< Back to Article
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 9
Suggested scenario for generation of soma-potential noise in the in vivo situation with a combination of 
membrane current sources, presumably due to intrinsic ion channels, and synaptic current sources.
Both sources are assumed uncorrelated and homogeneously spread out across a ball and stick neuron. (A) Excerpt of real-time soma potential following injection of synaptic noise through an exponential synapse (white noise filtered through Eq. (117), blue line), 
noise, putatively from intrinsic ion channel (white noise filtered through a 
filter, red line), and sum of both (black line). (B) Histogram over soma potential for the three situations in A (50 s period with a sampling rate of 10 kHz). (C) Soma-potential PSDs for five cases: the three cases in A (
; exponential synapse, Eq. (117); sum of 
and exponential synapse) as well as alpha-function synapse (Eq. 118, green line) and sum of alpha-function synapse and 
(magenta line). All traces are normalized to the value of the summed PSDs for 
noise and exponential synapse for the lowest depicted frequency (0.1 Hz). (D) Locally (in frequency) estimated power-law coefficient 
, i.e., Eq. (116). The noise amplitudes are set so that soma-potential noise from (i) the 
current noise input has a standard deviation of 
= 0.6 mV (as seen in in vitro experiments [19]; frequencies between 0.2 and 100 Hz included in the noise variance sum) and (ii) total noise (synaptic+
) a standard deviation of 
= 2.5 mV (similar to in vivo experiments reported in Fig. 11 in [18]). Parameters used for the ball and stick neuron model is the default values (cf. caption of Fig. 3 and Table 1) except for the membrane resistance which has been reduced to 
to mimic an expected high conductance in an in vivo state [21]. The synaptic time constant is set to 
ms for the exponential synapse (Eq. 117) and 
ms for the alpha-function synapse (Eq. 118).
doi: https://doi.org/10.1371/journal.pcbi.1003928.g009