Abstract
Insulin released in response to a stepwise increase in glucose (square wave) is biphasic with a transient 5-10 min first-phase peak and a more sustained second phase. While the first phase is generally assumed to be rate-dependent and the second concentration-dependent, detailed studies of first-phase rate-sensitivity are lacking. We performed dynamic perifusion studies with human islets using customizable glucose ramps and established the corresponding insulin secretion time-profiles. First-phase release was defined as the excess insulin above that expected from the concentration-dependent second phase, and its dependence on the glucose gradient (rate of increase) was examined. The first-phase insulin release rate calculated this way increased with the gradient and fit well to a Hill-type sigmoid function with a half-maximal value around 1.25 mM/min (
=1.8,
=0.96). This aligns with our previously introduced glucose-insulin control system built on a general framework of a sigmoid proportional-integral-derivative (σPID) controller, a generalized PID controller more suitable for biological systems than linear ones as responses are bounded between zero and a maximum. Experimental results were used to slightly recalibrate this local glucose concentration-based computational model resulting in predictions in good agreement with measured first- and second-phase insulin secretions (
>0.90). Thus, glucose-stimulated insulin secretion (GSIS) of perifused human islets can be described well as the sum of a mainly rate-sensitive first phase, which is a sigmoid function of the glucose gradient with half-maximal activation around 1.25 mM/min, and a concentration-sensitive second phase, which is a sigmoid function of the glucose concentration with half-maximal activation near 8 mM.