Model of β-cell mitochondrial calcium handling and electrical activity. I. Cytoplasmic variables

We continue our development of a kinetic model of bursting electrical activity in the pancreatic beta-cell (J. Keizer and G. Magnus. Biophys. J. 56: 229-242, 1989), including the influence of Ca2+ handling by the mitochondria. Our minimal model of mitochondrial Ca2+ handling [G. Magnus and J. Keizer. Am. J. Physiol. 273 (Cell Physiol. 42): C717-C733, 1997] is expanded to include the D-glucose dependence of the rate of production of mitochondrial reducing equivalents. The Ca2+ dependence of the mitochondrial dehydrogenases, which is also included in the model, plays only a small role in the simulations, since the dehydrogenases appear to be maximally activated when D-glucose concentrations are sufficient to produce bursting. A previous model of ionic currents in the plasma membrane is updated using a recent experimental characterization of the dependence of the conductance of the ATP-sensitive K+ (KATP) current on adenine nucleotides. The resulting whole cell model is complex, involving 12 dynamic variables that couple Ca2+ handling in the cytoplasm and the mitochondria with electrical activity in the plasma and inner mitochondrial membranes. Simulations with the whole cell model give rise to bursting electrical activity similar to that seen in pancreatic islets and clusters of pancreatic beta-cells. The full D-glucose dose response of electrical activity is obtained if the cytosolic rate of ATP hydrolysis is a sigmoidal function of glucose. The simulations give the correct shape, period, and phase of the associated oscillations in cytosolic Ca2+, predict that the conductance of the KATP current oscillates out of phase with electrical activity [as recently observed in ob/ob mice (O. Larsson, H. Kindmark, R. Bränstrom, B. Fredholm, and P.-O. Berggren. Proc. Natl. Acad. Sci. USA 93: 5161-5165, 1996)], and make other novel predictions. In this model, bursting results because Ca2+ uptake into mitochondria during the active phase reduces the mitochondrial inner membrane potential, reducing the rate of production of ATP, which in turn activates the KATP current and repolarizes the plasma membrane.