Figure 1.
Collective oscillations of a population of 2000 neurons.
(A) Raster plot of neurons (in red the excitatory and in black the inhibitory neurons) for a
interval. (B) LFP time trace in a
interval for an external mean rate of
. (C) MUA signal calculated counting the number of spikes of the neural population per unit time. (D) LFP power spectrum calculated using the Welch method averaged over
trials. The gray horizontal bar delimits the gamma peak band (
).
Figure 2.
Phase locking between LFP and MUA of a network.
(A) LFP-MUA phase coherence for a single population. (B) Angle histogram of the phase difference between the LFP and MUA. The measures are averaged over 200 trials.
Figure 3.
Collective oscillations of two coupled bidirectionally neural populations.
The inter-areal axonal delay between the two neuronal pools is zero. (A) LFP time trace of the two populations in a
interval, for an external mean rate of
. The inset shows the averaged time correlation of
LFP pairs. (B) Phase coherence between the LFPs of the two networks for varying frequency. The measure is averaged over
trials. The black dashed line represents the threshold (
) above which the phase coherence is considered significant (in red). (C) Time shift between the LFP oscillations of the networks for varying frequency. Red crosses show the time shifts corresponding to the frequencies at which the phase coherence is above threshold. The time shift is calculated as
, where
is the phase difference at the frequency
of maximum phase coherence. The gray bar delimits the gamma peak band (
). The measure is averaged over
trials.
Figure 4.
Phase coherence of two coupled bidirectionally neural populations for three different values of the inter-areal axonal delays .
Phase coherence spectrum and corresponding representative time series for (A,B),
(C,D), and
(E,F). The inter-areal delays follow a gamma distribution with a mean equal to corresponding inter-areal axonal delay
. The gray bars on the x-axes of plots A, C, and E delimit the gamma peak band (
). The phase coherence measure is averaged over
trials.
Figure 5.
Phase coherence and time shift behavior in the case of bidirectional symmetric coupling for increasing inter-areal axonal delays .
(A) Frequency (black arrow) at which the power spectrum is maximum and extent of the gamma peak (gray bar) (results for only one population are shown, since they are the same for both populations). (B) Frequencies at which the phase coherence exhibits local maxima,
. (C) Phase coherence, in color code, as a function of frequency (y-axis) and of the inter-areal axonal delay
(x-axis). (D) Time shift
at the peak frequency
of the power spectrum. (E) Time shift
at
, the frequencies labeled in (B). The red line corresponds to
. The labels in panels B and E correspond to panels of Figure 4. (F) Time shift
, in color code, as a function of frequency (y-axis) and of the inter-areal axonal delay
(x-axis). The solid black lines in panels C and F show
(as in panel B) and the dashed black line represents the power spectrum maximum within the gamma range shown in panel A. In plots A, B, and C the total extent of the gamma peak is displayed as a vertical gray bar. In plot D, the arrows point at the gamma period and half of it,
being
. The measures are averaged over
trials for each
.
Figure 6.
Phase coherence in the case of bidirectional asymmetric coupling for increasing extra inputs.
Phase coherence between LFPs of the two networks, in color code, as a function of frequency (y-axis) and of the inter-areal axonal delay (x-axis) for different stimuli: (A)
, (B)
, (C)
, (D)
. The measures are averaged over
trials for each
and stimulus.
Figure 7.
Time shift in the case of bidirectional asymmetric coupling for increasing extra inputs.
Effective time shift in milliseconds between LFPs of the two networks, in color code, as a function of frequency (y-axis) and of the inter-areal axonal delay (x-axis) for different stimuli: (A)
, (B)
, (C)
, (D)
. The measures are averaged over
trials for each
and stimulus.
Figure 8.
Time shift behavior at the peak of power spectrum for increasing inter-areal axonal delays for different extra inputs.
Effect of the external input perturbation on the coupled neuronal populations for increasing stimulus strengths . (A) Frequency of the power spectrum peak. (B) Time shift corresponding to spectral peak frequency. The dashed lines show the ideal cases for which
and its anti-phase equivalent.
Figure 9.
Mutual information carried by LFP and MUA power spectrum of the receiver.
Mutual information between the set of stimuli and the neural response given by the LFP (A) and MUA (B) power spectra for increasing coupling delays
. The gray arrow in the color scale refers to significance threshold (
, bootstrap test). The measures are averaged over
trials for each
and stimulus.
Figure 10.
Carriers of information and signals.
Diagram of two oscillatory LFPs filtered around the power spectrum peak (), with a short spike train locked at their troughs for different
: (A)
, representing zero-lag synchronization and (B)
, representing anti-phase synchronization.