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. We have collaborated with the Hara laboratory for a number of years in work aimed at elucidating the structure of islets of Langerhans and how this structure might be altered in diabetes. β cells form 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. Graph theory provides a framework for such a characterization of β-cell mass, enabling quantification of the cytoarchitecture of the entire β-cell population in an islet. 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. Characterization alone does not afford insights into the processes maintaining this architecture. Here we formulate a dynamic graph theory of β-cell rearrangement in whole islets, to find the combination of processes that maintains equilibrium throughout a lifespan, as quantified by the invariance of graph characteristics. We found possible dynamic models to be highly constrained by topological characteristics of islet cytoarchitecture. An extensive search of parameter spaces for several degree- and age-dependent dynamic graph models showed the observed graph characteristics to be unattainable. These were achieved only when the removal of a β cell was dependent on the size of its cluster, independent of β-cell appearance. A modest increase in this size from control resulted in architecture found in T2D. Our results suggest that β-cell movement is not dependent on its connectivity or age but rather that it is used to maintain an optimal cluster size in both normal and T2D islets. The architectural quantification method developed here may aid in the assessment of islet transplant viability.
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