Diffusion induced oscillatory insulin secretion

Oscillatory secretion of insulin has been observed in many different experimental preparations. Here we examine a mathematical model for in vitro insulin secretion from pancreatic beta cells in a flow-through reactor. The analysis shows that oscillations result because of an important interplay between flow rate of the reactor and insulin diffusion. In particular, if the ratio of flow rate to volume of the reaction bed is too large, oscillations are eliminated, in contradiction to the conclusions of Maki and Keizer (L. W. Maki and Keizer J. Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells. Bull. Math. Biol., 57 (1995), 569–591). Furthermore, with reasonable numbers for the experimental parameters and the diffusion of insulin, the model equations do not exhibit oscillations.     

Oscillations in cytosolic free Ca2+, oxygen consumption, and insulin secretion in glucose-stimulated rat pancreatic islets

Insulin secretion in the intact organism, and by the perfused pancreas and groups of isolated perifused islets, is pulsatile. We have proposed a metabolic model of glucose-induced insulin secretion in which oscillations in the ATP/ADP ratio drive alterations in metabolic and electrical events that lead to insulin release. A key prediction of our model is that metabolically driven Ca2+ oscillations will also occur. Using the fluorescent Ca2+ probe, fura 2, digital image analysis, and sensitive O2 electrodes, we investigated cytosolic free Ca2+ responses and O2 consumption in perifused rat islets that had been maintained in culture for 1-4 days. We found that elevated ambient glucose increased the average cytosolic free Ca2+ level, the ATP/ADP ratio, and oxygen consumption, as previously found in freshly isolated islets. Oscillatory patterns were obtained for Ca2+, O2 consumption, and insulin secretion in the presence of 10 and 20 mM glucose. Very low amplitude oscillations in cytosolic free Ca2+ were observed at 3 mM nonstimulatory glucose levels. Evaluation of the Ca2+ responses of a large series of individual islets, monitored by digital image analysis and perifused at both 3 and 10 mM glucose, indicated that the rise in glucose concentration caused more than a doubling of the average cytosolic free Ca2+ value and a 4-fold increase in the amplitude of the oscillations with little change in period. The pattern of Ca2+ change within the islets was consistent with recruitment of responding cells. The coexistence of oscillations with similar periods in insulin secretion, oxygen consumption, and cytosolic free Ca2+ is consistent with the model of metabolically driven pulsatile insulin secretion.     

Model for glucagon secretion by pancreatic α-cells

Glucagon hormone is synthesized and released by pancreatic α-cells, one of the islet-cell types. This hormone, along with insulin, maintains blood glucose levels within the physiological range. Glucose stimulates glucagon release at low concentrations (hypoglycemia). However, the mechanisms involved in this secretion are still not completely clear. Here, using experimental calcium time series obtained in mouse pancreatic islets at low and high glucose conditions, we propose a glucagon secretion model for α-cells. Our model takes into account that the resupply of releasable granules is not only controlled by cytoplasmic Ca2+, as in other neuroendocrine and endocrine cells, but also by the level of extracellular glucose. We found that, although calcium oscillations are highly variable, the average secretion rates predicted by the model fall into the range of values reported in the literature, for both stimulated and non-stimulated conditions. For low glucose levels, the model predicts that there would be a well-controlled number of releasable granules refilled slowly from a large reserve pool, probably to ensure a secretion rate that could last for several minutes. Studying the α-cell response to the addition of insulin at low glucose, we observe that the presence of insulin reduces glucagon release by decreasing the islet Ca2+ level. This observation is in line with previous work reporting that Ca2+ dynamics, mainly frequency, is altered by insulin. Thus, the present results emphasize the main role played by Ca2+ and glucose in the control of glucagon secretion by α-cells. Our modeling approach also shows that calcium oscillations potentiate glucagon secretion as compared to constant levels of this cellular messenger. Altogether, the model sheds new light on the subcellular mechanisms involved in α-cell exocytosis, and provides a quantitative predictive tool for studying glucagon secretion modulators in physiological and pathological conditions.     

Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays

In the glucose-insulin regulatory system, ultradian insulin secretory oscillations are observed to have a period of 50-150 min. After pioneering work traced back to the 1960s, several mathematical models have been proposed during the last decade to model these ultradian oscillations as well as the metabolic system producing them. These currently existing models still lack some of the key physiological aspects of the glucose-insulin system. Applying the mass conservation law, we introduce two explicit time delays and propose a more robust alternative model for better understanding the glucose-insulin endocrine metabolic regulatory system and the ultradian insulin secretory oscillations for the cases of continuous enteral nutrition and constant glucose infusion. We compare the simulation profiles obtained from this two time delay model with those from the other existing models. As a result, we notice many unique features of this two delay model. Based on our intensive simulations, we suspect that one of the possibly many causes of ultradian insulin secretion oscillations is the time delay of the insulin secretion stimulated by the elevated glucose concentration.     

Glucose-induced metabolic oscillations parallel those of Ca(2+) and insulin release in clonal insulin-secreting cells. A multiwell approach to oscillatory cell behavior

Insulin secretion from glucose-stimulated pancreatic beta-cells is oscillatory, and this is thought to result from oscillations in glucose metabolism. One of the primary metabolic stimulus-secretion coupling factors is the ATP/ADP ratio, which can oscillate as a result of oscillations in glycolysis. Using a novel multiwell culture plate system, we examined oscillations in insulin release and the ATP/ADP ratio in the clonal insulin-secreting cell lines HIT T-15 and INS-1. Insulin secretion from HIT cells grown in multiwell plates oscillated with a period of 4 min, similar to that seen previously in perifusion experiments. Oscillations in the ATP/ADP ratio in cells grown under the same conditions also occurred with a period of 4 min, as did oscillations in [Ca(2+)](i) monitored by fluorescence microscopy. In INS-1 cells oscillations in insulin secretion, the ATP/ADP ratio, and [Ca(2+)](i) were also seen, but with a shorter period of about 1.5 min. These observations of oscillations in the ATP/ADP ratio are consistent with their proposed role in driving the oscillations in [Ca(2+)](i) and insulin secretion. Furthermore, these data show that, at least in the clonal beta-cell lines, cell contact or even circulatory connection is not necessary for synchronous oscillations induced by a rise in glucose.     

Methods for parameter identification in oscillatory networks and application to cortical and thalamic 600 Hz activity.

Directed information transfer in the human brain occurs presumably by oscillations. As of yet, most approaches for the analysis of these oscillations are based on time-frequency or coherence analysis. The present work concerns the modeling of cortical 600 Hz oscillations, localized within the Brodmann Areas 3b and 1 after stimulation of the nervus medianus, by means of coupled differential equations. This approach leads to the so-called parameter identification problem, where based on a given data set, a set of unknown parameters of a system of ordinary differential equations is determined by special optimization procedures. Some suitable algorithms for this task are presented in this paper. Finally an oscillatory network model is optimally fitted to the data taken from ten volunteers.     

Sustained simultaneous glycolytic and insulin oscillations in beta-cells

Chemical oscillation in glycolysis induced by glucose is an universal feature in all living cells. In beta-cells this is accompanied by sustained oscillations of concentration of insulin, which helps to keep the blood glucose level within optimum limits. Experiments in this regard had shown that the glycolytic and insulin oscillations are almost consistently in phase and their time periods are very close to each other at both high and low initial concentration of glucose. Experiments have also demonstrated the dynamical transition between the states of glycolytic oscillations indicating a saturation behaviour of glucose transporters at a higher glucose flow rate. We propose a phenomenological model to understand these simultaneous oscillations and how glycolysis provides a mechanism for pulsatory insulin secretion in the light of these basic experimental issues.     

Theoretical evaluation of the parameters of glucose metabolism on the basis of continuous glycemia monitoring data using mathematical modeling

The aim of this paper is to construct a mathematical model that takes the main physiological parameters of blood-glucose regulation into account, in order to identify these parameters for an individual patient according to continuous glucose-monitoring data. The constructed mathematical model consists of six ordinary differential equations that describe the dynamics of changes in glucose concentrations, as well as insulin and anti-insulin factors in the blood. Estimation of the parameters of the equations was performed using an evolutionary programming method. The model predictions were fitted to the continuous glucosemonitoring data. As a result of the identification of the model parameters for two patients with type 1 diabetes mellitus, the estimated insulin secretion was close to zero and the estimated glucose utilization and insulin clearance were increased in comparison with the data for healthy donors. Here, we present a personalized model of the regulation of blood glucose, which can be used to predict the results of continuous glucose monitoring depending on modification of the prescribed glucose-lowering therapy. This approach can significantly reduce the number of iterations of the selection of medical hypoglycemic therapy and therefore increase the effectiveness of treatment according to glucose-monitoring data.

     

Intra- and inter-islet synchronization of metabolically driven insulin secretion

Insulin secretion from pancreatic beta-cells is pulsatile with a period of 5-10 min and is believed to be responsible for plasma insulin oscillations with similar frequency. To observe an overall oscillatory insulin profile it is necessary that the insulin secretion from individual beta-cells is synchronized within islets, and that the population of islets is also synchronized. We have recently developed a model in which pulsatile insulin secretion is produced as a result of calcium-driven electrical oscillations in combination with oscillations in glycolysis. We use this model to investigate possible mechanisms for intra-islet and inter-islet synchronization. We show that electrical coupling is sufficient to synchronize both electrical bursting activity and metabolic oscillations. We also demonstrate that islets can synchronize by mutually entraining each other by their effects on a simple model "liver," which responds to the level of insulin secretion by adjusting the blood glucose concentration in an appropriate way. Since all islets are exposed to the blood, the distributed islet-liver system can synchronize the individual islet insulin oscillations. Thus, we demonstrate how intra-islet and inter-islet synchronization of insulin oscillations may be achieved.     

Insulin secretion and differential gene expression in glucose-responsive and -unresponsive MIN6 sublines

We have established two sublines derived from the insulin-secreting mouse pancreatic beta-cell line MIN6, designated m9 and m14. m9 Cells exhibit glucose-induced insulin secretion in a concentration-dependent manner, whereas m14 cells respond poorly to glucose. In m14 cells, glucose consumption and lactate production are enhanced, and ATP production is largely through nonoxidative pathways. Moreover, lactate dehydrogenase activity is increased, and hexokinase replaces glucokinase as a glucose-phosphorylating enzyme. The ATP-sensitive K(+) channel activity and voltage-dependent calcium channel activity in m14 cells are reduced, and the resting membrane potential is significantly higher than in m9 cells. Thus, in contrast to m9, a model for beta-cells with normal insulin response, m14 is a model for beta-cells with impaired glucose-induced insulin secretion. By mRNA differential display of these sublines, we found 10 genes to be expressed at markedly different levels. These newly established MIN6 cell sublines should be useful tools in the analysis of the genetic and molecular basis of impaired glucose-induced insulin secretion.     

Real-time analysis of intracellular glucose and calcium in pancreatic beta cells by fluorescence microscopy

Glucose is the physiological stimulus for insulin secretion in pancreatic beta cells. The uptake and phosphorylation of glucose initiate and control downstream pathways, resulting in insulin secretion. However, the temporal coordination of these events in beta cells is not fully understood. The recent development of the FLII(12)Pglu-700μ-δ6 glucose nanosensor facilitates real-time analysis of intracellular glucose within a broad concentration range. Using this fluorescence-based technique, we show the shift in intracellular glucose concentration upon external supply and removal in primary mouse beta cells with high resolution. Glucose influx, efflux, and metabolism rates were calculated from the time-dependent plots. Comparison of insulin-producing cells with different expression levels of glucose transporters and phosphorylating enzymes showed that a high glucose influx rate correlated with GLUT2 expression, but was largely also sustainable by high GLUT1 expression. In contrast, in cells not expressing the glucose sensor enzyme glucokinase glucose metabolism was slow. We found no evidence of oscillations of the intracellular glucose concentration in beta cells. Concomitant real-time analysis of glucose and calcium dynamics using FLII(12)Pglu-700μ-δ6 and fura-2-acetoxymethyl-ester determined a glucose threshold of 4mM for the [Ca(2+)](i) increase in beta cells. Indeed, a glucose concentration of 7mM had to be reached to evoke large amplitude [Ca(2+)](i) oscillations. The K(ATP) channel closing agent glibenclamide was not able to induce large amplitude [Ca(2+)](i) oscillations in the absence of glucose. Our findings suggest that glucose has to reach a threshold to evoke the [Ca(2+)](i) increase and subsequently initiate [Ca(2+)](i) oscillations in a K(ATP) channel independent manner.     

Dynamics and stability of a three-dimensional model of cell signal transduction

In this paper, we consider a three-dimensional model of cell signal transduction. In this model, the deactivation of signalling proteins occur throughout the cytosol and activation is localized to specific sites in the cell. We use matched asymptotic expansions to construct the dynamic solutions of signalling protein concentrations. The result of the asymptotic analysis is a system of ordinary differential equations. This reduced system is compared to numerical simulations of the full three-dimensional system. As well, we consider the stability of equilibrium solutions. We find that the systems under consideration may undergo sustained oscillations, hysteresis and other complex behaviors. The simulations of the full three-dimensional system agree with simulations of the reduced ordinary differential equations.     

A Model for Migratory B Cell Oscillations from Receptor Down-Regulation Induced by External Chemokine Fields

A long-standing paradigm in B cell immunology is that effective somatic hypermutation and affinity maturation require cycling between the dark zone and light zone of the germinal center. The cyclic re-entry hypothesis was first proposed based on considerations of the efficiency of affinity maturation using an ordinary differential equations model for B cell population dynamics. More recently, two-photon microscopy studies of B cell motility within lymph nodes in situ have revealed the complex migration patterns of B lymphocytes both in the preactivation follicle and post-activation germinal center. There is strong evidence that chemokines secreted by stromal cells and the regulation of cognate G-protein coupled receptors by these chemokines are necessary for the observed spatial cell distributions. For example, the distribution of B cells within the light and dark zones of the germinal center appears to be determined by the reciprocal interaction between the level of the CXCR4 and CXCR5 receptors and the spatial distribution of their respective chemokines CXCL12 and CXCL13. Computer simulations of individual-based models have been used to study the complex biophysical and mechanistic processes at the individual cell level, but such simulations can be challenging to parameterize and analyze. In contrast, ordinary differential equations are more tractable, but traditional compartment model formalizations ignore the spatial chemokine distribution that drives B cell redistribution. Motivated by the desire to understand the motility patterns observed in an individual-based simulation of B cell migration in the lymph node, we propose and analyze the dynamics of an ordinary differential equation model incorporating explicit chemokine spatial distributions. While there is experimental evidence that B cell migration patterns in the germinal center are driven by extrinsically regulated differentiation programs, the model shows, perhaps surprisingly, that feedback from receptor down-regulation induced by external chemokine fields can give rise to spontaneous interzonal and intrazonal oscillations in the absence of any extrinsic regulation. While the extent to which such simple feedback mechanisms contributes to B cell migration patterns in the germinal center is unknown, the model provides an alternative hypothesis for how complex B cell migration patterns might arise from very simple mechanisms.     

A model for glucose-induced wave propagation in pancreatic islets of Langerhans

A reaction-diffusion type model is constructed, describing the spatio-temporal dynamics of the basic intracellular variables assumed to be involved in the initiation of the insulin secretion process by beta -cells in the pancreatic islets of Langerhans. The model includes equations for the electric membrane potential of the cells, with respective kinetics for ionic currents, for concentrations of both free and stored intracellular calcium, and for the intra- and extracellular concentrations of glucose. An empirical expression connecting the equation for the intracellular glucose concentration to the electrical equation is introduced. The model reproduces the events observed in experiments in vitro upon external glucose application to the islets of Langerhans, such as usual bursting oscillations of the membrane potential and corresponding oscillations of the intracellular calcium concentration. It also allows simulation of electric wave propagation through the islet, initiated by the spatial gradient of glucose concentration within the islet. The gradient emerges due to glucose diffusing into the islets from the external medium, being high at the edges. The latter results show that glucose diffusion presents a means for wave initiation in the islets, which supports our previous assumption (Aslanidi et al., 2001).     

Relating damped oscillations to sustained limit cycles describing real and ideal batch fermentation processes

A batch fermentation model is presented in which the specific growth rate and yield functions are chosen such that sustained oscillations in both the cell and substrate concentration occur. This phenomenon is shown to be a Hopf bifurcation in the underlying system of non-linear ordinary differential equations which comprises the model. It is shown that for oscillations in the substrate concentration to occur it is necessary for the yield term to depend on both the cell and substrate levels.     

The mass, but not the frequency, of insulin secretory bursts in isolated human islets is entrained by oscillatory glucose exposure

Insulin is secreted in discrete insulin secretory bursts. Regulation of insulin release is accomplished almost exclusively by modulation of insulin pulse mass, whereas the insulin pulse interval remains stable at approximately 4 min. It has been reported that in vivo insulin pulses can be entrained to a pulse interval of approximately 10 min by infused glucose oscillations. If oscillations in glucose concentration play an important role in the regulation of pulsatile insulin secretion, abnormal or absent glucose oscillations, which have been described in type 2 diabetes, might contribute to the defective insulin secretion. Using perifused human islets exposed to oscillatory vs. constant glucose, we questioned 1) whether the interval of insulin pulses released by human islets is entrained to infused glucose oscillations and 2) whether the exposure of islets to oscillating vs. constant glucose confers an increased signal for insulin secretion. We report that oscillatory glucose exposure does not entrain insulin pulse frequency, but it amplifies the mass of insulin secretory bursts that coincide with glucose oscillations (P < 0.001). Dose-response analyses showed that the mode of glucose drive does not influence total insulin secretion (P = not significant). The apparent entrainment of pulsatile insulin to infused glucose oscillations in nondiabetic humans in vivo might reflect the amplification of underlying insulin secretory bursts that are detected as entrained pulses at the peripheral sampling site, but without changes in the underlying pacemaker activity.     

Intra-islet insulin suppresses glucagon release via GABA-GABAA receptor system

Excessive secretion of glucagon is a major contributor to the development of diabetic hyperglycemia. Secretion of glucagon is regulated by various nutrients, with glucose being a primary determinant of the rate of alpha cell glucagon secretion. The intra-islet action of insulin is essential to exert the effect of glucose on the alpha cells since, in the absence of insulin, glucose is not able to suppress glucagon release in vivo. However, the precise mechanism by which insulin suppresses glucagon secretion from alpha cells is unknown. In this study, we show that insulin induces activation of GABAA receptors in the alpha cells by receptor translocation via an Akt kinase-dependent pathway. This leads to membrane hyperpolarization in the alpha cells and, ultimately, suppression of glucagon secretion. We propose that defects in this pathway(s) contribute to diabetic hyperglycemia.     

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.