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Insulin pulsatility is important to hepatic response in regulating blood glucose. Growing evidence suggests that insulin-secreting pancreatic β-cells can adapt to chronic disruptions of pulsatility to rescue this physiologically important behavior. We determined the time scale for adaptation and examined potential ion channels underlying it. We induced the adaptation both by chronic application of the ATPsensitive K+ [K(ATP)] channel blocker tolbutamide and by application of the depolarizing agent potassium chloride (KCl). Acute application of tolbutamide without pretreatment results in elevated Ca2+ as measured by fura-2AM and the loss of endogenous pulsatility. We show that after chronic exposure to tolbutamide (12-24 h), Ca2+ oscillations occur with subsequent acute tolbutamide application. The same experiment was conducted with potassium chloride (KCl) to directly depolarize the β-cells. Once again, following chronic exposure to the cell stimulator, the islets produced Ca2+ oscillations when subsequently exposed to tolbutamide. These experiments suggest that it is the chronic stimulation, and not tolbutamide desensitization, that is responsible for the adaptation that rescues oscillatory β-cell activity. This compensatory response also causes islet glucose sensitivity to shift rightward following chronic tolbutamide treatment. Mathematical modeling shows that a small increase in the number of K(ATP) channels in the membrane is one adaptation mechanism that is compatible with the data. To examine other compensatory mechanisms, pharmacological studies provide support that Kir2.1 and TEAsensitive channels play some role. Overall, this investigation demonstrates β-cell adaptability to overstimulation, which is likely an important mechanism for maintaining glucose homeostasis in the face of chronic stimulation. [ABSTRACT FROM AUTHOR]

Pulsatile insulin secretion into the portal vein from the many pancreatic islets of Langerhans is critical for efficient glucose homeostasis. The islets are themselves endogenous oscillators, but since they are not physically coupled it is not obvious how their oscillations are synchronized across the pancreas. It has been proposed that synchronization of islets is achieved through periodic activity of intrapancreatic ganglia, and indeed there are data supporting this proposal. Postganglionic nerves are cholinergic, and their product, acetylcholine, can influence islet β-cells through actions on M3 muscarinic receptors which are coupled to Gq type G-proteins. In addition, the neurons secrete several peptide hormones that act on β-cell receptors. The data supporting synchronization via intrapancreatic ganglia are, however, limited. In particular, it has not been shown that trains of muscarinic pulses are effective at synchronizing islets in vitro. Also, if as has been suggested, there is a ganglionic pacemaker driving islets to a preferred frequency, no neural circuitry for this pacemaker has been identified. In this study, both points are addressed using a microfluidic system that allows for the pulsed application of the muscarinic agonist carbachol. We find that murine islets are entrained and synchronized over a wide range of frequencies when the carbachol pulsing is periodic, adding support to the hypothesis that ganglia can synchronize islets in vivo. We also find that islet synchronization is very effective even if the carbachol pulses are applied at random times. This suggests that a neural pacemaker is not needed; all that is required is that islets receive occasional coordinated input from postganglionic neurons. The endogenous rhythmic activity of the islets then sets the frequency of the islet population rhythm, while the input from ganglia acts only to keep the islet oscillators in phase. [ABSTRACT FROM AUTHOR]

Insulin secretion from pancreatic islet β-cells occurs in a pulsatile fashion, with a typical period of ∼5 min. The basis of this pulsatility in mouse islets has been investigated for more than four decades, and the various theories have been described as either qualitative or mathematical models. In many cases the models differ in their mechanisms for rhythmogenesis, as well as other less important details. In this Perspective, we describe two main classes of models: those in which oscillations in the intracellular Ca2+ concentration drive oscillations in metabolism, and those in which intrinsic metabolic oscillations drive oscillations in Ca2+ concentration and electrical activity. We then discuss nine canonical experimental findings that provide key insights into the mechanism of islet oscillations and list the models that can account for each finding. Finally, we describe a new model that integrates features from multiple earlier models and is thus called the Integrated Oscillator Model. In this model, intracellular Ca2+ acts on the glycolytic pathway in the generation of oscillations, and it is thus a hybrid of the two main classes of models. It alone among models proposed to date can explain all nine key experimental findings, and it serves as a good starting point for future studies of pulsatile insulin secretion from human islets. [ABSTRACT FROM AUTHOR]

Plasma insulin oscillations are known to have physiological importance in the regulation of blood glucose. In insulin-secreting β-cells of pancreatic islets, K(ATP) channels play a key role in regulating glucose-dependent insulin secretion. In addition, they convey oscillations in cellular metabolism to the membrane by sensing adenine nucleotides, and are thus instrumental in mediating pulsatile insulin secretion. Blocking K(ATP) channels pharmacologically depolarizes the β-cell plasma membrane and terminates islet oscillations. Surprisingly, when K(ATP) channels are genetically knocked out, oscillations in islet activity persist, and relatively normal blood glucose levels are maintained. Compensation must therefore occur to overcome the loss of K(ATP) channels in K(ATP) knockout mice. In a companion study, we demonstrated a substantial increase in Kir2.1 protein occurs in β-cells lacking K(ATP) because of SUR1 deletion. In this report, we demonstrate that β-cells of SUR1 null islets have an upregulated inward rectifying K+ current that helps to compensate for the loss of K(ATP) channels. This current is likely due to the increased expression of Kir2.1 channels. We used mathematical modeling to determine whether an ionic current having the biophysical characteristics of Kir2.1 is capable of rescuing oscillations that are similar in period to those of wild-type islets. By experimentally testing a key model prediction we suggest that Kir2.1 current upregulation is a likely mechanism for rescuing the oscillations seen in islets from mice deficient in K(ATP) channels. [ABSTRACT FROM AUTHOR]

Pancreatic islets manage elevations in blood glucose level by secreting insulin into the bloodstream in a pulsatile manner. Pulsatile insulin secretion is governed by islet oscillations such as bursting electrical activity and periodic Ca2+ entry in β-cells. In this report, we demonstrate that although islet oscillations are lost by fixing a glucose stimulus at a high concentration, they may be recovered by subsequently converting the glucose stimulus to a sinusoidal wave. We predict with mathematical modeling that the sinusoidal glucose signal’s ability to recover islet oscillations depends on its amplitude and period, and we confirm our predictions by conducting experiments with islets using a microfluidics platform. Our results suggest a mechanism whereby oscillatory blood glucose levels recruit non-oscillating islets to enhance pulsatile insulin output from the pancreas. Our results also provide support for the main hypothesis of the Dual Oscillator Model, that a glycolytic oscillator endogenous to islet β-cells drives pulsatile insulin secretion. [ABSTRACT FROM AUTHOR]

Pancreatic islets exhibit bursting oscillations in response to elevated blood glucose. These oscillations are accompanied by oscillations in the free cytosolic Ca2+ concentration (Cac), which drives pulses of insulin secretion. Both islet Ca2+ and metabolism oscillate, but there is some debate about their interrelationship. Recent experimental data show that metabolic oscillations in some cases persist after the addition of diazoxide (Dz), which opens K(ATP) channels, hyperpolarizing β- cells and preventing Ca2+ entry and Ca2+ oscillations. Further, in some islets in which metabolic oscillations were eliminated with Dz, increasing the cytosolic Ca2+ concentration by the addition of KCl could restart the metabolic oscillations. Here we address why metabolic oscillations persist in some islets but not others, and why raising Cac restarts oscillations in some islets but not others. We answer these questions using the dual oscillator model (DOM) for pancreatic islets. The DOM can reproduce the experimental data and shows that the model supports two different mechanisms for slow metabolic oscillations, one that requires calcium oscillations and one that does not. [ABSTRACT FROM AUTHOR]

We used the patch clamp technique in situ to test the hypothesis that slow oscillations in metabolism mediate slow electrical oscillations in mouse pancreatic islets by causing oscillations in KATP channel activity. Total conductance was measured over the course of slow bursting oscillations in surface β-cells of islets exposed to 11.1 mM glucose by either switching from current clamp to voltage clamp at different phases of the bursting cycle or by clamping the cells to -60 mV and running two-second voltage ramps from -120 to -50 mV every 20 s. The membrane conductance, calculated from the slopes of the ramp current-voltage curves, oscillated and was larger during the silent phase than during the active phase of the burst. The ramp conductance was sensitive to diazoxide, and the oscillatory component was reduced by sulfonylureas or by lowering extracellular glucose to 2.8 mM, suggesting that the oscillatory total conductance is due to oscillatory KATP channel conductance. We demonstrate that these results are consistent with the Dual Oscillator model, in which glycolytic oscillations drive slow electrical bursting, but not with other models in which metabolic oscillations are secondary to calcium oscillations. The simulations also confirm that oscillations in membrane conductance can be well estimated from measurements of slope conductance and distinguished from gap junction conductance. Furthermore, the oscillatory conductance was blocked by tolbutamide in isolated β-cells. The data, combined with insights from mathematical models, support a mechanism of slow (~5 min) bursting driven by oscillations in metabolism, rather than by oscillations in the intracellular free calcium concentration. [ABSTRACT FROM AUTHOR]

Pulses of insulin from pancreatic beta-cells help maintain blood glucose in a narrow range, although the source of these pulses is unclear. It has been proposed that a positive feedback circuit exists within the glycolytic pathway, the autocatalytic activation of phosphofructokinase-1 (PFK1), which endows pancreatic beta-cells with the ability to generate oscillations in metabolism. Flux through PFK1 is controlled by the bifunctional enzyme PFK2/FBPase2 (6-phosphofructo-2-kinase/fructose- 2,6-bisphosphatase) in two ways: via (1) production/degradation of fructose-2,6-bisphosphate (Fru2,6-BP), a potent allosteric activator of PFK1, as well as (2) direct activation of glucokinase due to a protein-protein interaction. In this study, we used a combination of live-cell imaging and mathematical modeling to examine the effects of inducibly-expressed PFK2/ FBPase2 mutants on glucose-induced Ca2+ pulsatility in mouse islets. Irrespective of the ability to bind glucokinase, mutants of PFK2/FBPase2 that increased the kinase:phosphatase ratio reduced the period and amplitude of Ca2+ oscillations. Mutants which reduced the kinase:phosphatase ratio had the opposite effect. These results indicate that the main effect of the bifunctional enzyme on islet pulsatility is due to Fru2,6-BP alteration of the threshold for autocatalytic activation of PFK1 by Fru1,6-BP. Using computational models based on PFK1-generated islet oscillations, we then illustrated how moderate elevation of Fru-2,6-BP can increase the frequency of glycolytic oscillations while reducing their amplitude, with sufficiently high activation resulting in termination of slow oscillations. The concordance we observed between PFK2/FBPase2-induced modulation of islet oscillations and the models of PFK1-driven oscillations furthermore suggests that metabolic oscillations, like those found in yeast and skeletal muscle, are shaped early in glycolysis. [ABSTRACT FROM AUTHOR]

We describe a novel dynamic mechanism for episodic or compound bursting oscillations, in which bursts of electrical impulses are clustered together into episodes, separated by long silent phases. We demonstrate the mechanism for episodic bursting using a minimal mathematical model for "phantom bursting." Depending on the location in parameter space, this model can produce fast, medium, or slow bursting, or in the present case, fast, slow, and episodic bursting. The episodic bursting is modestly robust to noise and to parameter variation, and the effect that noise has on the episodic bursting pattern is quite different from that of an alternate episodic burst mechanism in which the slow envelope is produced by metabolic oscillations. This mechanism could account for episodic bursting produced in endocrine cells or neurons, such as pancreatic islets or gonadotropin releasing neurons of the hypothalamus. [ABSTRACT FROM AUTHOR]

Cytosolic Ca2+ dynamics are important in the regulation of insulin secretion from the pancreatic β-cells within islets of Langerhans. These dynamics are sculpted by the endoplasmic reticulum (ER), which takes up Ca2+ when cytosolic levels are high and releases it when cytosolic levels are low. Calcium uptake into the ER is through sarcoendoplasmic reticulum Ca2+-ATPases, or SERCA pumps. Two SERCA isoforms are expressed in the β-cell: the high Ca2+ affinity SERCA2b pump and the low affinity SERCA3 pump. Recent experiments with islets from SERCA3 knockout mice have shown that the cytosolic Ca2+ oscillations from the knockout islets are characteristically different from those of wild type islets.While the wild type islets often exhibit compound Ca2+ oscillations, composed of fast oscillations superimposed on much slower oscillations, the knockout islets rarely exhibit compound oscillations, but produce slow (single component) oscillations instead. Using mathematical modeling, we provide an explanation for this difference. We also investigate the effect that SERCA2b inhibition has on the model β-cell. Unlike SERCA3 inhibition, we demonstrate that SERCA2b inhibition has no long-term effect on cytosolic Ca2+ oscillations unless a store-operated current is activated. [ABSTRACT FROM AUTHOR]

Impairment of insulin secretion from the β-cells of the pancreatic islets of Langerhans is central to the development of type 2 diabetes mellitus and has therefore been the subject of much investigation. Great advances have been made in this area, but the mechanisms underlying the pulsatility of insulin secretion remain controversial. The period of these pulses is 4–6 min and reflects oscillations in islet membrane potential and intracellular free Ca2+ Pulsatile blood insulin levels appear to play an important physiological role in insulin action and are lost in patients with type 2 diabetes and their near relatives. We present evidence for a recently developed β-cell model, the ‘dual oscillator model,’ in which oscillations in activity are due to both electrical and metabolic mechanisms. This model is capable of explaining much of the available data on islet activity and offers possible resolutions of a number of longstanding issues. The model, however, still lacks direct confirmation and raises new issues. In this article, we highlight both the successes of the model and the challenges that it poses for the field. [ABSTRACT FROM AUTHOR]

Pulsatile insulin secretion in vivo is believed to be derived, in part, from the intrinsic glucose-dependent intracellular calcium concentration ([Ca2+]i) pulsatility of individual islets. In isolation, islets display fast, slow, or mixtures of fast and slow [Ca2+]i oscillations. We show that the period of islet [Ca2+]i oscillations is unique to each mouse, with the islets from an individual mouse demonstrating similar rhythms to one another. Based on their rhythmic period, mice were broadly classified as being either fast (0.65 +/- 0.1 min; n = 6 mice) or slow (4.7 +/- 0.2 min; n = 15 mice). To ensure this phenomenon was not an artifact of islet-to-islet communication, we confirmed that islets cultured in isolation (period: 2.9 +/- 0.1 min) were not statistically different from islets cultured together from the same mouse (3.1 +/- 0.1 min, P > 0.52, n = 5 mice). We also compared pulsatile insulin patterns measured in vivo with islet [Ca2+]i patterns measured in vitro from six mice. Mice with faster insulin pulse periods corresponded to faster islet [Ca2+]i patterns, whereas slower insulin patterns corresponded to slower [Ca2+]i patterns, suggesting that the insulin rhythm of each mouse is preserved to some degree by its islets in vitro. We propose that individual mice have characteristic oscillatory [Ca2+]i patterns, which are imprinted in vivo through an unknown mechanism. [ABSTRACT FROM AUTHOR]

Insulin-secreting β-cells, located within the pancreatic islets of Langerhans, are excitable cells that produce regular bursts of action potentials when stimulated by glucose. This system has been the focus of mathematical investigation for two decades, spawning an array of mathematical models. Recently, a new class of models has been introduced called ‘phantom bursters’ [Bertram et al. (2000) Biophys. J. 79, 2880–2892], which accounts for the wide range of burst frequencies exhibited by islets via the interaction of more than one slow process. Here, we describe one implementation of the phantom bursting mechanism in which intracellular Ca2+ controls the oscillations through both direct and indirect negative feedback pathways. We show how the model dynamics can be understood through an extension of the fast/slow analysis that is typically employed for bursting oscillations. From this perspective, the model makes use of multiple degrees of freedom to generate the full range of bursting oscillations exhibited by β-cells. The model also accounts for a wide range of experimental phenomena, including the ubiquitous triphasic response to the step elevation of glucose and responses to perturbations of internal Ca2+ stores. Although it is not presently a complete model of all β-cell properties, it demonstrates the design principles that we anticipate will underlie future progress in β-cell modeling. [Copyright &y& Elsevier]

The electrical activity of insulin-secreting pancreatic islets of Langerhans is characterized by bursts of action potentials. Most often this bursting is periodic, but in some cases it is modulated by an underlying slower rhythm. We suggest that the modulatory rhythm for this complex bursting pattern is due to oscillations in glycolysis, while the bursting itself is generated by some other slow process. To demonstrate this hypothesis, we couple a minimal model of glycolytic oscillations to a minimal model for activity-dependent bursting in islets. We show that the combined model can reproduce several complex bursting patterns from mouse islets published in the literature, and we illustrate how these complex oscillations are produced through the use of a fast/slow analysis. [Copyright &y& Elsevier]

While individual pancreatic islets exhibit oscillations in free calcium and insulin secretion in response to glucose in vitro, how these oscillations are coordinated between islets in vivo is poorly understood. This is a significant gap in our knowledge as islet-islet oscillations must be synchronized for the pancreas to produce pulses of insulin. To ascertain how synchronization might be accomplished, we simultaneously monitored free Ca levels in 4-6 islets using the Ca sensing dye fura-2. Mouse islets were isolated using collagenase digestion and maintained in culture overnight. When placed in a chamber held at 37° C and perifused with saline containing 11.1 mM glucose, islets exhibited regular Ca oscillations with a period of 3-6 minutes. Under these conditions, the Ca oscillations of neighboring islets were asynchronous even though the periods of the oscillations were similar. However, a 15 see application of the cholinergic agonist carbachol (25/µM) caused profound islet to islet synchronization in >50 experiments. In contrast, application of the adrenergic agonists clonidine or norepinephrine or the depolarizing agents KCI or tolbutamide failed to synchronize the islets. The action of carbachol was glucose-dependent, as carbachol applied in saline containing 5.5 or 7.5 mM glucose was much less effective in synchronizing neighboring islets. Cholinergic agonists increase both Ca influx and ER Ca release in islet beta cells. Synchronization persisted in islets treated with 1 µM thapsigargin to deplete their ER Ca stores suggesting that Ca influx is sufficient for islet to islet synchronization. Parallel computer simulations of model islets suggest a dynamic mechanism for the synchronization that we observe. These results suggest that acetylcholine release from intrapancreatic neurons may help mediate islet to islet synchronization within the pancreas and the coordination of islet secretory oscillations. Supported by NIH DK RO146409 and NSF DMS 0613179. [ABSTRACT FROM AUTHOR]

A microfluidic system was developed to produce sinusoidal waveforms of glucose to entrain oscillations of intracellular [Ca2+] in islets of Langerhans. The work described is an improvement to a previously reported device where two pneumatic pumps delivered pulses of glucose and buffer to a mixing channel. The mixing channel acted as a low pass filter to attenuate these pulses to produce the desired final concentration. Improvements to the current device included increasing the average pumping frequency from 0.83 to 3.33 Hz by modifying the on-chip valves to minimize adhesion between the PDMS and glass within the valve. The cutoff frequency of the device was increased from 0.026 to 0.061 Hz for sinusoidal fluorescein waves by shortening the length of the mixing channel to 3.3 cm. The value of the cutoff frequency was chosen between the average pumping frequency and the low frequency (∼0.0056 Hz) glucose waves that were needed to entrain the islets of Langerhans. In this way, the pulses from the pumps were attenuated greatly but the low-frequency glucose waves were not. With the use of this microfluidic system, a total flow rate of 1.5 ± 0.1 μL min-1 was generated and used to deliver sinusoidal waves of glucose concentration with a median value of 11 mM and amplitude of 1 mM to a chamber that contained an islet of Langerhans loaded with the Ca2+-sensitive fluorophore, indo-1. Entrainment of the islets was demonstrated by pacing the rhythm of intracellular [Ca2+] oscillations to oscillatory glucose levels produced by the device. The system should be applicable to a wide range of cell types to aid understanding cellular responses to dynamically changing stimuli. [ABSTRACT FROM AUTHOR]

• Slow electrical bursting in single beta-cells could be due to either phantom bursting or intrinsic glycolytic oscillations. • Sensitivity to noise can be understood using a fast-slow decomposition of the multi-timescale system. • These single-cell results suggest that bursting in intact islets could be due to either a phantom bursting mechanism or intrinsic glycolytic oscillations. Insulin is secreted by pancreatic β -cells that are electrically coupled into micro-organs called islets of Langerhans. The secretion is due to the influx of Ca2+ ions that accompany electrical impulses, which are clustered into bursts. So-called "medium bursting" occurs in many β -cells in intact islets, while in other islets the β -cells exhibit "slow bursting", with a much longer period. Each burst brings in Ca2+ that, through exocytosis, results in insulin secretion. When isolated from an islet, β -cells behave very differently. The electrical activity is much noisier, and consists primarily of trains of irregularly-timed spikes, or fast or slow bursting. Medium bursting, so often seen in intact islets, is rarely if ever observed. In this study, we examine what the isolated cell behavior can tell us about the mechanism for bursting in intact islets. A previous mathematical study concluded that the slow bursting observed in isolated β -cells, and therefore most likely in islets, must be due to intrinsic glycolytic oscillations, since this mechanism for bursting is robust to noise. It was demonstrated that an alternate mechanism, phantom bursting, was very sensitive to noise, and therefore could not account for the slow bursting in single cells. We re-examine these conclusions, motivated by recent experimental and mathematical modeling evidence that slow bursting in intact islets is, at least in many cases, driven by the phantom bursting mechanism and not endogenous glycolytic oscillations. We employ two phantom bursting models, one minimal and the other more biophysical, to determine the sensitivity of medium and slow bursting to electrical current noise. In the minimal model, both forms of bursting are highly sensitive to noise. In the biophysical model, while medium bursting is sensitive to noise, slow bursting is much less sensitive. This suggests that the slow bursting seen in isolated β -cells may be due to a phantom bursting mechanism, and by extension, slow bursting in intact islets may also be driven by this mechanism. [ABSTRACT FROM AUTHOR]

Insulin-secreting β -cells of pancreatic islets of Langerhans produce bursts of electrical impulses, resulting in intracellular Ca 2 + oscillations and pulsatile insulin secretion. The mechanism for this bursting activity has been the focus of mathematical modeling for more than three decades, and as new data are acquired old models are modified and new models are developed. Comprehensive models must now account for the various modes of bursting observed in islet β -cells, which include fast bursting, slow bursting, and compound bursting. One such model is the Integrated Oscillator Model (IOM), in which β -cell electrical activity, intracellular Ca 2 + , and glucose metabolism interact via numerous feedforward and feedback pathways. These interactions can produce metabolic oscillations with a sawtooth time course or a pulsatile time course, reflecting very different oscillation mechanisms. In this report, we determine conditions favorable to one form of oscillations or the other, and examine the transitions between modes of bursting and the relationship of the transitions to the patterns of metabolic oscillations. Importantly, this work clarifies what can be expected in experimental measurements of β -cell oscillatory activity, and suggests pathways through which oscillations of one type can be converted to oscillations of another type. [ABSTRACT FROM AUTHOR]

Abstract: Bursting oscillations are common in neurons and endocrine cells. One type of bursting model with two slow variables has been called ‘phantom bursting’ since the burst period is a blend of the time constants of the slow variables. A phantom bursting model can produce bursting with a wide range of periods: fast (short period), medium, and slow (long period). We describe a measure, which we call the ‘dominance factor’, of the relative contributions of the two slow variables to the bursting produced by a simple phantom bursting model. Using this tool, we demonstrate how the control of different phases of the burst can be shifted from one slow variable to another by changing a model parameter. We then show that the dominance curves obtained as a parameter is varied can be useful in making predictions about the resetting properties of the model cells. Finally, we demonstrate two mechanisms by which phase-independent resetting of a burst can be achieved, as has been shown to occur in the electrical activity of pancreatic islets. [Copyright &y& Elsevier]