A modified cable formalism for modeling neuronal membranes at high frequencies

¹ CNRS

^* To whom correspondence should be addressed. E-mail: destexhe{at}iaf.cnrs-gif.fr.

Submitted on May 25, 2007
Revised on June 11, 2007
Accepted on 11 September 2007

	Abstract

Intracellular recordings of cortical neurons in vivo display intense subthreshold membrane potential (V_m) activity. The power spectral density (PSD) of the V_m displays a power-law structure at high frequencies (>50Hz) 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.

Key Words: Cable equations, Dendrites, Membrane noise, Membrane potential, Voltage attenuation