2 5 M ay 2 00 7 A modified cable formalism for modeling neuronal membranes at high frequencies

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.