Weibull-type limiting distribution for replicative systems

Development, growth and maintenance of β-cell mass: models are also part of the story

Pancreatic β-cells in the islets of Langerhans play a crucial role in regulating glucose homeostasis in the circulation. Loss of β-cell mass or function due to environmental, genetic and immunological factors leads to the manifestation of diabetes mellitus. The mechanisms regulating the dynamics of pancreatic β-cell mass during normal development and diabetes progression are complex. To fully unravel such complexity, experimental and clinical approaches need to be combined with mathematical and computational models. In the natural sciences, mathematical and computational models have aided the identification of key mechanisms underlying the behavior of systems comprising multiple interacting components. A number of mathematical and computational models have been proposed to explain the development, growth and death of pancreatic β-cells. In this review, we discuss some of these models and how their predictions provide novel insight into the mechanisms controlling β-cell mass during normal development and diabetes progression. Lastly, we discuss a handful of the major open questions in the field.

Mathematical models of pancreatic islet size distributions

The islets of Langerhans, ranging in size from clusters of a few cells to several thousand cells, are scattered near large blood vessels. While the β-cell mass in mammals is proportional to body weight, the size ranges of islets are similar between species with different body sizes, possibly reflecting an optimal functional size. The large range of islet sizes suggests a stochastic developmental process. It is not fully understood how islets develop to reach such size distributions, and how their sizes change under certain physiological and pathological conditions such as development, pregnancy, aging, obesity, and diabetes. The lack of a high-resolution in vivo imaging technique for pancreatic islets implies that the only data available to elucidate the dynamics of islet development are cross-sectional quantifications of islet size distributions. In this review, we infer biological processes affecting islet morphology in the large by examining changes of islet size distributions. Neonatal islet formation and growth is shown as a particular example of developing a mathematical model of islet size distribution. Application of this modeling to elucidate islet changes under other conditions is also discussed.