GLUT4 is an insulin-responsive glucose transporter protein and only exists embedded in membrane structures of adipocytes (fat) and muscle cells. It recycles to the plasma membrane (PM) via the endosomes but is also sequestered internally. When expressed on the PM it allows the transport of glucose in and out of the cell. The application of insulin releases otherwise sequestered GLUT4 to recycle to the PM. GLUT4 is exocytosed via small membrane vesicles, which fuse with the PM. The application of insulin to a cell in the basal state causes an initial burst of fusion events (which may be detected using TIRF microscopy) and then the rate returns to a steady lower level, in some cases similar to that observed in the basal case. However, the cell surface GLUT4 level remains 10-25-fold higher. It is also been observed that the endocytosis rate remains relatively constant irrespective of the insulin dose.
A model for this process is proposed, inspired by the presence of the microtubules that cross the cytoplasm of the cells. Microtubules are implicated in the sorting of different endocytic vesicular contents and have well characterised molecular motors which control the movement of vesicles down their lengths. GLUT4 vesicles have been observed to be transported along microtubules.
The GLUT4 recycling system is represented as a closed Markovian queueing network with finite capacity queues representing the microtubule system, and infinite server queues representing the diffusion and endocytosis of GLUT4 on the PM, and the release of vesicles from the endosomes.
The viability of the model is demonstrated via the calculation of the performance indices of the closed queueing network for some limiting cases and model simulations which are compared with experimental data of the GLUT4 trafficking system from TIRF and bulk assay experiments.