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 α, β and δ cells, which secrete glucagon, insulin, and somatostatin, respectively, to regulate plasma glucose. β 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 β cells in an islet, it is important to characterize it quantitatively. However, quantification of the seemingly stochastic cytoarchitecture of β cells in an islet requires mathematical methods that can capture topological connectivity in the entire β-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 β-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 β-cell rearrangement is dependent on its connectivity in order to maintain an optimal cluster size in both normal and T2D islets.Author Summary: High or low blood glucose levels are detrimental to human health. The hormone-secreting cells primarily responsible for maintaining glucose at physiologically appropriate levels are embedded in small clusters within the pancreas, the so-called islets of Langerhans. These islets have an irregular arrangement of cells, β cells that secrete insulin, α cells that secrete glucagon, and other cells with less well-understood functions. While the arrangement of β cells is irregular, these cells need to be touching for the islet to respond to glucose with insulin secretion. We first use a mathematical formalism called graph theory to show that cell arrangements in islets from diabetic and control donors are significantly different. The question we then address is: Is there some set of moves of islet cells that will preserve the observed arrangement? The aim is to gain insight into the biological processes by which islets are formed and maintained. We find moves on β-cell graphs that leave the same significant aspects of cell arrangements unchanged. These moves turn out to be severely restricted, and suggest that β cells may prefer to move from larger clusters but can move to a cluster of any size, possibly to maximize their exposure to blood vessels.