A MATHEMATICAL-MODEL OF OSCILLATORY INSULIN-SECRETION

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 (S(g) and S(i), respectively) to the secretory period. Sets of 100 simulations for different values of S(g) and S(i) 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.