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.

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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 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 μm 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.

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Promising strategies for neural tissue engineering are based on the use of three-dimensional substrates for cell anchorage and tissue development. In this work, fibrillar scaffolds composed of electrospun randomly- and aligned-oriented fibers coated with plasma synthesized pyrrole polymer, doped and undoped with iodine, were fabricated and characterized. Infrared spectroscopy, thermogravimetric analysis, and X-ray diffraction analysis revealed the functional groups and molecular integration of each scaffold, as well as the effect of plasma polymer synthesis on crystallinity. Scanning microscopy imaging demonstrated the porous fibrillar micrometric structure of the scaffolds, which afforded adhesion, infiltration, and survival for the neural cells. Orientation analysis of electron microscope images confirmed the elongation of neurite-like cell structures elicited by undoped plasma pyrrole polymer-coated aligned scaffolds, without any biochemical stimuli. The MTT colorimetric assay validated the biocompatibility of the fabricated composite materials, and further evidenced plasma pyrrole polymer-coated aligned scaffolds as permissive substrates for the support of neural cells. These results suggest plasma synthesized pyrrole polymer-coated aligned scaffolds are promising materials for tissue engineering applications.