A mathematical model of oscillatory insulin secretion

Abstract

Insulin is secreted in sustained oscillatory fashion from isolated islets of Langerhans. This finding has led to the assumption of an underlying synchronizing process that coordinates insulin oscillations. This assumption was tested by developing a mathematical model of oscillatory insulin secretion in which we included degree of synchrony as a parameter. We first evaluated insulin oscillations in perifused isolated rat islets, using spectral analysis to determine their regularity and frequency. A parsimonious mathematical model was developed to account for these characteristics. The model postulates a group of secretory units discharging at discrete intervals with the same underlying period. Variation from two sources, phase differences between units (synchrony) and regularity within units, is introduced by adding two normally distributed random variables with standard deviations (Sg and Si, respectively) to the secretory period. Sets of 100 simulations for different values of Sg and Si were run. Results of the simulations suggest that the system tolerates a relatively large degree of asynchrony yet still demonstrates regularity of oscillations on spectral analysis. Comparison with perifusion data suggests that a moderate degree of asynchrony between islets can best account for the pattern of insulin oscillations observed. This model provides a theoretical basis for the study of mechanisms for insulin oscillations.

Intra- and Inter-Islet Synchronization of Metabolically Driven Insulin Secretion

“…In contrast, it has been suggested that an intrapancreatic, neuronal pacemaker is responsible for synchronizing the pulsatile insulin secretion from the many islets in the pancreas (3,19,25). However, as mentioned, and studied previously (2,24,39), this would not explain how single islets or groups of islets can be entrained. If a pancreatic pacemaker was solely responsible for the entrainment, then this effect would be lost when the islets were separated from the pancreas.…”

“…However, pulsatile insulin secretion has been observed in individual b-cells (22) and islets (1,2,23), demonstrating that such a pacemaker has, at most, a synchronizing function. It has also been shown that groups of islets (2,24) and pieces of pancreas containing electrically silent ganglia (25) exhibit oscillatory release of the hormone. Hence, there must be additional synchronizing mechanisms.…”

The in vivo regulation of pulsatile insulin secretion

“…The coupling of cyclic metabolism to pulsatile in vitro release has been addressed in an excellent review by Tornheim [112]. Mathematical models have been used to better understand the mechanisms underlying coordinate pulsatile release [113,114]. Comparisons of exact measures of secretory burst shape, duration, frequency and secretory process orderliness of in vitro and in vivo insulin secretory bursts could further underline the link between intracellular beta-cell events, to large amplitude in vivo pulsatile insulin release.…”

Pulsatile Insulin Secretion: Detection, Regulation, and Role in Diabetes

“…As for the coupling of cyclic metabolism to pulsatile in vitro release, this has been addressed in detail in an excellent review by Tornheim (104). Mathematical models have been employed to improve understanding of the mechanisms underlying the coordinate pulsatile release (105,106). Comparison of exact measures of secretory burst shape, duration, frequency, and secretory process orderliness of in vitro and in vivo insulin secretory bursts may further underline the linkage from intracellular ␤-cell events to large amplitude in vivo pulsatile insulin release.…”