Fractal Behavior of the Pancreatic ß-Cell Near the Percolation Threshold: Effect of the KATP Channel On the Electrical Response.

The molecular system built with true chemical bonds or strong molecular interaction can be described using conceptual mathematical tools. Modeling of the natural generated ionic currents on the human pancreatic ß-cell activity had been already studied using complicated analytical models. In our present contribution, we prove the same using our simple electrical model. The ionic currents are associated with different proteins membrane channels (K-Ca, K(v), K(ATP), Ca(v)-L) and Na/Ca Exchanger (NCX). The proteins are Ohmic conductors and are modeled by conductance randomly distributed. Switches are placed in series with conductances in order to highlight the channel activity. However, the KATP channel activity is stimulated by glucose, and the NCX's conductance change according to the intracellular calcium concentration. The percolation threshold of the system is calculated by the fractal nature of the infinite cluster using the Tarjan's depth-first-search algorithm. It is shown that the behavior of the internal concentration of Ca(2+) and the membrane potential are modulated by glucose. The results confirm that the inhibition of KATP channels depolarizes the membrane and increases the influx of [Ca(2+)]i through NCX and Ca(v)-L channel for high glucose concentrations.

Modelisation of the contribution of the Na/Ca exchanger to cell membrane potential and intracellular ion concentrations.

Modelisation plays a significant role in the study of ion transfer through the cell membrane and in the comprehension of cellular excitability. We were interested in the selective ion transfers through the K(Ca), Na(v), Ca(v) channels and the Na/Ca exchanger (NCX). The membrane behaves like an electric circuit because of the existence of ion gradients maintained by the cell. The non-linearity of this circuit gives rise to complex oscillations of the membrane potential. By application of the finite difference method (FDM) and the concept of percolation we studied the role of the NCX in the regulation of the intracellular Ca(2+) concentration and the oscillations of the membrane potential. The fractal representation of the distribution of active channels allows us to follow the diffusion of intracellular Ca(2+) ions. These calculations show that the hyperpolarization and the change in the burst duration of the membrane potential are primarily due to the NCX.