Immunocytochemical and ultrastructural heterogeneities of normal and glibenclamide stimulated pancreatic beta cells in the rat

Light scattering as an intrinsic indicator for pancreatic islet cell mass and secretion

The pancreatic islet of Langerhans is composed of endocrine cells producing and releasing hormones from secretory granules in response to various stimuli for maintenance of blood glucose homeostasis. In order to adapt to a variation in functional demands, these islets are capable of modulating their hormone secretion by increasing the number of endocrine cells as well as the functional response of individual cells. A failure in adaptive mechanisms will lead to inadequate blood glucose regulation and thereby to the development of diabetes. It is therefore necessary to develop tools for the assessment of both pancreatic islet mass and function, with the aim of understanding cellular regulatory mechanisms and factors guiding islet plasticity. Although most of the existing techniques rely on the use of artificial indicators, we present an imaging methodology based on intrinsic optical properties originating from mature insulin secretory granules within endocrine cells that reveals both pancreatic islet mass and function. We demonstrate the advantage of using this imaging strategy by monitoring in vivo scattering signal from pancreatic islets engrafted into the anterior chamber of the mouse eye, and how this versatile and noninvasive methodology permits the characterization of islet morphology and plasticity as well as hormone secretory status.

Streptozotocin-induced diabetes models: pathophysiological mechanisms and fetal outcomes

Glucose homeostasis is controlled by endocrine pancreatic cells, and any pancreatic disturbance can result in diabetes. Because 8% to 12% of diabetic pregnant women present with malformed fetuses, there is great interest in understanding the etiology, pathophysiological mechanisms, and treatment of gestational diabetes. Hyperglycemia enhances the production of reactive oxygen species, leading to oxidative stress, which is involved in diabetic teratogenesis. It has also been suggested that maternal diabetes alters embryonic gene expression, which might cause malformations. Due to ethical issues involving human studies that sometimes have invasive aspects and the multiplicity of uncontrolled variables that can alter the uterine environment during clinical studies, it is necessary to use animal models to better understand diabetic pathophysiology. This review aimed to gather information about pathophysiological mechanisms and fetal outcomes in streptozotocin-induced diabetic rats. To understand the pathophysiological mechanisms and factors involved in diabetes, the use of pancreatic regeneration studies is increasing in an attempt to understand the behavior of pancreatic beta cells. In addition, these studies suggest a new preventive concept as a treatment basis for diabetes, introducing therapeutic efforts to minimize or prevent diabetes-induced oxidative stress, DNA damage, and teratogenesis.

Impact of islet size on pancreatic islet transplantation and potential interventions to improve outcome

Better results have been recently reported in clinical pancreatic islet transplantation (ITX) due mostly to improved isolation techniques and immunosuppression; however, some limitations still exist. It is known that following transplantation, 30% to 60% of the islets are lost. In our study, we have investigated 1) the role of size as a factor affecting islet engraftment and 2) potential procedural manipulations to increase the number of smaller functional islets that can be transplanted. C57/BL10 mice were used as donors and recipients in a syngeneic islet transplant model. Isolated islets were divided by size (large, >300 μm; medium 150-300 μm; small, <150 μm). Each size was transplanted in chemically induced diabetic mice as full (600 IEQ), suboptimal (400 IEQ), and marginal mass (200 IEQ). Control animals received all size islets. Engraftment was defined as reversal of diabetes by day 7 posttransplantation. When the superiority of smaller islets was observed, strategies of overdigestion and fragmentation were adopted during islet isolation in the attempt to reduce islet size and improve engraftment. Smaller islets were significantly superior in engraftment compared to medium, large, and control (all sizes) groups. This was more evident when marginal mass data were compared. In all masses, success decreased as islet size increased. Once islets were engrafted, functionality was not affected by size. When larger islets were fragmented, a significant decrease in islet functionality was observed. On the contrary, if pancreata were slightly overdigested, although not as successful as small naive islets, an increase in engraftment was observed when compared to the control group. In conclusion, smaller islets are superior in engraftment following islet transplantation. Fragmentation has a deleterious effect on islet engraftment. Islet isolations can be performed by reducing islet size with slight overdigestion, and it can be safely adopted to improve clinical outcome.

Contribution of postnatally formed small beta cell aggregates to functional beta cell mass in adult rat pancreas

AIMS/HYPOTHESIS

Neogenesis of beta cells and their clustering to small aggregates is a key process in prenatal development of beta cell mass. We investigated the contribution of postnatally formed small aggregates to functional beta cell mass in adult rats.

METHODS

Conditions were defined for (1) counting total beta cell number in pancreases with relative error of <10% and (2) determining their distribution over aggregates of different size and over functionally different subpopulations.

RESULTS

Pancreases of 10-week-old male Wistar rats contained 2.8 ± 0.2 × 10⁶ beta cells, of which >90% was generated postnatally, involving: (1) neo-formation of 30,000 aggregates with diameter <50 μm including single cells; and (2) growth of 5,500 aggregates to larger sizes, accounting for 90% of the increase in cell number, with number of growing aggregates in the tail 50% greater than elsewhere. At 10 weeks, 86% of aggregates were <50 μm; compared with aggregates >200 μm, their beta cells exhibited a higher basal insulin content that was also resistant to glibenclamide-induced degranulation. The pool of Ki67-positive beta cells was sixfold larger than at birth and distributed over all aggregate sizes.

CONCLUSIONS/INTERPRETATION

We describe a method for in situ counting of beta cell numbers and subpopulations with low relative error. In adult rats, >90% of beta cells and beta cell aggregates are formed after birth. Aggregates <50 μm are more than 100-fold more abundant than aggregates >200 μm, which are selected for isolated islet studies. Their topographic and functional properties contribute to the functional heterogeneity of the beta cell population; their growth to larger aggregates with characteristic beta cell functions may serve future metabolic needs.

Morphological localisation of sulfonylurea receptor 1 in endocrine cells of human, mouse and rat pancreas

AIMS/HYPOTHESIS

Sulfonylurea receptor 1 (SUR1) is the regulatory subunit of ATP-sensitive K channels in beta cells. Morphological methods (immunohistochemistry and sulfonylurea binding) were used to establish the cellular and subcellular location of SUR1 in human and rodent islets.

RESULTS

In the human, mouse and rat pancreas, all endocrine cells of the islets were immunolabelled with an anti-SUR1 antibody, whereas tissues containing SUR2 were consistently negative, as were those from Sur1 (also known as Abcc8)(-/-) mice. In beta cells of the three species, the plasma membrane was distinctly stained, but SUR1 was mainly present over the cytoplasm, with an intensity that varied between cells. Electron microscopy showed that SUR1 was immunolocalised in insulin, glucagon and somatostatin granules. In rat beta cells degranulated by in vivo treatment with glibenclamide (known as glyburide in the USA and Canada), the insulin and SUR1 staining intensity was similarly decreased by approximately 45%, whereas SUR1 staining was not changed in non-beta cells. In all islet cells, binding of glibenclamide labelled with fluorescent dipyrromethane boron difluoride (BODIPY-FL) was punctate over the cytoplasm, compatible with the labelling of endocrine granules. A faint labelling persisted in Sur1 (-/-) mice, but it was not different from that obtained with BODIPY-FL alone used as negative control.

CONCLUSIONS/INTERPRETATION

Our study immunolocalised SUR1 in alpha, beta and delta cells of human, mouse and rat islets, and for the first time visualised it in the plasma membrane. We also show that SUR1 is abundant in endocrine granules, where its function remains to be established. No specific sulfonylurea-binding sites other than SUR1 are identified in islet cells by the glibenclamide-BODIPY-FL technique.

Morphological changes of isolated rat pancreatic islets: a structural, ultrastructural and morphometric study

Improved techniques for pancreatic islet extraction can yield a reasonable number of transplantable cells. However, the isolation and purification process may damage the islets and impair their physiological functions. The aim of this study was to determine the effect of the isolation procedure on the structure of isolated islets and to correlate this with their functionality. Islets were isolated from rat pancreata and purified by Eurocollins-Ficoll discontinuous density gradient processing, and then processed for light microscopy, and scanning and transmission electron microscopy. Morphometric analysis was also performed. Islet functionality was determined by reversal of streptozotocin-induced diabetes and the intraperitoneal glucose tolerance test in a syngeneic rat model of pancreatic islet transplantation. Fragments of variable size and shape comprised a relatively large proportion (26%) of the isolated endocrine tissue. Isolated islets showed slight alterations of cell ultrastructure. Major damage (including breakage of the plasma membrane) and loss of cells were observed in the peripheral cells of the isolated islets. An equal mass of islet equivalent (IEq, islets with an average diameter of 150 microm), but with a different islet equivalent/islet number ratio, was transplanted in diabetic animals. When larger and more complete islets were transplanted (higher ratio), better function of the graft was observed by reversal of hyperglycaemia and response to the glucose tolerance test as compared with the functionality and response of smaller (fragmented) islets transplanted (lower ratio). Digestion, trauma and hypoxia during isolation are responsible for qualitative and quantitative changes of isolated islets. Alterations in normal secretory function after the transplant were related to lower islet equivalent/islet number ratio. The incomplete integrity of the islets may explain the failure of the fine glycaemic metabolic regulation.

Effects of polyinosinic-polycytidylic acid and adoptive transfer of immune cells in the Lew.1AR1-iddm rat and in its coisogenic LEW.1AR1 background strain

The importance of the cellular immune system for the development of T1DM in the LEW.1AR1-iddm rat was investigated by use of polyinosinic-polycytidylic acid (Poly I:C) and by adoptive transfer of concanavalin A (Con A) activated lymphocytes from diabetic LEW.1AR1-iddm rats and the coisogenic LEW.AR1 background strain. Poly I:C treatment induced diabetes, characterized morphologically by a diffuse infiltration of the pancreas, in up to 20% of the animals of the coisogenic LEW.1AR1 background strain. It did not increase the diabetes incidence of 30% of the LEW.1AR1-iddm strain. In contrast Poly I:C treatment induced diabetes in up to 80% of the animals of the Mhc congenic LEW.1WR1 strain. Adoptive transfer of lymphocytes activated by the T-cell mitogen Con A from diabetic donors doubled the incidence of diabetes, characterized morphologically by a focal insulitis, in diabetes prone LEW.1AR1-iddm recipients. In contrast, animals of the LEW.1AR1 background strain did not develop diabetes after adoptive transfer. Moreover, adoptive transfer of Con A activated lymphocytes from LEW.1AR1 rats to LEW.1AR1-iddm rats with 30 or 60% diabetes incidence, significantly decreased the incidence of diabetes in LEW.1AR1-iddm rats with 60% diabetes incidence. The results show that autoreactive lymphocytes induce beta cell destruction in the LEW.1AR1-iddm rat, while the LEW.AR1 background strain apparently contains regulatory potential, which is able to counteract the autoimmune response.

Heterogeneity in distribution of amyloid-positive islets in type-2 diabetic patients

Amyloid-containing (A+) islets are characteristic for type-2 diabetes (T2D), but their abundance seems variable among patients. It is unclear whether the distribution of A+ islets follows a certain pattern or occurs randomly throughout the pancreatic organ. We investigated the topography of A+ islets in eight pancreata of T2D patients and eight sex- and age-matched non-diabetic subjects. Transversal sections of head, body and tail segments were stained with synaptophysin combined with Congo red to map/quantify islet tissue and amyloid. In the eight T2D pancreata, the overall percentage of A+ islets varied from 4% to 85%. Further analysis in body and tail indicated that peripheral regions exhibited higher percentages of A+ islets than central regions (averages of, respectively, 30% and 17%, P<0.05). Non-diabetic control pancreata also exhibited A+ islets, albeit at a 25-fold lower frequency; a tendency towards higher percentage of A+ islets in peripheral versus central regions was also observed. The higher percentage A+ islets in peripheral regions was associated with a higher density and relative islet over exocrine surface area. These observations on heterogeneity in abundance and distribution of A+ islets need consideration when sampling tissue for studies on human islet amyloidosis. The present methodology allows us to further investigate the susceptibility to amyloidosis of islets in peripheral regions of the pancreas.

Cytological and immunocytochemical characterization of the insulin secreting insulinoma cell line RINm5F

The rat insulinoma cell line RINm5F, an insulin secreting pancreatic beta cell line, has been used as an attractive model for basic studies of the mechanisms of insulin secretion and, more recently, as a model for the development of alternative methods for the treatment of diabetes. To elucidate the cytological properties and expression patterns of hormones of the gastro-entero-pancreatic system, suspensions of RINm5F cells were investigated by various methods including immunocytochemistry on serial semithin sections, quantitative immunocytochemistry, routine electron microscopy, immuno-electron microscopy, in situ hybridization, and TUNEL technique. At the ultrastructural level, several phenotypes of RIm5F cells were characterized by differences in the number, shape, size, and density of their secretory granules. The most common type contained a mixture of round granules varying in size and electron density. A second type predominantly contained relatively large, moderately dense granules. Moreover, a minority of cells was characterized by the occurrence of polymorphous electron dense granules or the complete absence of any secretory granules. The immunohistochemical data showed that, among the established islet hormones, insulin was present in more than 50% of cells, whereas glucagon and somatostatin occurred only sporadically. Though cells positive for pancreatic polypeptide (PP) were not found, PP-related peptides (NPY and PYY) however could be detected in a minority of cells. The great majority of RINm5F cells were immunoreactive for chromogranin B (CgB), followed by insulin, chromogranin A (CgA), and serotonin (5-HT). In addition to intercellular differences in the density of immunostaining, numerous colocalizations of immunoreactivities were found, suggesting that RINm5F cells represent a mixture of subtypes concerning the individual pattern of hormone expression. The present results reveal a wide range of heterogeneity with respect to the morphology and especially the hormone content between individual RINm5F cells.

Desensitization of insulin secretion

Desensitization of insulin secretion describes a reversible state of decreased secretory responsiveness of the pancreatic beta-cell, induced by a prolonged exposure to a multitude of stimuli. These include the main physiological stimulator, glucose, but also other nutrients like free fatty acids and practically all pharmacological stimulators acting by depolarization and Ca2+ influx into the beta-cell. Desensitization of insulin secretion appears to be an important step in the manifestation of type 2 diabetes and in the secondary failure of oral antidiabetic treatment. In this commentary, the basic concepts and the controversial issues in the field will be outlined. With regard to glucose-induced desensitization, two fundamentally opposing concepts have emerged. The first is that desensitization is the consequence of functional changes in the beta-cell that impair glucose-recognition. The second is that long-term increased secretory activity leads to a depletion of releasable insulin, often in spite of increased insulin synthesis. The latter concept is more appropriately termed beta-cell exhaustion. The same dichotomy applies to the desensitization evoked by pharmacological stimuli: again the relative contributions of a decreased insulin content versus alterations in signal transduction are in dispute. The action of tolbutamide on beta-cells may be an example of desensitization caused by a lack of releasable insulin since the signaling mechanisms are nearly unchanged, whereas the action of phentolamine, an imidazoline, induces a strong desensitization without reducing insulin content or secretory granules, apparently by abolishing Ca2+ influx. With pharmacological agents it seems that both, alterations in signal transduction and decreased availability of releasable insulin, can contribute to the desensitized state of the beta-cell, the relative contribution being variable depending upon the exact nature of the secretory stimulus.

Desensitization of insulin secretory response to imidazolines, tolbutamide, and quinine. I. Secretory and morphological studies

The desensitization of pancreatic B-cells against stimulation by insulin secretagogues that inhibit ATP-dependent K(+) channels (K(ATP) channels) was investigated by measuring insulin secretion of perifused pancreatic islets. Additionally, the islet insulin content and the number of secretory granules per B-cell were determined. Prior to the measurement of secretion, islets were cultured for 18 h in the presence or absence of the test agents in a cell-culture medium containing 5 mM glucose. The effects of three imidazolines, phentolamine, alinidine, and idazoxan (100 microM each) were compared with those of the well-characterized sulfonylurea, tolbutamide (500 microM), and those of the ion channel-blocking alkaloid, quinine (100 microM). Insulin secretion was strongly reduced upon re-exposure to phentolamine, alinidine, tolbutamide, and quinine, whereas idazoxan, which stimulated secretion only weakly, had no significant effect. The imidazoline secretagogues phentolamine and alinidine induced a cross-desensitization against the stimulatory effect of tolbutamide and quinine. A long-term depolarization with 40 mM KCl was also able to induce a significant reduction of the secretory response to all of the above secretagogues. The insulin content of cultured islets was moderately, but significantly reduced by alinidine, whereas the reduction by phentolamine, tolbutamide, and quinine was not significant. In contrast to these observations, the ultrastructural examination revealed that tolbutamide-treated B-cells had a high degree of degranulation, whereas the other test agents and 40 mM KCl produced only a partial degranulation, except for phentolamine, which produced no significant degranulation at all. These results suggest that the desensitization of insulin secretion is a common property of all agents that stimulate insulin secretion by depolarisation of the plasma membrane. Depending on the specific secretagogue, additional mechanisms, proximal and distal to Ca(2+) influx, appear to contribute to the desensitization (see Rustenbeck et al., pages 1695-1703, this issue).

Tolbutamide stimulation of pancreatic beta-cells involves both cell recruitment and increase in the individual Ca(2+) response

Individual pancreatic beta-cells are functionally heterogeneous. Their sensitivity to glucose is variable, so that the proportion of active cells increases with the glucose concentration (recruitment). We have investigated whether sulphonylureas also recruit beta-cells, by measuring cytoplasmic Ca(2+) ([Ca(2+)](i)) - the triggering signal of insulin secretion - in single cells and clusters of cells prepared from mouse islets. In 4 mM glucose, the threshold concentration of tolbutamide inducing a [Ca(2+)](i) rise was variable (5 - 50 microM). The proportion of responsive cells and clusters therefore increased with the tolbutamide concentration, to reach a maximum of 90% of the cells and 100% of the clusters. This recruitment occurred faster when the glucose concentration was increased from 4 to 5 mM (EC(50) of approximately 14 and approximately 4 microM tolbutamide respectively). Within responsive clusters little recruitment was observed; when a cluster was active, all or nearly all cells were active probably because of cell coupling. Thus, tolbutamide-induced [Ca(2+)](i) oscillations were synchronous in all cells of each cluster, whereas there was no synchrony between clusters or individual cells. Independently of cell recruitment, tolbutamide gradually augmented the magnitude of the [Ca(2+)](i) rise in single cells and clusters. This increase occurred over a broader range of concentrations than did recruitment (EC(50) of approximately 50 and 25 microM tolbutamide at 4 and 5 mM glucose respectively). Tolbutamide (10 microM) accelerated the recruitment of single cells and clusters brought about by increasing glucose concentrations (range of 3 - 7 mM instead of 4 - 10 mM glucose), and potentiated the amplification of the individual responses that glucose also produced. In conclusion, both metabolic (glucose) and pharmacologic (sulphonylurea) inhibition of K(+)-ATP channels recruits beta-cells to generate a [Ca(2+)](i) response. However, the response is not of an all-or-none type; it increases in amplitude with the concentration of either glucose or tolbutamide.

Emergent global oscillations in heterogeneous excitable media: the example of pancreatic beta cells

Using the standard van der Pol-FitzHugh-Nagumo excitable medium model, I demonstrate a generic mechanism, diversity, that provokes the emergence of global oscillations from individually quiescent elements in heterogeneous excitable media. This mechanism may be operating in the mammalian pancreas, where excitable beta cells, quiescent when isolated, are found to oscillate when coupled, despite the absence of a pacemaker region.

Ultrastructural evaluation of B-cell recruitment in virgin and pregnant offspring of diabetic mothers

Adult offspring of diabetic rat mothers display a disturbed glucose tolerance and gestational diabetes. The amount of endocrine pancreas and of B-cells is largely sufficient in these non-pregnant and pregnant youngsters. The present work aims a morphometric evaluation of B-cell activity in adult youngsters from control, mildly and severely diabetic mothers, in basal condition and in their adaptation to pregnancy. B-cells are divided, on basis of the ultrastructural morphology of their organelles, in dark non-activated B-cells and pale activated B-cells. These data are related to the concepts of functional B-cell heterogeneity and dose-dependent recruitment of pancreatic B-cells on stimulation. The recruitment of B-cells in each of the groups is evaluated from the proportion pale/dark B-cells. In control animals this is about 50/50, in both experimental groups there is a marked predominance of pale B-cells. During normal pregnancy, a shift occurs towards a majority of pale B-cells. In the offspring of diabetic mothers, the ratio does not further change during gestation. It can be concluded that the disturbance in B-cell stimulation and the development of gestational diabetes in offspring of diabetic mothers is associated with a maximal recruitment of the B-cells already in basal non-pregnant condition.

A comparative immunohistochemical study of pancreatic islets in laboratory animals (rats, dogs, minipigs, nonhuman primates)

The aim of the present study was to distinguish and describe the patterns of distribution of pancreatic islets within the pancreas of four species of laboratory animals, including rats, dogs, minipigs and monkeys, and furthermore, to identify immunohistochemically various islet cell types and characterize their content. Histopathological examinations were performed on sections stained with hematoxylin and eosin (H&E) and immunostained using rabbit polyclonal antibodies (pAb) against insulin, glucagon, pancreatic polypeptide (PP), somatostatin, chromogranin A, keratin, bombesin and gastrin, or mouse monoclonal antibodies (mAb) against synaptophysin, Leu-7 and proliferating cell nuclear antigen (PCNA) in three-step rabbit immunoperoxidase (PAP) and streptavidin/peroxidase (StreptABC/HRP) reactions. Positive immunohistochemical reactions were observed in the pancreatic islets of all animal species with all antibodies, except with anti-bombesin and anti-gastrin antibodies. Our results revealed that: 1) there is species specific regional arrangement of islets in the pancreas, 2) each species presents a characteristic distribution of cells producing different hormones. 3) immunoreactivity with immunohistochemical markers varies between species and/or age. The present comparative immunohistochemical study could be helpful for answering questions which are important for understanding some of the intricate mechanisms that govern the integrated function of the endocrine pancreas.

Ultrastructural and secretory heterogeneity of fa/fa (Zucker) rat islets

Many previous studies of obese rodents documented biochemical changes in pancreatic islets that contribute to hyperinsulinemia in vivo. Those studies used heterogeneous populations of islets, although the size of islets from obese rats ranges from < 100 to > 500 microm. Here, functional and morphological changes in size-sorted (< 125 and > 250 microm diameter) islets from obese Zucker (fa/fa) rats were correlated. Ultrastructural examination revealed that > 250 microm cultured islets had an increased number of immature secretory granules in the beta cells. The number of degranulated beta cells in > 250 and < 125 microm cultured islets from fa/fa rats was higher than in lean rat islets (33 vs 25%). The glucose EC50 values for cultured islets were 4.64 +/- 0.43, 7.9 +/- 0.70 and 7.29 +/- 1.64 mmol.l(-1) for > 250 microm, < 125 microm, and lean groups, respectively. Inhibition of insulin secretion by 10 mmol.l(-1) mannoheptulose was reduced by 50% in > 250 microm islets compared with small islets. Studies of individual beta cells by reverse hemolytic plaque assay revealed 3-fold more cells from > 250 microm islets were stimulated by 1.4 mmol.l(-1) glucose than cells from < 125 microm islets. We conclude that functional defects in mixed size populations of islets from fa/fa rats are mainly due to alterations in the large islets, whereas smaller islets have relatively normal function. Exposure to high glucose exacerbates morphological and functional differences of large islets, which could have important implications in the transition to noninsulin-dependent diabetes when beta cell insulin production is unable to compensate for hyperglycemia.

In vivo synchronous membrane potential oscillations in mouse pancreatic beta-cells: lack of co-ordination between islets

1. The properties of the oscillations in electrical activity of different beta-cells within the same islet of Langerhans, and of different islets within the same pancreas, recorded in vivo, are described. 2. Simultaneous recordings of two cells within the same islet showed that the oscillations were synchronous. A rapid increase in blood glucose led to the simultaneous appearance of a transitory phase of continuous electrical activity in both cells. These results indicate that under physiological conditions, the islets operate as a functional syncytium. 3. Simultaneous recordings of cells from two different islets within the same pancreas showed that the oscillations in the electrical activity were not synchronous, which suggests that each islet is a functionally independent unit. Rapid changes in blood glucose led to the appearance of a transitory phase of increased electrical activity in both islets, although of different duration. These results suggest that the endocrine pancreas lacks a pacemaker driving the electrical activity of all the islets. 4. The comparison of the degree of activation of different islets, simultaneously recorded at different glucose concentrations, indicated that all the islets had a similar sensitivity to glucose. Furthermore, when the glucose concentration was increased, the electrical activity in both islets increased in parallel, suggesting that the amount of insulin released due to the increase in glycaemia was produced by the simultaneous response of all the islets and not by the recruitment of islets with different sensitivities to glucose. 5. Our results predict that the synchronous electrical activity of all the cells within an islet will result in widespread intracellular calcium oscillations and pulsatile insulin secretion. The periodicity of the pulses of insulin secretion in different islets is suggested to be of slightly different length and asynchronous.