative to nerves and other islet cell types? How do they propagate? Are they always associated with pulses of insulin secretion? Further studies are also required to determine whether 'leader' cells are functionally essential to islet health, are pre-fated or can assume leader characteristics over time that relate to altered islet function under metabolic stress or in diabetes.
Before the present study, our understanding of the differences in molecular identity between hub and follower cells was fragmentary 21 . To explore this question here in an unbiased, transcriptomewide manner, we have leveraged the known properties of mouse hub cells, that is, elevated expression (at the protein level) of Gck and relatively weak expression of Insulin. We note that confirmation of similar properties for the fish hub/follower populations (that is, high Gck/low insulin/low Pdx1 immunoreactivity) was not possible here due to the absence of suitable antibodies for the Danio rerio Gck protein. Nonetheless, if we assume similar properties for the fish and mouse hub cells, our analyses reveal that, in both species, a population exists with characteristics that may be expected of these cells, notably elevated expression of genes involved in glucose metabolism and, in zebrafish, of genes involved in mitochondrial metabolism. Of note, a similar β-cell population was identified recently in mice by Pospisilik and colleagues 49 . Future studies, involving the direct isolation of hubs and followers based on function (for example, Ca 2+ dynamics), are needed to confirm or refute these findings.
In conclusion, we show in the present study that, examined in living animals, β-cells within the islet are highly connected in three dimensions and that this connectivity is tightened in response to a glucose challenge. As predicted from previous studies of isolated islets in vitro 18,21 , it has been shown that critical subpopulations of β-cells, which appear to generate Ca 2+ waves, serve a regulatory role in zebrafish and appear likely to do so in the mammalian islet as well. At this stage, it is not possible to investigate whether the leader cells are a distinct population with a distinct origin and development. However, we provide a preliminary analysis, using an imputation approach based on previously described proteomic properties of these populations 21 , to suggest they possess a distinct transcriptomic signature. Future challenges will involve isolating and characterizing these cells, as well as assessing the stability of each subgroup (that is, leader/hubs and followers). Taken together, our data provide further evidence for a division of labour within the islet in vivo in three different species, reinforcing the importance of β-cell heterogeneity for normal glucose responsiveness.

Methods
Zebrafish husbandry. Zebrafish wild-type (WT) AB, WIK and TL were used in all the experiments. Zebrafish were raised in standard conditions at 28 °C. Established transgenic lines used in this study were Tg(ins:gCaMP6s;cryaa:mCherry) 26 , Tg(ins:cdt1-mCherry;cryaa:GFP) 31 and Tg(gata1a:DsRed) 26 . Tg(ins:cdt1-mCherry) was utilized in preference to a pan-β-cell marker such as Tg(ins:mKO-nls) to allow for a clear separation of the spectra and simultaneous signal recordings from the GCaMP and mCherry channels, which was particularly important during fast imaging. All experiments were carried out in compliance with European Union and German laws (Tierschutzgesetz) and with the approval of the TU Dresden and the Landesdirektion Sachsen Ethics Committees (approval nos: AZ 24D-9168,11-1/2013-14, TV38/2015, T12/2016, and T13/2016, TVV50/2017 and TVV 45/2018)). In this study, all live imaging in vivo, compound and glucose injections, as well as experimental procedures were performed with zebrafish larvae that did not exceed the 5-dpf stage, as stated in the animal protection law (TierSchVersV §14). According to the EU directive 2010/63/EU, the use of these earlier zebrafish stages reduces the number of experimental animals, according to the principles of the 3Rs. Ex vivo live imaging of β-cells was performed with isolated islets from euthanized fish according to approval no. T12/2016.

Zebrafish glucose measurements.
Groups of ten larvae were pooled together, snap frozen in liquid nitrogen and then stored at −80 °C. After thawing on ice, 250 µl of phosphate-buffered saline (PBS) was added and the larvae were sonicated with an ultrasonic homogenizer (Bandelin, SONOPLUS), before centrifugation at 13,000g. Glucose concentration was determined using the BioVision Glucose Assay Kit (Biovision Inc.) according to the manufacturer's instructions.
Zebrafish live imaging. Embryos were treated with 0.003% (200 µM) 1-phenyl-2-thiourea to inhibit pigmentation from 1 dpf onwards. At 4.5 dpf, the larvae were anaesthetized using 0.4 g l -1 Tricaine. The larvae were mounted in glassbottomed microwell dishes (MatTek Corporation) using 1% low-melting agarose containing 0.4 g l -1 Tricaine. After the agarose was solidified, the dishes were filled with embryonic fish water and 0.4 g l -1 Tricaine. Live imaging was performed on an inverted laser scanning confocal system, ZEISS LSM 780, inverted with a C-Apochromat ×40/numerical aperture (NA) 1.2 water correction lens. In the Tg(ins:GCaMP6s);Tg(ins:cdt1-mCherry) double-transgenic animals, the GCaMP6 and mCherry signals were acquired simultaneously using the 488 nm and 561 nm laser lines. The GCaMP6 signal was rendered in green and the nuclear signal in red. Videos were recorded at a 10 s per image (0.1 Hz) frame rate unless indicated otherwise, with a Z-step thickness of 1.2 µm, covering on average 35 µm, and an XY Articles Nature MetabolisM resolution of 0.12 µm per pixel (512 × 512 pixels). Laser power was maintained as low as possible (<1.5%) to minimize phototoxicity. For faster imaging, we focused on a single plane, recording a frame every 300 ms with an XY resolution of 0.08 µm per pixel (512 × 512 pixels).
Zebrafish fast whole-islet live imaging. Whole-islet live imaging at an acquisition rate of 0.8 Hz, covering ~700 µm 3 , was achieved using resonant scanner technology with an inverted laser scanning confocal system (Leica SP5 MP) using an IRAPO L ×25/NA 0.95 water lens. Videos were recorded at ~0.8 Hz per Z-stack (~700 µm 3 ), with a Z-step thickness of 4.5 µm, covering on average 70 µm in depth, and an XY resolution of 0.24 µm per pixel (256 × 256 pixels). The resonant scanner was set at 8,000 Hz with a bidirectional line scanning to achieve maximum speed.
Selective two-photon laser ablation of leader cells. Live imaging and glucose injections were performed as described above using Tg(ins:gCaMP6s;cryaa:mCherry), Tg(ins:cdt1-mCherry;cryaa:GFP) larvae. Images were captured across a single confocal plane at an imaging acquisition rate of 6 frames s -1 (6 Hz). We performed three independent injections of glucose, separated by 5-min intervals. The 'leader cell' (that is, the temporally defined first responder) was identified by eye, based on the changes in GCaMP6 fluorescence after each glucose injection. The larvae were then transferred to a Leica SP5 MP confocal microscope, equipped with a two-photon laser and ×25/0.95 NA objective. An ROI was selected encompassing the centre of the nucleus of the cell to be ablated, covering a circle with an approximate diameter of 0.5 µm. The cell of interest was then exposed to two-photon laser irradiation at the output power of 2.0 W (wavelength λ = 800 nm) for 5 s to minimize possible damage to other areas. Then live imaging and pericardial injection were performed again, using the protocol above, and within 20 min of irradiation, to record the response after cell ablation. Control cells that were not the temporally defined first responders ('followers') were ablated with the same methodology as leader cells. To ensure that the laser ablation technique was highly localized to a single cell, as expected with this approach, islets were fixed immediately after the laser cell ablation (<10 min), and then labelled with insulin antibody and DAPI (see below).
Islet blood-flow imaging in zebrafish. Imaging of islet blood flow was performed using triple transgenic larvae Tg(ins:GCaMP6s);Tg(ins:cdt1-mCherry);Tg(gata1a:DsRed). Tg(gata1a:DsRed) reporter was used as a marker of red blood cells. Live imaging was performed on a ZEISS LSM 780 confocal microscope equipped with a C-Apochromat ×40/1.2 NA water correction lens. The GCaMP6s and mCherry signals from β-cells, and DsRed signals from blood cells, were simultaneously acquired using the 488-nm and 561-nm laser lines. The GCaMP6 signal was rendered in green. The blood cells and the nuclear signal of β-cells were rendered in red. We focused on a single plane and the videos were recorded at a frame rate of 1 frame per 155 ms (~6.4 Hz).

Mechanical heart stop in zebrafish.
To stop the blood flow in 4.5-dpf zebrafish larvae, a glass-pulled pipette (3.5-inch Drummond no. 3-000-203-G/X, Sutter pipette puller P-1000), with a manually blunted end, was used to exert direct pressure into the heart. The heart was blocked for around 400 s. The mechanical heart stopping was executed during live Ca 2+ imaging in the Tg(ins:GCaMP6s);Tg(ins:cdt1-mCherry) double-transgenic larvae, as described above. Videos were recorded at a 10 s frame rate (0.1 Hz), and a Z-step thickness of 2.8 µm, covering on average 50 µm, with a frame size of 512 × 512 pixels.

Identification of DBCs and VBCs.
The primary zebrafish islet contains both DBCs and VBCs. To interrogate whether embryonic derivation affected the identity of leader cells, injection of mRNA encoding H2B-RFP was performed to distinguish between DBCs and VBCs based on label dilution 37 . In this assay, DBCs retain the H2B-RFP label whereas VBCs dilute it. One-cell-stage embryos were injected with mRNA expressing H2B-mCherry. The pCS2+H2B-mCherry plasmid was maxiprepped, digested with the restriction nuclease KpnI and in vitro transcribed using the SP6 Transcription Kit (Ambion, AM1340) to generate mRNA. Then 100 pg of H2B-mCherry mRNA was injected into each embryo. Larvae were mounted as described above for whole-islet live imaging and glucose injections.
Postmortem staining for cell ablation in zebrafish. After the live imaging was performed, and the leader cells were temporally identified, the larvae were immediately fixed in 4% paraformaldehyde overnight. The samples were permeabilized with 1% PBT (Triton X-100) for 1 h. To avoid non-specific primary antibody binding, the samples were blocked for 2 h in PBTB (PBT + 4% BSA). Nuclear staining was performed using DAPI at 1:1,000 dilution. After the immunostaining with anti-insulin (polyclonal guinea-pig anti-insulin, Dako A0564, 1:300 dilution), the samples were mounted in Vectashield. The anti-insulin antibody has been previously validated to mark β-cells in zebrafish by using transgenic lines that express green fluorescent protein under the insulin promoter, and was also recently validated to show negative immunoreactivity in β-cells in homozygous mutant fish for the insulina gene 50 , confirming its high specificity. Images were acquired using Z-Stacks on a LSM 780 Zeiss confocal microscope. For image analysis, the nuclei of the β-cells were segmented using the DAPI channel.
Ex vivo imaging of primary and secondary zebrafish islets. The islet culture and imaging were performed as previously described 34 . Primary and secondary islets were isolated from 3-month post-fertilization Tg(ins:gCaMP6s; cryaa:mCherry) animals. The islets were stimulated with a ramp of 10 and 20 mM d-glucose (Sigma, G8270). The imaging culminated with the addition of 30 mM KCl (Sigma, P9451) in the same plate. Videos were recorded at a 2.5 s per image (0.25 Hz frame rate), in a single Z-plane and with an XY resolution of 0.59 µm per pixel (1,024 ×1,024 pixels). After imaging, individual β-cell ROIs were manually drawn using ImageJ. Fluorescence intensity was normalized using the minimum and maximum values of fluorescence intensity across frames for each cell. Cells that did not show an increase in GCaMP signal after KCl addition were not included in the analysis.
Image analysis from in vivo imaging of zebrafish. The cumulative population response of β-cells was quantified from maximum intensity projections of the Zstack. In the maximum intensity projection, the islet area was delimited manually using the ROI Manager in ImageJ (https://imagej.net/Fiji) 51 . Using the ROI, the integrated fluorescence intensity of GCaMP6 was extracted. The integrated fluorescence intensity was normalized for the whole imaging time using the following equation: where F T is the integrated fluorescence intensity at a given time and F max and F min are the maximum and minimum values recorded during the live imaging session, respectively. Single-cell signal analysis of GCaMP signal was performed either from single confocal slices covering a majority of imaged β-cells (2D) or by segmenting the nuclei from the Z-stacks using the nuclear mCherry signal (3D). For nuclear segmentation, the 3D image suite in ImageJ and the 3D iterative thresholding plugin, was used 52 . The following parameters were set based on the estimated approximate nuclear size of β-cells: minimum volume = 100 pixels; maximum volume = 1,200 pixels; criteria method = 'volume'; threshold method = 'volume'; value method = 10 units. This generated a voxel covering the nuclei of β-cells. Using the 3D ROI Manager plugin, we extracted the integrated fluorescence intensity from each voxel over time (F T ). To create 3D plots, we first extracted the centroids from each voxel and then plotted them using the R software and the package 'rgl' . Single-cell heat-maps based on 2D analysis were created using Excel and conditional formatting, setting the colours in a gradient from 0 to 1. For visualization, the brightness and contrast were adjusted uniformly across the times series using ImageJ, and the tool Brightness/Contrast.

Quantification of GCaMP6 fluorescence intensity in zebrafish images.
For the quantification of changes in GCaMP6 fluorescence on glucose or insulin injection in Fig. 1 and Supplementary Fig. 1, the cumulative response of all imaged β-cells to glucose injection was quantified. To this end, a comparison was made of the area under the curve (AUC) based on the normalized integrated fluorescence intensity 10 frames before and after the injections of glucose or insulin (covering 200 s of imaging) using the equation above.
For the quantification of changes in GCaMP6 fluorescence on laser cell ablation (see Fig. 4), the cumulative response of all imaged β-cells to glucose injection was quantified. In this case, the maximum value (F max ) was not used for normalization because such normalization could mask the effect of loss of response after cell ablation due to normalization to background fluorescence. Instead, we subtracted only the background from the imaging session using the following equation: The larvae were injected with three separate pulses of glucose before and after the ablation. For each injection the GCaMP AUC was calculated covering 200 frames after the glucose injection. The average AUC was calculated before and after the ablation and plotted as log 2 .
Spatial drift correction of zebrafish images. The red channel (cdt1-mCherry) signal from the β-cell nuclei was used to correct for spatial drift in the green GCaMP6s channel. A maximum projection of each Z-stack in the time series was entered into the Fiji plugin 'Descriptor-based series registration (2d/3d + t)' (https://imagej.net/Descriptor-based_registration (2d/3d)) 53 , applying the model 'Rigid (2d)' , with '3-dimensional quadratic fit' . A σ of 13 and threshold of 0.03 were applied to the detection of nuclear signal, with a minimum number of three neighbours, redundancy of 1 and a random sample consensus (Ransac) error of 5. Matching across time series was achieved using global optimization, unless indicated otherwise. Stabilization in the Z dimension was achieved using the Fiji 'Reslice' command. The 'Descriptor-based series registration (2d/3d + t)' plugin was used with nuclei detection sigma set to 5 and a threshold of 0.03.
Mouse husbandry. Male C57Bl/6 WT (18-25 g) mice were purchased from Charles River, and used as donor islet recipients. For in vivo measurements of cytosolic Ca 2+ in pancreatic β-cells, we generated mice that express GCaMP6f in β-cells were generated using the Cre-Lox system. Briefly, Ins1Cre mice (provided by J. Ferrer, Department of Medicine, Imperial College London) 39,40 were crossed with mice that express GCaMP6f downstream of a LoxP-flanked STOP cassette (Jackson Laboratory, stock no. 028865). Islets donated from either sex were used for transplantation. Mice were housed in groups of six in individually ventilated cages under controlled conditions (21-23 °C; 12 h light:12 h dark cycle). Male BALBc nu/ nu (Jackson Laboratory, stock no. 002019) recipients were used for human islet transplantation. Animals had free access to standard chow and water (irradiated for the immunocompetent mice). All animal procedures were approved and performed under the UK Home Office Animals (Scientific Procedures) Act 1986 (Project Licence to I.L., PA03F7F07 at Imperial College London). The project licence received internal institutional ethical approval as well as external Home Office approval).
Generation of adenovirus-expressing AV-GCaMP6m. A plasmid driving the expression of GCaMP6m under the control of the cytomegalovirus (CMV) promoter (CMV-AV-GCaMP6m) was generated using the pAdEasy system 54 . Briefly, pGP-CMV-GCaMP6m plasmid (Addgene plasmid no. 40754) was digested using BglII and NotI. The released GCaMP6m fragment was then purified and ligated into pShuttle-CMV vector (Addgene plasmid no. 16403). CMV-GCaMP6m was inserted by recombination into the adenoviral pAdEasy-1 vector (Addgene plasmid no. 16400) and transformed into electrocompetent BJ5183 cells. The isolated plasmid was subsequently amplified in reduced recombination rate (recA1) NEB-10β-competent Escherichia coli (New England BioLabs). After the transfection of AD293 cells with the linearized pAdEasy-CMV-GCaMP6m construct, cells were harvested and lysed to release virions. The virus was further amplified and purified by centrifugation on a CsCl gradient. Titration was performed by infecting AD293 cells with serially diluted viral stocks, counting positive cells through GCaMP6m fluorescence.
Islet transplantation into the murine ACE. Pancreatic islets were isolated and cultured as described previously 55 . For transplantation, 10-20 islets were aspirated with a 27-gauge blunt eye cannula (BeaverVisitec) connected to a 100 μl Hamilton syringe via 0.4-mm polyethylene tubing (Portex Limited). Before surgery, mice were anaesthetized with 2-4% isoflurane (Zoetis) and placed in a stereotactic frame to stabilize the head. The cornea was incised near the junction with the sclera, being careful not to damage the iris. Then, the blunt cannula, preloaded with islets, was inserted into the ACE and islets were expelled (average injection volume 20 µl for 10 islets). Carprofen (Bayer) and eye ointment were administered post-surgery.

In vivo Ca 2+ imaging of AV-GCaMP6m-infected murine islets in the ACE.
Before transplantation into the ACE of recipients, isolated islets (from WT C57/ BL6 donors, <24 weeks old or human islet donations) were infected with AV-GCaMP6m in vitro at a multiplicity of infection of 20 for 24 h. This approach, which was expected to allow the identification, if present, of functional islet subcompartments (that is, local groups of interacting β-cells) provided preferential infection of superficial β-cells (one to two cells deep). Of these, ~50% were infected. A minimum of 4 weeks was allowed for full implantation of transplanted islets before imaging. Imaging sessions were performed with the mouse held in a stereotactic frame and the eye gently retracted, with the animal maintained under 2-4% isoflurane anaesthesia. All imaging experiments were conducted using a spinning disc confocal microscope (Nikon Eclipse Ti, Crest spinning disc, 20× water dipping 1.0 NA objective). The signal from AV-GCaMP6m fluorophore (ex. 488 nm, em. 525 ± 25 nm) was monitored in time-series experiments for up to 20 min at a rate of 1 frame s -1 . Ca 2+ traces were recorded for 3 min before intraperitoneal glucose injection, with a mean blood glucose reading (across five islets in five separate animals) of 8 mmol l -1 . Three minutes into acquisitions mice received a 150-μl 30% (1.5 g kg -1 ) bolus of glucose intraperitoneally. Blood glucose was subsequently measured on a glucometer (Accu-Chek) at 2-min intervals from a tail vein nick until the end of experiments. Injection of glucose at 180 s raised blood glucose to an average of 28 mM for the remainder of the 10-min imaging series. As the mouse imaging experiments are the first of their kind, sample size (n = 5 islets in n = 5 animals) was determined to be adequate based on the magnitude and consistency of measurable differences between groups. This was in line with other studies examining islets in the ACE 22 .
In vivo Ca 2+ imaging of Ins1Cre-GCaMPf islets in the ACE. Ins1Cre-GCaMP6f (ex. 488 nm, em. 525 ± 25 nm)-expressing islets were isolated and transplanted into WT recipients (n = 5 islets in n = 5 different animals), and imaged as described above. Stream acquisitions of a single x/y plane of β-cells recorded 2-min datasets at 3 Hz. Islets (n = 5 islets in n = 5 different animals) were continuously monitored and the focus was manually adjusted to counteract movement. Islets (in the same imaging session) were imaged under both 'low glucose' (2-6 mM) and 'high glucose' (17-25 mM) conditions (randomly ordered). Blood glucose (tail nick, Accu-Chek glucometer) was assessed at 2-min intervals throughout. Low glucose readings were obtained after the intravenous administration of insulin (Actrapid, 0.3 ml of 1.0 IU ml -1 ), and high glucose was achieved with 200 µl of a 30% (2 g kg -1 ) intraperitoneal bolus of sugar. At the end of experiments, animals were allowed to recover and were further monitored for an hour for potential postoperative latent hypoglycaemia.
To extend the image acquisitions to collect 3D data (that is, three separate planes of β-cells across an islet), a piezo device was attached to the inverted objective. This allowed for rapid, precise, 15-µm Z-movements such that a threeslice Z-stack could be obtained at a whole-islet imaging rate of 1 frame s -1 . At this imaging speed, we could obtain 3D connectivity readouts for low and high glucose conditions (as described above, n = 3 islets in n = 3 different animals). As we became more expert with the ability of our platform, this number of experiments was sufficiently powered to demonstrate the rise in connectivity from low to high glucose in the 3D imaging experiments, Finally, islet Ca 2+ dynamics were examined during a longer period of glucose stimulation, to exclude the possibility that pan-islet connectivity is related to spatially aggregated β-cells simply responding acutely and synchronously to a rise in circulating glucose concentration. Five animals (five separate islets studied, in line with former acute experiments) were placed under isofluorane anaesthesia for 60 min. At the start of the imaging session an intraperitoneal bolus of sugar was administered. This led to a slow and sustained rise in circulating blood sugar (measured every 3-5 min via tail vein sampling, as before); 30-50 min into this imaging session, a 10-min single-plane islet recording was taken at 1 frame s -1 , manually readjusted in real time for movement. This was performed at 'high' glucose levels (that is, when blood sugar levels had risen after intraperitoneal glucose injection to a high, steady level >12 mmol l-1 ). We also report connectivity at a previous stage in the imaging session (10-20 min in) when circulating glucose levels were at an intermediate (medium glucose, 7-10 mmol l -1 ) range (but the islets were still exhibiting coordinated wave activity). In the same imaging session, the islets were recorded after intravenous administration of insulin when circulating levels of glucose were low (<4 mmol l -1 ). The same islet plane and β-cell ROIs were investigated under each of the three (low, medium and high) circulating glucose conditions. To ensure that the findings from this experiment were unaltered with the use of another anaesthetic, these experiments were repeated using ketamine (Zoetis) and xylazine (Bayer) (90 mg kg -1 and 4.5 mg kg -1 cocktail, respectively), with similar findings.
In vivo Ca 2+ imaging of AV-GCaMP6m-infected human islets. We studied the behaviour of 11 individual human islets (4 individual donors, age range 14-74 years, non-diabetic, body mass index range 21.5-29.2; see Supplementary  Fig. 5) that had been transduced with AV-GCaMP6m and transplanted into the ACE of (immunocompromised) BALB/c nu/nu mice. A human donor with diabetes (female, 54 years old, body mass index 24.4, type 2 diabetes for 10 years, insulin dependent for the last 1.5 years) provided islets for two experiments (separate islets in separate BALB/c nu/nu recipients). Human islets were obtained from multiple institutions (co-authors A.M.J.S. at the University of Alberta, Edmonton, Canada and P.M. at the University of Pisa, Italy). Permission for the use of human tissue was provided at Imperial College London by the Charing Cross Research Ethics Committee, REC reference no. 07/H0711/114. Human islets were obtained post mortem with next-of-kin and local and ethical permission at the sites of procurement. There was no selection procedure for the implantation of human donor islets, and they were implanted into recipient mice as they became available. Donor data are fully anonymized and no clinical data beyond age, sex and cause of death were available.
Following an imaging protocol described for the Ins1Cre-GCaMP6f mouse studies above, we measured human islet behaviour under imposed low (<4 mM) and high (>7 mM) glucose conditions. As BALB/c mice are resistant to glucose rises under anaesthesia, more successful imaging results were reported in the low glucose state. Image analysis: using Fiji (ImageJ) software (see above), images in the time series were individually time stamped, to maintain their absolute time information, before excluding frames in which resolution was poor or blurred by movement. Image series were then cropped and manually aligned across all frames using a predefined ROI as reference. Creating ROIs for analysis was guided by the emitted GCaMP fluorescence and the negative shadow of nuclei. For the virally infected islets, each ROI extended over the entirety of a cell, whereas ROIs in experiments with transgenic islets covered subcellular regions in close proximity to nuclei. Mean fluorescence intensity and XY(Z) coordinates for each cell within an islet (ROIs) were compiled and processed for connectivity analysis.
Pearson's (R-based) connectivity analyses. Correlation analyses between the Ca 2+ signal time series for all cell pairs in an imaged islet were performed with MATLAB using a custom-made script (available on request). Data were smoothed using a retrospective averaging method (previous ten values) and all traces were normalized to F0. Two-sided averaging techniques were not applied because this would have invalidated subsequent causality analyses. The correlation function R between all possible (smoothed) cell-pair combinations (excluding the autocorrelation) was assessed using Pearson's correlation. Data are displayed as heat-map matrices, indicating individual cell-pair connections on each axis (minimum = −1; maximum = 1). Given that data were not normally distributed (and hence resorting to either asymptotic P values or Monte Carlo-based ones would not be useful), the data were subsequently subjected to a bootstrap resampling to increase the accuracy of the confidence interval of the R value, and P <0.001 was deemed a statistically significant cell-cell connection. The Cartesian coordinates of the imaged cells were then taken into account in the construction of connectivity line maps. Cell pairs (R >0.25 and P <0.001 post-bootstrap) were connected with a straight line, the colour of which represented the correlation strength; it was assigned to a colourcoded light-dark ramp (R = 0.25-0.5 (green), R = 0.5-0.75 (yellow), R = 0.75-1.0 (red)). An average coefficient of positive connectivity was computed for each condition, by averaging the positive R values (excluding the autocorrelated cells) and the percentage of cells that were significantly connected to each other was elicited, for the purposes of group comparisons.
The immediate upstroke of an acute intravenous of glucose that is from a low to a high glucose setting was not examined. Consequently the 'first responders' in the mouse data-sets refer to the first β-cells observed to fire in a train of calcium waves during a period of more prolonged elevated glucose.

Signal binarization and Monte Carlo analysis.
To investigate what happens in the tail of the distribution, and go beyond the analysis of linear association provided by Pearson's correlation coefficient, the association between activity regimes was also looked at. This analysis was performed as described previously 20,21 . In brief, cells were considered to be either 'on' or 'off ' if the fluorescent signal exceeded a 20% noise threshold above baseline. Binarized data for each cell pair were assessed for cosynchronicity using the co-activity statistic where C is a coactivity coefficient (0 to +1), T i and T j represent the time spent in the active state for each given cell, and T ij represents the time during which both cells are active. Pairs were considered linked if their statistic displayed a higher than chance (P <0.01) probability of interaction versus a Monte Carlo-permutated version of the binarized matrix dataset. A probability distribution function of these connections (pooled across five islets) was presented as a log-log plot to look for a power-law relationship, the strength of which was quantified by the coefficient of determination (R 2 ) 53 .

Granger analysis.
The mouse Ins1Cre GCaMP6f-expressing islet series were subjected to a Granger causality analysis 32,33 . Individual cell-cell pairs were separately analysed (time lag 1-3 s, P <0.001) using Bonferroni's multiple comparison test. Granger-defined leaders, that is, those cells with the greatest number of causally linked followers, were compared with the temporally defined leaders with firing (in the high glucose condition) that preceded the remainder of the β-cell population. Granger leaders that persisted when the low, medium and high glucose experiments were performed on the same network of β-cells were spatially located on the islet map to understand their spatial distribution.

Zebrafish transcriptomic analysis (single-cell RNA-seq).
For single-cell RNA-seq of the zebrafish pancreatic cells using the 10x Genomics platform, cell suspension was prepared from primary islets of six 2 months post-fertilization Tg(ins:BB1.0L) 26 using the protocol described in Janjuha et al. 56 (n = 6 animals). The cell suspension was passed over a 30-µm cell filter (Miltenyi Biotec, 130-041-407) to remove debris and cell aggregates, adjusted with Hanks' Balanced Salt Solution (without calcium and magnesium) to a density of 800 cells µl -1 , and diluted with nuclease-free water according to the manufacturer's instructions to yield 5,000 cells. Subsequently, the cells were carefully mixed with reverse transcription mix before loading the cells on the 10x Genomics Chromium system 57 . After the gel emulsion bead suspension underwent the reverse transcription reaction, emulsion was broken and DNA purified using Silane beads. The complementary DNA was amplified with 10 cycles, following the guidelines of the 10x Genomics user manual. The 10x Genomics single-cell RNA-seq library preparation-involving fragmentation, dA tailing, adapter ligation and indexing PCR-was performed based on the manufacturer's protocol. After quantification, the libraries were sequenced on an Illumina NextSeq 550 machine using a HighOutput flowcell in paired-end mode (R1: 26 cycles; I1: 8 cycles; R2: 57 cycles), thus generating ~45 mio fragments. The raw sequencing data were then processed with the 'count' command of the Cell Ranger software (v.2.1.0) provided by 10x Genomics with the option '-expect-cells' set to 5,000 (all other options were used as per default). This yielded 2,625 cells. To build the reference for Cell Ranger, zebrafish genome (GRCz10) as well as gene annotation (Ensembl 87) were downloaded from Ensembl and the annotation was filtered with the 'mkgtf ' command of Cell Ranger (options: '--attribute=gene_biotype:protein_coding-attribute=gene_biotype:lincRNA --attribute=gene_biotype:antisense'). Genome sequence and filtered annotation were then used as input to the 'mkref ' command of Cell Ranger to build the appropriate Cell Ranger Reference.
Cluster analysis. The single-cell RNA-seq data from C57BL/6 mouse islets were downloaded from the National Center for Biotechnology Information Gene Expression Omnibus (GSE84133) 58 . UMI-filtered counts were analysed using the Seurat package 59 . The data were filtered and normalized and then highly variable genes identified for principal component analysis and graph-based clustering. In the mouse data, insulin, glucagon and somatostatin cells were largely separated into distinct clusters. The initial clustering of the fish data produced a single cluster containing cells expressing ins, gcga and sst1.1 (listed by ENSEMBL as the zebrafish orthologue of the Homo sapiens SST gene; similar data were obtained using the sst1.2 gene). This 'endocrine' cluster was separated from the other cells and re-clustered, producing distinct clusters for these three genes. The ins + clusters were combined and the few remaining cells positive for gcga, sst1.1 or gip, or negative for ins, were excluded. Within this group of β-cells, the intersection between the upper quartile of gck expression and the lower quartile of ins expression was identified as putative hub cells, based on the properties of these cells described previously 21 . Genes differentially expressed between the putative hub cells and remaining β-cells were identified using Wilcoxon's rank sum test, and the upregulated genes thus identified were tested for statistical overrepresentation of gene ontology Biological Process terms using Pantherdb.org 60 . Insulin-positive mouse cells were analysed in a similar manner, except that putative hub cells were classified as the intersection between the upper quartile of Gck expression and the lower two quartiles of Ins1 expression.
Statistical analysis. Statistical significance between two conditions was assessed using the paired or unpaired, Student's t-test. Interactions between multiple conditions were determined using one-or two-way analysis of variance (ANOVA) (with Tukey's or Bonferroni's post-hoc tests). Analyses were performed using GraphPad Prism (GraphPad Software v.8.0) and MATLAB (Mathworks) and significant P values are described in each relevant section. Values are plotted as mean ± s.e.m., unless otherwise stated.
Reporting Summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability
The data that support the findings of this study and the MATLAB codes for the various connectivity analyses described above are available from the corresponding authors upon request. Zebrafish islet RNA-seq data are deposited at the Gene Expression Omnibus repository with accession no. GSE123662.

October 2018
Corresponding author(s): Guy A. Rutter Last updated by author(s): Apr 11, 2019 Reporting Summary Nature Research wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency and transparency in reporting. For further information on Nature Research policies, see Authors & Referees and the Editorial Policy Checklist.

Statistics
For all statistical analyses, confirm that the following items are present in the figure legend, table legend, main text, or Methods section.

n/a Confirmed
The exact sample size (n) for each experimental group/condition, given as a discrete number and unit of measurement A statement on whether measurements were taken from distinct samples or whether the same sample was measured repeatedly The statistical test(s) used AND whether they are one-or two-sided Only common tests should be described solely by name; describe more complex techniques in the Methods section.
A description of all covariates tested A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons A full description of the statistical parameters including central tendency (e.g. means) or other basic estimates (e.g. regression coefficient) AND variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals) For null hypothesis testing, the test statistic (e.g. F, t, r) with confidence intervals, effect sizes, degrees of freedom and P value noted Give P values as exact values whenever suitable.

For Bayesian analysis, information on the choice of priors and Markov chain Monte Carlo settings
For hierarchical and complex designs, identification of the appropriate level for tests and full reporting of outcomes Estimates of effect sizes (e.g. Cohen's d, Pearson's r), indicating how they were calculated Our web collection on statistics for biologists contains articles on many of the points above.

Software and code
Policy information about availability of computer code Data collection Mouse/human: Correlation analyses between the Ca2+ signal time series for all cell pairs in an imaged islet were performed in MATLAB using a custom-made script (pasted below). We have stated in the article that we are happy to be contacted to share this code. We will now work on a "methods" paper to expand this methodology and make the full code available in a repository. Fish: ZEN software (Zeiss), LAS AF software (Leica), Magellan software (Tecan), 10X Genomics Chromium system software, Illumina NextSeq 550 software, R v3.5.0 and Seurat v2.3.4.

MATLAB CODE
Smoothing the data (entered as fluorescence over time by roi, extracted using image J), followed by pearson and connectivity analysis, including bootstrap steps %% smooth the data cells_smooth=one_sided_filter(cells_stand,10,1); Data Policy information about availability of data All manuscripts must include a data availability statement. This statement should provide the following information, where applicable: -Accession codes, unique identifiers, or web links for publicly available datasets -A list of figures that have associated raw data -A description of any restrictions on data availability The zerbafish single-cell transcriptomic data based on 10X sequencing are available at the GEO repository with an accession number GSE123662, available publicly as of April 5 th, 2019 (https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE123662).

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