  Using the FitzHugh-Nagumo equations to represent the oscillatory electrical
behavior of beta-cells, we develop a coupled oscillator network model with
cubic lattice topology, showing that the emergence of pacemakers or hubs in the
system can be viewed as a natural consequence of oscillator population
diversity. The optimal hub to non hub ratio is determined by the position of
the diversity-induced resonance maximum for a given set of FitzHugh-Nagumo
equation parameters and is predicted by the model to be in a range that is
fully consistent with experimental observations. The model also suggests that
hubs in a beta-cell network should have the ability to "switch on" and "off"
their pacemaker function. As a consequence, their relative amount in the
population can vary in order to ensure an optimal oscillatory performance of
the network in response to environmental changes, such as variations of an
external stimulus.
