Modeling the spatiotemporal distribution of Ca²⁺during action potential firing in human pancreaticβ-cells

Abstract

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.

Electrophysiological models of the human pancreatic δ‐cell: From single channels to the firing of action potentials

“…For the I KA current, we used the average values of the activation and inactivation time constants reported by Braun et al; that is, millisecond and milliseconds. The activation time constant of the L‐type Ca 2+ current and inactivation time constants of the T‐type Ca 2+ current and the voltage dependent Na + currents were estimated from the values reported in previous models of currents of human β‐cells (ie, τ mL = 1.25 ms, τ hT = 15 ms, τ Na = 2 ms) . For the I Kdr current, the time constants were modelled as a voltage‐dependent function, adopting the function obtained from the analysis of experimental data from human β‐cells (see Section 3.3).…”

“…It should be noted that since the I Kdr current in human δ‐cells shows an increasingly fast activation as the depolarizing pulse increases in magnitude (resembling the temporal course of the I Kdr currents in human β‐cells), the activation time constants for the I Kdr current were expressed as a voltage‐dependent function τ mKdr ( V m ). Due to the lack of experimental data specifically obtained from human δ‐cells, we adopted the voltage‐dependent function used in previous models of the human β‐cells (see Table ) …”

“…The activation time constant of the L-type Ca 2+ current and inactivation time constants of the T-type Ca 2+ current and the voltage dependent Na + currents were estimated from the values reported in previous models of currents of human β-cells (ie, τ mL = 1.25 ms, τ hT = 15 ms, τ Na = 2 ms). [26][27][28]31 For the I Kdr current, the time constants were modelled as a voltage-dependent function, adopting the function obtained from the analysis of experimental data from human β-cells (see Section 3.3). Experimental recordings of the macroscopic I Kdr currents showed a faster activation as the magnitude of the depolarized pulse increased, as was also observed in human β-cells (see fig.…”

“…Given the now known importance of paracrine signaling within the islets of Langerhans, mathematical modeling has been used to study the electrophysiological behavior of endocrine islet cells and the interactions between them within the pancreatic islets (see, for instance, Watts et al and Briant et al). It should be noted, however, that most of the models have been based on data from rodent cells, while only a few of them have been developed to describe the electrical activity of human β‐cells . While a model of the human α‐cell is still lacking, here, we present the first model of the electrical activity of the human δ‐cell.…”

“…It should be noted, however, that most of the models have been based on data from rodent cells, while only a few of them have been developed to describe the electrical activity of human β-cells. 19,[26][27][28][29] While a model of the human α-cell is still lacking, here, we present the first model of the electrical activity of the human δ-cell. Specifically, in this work, we aim to develop mathematical models capable of reproducing both the macroscopic currents and the action potentials generated in response to a glucose stimulus in human δ-cells based in the experimental work by Braun et al 1 2 | METHODOLOGY…”