Heterogeneity and nearest-neighbor coupling can explain small-worldness and wave properties in pancreatic islets

Many multicellular systems consist of coupled cells that work as a syncytium. The pancreatic islet of Langerhans is a well-studied example of such a microorgan. The islets are responsible for secretion of glucose-regulating hormones, mainly glucagon and insulin, which are released in distinct pulses. In order to observe pulsatile insulin secretion from the β-cells within the islets, the cellular responses must be synchronized. It is now well established that gap junctions provide the electrical nearest-neighbor coupling that allows excitation waves to spread across islets to synchronize the β-cell population. Surprisingly, functional coupling analysis of calcium responses in β-cells shows small-world properties, i.e., a high degree of local coupling with a few long-range "short-cut" connections that reduce the average path-length greatly. Here, we investigate how such long-range functional coupling can appear as a result of heterogeneity, nearest-neighbor coupling, and wave propagation. Heterogeneity is also able to explain a set of experimentally observed synchronization and wave properties without introducing all-or-none cell coupling and percolation theory. Our theoretical results highlight how local biological coupling can give rise to functional small-world properties via heterogeneity and wave propagation.