Collective sensing of $\beta$-cells generates the metabolic code at optimal islet size

Major part of a pancreatic islet is composed of beta cells that secrete insulin, a key hormone regulating influx of nutrients into all cells in a vertebrate organism to support nutrition, housekeeping or energy storage. Beta cells constantly communicate with each other using both direct, short-range interactions through gap junctions, and paracrine long-range signaling. However, how these cell interactions shape collective sensing and cell behavior in islets that leads to insulin release is unknown. When stimulated by specific ligands, primarily glucose, beta cells collectively respond with expression of a series of transient Ca$^{2+}$ changes on several temporal scales. Here we analyze a set of Ca$^{2+}$ spike trains recorded in acute rodent pancreatic tissue slice under physiological conditions. We found strongly correlated states of co-spiking cells coexisting with mostly weak pairwise correlations widespread across the islet. Furthermore, the collective Ca$^{2+}$ spiking activity in islet shows on-off intermittency with scaling of spiking amplitudes, and stimulus dependent autoassociative memory features. We use a simple spin glass-like model for the functional network of a beta cell collective to describe these findings and argue that Ca$^{2+}$ spike trains produced by collective sensing of beta cells constitute part of the islet metabolic code that regulates insulin release and limits the islet size.