Power Laws from Linear Neuronal Cable Theory: Power Spectral Densities of the Soma Potential, Soma Membrane Current and Single-Neuron Contribution to the EEG
Figure 2
Normalized power spectral densities (PSDs) for the soma current, the current-dipole moment (i.e., EEG contribution) and the soma potential for a ball and stick neuron and a pyramidal neuron.
A homogeneous density of noisy input currents is applied throughout the neural membrane. Columns 1 (ball and stick neuron) and 2 (pyramidal neuron) show PSDs for white-noise input, the blue and green lines correspond to uncorrelated and correlated input currents, respectively. Note that there is no green line in the two upper rows, since a homogeneous density of correlated inputs throughout the neuron gives no net soma current or dipole moment. An ensemble of PSDs from 20 single input currents for the ball and stick neuron and 107 single input currents for the pyramidal neuron is shown in grey. The results for the most distal synapses are shown in dark grey and the results for the proximal synapses in light grey, corresponding to the color shown in the filled circles at the respective neuron morphology (between columns 1 and 2). Column 3 illustrates how different power-law spectra of the input currents change the output PSDs: the blue, pink and brown lines express the PSD for uncorrelated white (constant), pink () and Brownian noise input (
), respectively. The values of
in legends denote estimated power-law exponents at 1000 Hz, i.e., the negative discrete log-log derivative,
. In the rightmost column the values of
correspond to pink noise input, for Brownian noise input and white-noise input the values are ‘+1’ and ‘−1’ with respect to the pink input, respectively, as indicated by the brown ‘+’ and the blue ‘−’. The ball and stick neuron was simulated with 200 dendritic segments (corresponding to the default parameters listed in Table 1), while the pyramidal neuron was simulated with 3214 dendritic segments. Broken lines correspond to the ball and stick neuron, whole lines to the pyramidal neuron.