A MATHEMATICAL-MODEL OF OSCILLATORY INSULIN-SECRETION

Insulin is secreted in sustained oscillatory fashion from isolated isl ets of Langerhans. This finding has led to the assumption of an underl ying synchronizing process that coordinates insulin oscillations. This assumption was tested by developing a mathematical model of oscillato ry insulin secretion in which we included degree of synchrony as a par ameter. 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 u nits discharging at discrete intervals with the same underlying period . Variation from two sources, phase differences between units (synchro ny) 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 dif ferent values of S(g) and S(i) were run. Results of the simulations su ggest that the system tolerates a relatively large degree of asynchron y yet still demonstrates regularity of oscillations on spectral analys is. 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 th e study of mechanisms for insulin oscillations.