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 addition, we study the consequences of beta-cell heterogeneity, and the arrangement of heterogeneous cells in the islet, for the macroscopic equations.