Mathematical Modelling of Insulin Regulation in Glucose Transport

Mammalian cells regulate glucose levels by translocating membrane embedded glucose transporter proteins to and from their outer cell membranes. The predominant transporter in fat and muscle cells is GLUT4 which is insulin-responsive.

The pathway by which the arrival of insulin triggers the translocation of GLUT4 can be considered as a black box where key biochemical players in the networks are known, but the structure and interactions between them are not. The aim of this mathematical modelling is to determine where the different effectors and perturbations impinge on the signalling network, giving valuable biological insight into the operation of the system. The modelling also allows the exploration of a variety of “what-if” scenarios that are difficult or impossible to implement experimentally.

At a smaller biophysical scale however, we know that GLUT4 is embedded in vesicles (small spheres of membrane) for transport. The vesicles then fuse with the destination membrane, and the GLUT4 is released. It has been suggested that the insulin regulation of vesicle fusion is not only limiting the appearance of GLUT4 at the cell surface but also regulating the drain on internal stores, and the extent to which vesicles are associated with the cell cytoskeleton. There is also evidence that the vesicles transit along microtubules suggesting that queues may be an appropriate model for the response of the system to insulin.

I will present some methods that I have been developing to create mean-field coupled ODE models of the translocation of GLUT4 in response to insulin and discuss some of the directions for the models of the underlying microscale system.