Mathematical modeling of the electrical activity of the pancreatic β-cell has been extremely important for understanding the cellular mechanisms involved in glucose-stimulated insulin secretion. Several models have been proposed over the last 30 y, growing in complexity as experimental evidence of the cellular mechanisms involved has become available. Almost all the models have been developed based on experimental data from rodents. However, given the many important differences between species, models of human β-cells have recently been developed. This review summarizes how modeling of β-cells has evolved, highlighting the proposed physiological mechanisms underlying β-cell electrical activity.

Intra-islet communication via electrical, paracrine and autocrine signals, is highly dependent on the organization of cells within the islets and is key for an adequate response to changes in blood glucose and other stimuli. In spite of the fact that relevant structural differences between mouse and human islet architectures have been described, the functional implications of these differences remain only partially understood. In this work, aiming to contribute to a better understanding of the relationship between structural and functional properties of pancreatic islets, we reconstructed human and mice islets in order to perform a structural comparison based on both morphologic and network-derived metrics. According to our results, human islets constitute a more efficient network from a connectivity viewpoint, mainly due to the higher proportion of heterotypic contacts between islet cells in comparison to mice islets.

We outline a general methodology based on computational optimization and experimental data to reconstruct human pancreatic islet architectures. By using the nuclei coordinates of islet cells obtained through DAPI staining, cell types identified by immunostaining, and cell size distributions estimated from capacitance measurements, reconstructed islets composed of non-overlapping spherical cells were obtained through an iterative optimization procedure. In all cases, the reconstructed architectures included >99% of the experimental identified cells, each of them having a radius within the experimentally reported ranges. Given the wide use of mathematical modeling for the study of pancreatic cells, and recently, of cell-cell interactions within the pancreatic islets, the methodology here proposed, also capable of identifying cell-to-cell contacts, is aimed to provide with a framework for modeling and analyzing experimentally-based pancreatic islet architectures.

Pancreatic islets are mini-organs composed of hundreds or thousands of ɑ, β and δ-cells, which, respectively, secrete glucagon, insulin and somatostatin, key hormones for the regulation of blood glucose. In pancreatic islets, hormone secretion is tightly regulated by both internal and external mechanisms, including electrical communication and paracrine signaling between islet cells. Given its complexity, the experimental study of pancreatic islets has been complemented with computational modeling as a tool to gain a better understanding about how all the mechanisms involved at different levels of organization interact. In this review, we describe how multicellular models of pancreatic cells have evolved from the early models of electrically coupled β-cells to models in which experimentally derived architectures and both electrical and paracrine signals have been considered.

We developed a model of a human β -cell by coupling a model of the electrical activity to a model of the buffered diffusion of Ca ²⁺ in a three-dimensional cell in order to simulate the spatiotemporal distribution of Ca ²⁺ in the intracellular space. Action potentials were produced by a Hodgkin-Huxley type model including different types of K ⁺ , Na ⁺ and Ca ²⁺ ionic channels while the buffered diffusion of Ca ²⁺ was simulated using the finite element method. In this model, Ca ²⁺ -dependent mechanisms (i.e. ionic channels and Ca ²⁺ extrusion mechanisms) are directly regulated by the concentration of Ca ²⁺ at the submembrane space estimated from the diffusion model. According to our simulations, the Ca ²⁺ transients produced by the electrical activity pattern are capable of reaching depths as high as 3 μ m from the Ca ²⁺ channels despite the buffering properties of the cytosol. In addition, we show that the activity of both Ca ²⁺ buffers and Ca ²⁺ extrusion mechanisms allows the continuous firing of action potentials by preventing the accumulation of Ca ²⁺ in the vicinity of the cell membrane. Finally, our simulations suggest that submembrane Ca ²⁺ domains are produced by the overlapping of Ca ²⁺ signals from neighbor clusters of Ca ²⁺ channels. In general, we present a model of the human pancreatic β -cell based on a new modeling framework that, in addition to simulate the electrical activity of the cell, is capable of considering the geometrical and spatial aspects of the cell in order to determine the temporal course of the Ca ²⁺ signal in the intracellular space.

The continuous interaction between experimental and theoretical work has proven to be extremely useful for the study of pancreatic cells and, recently, of pancreatic islets. This prolific interaction relies on the capability of implementing computational models and methods to derive quantitative data for the analysis and interpretation of experimental observations. In this addendum I introduce Isletlab, a multiplatform application developed to provide the research community with a user-friendly interface for the implementation of computational algorithms for the characterization and simulation of pancreatic islets.