The Beta Cell in Its Cluster: Stochastic Graphs of Beta Cell Connectivity in the Islets of Langerhans

Pancreatic islets of Langerhans consist of endocrine cells, primarily alpha, beta and delta cells, which secrete glucagon, insulin, and somatostatin, respectively, to regulate plasma glucose. beta cells form irregular locally connected clusters within islets that act in concert to secrete insulin upon glucose stimulation. Due to the central functional significance of this local connectivity in the placement of beta cells in an islet, it is important to characterize it quantitatively. However, quantification of the seemingly stochastic cytoarchitecture of beta cells in an islet requires mathematical methods that can capture topological connectivity in the entire beta-cell population in an islet. Graph theory provides such a framework. Using large-scale imaging data for thousands of islets containing hundreds of thousands of cells in human organ donor pancreata, we show that quantitative graph characteristics differ between control and type 2 diabetic islets. Further insight into the processes that shape and maintain this architecture is obtained by formulating a stochastic theory of beta-cell rearrangement in whole islets, just as the normal equilibrium distribution of the Ornstein-Uhlenbeck process can be viewed as the result of the interplay between a random walk and a linear restoring force. Requiring that rearrangements maintain the observed quantitative topological graph characteristics strongly constrained possible processes. Our results suggest that beta-cell rearrangement is dependent on its connectivity in order to maintain an optimal cluster size in both normal and T2D islets.