Size Distribution of Mouse Langerhans Islets

Abstract

Pancreatic beta-cells are clustered in islets of Langerhans, which are typically a few hundred micrometers in a variety of mammals. In this study, we propose a theoretical model for the growth of pancreatic islets and derive the islet size distribution, based on two recent observations: First, the neogenesis of new islets becomes negligible after some developmental stage. Second, islets grow via a random process, where any cell in an islet proliferates with the same rate regardless of the present size of the islet. Our model predicts either log-normal or Weibull distributions of the islet sizes, depending on whether cells in an islet proliferate coherently or independently. To confirm this, we also measure the islet size by selectively staining islets, which are exposed from exocrine tissues in mice after enzymatic treatment. Indeed revealed are skewed distributions with the peak size of approximately 100 cells, which fit well to the theoretically derived ones. Interestingly, most islets turned out to be bigger than the expected minimal size (approximately 10 or so cells) necessary for stable synchronization of beta-cells through electrical gap-junction coupling. The collaborative behavior among cells is known to facilitate synchronized insulin secretion and tends to saturate beyond the critical (saturation) size of approximately 100 cells. We further probe how the islets change as normal mice grow from young (6 weeks) to adult (5 months) stages. It is found that islets may not grow too large to maintain appropriate ratios between cells of different types. Our results implicate that growing of mouse islets may be regulated by several physical constraints such as the minimal size required for stable cell-to-cell coupling and the upper limit to keep the ratios between cell types. Within the lower and upper limits the observed size distributions of islets can be faithfully regenerated by assuming random and uncoordinated proliferation of each beta-cell at appropriate rates.

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

“…Jo et al (Jo et al, 2007) provided the theoretical foundations to investigate islet cell proliferation by implementing a branching cell division model with coherent proliferation. Cells replicate with a probability λ, and do not replicate with the complementary probability (1- λ) (Figure 4A).…”

Pancreatic beta cell lines and their applications in diabetes mellitus research

“…An adult mammalian pancreas is composed of an exocrine and an endocrine part, the latter containing groups of cells, the islets of langerhans, which play a key role in maintaining the appropriate level of nutrients in the blood and cellular depots (Jo et al, 2007). the islets of langerhans (Fig.…”

Phase transitions in pancreatic islet cellular networks and implications for type-1 diabetes

“…Figure 3 presents simulation results for R versus p for a set of 3D HCP lattices of varying network size N, all within the range of real islets which usually contain several thousand cells [58,59]. Plotted are the canonical mean: $$Rfalse(pfalse)=\sum _{n=0}^N\left(\begin{array}{c}N\\ n\end{array}\right)p^n{(1-p)}^{N-n}{R}_n,$$ where n is the number of occupied sites, and R n is the corresponding probability that, for any network of size N given exactly n of its sites occupied, there exists a cluster of connected nodes spanning the network in all three directions.…”