Analysis of possible mechanisms for in vitro oscillations of insulin secretion

We explore possible kinetic mechanisms responsible for the oscillatory (pulsatile) secretion of insulin observed in vitro when pancreatic islets or islet-derived cells are perifused with glucose. Three primary processes are included: 1) glucose stimulation of insulin secretion, controlled by glucokinase; 2) uptake of glucose through GLUT transporters; and 3) glucose metabolism. Perifusion is approximated as a limiting case of a chemical flow reactor. Using experimentally determined rate laws for the three processes, we examine the effects of exogenous insulin as a phenomenological activator and inhibitor of secretion. The resulting differential equations support oscillations using either direct or indirect inhibition by insulin. The oscillations have many of the characteristics observed in vitro, although the indirect model is in better overall agreement with experiment. We conclude that the mechanisms explored here may help explain insulin oscillations for HIT cells, but not for islets, and predict that oscillations can be modulated by including insulin in the perifusion medium.