Tolic, Mosekilde, Sturis, 2000

Model Status

This is the original unchecked version of the model imported from the previous CellML model repository, 24-Jan-2006.

Model Structure

Endocrine systems often secrete hormones in pulses. Examples include the release of growth hormone and gonadotropins, and also the secretion of insulin from the pancreas, which are secreted over intervals of 1-3 hours and 80-150 minutes respectively. It has been suggested that relative to constant or stochastic signals, oscillatory signals are more effective at producing a sustained response in the target cells. In addition to the slow insulin oscillations, there are more rapid pulses that occur every 8-15 minutes. The mechanisms underlying both types of oscillations are not fully understood, however it is thought that the more rapid oscillations may arise from an intrapancreatic pacemaker mechanism. One possible explanation of the slow insulin oscillations, is an instability in the insulin-glucose feedback system. This hypothesis has been the subject of a number of studies, including some which have developed a mathematical model of the insulin-glucose feedback system.

In 2000, Iva Marija Tolic, Erik Mosekilde and Jeppe Sturis published a paper, based on a previously published mathematical model of the insulin-glucose feedback regulation. They hoped to identify a possible mechanism behind the efficiency of oscillatory insulin secretions. Analysis of the original model revealed that the slow oscillations of insulin secretion could arise from a Hopf bifurcation in the insulin-glucose feedback mechanism. The model included several feedback loops (see the figure below), including: glucose stimulating pancreatic beta cells to secrete insulin, insulin stimulating glucose uptake and inhibiting hepatic glucose production, and also positive feedback as glucose enhances its own uptake. The model includes two significant delays, reflecting the fact that the effect of insulin on glucose utilisation is dependent on the concentration of insulin in a slowly equilibrating intercellular compartment as opposed to the concentration of the plasma insulin. The other delay is due to the time lag between the appearance of insulin in the plasma and its inhibitory effect on hepatic glucose production.

In order to gain insight into certain features of the model, Tolic et al. simplified it (version 2). In addition, they developed a third version of the model which accounted for the effect of hyperglycemic conditions on glucose production (version 3).

Model simulations suggested to Tolic et al. that the interaction of the oscillatory insulin supply with the glucose receptors of the glucose utilising cells was of minimal importance. This was because the oscillations in the concentration of the intercellular insulin were small, and changes in the average glucose utilisation only depend weakly on amplitude. However, with their model they were able to resolve conflicting results from clinical studies. Different experimental conditions will influence hepatic glucose release. If hepatic glucose release is occurring near its maximum limit, an oscillatory insulin supply will be more effective at lowering the blood glucose level than a constant supply. However, if the insulin level is sufficiently high to cause the hepatic release of glucose to virtually disappear, the opposite is observed. For insulin concentrations close to the point of inflection of the insulin-glucose dose-response curve, an oscillatory and a constant insulin secretion produce similar effects.

The complete original paper reference is cited below:

Modelling the Insulin-Glucose Feedback System: The Significance of Pulsatile Insulin Secretion, Iva Marija Tolic, Erik Mosekilde and Jeppe Sturis, 2000, Journal of Theoretical Biology , 207, 361-375. (A PDF version of the article is available to subscribers of the Journal of Theoretical Biology website.) PubMed ID: 11082306

A simplified diagram of the model. There are three main variables: G which represents the amount of glucose in the intercellular space and in the plasma, Ip which represents the amount of insulin in the plasma, and Ii which is the amount of insulin in the intercellular space. The black arrows represent transmembrane glucose and insulin exchange. The green arrows represent positive feedback loops.