Identification of Capacitance Distribution in Neuronal Membranes from a Fractional-Order Electrical Circuit and Whole-Cell Patch-Clamped Cells

Abstract

Passive electrical membrane properties are key determinants of signaling processes in brain cells, influencing input-output responses as well as action potential firing. We propose a novel interpretation of patch-clamp recordings that brings out the fractional dynamic of the electrical properties of cell membranes and provides a better knowledge of their microscopic behavior. The passive electrical properties of the cell membrane were modeled using an electrical equivalent circuit (EEC) consisting of a constant phase element (CPE) in parallel with a resistor. The Mittag-Leffler function was used to describe the non-exponential behavior of the voltage transients that are attributable to the processes of charging and discharging the membrane capacitance. The procedure proposed, based on circuit theory and fractional calculus, was used to study the voltage transients obtained in response to low-amplitude hyperpolarizing current pulses applied to cultured mice dorsal root ganglion (DRG) neurons under whole-cell current-clamp configuration. To further validate the method, we also analyzed the voltage transients obtained from hippocampal pyramidal neurons and glial cells recorded in mice brain slices in vitro using the short-time behavior of the resulting membrane voltages.