Aims/hypothesis The biological mechanism by which obesity predisposes to insulin resistance is unclear. One hypothesis is that larger adipose cells disturb metabolism via increased lipolysis. While studies have demonstrated that cell size increases in proportion to BMI, it has not been clearly shown that adipose cell size, independent of BMI, is associated with insulin resistance. The aim of this study was to test this widely held assumption by comparing adipose cell size distribution in 28 equally obese, otherwise healthy individuals who represented extreme ends of the spectrum of insulin sensitivity, as defined by the modified insulin suppression test. Subjects and methods Subcutaneous periumbilical adipose tissue biopsy samples were fixed in osmium tetroxide and passed through the Beckman Coulter Multisizer to obtain cell size distributions. Insulin sensitivity was quantified by the modified insulin suppression test. Quantitative real-time PCR for adipose cell differentiation genes was performed for 11 subjects. Results All individuals exhibited a bimodal cell size distribution. Contrary to expectations, the mean diameter of the larger cells was not significantly different between the insulin-sensitive and insulin-resistant individuals. Moreover, insulin resistance was associated with a higher ratio of small to large cells (1.66±1.03 vs 0.94±0.50, p=0.01). Similar cell size distributions were observed for isolated adipose cells. The real-time PCR results showed two-to threefold lower expression of genes encoding markers of adipose cell differentiation (peroxisome proliferator-activated receptor γ1 [PPARγ1], PPARγ2, GLUT4, adiponectin, sterol receptor element binding protein 1c) in insulinresistant compared with insulin-sensitive individuals. Conclusions/interpretation These results suggest that after controlling for obesity, insulin resistance is associated with an expanded population of small adipose cells and decreased expression of differentiation markers, suggesting that impairment in adipose cell differentiation may contribute to obesity-associated insulin resistance.

Pancreatic beta-cells in an intact Islet of Langerhans exhibit bursting electrical behavior. The Chay-Keizer model describes this using a calcium-activated potassium (K-Ca) channel, but cannot account for the irregular spiking of isolated beta-cells. Atwater I., L. Rosario, and E. Rojas, Cell Calcium. 4:451-461, proposed that the K-Ca channels, which are rarely open, are shared by several cells. This suggests that the chaotic behavior of isolated cells is stochastic. We have revised the Chay-Keizer model to incorporate voltage clamp data of Rorsman and Trube and extended it to include stochastic K-Ca channels. This model can describe the behavior of single cells, as well as that of clusters of cells tightly coupled by gap junctions. As the size of the clusters is increased, the electrical activity shows a transition from chaotic spiking to regular bursting. Although the model of coupling is over-simplified, the simulations lend support to the hypothesis that bursting is the result of channel sharing.

We develop a mathematical model that explicitly represents many of the known signaling components mediating translocation of the insulin-responsive glucose transporter GLUT4 to gain insight into the complexities of metabolic insulin signaling pathways. A novel mechanistic model of postreceptor events including phosphorylation of insulin receptor substrate-1, activation of phosphatidylinositol 3-kinase, and subsequent activation of downstream kinases Akt and protein kinase C-zeta is coupled with previously validated subsystem models of insulin receptor binding, receptor recycling, and GLUT4 translocation. A system of differential equations is defined by the structure of the model. Rate constants and model parameters are constrained by published experimental data. Model simulations of insulin dose-response experiments agree with published experimental data and also generate expected qualitative behaviors such as sequential signal amplification and increased sensitivity of downstream components. We examined the consequences of incorporating feedback pathways as well as representing pathological conditions, such as increased levels of protein tyrosine phosphatases, to illustrate the utility of our model for exploring molecular mechanisms. We conclude that mathematical modeling of signal transduction pathways is a useful approach for gaining insight into the complexities of metabolic insulin signaling.

Type 2 diabetes (T2DM) results when increases in beta cell function and/or mass cannot compensate for rising insulin resistance. Numerous studies have documented the longitudinal changes in metabolism that occur during the development of glucose intolerance and lead to T2DM. However, the role of changes in insulin secretion, both amount and temporal pattern has been understudied. Most of the insulin secreted from pancreatic beta cells of the pancreas is released in a pulsatile pattern, which is disrupted in T2DM. Here we review the evidence that changes in beta cell pulsatility occur during the progression from glucose intolerance to T2DM in humans, and contribute significantly to the etiology of the disease. We review the evidence that insulin pulsatility improves the efficacy of secreted insulin on its targets, particularly hepatic glucose production, but also examine evidence that pulsatility alters or is altered by changes in peripheral glucose uptake. Finally, we summarize our current understanding of the biophysical mechanisms responsible for oscillatory insulin secretion. Understanding how insulin pulsatility contributes to normal glucose homeostasis and is altered in metabolic disease states may help improve the treatment of T2DM.

We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (in Mathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation diagram. We use this to describe the phenomenological character of different types of bursting, addressing the issue of how well the bursting can be characterized given the limited amount of information often available in experimental settings.

of insulin secretion from the ␤-cells of the pancreatic islets of Langerhans is central to the development of type 2 diabetes mellitus and has therefore been the subject of much investigation. Great advances have been made in this area, but the mechanisms underlying the pulsatility of insulin secretion remain controversial. The period of these pulses is 4 -6 min and reflects oscillations in islet membrane potential and intracellular free Ca 2ϩ . Pulsatile blood insulin levels appear to play an important physiological role in insulin action and are lost in patients with type 2 diabetes and their near relatives. We present evidence for a recently developed ␤-cell model, the "dual oscillator model," in which oscillations in activity are due to both electrical and metabolic mechanisms. This model is capable of explaining much of the available data on islet activity and offers possible resolutions of a number of longstanding issues. The model, however, still lacks direct confirmation and raises new issues. In this article, we highlight both the successes of the model and the challenges that it poses for the field.pancreatic ␤-cells; mathematical model; diabetes IN THE CONSENSUS MODEL for glucose-stimulated insulin secretion (GSIS) from pancreatic ␤-cells (Fig. 1A), glucose enters the cell through GLUT2 glucose transporters and is metabolized to increase the ATP/ADP ratio, which in turn closes ATP-sensitive K ϩ (K ATP ) channels. This depolarizes the membrane, which opens L-type Ca 2ϩ channels and promotes Ca 2ϩ influx. The resulting increase in the cytosolic Ca 2ϩ concentration evokes exocytosis of insulin granules. The development of this model represented a major achievement that overturned early, more orthodox suggestions that glucose acted through a receptor, like many other signals for hormone secretion. This model has not been reversed by subsequent findings, although it has been extended by consideration of noncalcium amplifying factor(s) of yet undetermined identity (35). Nonetheless, the consensus picture is essentially a static view, as it fails to account for important dynamic features of GSIS, in particular, its pulsatile nature. Oscillations in insulin secretion have been measured in vivo (59, 65), in the perifused pancreas (76), and in isolated islets (4,27,46,70). The oscillations typically have two components; the faster component has a period of tens of seconds (6,27,59), and the slower component has a period of 4 -6 min (59,65,66). This latter component appears to play an important physiological role in insulin action (54) and is lost in patients with type 2 diabetes and their near relatives (53,60,64,87). In this article we discuss a nascent model that includes the consensus mechanism but also offers an integrated account of both the "fast" (tens of seconds) and "slow" (4 -6 min) insulin oscillations in secretion and their interactions. We propose that the fast oscillations result from electrical mechanisms, predominantly feedback of cytosolic free calcium on plasma membrane ion channels, and that ...

Pancreatic islets of Langerhans produce bursts of electrical activity when exposed to stimulatory glucose levels. These bursts often have a regular repeating pattern, with a period of 10-60 s. In some cases, however, the bursts are episodic, clustered into bursts of bursts, which we call compound bursting. Consistent with this are recordings of free Ca2+ concentration, oxygen consumption, mitochondrial membrane potential, and intraislet glucose levels that exhibit very slow oscillations, with faster oscillations superimposed. We describe a new mathematical model of the pancreatic beta-cell that can account for these multimodal patterns. The model includes the feedback of cytosolic Ca2+ onto ion channels that can account for bursting, and a metabolic subsystem that is capable of producing slow oscillations driven by oscillations in glycolysis. This slow rhythm is responsible for the slow mode of compound bursting in the model. We also show that it is possible for glycolytic oscillations alone to drive a very slow form of bursting, which we call "glycolytic bursting." Finally, the model predicts that there is bistability between stationary and oscillatory glycolysis for a range of parameter values. We provide experimental support for this model prediction. Overall, the model can account for a diversity of islet behaviors described in the literature over the past 20 years.

The P2X7 receptor is a trimeric channel with three binding sites for ATP, but how the occupancy of these sites affects gating is still not understood. Here we show that naïve receptors activated and deactivated monophasically at low and biphasically at higher agonist concentrations. Both phases of response were abolished by application of Az10606120, a P2X7R-specific antagonist. The slow secondary growth of current in the biphasic response coincided temporally with pore dilation. Repetitive stimulation with the same agonist concentration caused sensitization of receptors, which manifested as a progressive increase in the current amplitude, accompanied by a slower deactivation rate. Once a steady level of the secondary current was reached, responses at high agonist concentrations were no longer biphasic but monophasic. Sensitization of receptors was independent of Na+ and Ca2+ influx and about 30-min washout was needed to reestablish the initial gating properties. T15E- and T15K-P2X7 mutants showed increased sensitivity for agonists, responded with monophasic currents at all agonist concentrations, activated immediately with dilated pores, and deactivated slowly. The complex pattern of gating exhibited by wild-type channels can be accounted for by a Markov state model that includes negative cooperativity of agonist binding to unsensitized receptors caused by the occupancy of one or two binding sites, opening of the channel pore to a low conductance state when two sites are bound, and sensitization with pore dilation to a high conductance state when three sites are occupied.