Albert Goldbeter and Nicolas Markadieu

Unite de Chronobiologie theorique, Faculte des Sciences,
Universite Libre de Bruxelles, B-1050 Brussels, Belgium

On the basis of experimental observations, it has been suggested that
glycolytic oscillations underlie the pulsatile secretion of insulin by
pancreatic beta cells, with a periodicity of about 13 min. If this were the
case, the question arises as to how beta cells located in different islets
of Langerhans synchronize to produce oscillations in plasma levels of
insulin. In the absence of synchronization of different islets, a flat
profile of insulin would indeed be expected instead of the observed
oscillations. We have addressed this question by means of a theoretical
approach based on the use of a two-variable model for glycolytic
oscillations. In spite of its simplicity, this model of a product-activated
allosteric enzyme reaction accounts for a large number of observations on
the role of phosphofructokinase in glycolytic oscillations. We investigate
the various modes of dynamic behavior resulting from the coupling of
several glycolytic oscillators, when taking into account the regulation
exerted by insulin on the level of glucose which serves as substrate for
glycolytic oscillations. Thus the coupling occurs in the model through the
secretion of insulin by pancreatic beta cells undergoing glycolytic
oscillations, via the control of the substrate (glucose) input to all
oscillators present in the medium. Bifurcation diagrams are obtained for
the cases where insulin secretion is controlled by the product or by the
substrate of the glycolytic oscillator. Conditions where the oscillators
operate in or out of phase will be described.