SUMMARY
The Ca2+ modulated pulsatile secretion of glucagon and insulin by pancreatic α and β cells plays a key role in glucose homeostasis. However, how α and β cells coordinate via paracrine interaction to produce various Ca2+ oscillation patterns is still elusive. Using a microfluidic device and transgenic mice in which α and β cells were labeled with different colors, we were able to record islet Ca2+ signals at single cell level for long times. Upon glucose stimulation, we observed heterogeneous Ca2+ oscillation patterns intrinsic to each islet. After a transient period, the oscillations of α and β cells were globally phase-locked, i.e., the two types of cells in an islet each oscillate synchronously but with a phase shift between the two. While the activation of α cells displayed a fixed time delay of ~20 s to that of β cells, β cells activated with a tunable delay after the α cells. As a result, the tunable phase shift between α and β cells set the islet oscillation period and pattern. Furthermore, we demonstrated that the phase shift can be modulated by glucagon. A mathematical model of islet Ca2+ oscillation taking into consideration of the paracrine interaction was constructed, which quantitatively agreed with the experimental data. Our study highlights the importance of cell-cell interaction to generate stable but tunable islet oscillation patterns.
INTRODUCTION
To precisely regulate the blood glucose level1–3, glucose elevation induces Ca2+ oscillation in pancreatic islet cells, which may trigger the pulsatile secretion of insulin and glucagon4–7. Dampening and disappearance of islet Ca2+ oscillation is an early biomarker in the pathogenesis of type 2 diabetes8–11. Multiple types of glucose-stimulated oscillation patterns have been observed in islets, including fast (~20 s cycle), slow (~100 s cycle), and mixed oscillations (20~100 s cycle)12–14. While different mathematical models have been proposed to explain the underlying mechanism15–20, most focused on the intrinsic properties of single or coupled β cells, such as the endoplasmic reticulum Ca2+ buffering capacity18 and the slow metabolic cycle of ATP/ADP ratio during glucose stimulation17. These β cell-centric models, however, may not fully explain the observed variety of oscillation patterns in islets. Only slow Ca2+ oscillations are mostly seen in isolated β cells21–24. Furthermore, glucagon accelerates the Ca2+ oscillation in isolated β cells25. The islet is a micro-organ in which multiple cell types closely interact. The α and β cells show highly correlated Ca2+ oscillation patterns26 and periodic release of insulin and glucagon is temporally coupled both in vitro4,27 and in vivo6,7,28,29. Thus the extensive autocrine and paracrine interactions between α and β cells30–35 may modulate or even dictate the islet oscillation modes.
The challenge to test such a hypothesis lies in resolving the identity of individual cells and monitoring their activity in live islets simultaneously. In addition, because the spatial organization of α and β cells are highly heterogeneous from islet to islet36,37, quantitative comparison of Ca2+ oscillations in different islets is necessary. To address these problems, we have developed a microfluidic device attached to the spinning-disc confocal microscope, which allowed individual cells to be imaged under physiological conditions for up to ~2 hrs. By the long-term imaging of islets undergoing repeated glucose stimulation, we found that the oscillation mode represents intrinsic properties of the islet. By constructing a new transgenic mice line, we could identify the cell types in live islets accurately. Quantitative analysis revealed generic features as well as quantitative relationships in the oscillation patterns across many islets. In particular, we found that oscillations of the islet α and β cells are each synchronized but phase shifted, and that the value of the phase shift between α and β cells determines the oscillation mode. Finally, we developed a coarse-grained mathematical model incorporating paracrine interactions between α and β cells. The model reproduced key quantitative features of the experimentally observed oscillations and suggested that different oscillation modes may come from the varied paracrine controls.
RESULTS
Glucose-Evoked Ca2+ Oscillation Represents an Intrinsic Property of the Islet
To provide a stable and controllable environment for long-term imaging of intact islets, we developed a microfluidic device (Fig. 1A). On one side, we designed an inlet port to load the islet (300 μm in width and 270 μm in height), which could be sealed after loading. The chip could trap islets of different sizes with a descending PDMS ceiling (270, 180, 150, 110, 80, and 50 μm in height). On the side opposite the inlet, five independent input channels merged into one channel upstream of the islet trapping site. Such a device enabled long-term and stable imaging of islets even during the switching of different perfusion solutions. For instance, when glucose concentration in the perfusion solution was increased from 3 to 10 mM (3G to 10G), all islets exhibited an initial rapid rise in cytosolic Ca2+, followed by a gradual appearance of fast (cycle<60 s, 31 of 46 islets), slow (cycle>60 s, 9 of 46 islets) or mixed (6 of 46 islets) Ca2+ oscillations (Fig. 1B). In contrast, although high glucose still evoked the initial increase in cytosolic Ca2+ concentration, no following periodic Ca2+ oscillations were observed in isolated islets from diabetic db/db mice (9 of 9 islets, Fig. 1B lower panel)10,11, suggesting the critical role of Ca2+ oscillation in maintaining normal hormone release and glucose homeostasis. While different islets displayed largely variable Ca2+ oscillations, the second round of 10G stimulation in the same islet evoked an oscillation frequency nearly identical to the first round (Fig. 1C). The spatial activation profiles were also similar, as almost identical cells lighted up at the designated times of Ca2+ cycles during the two rounds of stimulation (Fig. 1D). Quantitatively, sequential activations of islet cells between the two rounds of stimulation showed a significantly higher similarity index than random association (Fig. 1E, See Methods). Therefore, specific oscillation modes represent a robust intrinsic property of individual islets, possibly determined by the fixed spatial organization of the islet.
Identification of Islet α and β Cell Types Using Transgenic Mice
To probe the specific micro-organization of an islet and to distinguish the Ca2+ activities between α and β cells, we generated Glu-Cre+; GCaMP6ff/+; Ins2-RCaMP1.07 mice in which α and β cells were labeled with the green and red fluorescent Ca2+ sensor, GCaMP6f and RCaMP1.07, respectively (Fig. 2A, see Methods). Because the vector was randomly inserted into the genome using the PiggyBac transposon system, β cells were sparsely labeled (9.4%, Figs. 2B and S1). RCaMP1.07 is a Ca2+ sensor with a fluorescence on-rate similar to GCaMP6f38 and Cal-520 AM (Figs. S2C and S2D). We confirmed the labeling accuracy by immunofluorescence (Figs. 2C and S1). The RCaMP1.07 expressing islet cells were 100% insulin-positive, while the GCaMP6f expressing islet cells were 95.5% glucagon positive (Fig. S1A and S1B). This result was also confirmed in intact islets using immunofluorescence labeling (Figs. S1C and S1D) and pharmacology experiments (Figs. S2A and S2B). The GCaMP6f expressing cells responded to both NE and glutamate stimulation, while the RCaMP1.07 expressing cells were silent under both stimuli. These data both reinforced the expression specificity of α and β cells, and non-detectable overlaps in emission spectrums between GCaMP6f (525/50 nm) and RCaMP1.07 (600/50 nm) (Figs. 2D and S2E).
Under resting glucose stimulation, β cells remained silent while α cells demonstrated variable Ca2+ transients (Fig. 2E, Video 1), agreeing with the previous reports26. Therefore, the mean Ca2+ transients of β cells were flat, while we noticed a fluctuated mean Ca2+ trace of α cells. Upon elevated glucose stimulation, β cells always responded with large initial rises in cytosolic Ca2+ followed by slow decays.
In contrast, α cells demonstrated two opposite Ca2+ responses (Fig. 2F): within the first five minutes after the 10G stimulation, the majority of α responder (84%) were significantly inhibited, while the remaining cells (16%) showed evoked Ca2+ transients (n=179 α cells from 5 islets). Combined with 25 mM KCl stimulation, we found that 10G activated more α cells than 3G (Fig. 2H). Although this minor population of α cells did not fit the consensus, glucose-stimulated Ca2+ responses in some α cells were also noted previously39,40. Therefore, there exist two types of α cells in intact islets.
Islet α and β Cells Are Globally Phase-Locked
At the later stage of 10G stimulation, different pools of α cells in the islet became synchronized, accompanied by synchronized Ca2+ oscillations from β cells (Fig. 2E). Indeed, while less than 5% of α cells demonstrated correlated Ca2+ transients at the resting and the initial glucose stimulation stages, more than 70% became synchronized later (Figs. 2G, 3A and 3B, Video 2). Unlike β cells interconnected by the gap junction protein Connexin36 to achieve synchronization41–45, α cells do not express gap junction proteins and are thus not physically connected46. Because mean Ca2+ peaks of α cells displayed a fixed delay to those of β cells (~20 s), we hypothesized that the highly synchronous α cell activity might be due to stable phase-locking to the β cell activity (Figs. 3C and 3D). Consistent with tightly inhibited α cells originating from their neighboring β cells, we observed global α cell activation after the turning-off of β cells (Fig. 3E). Intriguingly, phase-locking with similar temporal characteristics was also present in slow and mixed oscillations (Fig. 3F, Videos 3 and 4), suggesting a common underlying mechanism.
The existence of phase-locked cells was also found in islets labeled with a non-targeted genetic Ca2+ sensor or loaded with the trappable Ca2+ dye (Video 5 and 6). In Ella-Cre+; GCaMP6ff/+ islets in which all islet cells were labeled with GCaMP6f, islet cells could also be classified into two groups that are phase-locked (Video 5). In addition, in the Glu-Cre+; tdTomatof/+ islet loaded with Cal-520 AM, we found that one of the two phase-locked cell populations colocalized with the genetically labeled red α cells (Video 6). Therefore, these data demonstrated that α cells are stably and globally phase-locked to β cells under elevated glucose stimulation in general.
Variable Delay of β Cell Activation After α Cell Determines the Oscillation Mode
To non-biasedly sort out critical parameters differentiating various Ca2+ oscillation patterns, we quantitatively defined features of each oscillation cycle of alternately activated α and β cells (Figs. 4A and S3). The oscillation period T was defined as the time window between one cycle of β cell activation, which was split into two parts divided by the α cell activation: the waiting time for α cell to activate after β cell activation (Tβα) and the waiting time for β cell to activate after α cell activation (Tαβ). The phase difference (Δθ) of two types of cells was defined as the ratio between Tβα and T. There were multiple ways to determine these quantities – either using the peak, 25%, 50%, or 75% decrease - and they did not change the outcome of the analysis (Figs. S4B-D). In total, we defined 13 features that recapitulated different characteristics of the α and β cell Ca2+ dynamics, such as the rise and decay time of the activation for α and β cells, the Full Width at Half Maximum (FWHM) (Table 1, and see Methods for detailed definitions). Based on these parameters, the oscillating cycles were vectorized and assembled into a feature matrix. Next, by dimension reduction of these parameters with the UMAP algorithm47, oscillations could be classified into the fast and the slow ones (Fig. 4B), in which T, Δθ, Tαβ and FWHM of β cells demonstrated significant inter-group differences (Figs. 4C and S4A). The T for the fast oscillations centered at ~30 s, threefold smaller than the slow ones (~104 s). Similarly, the average Δθ for the rapid oscillations was threefold larger than the slow ones (~0.6 versus ~0.2, Table 1). While the mean Tβα was almost indistinguishable between fast and slow oscillations, the Tαβ of the former was smaller than the latter (~11 s versus ~86 s, Table 1). The distribution of β cells’ FWHM for the fast oscillations was different from that of the slow ones, with a mean FWHM at ~12 s for the fast oscillations and ~34 s for the slow oscillations (Fig. 4C and Table 1). In contrast, the distributions of FWHM for α cells between the fast and slow oscillations were more similar (Fig. 4C), This implies a higher FWHM ratio of the Ca2+ transients of α to β cells in the fast Ca2+ oscillations (~1.02) than in the slow oscillations (~0.44) (Fig. S4A).
As T, Δθ, Tαβ and Tβα were inter-dependent parameters, we further evaluated their relationship using scatter plots (Fig. 4D). It was apparent that Tβα remained constant across different T. In contrast, Tαβ increased linearly with T. These findings strongly suggest a key role of Tαβ in determining the period (hence the mode) of β cell oscillation. While a short waiting time Tαβ leads to fast oscillations, long waiting time Tαβ confers slow ones. Given the α cells displayed a fixed delay of ~20 s to the β cells, the phase-shift between α and β cells varied with the delay of β cells. For example, when the β cells had little delay (~0 s) to the α cells (Fig. 4D, Tβα=~20 s, Tαβ=~0 s, T=~20 s), the α and β cells were nearly in-phase (Δθ~=1). When the β cell’s delay was around ~20 s (Tβα~=Tαβ=20 s, T=~40 s), the α and β cells were nearly anti-phase (Δθ~=0.5). Finally, when the β cells waited much longer than the α cells (Tβα~=20 s, Tαβ~=180 s, T=~200 s), the α and β cells appeared nearly in-phase again but with Ca2+ transient much differed from the first case (Δθ~=0.1). Note the apparent order of α and β cell activation depended on the relative value of Tαβ and Tβα. The fast oscillation might show a near in-phase locking with α ahead of β cell due to a shorter Tαβ than Tβα, and the slow oscillation might also show a near in-phase locking but with β ahead of α cell due to a shorter Tβα than Tαβ (Figs. 3B, 3C and 3F). These relationships hold for various oscillation modes as indicated by the different colors in Fig. 4D.
Interestingly, sometimes we observed that the phase shift between α and β cells underwent an initial transient period during which it changes in time before stabilizing at a steady value. This was usually due to a changing delay of β cell activation after α cell activation. As it is shown in Fig. 4E, while Tβα remained stable at 20 s during the whole process, Tαβ started from 4 s, extended to 15 s in the next ten oscillations, and finally stabilized at 10 s. Correspondingly, α and β cells started from a phase shift Δθ=0.78 (Tβα=20 s, Tαβ=4 s) at first, then gradually established a phase shift Δθ=0.58 (Tβα=20 s, Tαβ =15 s), before finally stabilized at Δθ=0.66 (Tβα=20 s, Tαβ=10 s) (Table S1, n=3 islets). This data corroborated our analysis conducted in multiple islets and pointed to the possibility of dynamic changes in the interactions between α and β cells in the same islet. Because isolated single β cells displayed only slow oscillation with a period of about 6 minutes (Figs. S5A and S5B), we speculate that increased stimulatory effect from α cells to β cells may push β cells to oscillate in the fast mode.
Mathematical Modeling
We observed that islets show heterogeneous yet intrinsic oscillation patterns under high glucose stimulation. To better understand the origin of various oscillation modes and the factors controlling them, we developed a mathematical model incorporating interactions between α and β cells.
α-β Phase Oscillator Model
Given the fact that both α cells and the β cells in an islet were globally synchronized respectively, we simplified the islet as a model of two coupled “cells” - an α cell and a β cell (Fig. 5A). The oscillation of each cell was described by a phase variable θ, which was driven by an intrinsic force and a paracrine force (Fig. 5B, see Methods). The intrinsic term corresponded to the oscillation frequency of the single isolated cells. As shown by previous and our studies, single β cells oscillate with a period ~3-6 minutes, and single α cells oscillate with a period ~30-60 seconds (Fig. S5). The paracrine term consisted of three parts: fs(θ) represented the hormone secretion, frα(θ) represented the paracrine inhibition of α cells by β cells and frβ(θ) represented the paracrine stimulation of β cells by α cells. The main results of the model were insensitive to the choice of the specific forms of fs(θ), frα(θ) and frβ(θ) as long as they were periodic functions resembling the general characteristic of the biology (see Figs. S6 and S7 for details). The coefficients Kαβ and Kβα represented the coupling strengths between the α and β cells. Note that this is a two-phase model without providing any information on the amplitude of the oscillation. Its behavior can be characterized by the “winding number” defined as the asymptotic ratio of the two phases w=θα/θβ (Fig. 5C).
Slow, Fast, and Mixed Oscillations
By adjusting the coupling strengths (Kαβ and Kβα) between the α and β cells, our model displayed all three types of the oscillation behaviors observed in experiments (cases 1-3, Fig. 5D). When α cell weakly stimulated β cell (small Kαβ), the model islet generally showed slow oscillations. When α cell and β cell were strongly coupled with each other (large Kβα and Kαβ), the model islet generally showed fast oscillations. When α cell strongly stimulated β cell and β cell weakly inhibited α cell (large Kαβ and small Kβα), the model islet generally showed mixed oscillations. With very weak coupling between α and β cells, the model displayed an oscillation behavior similar to uncoupled single cells but not islet experiments (Fig. 5D, case 4). Further quantification found the phase difference Δθ and the period T displayed an inverse proportional relationship (Fig. 5F, left panel), which was because of a constant waiting time of the α cell regardless of the oscillation modes (Fig. 5F, middle panel), similar to the experimental data (Fig. 4D). The coupling coefficients changed only the waiting time of the β cell, and further determined the period (Fig. 5F, right panel).
Phase Locking Between α and β Cells
We next analyzed the model’s behavior by systematically varying the coupling strengths between the α and β cells. We found that the α and β cells were generally phase-locked, i.e., their phases were dependent on each other with a fixed relationship characterized by the winding number w (Fig. 5C). By plotting the winding number’s dependence on the coupling strengths, we obtained the phase space of the system of two coupled oscillators (Fig. 5E). It formed a two-dimensional Arnold tongues48, which could be separated into four regions (Fig. 5E, see Methods). In region 1, the α cell and the β cell are locked on the w=1/1 mode. That is, when θβ finishes one cycle ([0,2π]), θα will also finish one cycle. An example of this oscillation mode is shown in Fig. 5D (upper panel). In region 2, the two cells are locked in the mode w=0/1. That is, when θβ finishes one cycle ([0,2π]), θα cannot finish a full cycle before being pushed back (Fig. 5D (middle-upper panel)). Here the strong stimulation from α to β induces a fast oscillation frequency, while the strong repression from β to α prevents the α cell from finishing a full cycle every time it is activated. In region 3, the two cells are locked with 0<w<1. In particular, there exist w=m/n modes, where m<n are both integers. In a mode with w=m/n, when θβ finishes n cycles ([0,2nπ]), θα will finish m cycle(s) ([0, 2mπ]). In the example with w=1/2 shown in Fig. 5D (middle-lower panel), while each activation of the β cell can finish one full cycle, the first activation of α cell cannot finish a full cycle before being pushed back, and only the second activation can finish a full cycle. Although only a few modes are shown in region 3 for clarity, it can be proved rigorously that region 3 contains all the modes, with w being a rational number between 0 and 1 (unpublished). In region 4, the two phases are locked with w>1, which means that α cell will finish more cycles than β cell. An example of w=3/1 is shown in Fig. 5D (lower panel). In this region, α and β cells couple weakly. At the upper left corner Kαβ=Kβα=0, α and β cells completely decouple and beat on their intrinsic frequencies. Note that while w jumps discontinuously with continuously varying parameters, the average period of β cell oscillation changes smoothly (Fig. 5E, heat map). Thus, the paracrine interaction between α and β cells offers robust and tunable oscillation patterns and periods.
Model Prediction and Verification
A prediction of the model was that the oscillation period may be tuned with the strengths of paracrine interaction, depending on the original position of the islet system in the phase space (Figs. 5E, heat map, 6B, S8E and S9F). In particular, increasing the activation from α cell to β cell (Kαβ) could increase the oscillation period, especially in islets of slow oscillations (Fig. 5E, heat map). We applied glucagon (100 nM) to the islets showing fast and slow oscillations (Figs. 6A and S8A). While adding glucagon did not affect fast oscillating islets, it switched islets harboring slow oscillations into fast ones. According to our model, the change of oscillation period was due to stronger paracrine interactions that reduced the waiting time Tαβ without affecting the waiting time Tβα, which faithfully recapitulated the experimental data (Figs. 6B-D and S8B-E). On the other hand, the model predicted that reducing the effect of glucagon may lead to more autonomous cellular regulation and slow oscillations (Figs. 6B, 6F and S9F). Indeed, by combining insulin and the GCGR and GLP-1R antagonists (MK0893 (MK) and Exendin 9-39 (Ex9)) to inhibit glucagon secretion and its downstream target30,31, ~50% of the fast oscillatory islets switched to slow oscillations (Fig. 6A). The change of modes reversed back when the inhibitory agents were removed (Fig. S9A). Islets’ fast-to-slow mode switching critically relied on the activation level of glucagon’s downstream target. A weaker glucagon receptor antagonist combination prolonged the islet oscillation period without inducing fast-to-slow mode switching (Figs. S9B and S9C). The β-cell-specific GCGR knockout mice (Ins1-cre;Gcgrf/f)49 had fewer fast oscillation islets (Fig. S9D). And ~50% of the fast oscillation Ins1-cre;Gcgrf/f islets turned into slow oscillations with the weaker glucagon receptor antagonist combination (Fig. S9E).
Finally, our model also predicted that in mixed oscillation modes, decay times of Ca2+ transients in α cells were different - only the last Ca2+ transient in each cluster of cycles of mixed oscillation was independent of β cells, while all other ones were repressed by β cells and should descend faster (Fig. 6G). By analyzing the Ca2+ traces of islets with mixed oscillation modes, we confirmed that the decay times of α cell transients fell into two groups: the Ca2+ transients in α cells just preceding an uprising of β cell activation decayed faster. In contrast, the ones posterior to β cell transients exhibited a significantly slower decay (Fig. 6H). Overall, the agreement between the model and experiment highlights the importance of α-β interactions in shaping up the oscillation modes.
DISCUSSION
In this study, we developed a microfluidic device that enabled stable and repeatable long-term imaging of Ca2+ activities of islets at single-cell resolution. Despite the apparent heterogeneity in Ca2+ activities across different islets, individual islets exhibited their own spatial and temporal patterns of Ca2+ oscillations that were repeatable under multiple rounds of glucose stimulation. This suggests that the oscillation mode results from some intrinsic properties of the islet, possibly correlated with different cell types and their spatial distributions.
By using the Glu-Cre+; GCaMP6ff/+; Ins2-RCaMP1.07 transgenic mice, we discovered that the α and β cells were globally phase-locked to various oscillation modes. The PiggyBac approach led to the sparse labeling of β cells – it enabled a clear separation of α and β cell Ca2+ dynamics. Besides α and β cells, pancreatic islet δ cells have recently received increasing attention in glucose regulation50, which are not included in the current model. δ cells are connected to β cells by gap junctions and exhibit Ca2+ activities similar to β cells51. It releases somatostatin to strongly inhibit both α and β cells. Further study about the δ cell Ca2+ dynamics and simultaneous α, β, and δ cell Ca2+ imaging would be important to understand the role of δ cell in tuning α and β phase-locking patterns. In the current mathematical model, the role of δ cells in regulating the oscillation modes was lump-summed together with that of β cells. It is essential to differentiate the two types of cells in future modeling.
A key finding in our study is that the time delay for α cells’ activation following the activation of β cells (Tβα) was invariant, regardless of the islet-to-islet variations in oscillation frequencies and modes. This observation of invariant Tβα echoed nicely with the ~20 seconds recovery time of α cells from the relief of optogenetic activation of β and δ cells51. Therefore, Tβα is likely to be determined by one or more secretin released by β and δ cells, including insulin, Zn2+, ATP, GABA, and somatostatin52.
In contrast, what varied in different islets under different conditions was the time delay of β cells’ activation following that of α cells (Tαβ). Our and previous studies suggest that glucagon is a contributing factor in tuning the oscillation mode13. Our work showed that increased glucagon level tunes on the oscillation modes by reducing the waiting time of β cells (Tαβ). Glucagon may elevate cytosolic Ca2+ concentration and increase oscillation frequency, both through cAMP-dependent53,54 and independent pathways55–58. On the other hand, blocking glucagon receptors with MK0893 and Exendin 9-39 could not fully slow down WT islets. We speculate that this may be because pharmacological inhibitors cannot completely block the endogenous glucagon function of pancreatic islets. Consistent with this, MK0893 and Exendin 9-39 induced fast-to-slow mode switching in the Ins1-cre;Gcgrf/f islets, and a combination of insulin, MK0893 and Exendin 9-39 was able to turn fast oscillations into slow ones. The specific molecular mechanism for this synergy effect needs future investigation.
The fixed α cell delay and glucagon-tuned β cell delay imply that the value of the phase shift depends on the oscillation frequency (Fig. S10). Islet β cell Ca2+ oscillation modes are influenced by two regulatory processes – the fast-paracrine stimulation and the slow intrinsic activation. Once α cells release a large amount of glucagon, their stimulatory effects on β cells would significantly reduce the waiting time for β cell activation and the islet would oscillate with a frequency much faster than β cells’ intrinsic frequencies (α paracrine dominant). If α cells fail to release enough glucagon, or the downstream effects of glucagon are inhibited, β cells in the islet would oscillate with a frequency close to their intrinsic ones (β intrinsic dominant). Indeed, the α and β cells appeared nearly in-phase for both fast oscillations with periods close to 20s and slow oscillations with period ~180s. There is a continuum between the two extreme cases. E.g., for oscillations with period ~40s, α and β cells appeared nearly anti-phase.
In our study, both experimental observations and model simulations showed a robust phase-locking phenomenon between α and β cells. It is known that faster islet Ca2+ oscillations display more regular oscillation patterns13,59. In light of our findings, the increased regularity may come from the increased stability in phase-locking: more rapid oscillation implies more robust activation from α to β cells and thus a tighter regulation. The Ca2+ oscillation of the two types of cells can phase-lock to a variety of modes determined by the paracrine interactions, which not only have different oscillation frequencies, but also display a range of other quantitative features such as the winding number and the ratio of the half-widths for α and β transients. Phase-locking to different frequencies and modes could ensure a stable and tunable secretion of insulin and glucagon. A variety of β cell Ca2+ oscillation modes were observed in vivo, including those of fast ones60–62. Further studies combining islet Ca2+ imaging with real-time detection of α and β cell secretion are needed to investigate the physiological roles of the phase-locking and its dependency on paracrine interactions.
Previous studies tried to explain the distinct Ca2+ oscillation modes in intact islets with single beta-cell models, which did not consider the contribution from other cell types in islets15–18. Our model emphasized how paracrine interactions may play important roles in various islet Ca2+ oscillation modes. It is conceivable that both intrinsic properties of single cells and interactions among different cell types may contribute to the regulation of islet Ca2+ oscillation modes. Further investigation using pseudo-islets with varying compositions of α and β cells may help to differentiate the roles of intrinsic and paracrine contributions63.
AUTHOR CONTRIBUTIONS
C.T. and L.C. conceived and supervised the study, and wrote the manuscript.
H.R. led the project, designed experiments, carried out data analysis and mathematical modeling, and wrote the manuscript.
Y.L. designed and manufactured the microfluidic chip, designed and performed experiments, and wrote the manuscript.
C.H. designed and performed experiments, and wrote the manuscript.
X.Y. contributed to Figure preparation and supervised experiments, Y.Y and K.S. contributed to the mathematical modeling, B.S. and S.W. contributed to data analysis.
DECLARATION OF INTERESTS
The authors have no competing financial interests to declare.
ACKNOWLEDGMENTS
We thank Erik Gylfe, Anders Tengholm, Yanmei Liu, Louis Tao and Alexander Valentin Nielsen for helpful discussions. We thank Chunxiong Luo and Shujing Wang for their help with the microfluidic chip design. We thank Daniel Tang and Iain Bruce for manuscript editing. We thank Xiaowei Chen for sharing mice lines. This work was supported by grants from the Chinese Ministry of Science and Technology (2015CB910300), National Natural Science Foundation of China (81925022, 92054301), The National Key Research and Development Program of China (SQ2016YFJC040028, 2018YFA0900700), NSFC Innovation group projects (31821091) and the Beijing Natural Science Foundation (L172003, 7152079, 5194026).
Footnotes
↵6 Lead Contact