A threshold distribution hypothesis for packet storage of insulin and its mathematical modeling

Abstract

Phases of insulin release were studied in the perfused pancreas during a variety of glucose stimulation patterns. Patterns included staircase stimulations, constant prolonged single steps, restimulations, and ramp functions. Except at low concentrations, prolonged single steps of glucose elicited early spikes of insulin and a slowly rising second phase. Total insulin in the initial spikes increased with higher glucose concentrations. However, the time-related pattern of these spikes was similar in all cases; ratios of initial secretion rate to total insulin released were constant. Total insulin released in this early phase approximated a sigmoidal function of glucose concentration; mathematical differentiation of this function gave a skewed bell-shaped distribution curve. Staircase stimulations caused insulin to be released as a series of transient spikes which did not correlate with the increment of glucose but rather to the available insulin for a given glucose concentration minus that released in previous steps. The sum of total insulin released as spikes in a staircase series leading to a given glucose concentration was the same as when that concentration was used as a single step. Interrupted prolonged glucose infusions indicated the second phase of insulin release could prime the pancreas and that the first and second phases were interrelated. When glucose was perfused as ramp functions of slow, increasing, concentration, phasic response disappeared.A previous two-compartmental model was expanded to include a threshold or sensitivity distribution hypothesis. This hypothesis proposes that labile insulin is not stored in a homogeneous form but as packets with a bell-shaped distribution of thresholds to glucose. These packets respond quickly when their threshold levels to glucose are reached or exceeded. Data from single step stimulations were utilized for constructing a mathematical model which simulated satisfactorily the various stimulation patterns.