Closing in on the Mechanisms of Pulsatile Insulin Secretion

Network representation of multicellular activity in pancreatic islets: Technical considerations for functional connectivity analysis

Within the islets of Langerhans, beta cells orchestrate synchronized insulin secretion, a pivotal aspect of metabolic homeostasis. Despite the inherent heterogeneity and multimodal activity of individual cells, intercellular coupling acts as a homogenizing force, enabling coordinated responses through the propagation of intercellular waves. Disruptions in this coordination are implicated in irregular insulin secretion, a hallmark of diabetes. Recently, innovative approaches, such as integrating multicellular calcium imaging with network analysis, have emerged for a quantitative assessment of the cellular activity in islets. However, different groups use distinct experimental preparations, microscopic techniques, apply different methods to process the measured signals and use various methods to derive functional connectivity patterns. This makes comparisons between findings and their integration into a bigger picture difficult and has led to disputes in functional connectivity interpretations. To address these issues, we present here a systematic analysis of how different approaches influence the network representation of islet activity. Our findings show that the choice of methods used to construct networks is not crucial, although care is needed when combining data from different islets. Conversely, the conclusions drawn from network analysis can be heavily affected by the pre-processing of the time series, the type of the oscillatory component in the signals, and by the experimental preparation. Our tutorial-like investigation aims to resolve interpretational issues, reconcile conflicting views, advance functional implications, and encourage researchers to adopt connectivity analysis. As we conclude, we outline challenges for future research, emphasizing the broader applicability of our conclusions to other tissues exhibiting complex multicellular dynamics.

STIM1 regulates pancreatic β-cell behaviour: A modelling study

Pancreatic β-cells are equipped with the molecular machinery allowing them to respond to high glucose levels in the form of electrical activity and Ca2+ oscillations. These oscillations drive insulin secretion. Two key ionic mechanisms involved in this response are the Store-Operated Current and the current through ATP-dependent K+ channels. Both currents have been shown to be regulated by the protein STIM1, but this dual regulation by STIM1 has not been studied before. In this paper, we use mathematical modelling to gain insight into the role of STIM1 in the β-cell response. We extended a previous β-cell model to include the dynamics of STIM1 and described the dependence of the ATP-dependent K+ current on STIM1. Our simulations suggest that the total concentration of STIM1 modifies the bursting frequency, the burst duration and the intracellular Ca2+ levels. These results are in good agreement with experimental reports, and the contribution of the studied currents to electrical activity and Ca2+ dynamics is discussed. The model predicts that in the absence of STIM1 the excitability of the plasma membrane increases and that the glucose threshold for electrical activity is shifted to lower concentrations. These computational predictions may be related to impaired insulin secretion under conditions of reduced STIM1 in the diabetic state.

Periodic insulin stimulation of Akt: Dynamic steady states and robustness

The periodic secretion of insulin is a salient feature of the blood glucose control system in vivo. Insulin levels in the blood exhibit oscillations on multiple time scales - rapid, ultradian, and circadian - and the improved metabolic regulation resulting from pulsatile insulin release has been well established. Although numerous mathematical models investigating the causal mechanisms of insulin oscillations have appeared in the literature, to date there has been comparatively little attention given to the influence of periodic insulin stimulation on downstream components of the insulin signalling pathway. In this paper, we explore the effect of high frequency periodic insulin stimulation on Akt (also known as PKB), a crucial crosstalk node in the insulin signalling pathway that coordinates metabolic and mitogenic processes in the cell. We analyse a mathematical model of Akt translocation to the plasma membrane under both single step insulin perturbations and periodic insulin stimulation with an emphasis on - but not limited to - the physiological range of parameter values. It was shown that the system rapidly attains a robust dynamic steady state entrained to the periodic insulin stimulation. Moreover, the translocation of Akt to the plasma membrane in the model permits a sufficient level of phosphorylation to trigger downstream metabolic regulators. However, the modelling also indicated that further investigation of this activation process is required to determine whether the response of Akt is a key determinant of the enhanced metabolic control observed under periodic insulin stimulation.

Relations between Glucose and d-Amino Acids in the Modulation of Biochemical and Functional Properties of Rodent Islets of Langerhans

The cell-to-cell signaling role of d-amino acids (d-AAs) in the mammalian endocrine system, particularly in the islets of Langerhans, has drawn growing interest for their potential involvement in modulating glucose metabolism. Previous studies found colocalization of serine racemase [produces d-serine (d-Ser)] and d-alanine (d-Ala) within insulin-secreting beta cells and d-aspartate (d-Asp) within glucagon-secreting alpha cells. Expressed in the islets, functional N-methyl-d-aspartate receptors are involved in the modulation of glucose-stimulated insulin secretion and have binding sites for several d-AAs. However, knowledge of the regulation of d-AA levels in the islets during glucose stimulation as well as the response of islets to different levels of extracellular d-AAs is limited. In this study, we determined the intracellular and extracellular levels of d-Ser, d-Ala, and d-Asp in cultures of isolated rodent islets exposed to different levels of extracellular glucose. We found that the intracellular levels of the enantiomers demonstrated large variability and, in general, were not affected by extracellular glucose levels. However, significantly lower levels of extracellular d-Ser and d-Ala were observed in the islet media supplemented with 20 mM concentration of glucose compared to the control condition utilizing 3 mM glucose. Glucose-induced oscillations of intracellular free calcium concentration ([Ca2+]i), a proxy for insulin secretion, were modulated by the exogenous application of d-Ser and d-Ala but not by their l-stereoisomers. Our results provide new insights into the roles of d-AAs in the biochemistry and function of pancreatic islets.

KATP channel activity and slow oscillations in pancreatic beta cells are regulated by mitochondrial ATP production

Pancreatic beta cells secrete insulin in response to plasma glucose. The ATP-sensitive potassium channel (KATP ) links glucose metabolism to islet electrical activity in these cells by responding to increased cytosolic [ATP]/[ADP]. It was recently proposed that pyruvate kinase (PK) in close proximity to beta cell KATP locally produces the ATP that inhibits KATP activity. This proposal was largely based on the observation that applying phosphoenolpyruvate (PEP) and ADP to the cytoplasmic side of excised inside-out patches inhibited KATP . To test the relative contributions of local vs. mitochondrial ATP production, we recorded KATP activity using mouse beta cells and INS-1 832/13 cells. In contrast to prior reports, we could not replicate inhibition of KATP activity by PEP + ADP. However, when the pH of the PEP solutions was not corrected for the addition of PEP, strong channel inhibition was observed as a result of the well-known action of protons to inhibit KATP . In cell-attached recordings, perifusing either a PK activator or an inhibitor had little or no effect on KATP channel closure by glucose, further suggesting that PK is not an important regulator of KATP . In contrast, addition of mitochondrial inhibitors robustly increased KATP activity. Finally, by measuring the [ATP]/[ADP] responses to imposed calcium oscillations in mouse beta cells, we found that oxidative phosphorylation could raise [ATP]/[ADP] even when ADP was at its nadir during the burst silent phase, in agreement with our mathematical model. These results indicate that ATP produced by mitochondrial oxidative phosphorylation is the primary controller of KATP in pancreatic beta cells. KEY POINTS: Phosphoenolpyruvate (PEP) plus adenosine diphosphate does not inhibit KATP activity in excised patches. PEP solutions only inhibit KATP activity if the pH is unbalanced. Modulating pyruvate kinase has minimal effects on KATP activity. Mitochondrial inhibition, in contrast, robustly potentiates KATP activity in cell-attached patches. Although the ADP level falls during the silent phase of calcium oscillations, mitochondria can still produce enough ATP via oxidative phosphorylation to close KATP . Mitochondrial oxidative phosphorylation is therefore the main source of the ATP that inhibits the KATP activity of pancreatic beta cells.

β-cell intrinsic dynamics rather than gap junction structure dictates subpopulations in the islet functional network

Diabetes is caused by the inability of electrically coupled, functionally heterogeneous β-cells within the pancreatic islet to provide adequate insulin secretion. Functional networks have been used to represent synchronized oscillatory [Ca2+] dynamics and to study β-cell subpopulations, which play an important role in driving islet function. The mechanism by which highly synchronized β-cell subpopulations drive islet function is unclear. We used experimental and computational techniques to investigate the relationship between functional networks, structural (gap junction) networks, and intrinsic β-cell dynamics in slow and fast oscillating islets. Highly synchronized subpopulations in the functional network were differentiated by intrinsic dynamics, including metabolic activity and KATP channel conductance, more than structural coupling. Consistent with this, intrinsic dynamics were more predictive of high synchronization in the islet functional network as compared to high levels of structural coupling. Finally, dysfunction of gap junctions, which can occur in diabetes, caused decreases in the efficiency and clustering of the functional network. These results indicate that intrinsic dynamics rather than structure drive connections in the functional network and highly synchronized subpopulations, but gap junctions are still essential for overall network efficiency. These findings deepen our interpretation of functional networks and the formation of functional subpopulations in dynamic tissues such as the islet.

Deconstructing the integrated oscillator model for pancreatic β-cells

Electrical bursting oscillations in the β-cells of pancreatic islets have been a focus of investigation for more than fifty years. This has been aided by mathematical models, which are descendants of the pioneering Chay-Keizer model. This article describes the key biophysical and mathematical elements of this model, and then describes the path forward from there to the Integrated Oscillator Model (IOM). It is both a history and a deconstruction of the IOM that describes the various elements that have been added to the model over time, and the motivation for adding them. Finally, the article is a celebration of the 40th anniversary of the publication of the Chay-Keizer model.

Both electrical and metabolic coupling shape the collective multimodal activity and functional connectivity patterns in beta cell collectives: A computational model perspective

Pancreatic beta cells are coupled excitable oscillators that synchronize their activity via different communication pathways. Their oscillatory activity manifests itself on multiple timescales and consists of bursting electrical activity, subsequent oscillations in the intracellular Ca^{2+}, as well as oscillations in metabolism and exocytosis. The coordination of the intricate activity on the multicellular level plays a key role in the regulation of physiological pulsatile insulin secretion and is incompletely understood. In this paper, we investigate theoretically the principles that give rise to the synchronized activity of beta cell populations by building up a phenomenological multicellular model that incorporates the basic features of beta cell dynamics. Specifically, the model is composed of coupled slow and fast oscillatory units that reflect metabolic processes and electrical activity, respectively. Using a realistic description of the intercellular interactions, we study how the combination of electrical and metabolic coupling generates collective rhythmicity and shapes functional beta cell networks. It turns out that while electrical coupling solely can synchronize the responses, the addition of metabolic interactions further enhances coordination, the spatial range of interactions increases the number of connections in the functional beta cell networks, and ensures a better consistency with experimental findings. Moreover, our computational results provide additional insights into the relationship between beta cell heterogeneity, their activity profiles, and functional connectivity, supplementing thereby recent experimental results on endocrine networks.

Insulin C-peptide secretion on-a-chip to measure the dynamics of secretion and metabolism from individual islets

First-phase glucose-stimulated insulin secretion is mechanistically linked to type 2 diabetes, yet the underlying metabolism is difficult to discern due to significant islet-to-islet variability. Here, we miniaturize a fluorescence anisotropy immunoassay onto a microfluidic device to measure C-peptide secretion from individual islets as a surrogate for insulin (InsC-chip). This method measures secretion from up to four islets at a time with ∼7 s resolution while providing an optical window for real-time live-cell imaging. Using the InsC-chip, we reveal two glucose-dependent peaks of insulin secretion (i.e., a double peak) within the classically defined 1st phase (<10 min). By combining real-time secretion and live-cell imaging, we show islets transition from glycolytic to oxidative phosphorylation (OxPhos)-driven metabolism at the nadir of the peaks. Overall, these data validate the InsC-chip to measure glucose-stimulated insulin secretion while revealing new dynamics in secretion defined by a shift in glucose metabolism.

Novel regulators of islet function identified from genetic variation in mouse islet Ca2+ oscillations

Insufficient insulin secretion to meet metabolic demand results in diabetes. The intracellular flux of Ca2+ into β-cells triggers insulin release. Since genetics strongly influences variation in islet secretory responses, we surveyed islet Ca2+ dynamics in eight genetically diverse mouse strains. We found high strain variation in response to four conditions: (1) 8 mM glucose; (2) 8 mM glucose plus amino acids; (3) 8 mM glucose, amino acids, plus 10 nM glucose-dependent insulinotropic polypeptide (GIP); and (4) 2 mM glucose. These stimuli interrogate β-cell function, α- to β-cell signaling, and incretin responses. We then correlated components of the Ca2+ waveforms to islet protein abundances in the same strains used for the Ca2+ measurements. To focus on proteins relevant to human islet function, we identified human orthologues of correlated mouse proteins that are proximal to glycemic-associated single-nucleotide polymorphisms in human genome-wide association studies. Several orthologues have previously been shown to regulate insulin secretion (e.g. ABCC8, PCSK1, and GCK), supporting our mouse-to-human integration as a discovery platform. By integrating these data, we nominate novel regulators of islet Ca2+ oscillations and insulin secretion with potential relevance for human islet function. We also provide a resource for identifying appropriate mouse strains in which to study these regulators.

ER stress increases expression of intracellular calcium channel RyR1 to modify Ca2+ homeostasis in pancreatic beta cells

Pancreatic beta cells maintain glucose homeostasis by secreting pulses of insulin in response to a rise in plasma glucose. Pulsatile insulin secretion occurs as a result of glucose-induced oscillations in beta-cell cytosolic Ca2+. The endoplasmic reticulum (ER) helps regulate beta-cell cytosolic Ca2+, and ER stress can lead to ER Ca2+ reduction, beta-cell dysfunction, and an increased risk of type 2 diabetes. However, the mechanistic effects of ER stress on individual calcium channels are not well understood. To determine the effects of tunicamycin-induced ER stress on ER inositol 1,4,5-triphosphate receptors (IP3Rs) and ryanodine receptors (RyRs) and their involvement in subsequent Ca2+ dysregulation, we treated INS-1 832/13 cells and primary mouse islets with ER stress inducer tunicamycin (TM). We showed TM treatment increased RyR1 mRNA without affecting RyR2 mRNA and decreased both IP3R1 and IP3R3 mRNA. Furthermore, we found stress reduced ER Ca2+ levels, triggered oscillations in cytosolic Ca2+ under subthreshold glucose conditions, and increased apoptosis and that these changes were prevented by cotreatment with the RyR1 inhibitor dantrolene. In addition, we demonstrated silencing RyR1-suppressed TM-induced subthreshold cytosolic Ca2+ oscillations, but silencing RyR2 did not affect these oscillations. In contrast, inhibiting IP3Rs with xestospongin-C failed to suppress the TM-induced cytosolic Ca2+ oscillations and did not protect beta cells from TM-induced apoptosis although xestospongin-C inclusion did prevent ER Ca2+ reduction. Taken together, these results show changes in RyR1 play a critical role in ER stress-induced Ca2+ dysfunction and beta-cell apoptosis.

Ca2+ release or Ca2+ entry, that is the question: what governs Ca2+ oscillations in pancreatic β cells?

The standard model for Ca2+ oscillations in insulin-secreting pancreatic β cells centers on Ca2+ entry through voltage-activated Ca2+ channels. These work in combination with ATP-dependent K+ channels, which are the bridge between the metabolic state of the cells and plasma membrane potential. This partnership underlies the ability of the β cells to secrete insulin appropriately on a minute-to-minute time scale to control whole body plasma glucose. Though this model, developed over more than 40 years through many cycles of experimentation and mathematical modeling, has been very successful, it has been challenged by a hypothesis that calcium-induced calcium release from the endoplasmic reticulum through ryanodine or inositol trisphosphate (IP3) receptors is instead the key driver of islet oscillations. We show here that the alternative model is in fact incompatible with a large body of established experimental data and that the new observations offered in support of it can be better explained by the standard model.

Simultaneous Measurement of Changes in Mitochondrial and Endoplasmic Reticulum Free Calcium in Pancreatic Beta Cells

The free calcium (Ca2+) levels in pancreatic beta cell organelles have been the subject of many recent investigations. Under pathophysiological conditions, disturbances in these pools have been linked to altered intracellular communication and cellular dysfunction. To facilitate studies of subcellular Ca2+ signaling in beta cells and, particularly, signaling between the endoplasmic reticulum (ER) and mitochondria, we designed a novel dual Ca2+ sensor which we termed DS-1. DS-1 encodes two stoichiometrically fluorescent proteins within a single plasmid, G-CEPIA-er, targeted to the ER and R-CEPIA3-mt, targeted to mitochondria. Our goal was to simultaneously measure the ER and mitochondrial Ca2+ in cells in real time. The Kds of G-CEPIA-er and R-CEPIA3-mt for Ca2+ are 672 and 3.7 μM, respectively. Confocal imaging of insulin-secreting INS-1 832/13 expressing DS-1 confirmed that the green and red fluorophores correctly colocalized with organelle-specific fluorescent markers as predicted. Further, we tested whether DS-1 exhibited the functional properties expected by challenging an INS-1 cell to glucose concentrations or drugs having well-documented effects on the ER and mitochondrial Ca2+ handling. The data obtained were consistent with those seen using other single organelle targeted probes. These results taken together suggest that DS-1 is a promising new approach for investigating Ca2+ signaling within multiple organelles of the cell.

High-resolution analysis of the cytosolic Ca2+ events in β cell collectives in situ

The release of peptide hormones is predominantly regulated by a transient increase in cytosolic Ca2+ concentration ([Ca2+]c). To trigger exocytosis, Ca2+ ions enter the cytosol from intracellular Ca2+ stores or from the extracellular space. The molecular events of late stages of exocytosis, and their dependence on [Ca2+]c, were extensively described in isolated single cells from various endocrine glands. Notably, less work has been done on endocrine cells in situ to address the heterogeneity of [Ca2+]c events contributing to a collective functional response of a gland. For this, β cell collectives in a pancreatic islet are particularly well suited as they are the smallest, experimentally manageable functional unit, where [Ca2+]c dynamics can be simultaneously assessed on both cellular and collective level. Here, we measured [Ca2+]c transients across all relevant timescales, from a subsecond to a minute time range, using high-resolution imaging with a low-affinity Ca2+ sensor. We quantified the recordings with a novel computational framework for automatic image segmentation and [Ca2+]c event identification. Our results demonstrate that under physiological conditions the duration of [Ca2+]c events is variable, and segregated into three reproducible modes, subsecond, second, and tens of seconds time range, and are a result of a progressive temporal summation of the shortest events. Using pharmacological tools we show that activation of intracellular Ca2+ receptors is both sufficient and necessary for glucose-dependent [Ca2+]c oscillations in β cell collectives, and that a subset of [Ca2+]c events could be triggered even in the absence of Ca2+ influx across the plasma membrane. In aggregate, our experimental and analytical platform was able to readily address the involvement of intracellular Ca2+ receptors in shaping the heterogeneity of [Ca2+]c responses in collectives of endocrine cells in situ.NEW & NOTEWORTHY Physiological glucose or ryanodine stimulation of β cell collectives generates a large number of [Ca2+]c events, which can be rapidly assessed with our newly developed automatic image segmentation and [Ca2+]c event identification pipeline. The event durations segregate into three reproducible modes produced by a progressive temporal summation. Using pharmacological tools, we show that activation of ryanodine intracellular Ca2+ receptors is both sufficient and necessary for glucose-dependent [Ca2+]c oscillations in β cell collectives.

Coordination of pancreatic islet rhythmic activity by delayed negative feedback

Secretion of insulin from the pancreas is pulsatile, driven by intrinsic oscillations within individual islets of Langerhans. The secretions are coordinated among the many islets distributed throughout the pancreas producing a synchronized rhythm in vivo that is essential for maintaining normal glucose levels. One hypothesized mechanism for the coordination of islet activity is negative feedback, whereby sequestration of glucose in response to elevated insulin leads to a reduction in the blood glucose level that is sensed by the islet population. This global signal of glucose then coordinates the individual islets. In this study, we tested how this coordination mechanism is affected by time delays in the negative feedback, using a microfluidic system to monitor Ca2+ levels in a small population of islets and implementing glucose control through a negative feedback system. We found that islet synchronization occurs even with time delays in the feedback of up to 7 min. We also found that a second, slower closed-loop oscillation period is produced during delayed feedback in which islet oscillations are clustered into episodes. The period of this second oscillatory mode increases with the time delay and appears to be a second stable behavior that coexists with the faster synchronized oscillation. The general conclusion is that islet coordination through negative feedback is a viable means of islet coordination that is robust to delays in the timing of the feedback, and could complement other potential coordination mechanisms such as entrainment by pancreatic ganglia.NEW & NOTEWORTHY Insulin secretion from islets of Langerhans is rhythmic, and these rhythms are coordinated to produce oscillatory plasma insulin levels. Using a combination of microfluidics and computational modeling, we demonstrate that coordination can occur through negative feedback of the type provided by the liver, even if that feedback is delayed by several minutes. We also demonstrate that a second, slower, mode of oscillations can occur when feedback is delayed where faster oscillations are grouped into episodes.

Use of c-peptide as a measure of cephalic phase insulin release in humans

Cephalic phase insulin release (CPIR) is a rapid pulse of insulin secreted within minutes of food-related sensory stimulation. Understanding the mechanisms underlying CPIR in humans has been hindered by its small observed effect size and high variability within and between studies. One contributing factor to these limitations may be the use of peripherally measured insulin as an indicator of secreted insulin, since a substantial portion of insulin is metabolized by the liver before delivery to peripheral circulation. Here, we investigated the use of c-peptide, which is co-secreted in equimolar amounts to insulin from pancreatic beta cells, as a proxy for insulin secretion during the cephalic phase period. Changes in insulin and c-peptide were monitored in 18 adults over two repeated sessions following oral stimulation with a sucrose-containing gelatin stimulus. We found that, on average, insulin and c-peptide release followed a similar time course over the cephalic phase period, but that c-peptide showed a greater effect size. Importantly, when insulin and c-peptide concentrations were compared across sessions, we found that changes in c-peptide were significantly correlated at the 2 min (r = 0.50, p = 0.03) and 4 min (r = 0.65, p = 0.003) time points, as well as when participants' highest c-peptide concentrations were considered (r = 0.64, p = 0.004). In contrast, no significant correlations were observed for changes in insulin measured from the sessions (r = -0.06-0.35, p > 0.05). Herein, we detail the individual variability of insulin and c-peptide concentrations measured during the cephalic phase period, and identify c-peptide as a valuable metric for insulin secretion alongside insulin concentrations when investigating CPIR.

Metabolic cycles and signals for insulin secretion

In this review, we focus on recent developments in our understanding of nutrient-induced insulin secretion that challenge a key aspect of the "canonical" model, in which an oxidative phosphorylation-driven rise in ATP production closes KATP channels. We discuss the importance of intrinsic β cell metabolic oscillations; the phasic alignment of relevant metabolic cycles, shuttles, and shunts; and how their temporal and compartmental relationships align with the triggering phase or the secretory phase of pulsatile insulin secretion. Metabolic signaling components are assigned regulatory, effectory, and/or homeostatic roles vis-à-vis their contribution to glucose sensing, signal transmission, and resetting the system. Taken together, these functions provide a framework for understanding how allostery, anaplerosis, and oxidative metabolism are integrated into the oscillatory behavior of the secretory pathway. By incorporating these temporal as well as newly discovered spatial aspects of β cell metabolism, we propose a much-refined MitoCat-MitoOx model of the signaling process for the field to evaluate.

Pulsatile Basal Insulin Secretion Is Driven by Glycolytic Oscillations

In fasted and fed states, blood insulin levels are oscillatory. While this phenomenon is well studied at high glucose levels, comparatively little is known about its origin under basal conditions. We propose a possible mechanism for basal insulin oscillations based on oscillations in glycolysis, demonstrated using an established mathematical model. At high glucose, this is superseded by a calcium-dependent mechanism.

Pancreatic α and β cells are globally phase-locked

The Ca²⁺ modulated pulsatile glucagon and insulin secretions by pancreatic α and β cells play a crucial role in glucose homeostasis. However, how α and β cells coordinate to produce various Ca²⁺ oscillation patterns is still elusive. Using a microfluidic device and transgenic mice, we recorded Ca²⁺ signals from islet α and β cells, and observed heterogeneous Ca²⁺ oscillation patterns intrinsic to each islet. After a brief period of glucose stimulation, α and β cells’ oscillations were globally phase-locked. 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 period. Moreover, islet α cell number correlated with oscillation frequency. We built a mathematical model of islet Ca²⁺ oscillation incorporating paracrine interactions, which quantitatively agreed with the experimental data. Our study highlights the importance of cell-cell interaction in generating stable but tunable islet oscillation patterns.

The Ca²⁺ modulated pulsatile glucagon and insulin secretions by pancreatic α and β cells are critical in glucose homeostasis. Here the authors show that the Ca²⁺ oscillations of α and β cells are phase-locked, and that the oscillation pattern is tuned by paracrine interactions between α and β cells.

From Isles of Königsberg to Islets of Langerhans: Examining the Function of the Endocrine Pancreas Through Network Science

Islets of Langerhans are multicellular microorgans located in the pancreas that play a central role in whole-body energy homeostasis. Through secretion of insulin and other hormones they regulate postprandial storage and interprandial usage of energy-rich nutrients. In these clusters of hormone-secreting endocrine cells, intricate cell-cell communication is essential for proper function. Electrical coupling between the insulin-secreting beta cells through gap junctions composed of connexin36 is particularly important, as it provides the required, most important, basis for coordinated responses of the beta cell population. The increasing evidence that gap-junctional communication and its modulation are vital to well-regulated secretion of insulin has stimulated immense interest in how subpopulations of heterogeneous beta cells are functionally arranged throughout the islets and how they mediate intercellular signals. In the last decade, several novel techniques have been proposed to assess cooperation between cells in islets, including the prosperous combination of multicellular imaging and network science. In the present contribution, we review recent advances related to the application of complex network approaches to uncover the functional connectivity patterns among cells within the islets. We first provide an accessible introduction to the basic principles of network theory, enumerating the measures characterizing the intercellular interactions and quantifying the functional integration and segregation of a multicellular system. Then we describe methodological approaches to construct functional beta cell networks, point out possible pitfalls, and specify the functional implications of beta cell network examinations. We continue by highlighting the recent findings obtained through advanced multicellular imaging techniques supported by network-based analyses, giving special emphasis to the current developments in both mouse and human islets, as well as outlining challenges offered by the multilayer network formalism in exploring the collective activity of islet cell populations. Finally, we emphasize that the combination of these imaging techniques and network-based analyses does not only represent an innovative concept that can be used to describe and interpret the physiology of islets, but also provides fertile ground for delineating normal from pathological function and for quantifying the changes in islet communication networks associated with the development of diabetes mellitus.

β Cell-specific deletion of Zfp148 improves nutrient-stimulated β cell Ca2+ responses

Insulin secretion from pancreatic β cells is essential for glucose homeostasis. An insufficient response to the demand for insulin results in diabetes. We previously showed that β cell-specific deletion of Zfp148 (β-Zfp148KO) improves glucose tolerance and insulin secretion in mice. Here, we performed Ca2+ imaging of islets from β‑Zfp148KO and control mice fed both a chow and a Western-style diet. β-Zfp148KO islets demonstrated improved sensitivity and sustained Ca2+ oscillations in response to elevated glucose levels. β-Zfp148KO islets also exhibited elevated sensitivity to amino acid-induced Ca2+ influx under low glucose conditions, suggesting enhanced mitochondrial phosphoenolpyruvate-dependent (PEP-dependent), ATP-sensitive K+ channel closure, independent of glycolysis. RNA-Seq and proteomics of β-Zfp148KO islets revealed altered levels of enzymes involved in amino acid metabolism (specifically, SLC3A2, SLC7A8, GLS, GLS2, PSPH, PHGDH, and PSAT1) and intermediary metabolism (namely, GOT1 and PCK2), consistent with altered PEP cycling. In agreement with this, β-Zfp148KO islets displayed enhanced insulin secretion in response to l-glutamine and activation of glutamate dehydrogenase. Understanding pathways controlled by ZFP148 may provide promising strategies for improving β cell function that are robust to the metabolic challenge imposed by a Western diet.

Oscillations in K(ATP) conductance drive slow calcium oscillations in pancreatic β-cells

ATP-sensitive K+ (K(ATP)) channels were first reported in the β-cells of pancreatic islets in 1984, and it was soon established that they are the primary means by which the blood glucose level is transduced to cellular electrical activity and consequently insulin secretion. However, the role that the K(ATP) channels play in driving the bursting electrical activity of islet β-cells, which drives pulsatile insulin secretion, remains unclear. One difficulty is that bursting is abolished when several different ion channel types are blocked pharmacologically or genetically, making it challenging to distinguish causation from correlation. Here, we demonstrate a means for determining whether activity-dependent oscillations in K(ATP) conductance play the primary role in driving electrical bursting in β-cells. We use mathematical models to predict that if K(ATP) is the driver, then contrary to intuition, the mean, peak, and nadir levels of ATP/ADP should be invariant to changes in glucose within the concentration range that supports bursting. We test this in islets using Perceval-HR to image oscillations in ATP/ADP. We find that mean, peak, and nadir levels are indeed approximately invariant, supporting the hypothesis that oscillations in K(ATP) conductance are the main drivers of the slow bursting oscillations typically seen at stimulatory glucose levels in mouse islets. In conclusion, we provide, for the first time to our knowledge, causal evidence for the role of K(ATP) channels not only as the primary target for glucose regulation but also for their role in driving bursting electrical activity and pulsatile insulin secretion.

Slow oscillations persist in pancreatic beta cells lacking phosphofructokinase M

Pulsatile insulin secretion by pancreatic beta cells is necessary for tight glucose control in the body. Glycolytic oscillations have been proposed as the mechanism for generating the electrical oscillations underlying pulsatile insulin secretion. The glycolytic enzyme 6-phosphofructokinase-1 (PFK) synthesizes fructose-1,6-bisphosphate (FBP) from fructose-6-phosphate. It has been proposed that the slow electrical and Ca2+ oscillations (periods of 3-5 min) observed in islets result from allosteric feedback activation of PFKM by FBP. Pancreatic beta cells express three PFK isozymes: PFKL, PFKM, and PFKP. A prior study of mice that were engineered to lack PFKM using a gene-trap strategy to delete Pfkm produced a mosaic reduction in global Pfkm expression, but the islets isolated from the mice still exhibited slow Ca2+ oscillations. However, these islets still expressed residual PFKM protein. Thus, to more fully test the hypothesis that beta cell PFKM is responsible for slow islet oscillations, we made a beta-cell-specific knockout mouse that completely lacked PFKM. While PFKM deletion resulted in subtle metabolic changes in vivo, islets that were isolated from these mice continued to exhibit slow oscillations in electrical activity, beta cell Ca2+ concentrations, and glycolysis, as measured using PKAR, an FBP reporter/biosensor. Furthermore, simulations obtained with a mathematical model of beta cell activity shows that slow oscillations can persist despite PFKM loss provided that one of the other PFK isoforms, such as PFKP, is present, even if its level of expression is unchanged. Thus, while we believe that PFKM may be the main regulator of slow oscillations in wild-type islets, PFKP can provide functional redundancy. Our model also suggests that PFKM likely dominates, in vivo, because it outcompetes PFKP with its higher FBP affinity and lower ATP affinity. We thus propose that isoform redundancy may rescue key physiological processes of the beta cell in the absence of certain critical genes.

Glucose-Stimulated Calcium Dynamics in Beta Cells From Male C57BL/6J, C57BL/6N, and NMRI Mice: A Comparison of Activation, Activity, and Deactivation Properties in Tissue Slices

Although mice are a very instrumental model in islet beta cell research, possible phenotypic differences between strains and substrains are largely neglected in the scientific community. In this study, we show important phenotypic differences in beta cell responses to glucose between C57BL/6J, C57BL/6N, and NMRI mice, i.e., the three most commonly used strains. High-resolution multicellular confocal imaging of beta cells in acute pancreas tissue slices was used to measure and quantitatively compare the calcium dynamics in response to a wide range of glucose concentrations. Strain- and substrain-specific features were found in all three phases of beta cell responses to glucose: a shift in the dose-response curve characterizing the delay to activation and deactivation in response to stimulus onset and termination, respectively, and distinct concentration-encoding principles during the plateau phase in terms of frequency, duration, and active time changes with increasing glucose concentrations. Our results underline the significance of carefully choosing and reporting the strain to enable comparison and increase reproducibility, emphasize the importance of analyzing a number of different beta cell physiological parameters characterizing the response to glucose, and provide a valuable standard for future studies on beta cell calcium dynamics in health and disease in tissue slices.

Basal and Stress-Induced Network Activity in the Adrenal Medulla In Vivo

The adrenal medulla plays a critical role in mammalian homeostasis and the stress response. It is populated by clustered chromaffin cells that secrete epinephrine or norepinephrine along with peptides into the bloodstream affecting distant target organs. Despite been heavily studied, the central control of adrenal medulla and in-situ spatiotemporal responsiveness remains poorly understood. For this work, we continuously monitored the electrical activity of individual adrenomedullary chromaffin cells in the living anesthetized rat using multielectrode arrays. We measured the chromaffin cell activity under basal and physiological stress conditions and characterized the functional micro-architecture of the adrenal medulla. Under basal conditions, chromaffin cells fired action potentials with frequencies between ~0.2 and 4 Hz. Activity was almost completely driven by sympathetic inputs coming through the splanchnic nerve. Chromaffin cells were organized into independent local networks in which cells fired in a specific order, with latencies from hundreds of microseconds to a few milliseconds. Electrical stimulation of the splanchnic nerve evoked almost exactly the same spatiotemporal firing patterns that occurred spontaneously. Hypoglycemic stress, induced by insulin administration resulted in increased activity of a subset of the chromaffin cells. In contrast, respiratory arrest induced by lethal anesthesia resulted in an increase in the activity of virtually all chromaffin cells before cessation of all activity. These results suggest a stressor-specific activation of adrenomedullary chromaffin cell networks and revealed a surprisingly complex electrical organization that likely reflects the dynamic nature of the adrenal medulla's neuroendocrine output during basal conditions and during different types of physiological stress.

Symbiosis of Electrical and Metabolic Oscillations in Pancreatic β-Cells

Insulin is secreted in a pulsatile pattern, with important physiological ramifications. In pancreatic β-cells, which are the cells that synthesize insulin, insulin exocytosis is elicited by pulses of elevated intracellular Ca²⁺ initiated by bursts of electrical activity. In parallel with these electrical and Ca²⁺ oscillations are oscillations in metabolism, and the periods of all of these oscillatory processes are similar. A key question that remains unresolved is whether the electrical oscillations are responsible for the metabolic oscillations via the effects of Ca²⁺, or whether the metabolic oscillations are responsible for the electrical oscillations due to the effects of ATP on ATP-sensitive ion channels? Mathematical modeling is a useful tool for addressing this and related questions as modeling can aid in the design of well-focused experiments that can test the predictions of particular models and subsequently be used to improve the models in an iterative fashion. In this article, we discuss a recent mathematical model, the Integrated Oscillator Model (IOM), that was the product of many years of development. We use the model to demonstrate that the relationship between calcium and metabolism in beta cells is symbiotic: in some contexts, the electrical oscillations drive the metabolic oscillations, while in other contexts it is the opposite. We provide new insights regarding these results and illustrate that what might at first appear to be contradictory data are actually compatible when viewed holistically with the IOM.

The Human Islet: Mini-Organ With Mega-Impact

This review focuses on the human pancreatic islet-including its structure, cell composition, development, function, and dysfunction. After providing a historical timeline of key discoveries about human islets over the past century, we describe new research approaches and technologies that are being used to study human islets and how these are providing insight into human islet physiology and pathophysiology. We also describe changes or adaptations in human islets in response to physiologic challenges such as pregnancy, aging, and insulin resistance and discuss islet changes in human diabetes of many forms. We outline current and future interventions being developed to protect, restore, or replace human islets. The review also highlights unresolved questions about human islets and proposes areas where additional research on human islets is needed.

Bayesian metamodeling of complex biological systems across varying representations

Comprehensive modeling of a whole cell requires an integration of vast amounts of information on various aspects of the cell and its parts. To divide and conquer this task, we introduce Bayesian metamodeling, a general approach to modeling complex systems by integrating a collection of heterogeneous input models. Each input model can in principle be based on any type of data and can describe a different aspect of the modeled system using any mathematical representation, scale, and level of granularity. These input models are 1) converted to a standardized statistical representation relying on probabilistic graphical models, 2) coupled by modeling their mutual relations with the physical world, and 3) finally harmonized with respect to each other. To illustrate Bayesian metamodeling, we provide a proof-of-principle metamodel of glucose-stimulated insulin secretion by human pancreatic β-cells. The input models include a coarse-grained spatiotemporal simulation of insulin vesicle trafficking, docking, and exocytosis; a molecular network model of glucose-stimulated insulin secretion signaling; a network model of insulin metabolism; a structural model of glucagon-like peptide-1 receptor activation; a linear model of a pancreatic cell population; and ordinary differential equations for systemic postprandial insulin response. Metamodeling benefits from decentralized computing, while often producing a more accurate, precise, and complete model that contextualizes input models as well as resolves conflicting information. We anticipate Bayesian metamodeling will facilitate collaborative science by providing a framework for sharing expertise, resources, data, and models, as exemplified by the Pancreatic β-Cell Consortium.

Glucose-dependent activation, activity, and deactivation of beta cell networks in acute mouse pancreas tissue slices

Many details of glucose-stimulated intracellular calcium changes in β cells during activation, activity, and deactivation, as well as their concentration-dependence, remain to be analyzed. Classical physiological experiments indicated that in islets, functional differences between individual cells are largely attenuated, but recent findings suggest considerable intercellular heterogeneity, with some cells possibly coordinating the collective responses. To address the above with an emphasis on heterogeneity and describing the relations between classical physiological and functional network properties, we performed functional multicellular calcium imaging in mouse pancreas tissue slices over a wide range of glucose concentrations. During activation, delays to activation of cells and any-cell-to-first-responder delays are shortened, and the sizes of simultaneously responding clusters increased with increasing glucose concentrations. Exactly the opposite characterized deactivation. The frequency of fast calcium oscillations during activity increased with increasing glucose up to 12 mM glucose concentration, beyond which oscillation duration became longer, resulting in a homogenous increase in active time. In terms of functional connectivity, islets progressed from a very segregated network to a single large functional unit with increasing glucose concentration. A comparison between classical physiological and network parameters revealed that the first-responders during activation had longer active times during plateau and the most active cells during the plateau tended to deactivate later. Cells with the most functional connections tended to activate sooner, have longer active times, and deactivate later. Our findings provide a common ground for recent differing views on β cell heterogeneity and an important baseline for future studies of stimulus-secretion and intercellular coupling.NEW & NOTEWORTHY We assessed concentration-dependence in coupled β cells, degree of functional heterogeneity, and uncovered possible specialized subpopulations during the different phases of the response to glucose at the level of many individual cells. To this aim, we combined acute mouse pancreas tissue slices with functional multicellular calcium imaging over a wide range from threshold (7 mM) and physiological (8 and 9 mM) to supraphysiological (12 and 16 mM) glucose concentrations, classical physiological, and advanced network analyses.

Intercellular Communication in the Islet of Langerhans in Health and Disease

Blood glucose homeostasis requires proper function of pancreatic islets, which secrete insulin, glucagon, and somatostatin from the β-, α-, and δ-cells, respectively. Each islet cell type is equipped with intrinsic mechanisms for glucose sensing and secretory actions, but these intrinsic mechanisms alone cannot explain the observed secretory profiles from intact islets. Regulation of secretion involves interconnected mechanisms among and between islet cell types. Islet cells lose their normal functional signatures and secretory behaviors upon dispersal as compared to intact islets and in vivo. In dispersed islet cells, the glucose response of insulin secretion is attenuated from that seen from whole islets, coordinated oscillations in membrane potential and intracellular Ca2+ activity, as well as the two-phase insulin secretion profile, are missing, and glucagon secretion displays higher basal secretion profile and a reverse glucose-dependent response from that of intact islets. These observations highlight the critical roles of intercellular communication within the pancreatic islet, and how these communication pathways are crucial for proper hormonal and nonhormonal secretion and glucose homeostasis. Further, misregulated secretions of islet secretory products that arise from defective intercellular islet communication are implicated in diabetes. Intercellular communication within the islet environment comprises multiple mechanisms, including electrical synapses from gap junctional coupling, paracrine interactions among neighboring cells, and direct cell-to-cell contacts in the form of juxtacrine signaling. In this article, we describe the various mechanisms that contribute to proper islet function for each islet cell type and how intercellular islet communications are coordinated among the same and different islet cell types. © 2021 American Physiological Society. Compr Physiol 11:2191-2225, 2021.

Measurement of Pulsatile Insulin Secretion: Rationale and Methodology

Pancreatic β-cells are responsible for the synthesis and exocytosis of insulin in response to an increase in circulating glucose. Insulin secretion occurs in a pulsatile manner, with oscillatory pulses superimposed on a basal secretion rate. Insulin pulses are a marker of β-cell health, and secretory parameters, such as pulse amplitude, time interval and frequency distribution, are impaired in obesity, aging and type 2 diabetes. In this review, we detail the mechanisms of insulin production and β-cell synchronization that regulate pulsatile insulin secretion, and we discuss the challenges to consider when measuring fast oscillatory secretion in vivo. These include the anatomical difficulties of measuring portal vein insulin noninvasively in humans before the hormone is extracted by the liver and quickly removed from the circulation. Peripheral concentrations of insulin or C-peptide, a peptide cosecreted with insulin, can be used to estimate their secretion profile, but mathematical deconvolution is required. Parametric and nonparametric approaches to the deconvolution problem are evaluated, alongside the assumptions and trade-offs required for their application in the quantification of unknown insulin secretory rates from known peripheral concentrations. Finally, we discuss the therapeutical implication of targeting impaired pulsatile secretion and its diagnostic value as an early indicator of β-cell stress.

The effects of beta-cell mass and function, intercellular coupling, and islet synchrony on [Formula: see text] dynamics

Type 2 diabetes (T2D) is a challenging metabolic disorder characterized by a substantial loss of [Formula: see text]-cell mass and alteration of [Formula: see text]-cell function in the islets of Langerhans, disrupting insulin secretion and glucose homeostasis. The mechanisms for deficiency in [Formula: see text]-cell mass and function during the hyperglycemia development and T2D pathogenesis are complex. To study the relative contribution of [Formula: see text]-cell mass to [Formula: see text]-cell function in T2D, we make use of a comprehensive electrophysiological model of human [Formula: see text]-cell clusters. We find that defect in [Formula: see text]-cell mass causes a functional decline in single [Formula: see text]-cell, impairment in intra-islet synchrony, and changes in the form of oscillatory patterns of membrane potential and intracellular [Formula: see text] concentration, which can lead to changes in insulin secretion dynamics and in insulin levels. The model demonstrates a good correspondence between suppression of synchronizing electrical activity and published experimental measurements. We then compare the role of gap junction-mediated electrical coupling with both [Formula: see text]-cell synchronization and metabolic coupling in the behavior of [Formula: see text] concentration dynamics within human islets. Our results indicate that inter-[Formula: see text]-cellular electrical coupling depicts a more important factor in shaping the physiological regulation of islet function and in human T2D. We further predict that varying the whole-cell conductance of delayed rectifier [Formula: see text] channels modifies oscillatory activity patterns of [Formula: see text]-cell population lacking intercellular coupling, which significantly affect [Formula: see text] concentration and insulin secretion.

Small subpopulations of β-cells do not drive islet oscillatory [Ca2+] dynamics via gap junction communication

The islets of Langerhans exist as multicellular networks that regulate blood glucose levels. The majority of cells in the islet are excitable, insulin-producing β-cells that are electrically coupled via gap junction channels. β-cells are known to display heterogeneous functionality. However, due to gap junction coupling, β-cells show coordinated [Ca²⁺] oscillations when stimulated with glucose, and global quiescence when unstimulated. Small subpopulations of highly functional β-cells have been suggested to control [Ca²⁺] dynamics across the islet. When these populations were targeted by optogenetic silencing or photoablation, [Ca²⁺] dynamics across the islet were largely disrupted. In this study, we investigated the theoretical basis of these experiments and how small populations can disproportionality control islet [Ca²⁺] dynamics. Using a multicellular islet model, we generated normal, skewed or bimodal distributions of β-cell heterogeneity. We examined how islet [Ca²⁺] dynamics were disrupted when cells were targeted via hyperpolarization or populations were removed; to mimic optogenetic silencing or photoablation, respectively. Targeted cell populations were chosen based on characteristics linked to functional subpopulation, including metabolic rate of glucose oxidation or [Ca²⁺] oscillation frequency. Islets were susceptible to marked suppression of [Ca²⁺] when ~10% of cells with high metabolic activity were hyperpolarized; where hyperpolarizing cells with normal metabolic activity had little effect. However, when highly metabolic cells were removed from the model, [Ca²⁺] oscillations remained. Similarly, when ~10% of cells with either the highest frequency or earliest elevations in [Ca²⁺] were removed from the islet, the [Ca²⁺] oscillation frequency remained largely unchanged. Overall, these results indicate small populations of β-cells with either increased metabolic activity or increased frequency are unable to disproportionately control islet-wide [Ca²⁺] via gap junction coupling. Therefore, we need to reconsider the physiological basis for such small β-cell populations or the mechanism by which they may be acting to control normal islet function.

Many biological systems can be studied using network theory. How heterogeneous cell subpopulations come together to create complex multicellular behavior is of great value in understanding function and dysfunction in tissues. The pancreatic islet of Langerhans is a highly coupled structure that is important for maintaining blood glucose homeostasis. β-cell electrical activity is coordinated via gap junction communication. The function of the insulin-producing β-cell within the islet is disrupted in diabetes. As such, to understand the causes of islet dysfunction we need to understand how different cells within the islet contribute to its overall function via gap junction coupling. Using a computational model of β-cell electrophysiology, we investigated how small highly functional β-cell populations within the islet contribute to its function. We found that when small populations with greater functionality were introduced into the islet, they displayed signatures of this enhanced functionality. However, when these cells were removed, the islet, retained near-normal function. Thus, in a highly coupled system, such as an islet, the heterogeneity of cells allows small subpopulations to be dispensable, and thus their absence is unable to disrupt the larger cellular network. These findings can be applied to other electrical systems that have heterogeneous cell populations.

Assessing Different Temporal Scales of Calcium Dynamics in Networks of Beta Cell Populations

Beta cells within the pancreatic islets of Langerhans respond to stimulation with coherent oscillations of membrane potential and intracellular calcium concentration that presumably drive the pulsatile exocytosis of insulin. Their rhythmic activity is multimodal, resulting from networked feedback interactions of various oscillatory subsystems, such as the glycolytic, mitochondrial, and electrical/calcium components. How these oscillatory modules interact and affect the collective cellular activity, which is a prerequisite for proper hormone release, is incompletely understood. In the present work, we combined advanced confocal Ca2+ imaging in fresh mouse pancreas tissue slices with time series analysis and network science approaches to unveil the glucose-dependent characteristics of different oscillatory components on both the intra- and inter-cellular level. Our results reveal an interrelationship between the metabolically driven low-frequency component and the electrically driven high-frequency component, with the latter exhibiting the highest bursting rates around the peaks of the slow component and the lowest around the nadirs. Moreover, the activity, as well as the average synchronicity of the fast component, considerably increased with increasing stimulatory glucose concentration, whereas the stimulation level did not affect any of these parameters in the slow component domain. Remarkably, in both dynamical components, the average correlation decreased similarly with intercellular distance, which implies that intercellular communication affects the synchronicity of both types of oscillations. To explore the intra-islet synchronization patterns in more detail, we constructed functional connectivity maps. The subsequent comparison of network characteristics of different oscillatory components showed more locally clustered and segregated networks of fast oscillatory activity, while the slow oscillations were more global, resulting in several long-range connections and a more cohesive structure. Besides the structural differences, we found a relatively weak relationship between the fast and slow network layer, which suggests that different synchronization mechanisms shape the collective cellular activity in islets, a finding which has to be kept in mind in future studies employing different oscillations for constructing networks.

Mathematical Modeling for the Physiological and Clinical Investigation of Glucose Homeostasis and Diabetes

Mathematical modeling in the field of glucose metabolism has a longstanding tradition. The use of models is motivated by several reasons. Models have been used for calculating parameters of physiological interest from experimental data indirectly, to provide an unambiguous quantitative representation of pathophysiological mechanisms, to determine indices of clinical usefulness from simple experimental tests. With the growing societal impact of type 2 diabetes, which involves the disturbance of the glucose homeostasis system, development and use of models in this area have increased. Following the approaches of physiological and clinical investigation, the focus of the models has spanned from representations of whole body processes to those of cells, i.e., from in vivo to in vitro research. Model-based approaches for linking in vivo to in vitro research have been proposed, as well as multiscale models merging the two areas. The success and impact of models has been variable. Two kinds of models have received remarkable interest: those widely used in clinical applications, e.g., for the assessment of insulin sensitivity and β-cell function and some models representing specific aspects of the glucose homeostasis system, which have become iconic for their efficacy in describing clearly and compactly key physiological processes, such as insulin secretion from the pancreatic β cells. Models are inevitably simplified and approximate representations of a physiological system. Key to their success is an appropriate balance between adherence to reality, comprehensibility, interpretative value and practical usefulness. This has been achieved with a variety of approaches. Although many models concerning the glucose homeostasis system have been proposed, research in this area still needs to address numerous issues and tackle new opportunities. The mathematical representation of the glucose homeostasis processes is only partial, also because some mechanisms are still only partially understood. For in vitro research, mathematical models still need to develop their potential. This review illustrates the problems, approaches and contribution of mathematical modeling to the physiological and clinical investigation of glucose homeostasis and diabetes, focusing on the most relevant and stimulating models.

Pyruvate Kinase Controls Signal Strength in the Insulin Secretory Pathway

Pancreatic β cells couple nutrient metabolism with appropriate insulin secretion. Here, we show that pyruvate kinase (PK), which converts ADP and phosphoenolpyruvate (PEP) into ATP and pyruvate, underlies β cell sensing of both glycolytic and mitochondrial fuels. Plasma membrane-localized PK is sufficient to close K_ATP channels and initiate calcium influx. Small-molecule PK activators increase the frequency of ATP/ADP and calcium oscillations and potently amplify insulin secretion. PK restricts respiration by cyclically depriving mitochondria of ADP, which accelerates PEP cycling until membrane depolarization restores ADP and oxidative phosphorylation. Our findings support a compartmentalized model of β cell metabolism in which PK locally generates the ATP/ADP required for insulin secretion. Oscillatory PK activity allows mitochondria to perform synthetic and oxidative functions without any net impact on glucose oxidation. These findings suggest a potential therapeutic route for diabetes based on PK activation that would not be predicted by the current consensus single-state model of β cell function.

Multifaceted Control of GR Signaling and Its Impact on Hepatic Transcriptional Networks and Metabolism

Glucocorticoids (GCs) and the glucocorticoid receptor (GR) are important regulators of development, inflammation, stress response and metabolism, demonstrated in various diseases including Addison's disease, Cushing's syndrome and by the many side effects of prolonged clinical administration of GCs. These conditions include severe metabolic challenges in key metabolic organs like the liver. In the liver, GR is known to regulate the transcription of key enzymes in glucose and lipid metabolism and contribute to the regulation of circadian-expressed genes. Insights to the modes of GR regulation and the underlying functional mechanisms are key for understanding diseases and for the development of improved clinical uses of GCs. The activity and function of GR is regulated at numerous levels including ligand availability, interaction with heat shock protein (HSP) complexes, expression of GR isoforms and posttranslational modifications. Moreover, recent genomics studies show functional interaction with multiple transcription factors (TF) and coregulators in complex transcriptional networks controlling cell type-specific gene expression by GCs. In this review we describe the different regulatory steps important for GR activity and discuss how different TF interaction partners of GR selectively control hepatic gene transcription and metabolism.

Phantom bursting may underlie electrical bursting in single pancreatic β-cells

Insulin is secreted by pancreatic β-cellsthat 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-cellsin intact islets, while in other islets the β-cellsexhibit "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-cellsbehave 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-cellsmay be due to a phantom bursting mechanism, and by extension, slow bursting in intact islets may also be driven by this mechanism.

β Cells Operate Collectively to Help Maintain Glucose Homeostasis

Residing in the islets of Langerhans in the pancreas, β cells contribute to glucose homeostasis by managing the body's insulin supply. Although it has been acknowledged that healthy β cells engage in heavy cell-to-cell communication to perform their homeostatic function, the exact role and effects of such communication remain partly understood. We offer a novel, to our knowledge, perspective on the subject in the form of 1) a dynamical network model that faithfully mimics fast calcium oscillations in response to above-threshold glucose stimulation and 2) empirical data analysis that reveals a qualitative shift in the cross-correlation structure of measured signals below and above the threshold glucose concentration. Combined together, these results point to a glucose-induced transition in β-cell activity thanks to increasing coordination through gap-junctional signaling and paracrine interactions. Our data and the model further suggest how the conservation of entire cell-cell conductance, observed in coupled but not uncoupled β cells, emerges as a collective phenomenon. An overall implication is that improving the ability to monitor β-cell signaling should offer means to better understand the pathogenesis of diabetes mellitus.

Diabetes-associated genetic variation in TCF7L2 alters pulsatile insulin secretion in humans

BACKGROUNDMetabolic disorders such as type 2 diabetes have been associated with a decrease in insulin pulse frequency and amplitude. We hypothesized that the T allele at rs7903146 in TCF7L2, previously associated with β cell dysfunction, would be associated with changes in these insulin pulse characteristics.METHODSTwenty-nine nondiabetic subjects (age 46 ± 2, BMI 28 ± 1 kg/m2) participated in this study. Of these, 16 were homozygous for the C allele at rs7903146 and 13 were homozygous for the T allele. Deconvolution of peripheral C-peptide concentrations allowed the reconstruction of portal insulin secretion over time. These data were used for subsequent analyses. Pulse orderliness was assessed by approximate entropy (ApEn), and the dispersion of insulin pulses was measured by a frequency dispersion index (FDI) after a Fast Fourier Transform (FFT) of individual insulin secretion rates.RESULTSDuring fasting conditions, the CC genotype group exhibited decreased pulse disorderliness compared with the TT genotype group (1.10 ± 0.03 vs. 1.19 ± 0.04, P = 0.03). FDI decreased in response to hyperglycemia in the CC genotype group, perhaps reflecting less entrainment of insulin secretion during fasting.CONCLUSIONDiabetes-associated variation in TCF7L2 is associated with decreased orderliness and pulse dispersion, unchanged by hyperglycemia. Quantification of ApEn and FDI could represent novel markers of β cell health.FUNDINGThis work was funded by US NIH (DK78646, DK116231), University of Padova research grant CPDA145405, and Mayo Clinic General Clinical Research Center (UL1 TR000135).

Random Matrix Analysis of Ca2+ Signals in β-Cell Collectives

Even within small organs like pancreatic islets, different endocrine cell types and subtypes form a heterogeneous collective to sense the chemical composition of the extracellular solution and compute an adequate hormonal output. Erroneous cellular processing and hormonal output due to challenged heterogeneity result in various disorders with diabetes mellitus as a flagship metabolic disease. Here we attempt to address the aforementioned functional heterogeneity with comparing pairwise cell-cell cross-correlations obtained from simultaneous measurements of cytosolic calcium responses in hundreds of islet cells in an optical plane to statistical properties of correlations predicted by the random matrix theory (RMT). We find that the bulk of the empirical eigenvalue spectrum is almost completely described by RMT prediction, however, the deviating eigenvalues that exist below and above RMT spectral edges suggest that there are local and extended modes driving the correlations. We also show that empirical nearest neighbor spacing of eigenvalues follows universal RMT properties regardless of glucose stimulation, but that number variance displays clear separation from RMT prediction and can differentiate between empirical spectra obtained under non-stimulated and stimulated conditions. We suggest that RMT approach provides a sensitive tool to assess the functional cell heterogeneity and its effects on the spatio-temporal dynamics of a collective of beta cells in pancreatic islets in physiological resting and stimulatory conditions, beyond the current limitations of molecular and cellular biology.

Intact pancreatic islets and dispersed beta-cells both generate intracellular calcium oscillations but differ in their responsiveness to glucose

Pancreatic islets produce pulses of insulin and other hormones that maintain normal glucose homeostasis. These micro-organs possess exquisite glucose-sensing capabilities, allowing for precise changes in pulsatile insulin secretion in response to small changes in glucose. When communication among these cells is disrupted, precision glucose sensing falters. We measured intracellular calcium patterns in 6-mM-steps between 0 and 16 mM glucose, and also more finely in 2-mM-steps from 8 to 12 mM glucose, to compare glucose sensing systematically among intact islets and dispersed islet cells derived from the same mouse pancreas in vitro. The calcium activity of intact islets was uniformly low (quiescent) below 4 mM glucose and active above 8 mM glucose, whereas dispersed beta-cells displayed a broader activation range (2-to-10 mM). Intact islets exhibited calcium oscillations with 2-to-5-min periods, yet beta-cells exhibited longer 7-10 min periods. In every case, intact islets showed changes in activity with each 6-mM-glucose step, whereas dispersed islet cells displayed a continuum of calcium responses ranging from islet-like patterns to stable oscillations unaffected by changes in glucose concentration. These differences were also observed for 2-mM-glucose steps. Despite the diversity of dispersed beta-cell responses to glucose, the sum of all activity produced a glucose dose-response curve that was surprisingly similar to the curve for intact islets, arguing against the importance of "hub cells" for function. Beta-cells thus retain many of the features of islets, but some are more islet-like than others. Determining the molecular underpinnings of these variations could be valuable for future studies of stem-cell-derived beta-cell therapies.

Mathematical Modelling of Endocrine Systems

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

Towards feedback-controlled nanomedicines for smart, adaptive delivery

IMPACT STATEMENT

The timing and rate of release of pharmaceuticals from advanced drug delivery systems is an important property that has received considerable attention in the scientific literature. Broadly, these mostly fall into two classes: controlled release with a prolonged release rate or triggered release where the drug is rapidly released in response to an environmental stimulus. This review aims to highlight the potential for developing adaptive release systems that more subtlety modulate the drug release profile through continuous communication with its environment facilitated through feedback control. By reviewing the key elements of this approach in one place (fundamental principles of nanomedicine, enzymatic nanoreactors for medical therapies and feedback-controlled chemical systems) and providing additional motivating case studies in the context of chronobiology, we hope to inspire innovative development of novel "chrononanomedicines."

Synchronization of pancreatic islets by periodic or non-periodic muscarinic agonist pulse trains

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 G_q 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.

Microfluidic-enabled quantitative measurements of insulin release dynamics from single islets of Langerhans in response to 5-palmitic acid hydroxy stearic acid

Proper release of insulin from pancreatic islets of Langerhans is essential for maintaining glucose homeostasis. For full efficacy, both the pattern and the amount of hormone release are critical. It is therefore important to understand how insulin levels are secreted from single islets in both a quantitative fashion and in a manner that resolves temporal dynamics. In this study, we describe a microfluidic analytical system that can both quantitatively monitor insulin secretion from single islets while simultaneously maintaining high temporal sampling to resolve dynamics of release. We have applied this system to determine the acute and chronic effects of a recently-identified lipid, 5-palmitic acid hydroxy stearic acid (5-PAHSA), which is a member of the fatty acid hydroxy fatty acid class of lipids that are upregulated in healthy individuals. Chronic incubation (48 h) with 5-PAHSA significantly increased glucose-stimulated insulin secretion (GSIS) in murine islets compared to chronic incubation without the lipid or in the presence of palmitic acid (PA). The studies were continued in human islets from both healthy donors and donors diagnosed with type 2 diabetes mellitus (T2DM). Total amounts of GSIS were not only augmented in islets that were chronically incubated with 5-PAHSA, but the dynamic insulin release profiles also improved as noted by more pronounced insulin oscillations. With this quantitative microfluidic system, we have corroborated the anti-diabetic effects of 5-PAHSA by demonstrating improved islet function after chronic incubation with this lipid via improved oscillatory dynamics along with higher basal and peak release rates.

The cell biology of systemic insulin function

Insulin is the paramount anabolic hormone, promoting carbon energy deposition in the body. Its synthesis, quality control, delivery, and action are exquisitely regulated by highly orchestrated intracellular mechanisms in different organs or "stations" of its bodily journey. In this Beyond the Cell review, we focus on these five stages of the journey of insulin through the body and the captivating cell biology that underlies the interaction of insulin with each organ. We first analyze insulin's biosynthesis in and export from the β-cells of the pancreas. Next, we focus on its first pass and partial clearance in the liver with its temporality and periodicity linked to secretion. Continuing the journey, we briefly describe insulin's action on the blood vasculature and its still-debated mechanisms of exit from the capillary beds. Once in the parenchymal interstitium of muscle and adipose tissue, insulin promotes glucose uptake into myofibers and adipocytes, and we elaborate on the intricate signaling and vesicle traffic mechanisms that underlie this fundamental function. Finally, we touch upon the renal degradation of insulin to end its action. Cellular discernment of insulin's availability and action should prove critical to understanding its pivotal physiological functions and how their failure leads to diabetes.