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

Minimal mathematical models were developed to describe the electrophysiological properties of human δ-cells. Markov models of single channels were first developed based on the analysis of electrophysiological data. Monte Carlo simulations of voltage-clamp experiments were performed in an iteratively optimization procedure to estimate the number of channels required to reproduce the main characteristics of the macroscopic currents recorded experimentally. A membrane model of the firing of action potentials was then developed based on the kinetic schemes of single channels and the number of channels estimated. We showed that macroscopic currents of human δ-cells can be reproduced by minimal models of single channels when the appropriate number of channels is considered. In addition, our simulations suggest that human δ-cells are capable of generating action potentials through the interaction of the ionic currents involved. Finally, we determined the relative contribution of the currents underlying the firing of action potentials in human pancreatic δ-cells, which allowed us to propose a qualitative model of an action potential in terms of the underlying ionic currents.