On the emergent dynamics and synchronization of β-cells networks in response to space-time varying glucose stimuli

Recent findings based on calcium fluorescence imaging of pancreatic islets, also combined with optoge- netic techniques, showed that β-cells synchronization underlie a small-world and scale-free functional organization, where specified hubs are responsible of the emergent coordination in electrical activity. De- spite these features were suggested to be linked to an efficient spreading of information and calcium waves, it is still unclear from what they emerge, if they can still be observed when different dynamical variables are used to build functional networks, and how they vary upon changes in control parameters. In this work we investigate this aspect with a novel hybrid discrete-continuum mathematical model, coupling the stochastic electrical dynamics of β-cell clusters to nonlinear reaction–diffusion of glucose. By analyzing cells activity with the use of dynamical functional networks computed on the correlations between cells membrane voltage signals, we recover functional features in accordance to experimental observations. We further show that such properties are observed during specific phases of the complex electrical bursting oscillation, and are affected by glucose diffusion. These results suggest that functional properties derived from experimental calcium signals, on a time scale on the order of tens of seconds, are also recovered at a much faster time scale, i.e., on the order of hundreds of milliseconds. We finally de- scribe how such functional features are strongly linked to synchronization patterns, in which coordinated sub-clusters of cells naturally emerge from the underlying dynamics.