A modified cable formalism for modeling neuronal membranes at high frequencies

TL;DR

This paper introduces a modified cable model incorporating non-ideal capacitors to better explain high-frequency membrane potential activity in neurons, aligning theoretical predictions with experimental observations.

Contribution

It develops an analytical non-ideal cable model that accurately captures high-frequency membrane dynamics, improving upon traditional models.

Findings

Non-ideal cable models match experimental high-frequency PSD slopes.

High frequencies are transmitted more effectively in non-ideal cables.

Traditional models underestimate high-frequency membrane activity.

Abstract

Intracellular recordings of cortical neurons in vivo display intense subthreshold membrane potential (Vm) activity. The power spectral density (PSD) of the Vm displays a power-law structure at high frequencies (>50 Hz) with a slope of about -2.5. This type of frequency scaling cannot be accounted for by traditional models, as either single-compartment models or models based on reconstructed cell morphologies display a frequency scaling with a slope close to -4. This slope is due to the fact that the membrane resistance is "short-circuited" by the capacitance for high frequencies, a situation which may not be realistic. Here, we integrate non-ideal capacitors in cable equations to reflect the fact that the capacitance cannot be charged instantaneously. We show that the resulting "non-ideal" cable model can be solved analytically using Fourier transforms. Numerical simulations using a ball-and-stick model yield membrane potential activity with similar frequency scaling as in the experiments. We also discuss the consequences of using non-ideal capacitors on other cellular properties such as the transmission of high frequencies, which is boosted in non-ideal cables, or voltage attenuation in dendrites. These results suggest that cable equations based on non-ideal capacitors should be used to capture the behavior of neuronal membranes at high frequencies.