Multiscale Modeling of Electrical and Intracellular Activity in the Pancreas: The Islet Tridomain Equations

Abstract

We derive continuum models of the electrical syncytia of the pancreatic islet of Langerhans using homogenization. Beta-cells in the islets are coupled in their intra- and extracellular potential fields via membrane currents and can exchange calcium (and metabolite) via direct intracellular communication through gap junctional connections. In earlier work, Goel, Sneyd, and Friedman [Multiscale Model. Simul., 5 (2006), pp. 1045–1062] have derived homogenized models of cytosolic calcium and endoplasmic reticulum (ER) calcium in cells. The islet tridomain presented here extends that scheme to three domains: the extracellular space, the cytosol, and the intracellular ER (or sarcoplasmic reticulum (SR)) are each represented at every point in space. We also consider three different models of gap junctions: as pores, as semipermeable membranes, and as thin conductors. We derive the macroscopic equations for all three cases. The islet tridomain equations are different depending on the gap junction model. In additi...