We have collaborated with the Hara, Ahlgren and Sorenson laboratories in formulating a quantitative understanding of various aspects of islet development from their data. Although the islets of Langerhans occupy only about 1% volume of the pancreas, they play a critical role in the homeostasis of blood glucose. Islets have three major endocrine cell types. Alpha and beta cells secrete glucagon and insulin for counteracting low and high glucose levels, respectively. Delta cells secrete somatostatin which inhibits both glucagon and insulin secretion. Islets range in size from clusters of a few cells to several thousand cells. Furthermore, different species have different islet architectures. Rodent islets have a characteristic structure where beta cells are located in the islet core, while alpha and delta cells are distributed on the islet mantle. In human islets, on the other hand, non-beta cells are also distributed within the islet core. In spite of this anatomical knowledge, we still do not understand the design principles of islet architecture: the functional importance of islet size, and cell arrangement. In this review, we focus on some of the quantitative dynamic information that can be extracted from data on the size distributions of islets. Understanding how islets appear and grow in embryonic/neonatal development, pregnancy, aging, obesity, or type 1/2 diabetes, is important because islet number and size increases are directly related to the increase of beta-cell mass. However, it is technically intractable to examine the in vivo formation of new islets and the proliferation potential of cells in islets. Since real-time monitoring of changes in islets is currently not possible, most studies have relied on cross-sectional data from different animals at different conditions. In such studies it is necessary to extract significant changes between the different conditions that can be masked by large variations between individual animals. Changes in islet number and size can be statistically represented by changes in islet size distribution. In principle, therefore, we can examine biological processes in islets in various interesting conditions by mathematically analyzing changes in islet size distributions. A prerequisite for such analyses is the precise measurement of islet sizes. There are three ways to measure size of islets: (i) on an appropriately stained pancreatic section;(ii) after isolation from a pancreas;and (iii) in an intact pancreas. The first method has been used most frequently. Although this immunohistochemical method has the advantages that it allows high resolution imaging of islets on 2-dimensional pancreatic sections, and multiple stains for different molecules, it has the fundamental limitation of revealing only randomly placed cross-sections through islets. To quantitate characteristics of 3-dimensional islets, the second method isolates islets from the exocrine tissue. However, enzyme treatments used in the isolation process may affect islet morphology. In particular, some small islets may be lost during the isolation process. The last method is ideal for measuring sizes of entire islets without any modification. One difficulty is to distinguish islets from the exocrine pancreas. Dithizone and insulin antibody have been used to stain Zn2+ and insulin specifically expressed in beta-cells. Another novel way is to use a transgenic mouse that intrinsically expresses green fluorescent proteins specifically in beta-cells. To expose the stained or fluorescent islets embedded in the exocrine pancreas, the pancreas is placed between a glass slide and a cover slip. The projected area of each islet in an intact pancreas is measured. Note that once a pancreas loses its structural retention from the tight connection to the surrounding gut, duodenum, colon, and spleen, it naturally shrinks into a lump of soft tissue. When it is placed on a slide glass, it becomes a semi-2-dimensional object. A different approach uses optical projection tomography to measure islet size in an intact pancreas that is placed in agarose gel to preserve its 3-dimensional structure. Combined with these novel techniques, recent image analysis tools allow precise and automatic measurement of islet size, morphology, and location in a pancreas. Thus, current technologies fall short in their ability to monitor changes of islets in a live animal over a reasonably long period, but we can obtain precise measurement snapshots of islet size distributions from excised pancreata. Mathematical modeling can be used to overcome experimental limitations, and extract dynamic information based on the changes between the snapshots. In this review, we introduce a methodology for the inference of biological processes based on changes of (islet) size distributions. Similar mathematical methods have been used by us to analyze temporal changes of size distributions of fat cells. We have used mathematical modeling to model islet development in a variety of conditions, in development, in pregnancy, and in disease (type 1 and 2 diabetes). We are continuing our work to better understand the determinants of islet architecture, which varies between species, though the probability distributions of islet sizes are similar between species.
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