Fig 1.
Schematic of model used in the simulations.
Two neocortical areas were uni-directionally connected via a feedforward connection. Both areas consisted of excitatory (RS) neurons and inhibitory (FS, LTS) neurons. Reciprocal connections existed between the excitatory and inhibitory populations within one area. Neurons of each cell type were also recurrently connected within each area. The input to the FS neurons was modulated by an alpha-band oscillatory drive from the pulvinar. The pulvinar neurons were not explicitly modeled. The effect of varying the relative alpha phase Δϕ on communication between the neocortical areas was tested.
Fig 2.
Gamma oscillations emerged spontaneously from the reciprocal interaction between E cells and I cells.
(A) Rastergram of excitatory (red) and inhibitory (blue) neurons in one population during an interval of 1000 ms. Gamma oscillations are visible as vertical alignment of spike times. (B) The spike time histogram (STH) reveals the gamma oscillations (bin width Δt = 1 ms) in both excitatory and inhibitory cells. (C) The power spectral density of the E-population STH, showing gamma oscillations between 30 and 50 Hz. Data was averaged over 10 trials, the shaded areas represent the standard error of the mean (SEM). (D) Increasing the input current to excitatory neurons increases gamma power, while increasing input current to the inhibitory neurons decreases gamma power. The current to excitatory cells is varied along the y-direction, whereas that to the inhibitory cells is varied along the x-axis, the resulting gamma power is color-coded according to the color bar shown on the right of the panel. (E) The frequency of the gamma oscillation increases with increasing input to the excitatory as well as the inhibitory neurons.
Fig 3.
The alpha drive from the pulvinar modulates gamma power in a phasic manner.
(A,B) The alpha modulation from the pulvinar drive to the I-cells is clearly visible in both (A) the rastergram and (B) the STH. (C) The power spectral density of the E-cell STH had peaks both in the alpha and gamma band. Data was averaged over 10 trials, the shaded areas represent the standard error of the mean (SEM). (D) The gamma power was modulated by the phase of the alpha oscillation. Top: The spectrogram obtained via a wavelet analysis. Bottom: The gamma power (20–50 Hz; green line) is locked to the phase of the modulating alpha oscillation (blue line). (E) The gamma power (green line) follows the peak activity of excitatory neurons (red line), whereas the peak for the inhibitory neuronal firing (blue line) is approximately out of phase with gamma power. Data was averaged over 10 trials, the error bars represent the standard error of the mean (SEM).
Fig 4.
Gamma coherence is modulated by the phase difference between the alpha oscillations from the pulvinar that each area receives.
For all panels data was averaged over 10 trials, the error bars or shaded areas represent the standard error of the mean (SEM). (A) Gamma coherence between area 1 and 2 depends strongly on the alpha phase difference. The blue arrow indicates the optimal and the green arrow indicates the least optimal alpha phase difference. (B) The firing rate of excitatory (red) and inhibitory (blue) neurons of the second area did not vary strongly with alpha phase difference. (C,D) The overall coherence can be resolved in a contribution due to a correlation in amplitude and a phase coherence, which are shown panel C and D, respectively. The amplitude coherence varied much less with alpha phase difference than the phase coherence. The dashed line in A,C, and D represent the bias in the coherence, which was determined by calculating the coherence between randomly shuffled trials. The amplitude coherence is more strongly biased than the phase coherence, due to the similar alpha modulation in both areas. (E) When comparing the coherence spectrum for the optimal alpha phase (-90°, blue) with the least optimal alpha phase (90°, green), the difference in coherence occurs only in to the gamma band, the peak of the coherence in the alpha band is unaffected. (F) The strength of the modulation with alpha phase increases with the amplitude of the alpha modulation, primarily by reducing the coherence at the least optimal alpha phase.
Fig 5.
Spiking activity of individual neurons is coupled to local gamma rhythms.
The conditions with the best alpha phase difference (blue) and the worst alpha phase difference (green) are compared. (A) Normalized spike counts of area 1 aligned well to the local gamma rhythm in area 1. Here, and in the two following panels, we plot the spike probability as a function of a phase normalized to 1. (B) Normalized spike counts of area 2 also aligned well to the local gamma rhythm in area 2. (C) Normalized spike counts of area 1 aligned to the non-local gamma rhythm from area 2 at a phase of approximately 90°. (D) The probability of an area 2 spike following an area 1 spike is modulated by the area 1 gamma phase. It peaks for the area 1 gamma phase at which most area 1 spikes occur. (E) Probability of an area 2 spike following an area 1 spike is modulated by the area 2 gamma phase but it peaks at a different area 2 gamma phase, namely the one where most area 1 spikes arrive rather than the phase for which most area 2 spikes occur. Data was averaged over 10 trials, the error bars represent the standard error of the mean (SEM).
Fig 6.
Response to a stimulus response was strongly affected by alpha phase difference.
(A) Upon stimulus presentation the E and I population activity in area 1 increased strongly, yielding both a transient increase due to and immediately following the stimulus onset (highlighted by the gray bar) as well as a higher sustained rate during the period that the stimulus was presented. The bottom panel represents the stimulus time course. (B) The response of the network (firing rate during 30 ms after stimulus onset, represented by the gray bar in panel A) to the stimulus depends on at what alpha phase the stimulus onset occurs. A strong increase in response is found when the stimulus is active (solid line) compared to when there is no stimulus (dashed line). (C) The increase in firing rate of area 1 from baseline in response to the stimulus was twice as high for an optimal alpha phase compared to that for the least optimal phase. (D) The response of the second area depends both on the alpha phase of area 1 at stimulus onset (y-axis) as well as on the alpha phase difference between area 1 and area 2 (x-axis). (E) A cross section of the response surface in panel D taken at the optimal alpha phase of area 1 (0°, dashed line in panel D) highlights the effect of relative phase. Although both the baseline response (dashed line) as well as the stimulus response (solid line) are modulated by the alpha phase difference, the modulation of the latter is much stronger. (F) The difference between stimulus and baseline response is modulated by a factor of about two by the alpha phase difference between area 1 and area 2. Hence, the two phase factors have an approximately equal effect, in essence acting as a gate, which is only open if both are optimal. Data was averaged over 10 trials, the error bars represent the standard error of the mean (SEM).
Fig 7.
Stimulus discrimination in the receiving cortical area is influenced by alpha phase difference with the sending cortical area.
(A) The excitatory populations of both areas were divided in 2 subpopulations that were individually stimulated. Each subpopulation in area 1 was selectively connected to the corresponding one in area 2. (B) The degree to which information send from the first area that could be retrieved from the response of the second area depended both on alpha phase of area 1 at stimulus onset (y-axis) as well as on the alpha phase difference between area 1 and area 2 (x-axis), in a similar fashion as the stimulus response characterized in Fig 6D. (C) A cross section at the optimal alpha phase of area 1 (0°, dashed line in panel 7D) highlights the effect of relative phase. The information transfer from area 1 to area 2 attained peak values at the same alpha phase difference where stimulus response of area 2 was highest. (D) When less neurons in area 2 were available for decoding, the performance decreased. For 200 neurons decoding performance is always 100% and the alpha phase difference is not relevant. However, for more challenging tasks for which there are fewer neurons available for decoding the optimal alpha phase difference is essential for adequate decoding. Data was averaged over 10 trials, the error bars represent the standard error of the mean (SEM).
Fig 8.
In bidirectional networks the alpha phase difference determines the direction of communication.
(A) Schematic of the model with bidirectional connections between both areas. (B) With bidirectional connectivity the gamma coherence has peaks at two distinct alpha phase differences (solid line; baseline is represented by dotted line). (C) For an alpha phase difference of -90° Granger causality from area 1 to area 2 (red) is much stronger. (D) For an alpha phase difference of 90° the granger causality from area 2 to area 1 (blue) dominates. (E) At zero alpha phase difference Granger causality is equal in both directions (red, from area 1 to area 2, blue from area 2 to area 1) and shows a clear peak in the gamma band. Data was averaged over 10 trials, shaded areas represent the standard error of the mean (SEM).
Table 1.
Parameter values for the different neuron types used in the model.
Table 2.
Connectivity strength between the different neuron types.
Table 3.
Noise parameters for different neuron types.