We have carried out an important test (described in the next paragraph) of our comprehensive model for oscillations of membrane potential and calcium on time scales ranging from seconds to minutes. These lead to corresponding oscillations of insulin secretion. The basic hypothesis of the model is that the faster (tens of seconds) oscillations stem from feedback of calcium onto ion channels, likely calcium-activated potassium (K(Ca)) channels and ATP-dependent potassium (K(ATP)) channels, whereas the slower (five minutes) oscillations stem from oscillations in metabolism. The metabolic oscillations are transduced into electrical oscillations via the K(ATP) channels. The latter, notably, are a first-line target of insulin-stimulating drugs, such as the sulfonylureas (tolbutamide, glyburide) used in the treatment of Type 2 Diabetes. The model thus consists of an electrical oscillator (EO) and a metabolic (glycolytic) oscillator (G)) and is referred to as the Dual Oscillator Model (DOM). A key prediction of the DOM is that metabolic oscillations can occur in the absence of calcium oscillations. This differs from other models for islet oscillations in which the metabolic oscillations are secondary to calcium oscillations, which can affect metabolism by either increasing consumption of ATP by calcium pumps or by decreasing production of ATP by shunting the mitochondrial membrane potential. The latter class of models had gained support from experiments showing that metabolic oscillations were abolished by blocking calcium entry into islet cells using the K(ATP) channel opener diazoxide. We previously showed that the DOM was consistent with such behavior because reducing calcium entry reduces ATP consumption and inhibits glycolysis at phosphofructokinase. We have now shown that oscillations in NAD(P)H persist in a subset of islets exposed to diazoxide. Whereas the inhibition of oscillations by diazoxide is compatible with both the DOM and calcium-driven metabolic oscillations, the persistence of oscillations is compatble only with the DOM or other models in which metabolic oscillations are autonomous of calcium oscillations. As a further stringent test of the DOM we showed that in a subset of islets in which oscillations were inhibited by diazoxide they could be restored by raising external KCl. This depolarizes the islets and promotes calcium entry, reactivating the calcium pumps. Together all the experiments support the hypothesis that metabolic oscillations depend on the calcium level but not on oscillations in calcium. See Ref. # 1. We have extended previous work showing that islets from a given mouse tend to have similar periods (i.e. mainly slow or mainly fast) whereas islets from different mice have variable periods, a phenomenon we call imprinting. This is of physiological significance because our models have shown that it is much easier to synchronize the islets in the pancreas if the islets have similar periods, and unless the islets are synchronized there would not be whole-body oscillations in insulin in the circulation. We examined the question of whether imprinting is genetic in origin by testing in-bred C57BL/6J mice and found the same phenomenon - variability among mice but uniformity with a mouse. Thus, imprinting is not genetic. We further demonstrated this by resetting islets from slow to fast by removing and restoring glucose. Thus, imprinting may depend on the metabolic status or history of the animal. Finally we used a novel microfluidic chip platform to show that imprinting is found not only in calcium oscillations but also in oscillations in insulin secretion. See Ref. # 2. Insulin secretion is stimulated primarily by increases in glucose but can be potentiated by other inputs. Notable among these is glucagon-like peptide 1 (GLP1), which is secreted by endocrine cells in the small intestine. GLP1 binding to beta cells increases cAMP, which both acutely increases the efficiency of calcium-mediated exocytosis and promotes beta-cell survival and proliferation in response to maintained need. We developed a model of cAMP production and diffusion within beta cells to address the question of how islets can distinguish between a short-term need to increase secretion in response to, for example, a meal, and a long term need to increase beta-cell mass in response to chronic overstimulation. Experiments by others had shown that pulsatile stimulation of cAMP production resulted in elevation of cAMP only in the cell periphery but maintained stimulation led to translocation of protein kinase A (PKA), a downstream effector of cAMP, to the nucleus, where it can activate transcription factors that can trigger proliferation and other longer term responses. We demonstrated with the model that hindered diffusion could account for these observations. Of particular interest, however, we found that the diffusion barrier must be localized at the nuclear envelope. This prediction potentially can assist in the search for previously unappreciated binding proteins in the nuclear membrane that could mediate this localized buffering effect. See Ref. # 3. The mathematical models we have been developing in order to understand beta-cell function can also be applied to the task of engineering replacement beta cells to treat insulin-deficient diabetes, whether type 1 or type 2. We have reviewed the lessons that have been learned, showing a hierarchy of models of increasing sophistication that capture more and more features of beta-cell calcium handling and oscillations. Minimal models that have garden variety electrical spiking can provide minimal functionality provided the cells are equipped with K(ATP) channels, but more elaborate cells could provide enhanced function. In turn, engineered cells may shed light on the mechanisms of real beta cells on the principle that if you can build it you understand it. They can also potentially give insight into how cells regulate the various elements quantitatively to produce a robust phenotype. See Ref. # 4.
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