A primer on modelling pancreatic islets: from models of coupled β-cells to multicellular islet models

Abstract

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.

Keywords: Computational model; diabetes mellitus; gap-junctions; islets; mathematical model; paracrine.

Graphical abstract

Figure 1.

A. Electrical coupling through gap-junctions between three hypothetical β-cells can be modeled using Eq. 2 where $I_{ion,i}$ represents the currents through the ionic channels and the coupling currents $I_{12}$, $I_{13}$ (and $I_{21}$, $I_{31}$) are described by Eq. 1. B. Other models considered the changes in concentration and flow of ions (e.g., Ca²⁺ and K⁺) and metabolites (e.g., FBP, G6P) through gap-junctions (GJ) in addition to the voltage differences between connected cells.

Figure 2.

A. One-dimensional arrangement of clusters of cells including a coupled pair of cells and an open-ended line composed of 10 coupled cells. According to the continuous approximation, the propagation of electrical signals through a linear arrangement of cells can be approximated by Eq. 5 where it is assumed that each cell contributes with ∆x to the length of the continuous line (see main text for details). B. Bi-dimensional arrangement of cells including the simple and hexagonal cubic packing (SCP and HCP, respectively). C-F. Three-dimensional structures used in multicellular models of pancreatic cells. In C-E, green and black cells represent active and inactive cells, respectively, as modeled using the discrete probabilistic approach based on percolation theory. In F, red, green and blue cells represent the ɑ, β and δ-cells, respectively.

Figure 3.

A. According to the channel sharing and heterogeneity hypothesis, robust bursting observed in β-cells of intact islets (top panel) is a result of coupling of a large number of cells, while in small clusters (middle panel) and isolated cells (bottom panel), irregular bursting is regularly observed. B. A simulated islet composed of heterogeneous β-cells (i.e., slow and fast bursting cells) show intermediate bursting as a result of cell coupling. C. The origin and propagation of waves in clusters of β-cells has been an aspect extensively studied using computational models. D. Multicellular models have been used to evaluate the existence and role of hubs, leader and first responder β-cells. E. Following a glucose challenge, first responder cells participate during the first phase of oscillations while hub and leader cells are thought to be relevant during the second phase.

Figure 4.

A. Diagram of the communication signals included in the multicellular model of Briant et al. When active, β-cells promote the activity of δ-cells due to the electrical communication between them via gap-junctions. Somatostatin secretion then inhibits the secretion of glucagon from ɑ-cells. B. The model by Watts et al. includes paracrine signals between the three types of cells. C. Model of coupled oscillators used by Hoang et al. to simulate the paracrine interactions between the ɑ, β and δ-cells. Note that only one cell of each type is shown while the model included hundreds or thousands of cells. ATP: adenosine triphosphate, KATP: ATP-dependent K⁺ channels, VDCC: voltage-dependent Ca²⁺ channels, GJ: gap-junctions, GIRK: G-protein coupled inwardly-rectifying K⁺ channel.